wwwelab - User contributions [en]

Mag 3D Aparato Experimental

2026-06-24T13:00:48Z

Ist12916: /* Conexões elétricas */

=Descrição da construção 3D=

Todas as peças plásticas utilizadas neste projeto e cuja montagem é descrita de seguida, podem ser encontradas e descarregadas no [https://www.printables.com/model/1649643-mag3d_kit/files seguinte link].

A experiência Mag3D consiste (i) numa espira magnética retangular de elevada razão de aspeto, com ângulo ajustável e (ii) num carrinho móvel equipado com um sensor magnético.

{|
|[[File:ProjecaoLateral Medium.png|thumb|x400px|Top|Vista lateral da experiência.]]
|}
A correia, ligada ao carrinho, é puxada pelo motor através da engrenagem do motor de translação. O carrinho, subsequentemente, é puxado ao longo do perfil de alumínio, chegando ao fim do percurso quando atinge o interruptor fim-de-curso da translação.

A espira gira em torno do círculo central, controlada pelo motor axial, chegando ao limite do seu movimento quando atinge o interruptor fim-de-curso do movimento axial da espira.

{|
|[[File:VistaAereaMAG3D Medium.png|thumb|x400px|Top|Vista de cima da experiência.]]
|}

{|
|[[File:VistaFrontalMAG3D Medium.png|x400px|Top|Vista de frente da experiência.]]
|}

==Montagem==

===Passo 1===

A montagem do suporte da espira consiste na ligação das três peças que o constituem, ligadas pelo aperto de 4 parafusos M3 de 8mm. Posteriormente é enrolado o cabo elétrico AWG24 envernizado compreendendo 50 voltas.

{|
|[[File:SuporteEspira Medium.png|x400px|Top|Montagem da espira.]]
|}

===Passo 2===

Peças necessárias:

{|
|[[File:ConjuntoSuporteEspira Medium1.png|x400px|Top|Peças necessárias para a montagem do suporte da espira.]]
|}

Parafusos necessários:
2 Parafusos (M3 16 mm) e duas porcas.
Inserir a peça: translation_lower_gear_holder no final da extrusão de alumínio (qualquer ponta serve).

{|
|[[File:PerfilAluminioSuportemotor Medium.png|x400px|Top|]]
|}

Inserir o motor, com os parafusos (2 Parafusos M3 de 8 mm e 2 porcas):

{|
|[[File:MotorTranslacaoHorizontal Medium.png|x400px|Top|]]
|}

Inserir nos lados respectivos, as peças switch_stabilizer_to_rail_connector e motor_stabilizer_to_rail_connector, sem apertar:

{|
|[[File:VigasDeAssentamento Medium.png|x400px|Top|]]
|}

Preparar as peças coil_assembly_coil_holder_right, coil_assembly_coil_holder_left inserindo porcas M3 nos orifícios assinalados na imagem:

{|
|[[File:CremalheiraEsquerdal Medium.png|x400px|Top|]]
|}

Juntar as peças coil_assembly_coil_holder_right, coil_assembly_coil_holder_left à peça central da espira middle_coil usando os parafusos M3 de 20 mm. NOTA: a orientação das peças é indiferente, embora seja preferível que as cabeças dos parafusos estejam na mesma face da espira, ou seja, que os parafusos (dos dois lados) tenham a mesma orientação.

{|
|[[File:FixacaoEspiraCremalheira Medium.png|x400px|Top|]]
|}

As peças devem ficar como mostrado em baixo:

{|
|[[File:EspiraMontadaSecaoCentral Medium.png|x400px|Top|Suporte rotativo da espira montado.]]
|}

Adicionar os interruptores de fim-de-curso (2) aos suportes (switch_holder) usando parafusos M3 de 16 mm de comprimento:

{|
|[[File:AcessorioMicroSwitch Medium.png|x400px|Top|]]
|}

NOTA: a patilha branca deve ser afastada gentilmente com um x-ato ou uma lamina relativamente fina, de forma a permitir o parafuso ser inserido:

{|
|[[File:SuporteMicroSwitch Medium.png|x400px|Top|]]
|}
Inserir dos dois interruptores nas peças coil_assembly_left_stabilizer, coil_assembly_right_stabilizer, onde na segunda peça também se deve inserir o motor usando parafusos de INSERIR TAMANHO:
{|
|[[File:PosicionamentoSwitchSuporteEspira Medium.png|x400px|Top|]]
|}
{|
|[[File:Estabilizador ComMotor Medium.png|x400px|Top|]]
|}
Inserir de cada lado, as peças dos suportes respectivas:
{|
|[[File:SistemaRotativoMAG3D Medium.png|x400px|Top|]]
|}

Prender o coil_assembly_Stepper_gear, ao motor com um parafuso M3 de 8mm.

{|
|[[File:Cremalheira e pinhao Medium.png|x400px|Top|]]
|}

Inserir translation_stage_upper_gear no motor e inserir o <i>threaded insert</i> M2 com um ferro de soldar encontado à peça (How to use Brass Inserts on 3D Prints: make your own tips, cheap!, How to Install Heat Set Inserts into your 3D Prints | Markforged Reinforced), e usar um parafuso M2 de 8 mm para prender a engrenagem ao motor. NOTA: não apertar com muita força para o <i>threaded insert</i> não sair.
{|

|[[File:InsercaoThreadeInsert Medium.png|x400px|Top|Instruções para a inserção do <i>threaded insert</i>.]]
|}

Prender o coil_assembly_left_stabilizer, coil_assembly_right_stabilizer às peças switch_stabilizer_to_rail_connector e motor_stabilizer_to_rail_connector com parafusos 16 mm:

{|
|[[File:PromenorCorpoCentral Medium.png|x400px|Top|]]
|}

Inserir o sensor_base na extrusão de alumínio e o translation_lower_gear_holder no final da extrusão:

{|
|[[File:PosicionamentoDoTensionador Medium.png|x400px|Top|]]
|}

Prender a correia à sensor_base com belt_locking_left e belt_locking:_right com parafusos M3 de 12 mm:
{|
|[[File:FixadorDaCorreia Medium.png|x400px|Top|]]
|}

Prender as sensor_holder_right e sensor_holder_left à sensor_base com parausos M3 de 8mm e prender o sensor com parafusos M2.

{|
|[[File:FixacaoSensorMagnetico Medium.png|x400px|Top|]]
|}

Inserir a peça translation_stage_lower_gear na translation_stage_gear_holder com um parafuso M6 com parte não roscada do parafuso A correia deve passar por dentro (a correia não é visivelr na foto em baixo):

{|
|[[File:Tensionador Medium.png|x400px|Top|]]
|}

Prender a peça translation_stage_gear_holder à translation_lower_gear_holder com um parafuso M6 e uma porca:

{|
|[[File:FixacaoTensionador Medium.png|x400px|Top|]]
|}

Ao apertar o parafuso, o centro deve ficar em tensão. O kit encontra-se montado:

{|
|[[File:ProjecaoAnterior Medium.png|x400px|Top|]]
|}

{|
|[[File:VistaLateralMAG3D Medium.png|x400px|Top|]]
|}
{|
|[[File:BirdEyeView Medium.png|x400px|Top|]]
|}

===Conexões elétricas===

O esquema geral das ligações elétricas é o seguinte:

{|
|[[File:EsquemaEletrico Medium.png|x400px|Top|]]
|}

Os componentes elétricos da experiência são:
Os <i>relays</i> com três funções: (i) ligar e desligar a fonte AC, (ii) controlar a voltagem da espira, seleccionando a alimentação de 12 ou 6V e (iii) ligar uma lâmpada led externa para melhor iluminação da experiência.

O conversor analõgico-digital (ADC) permite medir a voltagem aos terminais de uma resistência de <i>shunt</i> de 0.1 Ohm, sendo esta convertida para a medida da intensidade de corrente que atravessa a espira.

Os <i>stepper drivers</i> controlam os motores. Finalmente, os interruptores fim-de-curso, sinalizam o parqueamento da bobine ou do sensor quando pressionados.

Mag 3D Aparato Experimental

2026-06-24T12:51:29Z

Ist12916:

=Descrição da construção 3D=

Todas as peças plásticas utilizadas neste projeto e cuja montagem é descrita de seguida, podem ser encontradas e descarregadas no [https://www.printables.com/model/1649643-mag3d_kit/files seguinte link].

A experiência Mag3D consiste (i) numa espira magnética retangular de elevada razão de aspeto, com ângulo ajustável e (ii) num carrinho móvel equipado com um sensor magnético.

{|
|[[File:ProjecaoLateral Medium.png|thumb|x400px|Top|Vista lateral da experiência.]]
|}
A correia, ligada ao carrinho, é puxada pelo motor através da engrenagem do motor de translação. O carrinho, subsequentemente, é puxado ao longo do perfil de alumínio, chegando ao fim do percurso quando atinge o interruptor fim-de-curso da translação.

A espira gira em torno do círculo central, controlada pelo motor axial, chegando ao limite do seu movimento quando atinge o interruptor fim-de-curso do movimento axial da espira.

{|
|[[File:VistaAereaMAG3D Medium.png|thumb|x400px|Top|Vista de cima da experiência.]]
|}

{|
|[[File:VistaFrontalMAG3D Medium.png|x400px|Top|Vista de frente da experiência.]]
|}

==Montagem==

===Passo 1===

A montagem do suporte da espira consiste na ligação das três peças que o constituem, ligadas pelo aperto de 4 parafusos M3 de 8mm. Posteriormente é enrolado o cabo elétrico AWG24 envernizado compreendendo 50 voltas.

{|
|[[File:SuporteEspira Medium.png|x400px|Top|Montagem da espira.]]
|}

===Passo 2===

Peças necessárias:

{|
|[[File:ConjuntoSuporteEspira Medium1.png|x400px|Top|Peças necessárias para a montagem do suporte da espira.]]
|}

Parafusos necessários:
2 Parafusos (M3 16 mm) e duas porcas.
Inserir a peça: translation_lower_gear_holder no final da extrusão de alumínio (qualquer ponta serve).

{|
|[[File:PerfilAluminioSuportemotor Medium.png|x400px|Top|]]
|}

Inserir o motor, com os parafusos (2 Parafusos M3 de 8 mm e 2 porcas):

{|
|[[File:MotorTranslacaoHorizontal Medium.png|x400px|Top|]]
|}

Inserir nos lados respectivos, as peças switch_stabilizer_to_rail_connector e motor_stabilizer_to_rail_connector, sem apertar:

{|
|[[File:VigasDeAssentamento Medium.png|x400px|Top|]]
|}

Preparar as peças coil_assembly_coil_holder_right, coil_assembly_coil_holder_left inserindo porcas M3 nos orifícios assinalados na imagem:

{|
|[[File:CremalheiraEsquerdal Medium.png|x400px|Top|]]
|}

Juntar as peças coil_assembly_coil_holder_right, coil_assembly_coil_holder_left à peça central da espira middle_coil usando os parafusos M3 de 20 mm. NOTA: a orientação das peças é indiferente, embora seja preferível que as cabeças dos parafusos estejam na mesma face da espira, ou seja, que os parafusos (dos dois lados) tenham a mesma orientação.

{|
|[[File:FixacaoEspiraCremalheira Medium.png|x400px|Top|]]
|}

As peças devem ficar como mostrado em baixo:

{|
|[[File:EspiraMontadaSecaoCentral Medium.png|x400px|Top|Suporte rotativo da espira montado.]]
|}

Adicionar os interruptores de fim-de-curso (2) aos suportes (switch_holder) usando parafusos M3 de 16 mm de comprimento:

{|
|[[File:AcessorioMicroSwitch Medium.png|x400px|Top|]]
|}

NOTA: a patilha branca deve ser afastada gentilmente com um x-ato ou uma lamina relativamente fina, de forma a permitir o parafuso ser inserido:

{|
|[[File:SuporteMicroSwitch Medium.png|x400px|Top|]]
|}
Inserir dos dois interruptores nas peças coil_assembly_left_stabilizer, coil_assembly_right_stabilizer, onde na segunda peça também se deve inserir o motor usando parafusos de INSERIR TAMANHO:
{|
|[[File:PosicionamentoSwitchSuporteEspira Medium.png|x400px|Top|]]
|}
{|
|[[File:Estabilizador ComMotor Medium.png|x400px|Top|]]
|}
Inserir de cada lado, as peças dos suportes respectivas:
{|
|[[File:SistemaRotativoMAG3D Medium.png|x400px|Top|]]
|}

Prender o coil_assembly_Stepper_gear, ao motor com um parafuso M3 de 8mm.

{|
|[[File:Cremalheira e pinhao Medium.png|x400px|Top|]]
|}

Inserir translation_stage_upper_gear no motor e inserir o <i>threaded insert</i> M2 com um ferro de soldar encontado à peça (How to use Brass Inserts on 3D Prints: make your own tips, cheap!, How to Install Heat Set Inserts into your 3D Prints | Markforged Reinforced), e usar um parafuso M2 de 8 mm para prender a engrenagem ao motor. NOTA: não apertar com muita força para o <i>threaded insert</i> não sair.
{|

|[[File:InsercaoThreadeInsert Medium.png|x400px|Top|Instruções para a inserção do <i>threaded insert</i>.]]
|}

Prender o coil_assembly_left_stabilizer, coil_assembly_right_stabilizer às peças switch_stabilizer_to_rail_connector e motor_stabilizer_to_rail_connector com parafusos 16 mm:

{|
|[[File:PromenorCorpoCentral Medium.png|x400px|Top|]]
|}

Inserir o sensor_base na extrusão de alumínio e o translation_lower_gear_holder no final da extrusão:

{|
|[[File:PosicionamentoDoTensionador Medium.png|x400px|Top|]]
|}

Prender a correia à sensor_base com belt_locking_left e belt_locking:_right com parafusos M3 de 12 mm:
{|
|[[File:FixadorDaCorreia Medium.png|x400px|Top|]]
|}

Prender as sensor_holder_right e sensor_holder_left à sensor_base com parausos M3 de 8mm e prender o sensor com parafusos M2.

{|
|[[File:FixacaoSensorMagnetico Medium.png|x400px|Top|]]
|}

Inserir a peça translation_stage_lower_gear na translation_stage_gear_holder com um parafuso M6 com parte não roscada do parafuso A correia deve passar por dentro (a correia não é visivelr na foto em baixo):

{|
|[[File:Tensionador Medium.png|x400px|Top|]]
|}

Prender a peça translation_stage_gear_holder à translation_lower_gear_holder com um parafuso M6 e uma porca:

{|
|[[File:FixacaoTensionador Medium.png|x400px|Top|]]
|}

Ao apertar o parafuso, o centro deve ficar em tensão. O kit encontra-se montado:

{|
|[[File:ProjecaoAnterior Medium.png|x400px|Top|]]
|}

{|
|[[File:VistaLateralMAG3D Medium.png|x400px|Top|]]
|}
{|
|[[File:BirdEyeView Medium.png|x400px|Top|]]
|}

===Conexões elétricas===

O esquema geral das ligações elétricas é o seguinte:

{|
|[[File:EsquemaEletrico Medium.png|x400px|Top|]]
|}

Os componentes elétricos da experiência são:
O <i>relay</i> com três funções: i) ligar e desligar a fonte AC, ii) controlar a voltarem da espira, seleccionando a alimentação de 12 ou 6V e iii) ligar uma lâmpada led externo para melhor iluminação da experiência.

O ADC mede a voltagem aos terminais de uma resistência de <i>shunt</i> de 0.1 Ohm, sendo esta convertida para uma medida da intensidade da corrente que atravessa a espira.

Os <i>stepper drivers</i> controlam os motores. Finalmente, os interruptores fim-de-curso, sinalizam quando pressionados o parqueamento da bobine ou do sensor.

Péndulo mundial

2026-06-18T08:27:10Z

Ist12916: /* Aparato experimental */

= Descripción =
[[File:Soyuz VS03 liftoff.jpg||thumb|Soyuz lift-off from French Guiana @ 5º north of the Equator .|right|border|236px]]
Los cohetes se lanzan al espacio desde las latitudes ecuatoriales. Esto se debe al hecho de que el peso aparente de los objetos se reduce gradualmente desde los polos hasta el ecuador. ¡Nos sentiremos más ligeros en el ecuador que en los polos!

Esta pequeña diferencia en el peso aparente permite que el mismo cohete lance cargas más pesadas en órbita si se lanza más cerca del ecuador. Por ejemplo, un cohete Soyuz que se lanza en órbita geoestacionaria desde la Guayana Francesa (5ºN) puede transportar 3 toneladas, mientras que solo será capaz de lanzar 1,7 toneladas de carga cuando se lance desde Baikonur, Kazajstán (46ºN).

El objetivo de este experimento es encontrar el valor de la gravedad "constante" a través de una constelación de péndulos colocados en varias latitudes y operados remotamente, a través de Internet, por cualquier persona.

Se espera que los países de la CPLP puedan contribuir a este esfuerzo, acercando a estudiantes, maestros y ciudadanos interesados.

Hay dos actividades diferentes que ocurren simultáneamente: (i) acceso, a través del laboratorio elecrónico, de los péndulos ubicados en diferentes latitudes y (ii) la construcción y operación local en las escuelas o en tu casa.

Lisboa, Ilhéus, Faro y Río de Janeiro fueron las primeras ciudades en contribuir a la red en enero de 2013, haciendo posible que ocurran los primeros ajustes de datos experimentales a la ecuación teórica dentro de nuestro proyecto que describe cómo la gravedad cambia con la latitud.

Si desea formar parte de la nueva red World Pendulum, contáctenos enviándonos un [mailto: wwwelab@ist.utl.pt email].

<div class = "toccolours mw-collapsible mw-collapsed" style = "width: 420px">
'''Enlaces'''
<div class = "mw-collapsible-content">

* Video Faro: rtsp: //elabmc.ist.utl.pt/worldpendulum_ccvalg.sdp
* Video Lisboa: rtsp: //elabmc.ist.utl.pt/worldpendulum_planetarium.sdp
* Video Ilhéus: rtsp: //elabmc.ist.utl.pt/worldpendulum_ilheus.sdp
* Video Río Janeiro: rtsp: //elabmc.ist.utl.pt/worldpendulum_puc.sdp
* Video Maputo: rtsp: //elabmc.ist.utl.pt/worldpendulum_maputo.sdp
* Video Santo Tomé: rtsp: //elabmc.ist.utl.pt/wp_saotome.sdp
* Laboratorio: Básico en [http://e-lab.ist.eu e-lab.ist.eu]
* Sala de control: Péndulo mundial
* Grado: *

</div>
</div>

== A quién le gusta esta idea ==

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[[File:LogoSPF long.jpg|border|180px]]
[[File:logo_EPS_blue.gif|border|80px]]
[[File:Logo mar.png|border|80px]]
[[File:LogoPlanetarioGulbenkian.png|border|180px]]
[[File:LogoCCVALG.png|border|204px|border|180px]]
[[File:LogoPlanetarioRioJaneiro.png|border|180px]]
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[[File:Cenfim Logo.jpg|border|180px]]
[[File:LogoPUC.PNG|border|60px]]
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[[File:UFRPE.jpg|border|60px]]
[[File:Logo_DGAE.png|border|380px]]
[[File:LogosBeneficairesErasmus+RIGHT EN.jpg|border|280px]]

= Aparato experimental =
El diseño del péndulo utilizado se basó en el diseño del Dr. Jodl <ref name = "jodl">World pendulum—a distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude, Grober S, Vetter M, Eckert B and Jodl H J, European Journal of Physics - EUR J PHYS , vol. 28, no. 3, pp. 603-613, 2007</ref>. Se hicieron algunos cambios menores para permitir que el mismo diseño se repita fácilmente en las escuelas secundarias. Los datos relativos a cada péndulo son los siguientes:

[[File: WordlPendulum.JPG | thumb | Pendulum utilizado para el experimento de gravedad estándar de péndulo mundial.]]
[[File: Stringsuport.png | thumb | Soporte de cadena de péndulo para evitar errores de alargamiento. El cable se fija soldando a un tornillo M4 de latón de 40 mm de largo.]]

{| class = "wikitable"
! colspan = "6" | Tamaños físicos por lugar
|-
| Sitio
| Latitud
| Longitud
| Altitud (m)
| Longitud del cable(mm)
| Diámetro de la esfera (mm)
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Dili]
| 8°33'31"S
| 125°34'26"W
| 10
| 2837.25 +/- 0.5 @27ºC
| 80.8 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/31/1 Luanda-EPL]
| 8° 50' 1"S
| 13°14'37"W
| 70
| 2375.0 +/- 0.5 @27ºC
| 80.5 +/- 0.1
|-
| CCV_Algarve/Faro
| 37º00'N
| 7º56'W
| 10
| 2677 +/- 0.5 @23ºC
| 80.5 +/- 1.0
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220
| 2832.0 +/- 0.5 @23ºC
| 81.0 +/- 1.0
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20
| 2677 +/- 0.5 @19ºC
| 80.5 +/- 1.0
|-
| Maputo
| 25º56'S
| 32º36'E
| 80
| 2609.8 +/- 0.5 @27ºC
| 80.5 +/- 1.0
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50
| 2756.5 +/- 0.5 @29ºC
| 81.8 +/- 0.5
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150
| 2803 +/- 0.5 @25ºC
| 80.1 +/- 0.5
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2824 +/- 1
| 81.8 +/- 0.1
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40
| 2832,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650
| 2824 +/- 0.5 @20ºC
| 82.0 +/- 0.1
|-
| Bogotá - UNAD
| 4°35'N
| 74°5'W
| 2500
| 2835 +/- 0.5
| 82.0 +/- 0.1
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82
| 2800 + /- 0.5 @28ºC
| 81.9 +/- 0.1
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552
| 2825 +/- 0.5 @27ºC
| 81.9 +/- 0.1
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30
| 2827.5 +/- 0.5 @28ºC
| 81.8 +/- 0.1
|-
| Panama city - USMA
| 9°1'N
| 79°37'W
| 130
| 2800.0 +/- 0.5 @35ºC
| 81.8 +/- 0.1
|-
| Brasilia - UnB
| 15° 46'S
| 47° 52'W
| 1034
| 2826.8 mm +/- 0.5 @26ºC
| 81.4 +/- 0.1
|-
| Marseille - ECM
| 43°20.6'N
| 5°26.2'E
| 162
| 2817.0 mm +/- 0.5 @22ºC
| 82.0 +/- 0.1
|-
| Punta Arenas - UMag
| 53°8'S
| 70°52'W
| 40
| 2823 +/- 0.5 @16.4ºC
| 81.7 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/38/1 Lubango-ISCED]
| 14°55'S
| 13°29'E
| 1787
| 1805.2 +/- 0.5 @26ºC
| 82.2 +/- 0.1
|}

{| class = "wikitable"
! colspan = "2" | Cantidades típicas
|-
| Longitud de cadena (sin contar la esfera) || 2705mm +/- 0.5mm
|-
| Masa de esfera || 2kg +/- 75g
|-
| Diámetro de esfera || 81.2mm +/- 1.5mm
|-
| Cadena || Remanio (r) - Acero inoxidable (níquel cromo)- 0,4mm
|-
| Módulo de elasticidad de la cuerda || ~ 200GPa
|-
| Sistema de medición del período de oscilación || Microprocesador con 7,3728MHz - 30ppm de cristal+ láser + fotodiodo PIN
|-
| Alambre CTE (25-500ºC) (Coeficiente de expansión térmica) || ~ 14 x 10 <sup> -6 </sup> K <sup> -1 </sup>
|}

El aparato experimental se puede adaptar fácilmente a la operación humana, utilizando un buen cronómetro, para la ejecución local. Las estructuras de acero inoxidable pueden fabricarse en latón o bronce para facilitar el mecanizado. El cable utilizado puede ser reemplazado por un cable de acero para pesca deportiva y la masa puede ser reemplazada por un peso de entrenamiento de lanzamiento de pesas olímpico, que pesa 2 kg. Se debe usar una cinta de medición calibrada para medir la longitud del cable "," unos días después de ensamblar el aparato para permitir la expansión del cable ".

= Socios locales =
El péndulo <ref name="serway">Physics for scientists and engineers, 5th edition, Hardcourt College Publishers, R.Serway and R. Beichner, 2000</ref>, aunque uno de los sistemas más simples comúnmente estudiados, es uno de los más rico en términos de física.

Para construir un péndulo preciso, los factores más importantes son la medición precisa de la longitud del cable, su calidad y la de los soportes del péndulo. La selección de una masa entre 1 y 4 kg asegura que el error del período del péndulo sea lo suficientemente pequeño como para que se puedan detectar pequeños cambios de gravedad locales (menores del 0.1%), siempre que se use un cronómetro preciso para el cronometraje.

Se puede ensamblar un aparato local utilizando materiales fácilmente disponibles y los valores locales de <em> "g" </em> determinados usando dicho aparato se pueden comparar con los obtenidos a través de la constelación de péndulo remoto y el modelo teórico.

La recopilación de estos datos a través de una red social permitirá una descripción más precisa de cómo <em> "g" </em> varía en todo el mundo. El "Péndulo mundial" puede ser una red de colaboración importante para la difusión de la física en las escuelas.

Las instrucciones sobre cómo construir tal péndulo están disponibles en [[Precision Pendulum]].
La documentación del desarrollo y construcción de un péndulo está disponible en [[Precision Pendulum]] mientras que las instrucciones sobre cómo ensamblarlo están disponibles en [[Precision Pendulum Assembly]].

Si desea formar parte de la nueva red World Pendulum, contáctenos enviándonos un [mailto: wwwelab@ist.utl.pt email].

= Física =
Determinar la aceleración de la gravedad en diferentes partes del mundo plantea preguntas sobre la importancia de los modelos en física. Es posible mostrar que la aceleración de la gravedad al nivel del mar cambia con la latitud y, por lo tanto, se necesita una corrección para cada ubicación individual. Este proceso nos permite desmitificar la ciencia y corregir el "mito urbano" existente en torno a algunas constantes físicas que solo son verdaderamente constantes cuando se realizan algunas aproximaciones. En este caso particular, mostraremos cómo la introducción de correcciones sucesivas a la "constante" de la gravedad conducirá a valores más cercanos a los obtenidos experimentalmente.

== Modelo geofísico ==
El punto de partida es el valor constante de uso común de 9.81 ms <sup> -2 </sup>. Esto se obtiene al considerar que la Tierra es (i) una esfera (ii) que no está girando. Es trivial notar que este modelo, debido a la simetría de la forma esférica, no permite valores diferentes en diferentes ubicaciones. Esto cambia tan pronto como se tienen en cuenta la dinámica de rotación de la Tierra y la forma elipsoide (aplanamiento de los polos). Estos factores permiten que la gravedad cambie con la latitud, y de hecho, estos dos factores son los dos más importantes en este fenómeno, superando cualquier otro efecto, como (i) altitud, (ii) fuerzas de marea y (iii) composición del subsuelo .

Para demostrar estos aspectos más finos, la aceleración de la gravedad debe determinarse en varias latitudes alrededor del globo distantes entre sí. Usando los datos recopilados, los estudiantes pueden preguntarse qué tan "constante" es realmente el valor y mejorar su intuición de la gravedad.

=== Estudios experimentales ===
==== Variación con latitud ====
Como se ve, el primer estudio posible consiste en usar los péndulos remotos para obtener una medición de la aceleración de la gravedad local para cada ubicación en la que se basan. Al considerar (o no) varios factores, es posible ajustar los datos a un experimento Descripción de la Tierra utilizando armónicos esféricos (ecuación \ eqref {harmonica-esferica}). Este trabajo experimental puedese llevará a cabo utilizando la constelación de péndulo de e-lab y [http://rcl-munich.informatik.unibw-muenchen.de/ los péndulos de nuestro socio].

==== Determinación local ====
Siguiendo las instrucciones disponibles en este wiki - [[Precision_Pendulum]] - o usando cualquier otro tipo de diseño que resulte en un aparato riguroso, se construye un péndulo local. Entonces es posible realizar mediciones de la gravedad local, siempre que se use un buen cronómetro. Además, también es posible contribuir al enriquecimiento de la red mundial.

==== [[Tidal study | Estudio de mareas]] ====
Usando un almanaque apropiado para la ubicación, puede obtener los tiempos de alineaciones particulares de Luna / Sol (luna llena, luna nueva, creciente creciente y gibosa creciente). Al trazar un gráfico que abarque varios meses, se puede intentar verificar y cuantificar la influencia de las fuerzas de marea y las alineaciones Luna / Sol en el peso aparente. Es posible intentar y verificar la correlación entre las fases de la Luna y los cambios en la medición de la gravedad local, haciendo un estudio de un mes o un año.
Los efectos de las mareas están en el límite de detección por los péndulos de la constelación de e-lab. Para que el experimento tenga éxito, es necesario ser muy riguroso en el momento en que se realizan las corridas experimentales y algunas técnicas numéricas avanzadas, como la transformada de Fourier, deben emplearse para que la señal se extraiga de los datos.

==== Análisis de torsión de alambre ====
[[File: Torcao.jpg || thumb | Efecto de la torsión del alambre y la elipticidad de la esfera en la medición de la velocidad del péndulo. | Right | border | 240px]]
Quienes presten más atención notarán que la velocidad de la masa cambia debido a la torsión del alambre y debido a que la masa no es una esfera perfecta. Esto se ilustra en la imagen a la derecha. El péndulo puede estudiarse teniendo en cuenta el efecto de la torsión del alambre (para ello se recomienda el uso de las ecuaciones de Euler-Lagrange).

== Movimiento circular uniformemente acelerado ==
La velocidad de la esfera en el punto más bajo de la trayectoria se determina midiendo cuánto tiempo se interrumpe el rayo láser. Conociendo el diámetro de la esfera, es trivial determinar la velocidad en el origen. A partir de esto, se puede calcular la energía cinética máxima y determinar la altura de lanzamiento del péndulo. El punto de lanzamiento calculado se puede comparar con el real.

=Proveedores de latitud =

[[file:G_latitude.png|link=https://docs.google.com/a/kic-innoenergy.com/spreadsheet/oimg?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE&oid=1&zx=hfmrs4egtbuf|thumb|La constante gravitacional trazada contra la latitud con puntos de interés en todo el mundo resaltados. La isla Príncipe está por encima de la latitud cero. El valor de Lisboa se obtuvo con el experimento actual y ya se trazó en exceso en el gráfico.]]

El idioma es un factor de nacionalidad importante ("Mi patria es el idioma portugués", F. Pessoa) y una forma sencilla de definir lo que se llama países hermanos ("países irmãos"). Solo cuatro idiomas se difunden en todo el mundo, siendo el portugués uno de ellos. La comunidad de habla portuguesa cubre latitudes de ~ 30S a ~ 40N, casi un tramo de 75º en el ecuador. Por lo tanto, los países CPLP pueden ayudar siendo "proveedores de latitud" (ver Figura).

Para llevar a cabo este experimento mundial, se necesitan al menos cuatro puntos espaciados para tener un ajuste adecuado. Pero debido a la fuerte no linealidad de la ecuación, se necesitan más puntos para proporcionar un ajuste adecuado, en particular en la "rodilla" cerca del ecuador de la Tierra. El propio Brasil puede proporcionar casi cuatro puntos cruciales cerca del ecuador (por ejemplo, Recife 8º, Salvador - 12º, Río de Janeiro - 23º, Porto Alegre - 30º) pero carece de puntos con una latitud donde la característica varía más fuertemente, la región casi lineal alrededor 30º a 60º, donde Portugal puede dar dos buenos puntos (por ejemplo, Porto - 37º y Faro - 41º). Mozambique puede contribuir con 27º (Maputo) y S. Tomé e Principe o Brasil son buenas opciones para cubrir el ecuador. Angola podría dar puntos complementarios a los adquiridos en Brasil, ya que la sensibilidad de la medición es más pronunciada cerca del ecuador y los polos.

= Ajuste de datos =
Referencias disponibles <ref name="serway"></ref> <ref name="rcl">http://rcl-munich.informatik.unibw-muenchen.de/</ref> <ref name="olsom">Nelson, Robert; M. G. Olsson (February 1987). "The pendulum - Rich physics from a simple system". American Journal of Physics 54 (2):
doi:10.1119/1.14703</ref> <ref name="gauld">Pendulums in the Physics Education Literature: A Bibliography, Gauld, Colin 2004 Science & Education, issue 7, volume 13, 811-832
(http://dx.doi.org/10.1007/s11191-004-9508-7)</ref> <ref name="qureshi">The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach, M I Qureshi et al 2010 Eur. J. Phys. 31 1485(http://dx.doi.org/10.1088/0143-0807/31/6/014)</ref> <ref name="ochs"> A comprehensive analytical solution of the nonlinear pendulum, Karlheinz Ochs 2011 Eur. J. Phys. 32 479 (http://dx.doi.org/10.1088/0143-0807/32/2/019)</ref> dan una muy buena descripción del modelo matemático necesario para ajustar los datos. Si se tienen en cuenta todos los factores principales, la gravedad en función de la latitud viene dada por:

<matemáticas>
g_ {n} (\ varphi) = 9.780 326 772 \ times [1 + 0.005 302 33 \ cdot sin ^ {2} (\ varphi) - 0.000 005 89 \ cdot sin ^ {2} (2 \ varphi)]
</math>

donde \ (\ varphi \) es la latitud. Esta expresión es una de las mejores aproximaciones experimentales y los resultados del acuerdo de estandarización para ajustar la superficie de referencia del Sistema Geodésico Mundial (WSG84) a un elipsoide con radio r <sub> 1 </sub> = 6378137m en el ecuador y r <sub> 2 </sub> = 6356752m de radio semi-menor polar.
Esta fórmula tiene en cuenta el hecho de que la Tierra es un elipsoide y que hay un aumento adicional en la aceleración de la gravedad cuando uno se acerca a los polos, debido a una fuerza centrífuga más débil. Sin embargo, los estudiantes podrían obtener una aproximación no armónica de primer orden teniendo en cuenta solo la fuerza centrífuga. Luego, como un segundo paso, podrían incluir los otros dos errores principales, la fuerza centrífuga y el formato de elipsoide de la Tierra.

[[File: Period_over_time.png | thumb | La variabilidad del período con el tiempo transcurrido (ángulo de amplitud <7,5º), que muestra que este error es inferior al 0,05% independientemente de la amplitud inicial.]]

Las imágenes muestran la desviación esperada de la "aceleración constante de la Tierra", la aceleración real para cada latitud. Hemos trazado el punto ya obtenido con este aparato en Lisboa y las marcas sobre las latitudes esperadas para futuros socios.
Por supuesto, estas aproximaciones no incluyen una fuente importante de desviación de los datos reales al modelo matemático, el error experimental, ya que no incluimos la fuente experimental de error. Sin embargo, esos errores sistemáticos podrían estar bajo la precisión esperada necesaria (0,1%) para la aproximación anterior si se considera un diseño cuidadoso del aparato. Sin embargo, esos errores deben discutirse en cursos avanzados y su peso debe probarse al considerar el péndulo real.

= Notas históricas =
La importancia del péndulo como base de los relojes y cronógrafos solo fue derrocada cuando la Royal Society convenció al parlamento inglés de crear un premio, que oscilaba entre 10k £ y 20k £ (equivalente hoy en día a más de 3.5M €), por la invención de un cronógrafo. eso no dependía de eso. La precisión temporal de los sistemas basados en péndulo solo se ve mejorada por los sistemas electrónicos modernos.

En la edad del descubrimiento, la longitud se determinó con un alto error, ya que los relojes y cronógrafos dependían de péndulos y estos eran muy sensibles a los barcos que se balanceaban, sufrían cambios en la frecuencia o incluso se detenían. La longitud local se calculó comparando la hora solar (u hora estelar) con la hora del reloj del barco.

= Referencias =

<references />

= Enlaces =
* [[Pêndulo Mundial | Versión portuguesa (Versão em Português)]]
*[[World Pendulum | Versión en inglés (English Version)]]
* [https://www.youtube.com/watch?v=ZOOFw_Nlee8&feature=youtu.be Construyendo tu propio péndulo]

Pêndulo Mundial

2026-06-18T08:26:39Z

Ist12916: /* Aparato experimental */

=Descrição=
[[File:Soyuz VS03 liftoff.jpg||thumb|Decolagem da Soyuz na Guiana francesa @ 5º a norte do equador.|right|border|236px]]
Os foguetões são enviados para o espaço a partir de latitudes equatoriais. Isto deve-se ao facto do peso aparente ser gradualmente reduzido desde os pólos até o equador. Efectivamente sentir-nos-emos mais leves no equador do que nos pólos!

É esta ligeira diferença que permite poupar toneladas de combustível quando um foguetão é lançado em órbita a partir do equador. Por exemplo, o lançamento para uma orbita geoestacionária pela Soyuz a partir da Guiana Francesa (5ºN) permite colocar 3 toneladas(ton) em órbita ao invés das habituais 1,7 ton quando lançada de Baikonur no Cazaquistão (46ºN).

O objetivo desta experiência consiste em determinar em vários pontos do globo a “constante da gravidade” através duma constelação de pêndulos colocados em várias latitudes e operados remotamente por qualquer pessoa através da internet. Espera-se que vários países da CPLP possam contribuir para esse esforço, aproximando estudantes, professores e cidadãos interessados no conhecimento físico do nosso planeta. Existem duas atividades a decorrer em paralelo: (i) o acesso através do e-lab a pêndulos em várias latitudes e (ii) a construção e [https://docs.google.com/a/kic-innoenergy.com/spreadsheet/ccc?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE#gid=0 operação local em escolas] com o apoio da comunidade do [http://fqnosecundario.ning.com/ FQ em Rede].

Lisboa, Ilhéus, Faro e Rio de Janeiro foram as primeiras cidades a contribuir para a rede em Janeiro de 2013, permitindo efectuar um ajuste dos dados experimentais à equação teórica que descreve a variação da gravidade com a latitude.

Se quiser fazer parte da rede do Pêndulo Mundial, por favor envie-nos um [mailto:wwwelab@ist.utl.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Ligações'''
<div class="mw-collapsible-content">

*Video Faro: rtsp://elabmc.ist.utl.pt/worldpendulum_ccvalg.sdp
*Video Lisboa: rtsp://elabmc.ist.utl.pt/worldpendulum_planetarium.sdp
*Video Ilhéus: rtsp://elabmc.ist.utl.pt/worldpendulum_ilheus.sdp
*Video Rio Janeiro: rtsp://elabmc.ist.utl.pt/worldpendulum_puc.sdp
*Video Maputo: rtsp://elabmc.ist.utl.pt/wp_epm.sdp
*Video São Tomé: rtsp://elabmc.ist.utl.pt/wp_saotome.sdp
*Laboratório: Básico em [http://e-lab.ist.eu e-lab.ist.eu]
*Sala de controlo: Pêndulo Mundial
*Nível: *

</div>
</div>

==Quem gosta desta iniciativa==
[[File:PBA B1 1.png|border|180px]]
[[File:LogoSPF long.jpg|border|180px]]
[[File:logo_EPS_blue.gif|border|80px]]
[[File:Logo mar.png|border|80px]]
[[File:LogoPlanetarioGulbenkian.png|border|180px]]
[[File:LogoCCVALG.png|border|204px|border|180px]]
[[File:LogoPlanetarioRioJaneiro.png|border|180px]]
[[File:Logo info tech.png|border|180px]]
[[File:Logo_tap.png|border|180px]]
[[File:Cenfim Logo.jpg|border|180px]]
[[File:LogoPUC.PNG|border|60px]]
[[File:UESC BRASÃO ref.jpg|border|60px]]
[[File:UFRPE.jpg|border|60px]]
[[File:Logo_DGAE.png|border|380px]]
[[File:LogosBeneficairesErasmus+RIGHT EN.jpg|border|280px]]

=Aparato experimental=
Os pêndulos utilizados nas experiências são baseados no desenho do Dr. Jodl <ref name="jodl">World pendulum—a distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude, Grober S, Vetter M, Eckert B and Jodl H J, European Journal of Physics - EUR J PHYS , vol. 28, no. 3, pp. 603-613, 2007</ref>. Algumas alterações menores foram introduzidas ao nível do manuseamento da massa e na adaptação a materiais simples de encontrar de forma a permitir a replicação em escolas secundárias (ensino médio). Os dados seguintes foram utilizados na sua construção:

[[File:WordlPendulum.JPG|thumb|Exemplo de pêndulo utilizado para a determinação da aceleração da gravidade.]]

[[File:Stringsuport.png|thumb|Suporte do cabo de ligação à massa que permite evitar alongamentos indesejados durante as oscilações. O cabo é fixo ou com uma agulha de seringa endovenosa ou com um parafuso M4 de latão perfurado interiormente a 1mm.]]

{| class="wikitable"
!colspan="6"|Caracteristícas físicas particulares
|-
| Local
| Latitude
| Longitude
| Altitude (m)
| Comprimento do fio (mm)
| Diâmetro da esfera (mm)
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Dili]
| 8°33'31"S
| 125°34'26"W
| 10
| 2837.25 +/- 0.5 @27ºC
| 80.8 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/31/1 Luanda-EPL]
| 8° 50' 1"S
| 13°14'37"W
| 70
| 2375.0 +/- 0.5 @27ºC
| 80.5 +/- 0.1
|-
| CCV_Algarve/Faro
| 37º00'N
| 7º56'W
| 10
| 2677 +/- 0.5 @23ºC
| 80.5 +/- 1.0
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220
| 2832.0 +/- 0.5 @23ºC
| 81.0 +/- 1.0
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20
| 2628.5 +/- 0.5 @19ºC
| 80.8 (47.2) +/- 0.5
|-
| Maputo
| 25º56'S
| 32º36'E
| 80
| 2609.8 +/- 0.5 @27ºC
| 80.5 +/- 1.0
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50
| 2756.5 +/- 0.5 @29ºC
| 81.8 +/- 0.5
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150
| 2803 +/- 0.5 @25ºC
| 80.1 +/- 0.5
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2824 +/- 1
| 81.8 +/- 0.1
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40
| 2832,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2500
| 2824 +/- 0.5
| 82.0 +/- 0.1
|-
| Bogotá - UNAD
| 4°35'N
| 74°5'W
| 2650
| 2835 +/- 0.5
| 82.0 +/- 0.1
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82
| 2800 + /- 0.5 @28ºC
| 81.9 +/- 0.1
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552
| 2825 +/- 0.5 @27ºC
| 81.9 +/- 0.1
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30
| 2827.5 +/- 0.5 @28ºC
| 81.8 +/- 0.1
|-
| Panama city - USMA
| 9°1'N
| 79°37'W
| 130
| 2800.0 +/- 0.5 @35ºC
| 81.8 +/- 0.1
|-
| Brasilia - UnB
| 15° 46'S
| 47° 52'W
| 1034
| 2826.8 +/- 0.5 @26ºC
| 81.4 +/- 0.1
|-
| Marseille - ECM
| 43°20.6'N
| 5°26.2'E
| 162
| 2817.0 +/- 0.5 @22ºC
| 82.0 +/- 0.1
|-
| Punta Arenas - UMag
| 53°8'S
| 70°52'W
| 40
| 2823 +/- 0.5 @16.4ºC
| 81.7 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/38/1 Lubango-ISCED]
| 14°55'S
| 13°29'E
| 1787
| 1805.2 +/- 0.5 @26ºC
| 82.2 +/- 0.1
|}

{| class="wikitable"
!colspan="2"|Características nominais
|-
| Comprimento do cabo (raio da esfera não incluído!) || 2705mm +/- 0.5mm
|-
| Massa da esfera || 2kg +/- 75g
|-
| Diâmetro da esfera || 81.2mm +/-1.5mm
|-
| Cabo || Remanium(r) - Stainless steel (Nickel chromium)
- 0,4mm
|-
| Módulo de elasticidade do cabo || ~200GPa
|-
| Cronómetro || Microcontrolador com cristal de 7,3728MHz - 30ppm + laser + PIN foto-díodo
|-
| Wire CTE (25-500ºC) (Coeficiente expansão térmico do cabo) || ~14 x 10<sup>-6</sup> K<sup>-1</sup>
|}

A montagem experimental pode ser facilmente adaptada à operação humana para execução local, realizada apenas com o auxilio de um bom cronómetro. As estruturas de aço inox podem ser realizadas em latão ou bronze facilitando a sua talha.

O cabo empregue pode ser substituído por cabo de aço de pesca desportiva e a massa adquirida numa loja de desporto, tendo sido empregue neste caso uma de 2kg do treino do lançamento do peso olímpico. Deve ser utilizado uma fita-métrica calibrada para medir o comprimento do cabo '''depois''' de utilizar o sistema por alguns dias.

=Parceiros locais=
O pêndulo <ref name="serway">Physics for scientists and engineers, 5th edition, Hardcourt College Publishers, R.Serway and R. Beichner, 2000</ref> é um dos dispositivos experimentais com maior riqueza física apesar da sua simplicidade. Efetivamente só a medida do seu cabo e a sua qualidade e dos apoios são relevantes para a construção precisa do instrumento.

Seleccionando uma massa entre 1 a 4 kg, o erro relativo ao período será suficientemente pequeno para se detetar as variações requeridas na aceleração da gravidade (inferiores a 0,1%) desde que se use um cronómetro preciso.

Uma montagem local pode ser realizada facilmente com recursos a materiais simples de encontrar e comparado o valor determinado para o <em>"g"</em> local com os da constelação remota de pêndulos.

A colecção destes dados através duma rede social permitirá fazer uma descrição mais precisa da variabilidade de <em>g's</em> em torno do globo. O "pendulo mundial" poderá ser uma importante rede colaborativa para a disseminação e o envolvimento da física nas escolas.

A construção e desenvolvimento do pendulo está detalhada em [[Precision Pendulum]] enquanto que as instruções para a sua montagem estão em [[Precision Pendulum Assembly]].

Se quiser fazer parte da rede do Pêndulo Mundial, por favor envie-nos um [mailto:wwwelab@ist.utl.pt mail].

=Física=
A determinação da aceleração da gravidade em diferentes partes do globo levanta questões sobre a importância da modelização em física. Partindo do principio que a força da aceleração é constante ao nível do mar, pode-se mostrar contudo que que esta "constante" varia ligeiramente com a latitude e tem por isso de ser corrigida consoante o lugar onde nos encontramos. Este processo permite desmistificar a ciência e corrigir o "mito urbano" existente em torno de muitas constantes que só o são com muitas aproximações. Neste caso particular mostraremos como a introdução de correcções sucessivas à "constante da gravidade" levará a valores mais próximos dos estimados experimentalmente.

==Modelo geofísico==
O ponto de partida é a aproximação do modelo geofísico da Terra, como sendo (i) uma esfera (ii) não-rotante cuja aproximação mais conhecida atribui o valor de 9,81 ms<sup>-2</sup>. É trivial notar que este modelo, devido à simetria da esfera, leva a valores uniformes em qualquer latitude da Terra. Mas assim que introduzimos a dinâmica do movimento terrestre aperceber-nos-emos que este valor passa a depender da latitude bem como se considerarmos a terra um elipsóide devido ao achatamento nos pólos. Com efeito estes dois aspetos são as principais causas do desvio da "constante da gravidade" com a latitude <ref name="jodl"></ref> e superam todos os outros efeitos tais como (i) a altitude do lugar, (ii) as marés ou (iii) a constituição do sub-solo próximo ao lugar.

Para demonstrar estes aspetos mais finos, a aceleração da gravidade tem de ser determinada em várias latitudes sobre o globo e bastante afastadas entre si. Com estas medidas obtidas em rede, os alunos poderão questionar-se sobre a "constante" e interpretar melhor a força da gravidade.

===Estudos experimentais===
====Variação com a latitude====
Como se viu, o primeiro estudo possivel consiste na utilização dos pêndulos remotos e verificar qual a aceleração da gravidade aparente nesses vários locais. Através da introdução (ou desprezo) de vários ajustes tenta-se chegar graficamente a um ajuste da descrição experimental da terra usando harmónicos esféricos (equação \eqref{harmonica-esferica}).
Este estudo pode ser conduzido usando a constelação de pêndulos do e-lab e de [http://rcl-munich.informatik.unibw-muenchen.de/ outros parceiros].

====Determinação local====
Seguindo as instruções descritas nesta wiki - [[Precision_Pendulum]] - ou usando outro tipo de construção rigorosa dum pêndulo, produz-se e instala-se um pêndulo local e contribui-se para o enriquecimento da folha de cálculo da [https://docs.google.com/a/kic-innoenergy.com/spreadsheet/ccc?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE#gid=0 rede do pêndulo mundial].

====[[Estudo das marés]]====
Com base num almanaque <ref name0"OAL">http://www.oal.ul.pt/index.php?link=dados2012</ref> obtém-se as datas/horas dos dias de alinhamento da lua com o Sol (marés vivas ou lua-cheia e lua nova) e quando estamos em quarto crescente ou minguante. Traçando um gráfico ao longo de vários meses tenta-se verificar e quantificar a influência das marés e do alinhamento da Lua com o Sol no peso aparente.
Desta forma pode-se tentar associar às marés (luas) e ao movimento de translação eventuais flutuações medidas na aceleração aparente da gravidade, fazendo um estudo com um período mensal e/ou anual (p.exemplo ver as diferenças no periélio de Janeiro c/ lua nova e no afélio de Julho com lua cheia).
O efeito de maré está no limite da deteção dos pendulos usados pelo que é necessário um grande rigôr na hora (a influência solar é muito superior à lunar mas a flutuação é inferior) e o emprego de técnicas numéricas avançadas usando por exemplo a transformada de Fourier.

====Análise da torção no fio====
[[File:Torcao.jpg||thumb|Efeito da torção do fio e da elipticidade da esfera que origina um erro regular na medida pela fotocélula da velocidade na origem.|right|border|240px]]
Para os mais atentos, a velocidade na origem apresenta uma variação devido à torção do fio e à não-esfericidade da massa. O gráfico anexo demonstra isso. Pode ser efetuado o estudo do pêndulo considerando a massa da bola e a torção no fio, recomendando-se o uso das equações de euler-lagrange.

==Movimento circular uniformemente acelerado==

A velocidade de transito da esfera no ponto inferior da trajetória é determinada pela medida do tempo de interrupção do feixe laser.
Com efeito, sabendo o diâmetro da esfera é imediato determinar a velocidade na origem podendo ser inferida a energia cinética máxima. Deste modo, sabendo o comprimento do cabo, pode-se calcular o ponto de lançamento da esfera e confrontar com o ponto de lançamento.

=Provedores de latitude"=
[[file:G_latitude.png|link=https://docs.google.com/a/kic-innoenergy.com/spreadsheet/oimg?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE&oid=1&zx=hfmrs4egtbuf|thumb|Gráfico com a aceleração da gravidade a determinar pela rede. São Tomé e Príncipe está mesmo sobre o equador.
O valor de Lisboa já foi estabelecido experimentalmente.]]

A língua é um fator importante da nacionalidade ("a minha pátria á a língua portuguesa", F. Pessoa) e uma maneira simples de definir os chamados "países irmãos". Na prática só quatro línguas estão disseminadas no globo, sendo uma delas o português. Naquilo que nos interessa, o português cobre latitudes de ~30ºS a ~42ºN, quase 75º de variação sobre o equador. Deste modo os países da CPLP poderão servir como "provedores de latitude" (ver figura).

Para realizar esta experiência e ajustar pontos relevantes à nossa curva experimental precisaremos de pelo menos quatro pontos espaçados em latitude. Mas devido à não-linearidade da equação mais pontos serão convenientes para obter um ajuste firme, principalmente em torno do "joelho" nas latitudes de 10º-30º. Só o Brasil por si permite obter grade parte deste conjunto de pontos (Recife 8º, Salvador – 12º, Rio de Janeiro – 23º, Porto Alegre – 30º) mas não permite suprir os pontos onde a aceleração da gravidade varia mais rapidamente, a região quase linear entre 30º e 60º onde Portugal pode contribuir com dois pontos, por exemplo 37º e 41º. Moçambique e Angola podem contribuir com pontos redundantes próximos ao equador e S. Tomé e Príncipe, Brasil e Cabo Verde com valores equatoriais.

=Ajuste experimental=
Existem inúmeras fontes de informação sobre o pêndulo <ref name="serway"></ref> <ref name="rcl">http://rcl-munich.informatik.unibw-muenchen.de/</ref> <ref name="olsom">Nelson, Robert; M. G. Olsson (February 1987). "The pendulum - Rich physics from a simple system". American Journal of Physics 54 (2):
doi:10.1119/1.14703</ref> <ref name="gauld">Pendulums in the Physics Education Literature: A Bibliography, Gauld, Colin 2004 Science & Education, issue 7, volume 13, 811-832
(http://dx.doi.org/10.1007/s11191-004-9508-7)</ref> <ref name="qureshi">The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach, M I Qureshi et al 2010 Eur. J. Phys. 31 1485(http://dx.doi.org/10.1088/0143-0807/31/6/014)</ref> <ref name="ochs"> A comprehensive analytical solution of the nonlinear pendulum, Karlheinz Ochs 2011 Eur. J. Phys. 32 479 (http://dx.doi.org/10.1088/0143-0807/32/2/019)</ref>. Se forem tidas em conta todas as influências significativas a equação harmónica na latitude que resulta pode ser expressa por:

<math>
g_{n}(\varphi) = 9.780 326 772\times[1 + 0.005 302 33 \cdot sin^{2}(\varphi) - 0.000 005 89 \cdot sin^{2}(2\varphi)] \label{harmonica-esferica}
</math>

onde $\varphi$ é a latitude do lugar. Esta expressão é uma das que melhor ajusta os resultados experimentais de acordo com o "World Geodetic System datum surface (WSG84)", considerando a terra como um elipsóide de raio r<sub>1</sub>=6378137m no equador e r<sub>2</sub>=6356752m como o raio semi-menor polar.

Propõe-se que se derive pelo menos a correção devido à força centrífuga e do achatamento dos pólos.

[[File:Period_over_time.png|thumb|Variabilidade do período com o tempo decorrido e consequentemente com a amplitude.(ângulo < 7,5º) demonstrando que o erro é inferior a 0,05%.]]

Na figura mostra-se o desvio da "constante da gravidade", ou seja o valor real em função da latitude. Estão marcadas as latitudes de alguns possíveis parceiros. Houve a preocupação de evitar que qualquer erro experimental excedesse os 0,05%, tendo em conta um desenho preciso da montagem experimental de forma a conseguir obter a precisão final mínima de 0,1% para poder comparar os dados.

=Notas históricas=
A importância do pêndulo como elemento base dos relógios e cronografos só foi destronada quando a Royal Society convenceu o parlamento inglesa a instituir um prémio de 10k£ a 20k£ (atualmente mais de 3,5M€) para a invenção dum cronografo que não dependesse dele. Com efeito a precisão do pêndulo na determinação do tempo só é ultrapassada por sistemas eletrónicos modernos.

Efetivamente, à data dos descobrimentos, a longitude só era determinada com um elevado erro, uma vez que os relógios e cronografos dependiam do pendulo e este era muito sensivel às oscilações dos navios, alterando a sua frequência ou até parando. A hora local do navio era utilizada para comparar com a hora solar (ou estelar) e com esta diferença estabelecia-se a longitude do lugar.

=Bibliografia=

<references />

=Ligações=
*[[World Pendulum | Versão em Inglês (English Version)]]
*[[Péndulo mundial| Spanish version (Versión en español)]]
*[https://www.youtube.com/watch?v=ZOOFw_Nlee8&feature=youtu.be Constrói o teu pêndulo]

World Pendulum

2026-06-18T08:25:39Z

Ist12916: /* Experimental apparatus */

=Description=
[[File:Soyuz VS03 liftoff.jpg||thumb|Soyuz lift-off from French Guiana @ 5º north of the Equator .|right|border|236px]]
Rockets are launched to space from equatorial latitudes. This is due to the fact that the apparent weight of objects is gradually reduced from the poles to the equator. We will feel lighter at the equator than at the poles!

This small difference in apparent weight allows the same rocket to launch heavier payloads into orbit if launched nearer from the equator. For example, a Soyuz rocket launching into geostationary orbit from the French Guiana (5ºN) can carry 3 tons while it will only be capable of launching 1.7 tons of cargo when launched from Baikonur, Kazakhstan (46ºN).

The goal of this experiment is to find the value of the gravity "constant" through a constellation of pendulums placed in various latitudes and remotely operated, through the internet, by anyone.

It is expected that CPLP countries can contribute to this effort, bringing students, teachers and interested citizens closer together.

There are two different activities occurring simultaneously: (i) access, through e-lab, of the pendulums located in different latitudes and (ii) the construction and local operation in schools or at home.

Lisboa, Ilhéus, Faro e Rio de Janeiro were the first cities to contribute to the network in January 2013, making it possible for the first fits of experimental data to the theoretical equation within our project that describes how gravity changes with latitude to occur.

If you want to be a part of the World Pendulum network, please contact us by sending us an [mailto:wwwelab@ist.utl.pt email].

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Video Faro: rtsp://elabmc.ist.utl.pt/worldpendulum_ccvalg.sdp
*Video Lisboa: rtsp://elabmc.ist.utl.pt/worldpendulum_planetarium.sdp
*Video Ilhéus: rtsp://elabmc.ist.utl.pt/worldpendulum_ilheus.sdp
*Video Rio Janeiro: rtsp://elabmc.ist.utl.pt/worldpendulum_puc.sdp
*Video Maputo: rtsp://elabmc.ist.utl.pt/worldpendulum_maputo.sdp
*Video São Tomé: rtsp://elabmc.ist.utl.pt/wp_saotome.sdp
*Laboratory: World Pendulum in [https://elab.vps.tecnico.ulisboa.pt:8000/ free.elab]
*Control room: Choose a location
*Grade: *

</div>
</div>

==Who likes this idea==

[[File:PBA B1 1.png|border|180px|border|180px]]
[[File:LogoSPF long.jpg|border|180px]]
[[File:logo_EPS_blue.gif|border|80px]]
[[File:Logo mar.png|border|80px]]
[[File:LogoPlanetarioGulbenkian.png|border|180px]]
[[File:LogoCCVALG.png|border|204px|border|180px]]
[[File:LogoPlanetarioRioJaneiro.png|border|180px]]
[[File:Logo info tech.png|border|180px]]
[[File:Logo_tap.png|border|180px]]
[[File:Cenfim Logo.jpg|border|180px]]
[[File:LogoPUC.PNG|border|60px]]
[[File:UESC BRASÃO ref.jpg|border|60px]]
[[File:UFRPE.jpg|border|60px]]
[[File:Logo_DGAE.png|border|380px]]
[[File:LogosBeneficairesErasmus+RIGHT EN.jpg|border|280px]]

=Experimental apparatus=
The pendulum design used was based in Dr. Jodl's design<ref name="jodl">World pendulum—a distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude, Grober S, Vetter M, Eckert B and Jodl H J, European Journal of Physics - EUR J PHYS , vol. 28, no. 3, pp. 603-613, 2007</ref>. By following this approach we can contribute to have more comparable experiments. Some minor changes were made to allow the same design to be easily replicated in high schools. The data concerning each pendulum follows:

[[File:WordlPendulum.JPG|thumb|Pendulum used for the world pendulum standard gravity experiment.]]
[[File:Stringsuport.png|thumb|Pendulum string support to avoid elongation errors. The cable is fixed by soldering it into a brass M4 screw 40mm long.]]
[[File:Launcher_2.png|thumb|Standard launcher of the pendulum mass for the World Pendulum Alliance (WPA). This launcher uses a V-slot rail technology and it is characterized by a maximum horizontal launching distance of 250 mm.]]

{| class="wikitable"
!colspan="6"|Physical sizes by place
|-
| Place
| Latitude
| Longitude
| Altitude (m)
| Cable length (mm)
| Sphere diameter (mm)
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Dili-EPD]
| 8°'31"S
| 125°34'26"W
| 10
| 2837.25 +/- 0.5 @27ºC
| 80.8 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/31/1 Luanda-EPL]
| 8° 50' 1"S
| 13°14'37"W
| 70
| 2375.0 +/- 0.5 @27ºC
| 80.5 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/9/1 Oeiras-IST]
| 38°44'14.23"N
| 9°18'10.85"W
| 210
| 8.1385 +/- 0.5 @25ºC
| 101 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Faro-CCV Algarve]
| 37º00'N
| 7º56'W
| 10
| 2677 +/- 0.5 @23ºC
| 77.5 +/- 1.0
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220
| 2832.0 +/- 0.5 @23ºC
| 81.0 +/- 1.0
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/2/2 Lisbon-Planetarium]
| 38º41'N
| 9º12'W
| 20
| 2628.5 +/- 0.5 @19ºC
| 80.8 (47.2) +/- 0.5
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/16/1 Maputo-EPM]
| 25º56'S
| 32º36'E
| 80
| 2609.8 +/- 0.5 @27ºC
| 80.5 +/- 1.0
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/10/1 São Tomé-EPSTP]
| 0º21'N
| 6º43'E
| 50
| 2756.5 +/- 0.5 @29ºC
| 81.8 +/- 0.5
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150
| 2803 +/- 0.5 @25ºC
| 80.1 +/- 0.5
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2824 +/- 1
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/14/1 Rio de Janeiro-PUC]
| 22º54.1'S
| 43º12'W
| 50
| 2826,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40
| 2832,0 +/- 0.5
| 81.6 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/12/1 Bogotá-UniAndes]
| 4°36'N
| 74°3'W
| 2500
| 2824 +/- 0.5
| 82.0 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/13/1 Bogotá-UNAD]
| 4°35'N
| 74°5'W
| 2650
| 2835 +/- 0.5
| 82.0 +/- 0.1
|-
| Panama city-UTP
| 9°1.3'N
| 79°31.9'W
| 82
| 2800 + /- 0.5 @28ºC
| 81.9 +/- 0.1
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552
| 2825 +/- 0.5 @27ºC
| 81.9 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/11/1 Valparaiso-UTFSM]
| 33°1'S
| 71°37'W
| 30
| 2827.5 +/- 0.5 @28ºC
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/17/1 Panama city-USMA]
| 9°1'N
| 79°37'W
| 130
| 2800.0 +/- 0.5 @35ºC
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/18/1 Brasilia-UnB]
| 15° 46'S
| 47° 52'W
| 1034
| 2826.8 mm +/- 0.5 @26ºC
| 81.4 +/- 0.1
|-
| Marseille - ECM
| 43°20.6'N
| 5°26.2'E
| 162
| 2817.0 mm +/- 0.5 @22ºC
| 82.0 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/15/1 Punta Arenas-UMag]
| 53°8'S
| 70°52'W
| 40
| 2823 +/- 0.5 @16.4ºC
| 81.7 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/38/1 Lubango-ISCED]
| 14°55'S
| 13°29'E
| 1787
| 1805.2 +/- 0.5 @26ºC
| 82.2 +/- 0.1
|}

{| class="wikitable"
!colspan="2"|Typical quantities
|-
| Cable length (not counting the sphere) || min: 0.5 m nominal: 2.8m max: 12m
|-
| Sphere mass || 2kg +/- 75g
|-
| Sphere diameter || 81.2mm +/-1.5mm
|-
| Cable || Remanium(r) - Stainless steel (Nickel chromium)
- 0,4mm
|-
| Cable modulus of elasticity || ~200 GPa
|-
|Cable shear modulus (modulus of rigidity)|| 48-60 GPa
|-
| Oscillation period measurement system || Microprocessor with 7,3728MHz - 30ppm crystal
+ laser + PIN photodiode
|-
| Wire CTE (25-500ºC) (Coefficient of thermal expansion) || ~14 x 10<sup>-6</sup> K<sup>-1</sup>
|}

{| class="wikitable"
!colspan="2"|Penulum length limits*
|-
| Minimum || ~1.5 m
|-
| Maximum || virtually no limit (~63.5 m)
|}
<nowiki>*</nowiki>These limits were estimated for the standard World Pendulum Alliance launcher (WPA). A photo of a standard WPA launcher is shown on the figure on the right.
Check [http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Precision_Pendulum_Assembly:_Apparatus_description#Pendulum_length_limits Pendulum length limits] to understand how these limits were obtained.

The experimental apparatus can be easily adapted to human operation, using a good chronometer, for local execution. The stainless steel structures can made in by brass or bronze for easier machining. The cable used can be replaced by a sport fishing steel cable and the mass can be replaced by a Olympic weight throw training weight, weighing 2Kg. A calibrated measuring tape should be used to measure the cable length, '''a few days after assembling the apparatus to allow for cable expansion'''.

=Local partners=
The pendulum<ref name="serway">Physics for scientists and engineers, 5th edition, Hardcourt College Publishers, R.Serway and R. Beichner, 2000</ref>, although one of the simplest systems commonly studied, is one of the richest in terms of physics.

In order to build a precise pendulum the most important factors are the precise measurement of the length of the cable, its quality, and of that of the pendulum supports. Selecting a mass between 1 to 4 Kg ensures that the pendulum's period error will be small enough for small local gravity changes (smaller than 0.1%) to be detectable, as long as a precise chronometer is used for timekeeping.

A local apparatus can be assembled using readily available materials and the local <em>"g"</em> values determined using such an apparatus can then be compared to the ones obtained through the remote pendulum constellation and the theoretical model.

Collecting this data through a social network will allow a more precise description of how <em>"g"</em> varies around the globe. The "World Pendulum" can be an important collaborative network for the dissemination of physics in schools.

Instructions on how to build such a pendulum are available in [[Precision Pendulum]].
The documentation of the development and construction of a pendulum are available in [[Precision Pendulum]] while the instructions on how to assemble it are available in [[Precision Pendulum Assembly]].

If you want to be a part of the World Pendulum network, please contact us by sending us an [mailto:wwwelab@ist.utl.pt email].

=Physics=
Determining gravity's acceleration in different parts of the globe raises questions about the importance of models in physics. It's possible to show that gravity's acceleration at sea level changes with latitude, and therefore a correction is needed for each individual location. This process allows us to demystify science and correct the existing "urban myth" around some physical constants that only are truly constant when some approximations are done. In this particular case, we will show how the introduction of successive corrections to gravity's "constant" will lead to values closer to those experimentally obtained.

==Geophysical model==
The starting point is the commonly used, constant, value of 9.81 ms<sup>-2</sup>. This is obtained by considering the Earth as being (i) a sphere (ii) that is not rotating. It's trivial to note that this model, due to the symmetry of the spherical form, does not allow for different values in different locations. This changes as soon as Earth's rotation dynamics and ellipsoid shape (flattening of the poles) are taken in account. These factors allow for gravity to change with latitude, and in fact these two factors are the two most important ones in this phenomena, outweighing every other effect, such as (i) altitude, (ii) tidal forces, and (iii) subsoil composition.

To demonstrate these finer aspects, gravity's acceleration must be determined in various latitudes around the globe distant from each other. Using the data collected, students can then ask themselves about how "constant" the value truly is and improve their intuition of gravity.

===Experimental studies===
====Variation with latitude====
As seen, the first possible study consists of using the remote pendulums to obtain a measurement of the local gravity acceleration for each location they're based in. Through considering (or not) several factors, it is possible to fit the data to a experimental description of the Earth using spherical harmonics (equation \eqref{harmonica-esferica}). This experimental work can be conducted using e-lab's pendulum constellation and [http://rcl-munich.informatik.unibw-muenchen.de/ our partner's pendulums].

====Local determination====
Following the instructions available in this wiki - [[Precision_Pendulum]] - or using any other kind of design that results in a rigorous apparatus, a local pendulum is built. It's then possible for measurements of local gravity to be made, as long as a good chronometer is used. Furthermore, it's also possible to contribute to the enrichment of the World Pendulum network's [https://docs.google.com/a/kic-innoenergy.com/spreadsheet/ccc?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE#gid=0 spreadsheet].

====[[Tidal study]]====
Using an almanac appropriate for the location, on can obtain the times of particular Moon/Sun alignments (full moon, new moon, waxing crescent and waxing gibbous). Plotting a graph spanning several months, one can try to verify and quantify the influence of tidal forces and Moon/Sun alignments in the apparent weight. It's possible to try and verify the correlation between Moon phases and changes in measurement of local gravity, by making a month or year-long study.
Tidal effects are on the limit of detection by the pendulums of the e-lab constellation. For the experiment to be successful, it's necessary to be very rigorous on the time at which the experimental runs are made and some advanced numerical techniques, like the Fourier transform, need to by employed for the signal to be extracted from the data.

====Analysis of wire torsion ====
[[File:Torcao.jpg||thumb|Effect of wire torsion and sphere ellipticity in the measurement of pendulum speed.|right|border|240px]]
Those paying more attention will note that the speed of the mass changes due to wire torsion and due to the mass not being a perfect sphere. This is pictured in the image to the right. The pendulum can be studied taking into account the effect of the wire torsion (the use of Euler-Lagrange equations is recommended for this).
As such the harmonic rotational movement arising from this gives a period of motion that can be showed to be equal to:
<math>
T=2\pi \times \sqrt{\frac{I}{\kappa}},\; I(Sphere)=\frac{2}{5}mr^2, \; \kappa=\frac{\nu \pi r_{cable}^4}{2l_{cable}}
</math>

The shear or rigidity modulus ν can then be determine after computing κ by analyzing this spurious oscillation.

==Uniformly accelerated circular movement==
The speed of the sphere in the lowest point of the trajectory is determined by measuring how much time the laser beam is interrupted. Knowing the sphere diameter, it's trivial to determine the speed at the origin. From this, the maximum kinetic energy can be calculated and the launching height of the pendulum determined. The calculated launching point can then be compared with the real one.

=Latitude provideres=

[[file:G_latitude.png|link=https://docs.google.com/a/kic-innoenergy.com/spreadsheet/oimg?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE&oid=1&zx=hfmrs4egtbuf|thumb|The gravitational constant plotted against latitude with points of interest around the globe highlighted. Principe Island is just over zero latitude. Lisbon value was obtained with the current experiment and already over plotted on the graphic.]]

Language is an important nationality factor ("My fatherland is the Portuguese language.", F. Pessoa) and a simple way to define what is called brother countries ("países irmãos"). Only four languages are disseminated around the world, Portuguese being one of them. The Portuguese speaking community covers latitudes from ~30S to ~40N, almost a 75º span across the equator. Therefore, CPLP countries can help by being "latitude providers" (see Figure).

To conduct this world experiment, at least four spaced points are needed in order to have a proper fit. But due to the strong non-linearity of the equation, more points are needed to provide a suitable adjustment, in particular on the "knee" close to the earth’s equator. Brazil itself can provide almost four crucial points close to the equator (e.g. Recife 8º, Salvador – 12º, Rio de Janeiro – 23º, Porto Alegre – 30º) but lacks points with a latitude where the characteristic varies more strongly, the almost linear region around 30º to 60º, where Portugal can give two good points (e.g. Porto - 37º and Faro - 41º). Mozambique can contribute with 27º (Maputo) and S. Tomé e Principe or Brazil are both good choices to cover the equator. Angola could give complementary points to those acquired in Brazil, as the sensibility of the measurement is more pronounced close to the equator and the poles.

=Data fitting=
Available references <ref name="serway"></ref> <ref name="rcl">http://rcl-munich.informatik.unibw-muenchen.de/</ref> <ref name="olsom">Nelson, Robert; M. G. Olsson (February 1987). "The pendulum - Rich physics from a simple system". American Journal of Physics 54 (2):
doi:10.1119/1.14703</ref> <ref name="gauld">Pendulums in the Physics Education Literature: A Bibliography, Gauld, Colin 2004 Science & Education, issue 7, volume 13, 811-832
(http://dx.doi.org/10.1007/s11191-004-9508-7)</ref> <ref name="qureshi">The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach, M I Qureshi et al 2010 Eur. J. Phys. 31 1485(http://dx.doi.org/10.1088/0143-0807/31/6/014)</ref> <ref name="ochs"> A comprehensive analytical solution of the nonlinear pendulum, Karlheinz Ochs 2011 Eur. J. Phys. 32 479 (http://dx.doi.org/10.1088/0143-0807/32/2/019)</ref> give a very good description of the mathematical model needed to fit the data. If all major factors are taken into account, gravity as a function of latitude is given by:

<math>
g_{n}(\varphi) = 9.780 326 772\times[1 + 0.005 302 33 \cdot sin^{2}(\varphi) - 0.000 005 89 \cdot sin^{2}(2\varphi)]
</math>

where $\varphi$ is the latitude. This expression is one of the best experimental approximations and results from the standardization agreement to adjust the World Geodetic System datum surface (WSG84) to an ellipsoid with radius r<sub>1</sub>=6378137m at the equator and r<sub>2</sub>=6356752m polar semi-minor radius.
This formula takes into account the fact that the Earth is an ellipsoid and that there is an additional increase in the acceleration of gravity when one moves nearer to the poles, due to a weaker centrifugal force. Nevertheless the students could derive a non-harmonic, first order approximation by taking into account only centrifugal force. Then, as a second step, they could include the two other major errors, the centrifugal force and earth’s ellipsoid format.

[[File:Period_over_time.png|thumb|The variability of the period with elapsed time (angle amplitude < 7,5º), showing that this error is less than 0,05% regardless initial amplitude.]]

The pictures shows the expected deviation from the “earth’s constant acceleration”, the real acceleration for each latitude. We have plotted the point already obtained with this apparatus in Lisbon and the marks over the expected latitudes for future partners.
Of course these approximations do not include one important source of deviation from real data to the mathematical model, the experimental error, as we do not include the experimental source of error. However, those systematic errors could be under the expected precision needed (0,1%) for the former approximation if a careful design of the apparatus is considered. Nevertheless those errors must be discussed in advanced courses and their weight must be proved when considering the real pendulum.

=Historical notes=
The pendulum importance as the basis of clocks and chronographs was only overthrown when the Royal Society convinced the English parliament to create an award, ranging from 10k£ to 20k£ (equivalent nowadays to more than 3.5M€), for the invention of a chronograph that didn't depend on it. The time precision of pendulum based systems is only bettered by modern electronic systems.

In the discovery age longitude was determined with a high error, since clocks and chronographs were reliant on pendulums and these were very sensitive to ships rocking, suffering changes in frequency or even stopping. Local longitude was calculated by comparing the solar hour (or stellar hour) with the ship's clock time.

=Frequently asked questions=

How long would it take to replace the cable that holds the sphere?

The remanium cable is a very strong material and only need to be replace in case of misuse.

Over time the cable can have some extension?

Cable length should undergone a rectified measure after ~3 months installation and thereafter once a year.

The temperature where the pendulum is installed interferes with the results of the experiments?

The variation induced by temperature is relevant when it comes to very precise measurements such as tide detection (local fluctuations), the reason why it is reported. NOTE that in some situations, due to incorrect housing of the temperature sensor, temperature increases during the reading as the sensor can be close to the power electronics devices. So, we advise a wise use of it.

Are the various pendulums subjected to regular calibrations?
Regular calibrations shall take place at least once a year. Nevertheless we can not guarantee that every partner assure a regular calibration of the pendulums. Please monitor the course of each experience and use critical thinking in the face of any results obtained.

What is the difference in measuring the cable with a laser or a tape measure, there is a noticeable difference between the two methods?

Usually both methods give the same incertitude because the limiting factor is the positioning of both devices by human usage which is barely the same, surpassing the intrinsic error of each device.

The use of a frontal camera to analyze the motion of the pendulum, make a recording and then use some image analysis software to study the movements and oscillations will give good results?

This results can be obtained with the camera on top as well, a movie can be shot and analyses on Tracker software for instance.

=References=

<references />

=Links=
*[[Pêndulo Mundial | Portuguese version (Versão em Português)]]
*[[Péndulo mundial| Spanish version (Versión en español)]]
*[https://www.youtube.com/watch?v=ZOOFw_Nlee8&feature=youtu.be Building your own pendulum]

World Pendulum

2026-06-17T16:24:37Z

Ist12916: /* Experimental apparatus */

=Description=
[[File:Soyuz VS03 liftoff.jpg||thumb|Soyuz lift-off from French Guiana @ 5º north of the Equator .|right|border|236px]]
Rockets are launched to space from equatorial latitudes. This is due to the fact that the apparent weight of objects is gradually reduced from the poles to the equator. We will feel lighter at the equator than at the poles!

This small difference in apparent weight allows the same rocket to launch heavier payloads into orbit if launched nearer from the equator. For example, a Soyuz rocket launching into geostationary orbit from the French Guiana (5ºN) can carry 3 tons while it will only be capable of launching 1.7 tons of cargo when launched from Baikonur, Kazakhstan (46ºN).

The goal of this experiment is to find the value of the gravity "constant" through a constellation of pendulums placed in various latitudes and remotely operated, through the internet, by anyone.

It is expected that CPLP countries can contribute to this effort, bringing students, teachers and interested citizens closer together.

There are two different activities occurring simultaneously: (i) access, through e-lab, of the pendulums located in different latitudes and (ii) the construction and local operation in schools or at home.

Lisboa, Ilhéus, Faro e Rio de Janeiro were the first cities to contribute to the network in January 2013, making it possible for the first fits of experimental data to the theoretical equation within our project that describes how gravity changes with latitude to occur.

If you want to be a part of the World Pendulum network, please contact us by sending us an [mailto:wwwelab@ist.utl.pt email].

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Video Faro: rtsp://elabmc.ist.utl.pt/worldpendulum_ccvalg.sdp
*Video Lisboa: rtsp://elabmc.ist.utl.pt/worldpendulum_planetarium.sdp
*Video Ilhéus: rtsp://elabmc.ist.utl.pt/worldpendulum_ilheus.sdp
*Video Rio Janeiro: rtsp://elabmc.ist.utl.pt/worldpendulum_puc.sdp
*Video Maputo: rtsp://elabmc.ist.utl.pt/worldpendulum_maputo.sdp
*Video São Tomé: rtsp://elabmc.ist.utl.pt/wp_saotome.sdp
*Laboratory: World Pendulum in [https://elab.vps.tecnico.ulisboa.pt:8000/ free.elab]
*Control room: Choose a location
*Grade: *

</div>
</div>

==Who likes this idea==

[[File:PBA B1 1.png|border|180px|border|180px]]
[[File:LogoSPF long.jpg|border|180px]]
[[File:logo_EPS_blue.gif|border|80px]]
[[File:Logo mar.png|border|80px]]
[[File:LogoPlanetarioGulbenkian.png|border|180px]]
[[File:LogoCCVALG.png|border|204px|border|180px]]
[[File:LogoPlanetarioRioJaneiro.png|border|180px]]
[[File:Logo info tech.png|border|180px]]
[[File:Logo_tap.png|border|180px]]
[[File:Cenfim Logo.jpg|border|180px]]
[[File:LogoPUC.PNG|border|60px]]
[[File:UESC BRASÃO ref.jpg|border|60px]]
[[File:UFRPE.jpg|border|60px]]
[[File:Logo_DGAE.png|border|380px]]
[[File:LogosBeneficairesErasmus+RIGHT EN.jpg|border|280px]]

=Experimental apparatus=
The pendulum design used was based in Dr. Jodl's design<ref name="jodl">World pendulum—a distributed remotely controlled laboratory (RCL) to measure the Earth's gravitational acceleration depending on geographical latitude, Grober S, Vetter M, Eckert B and Jodl H J, European Journal of Physics - EUR J PHYS , vol. 28, no. 3, pp. 603-613, 2007</ref>. By following this approach we can contribute to have more comparable experiments. Some minor changes were made to allow the same design to be easily replicated in high schools. The data concerning each pendulum follows:

[[File:WordlPendulum.JPG|thumb|Pendulum used for the world pendulum standard gravity experiment.]]
[[File:Stringsuport.png|thumb|Pendulum string support to avoid elongation errors. The cable is fixed by soldering it into a brass M4 screw 40mm long.]]
[[File:Launcher_2.png|thumb|Standard launcher of the pendulum mass for the World Pendulum Alliance (WPA). This launcher uses a V-slot rail technology and it is characterized by a maximum horizontal launching distance of 250 mm.]]

{| class="wikitable"
!colspan="6"|Physical sizes by place
|-
| Place
| Latitude
| Longitude
| Altitude (m)
| Cable length (mm)
| Sphere diameter (mm)
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Dili-EPD]
| 8°'31"S
| 125°34'26"W
| 10
| 2837.25 +/- 0.5 @27ºC
| 80.8 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/31/1 Luanda-EPL]
| 8° 50' 1"S
| 13°14'37"W
| 70
| 2375.0 +/- 0.5 @27ºC
| 80.5 +/- 0.1
|-
| [http://elab.vps.tecnico.ulisboa.pt:8000/execution/create/9/1 Oeiras-IST]
| 38°44'14.23"N
| 9°18'10.85"W
| 210
| 8.1385 +/- 0.5 @25ºC
| 101 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/8/1 Faro-CCV Algarve]
| 37º00'N
| 7º56'W
| 10
| 2677 +/- 0.5 @23ºC
| 77.5 +/- 1.0
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220
| 2832.0 +/- 0.5 @23ºC
| 81.0 +/- 1.0
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/2/2 Lisbon-Planetarium]
| 38º41'N
| 9º12'W
| 20
| 2628.5 +/- 0.5 @19ºC
| 80.8 (47.2) +/- 0.5
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/16/1 Maputo-EPM]
| 25º56'S
| 32º36'E
| 80
| 2609.8 +/- 0.5 @27ºC
| 80.5 +/- 1.0
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/10/1 São Tomé-EPSTP]
| 0º21'N
| 6º43'E
| 50
| 2756.5 +/- 0.5 @29ºC
| 81.8 +/- 0.5
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150
| 2803 +/- 0.5 @25ºC
| 80.1 +/- 0.5
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2824 +/- 1
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/14/1 Rio de Janeiro-PUC]
| 22º54.1'S
| 43º12'W
| 50
| 2826,0 +/- 0.5
| 81.6 +/- 0.1
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40
| 2832,0 +/- 0.5
| 81.6 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/12/1 Bogotá-UniAndes]
| 4°36'N
| 74°3'W
| 2500
| 2824 +/- 0.5
| 82.0 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/13/1 Bogotá-UNAD]
| 4°35'N
| 74°5'W
| 2650
| 2835 +/- 0.5
| 82.0 +/- 0.1
|-
| Panama city-UTP
| 9°1.3'N
| 79°31.9'W
| 82
| 2800 + /- 0.5 @28ºC
| 81.9 +/- 0.1
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552
| 2825 +/- 0.5 @27ºC
| 81.9 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/11/1 Valparaiso-UTFSM]
| 33°1'S
| 71°37'W
| 30
| 2827.5 +/- 0.5 @28ºC
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/17/1 Panama city-USMA]
| 9°1'N
| 79°37'W
| 130
| 2800.0 +/- 0.5 @35ºC
| 81.8 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/18/1 Brasilia-UnB]
| 15° 46'S
| 47° 52'W
| 1034
| 2826.8 mm +/- 0.5 @26ºC
| 81.4 +/- 0.1
|-
| Marseille - ECM
| 43°20.6'N
| 5°26.2'E
| 162
| 2817.0 mm +/- 0.5 @22ºC
| 82.0 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/15/1 Punta Arenas-UMag]
| 53°8'S
| 70°52'W
| 40
| 2823 +/- 0.5 @16.4ºC
| 81.7 +/- 0.1
|-
| [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/xx/1 Lubango-ISCED]
| 14°54'S
| 13°50'E
| 1740
| 1805.2 +/- 0.5 @26ºC
| 82.2 +/- 0.1
|}

{| class="wikitable"
!colspan="2"|Typical quantities
|-
| Cable length (not counting the sphere) || min: 0.5 m nominal: 2.8m max: 12m
|-
| Sphere mass || 2kg +/- 75g
|-
| Sphere diameter || 81.2mm +/-1.5mm
|-
| Cable || Remanium(r) - Stainless steel (Nickel chromium)
- 0,4mm
|-
| Cable modulus of elasticity || ~200 GPa
|-
|Cable shear modulus (modulus of rigidity)|| 48-60 GPa
|-
| Oscillation period measurement system || Microprocessor with 7,3728MHz - 30ppm crystal
+ laser + PIN photodiode
|-
| Wire CTE (25-500ºC) (Coefficient of thermal expansion) || ~14 x 10<sup>-6</sup> K<sup>-1</sup>
|}

{| class="wikitable"
!colspan="2"|Penulum length limits*
|-
| Minimum || ~1.5 m
|-
| Maximum || virtually no limit (~63.5 m)
|}
<nowiki>*</nowiki>These limits were estimated for the standard World Pendulum Alliance launcher (WPA). A photo of a standard WPA launcher is shown on the figure on the right.
Check [http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Precision_Pendulum_Assembly:_Apparatus_description#Pendulum_length_limits Pendulum length limits] to understand how these limits were obtained.

The experimental apparatus can be easily adapted to human operation, using a good chronometer, for local execution. The stainless steel structures can made in by brass or bronze for easier machining. The cable used can be replaced by a sport fishing steel cable and the mass can be replaced by a Olympic weight throw training weight, weighing 2Kg. A calibrated measuring tape should be used to measure the cable length, '''a few days after assembling the apparatus to allow for cable expansion'''.

=Local partners=
The pendulum<ref name="serway">Physics for scientists and engineers, 5th edition, Hardcourt College Publishers, R.Serway and R. Beichner, 2000</ref>, although one of the simplest systems commonly studied, is one of the richest in terms of physics.

In order to build a precise pendulum the most important factors are the precise measurement of the length of the cable, its quality, and of that of the pendulum supports. Selecting a mass between 1 to 4 Kg ensures that the pendulum's period error will be small enough for small local gravity changes (smaller than 0.1%) to be detectable, as long as a precise chronometer is used for timekeeping.

A local apparatus can be assembled using readily available materials and the local <em>"g"</em> values determined using such an apparatus can then be compared to the ones obtained through the remote pendulum constellation and the theoretical model.

Collecting this data through a social network will allow a more precise description of how <em>"g"</em> varies around the globe. The "World Pendulum" can be an important collaborative network for the dissemination of physics in schools.

Instructions on how to build such a pendulum are available in [[Precision Pendulum]].
The documentation of the development and construction of a pendulum are available in [[Precision Pendulum]] while the instructions on how to assemble it are available in [[Precision Pendulum Assembly]].

If you want to be a part of the World Pendulum network, please contact us by sending us an [mailto:wwwelab@ist.utl.pt email].

=Physics=
Determining gravity's acceleration in different parts of the globe raises questions about the importance of models in physics. It's possible to show that gravity's acceleration at sea level changes with latitude, and therefore a correction is needed for each individual location. This process allows us to demystify science and correct the existing "urban myth" around some physical constants that only are truly constant when some approximations are done. In this particular case, we will show how the introduction of successive corrections to gravity's "constant" will lead to values closer to those experimentally obtained.

==Geophysical model==
The starting point is the commonly used, constant, value of 9.81 ms<sup>-2</sup>. This is obtained by considering the Earth as being (i) a sphere (ii) that is not rotating. It's trivial to note that this model, due to the symmetry of the spherical form, does not allow for different values in different locations. This changes as soon as Earth's rotation dynamics and ellipsoid shape (flattening of the poles) are taken in account. These factors allow for gravity to change with latitude, and in fact these two factors are the two most important ones in this phenomena, outweighing every other effect, such as (i) altitude, (ii) tidal forces, and (iii) subsoil composition.

To demonstrate these finer aspects, gravity's acceleration must be determined in various latitudes around the globe distant from each other. Using the data collected, students can then ask themselves about how "constant" the value truly is and improve their intuition of gravity.

===Experimental studies===
====Variation with latitude====
As seen, the first possible study consists of using the remote pendulums to obtain a measurement of the local gravity acceleration for each location they're based in. Through considering (or not) several factors, it is possible to fit the data to a experimental description of the Earth using spherical harmonics (equation \eqref{harmonica-esferica}). This experimental work can be conducted using e-lab's pendulum constellation and [http://rcl-munich.informatik.unibw-muenchen.de/ our partner's pendulums].

====Local determination====
Following the instructions available in this wiki - [[Precision_Pendulum]] - or using any other kind of design that results in a rigorous apparatus, a local pendulum is built. It's then possible for measurements of local gravity to be made, as long as a good chronometer is used. Furthermore, it's also possible to contribute to the enrichment of the World Pendulum network's [https://docs.google.com/a/kic-innoenergy.com/spreadsheet/ccc?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE#gid=0 spreadsheet].

====[[Tidal study]]====
Using an almanac appropriate for the location, on can obtain the times of particular Moon/Sun alignments (full moon, new moon, waxing crescent and waxing gibbous). Plotting a graph spanning several months, one can try to verify and quantify the influence of tidal forces and Moon/Sun alignments in the apparent weight. It's possible to try and verify the correlation between Moon phases and changes in measurement of local gravity, by making a month or year-long study.
Tidal effects are on the limit of detection by the pendulums of the e-lab constellation. For the experiment to be successful, it's necessary to be very rigorous on the time at which the experimental runs are made and some advanced numerical techniques, like the Fourier transform, need to by employed for the signal to be extracted from the data.

====Analysis of wire torsion ====
[[File:Torcao.jpg||thumb|Effect of wire torsion and sphere ellipticity in the measurement of pendulum speed.|right|border|240px]]
Those paying more attention will note that the speed of the mass changes due to wire torsion and due to the mass not being a perfect sphere. This is pictured in the image to the right. The pendulum can be studied taking into account the effect of the wire torsion (the use of Euler-Lagrange equations is recommended for this).
As such the harmonic rotational movement arising from this gives a period of motion that can be showed to be equal to:
<math>
T=2\pi \times \sqrt{\frac{I}{\kappa}},\; I(Sphere)=\frac{2}{5}mr^2, \; \kappa=\frac{\nu \pi r_{cable}^4}{2l_{cable}}
</math>

The shear or rigidity modulus ν can then be determine after computing κ by analyzing this spurious oscillation.

==Uniformly accelerated circular movement==
The speed of the sphere in the lowest point of the trajectory is determined by measuring how much time the laser beam is interrupted. Knowing the sphere diameter, it's trivial to determine the speed at the origin. From this, the maximum kinetic energy can be calculated and the launching height of the pendulum determined. The calculated launching point can then be compared with the real one.

=Latitude provideres=

[[file:G_latitude.png|link=https://docs.google.com/a/kic-innoenergy.com/spreadsheet/oimg?key=0AkxMmuJA92wgdHZnWHk5WHhaQldINGFqSTl6OGdpSlE&oid=1&zx=hfmrs4egtbuf|thumb|The gravitational constant plotted against latitude with points of interest around the globe highlighted. Principe Island is just over zero latitude. Lisbon value was obtained with the current experiment and already over plotted on the graphic.]]

Language is an important nationality factor ("My fatherland is the Portuguese language.", F. Pessoa) and a simple way to define what is called brother countries ("países irmãos"). Only four languages are disseminated around the world, Portuguese being one of them. The Portuguese speaking community covers latitudes from ~30S to ~40N, almost a 75º span across the equator. Therefore, CPLP countries can help by being "latitude providers" (see Figure).

To conduct this world experiment, at least four spaced points are needed in order to have a proper fit. But due to the strong non-linearity of the equation, more points are needed to provide a suitable adjustment, in particular on the "knee" close to the earth’s equator. Brazil itself can provide almost four crucial points close to the equator (e.g. Recife 8º, Salvador – 12º, Rio de Janeiro – 23º, Porto Alegre – 30º) but lacks points with a latitude where the characteristic varies more strongly, the almost linear region around 30º to 60º, where Portugal can give two good points (e.g. Porto - 37º and Faro - 41º). Mozambique can contribute with 27º (Maputo) and S. Tomé e Principe or Brazil are both good choices to cover the equator. Angola could give complementary points to those acquired in Brazil, as the sensibility of the measurement is more pronounced close to the equator and the poles.

=Data fitting=
Available references <ref name="serway"></ref> <ref name="rcl">http://rcl-munich.informatik.unibw-muenchen.de/</ref> <ref name="olsom">Nelson, Robert; M. G. Olsson (February 1987). "The pendulum - Rich physics from a simple system". American Journal of Physics 54 (2):
doi:10.1119/1.14703</ref> <ref name="gauld">Pendulums in the Physics Education Literature: A Bibliography, Gauld, Colin 2004 Science & Education, issue 7, volume 13, 811-832
(http://dx.doi.org/10.1007/s11191-004-9508-7)</ref> <ref name="qureshi">The exact equation of motion of a simple pendulum of arbitrary amplitude: a hypergeometric approach, M I Qureshi et al 2010 Eur. J. Phys. 31 1485(http://dx.doi.org/10.1088/0143-0807/31/6/014)</ref> <ref name="ochs"> A comprehensive analytical solution of the nonlinear pendulum, Karlheinz Ochs 2011 Eur. J. Phys. 32 479 (http://dx.doi.org/10.1088/0143-0807/32/2/019)</ref> give a very good description of the mathematical model needed to fit the data. If all major factors are taken into account, gravity as a function of latitude is given by:

<math>
g_{n}(\varphi) = 9.780 326 772\times[1 + 0.005 302 33 \cdot sin^{2}(\varphi) - 0.000 005 89 \cdot sin^{2}(2\varphi)]
</math>

where $\varphi$ is the latitude. This expression is one of the best experimental approximations and results from the standardization agreement to adjust the World Geodetic System datum surface (WSG84) to an ellipsoid with radius r<sub>1</sub>=6378137m at the equator and r<sub>2</sub>=6356752m polar semi-minor radius.
This formula takes into account the fact that the Earth is an ellipsoid and that there is an additional increase in the acceleration of gravity when one moves nearer to the poles, due to a weaker centrifugal force. Nevertheless the students could derive a non-harmonic, first order approximation by taking into account only centrifugal force. Then, as a second step, they could include the two other major errors, the centrifugal force and earth’s ellipsoid format.

[[File:Period_over_time.png|thumb|The variability of the period with elapsed time (angle amplitude < 7,5º), showing that this error is less than 0,05% regardless initial amplitude.]]

The pictures shows the expected deviation from the “earth’s constant acceleration”, the real acceleration for each latitude. We have plotted the point already obtained with this apparatus in Lisbon and the marks over the expected latitudes for future partners.
Of course these approximations do not include one important source of deviation from real data to the mathematical model, the experimental error, as we do not include the experimental source of error. However, those systematic errors could be under the expected precision needed (0,1%) for the former approximation if a careful design of the apparatus is considered. Nevertheless those errors must be discussed in advanced courses and their weight must be proved when considering the real pendulum.

=Historical notes=
The pendulum importance as the basis of clocks and chronographs was only overthrown when the Royal Society convinced the English parliament to create an award, ranging from 10k£ to 20k£ (equivalent nowadays to more than 3.5M€), for the invention of a chronograph that didn't depend on it. The time precision of pendulum based systems is only bettered by modern electronic systems.

In the discovery age longitude was determined with a high error, since clocks and chronographs were reliant on pendulums and these were very sensitive to ships rocking, suffering changes in frequency or even stopping. Local longitude was calculated by comparing the solar hour (or stellar hour) with the ship's clock time.

=Frequently asked questions=

How long would it take to replace the cable that holds the sphere?

The remanium cable is a very strong material and only need to be replace in case of misuse.

Over time the cable can have some extension?

Cable length should undergone a rectified measure after ~3 months installation and thereafter once a year.

The temperature where the pendulum is installed interferes with the results of the experiments?

The variation induced by temperature is relevant when it comes to very precise measurements such as tide detection (local fluctuations), the reason why it is reported. NOTE that in some situations, due to incorrect housing of the temperature sensor, temperature increases during the reading as the sensor can be close to the power electronics devices. So, we advise a wise use of it.

Are the various pendulums subjected to regular calibrations?
Regular calibrations shall take place at least once a year. Nevertheless we can not guarantee that every partner assure a regular calibration of the pendulums. Please monitor the course of each experience and use critical thinking in the face of any results obtained.

What is the difference in measuring the cable with a laser or a tape measure, there is a noticeable difference between the two methods?

Usually both methods give the same incertitude because the limiting factor is the positioning of both devices by human usage which is barely the same, surpassing the intrinsic error of each device.

The use of a frontal camera to analyze the motion of the pendulum, make a recording and then use some image analysis software to study the movements and oscillations will give good results?

This results can be obtained with the camera on top as well, a movie can be shot and analyses on Tracker software for instance.

=References=

<references />

=Links=
*[[Pêndulo Mundial | Portuguese version (Versão em Português)]]
*[[Péndulo mundial| Spanish version (Versión en español)]]
*[https://www.youtube.com/watch?v=ZOOFw_Nlee8&feature=youtu.be Building your own pendulum]

Light Polarization with multiple polarizers

2026-06-08T08:02:58Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Trieste (º) || @Oeiras (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1 ||46.77 ± 1
|-
| 2 || 44.3 ± 1 || 33.5 ± 1 || 47.19 ± 1
|-
| 3 || 34.6 ± 1 || 34.2 ± 1 ||48.68 ± 1
|-
| 4 || 41.0 ± 1 || 34.9 ± 1 || 46.54 ± 1
|-
| 5 || 39.2 ± 1 || 35.6 ± 1 ||52.16 ± 1
|}

[[image:CrossPolarization.png | O ajuste da função tem um comportamento $cos(\alpha)^4$ quando é feito um varrimento de um polarizador intermédio entre dois alinhados.|thumb|320px]]

If we consider a cross polarization between more than two polarizers like an intermediate polarizer sweep, and if the adjacent ones are aligned, we get the $cos(\alpha)^4$ fit to the characteristic which can be seen in the following graph. As such, two terms will match the characteristic e.g. $cos(\alpha_{12})^2 \times (cos(\alpha_{23})^2$ and as $\alpha_1=\alpha_3$, when $\alpha_2$ makes a sweep, we get $cos(\alpha_{12})^2 \times cos(-\alpha_{12})^2 = cos(\alpha_{12})^4$. The $cos(\alpha)^2$ is plotted to highlight the differences.

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Light Polarization with multiple polarizers

2026-06-08T08:01:58Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Trieste (º) || @Oeiras (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1 ||46.77 ± 1
|-
| 2 || 44.3 ± 1 || 33.5 ± 1 || 47.19 ± 1
|-
| 3 || 34.6 ± 1 || 34.2 ± 1 ||48.68 ± 1
|-
| 4 || 41.0 ± 1 || 34.9 ± 1 || 46.54 ± 1
|-
| 5 || 39.2 ± 1 || 35.6 ± 1 ||52.16 ± 1
|}

[[image:CrossPolarization.png | O ajuste da função tem um comportamento $cos(\alpha)^4$ quando é feito um varrimento de um polarizador intermédio entre dois alinhados.|thumb|320px]]

If we consider a cross polarization between more than two polarizers like an intermediate polarizer sweep, and if the adjacent ones are aligned, we get the $cos(\alpha)^4$ fit to the characteristic and can be seen in the following graph. As such, two terms will match the characteristic e.g. $cos(\alpha_{12})^2 \times (cos(\alpha_{23})^2$ and as $\alpha_1=\alpha_3$, when $\alpha_2$ makes a sweep, we get $cos(\alpha_{12})^2 \times cos(-\alpha_{12})^2 = cos(\alpha_{12})^4$. The $cos(\alpha)^2$ is plotted to highlight the differences.

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Light Polarization with multiple polarizers

2026-06-08T07:55:31Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Trieste (º) || @Oeiras (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1 ||
|-
| 2 || 44.3 ± 1 || 33.5 ± 1 ||
|-
| 3 || 34.6 ± 1 || 34.2 ± 1 ||
|-
| 4 || 41.0 ± 1 || 34.9 ± 1 ||
|-
| 5 || 39.2 ± 1 || 35.6 ± 1 ||
|}

If we consider a cross polarization between more than two polarizers like an intermediate polarizer sweep, and if the adjacent ones are aligned, we get the $cos(\alpha)^4$ fit to the characteristic and can be seen in the following graph. As such, two terms will match the characteristic e.g. $cos(\alpha_{12})^2 \times (cos(\alpha_{23})^2$ and as $\alpha_1=\alpha_3$, when $\alpha_2$ makes a sweep, we get $cos(\alpha_{12})^2 \times cos(-\alpha_{12})^2 = cos(\alpha_{12})^4$. The $cos(\alpha)^2$ is plotted to highlight the differences.

[[file:CrossPolarization.png]]

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Repositório de Conteúdos

2026-06-06T08:45:58Z

Ist12916:

Bem-vindo à wiki do e-lab. Aqui serão reunidos artigos com a documentação e textos de apoio às experiências dos laboratórios remotos do IST.

NOTA IMPORTANTE: Iremos migrar todos os laboratórios do elab para o novo [http://elab.tecnico.ulisboa.pt ''Framework for Remote Experiments in Education'' (FREE).] As experiências serão gradualmente transferidas para esta plataforma. As experiências em FREE têm uma ligação directa na lista abaixo.

=Introdução=
O e-lab é um espaço onde podem ser realizadas experiências reais através da Internet.

As experiências estão montadas e instaladas fisicamente num laboratório do [http://www.ist.utl.pt/ Instituto Superior Técnico] ou em escolas e centros de ciência parceiras. A experiencia é controlada pelo seu administrador, que não é mais do que o primeiro membro da lista de espera dos utilizadores interessados em realizá-la. Existe, também, uma lista que permite, por exemplo, que um professor realize a experiência e os seus alunos recebam em simultâneo a imagem e os dados, apesar de poderem estar em locais fisicamente distantes.

Os dados das experiências e a imagem dos acontecimentos (vídeos) são captados por meio de sensores conectados, directa ou indirectamente, a um computador central, de onde são difundidos através da Internet.

Cada '''sala de controlo''', que corresponde a uma determinada experiência, dispõe dum espaço próprio, onde se sugere um protocolo experimental, sugestões de variantes à experiência, bem como as explicações e análises dos dados. Cada sala de controlo dispõe, também, de um chat onde todos podem tecer comentários e trocar informação sobre a experiência e sobre a análise dos dados.

Sala de controlo, aparato experimental, protocolo e montagem experimental são conceitos fundamentais no e-lab:

* '''Sala de controlo:''' ambiente virtual para controlo dum aparato experimental real incluído num determinado laboratório.
* '''Aparato experimental:''' equipamento que permite realizar determinada experiência.
* '''Montagem experimental:''' configuração do aparato experimental de acordo com o protocolo a executar.
* '''Protocolo:''' sequência da execução da experiência com a respectiva selecção e configuração da montagem experimental.

Os utilizadores do portal e-escola podem enviar sugestões ou relatórios das suas experiências para [mailto:wwwelab@ist.utl.pt este endereço].

O IST providencia ainda [[Cursos de Formação]] a docentes do ensino secundário.

Há também uma página de apoio a [[Estudantes Brasileiros]].

O projecto [[Pêndulo Mundial]] é um bom exemplo dos nossos planos para o futuro.

=Experiências=

{{Launch}}
Antes de tentar iniciar o ReC elab, certifique-se de ter instalado o JAVA e o VLC e todas as permissões de segurança definidas como explicado nas [[Add_e-lab_to_Java's_Security_Exception_Site_List | PERGUNTAS FREQUENTES]]

==Laboratório Básico==
*[[Queda de Graves (determinação de g)]]
*[[Conservação do Momento Linear]]
*[[Variação da Pressão num Líquido com a Profundidade]]
*[[Estatística de Dados]]
*[[Lei de Boyle-Mariotte]]
*[[Lei de Hooke]]
*[[Determinação da Velocidade do Som]]
*[[Pêndulo de Haste Rígida]] (em construção)
*[[Determinação do consumo de água em plantas]](em construção)
*[[Painel_Fotovoltaico | Painel Fotovoltaico]]
*[[Plano Inclinado| Plano Inclinado]]
*[[Pêndulo Mundial]]

==Laboratório Intermédio==
*[[Determinação da Condutividade Térmica em Metais]]
*[[Atenuação da Radiação em Diferentes Materiais]] 
*[[Estação Metreológica]]
*[[Oscilações de um Pêndulo Amortecido | Pendulo Amortecido]]
*[[Conservação do Momento Angular]]
*[[Optica de uma Câmara Estenopeica (Pinhole)]]
*[[Estudos de Óptica num Prisma Semi-cilíndrico]]
*[[Campo de indução magnético criado por 2 condutores]]
*[[Polarização da Luz]]
*[[Polarização da luz com múltiplos polarizadores]]
*[[Determinação da Constante de Planck]]

==Laboratório Avançado==
*[[Estudo de Estacionárias]]
*[[Determinação da Constante Adiabática do Ar]]
*[[Propagação de Solitões num Meio Viscoso]]
*[[Determinação da Constante Dieléctrica num Condensador Cilíndrico]]
*[[Sonda de Langmuir]]
*[[Curva de Paschen]]

=Mais Informações=

*[[Publications | Publicações]]

*[[Hall of fame | Colaboradores do e-lab]]

*[[Como instalar o Java]]

*[[Executar o e-lab a partir da command prompt]]

*[[Adicionar o e-lab às excepções de segurança do Java]]

*[[Training | Programas de formação]]

=Ferramentas=
[[file: TrackerTrajectoryCapture.png | Exemplo dum ajuste à trajectória de um dos pendulos mundiais efectuado com recurso ao Tracker|thumb|320px]]

*[[FAQ.pt]]
*[[Fitteia]]
*[[Editor Online de Latex]]
*[[Main Page|Lista de experiências]]
*[[My solutions]]

Alguns dos videos das experiências, nos casos relevantes, dispõem de resolução 640x480 de modo a permitir a análise de trajectórias com software apropriado, por exemplo o [https://physlets.org/tracker/ Tracker].

=Licensa=
<html>
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Licença Creative Commons" style="border-width:0" src="http://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />Esta obra e todos os conteúdos sob o portal do e-lab estão licenciados sob uma Licença <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons - Atribuição-Partilha nos termos da mesma licença 4.0 Internacional</a>.
</html>

File:CrossPolarization.png

2026-06-05T08:15:16Z

Ist12916: Effect of the sweep of an intermediate polarizer between two others.

== Summary ==
Effect of the sweep of an intermediate polarizer between two others.

Campo de indução magnético criado por 2 condutores

2026-06-02T13:47:12Z

Ist12916: /* Descrição */

=Descrição da experiência=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - Esta experiência consiste num conjunto de espiras retangulares capazes de criar um campo magnético no espaço. Como uma das dimensões é muito maior do que a outra, o problema poderá ser abordado em primeira aproximação como dois cabos infinitos, de solução matematicamente mais simples. ''Nota: o ângulo <math>θ</math> não representa a orientação da bobine mas antes o seu plano de montagem''|right|border|236px]]

O campo de indução magnética existe em todo o espaço que nos rodeia, quer pelo magnetismo natural terrestre e sideral quer criado pelo Homem. Podemos distinguir dois tipos de categorias, (i) os campos constantes com reduzida influência nos sistemas biológicos e (ii) os variáveis no tempo (AC), capazes de induzir correntes elétricas. Estes últimos, a partir de valores elevados podem ser prejudiciais, principalmente para humanos com próteses eletrónicas (p.ex. pacemakers).

No entanto as correntes elétricas que induzem esse campo magnético, gerados na sua maioria em circuitos elétricos incluindo as linhas de transmissão elétricas, são fechados ou seja, as correntes acabam por retornar à fonte (gerador ou bateria) por cabos muito próximos uns dos outros. É o que acontece nos nossos cabos domésticos onde os mais atentos certamente já repararam que andam sempre aos pares (o terceiro fio normalmente é a "terra" e não transporta energia, servindo apenas o propósito de proteção).

O objetivo desta experiência consiste em determinar o vetor do campo de indução magnética em vários pontos do espaço criado pelos dois condutores paralelos afastados entre si. O protocolo avançado sugere uma resolução matemática mais exigente duma bobine quadrada onde toda a geometria é tida em consideração. Para o efeito a experiência é dotada duma micro-sonda 3D que recolhe a intensidade do campo magnético nos pontos selecionados.

Como as correntes elétricas têm sempre um retorno aos geradores, as linhas de transmissão elétricas e muitos outros dispositivos eletromagnéticos têm uma física equivalente ao problema abordado nesta experiência.

[[Mag_3D_experimental_apparatus | Existe uma versão da experiencia para imprimir em 3D]]. Esta, é uma variação da presente experiência com componentes ''off the shelf'' e cujas partes principais podem ser impressas em qualquer tipo de plástico rigido numa impressora 3D, sendo controlada exclusivamente por um raspberry pi e com um conjunto minimo de acessórios e motorização.

Se quiser fazer parte da rede MEDEA, por favor envie-nos um [mailto:medea@spf.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Ligações'''
<div class="mw-collapsible-content">

*Laboratório: Intermédio em [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Sala de controlo: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Gravação]
*Nível: **

</div>
</div>

==Quem gosta desta iniciativa==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Aparato experimental=
Esta experiência tem duas versões ativas, uma baseada em bobines de cobre e outra empregando um sensor magnético de 3 eixos usando o circuito integrado LIS3MDL. A primeira utiliza uma corrente AC de 15 kHz e a segunda, mais recente, utiliza a frequência da rede de 50 Hz.

==Descrição==
Esta experiência [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consiste numa bobine retangular] com 20 ou 50 espiras que em primeira aproximação se pode considerar como dois cabos paralelos de cobre por onde passa uma corrente elétrica geradora dum campo de indução magnético. O fluxo magnético gerado pelo campo é detetado numa micro-sonda de três eixos (pick-up coil ou magnetometro) que permite reconstruir num plano préviamente selecionado a geometria vetorial magnética. Por razões práticas, o plano onde são recolhidos os dados encontra-se 15mm ou 8mm abaixo do eixo de rotação da bobine.

A razão desta implementação real numa bobine retangular (onde um dos lados é subtancialmente maior do que os extremos) deve-se à corrente ter de ser fechada nos extremos.

{|class="wikitable"
|+Dimensões das espiras
|-
|
|Versão original || Nova versão
|-
|Lado menor ''(2a)''
|89mm +/- 0.5mm
|70mm +/- 0.5mm
|-
|Lado maior ''(2b)''
|454mm +/- 0.5mm
|664mm +/- 0.5mm
|-
|Numero de espiras (AWG 24)
|20|| 44 (Oeiras) 50 (restantes)
|}
A micro-sonda é constituída por três bobinas quadrangulares enroladas sobre um torreão cúbico de PVC com 5mm de lado e 10 espiras cada. Cada uma destas espiras encontra-se orientada segundo 3 eixos ortogonais, sendo o sinal do campo magnético detectado e amplificado adequadamente por eletrónica concebida para o efeito (filtro sintonizado). No final determina-se a medida do fluxo magnético nesse pequeno volume segunda cada eixo. Refira-se que é usada uma excitação alternada da corrente (AC-30kHz) para se poder desprezar a contribuição do campo magnético terrestre e outros campos espúrios e não sendo utilizado nenhum metal nas proximidades que possa alterar a configuração do campo.

A experiência permite configurar o ângulo do observador com o plano dos cabos mais compridos e varrer radialmente segundo o eixo dos ''xx'' a distância a estes. Efetuando vários varrimentos é possível mapear a área em torno dos cabos. Um ângulo de 0º corresponde a posicionar a bobine na vertical (orientada segundo os eixo dos ''zz'') criando um campo maioritáriamente segundo os ''zz'' e a 90º esta fica orientada no eixo dos ''xx''. Na prática é a bobine rodada no eixo dos ''yy'', sendo o deslocamento da micro-sonda sempre segundo o eixo dos ''xx''.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Orientação duma bobine'''
<div class="mw-collapsible-content">
A definição da orientação duma bobine prende-se com o campo de indução gerado por esta segundo a regra da mão direita: assim adoptamos a definição de que uma bobine está alinhada na vertical ─ eixos dos ''zz'' ─ caso as suas espiras estejam bobinadas no plano ''xx-yy''.
</div>
</div>

Realça-se novamente que a micro-sonda desloca-se ligeiramente abaixo (15 mm) do plano médio definido pelos condutores para poder passar por estes ao ser efetuado o varrimento. Este facto tem grande importância no protocolo avançado na zona próxima aos condutores embora não seja relevante para o cálculo do campo longínquo. No caso da nova versão, o magnetometro desloca-se a 8mm do plano central de simetria da bobine.
----
Um aspeto importante a ter em atenção ''é a possível saturação do sinal na próximidade dos condutores''. Devido a este facto a corrente selecionada deve ser substancialmente reduzida quando se pretenda estudar esta região.
----

==Configuração==
Para executar a experiência o utilizador necessita de definir os seguintes parâmetros:
;Posição inicial:
:Localização da primeira aquisição sendo que a origem é no eixo da bobine;
;Posição final:
:Último ponto a se medido;
;Número de amostras:
:Número de posições onde são medidas as três componentes do campo de indução magnético e a corrente nas espiras;
;Corrente na bobine:
:Valor em percentagem da modulação da corrente por espira que permite seleccionar aproximadamente o valor da corrente em relação ao valro máximo. Para determinar o valor máximo da corrente há que efetuar uma medida com a modulação no ponto médio, a 50% e extrapolar. Este parametro é fundamental para regular a não saturação das medidas na região da bobine.
;Ângulo:
:Este ângulo permite seleccionar a orientação inicial da bobine tal como descrito na fig.1

==Resultados obtidos==
Após o lançamento da experiência é devolvida uma tabela com a data/hora de cada medida e a posição absoluta em ''xx'' seguida dos elementos medidos nesses pontos: as componentes do vetor do campo e a corrente que atravessava a espira nesse instante. Esta última medida permite estabelecer a estabilidade do gerador de corrente.

A aplicação permite ainda visualizar em tempo real os dados que vão sendo recolhidos.

=MEDEA=
Esta experiência é utilizada no projeto [http://medea.spf.pt MEDEA], uma parceria entre a SPF e REN, Redes Energéticas Nacionais. MEDEA É O acrónimo para designar a MEDição dos campos Electromagnéticos no Ambiente, realizado por alunos de várias escolas secundárias e profissionais e que visa medir o campo eléctrico e magnético no meio ambiente.

=Física=
A determinação do campo de indução magnético implica integrar a lei de Biot-Savart segundo o percurso da bobine, somando num ponto do espaço todas estas contribuições infinitésimais de uma forma vectorial.
No entanto a geometria foi seleccionada de forma a permitir usar um formalismo mais simples baseado na contribuição para o campo gerado por condutores infinitos.

==Campo gerado por dois cabos infinitos==

===No plano onde coexistem ambos os cabos===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decaímento do campo de indução magnético no plano de dois condutores infinitos com correntes anti-paralelas onde se pode verificar que o campo é anulado muito rapidamente para distâncias acima da distância de separação entre os condutores.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''zz'']]

Se considerarmos dois condutores de diâmetro desprezável separados por uma distancia ''d=2a'' onde o segundo é percorrido pela corrente de retorno do primeiro cabo, apesar do decaímento do campo de indução magnético de um condutor individual depender do inverso da distância (~1/r), ao considerarmos o efeito dos dois em conjunto esse decaímento é muito mais abrupto ficando com uma dependência do inverso do quadrado da distância em zonas distantes.

Isso mesmo pode ser verificado através da expressão simplificada obtida a partir da lei de Gauss e calculada no plano onde existem os dois condutores:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

onde

<math>
\frac{\mu _0 i}{2 \pi r}
</math>
representa o módulo do campo de indução magnético criado por um condutor linear infinito.

Os valores experimentais obtidos encontram-se na figura seguinte onde se mostram apenas as duas dimensões relevantes (segundo ''yy'' o campo é despresável por uma questão de simetria).

===No plano de simetria entre os cabos ===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''xx'']]

Nesta situação, o àngulo da bobine com o eixo dos 'xx'' é nulo e por uma questão de simetria, só existe campo segundo ''xx'' nesse eixo ortogonal ao plano definido pelos cabos. Numa região afastada podemos considerar que a distância ''r'' ao plano, dada por <math>\sqrt{a^2+x^2}</math> é próxima da sua ordenada no eixo e ambos os cabos ─ afastados entre si de ''2a'' ─ concorrem para gerarem um campo construtivo com o dobro da intensidade pelo que:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

e para <math> x \gg a </math> simplifica para:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Campo gerado por uma bobine retangular==

O estudo generalizado da geometria retangular implica o cálculo do campo de indução magnético através da integração da contribuição dos elementos infinitesimais da corrente sobre a espira<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref> cuja contribuição é:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

Esta integração pode ser simplificada considerando que a sonda se desloca apenas segundo o eixo dos ''xx'' para ''z=y=0'' (por razões práticas aproximamos a posição real ''y=-10mm≃0'') e por simetria pode-se estabelecer que o campo segundo os ''yy'' é nulo.

=Estudos experimentais=

==A orientação do campo==

A visualização dum campo vetorial nem sempre é bem conseguida. Na análise deste trabalho a melhor forma de proceder é usar um software que permita visualizar os vetores do campo de indução magnética a cada 10 mm numa projeção tridimensional.
Para tal sugere-se a utilização do Octave, Matemática, Pyton, IDL ou MatLab.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Neste link (BiotSavart.ipynb)] poderá encontrar uma simulação efetuada em Jupyter.

==Linhas de campo e curvas de nível==

Obtendo-se várias características fruto da seleção de ângulos diversos, consegue-se mapear numa superfície de simetria no plano ''xx-zz'' valores para o módulo do campo e a sua direção, analisando o seu comportamento espacial.
As linhas de campo, que seguem os vectores espacialmente, permitem identificar facilmente a orientação do fluxo magnético.
As curvas de nível ligam pontos do módulo do campo constante identificando as regiões do espaço onde a sua variação é maior ou menor pelo espaçamento entre elas.

=Bibliografia=

<references />

=Ligações=
*[[ Magnetic_field_created_by_two_wires | Versão em Inglês (English Version)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Campo de indução magnético criado por 2 condutores

2026-06-02T13:45:31Z

Ist12916: /* Aparato experimental */

=Descrição da experiência=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - Esta experiência consiste num conjunto de espiras retangulares capazes de criar um campo magnético no espaço. Como uma das dimensões é muito maior do que a outra, o problema poderá ser abordado em primeira aproximação como dois cabos infinitos, de solução matematicamente mais simples. ''Nota: o ângulo <math>θ</math> não representa a orientação da bobine mas antes o seu plano de montagem''|right|border|236px]]

O campo de indução magnética existe em todo o espaço que nos rodeia, quer pelo magnetismo natural terrestre e sideral quer criado pelo Homem. Podemos distinguir dois tipos de categorias, (i) os campos constantes com reduzida influência nos sistemas biológicos e (ii) os variáveis no tempo (AC), capazes de induzir correntes elétricas. Estes últimos, a partir de valores elevados podem ser prejudiciais, principalmente para humanos com próteses eletrónicas (p.ex. pacemakers).

No entanto as correntes elétricas que induzem esse campo magnético, gerados na sua maioria em circuitos elétricos incluindo as linhas de transmissão elétricas, são fechados ou seja, as correntes acabam por retornar à fonte (gerador ou bateria) por cabos muito próximos uns dos outros. É o que acontece nos nossos cabos domésticos onde os mais atentos certamente já repararam que andam sempre aos pares (o terceiro fio normalmente é a "terra" e não transporta energia, servindo apenas o propósito de proteção).

O objetivo desta experiência consiste em determinar o vetor do campo de indução magnética em vários pontos do espaço criado pelos dois condutores paralelos afastados entre si. O protocolo avançado sugere uma resolução matemática mais exigente duma bobine quadrada onde toda a geometria é tida em consideração. Para o efeito a experiência é dotada duma micro-sonda 3D que recolhe a intensidade do campo magnético nos pontos selecionados.

Como as correntes elétricas têm sempre um retorno aos geradores, as linhas de transmissão elétricas e muitos outros dispositivos eletromagnéticos têm uma física equivalente ao problema abordado nesta experiência.

[[Mag_3D_experimental_apparatus | Existe uma versão da experiencia para imprimir em 3D]]. Esta, é uma variação da presente experiência com componentes ''off the shelf'' e cujas partes principais podem ser impressas em qualquer tipo de plástico rigido numa impressora 3D, sendo controlada exclusivamente por um raspberry pi e com um conjunto minimo de acessórios e motorização.

Se quiser fazer parte da rede MEDEA, por favor envie-nos um [mailto:medea@spf.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Ligações'''
<div class="mw-collapsible-content">

*Laboratório: Intermédio em [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Sala de controlo: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Gravação]
*Nível: **

</div>
</div>

==Quem gosta desta iniciativa==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Aparato experimental=
Esta experiência tem duas versões ativas, uma baseada em bobines de cobre e outra empregando um sensor magnético de 3 eixos usando o circuito integrado LIS3MDL. A primeira utiliza uma corrente AC de 15 kHz e a segunda, mais recente, utiliza a frequência da rede de 50 Hz.

==Descrição==
Esta experiência [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consiste numa bobine retangular] com 20 ou 50 espiras que em primeira aproximação se pode considerar como dois cabos paralelos de cobre por onde passa uma corrente elétrica geradora dum campo de indução magnético. O fluxo magnético gerado pelo campo é detetado numa micro-sonda de três eixos (pick-up coil ou magnetometro) que permite reconstruir num plano préviamente selecionado a geometria vetorial magnética. Por razões práticas, o plano onde são recolhidos os dados encontra-se 15mm ou 8mm abaixo do eixo de rotação da bobine.

A razão desta implementação real numa bobine retangular (onde um dos lados é subtancialmente maior do que os extremos) deve-se à corrente ter de ser fechada nos extremos.

{|class="wikitable"
|+Dimensões das espiras
|-
|
|Versão original || Nova versão
|-
|Lado menor ''(2a)''
|89mm +/- 0.5mm
|70mm +/- 0.5mm
|-
|Lado maior ''(2b)''
|454mm +/- 0.5mm
|664mm +/- 0.5mm
|-
|Numero de espiras (AWG 24)
|20|| 44 (Oeiras) 50 (restantes)
|}
A micro-sonda é constituída por três bobinas quadrangulares enroladas sobre um torreão cúbico de PVC com 5mm de lado e 10 espiras cada. Cada uma destas espiras encontra-se orientada segundo 3 eixos ortogonais, sendo o sinal do campo magnético detectado e amplificado adequadamente por eletrónica concebida para o efeito (filtro sintonizado). No final determina-se a medida do fluxo magnético nesse pequeno volume segunda cada eixo. Refira-se que é usada uma excitação alternada da corrente (AC-30kHz) para se poder desprezar a contribuição do campo magnético terrestre e outros campos espúrios e não sendo utilizado nenhum metal nas proximidades que possa alterar a configuração do campo.

A experiência permite configurar o ângulo do observador com o plano dos cabos mais compridos e varrer radialmente segundo o eixo dos ''xx'' a distância a estes. Efetuando vários varrimentos é possível mapear a área em torno dos cabos. Um ângulo de 0º corresponde a posicionar a bobine na vertical (orientada segundo os eixo dos ''zz'') criando um campo maioritáriamente segundo os ''zz'' e a 90º esta fica orientada no eixo dos ''xx''. Na prática é a bobine rodada no eixo dos ''yy'', sendo o deslocamento da micro-sonda sempre segundo o eixo dos ''xx''.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Orientação duma bobine'''
<div class="mw-collapsible-content">
A definição da orientação duma bobine prende-se com o campo de indução gerado por esta segundo a regra da mão direita: assim adoptamos a definição de que uma bobine está alinhada na vertical ─ eixos dos ''zz'' ─ caso as suas espiras estejam bobinadas no plano ''xx-yy''.
</div>
</div>

Realça-se novamente que a micro-sonda desloca-se ligeiramente abaixo (15 mm) do plano médio definido pelos condutores para poder passar por estes ao ser efetuado o varrimento. Este facto tem grande importância no protocolo avançado na zona próxima aos condutores embora não seja relevante para o cálculo do campo longínquo.
----
Um aspeto importante a ter em atenção ''é a possível saturação do sinal na próximidade dos condutores''. Devido a este facto a corrente selecionada deve ser substancialmente reduzida quando se pretenda estudar esta região.
----

==Configuração==
Para executar a experiência o utilizador necessita de definir os seguintes parâmetros:
;Posição inicial:
:Localização da primeira aquisição sendo que a origem é no eixo da bobine;
;Posição final:
:Último ponto a se medido;
;Número de amostras:
:Número de posições onde são medidas as três componentes do campo de indução magnético e a corrente nas espiras;
;Corrente na bobine:
:Valor em percentagem da modulação da corrente por espira que permite seleccionar aproximadamente o valor da corrente em relação ao valro máximo. Para determinar o valor máximo da corrente há que efetuar uma medida com a modulação no ponto médio, a 50% e extrapolar. Este parametro é fundamental para regular a não saturação das medidas na região da bobine.
;Ângulo:
:Este ângulo permite seleccionar a orientação inicial da bobine tal como descrito na fig.1

==Resultados obtidos==
Após o lançamento da experiência é devolvida uma tabela com a data/hora de cada medida e a posição absoluta em ''xx'' seguida dos elementos medidos nesses pontos: as componentes do vetor do campo e a corrente que atravessava a espira nesse instante. Esta última medida permite estabelecer a estabilidade do gerador de corrente.

A aplicação permite ainda visualizar em tempo real os dados que vão sendo recolhidos.

=MEDEA=
Esta experiência é utilizada no projeto [http://medea.spf.pt MEDEA], uma parceria entre a SPF e REN, Redes Energéticas Nacionais. MEDEA É O acrónimo para designar a MEDição dos campos Electromagnéticos no Ambiente, realizado por alunos de várias escolas secundárias e profissionais e que visa medir o campo eléctrico e magnético no meio ambiente.

=Física=
A determinação do campo de indução magnético implica integrar a lei de Biot-Savart segundo o percurso da bobine, somando num ponto do espaço todas estas contribuições infinitésimais de uma forma vectorial.
No entanto a geometria foi seleccionada de forma a permitir usar um formalismo mais simples baseado na contribuição para o campo gerado por condutores infinitos.

==Campo gerado por dois cabos infinitos==

===No plano onde coexistem ambos os cabos===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decaímento do campo de indução magnético no plano de dois condutores infinitos com correntes anti-paralelas onde se pode verificar que o campo é anulado muito rapidamente para distâncias acima da distância de separação entre os condutores.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''zz'']]

Se considerarmos dois condutores de diâmetro desprezável separados por uma distancia ''d=2a'' onde o segundo é percorrido pela corrente de retorno do primeiro cabo, apesar do decaímento do campo de indução magnético de um condutor individual depender do inverso da distância (~1/r), ao considerarmos o efeito dos dois em conjunto esse decaímento é muito mais abrupto ficando com uma dependência do inverso do quadrado da distância em zonas distantes.

Isso mesmo pode ser verificado através da expressão simplificada obtida a partir da lei de Gauss e calculada no plano onde existem os dois condutores:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

onde

<math>
\frac{\mu _0 i}{2 \pi r}
</math>
representa o módulo do campo de indução magnético criado por um condutor linear infinito.

Os valores experimentais obtidos encontram-se na figura seguinte onde se mostram apenas as duas dimensões relevantes (segundo ''yy'' o campo é despresável por uma questão de simetria).

===No plano de simetria entre os cabos ===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''xx'']]

Nesta situação, o àngulo da bobine com o eixo dos 'xx'' é nulo e por uma questão de simetria, só existe campo segundo ''xx'' nesse eixo ortogonal ao plano definido pelos cabos. Numa região afastada podemos considerar que a distância ''r'' ao plano, dada por <math>\sqrt{a^2+x^2}</math> é próxima da sua ordenada no eixo e ambos os cabos ─ afastados entre si de ''2a'' ─ concorrem para gerarem um campo construtivo com o dobro da intensidade pelo que:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

e para <math> x \gg a </math> simplifica para:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Campo gerado por uma bobine retangular==

O estudo generalizado da geometria retangular implica o cálculo do campo de indução magnético através da integração da contribuição dos elementos infinitesimais da corrente sobre a espira<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref> cuja contribuição é:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

Esta integração pode ser simplificada considerando que a sonda se desloca apenas segundo o eixo dos ''xx'' para ''z=y=0'' (por razões práticas aproximamos a posição real ''y=-10mm≃0'') e por simetria pode-se estabelecer que o campo segundo os ''yy'' é nulo.

=Estudos experimentais=

==A orientação do campo==

A visualização dum campo vetorial nem sempre é bem conseguida. Na análise deste trabalho a melhor forma de proceder é usar um software que permita visualizar os vetores do campo de indução magnética a cada 10 mm numa projeção tridimensional.
Para tal sugere-se a utilização do Octave, Matemática, Pyton, IDL ou MatLab.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Neste link (BiotSavart.ipynb)] poderá encontrar uma simulação efetuada em Jupyter.

==Linhas de campo e curvas de nível==

Obtendo-se várias características fruto da seleção de ângulos diversos, consegue-se mapear numa superfície de simetria no plano ''xx-zz'' valores para o módulo do campo e a sua direção, analisando o seu comportamento espacial.
As linhas de campo, que seguem os vectores espacialmente, permitem identificar facilmente a orientação do fluxo magnético.
As curvas de nível ligam pontos do módulo do campo constante identificando as regiões do espaço onde a sua variação é maior ou menor pelo espaçamento entre elas.

=Bibliografia=

<references />

=Ligações=
*[[ Magnetic_field_created_by_two_wires | Versão em Inglês (English Version)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Multiple polarizers experimental apparatus

2026-06-02T09:55:23Z

Ist12916: /* Optical path calibration */

=Apparatus description=

{|
|[[File:exploded_kit_view.png|thumb|x250px|Left|Exploded view of the experimental kit.]]
|[[File:exploded_kit_view_1.png|thumb|x250px|Left|Exploded view of the experimental kit.]]
|}

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a Raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed_.png|thumb|x400px|Top|Parts needed for the assembly]]
|}
The following table can be used to check the number of parts to be printed and if supports are needed:
{| class="wikitable"
! Name !! Description !! Folders !! Number of parts !! Material !! Supports: necessary
|-
| Edge || Edge that supports the corners of the box || Structural Components || 6 || PLA || No
|-
| Edge Special Left || Special edge || Structural Components || 1 || PLA || No
|-
| Edge Special Right || Special edge || Structural Components || 1 || PLA || No
|-
| Larger Face || Box face along the length || Lids || 3 || PLA || No
|-
| Face Power Supply || Box face along length with cable hole || Lids || 1 || PLA || No
|-
| Smaller Face || Box face along the width || Lids || 2 || PLA || No
|-
| Power Supply Base || Bottom of the box with the power supply || Eletronics || 1 || PLA || No
|-
| Arduino Base || Arduino case || Eletronics || 1 || PLA || No
|-
| Arduino Case Top || Arduino case || Eletronics || 1 || PLA || No
|-
| Arduino Case Bottom || Arduino case || Eletronics || 1 || PLA || No
|-
| Raspberry Pie Case Middle || Raspberry Pie Box || Eletronics || 1 || PLA || No
|-
| Raspberry Pie Case Top || Raspberry Pie Box || Eletronics || 1 || PLA || No
|-
| Raspberry Pie Case Bottom || Raspberry Pie Box || Eletronics || 1 || PLA || No
|-
| Lid 2 Steppers || Box top that supports two motors || Polarizer Assembly || 1 || PLA || No
|-
| Lid 3 Steppers || Box top that supports two motors || Polarizer Assembly || 1 || PLA || No
|-
| Stepper_holder_left || Stepper motor support, compatible with the box cover with 2 supports || Polarizer Assembly || 1 || PLA || No
|-
| Stepper_holder_right || Stepper motor support, compatible with the box cover with 3 supports || Polarizer Assembly || 1 || PLA || No
|-
| Polarizer Support Detector || Support for the polarizer assembly, detector side || Polarizer Assembly || 1 || PLA || No
|-
| Polarizer Support led || Support for the polarizer assembly, emitter side || Polarizer Assembly || 1 || PLA || yes, for the pins that secure the polarizer
|-
| Bar || Support bar for polarizer supports; adjusts compression exerted || Polarizer Assembly || 1 || PLA || No
|-
| Gear || Gear wheel that fits behind each polarizer || Polarizer Assembly || 5 || PLA || No
|-
| Fixed Polarizer Holder || Fixed polarizer holder that fits into the polarizer Support led || Optical Assembly || 1 || PLA || yes
|-
| Detector Holder || Part that secures the LED adjuster || Optical Assembly || 1 || PLA || No
|-
| Detector Adjuster || Part that secures the LED holder || Optical Assembly || 1 || PLA || No
|-
| Led Ajuster || Part that secures the LED holder || Optical Assembly || 1 || PLA || yes, for the pins that secure the polarizer
|-
| Led Holder || LED and detector holder, which fits into the adjustment parts above || Optical Assembly || 2 || PLA || No
|-
| Base || Base for the camera || Camera_holder || 1 || || yes
|-
| Support || || Camera_holder || 3 || || yes
|-
| Arm || || Camera_holder || 1 || || yes
|-
| Joint || || Camera_holder || 1 || || yes
|}
2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the pulley.

35. Connect the pulley (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Pulley placement with the belt on]]
|}

36. Tighten the pulley.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the pulley]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, the drivers (1) for the step-motors and the light source and detection (2).

==Electronic component assembly==

1. Check if all the parts needed for the electronic component assembly of the experiment are available.
{|
|[[File:electric_assembly_parts.jpg|thumb|Parts needed for the electronic component assembly.]]
|}

2. Get the left floor of the electronic component (see the image below) and use a soldering iron to insert the heat inserts in the floor's holes, through the thermal insertion process.
{|
|[[File:electric_assembly_left_floor.jpg|thumb|Left floor of the electronic component.]]
|[[File:insercao_termica.jpg|thumb|Thermal insertion.]]
|}

3. Get the Arduino Mega box (see the image below) and bolt it to the floor.
{|
|[[File:arduino_case.jpg|thumb|Arduino Mega box.]]
|}

4. Use a soldering iron to insert the heat inserts in the box holes, through the thermal insertion process.
{|
|[[File:arduino_case_holes.jpg|thumb|Holes in the Arduino Mega box.]]
|}

5. Select a heat sink.
{|
|[[File:Heat_Sink.jpg|thumb|Heat Sink.]]
|}

6. Remove the paper protection.
{|
|[[File:paper_protection_removal.jpg|thumb|Remove the paper protection.]]
|[[File:paper_removed.jpg|thumb|Remove the paper protection.]]
|}

7. Glue the heat sink to the step-motor driver.
{|
|[[File:heat_sink_placement.jpg|thumb|Heat sink placement.]]
|[[File:heat_sink_placed.jpg|thumb|Heat sink placed.]]
|}

8. Repeat the steps 1, 2 and 3 for the other five step-motor drivers.

9. Place the step-motor driver on the RAMPS 1.4 (RepRap Arduino Mega Pololu Shield)
{|
|[[File:Placa_RAMPS.jpg|thumb|RAMPS 1.4.]]
|[[File:Placa_RAMPS_software.png|thumb|RAMPS 1.4 (software view).]]
|}

10. Check if the step-motor driver is well placed, meaning its ground connection is as shown in the image below and that the bolt (potentiometer) is on the opposite side of the power supply (in the case of the green and red step-motor drivers) or in the side of the power supply (in the case of the purple step-motor drivers).
{|
|[[File:drivers.png|thumb|Step-motor drivers models.]]
|[[File:driver_placement_software.png|thumb|Purple step-motor driver placement (software view).]]
|[[File:driver_placement_green.png|thumb|Purple and green step-motor driver placement.]]
|}

11. Repeat the steps 5 and 6 for the other five step-motor drivers.
{|
|[[File:driver_placement.jpg|thumb|RAMPS 1.4 with the step-motor drivers in place.]]
|}

12. Connect the switches to the wires.
{|
|[[File:switches_wires.jpg|thumb|Switches connection to the wires.]]
|}

13. Place the switches in the switch holder. Ensure you hear a "click" to confirm they are well positioned.
{|
|[[File:switches_placement.png|thumb|Switches positioning in the holder.]]
|}

14. Connect the step-motor wires to the step-motor drivers through the RAMPS 1.4. Check the pinouts connection through its colour and according to the information provided in the subsection [[#Step-motor drivers|Step-motor drivers]].
{|
|[[File:stepper_wires_placement.jpg|thumb|Wires connection in the RAMPS 1.4.]]
|[[File:stepper_array.png|thumb|Top-view of kit:numbering of thre steppers and respective switches.]]
|[[File:switches_wires_placement_software.png|thumb|Switches' wires (green) and step-motor wires (blue) (software view).]]
|}

15. Assemble the detector and photodiode electric circuit.
{|
|[[File:photodiode_circuit.jpg|thumb|Detector and photodiode electric circuit schematics.]]
|}

16. Place the electric circuit in the box corner, position it according to the holes, and bolt it.
{|
|[[File:electric_circuit.jpg|thumb|Switchers positioning in the switch holder.]]
|}

17. Get the top part of the Arduino Mega box and bolt it to the bottom part (attention to the wires when closing the box).
{|
|[[File:arduino_top_case.jpg|thumb|Top part of the Arduino Mega box.]]
|}

18. Repeat the step 2 for the right floor.
{|
|[[File:electric_assembly_right_floor.jpg|thumb|Right floor of the electronic component.]]
|}

19. Place the power supply on the right floor and secure it with bolts.
{|
|[[File:power_supply.jpg|thumb|Power supply.]]
|[[File:power_supply_top_view.jpg|thumb|Top view of the power supply.]]
|}

20. Get the bottom part of the Raspberry Pi box and repeat the step 4.
{|
|[[File:raspberry_pi_case.jpg|thumb|Raspberry Pi box.]]
|}

21. Bolt the Raspberry Pi to the box.
{|
|[[File:raspberry_pi.jpg|thumb|Raspberry Pi.]]
|}

22. Connect the middle part of the Raspberry Pi box to the bottom part.

23. Place the cover to close the box.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motor drivers can have multiple design outputs according to the producer. The stepper pin-outs are numbered from 1-6, from left to right from the front view (shaft pointing you, connector downwards).
The driver's location on the arduíno mezzanine relates to the step-motor according to the schema below:

{| border="1" style="width:150px; height:150px; text-align:center;"
|+ Driver to step-motor link
| style="width:66px; height:66px;" | 5
| style="width:66px; height:66px;" | 3
| style="width:66px; height:66px;" | N/A
|-
| style="width:66px; height:66px;" | 1
| style="width:66px; height:66px;" | 2
| style="width:66px; height:66px;" | 4
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Motherboard pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is fed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode. This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present.

As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass through the cascade of polarizers in parallel rays.]]
The optical path consists of a light source (1) (red LED) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light.

Then it is polarized by the fixed polarizer (3) before entering the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and it passes the second lens in order to focus on the detector, a photodiode (6).

Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise. This filter is not damned necessary and can be replaced by red cellophane paper or even absent in case of a fully opaque plastic structure.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays are later focused on the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#First assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for easy observation of such maxima. Consider having it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure of the second polarizer by rotating in block all the remaining polarizers and detect the maximum intensity and register it. Leave the second polarizer at rest in the measured maximum position. Now rotate again the remain block of polarizer simultaneously, and repeat the procedure for the detection of the maximums for the rest of them. Take note of all maximum values and publish them.

This process is based on keeping the attenuation exactly the same for the remain polarizers block while keeping the previous block that includes the one being calibrated rotating. As the previous block is already fully align the maximum will occur when

<math>
(cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizer film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

It is provided in the firmware a function able to rotate a set of polarizers in conjunction with each other. With this procedure local maximums can be inferred to confirm the previous determined values. In fact, if a group of the last polarizers are made to rotate in conjunction, the maximum is dictated by the first one to rotate in order to the last one fixed.

Later, when performing the experiments these values of offsets must be considered in order to eliminate the systematic error of the system.

= Software =
To properly use the experiment, commands and data retrieval have to be in place. This can be achieved in two ways acting through the serial connection to the Arduino Mega.

The firmware existing in the Arduino is able to (i) configure the experiment, (ii) run and retrieve the generated data, and (iii) execute some specialized functions in order to test, calibrate, and maintain the experiment. To interface with the firmware, one can use a Python proxy code (high-level software layer) capable of interoperating with the FREE server, or a terminal emulator like Minicom available for Linux that allows you to send and receive data over the serial connection.

== Raspberry FREE proxy ==
The Raspberry Pi is responsible for transmitting the video feed of the experiment and establishing communication with the FREE-Server by using a proxy interface. The FREE hosts the graphical user interface (GUI) to the clients. This section provides a concise overview of the procedure used to control all electronic components via the Arduino, as well as the communication protocols between the Arduino and the FREE-Server.

=== Communication model between the FREE-Server and the Raspberry PI ===
The communication between the server and the experiment follows the elab’s structured protocol that enables real-time interaction and data exchange. The central server, Exp Server, acts as an intermediary between users and the experimental apparatus (RPi Server). Users interact with Exp Server via a web interface made with Django, a high-level Python web framework, to configure and control the experiment parameters, while Exp Server directly relays these commands to the experimental setup.

The communication between Exp Server and RPi Server occurs over the internet using JSON-formatted messages, ensuring flexibility across different experimental configurations. Authentication is performed at the connection stage, where the RPi Server transmits an ID and a secret key for verification. Once authenticated, the Exp Server sends an experiment-specific configuration file to the RPi Server, which then establishes communication with the local controller using the predefined protocol [7]. Throughout the experiment, the RPi Server continuously exchanges status updates, experimental results, and error messages with the XP server, ensuring synchronized operation and real-time data accessibility for users.

=== Communication model between the Raspberry PI and the Arduino Mega ===
To enable seamless communication between the Arduino and the Raspberry Pi 4, the protocol ReC Generic Drive 11 was implemented, allowing the external user to have full control over the experiment and its status through a set of commands. The ReC Generic Drive is a generic communication protocol designed for remote laboratories, facilitating interaction between a software driver and experimental hardware. It enables seamless communication over serial ports (RS232), using structured messages where driver commands are in lowercase and hardware responses in uppercase.

The protocol ensures synchronization through message handshaking and timeout handling, supporting functions like identification, configuration, data transmission, experiment configuration, and error reporting.

By reading the Arduino’s serial port at a baud rate of 115200 bits per second, the user sends a bit string (ending with the character \r).

== Administrator Setup Instructions ==
To deploy a new instance of the multi-polarizer experiment, the Raspberry Pi proxy and the Arduino firmware must be configured and compiled. Follow these steps to ensure proper initialization:

<ol>
<li>Download the experiment repository via SSH:
<pre>git clone https://github.com/farrucho/multi-polarizer.git</pre></li>

<li>Modify the experiment ID in `main.cpp` to match the FREE server configuration:
<pre>expr.begin("ELAB_FIVEPOLARIZER");</pre></li>

<li>Adjust the motor directions and reference voltage in `user_define.cpp`:
<pre>uint8_t resetDir = HIGH; // Direction to trigger the switch. Test by moving backward to ensure it triggers correctly.
uint8_t dirToTop = LOW;
int vrefMode = 1;</pre></li>

<li>Identify the Arduino's serial port:
<pre>ls /dev/tty*</pre>
Update the `platformio.ini` file with the correct port (e.g., `monitor_port = /dev/ttyACM0`).</li>

<li>Compile and upload the firmware using PlatformIO from within the `e-lab` folder:
<pre>pio run -t upload -t monitor -t clean</pre></li>

<li>Configure the startup proxy script by editing `/etc/rc.local`:
<pre>sudo nano /etc/rc.local</pre>
Add the following lines before `exit 0`:
<pre>_IP=$(hostname -I) || true
if [ "$_IP" ]; then
printf "My IP address is %s\n" "$_IP"
fi
sleep 120
cd /home/elab/RPi_Proxy_fivepol
su elab -c "sh start-wp.sh &"</pre></li>

<li>Enable the `rc-local` service on boot using `systemctl`:
<pre>sudo systemctl enable rc-local
sudo systemctl start rc-local</pre></li>
</ol>

= Firmware =
The programming was done using the C++ language without any external libraries. To declare a component in the code, one simply provides the corresponding input pin and accesses the enable function to initialize it, as well as the `isTrigger` function to check whether the logical value read corresponds to the component’s trigger state. In this particular case, the switch is active on a LOW signal. Since all objects and respective components need to be initialized and turned off, each has corresponding enable/disable functions. Components connected to single read pins, declared as `pinMode` (such as switches and photodiodes), do not require a disable function since `pinMode` does not prevent reading the pins but rather helps define the type of input being processed.

In order to rotate the stepper motors, the operation consists of sending a pulse each time a rotation of 1.8º (0.36º effective) is desired. Since different RPM values require different pulse intervals, the frequency of sent pulses must be calculated accordingly. To execute a discrete sequence of steps based on a given angle in degrees, the rotate function was implemented. The motor rotates to the nearest low integer multiple of 1.8º relative to the provided angle.

The data acquisition interval is crucial for the final experiment since the goal is to optimize the user experience by minimizing waiting times when retrieving the intensity of light and scanning angle data. To address this, a global RPM of 600 revolutions per minute was used. With a scanning limit of 324º, the experimentally measured data acquisition time for scanning one or more polarizers simultaneously was approximately 40 seconds.

To further refine the voltage readings from the photodiode, an arithmetic mean of N points was implemented in the photodiode voltage reading function. By computing the arithmetic mean over 13 points of the value being measured, the standard deviation of this mean reduces the original standard deviation by ≈ 27.14%. This reduction was deemed acceptable for the experiment, as the data adjustment performed was successful.

== User Debugging and Serial Commands ==
For manual hardware testing and calibration, administrators can send direct serial commands to the Arduino using a terminal emulator like Minicom.

Connect to the terminal using the correct port identified earlier:
<pre>minicom -D /dev/ttyACM0</pre>

By sending a question mark `?` and pressing Enter, the firmware will return a help menu listing all available commands. Below is the explanation for each supported command:

{| class="wikitable"
! Command !! Parameters !! Description
|-
| `cur` || None || Returns the current configured parameters.
|-
| `str` || None || Starts the experiment sweep based on the previously configured parameters.
|-
| `stp` || None || Immediately stops the experiment and halts all motor movements.
|-
| `rst` || None || Resets and homes all stepper motors by moving them backward until their respective limit switches are triggered.
|-
| `ids` || None || Returns the hardware and firmware identification string.
|-
| `cfg` || `theta1 theta2 theta3 theta4 theta5` || Configures the starting or target positions (in steps) for each of the 5 polarizers. Limits are bound by `MAXIMUM_STEP`.
|-
| `led` || `on [0:255]` or `off` || Controls the red LED intensity using Pulse Width Modulation (PWM). Value ranges from 0 (off) to 255 (maximum brightness).
|-
| `lamp` || `on [0:255]` or `off` || Controls the auxiliar light source intensity using Pulse Width Modulation (PWM). Value ranges from 0 (off) to 255 (maximum brightness).
|-
| `set maxstep` || `[0:1000]` || Defines the maximum allowed mechanical limit for the polarizers. By default, 900 steps corresponds to the 900*0.36º=324.0º physical limit.
|-
| `set vref` || `[1:3]` || Adjusts the Analog-to-Digital Converter (ADC) reference voltage to prevent photodiode saturation depending on light intensity. (1: Vref = 1.1V, 2: Vref = 2.56V, 3: Vref = 5V).
|-
| `move forward` || `polarizer[1:5] steps[0:MAXIMUM_STEP]` || Manually rotates a specific polarizer forward by the designated number of steps.
|-
| `move backward` || `polarizer[1:5] steps[0:MAXIMUM_STEP]` || Manually rotates a specific polarizer backward by the designated number of steps.
|-
| `go to origin` || `polarizer[1:5]` || Commands a single specific polarizer to return to its zero/home position until it triggers its switch.
|}

=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]
*[https://www.printables.com/model/1293618-multi_polarizer_experiment Print your experiment]

Light Polarization with multiple polarizers

2026-06-02T09:17:12Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Trieste (º) || @Oeiras (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1 ||
|-
| 2 || 44.3 ± 1 || 33.5 ± 1 ||
|-
| 3 || 34.6 ± 1 || 34.2 ± 1 ||
|-
| 4 || 41.0 ± 1 || 34.9 ± 1 ||
|-
| 5 || 39.2 ± 1 || 35.6 ± 1 ||
|}

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Campo de indução magnético criado por 2 condutores

2026-05-29T08:08:19Z

Ist12916: /* Descrição da experiência */

=Descrição da experiência=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - Esta experiência consiste num conjunto de espiras retangulares capazes de criar um campo magnético no espaço. Como uma das dimensões é muito maior do que a outra, o problema poderá ser abordado em primeira aproximação como dois cabos infinitos, de solução matematicamente mais simples. ''Nota: o ângulo <math>θ</math> não representa a orientação da bobine mas antes o seu plano de montagem''|right|border|236px]]

O campo de indução magnética existe em todo o espaço que nos rodeia, quer pelo magnetismo natural terrestre e sideral quer criado pelo Homem. Podemos distinguir dois tipos de categorias, (i) os campos constantes com reduzida influência nos sistemas biológicos e (ii) os variáveis no tempo (AC), capazes de induzir correntes elétricas. Estes últimos, a partir de valores elevados podem ser prejudiciais, principalmente para humanos com próteses eletrónicas (p.ex. pacemakers).

No entanto as correntes elétricas que induzem esse campo magnético, gerados na sua maioria em circuitos elétricos incluindo as linhas de transmissão elétricas, são fechados ou seja, as correntes acabam por retornar à fonte (gerador ou bateria) por cabos muito próximos uns dos outros. É o que acontece nos nossos cabos domésticos onde os mais atentos certamente já repararam que andam sempre aos pares (o terceiro fio normalmente é a "terra" e não transporta energia, servindo apenas o propósito de proteção).

O objetivo desta experiência consiste em determinar o vetor do campo de indução magnética em vários pontos do espaço criado pelos dois condutores paralelos afastados entre si. O protocolo avançado sugere uma resolução matemática mais exigente duma bobine quadrada onde toda a geometria é tida em consideração. Para o efeito a experiência é dotada duma micro-sonda 3D que recolhe a intensidade do campo magnético nos pontos selecionados.

Como as correntes elétricas têm sempre um retorno aos geradores, as linhas de transmissão elétricas e muitos outros dispositivos eletromagnéticos têm uma física equivalente ao problema abordado nesta experiência.

[[Mag_3D_experimental_apparatus | Existe uma versão da experiencia para imprimir em 3D]]. Esta, é uma variação da presente experiência com componentes ''off the shelf'' e cujas partes principais podem ser impressas em qualquer tipo de plástico rigido numa impressora 3D, sendo controlada exclusivamente por um raspberry pi e com um conjunto minimo de acessórios e motorização.

Se quiser fazer parte da rede MEDEA, por favor envie-nos um [mailto:medea@spf.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Ligações'''
<div class="mw-collapsible-content">

*Laboratório: Intermédio em [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Sala de controlo: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Gravação]
*Nível: **

</div>
</div>

==Quem gosta desta iniciativa==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Aparato experimental=

==Descrição==
Esta experiência [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consiste numa bobine retangular] com 20 espiras que em primeira aproximação se pode considerar como dois cabos paralelos de cobre por onde passa uma corrente elétrica geradora dum campo de indução magnético. O fluxo magnético gerado pelo campo é detetado numa micro-sonda de três eixos (pick-up coil) que permite reconstruir num plano préviamente selecionado a geometria vetorial magnética. Por razões práticas, o plano onde são recolhidos os dados encontra-se 15 mm abaixo do eixo de rotação da bobine.

A razão desta implementação real numa bobine retangular (onde um dos lados é subtancialmente maior do que os extremos) deve-se à corrente ter de ser fechada nos extremos.

{|class="wikitable"
|+Dimensões das espiras
|-
|Lado menor ''(2a)''
|89mm +/- 0.5mm
|-
|Lado maior ''(2b)''

|454mm +/- 0.5mm
|-
|Numero de espiras
|20, (AWG 24)
|}
A micro-sonda é constituída por três bobinas quadrangulares enroladas sobre um torreão cúbico de PVC com 5mm de lado e 10 espiras cada. Cada uma destas espiras encontra-se orientada segundo 3 eixos ortogonais, sendo o sinal do campo magnético detectado e amplificado adequadamente por eletrónica concebida para o efeito (filtro sintonizado). No final determina-se a medida do fluxo magnético nesse pequeno volume segunda cada eixo. Refira-se que é usada uma excitação alternada da corrente (AC-30kHz) para se poder desprezar a contribuição do campo magnético terrestre e outros campos espúrios e não sendo utilizado nenhum metal nas proximidades que possa alterar a configuração do campo.

A experiência permite configurar o ângulo do observador com o plano dos cabos mais compridos e varrer radialmente segundo o eixo dos ''xx'' a distância a estes. Efetuando vários varrimentos é possível mapear a área em torno dos cabos. Um ângulo de 0º corresponde a posicionar a bobine na vertical (orientada segundo os eixo dos ''zz'') criando um campo maioritáriamente segundo os ''zz'' e a 90º esta fica orientada no eixo dos ''xx''. Na prática é a bobine rodada no eixo dos ''yy'', sendo o deslocamento da micro-sonda sempre segundo o eixo dos ''xx''.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Orientação duma bobine'''
<div class="mw-collapsible-content">
A definição da orientação duma bobine prende-se com o campo de indução gerado por esta segundo a regra da mão direita: assim adoptamos a definição de que uma bobine está alinhada na vertical ─ eixos dos ''zz'' ─ caso as suas espiras estejam bobinadas no plano ''xx-yy''.
</div>
</div>

Realça-se novamente que a micro-sonda desloca-se ligeiramente abaixo (15 mm) do plano médio definido pelos condutores para poder passar por estes ao ser efetuado o varrimento. Este facto tem grande importância no protocolo avançado na zona próxima aos condutores embora não seja relevante para o cálculo do campo longínquo.
----
Um aspeto importante a ter em atenção ''é a possível saturação do sinal na próximidade dos condutores''. Devido a este facto a corrente selecionada deve ser substancialmente reduzida quando se pretenda estudar esta região.
----

==Configuração==
Para executar a experiência o utilizador necessita de definir os seguintes parâmetros:
;Posição inicial:
:Localização da primeira aquisição sendo que a origem é no eixo da bobine;
;Posição final:
:Último ponto a se medido;
;Número de amostras:
:Número de posições onde são medidas as três componentes do campo de indução magnético e a corrente nas espiras;
;Corrente na bobine:
:Valor em percentagem da modulação da corrente por espira que permite seleccionar aproximadamente o valor da corrente em relação ao valro máximo. Para determinar o valor máximo da corrente há que efetuar uma medida com a modulação no ponto médio, a 50% e extrapolar. Este parametro é fundamental para regular a não saturação das medidas na região da bobine.
;Ângulo:
:Este ângulo permite seleccionar a orientação inicial da bobine tal como descrito na fig.1

==Resultados obtidos==
Após o lançamento da experiência é devolvida uma tabela com a data/hora de cada medida e a posição absoluta em ''xx'' seguida dos elementos medidos nesses pontos: as componentes do vetor do campo e a corrente que atravessava a espira nesse instante. Esta última medida permite estabelecer a estabilidade do gerador de corrente.

A aplicação permite ainda visualizar em tempo real os dados que vão sendo recolhidos.

=MEDEA=
Esta experiência é utilizada no projeto [http://medea.spf.pt MEDEA], uma parceria entre a SPF e REN, Redes Energéticas Nacionais. MEDEA É O acrónimo para designar a MEDição dos campos Electromagnéticos no Ambiente, realizado por alunos de várias escolas secundárias e profissionais e que visa medir o campo eléctrico e magnético no meio ambiente.

=Física=
A determinação do campo de indução magnético implica integrar a lei de Biot-Savart segundo o percurso da bobine, somando num ponto do espaço todas estas contribuições infinitésimais de uma forma vectorial.
No entanto a geometria foi seleccionada de forma a permitir usar um formalismo mais simples baseado na contribuição para o campo gerado por condutores infinitos.

==Campo gerado por dois cabos infinitos==

===No plano onde coexistem ambos os cabos===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decaímento do campo de indução magnético no plano de dois condutores infinitos com correntes anti-paralelas onde se pode verificar que o campo é anulado muito rapidamente para distâncias acima da distância de separação entre os condutores.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''zz'']]

Se considerarmos dois condutores de diâmetro desprezável separados por uma distancia ''d=2a'' onde o segundo é percorrido pela corrente de retorno do primeiro cabo, apesar do decaímento do campo de indução magnético de um condutor individual depender do inverso da distância (~1/r), ao considerarmos o efeito dos dois em conjunto esse decaímento é muito mais abrupto ficando com uma dependência do inverso do quadrado da distância em zonas distantes.

Isso mesmo pode ser verificado através da expressão simplificada obtida a partir da lei de Gauss e calculada no plano onde existem os dois condutores:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

onde

<math>
\frac{\mu _0 i}{2 \pi r}
</math>
representa o módulo do campo de indução magnético criado por um condutor linear infinito.

Os valores experimentais obtidos encontram-se na figura seguinte onde se mostram apenas as duas dimensões relevantes (segundo ''yy'' o campo é despresável por uma questão de simetria).

===No plano de simetria entre os cabos ===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''xx'']]

Nesta situação, o àngulo da bobine com o eixo dos 'xx'' é nulo e por uma questão de simetria, só existe campo segundo ''xx'' nesse eixo ortogonal ao plano definido pelos cabos. Numa região afastada podemos considerar que a distância ''r'' ao plano, dada por <math>\sqrt{a^2+x^2}</math> é próxima da sua ordenada no eixo e ambos os cabos ─ afastados entre si de ''2a'' ─ concorrem para gerarem um campo construtivo com o dobro da intensidade pelo que:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

e para <math> x \gg a </math> simplifica para:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Campo gerado por uma bobine retangular==

O estudo generalizado da geometria retangular implica o cálculo do campo de indução magnético através da integração da contribuição dos elementos infinitesimais da corrente sobre a espira<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref> cuja contribuição é:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

Esta integração pode ser simplificada considerando que a sonda se desloca apenas segundo o eixo dos ''xx'' para ''z=y=0'' (por razões práticas aproximamos a posição real ''y=-10mm≃0'') e por simetria pode-se estabelecer que o campo segundo os ''yy'' é nulo.

=Estudos experimentais=

==A orientação do campo==

A visualização dum campo vetorial nem sempre é bem conseguida. Na análise deste trabalho a melhor forma de proceder é usar um software que permita visualizar os vetores do campo de indução magnética a cada 10 mm numa projeção tridimensional.
Para tal sugere-se a utilização do Octave, Matemática, Pyton, IDL ou MatLab.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Neste link (BiotSavart.ipynb)] poderá encontrar uma simulação efetuada em Jupyter.

==Linhas de campo e curvas de nível==

Obtendo-se várias características fruto da seleção de ângulos diversos, consegue-se mapear numa superfície de simetria no plano ''xx-zz'' valores para o módulo do campo e a sua direção, analisando o seu comportamento espacial.
As linhas de campo, que seguem os vectores espacialmente, permitem identificar facilmente a orientação do fluxo magnético.
As curvas de nível ligam pontos do módulo do campo constante identificando as regiões do espaço onde a sua variação é maior ou menor pelo espaçamento entre elas.

=Bibliografia=

<references />

=Ligações=
*[[ Magnetic_field_created_by_two_wires | Versão em Inglês (English Version)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Campo de indução magnético criado por 2 condutores

2026-05-29T08:06:41Z

Ist12916:

=Descrição da experiência=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - Esta experiência consiste num conjunto de espiras retangulares capazes de criar um campo magnético no espaço. Como uma das dimensões é muito maior do que a outra, o problema poderá ser abordado em primeira aproximação como dois cabos infinitos, de solução matematicamente mais simples. ''Nota: o ângulo <math>θ</math> não representa a orientação da bobine mas antes o seu plano de montagem''|right|border|236px]]

O campo de indução magnética existe em todo o espaço que nos rodeia, quer pelo magnetismo natural terrestre e sideral quer criado pelo Homem. Podemos distinguir dois tipos de categorias, (i) os campos constantes com reduzida influência nos sistemas biológicos e (ii) os variáveis no tempo (AC), capazes de induzir correntes elétricas. Estes últimos, a partir de valores elevados podem ser prejudiciais, principalmente para humanos com próteses eletrónicas (p.ex. pacemakers).

No entanto as correntes elétricas que induzem esse campo magnético, gerados na sua maioria em circuitos elétricos incluindo as linhas de transmissão elétricas, são fechados ou seja, as correntes acabam por retornar à fonte (gerador ou bateria) por cabos muito próximos uns dos outros. É o que acontece nos nossos cabos domésticos onde os mais atentos certamente já repararam que andam sempre aos pares (o terceiro fio normalmente é a "terra" e não transporta energia, servindo apenas o propósito de proteção).

O objetivo desta experiência consiste em determinar o vetor do campo de indução magnética em vários pontos do espaço criado pelos dois condutores paralelos afastados entre si. O protocolo avançado sugere uma resolução matemática mais exigente duma bobine quadrada onde toda a geometria é tida em consideração. Para o efeito a experiência é dotada duma micro-sonda 3D que recolhe a intensidade do campo magnético nos pontos selecionados.

Como as correntes elétricas têm sempre um retorno aos geradores, as linhas de transmissão elétricas e muitos outros dispositivos eletromagnéticos têm uma física equivalente ao problema abordado nesta experiência.

[[Mag_3D_experimental_apparatus | Existe uma versão da experiencia para imprimir em 3D]] que é uma variação da presente experiência com componentes ''off the shelf'' e cujas partes principais podem ser impressas em qualquer tipo de plástico rigido numa impressora 3D.

Se quiser fazer parte da rede MEDEA, por favor envie-nos um [mailto:medea@spf.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Ligações'''
<div class="mw-collapsible-content">

*Laboratório: Intermédio em [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Sala de controlo: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Gravação]
*Nível: **

</div>
</div>

==Quem gosta desta iniciativa==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Aparato experimental=

==Descrição==
Esta experiência [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consiste numa bobine retangular] com 20 espiras que em primeira aproximação se pode considerar como dois cabos paralelos de cobre por onde passa uma corrente elétrica geradora dum campo de indução magnético. O fluxo magnético gerado pelo campo é detetado numa micro-sonda de três eixos (pick-up coil) que permite reconstruir num plano préviamente selecionado a geometria vetorial magnética. Por razões práticas, o plano onde são recolhidos os dados encontra-se 15 mm abaixo do eixo de rotação da bobine.

A razão desta implementação real numa bobine retangular (onde um dos lados é subtancialmente maior do que os extremos) deve-se à corrente ter de ser fechada nos extremos.

{|class="wikitable"
|+Dimensões das espiras
|-
|Lado menor ''(2a)''
|89mm +/- 0.5mm
|-
|Lado maior ''(2b)''

|454mm +/- 0.5mm
|-
|Numero de espiras
|20, (AWG 24)
|}
A micro-sonda é constituída por três bobinas quadrangulares enroladas sobre um torreão cúbico de PVC com 5mm de lado e 10 espiras cada. Cada uma destas espiras encontra-se orientada segundo 3 eixos ortogonais, sendo o sinal do campo magnético detectado e amplificado adequadamente por eletrónica concebida para o efeito (filtro sintonizado). No final determina-se a medida do fluxo magnético nesse pequeno volume segunda cada eixo. Refira-se que é usada uma excitação alternada da corrente (AC-30kHz) para se poder desprezar a contribuição do campo magnético terrestre e outros campos espúrios e não sendo utilizado nenhum metal nas proximidades que possa alterar a configuração do campo.

A experiência permite configurar o ângulo do observador com o plano dos cabos mais compridos e varrer radialmente segundo o eixo dos ''xx'' a distância a estes. Efetuando vários varrimentos é possível mapear a área em torno dos cabos. Um ângulo de 0º corresponde a posicionar a bobine na vertical (orientada segundo os eixo dos ''zz'') criando um campo maioritáriamente segundo os ''zz'' e a 90º esta fica orientada no eixo dos ''xx''. Na prática é a bobine rodada no eixo dos ''yy'', sendo o deslocamento da micro-sonda sempre segundo o eixo dos ''xx''.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Orientação duma bobine'''
<div class="mw-collapsible-content">
A definição da orientação duma bobine prende-se com o campo de indução gerado por esta segundo a regra da mão direita: assim adoptamos a definição de que uma bobine está alinhada na vertical ─ eixos dos ''zz'' ─ caso as suas espiras estejam bobinadas no plano ''xx-yy''.
</div>
</div>

Realça-se novamente que a micro-sonda desloca-se ligeiramente abaixo (15 mm) do plano médio definido pelos condutores para poder passar por estes ao ser efetuado o varrimento. Este facto tem grande importância no protocolo avançado na zona próxima aos condutores embora não seja relevante para o cálculo do campo longínquo.
----
Um aspeto importante a ter em atenção ''é a possível saturação do sinal na próximidade dos condutores''. Devido a este facto a corrente selecionada deve ser substancialmente reduzida quando se pretenda estudar esta região.
----

==Configuração==
Para executar a experiência o utilizador necessita de definir os seguintes parâmetros:
;Posição inicial:
:Localização da primeira aquisição sendo que a origem é no eixo da bobine;
;Posição final:
:Último ponto a se medido;
;Número de amostras:
:Número de posições onde são medidas as três componentes do campo de indução magnético e a corrente nas espiras;
;Corrente na bobine:
:Valor em percentagem da modulação da corrente por espira que permite seleccionar aproximadamente o valor da corrente em relação ao valro máximo. Para determinar o valor máximo da corrente há que efetuar uma medida com a modulação no ponto médio, a 50% e extrapolar. Este parametro é fundamental para regular a não saturação das medidas na região da bobine.
;Ângulo:
:Este ângulo permite seleccionar a orientação inicial da bobine tal como descrito na fig.1

==Resultados obtidos==
Após o lançamento da experiência é devolvida uma tabela com a data/hora de cada medida e a posição absoluta em ''xx'' seguida dos elementos medidos nesses pontos: as componentes do vetor do campo e a corrente que atravessava a espira nesse instante. Esta última medida permite estabelecer a estabilidade do gerador de corrente.

A aplicação permite ainda visualizar em tempo real os dados que vão sendo recolhidos.

=MEDEA=
Esta experiência é utilizada no projeto [http://medea.spf.pt MEDEA], uma parceria entre a SPF e REN, Redes Energéticas Nacionais. MEDEA É O acrónimo para designar a MEDição dos campos Electromagnéticos no Ambiente, realizado por alunos de várias escolas secundárias e profissionais e que visa medir o campo eléctrico e magnético no meio ambiente.

=Física=
A determinação do campo de indução magnético implica integrar a lei de Biot-Savart segundo o percurso da bobine, somando num ponto do espaço todas estas contribuições infinitésimais de uma forma vectorial.
No entanto a geometria foi seleccionada de forma a permitir usar um formalismo mais simples baseado na contribuição para o campo gerado por condutores infinitos.

==Campo gerado por dois cabos infinitos==

===No plano onde coexistem ambos os cabos===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decaímento do campo de indução magnético no plano de dois condutores infinitos com correntes anti-paralelas onde se pode verificar que o campo é anulado muito rapidamente para distâncias acima da distância de separação entre os condutores.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''zz'']]

Se considerarmos dois condutores de diâmetro desprezável separados por uma distancia ''d=2a'' onde o segundo é percorrido pela corrente de retorno do primeiro cabo, apesar do decaímento do campo de indução magnético de um condutor individual depender do inverso da distância (~1/r), ao considerarmos o efeito dos dois em conjunto esse decaímento é muito mais abrupto ficando com uma dependência do inverso do quadrado da distância em zonas distantes.

Isso mesmo pode ser verificado através da expressão simplificada obtida a partir da lei de Gauss e calculada no plano onde existem os dois condutores:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

onde

<math>
\frac{\mu _0 i}{2 \pi r}
</math>
representa o módulo do campo de indução magnético criado por um condutor linear infinito.

Os valores experimentais obtidos encontram-se na figura seguinte onde se mostram apenas as duas dimensões relevantes (segundo ''yy'' o campo é despresável por uma questão de simetria).

===No plano de simetria entre os cabos ===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''xx'']]

Nesta situação, o àngulo da bobine com o eixo dos 'xx'' é nulo e por uma questão de simetria, só existe campo segundo ''xx'' nesse eixo ortogonal ao plano definido pelos cabos. Numa região afastada podemos considerar que a distância ''r'' ao plano, dada por <math>\sqrt{a^2+x^2}</math> é próxima da sua ordenada no eixo e ambos os cabos ─ afastados entre si de ''2a'' ─ concorrem para gerarem um campo construtivo com o dobro da intensidade pelo que:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

e para <math> x \gg a </math> simplifica para:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Campo gerado por uma bobine retangular==

O estudo generalizado da geometria retangular implica o cálculo do campo de indução magnético através da integração da contribuição dos elementos infinitesimais da corrente sobre a espira<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref> cuja contribuição é:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

Esta integração pode ser simplificada considerando que a sonda se desloca apenas segundo o eixo dos ''xx'' para ''z=y=0'' (por razões práticas aproximamos a posição real ''y=-10mm≃0'') e por simetria pode-se estabelecer que o campo segundo os ''yy'' é nulo.

=Estudos experimentais=

==A orientação do campo==

A visualização dum campo vetorial nem sempre é bem conseguida. Na análise deste trabalho a melhor forma de proceder é usar um software que permita visualizar os vetores do campo de indução magnética a cada 10 mm numa projeção tridimensional.
Para tal sugere-se a utilização do Octave, Matemática, Pyton, IDL ou MatLab.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Neste link (BiotSavart.ipynb)] poderá encontrar uma simulação efetuada em Jupyter.

==Linhas de campo e curvas de nível==

Obtendo-se várias características fruto da seleção de ângulos diversos, consegue-se mapear numa superfície de simetria no plano ''xx-zz'' valores para o módulo do campo e a sua direção, analisando o seu comportamento espacial.
As linhas de campo, que seguem os vectores espacialmente, permitem identificar facilmente a orientação do fluxo magnético.
As curvas de nível ligam pontos do módulo do campo constante identificando as regiões do espaço onde a sua variação é maior ou menor pelo espaçamento entre elas.

=Bibliografia=

<references />

=Ligações=
*[[ Magnetic_field_created_by_two_wires | Versão em Inglês (English Version)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Admin

2026-05-29T06:45:43Z

Ist12916: /* Elab1 Network Hosts */

== Links for administrative private pages ==

[[Page Template]]

[[Cluster configuration|Node/apparatus table connections]]

[[dsPic-Raspberry programmer interface]]

[[REC Prototype function]]

[[:File:ReC_Generic_Driver.pdf | REC Generic Driver]]

[[Free Quiz Manual]]

== General info ==
=== Table of nodes ===

{| class="wikitable"
!colspan="6"|Control rooms
|-
| '''Hostname
| '''Experiment
| '''Stream
| '''Watch
| '''Serial
| '''Baud rate
|-
| elab100 -
| radiare
| [rtsp://elabmc.ist.utl.pt/radiare.sdp 5006]
| [http://consum.ist.utl.pt/radiare.html Watch]
| /dev/ttyS0
| 4800
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220m
| 2705mm +/- 0.5mm @23ºC
| 80.5 +/- 1.0 mm
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20m
| 2677mm +/- 0.5mm @19ºC
| 80.5 +/- 1.0 mm
|-
| Maputo
| 25º56'S
| 32º36'E
| 80m
| 2609.8mm +/- 0.5mm @27ºC
| 80.5 +/- 1.0 mm
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50m
| 2756.5mm +/- 0.5mm @29ºC
| 81.8 +/- 0.5 mm
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150m
| 2850mm +/- 0.5mm @25ºC
| 80.15 +/- 0.5 mm
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2756.5mm +/- 0.5mm
| 81.8mm
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40 m
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650 m
| 2815,3mm +/- 0.5mm
| 82.0mm
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552 m
| 2825mm +/- 0.5mm @27ºC
| 81.9mm
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|}

===Glassfish===
* Parar o glassfish:
«glassfishv3/bin/asadmin stop-domain»
* Caso este não pare, ao fim de 3 minutos, fazer mesmo o kill ao processo:
«ps aux | grep java», procurar o processo que está sediado em 'glassfishv3/'
* Ver o PID o processo e
«kill PID»
* Iniciar o glassfish:
«glassfishv3/bin/asadmin start-domain»

===Acesso elab===
O endereço é elab.ist.utl.pt e a PORTA é 22xx.

Maquinas Linux

login: elab
pass: jo......

Maquinas windows ser........

Uma vez no e-lab, para reiniciar, executar:
> /usr/local/ReC7.0/scripts/restartAllElab

(esperar que o script termine, antes de desligar sessão remota/putty))

Antes de reiniciar convém perceber se há alguém a fazer experiências:

> tail -n 100 /usr/local/ReC7.0/multicast/logins.txt

Normalmente para monitorizar e ver se há problema basta
Correr o comando anterior.
Se virem que já há algum tempo ninguém faz experiências, tentar
ligar ao eLab e ver se há realmente problemas.
Se por acaso estiver muita gente ligada e não tiverem sido executadas
experiências nos últimos 10->20 mins, é porque o sistema está ''halted''.

Reiniciar :)

No caso de o e-lab estar a funcionar, mas não aparecerem experiências, fazer:

> ping 192.168.0.121

Se não existir resposta, é porque faltou a electricidade e o cluster tem
de ser reiniciado. Se obtiverem resposta, tentem reiniciar toda a
plataforma.

===Video===
START Video

/home/elab/videos/wp_saotome.start

START Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh start

STOP Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh stop

[[technical pages|e-lab technical pages (connections diagrams, schematics, hardware configurations]]
http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Technical_pages&action=edit&redlink=1

=== Elab1 Network Hosts ===

{| class="wikitable sortable"
! IP atríbuido do DHCP
! IP Address Estático
! VPN IP
! MAC Address
! Hostname
! Experiment
! Location
! Status
! Notes
|-
| 192.168.0.17
| 192.168.0.210
| 10.7.0.23
| b8:27:eb:3f:c7:c0
| plano-inclinado
| Plano Inclinado
| Lisbon
| On
|
|-
| 192.168.0.14
| 192.168.0.211
| -
| b8:27:eb:89:30:7d
| colisione
| colisione
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Campo Magnético 3D
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Light Polarization
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| Sonda de Langmuir
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| elab200
| Lisbon
| -
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| pendulo gravitico
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| -
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Planck
| Lisbon
| On
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Gamma
| Lisbon
| -
|
|-
| 192.168.0.202
| -
| -
| -
| elab202
| -
| Lisbon
| Off
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| elab203
| Lisbon
| On
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| Condensador Cilíndrico
| Lisbon
| On
|
|-
| 192.168.0.250
| 192.168.0.216
| -
| b8:27:eb:ac:8c:3b
| fotovoltaico
| Painel Fotovoltaico
| Lisbon
| On
|
|-
| 192.168.0.100
| -
| -
| -
| elab100
| -
| Lisbon
| Off
|
|-
| 192.168.0.101
| -
| -
| -
| elab101
| -
| Lisbon
| Off
|
|-
| 192.168.0.102
| -
| -
| -
| elab102
| -
| Lisbon
| Off
|
|-
| 192.168.0.103
| -
| -
| -
| elab103
| -
| Lisbon
| Off
|
|-
| 192.168.0.104
| -
| -
| -
| elab104
| -
| Lisbon
| Off
|
|-
| 192.168.0.105
| -
| -
| -
| elab105
| -
| Lisbon
| Off
|
|-
| 192.168.0.106
| -
| -
| -
| elab106
| -
| Lisbon
| Off
|
|-
| 192.168.0.150
| -
| -
| -
| elab150
| -
| Lisbon
| On
|
|-
| 192.168.0.151
| -
| -
| -
| elab151
| -
| Lisbon
| Off
|
|-
| 192.168.0.152
| -
| -
| -
| elab152
| -
| Lisbon
| Off
|
|-
| 192.168.0.153
| -
| -
| -
| elab153
| -
| Lisbon
| Off
|
|-
| 192.168.0.154
| -
| -
| -
| elab154
| -
| Lisbon
| Off
|
|-
| -
| -
| 10.7.0.1
| -
| elab1
| -
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.3
| -
| orionte_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.4
| -
| planetarium_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.5
| -
| espav_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.6
| -
| luanda_vpn
| World Pendulum
| Luanda
| Off
|
|-
| -
| -
| 10.7.0.7
| -
| ccvalg_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.8
| -
| elab_vpn???
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.9
| -
| ecb1_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.10
| -
| puc_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.11
| -
| ccvsintra_vpn
| World Pendulum
| Sintra
| Off
|
|-
| -
| -
| 10.7.0.12
| -
| epm_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.13
| -
| mola_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.16
| -
| saotome_vpn
| World Pendulum
| São Tomé
| Off
|
|-
| -
| -
| 10.7.0.17
| -
| mag3d_vpn
| mag3d
| Remote
| Off
|
|-
| -
| -
| 10.7.0.20
| -
| hidrostat_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.22
| -
| labIE2_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.24
| -
| WP-PRG
| World Pendulum
| Prague
| On
|
|-
| -
| -
| 10.7.0.25
| -
| bsb_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.26
| -
| puq_umag_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.27
| -
| vap_vpn
| World Pendulum
| Valparaíso
| Off
|
|-
| -
| -
| 10.7.0.28
| -
| bog_unad_vpn
| World Pendulum
| Bogotá
| Off
|
|-
| -
| -
| 10.7.0.29
| -
| bog_uniandes_vpn
| World Pendulum
| Bogotá (Uniandes)
| Off
|
|-
| -
| -
| 10.7.0.30
| -
| pty_utp_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.31
| -
| pty_usma_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.32
| -
| WP-BCN
| World Pendulum
| Barcelona
| On
|
|-
| -
| -
| 10.7.0.33
| -
| WP-MRS
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.34
| -
| rio_puc2_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.35
| -
| WP-TAGUS
| World Pendulum
| IST Lisbon Taguspark
| On
|
|-
| -
| -
| 10.7.0.36
| -
| rai_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.37
| -
| scl_vpn
| -
| ?
| Off
|
|-
| 192.168.0.11
| 192.168.0.219
| 10.7.0.38
| -
| rpicavidade
| Cavidade
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:62:fe:ab
| WP-DIL
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:f4:7e:32
| WP-TAGUS
| World Pendulum
| Tagus
| On
|
|-
| -
| -
| 10.7.0.40
| -
| tagus_vpn
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.41
| -
| dev_vpn
| -
| Lisbon
| Off
|
|-
| 192.168.0.19
| 192.168.0.217
| 10.7.0.42
| d8:3a:dd:e0:a2:75
| elab
| Multi-Polarizer
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.43
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.44
| -
| -
| -
| -
| Off
|
|-
| -
| 192.168.0.218
| 10.7.0.45
| d8:3a:dd:e0:a2:87
| oeiras-elab
| Multi-Polarizer
| Oeiras
| On
|
|-
| -
| -
| 10.7.0.46
| d8:3a:dd:e3:4d:fe
| ictp
| Multi-Polarizer
| Trieste
| On
|
|-
| -
| -
| 200.128.66.240
| -
| ios
| -
| ?
| On
|
|-
|
|
|
| d8:3a:dd:35:63:4b
| mag3d26oeiras_vpn
| Mag2W
| Paredes
| On
| A ser corrigido para mag2W_paredes_vpn
|}

[[MediaWiki:Flash]]
[[MediaWiki:Youtube]]
[[MediaWiki:CaixaLigacoes]]
[[MediaWiki:Links]]

Admin

2026-05-29T06:40:57Z

Ist12916: /* Elab1 Network Hosts */

== Links for administrative private pages ==

[[Page Template]]

[[Cluster configuration|Node/apparatus table connections]]

[[dsPic-Raspberry programmer interface]]

[[REC Prototype function]]

[[:File:ReC_Generic_Driver.pdf | REC Generic Driver]]

[[Free Quiz Manual]]

== General info ==
=== Table of nodes ===

{| class="wikitable"
!colspan="6"|Control rooms
|-
| '''Hostname
| '''Experiment
| '''Stream
| '''Watch
| '''Serial
| '''Baud rate
|-
| elab100 -
| radiare
| [rtsp://elabmc.ist.utl.pt/radiare.sdp 5006]
| [http://consum.ist.utl.pt/radiare.html Watch]
| /dev/ttyS0
| 4800
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220m
| 2705mm +/- 0.5mm @23ºC
| 80.5 +/- 1.0 mm
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20m
| 2677mm +/- 0.5mm @19ºC
| 80.5 +/- 1.0 mm
|-
| Maputo
| 25º56'S
| 32º36'E
| 80m
| 2609.8mm +/- 0.5mm @27ºC
| 80.5 +/- 1.0 mm
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50m
| 2756.5mm +/- 0.5mm @29ºC
| 81.8 +/- 0.5 mm
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150m
| 2850mm +/- 0.5mm @25ºC
| 80.15 +/- 0.5 mm
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2756.5mm +/- 0.5mm
| 81.8mm
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40 m
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650 m
| 2815,3mm +/- 0.5mm
| 82.0mm
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552 m
| 2825mm +/- 0.5mm @27ºC
| 81.9mm
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|}

===Glassfish===
* Parar o glassfish:
«glassfishv3/bin/asadmin stop-domain»
* Caso este não pare, ao fim de 3 minutos, fazer mesmo o kill ao processo:
«ps aux | grep java», procurar o processo que está sediado em 'glassfishv3/'
* Ver o PID o processo e
«kill PID»
* Iniciar o glassfish:
«glassfishv3/bin/asadmin start-domain»

===Acesso elab===
O endereço é elab.ist.utl.pt e a PORTA é 22xx.

Maquinas Linux

login: elab
pass: jo......

Maquinas windows ser........

Uma vez no e-lab, para reiniciar, executar:
> /usr/local/ReC7.0/scripts/restartAllElab

(esperar que o script termine, antes de desligar sessão remota/putty))

Antes de reiniciar convém perceber se há alguém a fazer experiências:

> tail -n 100 /usr/local/ReC7.0/multicast/logins.txt

Normalmente para monitorizar e ver se há problema basta
Correr o comando anterior.
Se virem que já há algum tempo ninguém faz experiências, tentar
ligar ao eLab e ver se há realmente problemas.
Se por acaso estiver muita gente ligada e não tiverem sido executadas
experiências nos últimos 10->20 mins, é porque o sistema está ''halted''.

Reiniciar :)

No caso de o e-lab estar a funcionar, mas não aparecerem experiências, fazer:

> ping 192.168.0.121

Se não existir resposta, é porque faltou a electricidade e o cluster tem
de ser reiniciado. Se obtiverem resposta, tentem reiniciar toda a
plataforma.

===Video===
START Video

/home/elab/videos/wp_saotome.start

START Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh start

STOP Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh stop

[[technical pages|e-lab technical pages (connections diagrams, schematics, hardware configurations]]
http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Technical_pages&action=edit&redlink=1

=== Elab1 Network Hosts ===

{| class="wikitable sortable"
! IP atríbuido do DHCP
! IP Address Estático
! VPN IP
! MAC Address
! Hostname
! Experiment
! Location
! Status
! Notes
|-
| 192.168.0.17
| 192.168.0.210
| 10.7.0.23
| b8:27:eb:3f:c7:c0
| plano-inclinado
| Plano Inclinado
| Lisbon
| On
|
|-
| 192.168.0.14
| 192.168.0.211
| -
| b8:27:eb:89:30:7d
| colisione
| colisione
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Campo Magnético 3D
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Light Polarization
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| Sonda de Langmuir
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| elab200
| Lisbon
| -
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| pendulo gravitico
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| -
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Planck
| Lisbon
| On
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Gamma
| Lisbon
| -
|
|-
| 192.168.0.202
| -
| -
| -
| elab202
| -
| Lisbon
| Off
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| elab203
| Lisbon
| On
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| Condensador Cilíndrico
| Lisbon
| On
|
|-
| 192.168.0.250
| 192.168.0.216
| -
| b8:27:eb:ac:8c:3b
| fotovoltaico
| Painel Fotovoltaico
| Lisbon
| On
|
|-
| 192.168.0.100
| -
| -
| -
| elab100
| -
| Lisbon
| Off
|
|-
| 192.168.0.101
| -
| -
| -
| elab101
| -
| Lisbon
| Off
|
|-
| 192.168.0.102
| -
| -
| -
| elab102
| -
| Lisbon
| Off
|
|-
| 192.168.0.103
| -
| -
| -
| elab103
| -
| Lisbon
| Off
|
|-
| 192.168.0.104
| -
| -
| -
| elab104
| -
| Lisbon
| Off
|
|-
| 192.168.0.105
| -
| -
| -
| elab105
| -
| Lisbon
| Off
|
|-
| 192.168.0.106
| -
| -
| -
| elab106
| -
| Lisbon
| Off
|
|-
| 192.168.0.150
| -
| -
| -
| elab150
| -
| Lisbon
| On
|
|-
| 192.168.0.151
| -
| -
| -
| elab151
| -
| Lisbon
| Off
|
|-
| 192.168.0.152
| -
| -
| -
| elab152
| -
| Lisbon
| Off
|
|-
| 192.168.0.153
| -
| -
| -
| elab153
| -
| Lisbon
| Off
|
|-
| 192.168.0.154
| -
| -
| -
| elab154
| -
| Lisbon
| Off
|
|-
| -
| -
| 10.7.0.1
| -
| elab1
| -
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.3
| -
| orionte_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.4
| -
| planetarium_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.5
| -
| espav_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.6
| -
| luanda_vpn
| World Pendulum
| Luanda
| Off
|
|-
| -
| -
| 10.7.0.7
| -
| ccvalg_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.8
| -
| elab_vpn???
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.9
| -
| ecb1_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.10
| -
| puc_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.11
| -
| ccvsintra_vpn
| World Pendulum
| Sintra
| Off
|
|-
| -
| -
| 10.7.0.12
| -
| epm_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.13
| -
| mola_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.16
| -
| saotome_vpn
| World Pendulum
| São Tomé
| Off
|
|-
| -
| -
| 10.7.0.17
| -
| mag3d_vpn
| mag3d
| Remote
| Off
|
|-
| -
| -
| 10.7.0.20
| -
| hidrostat_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.22
| -
| labIE2_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.24
| -
| WP-PRG
| World Pendulum
| Prague
| On
|
|-
| -
| -
| 10.7.0.25
| -
| bsb_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.26
| -
| puq_umag_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.27
| -
| vap_vpn
| World Pendulum
| Valparaíso
| Off
|
|-
| -
| -
| 10.7.0.28
| -
| bog_unad_vpn
| World Pendulum
| Bogotá
| Off
|
|-
| -
| -
| 10.7.0.29
| -
| bog_uniandes_vpn
| World Pendulum
| Bogotá (Uniandes)
| Off
|
|-
| -
| -
| 10.7.0.30
| -
| pty_utp_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.31
| -
| pty_usma_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.32
| -
| WP-BCN
| World Pendulum
| Barcelona
| On
|
|-
| -
| -
| 10.7.0.33
| -
| WP-MRS
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.34
| -
| rio_puc2_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.35
| -
| WP-TAGUS
| World Pendulum
| IST Lisbon Taguspark
| On
|
|-
| -
| -
| 10.7.0.36
| -
| rai_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.37
| -
| scl_vpn
| -
| ?
| Off
|
|-
| 192.168.0.11
| 192.168.0.219
| 10.7.0.38
| -
| rpicavidade
| Cavidade
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:62:fe:ab
| WP-DIL
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:f4:7e:32
| WP-TAGUS
| World Pendulum
| Tagus
| On
|
|-
| -
| -
| 10.7.0.40
| -
| tagus_vpn
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.41
| -
| dev_vpn
| -
| Lisbon
| Off
|
|-
| 192.168.0.19
| 192.168.0.217
| 10.7.0.42
| d8:3a:dd:e0:a2:75
| elab
| Multi-Polarizer
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.43
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.44
| -
| -
| -
| -
| Off
|
|-
| -
| 192.168.0.218
| 10.7.0.45
| d8:3a:dd:e0:a2:87
| oeiras-elab
| Multi-Polarizer
| Oeiras
| On
|
|-
| -
| -
| 10.7.0.46
| d8:3a:dd:e3:4d:fe
| ictp
| Multi-Polarizer
| Trieste
| On
|
|-
| -
| -
| 200.128.66.240
| -
| ios
| -
| ?
| On
| -
|
| -
| -
| d8:3a:dd:35:63:4b
| mag3d26oeiras_vpn
| Mag2W
| Paredes
| On
| A ser corrigido para mag2W_paredes_vpn
|}

[[MediaWiki:Flash]]
[[MediaWiki:Youtube]]
[[MediaWiki:CaixaLigacoes]]
[[MediaWiki:Links]]

Mag 3D experimental apparatus

2026-04-24T12:26:07Z

Ist12916: /* Apparatus description */

=Apparatus description=
This experiment is composed by a set of 3D printed parts that holds a rectangular coils capable of rotating on an axis. In the middle point of this coils a rail supports a magnetic field detector that can move along side. Based on this geometric configuration it is possible to map the magnetic field.
The setup comprises two step-motors able (i) to rotate the coil around the middle longitudinal axis and (ii) to move the magnetic probe apart. The sensor is a popular 3-axis magnetometer () and can detect ranges +/-1.6 mT. For ultra-high precision is used the 155 Hz refresh rate but due to this frequency being very close to the network frequency (50Hz) only ~3 points are taken for each cycle.This can be mitigated by sampling over many cycles.

[[File:Mag3d_full_kit.png|thumb| CAD model of the experimental apparatus with the central squirrel-cage rotary positioner.|center|720px]]

=Mechanical Assembly=
The core of the experiment is a support structure with a rectangular-shape to hold a coil with 30 wounds of varnished copper wire (AWG 22/0.64mm). This support is hold by a squirrel cage able to rotate it in steps of 0.5º.
On the base, a rail carries on the top the magnetic sensor to collect the signal, 7mm below the coil center when in vertical position. Note that the orientation of the coil is dictated by the magnetic field, meaning in this situation that the magnetic field is vertical and the windings are in the horizontal plane.

==Order of assembly==

=Electronic circuit=

==Electronic component assembly==
3.2 Step-motor drivers
3.3 Light source and detection

4 Optical path

4.1 Optical path alignment
4.2 Optical path calibration

5 Software

5.1 Raspberry FREE proxy
5.1.1 Communication model between the FREE-Server and the Raspberry PI
5.1.2 Communication model between the Raspberry PI and the Arduino Mega
5.2 Firmware

File:Mag3d full kit.png

2026-04-24T12:21:15Z

Ist12916: Modelo CAD da Mag3D 50 Hz

== Summary ==
Modelo CAD da Mag3D 50 Hz

Mag 3D experimental apparatus

2026-04-23T07:33:17Z

Ist12916: /* Mechanical Assembly */

=Apparatus description=
This experiment is composed by a set of 3D printed parts that holds a rectangular coils capable of rotating on an axis. In the middle point of this coils a rail supports a magnetic field detector that can move along side. Based on this geometric configuration it is possible to map the magnetic field.
The setup comprises two step-motors able (i) to rotate the coil around the middle longitudinal axis and (ii) to move the magnetic probe apart. The sensor is a popular 3-axis magnetometer () and can detect ranges +/-1.6 mT. For ultra-high precision is used the 155 Hz refresh rate but due to this frequency being very close to the network frequency (50Hz) only ~3 points are taken for each cycle.This can be mitigated by sampling over many cycles.

=Mechanical Assembly=
The core of the experiment is a support structure with a rectangular-shape to hold a coil with 30 wounds of varnished copper wire (AWG 22/0.64mm). This support is hold by a squirrel cage able to rotate it in steps of 0.5º.
On the base, a rail carries on the top the magnetic sensor to collect the signal, 7mm below the coil center when in vertical position. Note that the orientation of the coil is dictated by the magnetic field, meaning in this situation that the magnetic field is vertical and the windings are in the horizontal plane.

==Order of assembly==

=Electronic circuit=

==Electronic component assembly==
3.2 Step-motor drivers
3.3 Light source and detection

4 Optical path

4.1 Optical path alignment
4.2 Optical path calibration

5 Software

5.1 Raspberry FREE proxy
5.1.1 Communication model between the FREE-Server and the Raspberry PI
5.1.2 Communication model between the Raspberry PI and the Arduino Mega
5.2 Firmware

Mag 3D experimental apparatus

2026-04-22T13:02:30Z

Ist12916: /* Mechanical Assembly */

=Apparatus description=
This experiment is composed by a set of 3D printed parts that holds a rectangular coils capable of rotating on an axis. In the middle point of this coils a rail supports a magnetic field detector that can move along side. Based on this geometric configuration it is possible to map the magnetic field.
The setup comprises two step-motors able (i) to rotate the coil around the middle longitudinal axis and (ii) to move the magnetic probe apart. The sensor is a popular 3-axis magnetometer () and can detect ranges +/-1.6 mT. For ultra-high precision is used the 155 Hz refresh rate but due to this frequency being very close to the network frequency (50Hz) only ~3 points are taken for each cycle.This can be mitigated by sampling over many cycles.

=Mechanical Assembly=
The core of the experiment is a support structure with a rectangular-shape to hold a coil with 50 wounds of varnished copper wire (AWG 22/0.64mm). This support is hold by a squirrel cage able to rotate it in steps of 0.5º.
On the base, a rail carries on the top the magnetic sensor to collect the signal, 5mm below the coil when in vertical position, meaning that the magnetic field is vertical and the windings are in the horizontal plane.

==Order of assembly==

=Electronic circuit=

==Electronic component assembly==
3.2 Step-motor drivers
3.3 Light source and detection

4 Optical path

4.1 Optical path alignment
4.2 Optical path calibration

5 Software

5.1 Raspberry FREE proxy
5.1.1 Communication model between the FREE-Server and the Raspberry PI
5.1.2 Communication model between the Raspberry PI and the Arduino Mega
5.2 Firmware

Magnetic field created by two wires

2026-02-12T07:44:59Z

Ist12916: /* Experiment description */

=Experiment description=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - This experiment consists of a set of rectangular coils capable of creating a magnetic field in space. Since one of the dimensions is much larger than the other, the problem may approached, in a mathematically simpler first approximation, as two infinite wires. ''Note: the angle <math>θ</math> do not express the coil orientation but the coil's construction plane''|right|border|236px]]

The magnetic field exists all around. It can be created by natural terrestrial and sidereal sources or by man. We can distinguish two types of fields, (i) constant fields with reduced influence in biological systems and (ii) variable fields (AC), capable of inducing electrical currents. The latter, if intense enough, can be harmful, mainly for people with electronic prosthetics (e.g. pacemakers).

However, most electric circuits that carry those currents, including power transmission lines, are closed, meaning that the electric charge will eventually return to the source (generator or battery) via cables in close proximity of each other. This is also what happens in domestic circuits where, the most observant have certainly already noticed, cables are always paired (the third wire is usually the 'earth' and doesn't carry power in normal operation, existing only for safety reasons).

The objective of this experiment is to determine the magnetic field vector created by two parallel conductors in several points in space. To achieve this, the experiment has a 3D micro-probe capable of detecting the intensity of the magnetic field in the selected points. The advanced protocol suggests a more mathematically demanding solution, where the full geometry of the rectangular coil is considered.

Since electrical currents always return to the generators, power transmission lines and many other electromagnetic devices exhibit behavior similar to the one described and studied in this experiment.

''Two version of this experiment are in production, being the newest version available as a [[Mag 3D experimental apparatus|3D printed apparatus]] to be replicated by any hobbyist.''



<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Links'''
<div class="mw-collapsible-content">

*Video: rtsp://elabmc.ist.utl.pt/mag3d.sdp
*Laboratory: Intermediate in [http://e-lab.ist.utl.pt elab.tecnico.ulisboa.pt]
*Control Room: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Recording]
*Grade: **

</div>
</div>

==Who likes this initiative==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Experimental Apparatus=

==Description==
This experiment [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consists of a 20 turns rectangular coil] that can, in first aproximation, be approached as two parallel copper wires carrying an electrical current that generates a magnetic field. The flux of the generated magnetic field is detected by a 3-axis micro-probe (pick-up coil), allowing the reconstruction of the magnetic field vector in the previously selected plane. For practical reasons, the plane where the measurements are made is 15mm below the rotation axis of the coil.

The reasoning behind this implementation as a rectangular coil (with one dimension much larger than the other) is that the current must be closed at the extremeties.

{|class="wikitable"
|+Coil size
|-
|Smaller side ''(2a)''
|89mm +/- 0.5mm
|-
|Larger side ''(2b)''

|454mm +/- 0.5mm
|-
|Number of turns
|20, (AWG 24)
|}

The micro-probe is made of 3 square coils with 10 turns each, winded on a PVC cube with side 5mm. Each of these coils is aligned with 3 orthogonal axes, and therefore the flux of the magnetic field in that small volume is determined in each axis. It is worth noting that an AC excitation current (30kHz) is used in order to minimize the effects of the Earth's magnetic field and other randomly ocurring fields. Futhermore, the detected magnetic field signal is adequately amplified by purpose built electronics (tuned filter) that reject signals with different frequencies. No metal is used in the proximity of the coils so as to not change the original configuration of the magnetic field.

The experiment allows the configuration of the angle of observation to the plane of the longer cables and the radial sweep of the distance to them, along the ''xx'' axis. It is possible to map the area around the cables by making several sweeps. A 0º angle corresponds to positioning the coil vertically (aligned with the ''zz'' axis), creating a field mainly in the ''zz'' axis direction. At 90º, the coil is aligned with the ''xx'' axis. In practice, the coils rotates around the ''yy'' axis and the micro-probe moves along the ''xx'' axis.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Coil orientation'''
<div class="mw-collapsible-content">
The definition of coil orientation is related to the direction of the magnetic field it creates according to the right-hand rule: the adopted definition is that a coil is vertically aligned ─ ''zz'' axis ─ if its turns are winded in the ''xx-yy'' plane.
</div>
</div>

Again, it is worth noting that the micro-probe moves slightly below (15mm) the conductors so it can move below them during a sweep. This is relevant on the advanced protocol in the area near the condutors but not for the calculation of the far field.
----
It is important to note that ''it's possible that the signal saturates when the probe is close to the wires''. Due to this, the selected current should be lowered when studying the region near the conductors.
----

==Configuration==
To execute the experiment, the user must define the following parameters:
;Initial position:
:Location of the first sample to be taken. The origin is the axis of the coil;
;Final position:
:Location of the last sample to be taken;
;Number of samples:
:Number of positions where the three componentes of the magnetic field and the current on the coils are measured;
;Current in the coil:
:Value, in percentage, of the modulation of the current per turn. This allows the aproximate selection of the value of the current in relation to the maximum. To determine the maximum value of current, it's necessary to run the experiment with modulation eg. 50% and to extrapolate for the desired value. This parameter is essential to avoid the saturation of the measurements in the region near the coil.
;Angle:
:Allows for the orientation of the coil to be selected, according to fig.1

==Results==
After launching the experiment, a table with date/hour of each measurement, the absolute position in the ''xx'' axis, and the elements measured in each point: the intensity of the components of the field vector and the current that is going through the coil, is returned.

Furthermore, the application allows the visualization in real time of the data being collected.

=MEDEA=
This experiment is used by schools part of the [http://medea.spf.pt MEDEA] project, a partnership between SPF and REN, Redes Energéticas Nacionais. MEDEA is the acronym for MEDição dos campos Electromagnéticos no Ambiente (measurement of electromagnetic fields in the environment). Participants are students of secondary and profissional schools.

=Physics=
The determination of the magnetic field implies integrating the Biot-Savart law along the coil, summing in a point of space all the infintesimal contribuitions.
However, due to the geometry of the problem, a simpler approach can be taken by considering that the conductors are infinite.

==Field generated by two infinite cables==

===In the plane where both cables exist===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decayment of the magnetic field in the plane of two infinte conductors with anti-parallel currents. The magnetic field is anuled very rapidly for distances much larger than the distance between conductors.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Components along ''zz'' and ''xx'' of the field created by the experiment with the coil aligned with the ''zz'' axis]]

The magnetic field decayment of a single conductor is function of (~1/r). However, considering two conductors of negligible diameter separeted by ''d=2a'', where one carries the return current of the other, the effect of both conductors gives a much faster decayment, function of (~1/r^2) for distances much larger than the distance between conductors.

This can be verified through the simplified expression, obtained by Gauss's Law and calculated in the plane of both conductors:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

where

<math>
\frac{\mu _0 i}{2 \pi r}
</math>

is the intensity of the magnetic field criated by a single infinite linear conductor.

The figures show values obtained experimentally. Only relevant dimensions are show (it can be shown that, by simmetry, the field along ''yy'' is negligible).

===In the symmetry plane between cables===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Components of the field along the ''zz'' and ''xx'' axes created by the experiment with the coil aligned along ''xx'']]

In this situation, the angle of the coil with the ''xx'' axis is 0 and, by symmetry, there is only field along ''xx'' in the axis orthogonal to the plane defined by the conductors. In a far region, it can be considered that the distance ''r'' to the plane, given by <math>\sqrt{a^2+x^2}</math>, is approximately the ordinate along the axis and the fields created by both cables ─ separated by a distance of ''2a'' ─ add up to generate a field with double the intensity:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

for <math> x \gg a </math>, this simplifies to:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Field generated by a rectangular coil==

The study of the rectangular geometry implies the calculation of the magnetic field through the integration of the contribuition of infinitesimal current elements along the coil<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref>:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

This integration can be simplified considering that the probe moves only along the ''xx'' axis, with ''z=y=0'' (for practical reasons, the real position is aproximated ''y=-10mm≃0''), and by simmetry, it can be established that the field along ''yy'' is 0.

=Experimental studies=

==Field orientantion==

It's not always easy to visualize a vectorial field. The best way to proceed in the analisys of this experiment is to use software that allows the visualization of the magnetic field vectors every 10mm in a tridimensional projection.

For this, Octave, Mathematica, Python, IDL, or Matlab are suggested.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb In this link (BiotSavart.ipynb)] a Jupyter simulation is shown.

==Field lines and level curves==

Running the experiment several times with diferent coil angles, it is possible to map the values of the direction and intensity of the magnetic field in the ''xx-zz'' plane.
Field lines follow the field vectors spacially and allow the identification of the orientation of the magnetic flux.
Level curves connect points where the intensity of the field is constant. It's, therefore, possible to identify the points with larger variation by analising the distance between curves.

=Bibliography=

<references />

=Links=
*[[ Campo de indução magnético criado por 2 condutores | Portuguese Version (Versão em Português)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Magnetic field created by two wires

2026-02-12T07:44:17Z

Ist12916: /* Experiment description */

=Experiment description=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - This experiment consists of a set of rectangular coils capable of creating a magnetic field in space. Since one of the dimensions is much larger than the other, the problem may approached, in a mathematically simpler first approximation, as two infinite wires. ''Note: the angle <math>θ</math> do not express the coil orientation but the coil's construction plane''|right|border|236px]]

The magnetic field exists all around. It can be created by natural terrestrial and sidereal sources or by man. We can distinguish two types of fields, (i) constant fields with reduced influence in biological systems and (ii) variable fields (AC), capable of inducing electrical currents. The latter, if intense enough, can be harmful, mainly for people with electronic prosthetics (e.g. pacemakers).

However, most electric circuits that carry those currents, including power transmission lines, are closed, meaning that the electric charge will eventually return to the source (generator or battery) via cables in close proximity of each other. This is also what happens in domestic circuits where, the most observant have certainly already noticed, cables are always paired (the third wire is usually the 'earth' and doesn't carry power in normal operation, existing only for safety reasons).

The objective of this experiment is to determine the magnetic field vector created by two parallel conductors in several points in space. To achieve this, the experiment has a 3D micro-probe capable of detecting the intensity of the magnetic field in the selected points. The advanced protocol suggests a more mathematically demanding solution, where the full geometry of the rectangular coil is considered.

Since electrical currents always return to the generators, power transmission lines and many other electromagnetic devices exhibit behavior similar to the one described and studied in this experiment.

Two version of this experiment are in production, being the newest version available as a [[Mag 3D experimental apparatus|3D printed apparatus]] to be replicated by any hobbyist.



<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Links'''
<div class="mw-collapsible-content">

*Video: rtsp://elabmc.ist.utl.pt/mag3d.sdp
*Laboratory: Intermediate in [http://e-lab.ist.utl.pt elab.tecnico.ulisboa.pt]
*Control Room: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Recording]
*Grade: **

</div>
</div>

==Who likes this initiative==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Experimental Apparatus=

==Description==
This experiment [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consists of a 20 turns rectangular coil] that can, in first aproximation, be approached as two parallel copper wires carrying an electrical current that generates a magnetic field. The flux of the generated magnetic field is detected by a 3-axis micro-probe (pick-up coil), allowing the reconstruction of the magnetic field vector in the previously selected plane. For practical reasons, the plane where the measurements are made is 15mm below the rotation axis of the coil.

The reasoning behind this implementation as a rectangular coil (with one dimension much larger than the other) is that the current must be closed at the extremeties.

{|class="wikitable"
|+Coil size
|-
|Smaller side ''(2a)''
|89mm +/- 0.5mm
|-
|Larger side ''(2b)''

|454mm +/- 0.5mm
|-
|Number of turns
|20, (AWG 24)
|}

The micro-probe is made of 3 square coils with 10 turns each, winded on a PVC cube with side 5mm. Each of these coils is aligned with 3 orthogonal axes, and therefore the flux of the magnetic field in that small volume is determined in each axis. It is worth noting that an AC excitation current (30kHz) is used in order to minimize the effects of the Earth's magnetic field and other randomly ocurring fields. Futhermore, the detected magnetic field signal is adequately amplified by purpose built electronics (tuned filter) that reject signals with different frequencies. No metal is used in the proximity of the coils so as to not change the original configuration of the magnetic field.

The experiment allows the configuration of the angle of observation to the plane of the longer cables and the radial sweep of the distance to them, along the ''xx'' axis. It is possible to map the area around the cables by making several sweeps. A 0º angle corresponds to positioning the coil vertically (aligned with the ''zz'' axis), creating a field mainly in the ''zz'' axis direction. At 90º, the coil is aligned with the ''xx'' axis. In practice, the coils rotates around the ''yy'' axis and the micro-probe moves along the ''xx'' axis.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Coil orientation'''
<div class="mw-collapsible-content">
The definition of coil orientation is related to the direction of the magnetic field it creates according to the right-hand rule: the adopted definition is that a coil is vertically aligned ─ ''zz'' axis ─ if its turns are winded in the ''xx-yy'' plane.
</div>
</div>

Again, it is worth noting that the micro-probe moves slightly below (15mm) the conductors so it can move below them during a sweep. This is relevant on the advanced protocol in the area near the condutors but not for the calculation of the far field.
----
It is important to note that ''it's possible that the signal saturates when the probe is close to the wires''. Due to this, the selected current should be lowered when studying the region near the conductors.
----

==Configuration==
To execute the experiment, the user must define the following parameters:
;Initial position:
:Location of the first sample to be taken. The origin is the axis of the coil;
;Final position:
:Location of the last sample to be taken;
;Number of samples:
:Number of positions where the three componentes of the magnetic field and the current on the coils are measured;
;Current in the coil:
:Value, in percentage, of the modulation of the current per turn. This allows the aproximate selection of the value of the current in relation to the maximum. To determine the maximum value of current, it's necessary to run the experiment with modulation eg. 50% and to extrapolate for the desired value. This parameter is essential to avoid the saturation of the measurements in the region near the coil.
;Angle:
:Allows for the orientation of the coil to be selected, according to fig.1

==Results==
After launching the experiment, a table with date/hour of each measurement, the absolute position in the ''xx'' axis, and the elements measured in each point: the intensity of the components of the field vector and the current that is going through the coil, is returned.

Furthermore, the application allows the visualization in real time of the data being collected.

=MEDEA=
This experiment is used by schools part of the [http://medea.spf.pt MEDEA] project, a partnership between SPF and REN, Redes Energéticas Nacionais. MEDEA is the acronym for MEDição dos campos Electromagnéticos no Ambiente (measurement of electromagnetic fields in the environment). Participants are students of secondary and profissional schools.

=Physics=
The determination of the magnetic field implies integrating the Biot-Savart law along the coil, summing in a point of space all the infintesimal contribuitions.
However, due to the geometry of the problem, a simpler approach can be taken by considering that the conductors are infinite.

==Field generated by two infinite cables==

===In the plane where both cables exist===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decayment of the magnetic field in the plane of two infinte conductors with anti-parallel currents. The magnetic field is anuled very rapidly for distances much larger than the distance between conductors.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Components along ''zz'' and ''xx'' of the field created by the experiment with the coil aligned with the ''zz'' axis]]

The magnetic field decayment of a single conductor is function of (~1/r). However, considering two conductors of negligible diameter separeted by ''d=2a'', where one carries the return current of the other, the effect of both conductors gives a much faster decayment, function of (~1/r^2) for distances much larger than the distance between conductors.

This can be verified through the simplified expression, obtained by Gauss's Law and calculated in the plane of both conductors:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

where

<math>
\frac{\mu _0 i}{2 \pi r}
</math>

is the intensity of the magnetic field criated by a single infinite linear conductor.

The figures show values obtained experimentally. Only relevant dimensions are show (it can be shown that, by simmetry, the field along ''yy'' is negligible).

===In the symmetry plane between cables===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Components of the field along the ''zz'' and ''xx'' axes created by the experiment with the coil aligned along ''xx'']]

In this situation, the angle of the coil with the ''xx'' axis is 0 and, by symmetry, there is only field along ''xx'' in the axis orthogonal to the plane defined by the conductors. In a far region, it can be considered that the distance ''r'' to the plane, given by <math>\sqrt{a^2+x^2}</math>, is approximately the ordinate along the axis and the fields created by both cables ─ separated by a distance of ''2a'' ─ add up to generate a field with double the intensity:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

for <math> x \gg a </math>, this simplifies to:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Field generated by a rectangular coil==

The study of the rectangular geometry implies the calculation of the magnetic field through the integration of the contribuition of infinitesimal current elements along the coil<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref>:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

This integration can be simplified considering that the probe moves only along the ''xx'' axis, with ''z=y=0'' (for practical reasons, the real position is aproximated ''y=-10mm≃0''), and by simmetry, it can be established that the field along ''yy'' is 0.

=Experimental studies=

==Field orientantion==

It's not always easy to visualize a vectorial field. The best way to proceed in the analisys of this experiment is to use software that allows the visualization of the magnetic field vectors every 10mm in a tridimensional projection.

For this, Octave, Mathematica, Python, IDL, or Matlab are suggested.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb In this link (BiotSavart.ipynb)] a Jupyter simulation is shown.

==Field lines and level curves==

Running the experiment several times with diferent coil angles, it is possible to map the values of the direction and intensity of the magnetic field in the ''xx-zz'' plane.
Field lines follow the field vectors spacially and allow the identification of the orientation of the magnetic flux.
Level curves connect points where the intensity of the field is constant. It's, therefore, possible to identify the points with larger variation by analising the distance between curves.

=Bibliography=

<references />

=Links=
*[[ Campo de indução magnético criado por 2 condutores | Portuguese Version (Versão em Português)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Mag 3D experimental apparatus

2026-02-12T07:30:31Z

Ist12916: Created page with "=Apparatus description= This experiment is composed by a set of 3D printed parts that holds a rectangular coils capable of rotating on an axis. In the middle point of this coi..."

=Apparatus description=
This experiment is composed by a set of 3D printed parts that holds a rectangular coils capable of rotating on an axis. In the middle point of this coils a rail supports a magnetic field detector that can move along side. Based on this geometric configuration it is possible to map the magnetic field.
The setup comprises two step-motors able (i) to rotate the coil around the middle longitudinal axis and (ii) to move the magnetic probe apart. The sensor is a popular 3-axis magnetometer () and can detect ranges +/-1.6 mT. For ultra-high precision is used the 155 Hz refresh rate but due to this frequency being very close to the network frequency (50Hz) only ~3 points are taken for each cycle.This can be mitigated by sampling over many cycles.

=Mechanical Assembly=
The core of the experiment is a support structure with a rectangular-shape to hold a coil with 50 wounds of varnished copper wire (awg 24). This support is hold by a squirrel cage able to rotate it in steps of 0.5º.
On the base, a rail carries on the top the magnetic sensor to collect the signal.

==Order of assembly==

=Electronic circuit=

==Electronic component assembly==
3.2 Step-motor drivers
3.3 Light source and detection

4 Optical path

4.1 Optical path alignment
4.2 Optical path calibration

5 Software

5.1 Raspberry FREE proxy
5.1.1 Communication model between the FREE-Server and the Raspberry PI
5.1.2 Communication model between the Raspberry PI and the Arduino Mega
5.2 Firmware

Campo de indução magnético criado por 2 condutores

2026-02-12T06:53:46Z

Ist12916: /* Descrição da experiência */

=Descrição da experiência=
[[File:Axes_&_Coil.png||thumb|Fig. 1 - Esta experiência consiste num conjunto de espiras retangulares capazes de criar um campo magnético no espaço. Como uma das dimensões é muito maior do que a outra, o problema poderá ser abordado em primeira aproximação como dois cabos infinitos, de solução matematicamente mais simples. ''Nota: o ângulo <math>θ</math> não representa a orientação da bobine mas antes o seu plano de montagem''|right|border|236px]]

O campo de indução magnética existe em todo o espaço que nos rodeia, quer pelo magnetismo natural terrestre e sideral quer criado pelo Homem. Podemos distinguir dois tipos de categorias, (i) os campos constantes com reduzida influência nos sistemas biológicos e (ii) os variáveis no tempo (AC), capazes de induzir correntes elétricas. Estes últimos, a partir de valores elevados podem ser prejudiciais, principalmente para humanos com próteses eletrónicas (p.ex. pacemakers).

No entanto as correntes elétricas que induzem esse campo magnético, gerados na sua maioria em circuitos elétricos incluindo as linhas de transmissão elétricas, são fechados ou seja, as correntes acabam por retornar à fonte (gerador ou bateria) por cabos muito próximos uns dos outros. É o que acontece nos nossos cabos domésticos onde os mais atentos certamente já repararam que andam sempre aos pares (o terceiro fio normalmente é a "terra" e não transporta energia, servindo apenas o propósito de proteção).

O objetivo desta experiência consiste em determinar o vetor do campo de indução magnética em vários pontos do espaço criado pelos dois condutores paralelos afastados entre si. O protocolo avançado sugere uma resolução matemática mais exigente duma bobine quadrada onde toda a geometria é tida em consideração. Para o efeito a experiência é dotada duma micro-sonda 3D que recolhe a intensidade do campo magnético nos pontos selecionados.

Como as correntes elétricas têm sempre um retorno aos geradores, as linhas de transmissão elétricas e muitos outros dispositivos eletromagnéticos têm uma física equivalente ao problema abordado nesta experiência.

Se quiser fazer parte da rede MEDEA, por favor envie-nos um [mailto:medea@spf.pt mail].

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Ligações'''
<div class="mw-collapsible-content">

*Laboratório: Intermédio em [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Sala de controlo: Mag_3D
*[http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/e_lab_Mag3D.m4v Gravação]
*Nível: **

</div>
</div>

==Quem gosta desta iniciativa==
[[File:LogoSPF long.jpg|border|200px|link=http://spf.pt]]
[[File:REN_logo.png|border|120px|link=http://http://www.ren.pt/pt-PT/sustentabilidade/medea/]]

=Aparato experimental=

==Descrição==
Esta experiência [http://www.elab.ist.utl.pt/wp-content/gallery/Mag3D/Videos/feX_Mag3d_GeometriaProblema.m4v consiste numa bobine retangular] com 20 espiras que em primeira aproximação se pode considerar como dois cabos paralelos de cobre por onde passa uma corrente elétrica geradora dum campo de indução magnético. O fluxo magnético gerado pelo campo é detetado numa micro-sonda de três eixos (pick-up coil) que permite reconstruir num plano préviamente selecionado a geometria vetorial magnética. Por razões práticas, o plano onde são recolhidos os dados encontra-se 15 mm abaixo do eixo de rotação da bobine.

A razão desta implementação real numa bobine retangular (onde um dos lados é subtancialmente maior do que os extremos) deve-se à corrente ter de ser fechada nos extremos.

{|class="wikitable"
|+Dimensões das espiras
|-
|Lado menor ''(2a)''
|89mm +/- 0.5mm
|-
|Lado maior ''(2b)''

|454mm +/- 0.5mm
|-
|Numero de espiras
|20, (AWG 24)
|}
A micro-sonda é constituída por três bobinas quadrangulares enroladas sobre um torreão cúbico de PVC com 5mm de lado e 10 espiras cada. Cada uma destas espiras encontra-se orientada segundo 3 eixos ortogonais, sendo o sinal do campo magnético detectado e amplificado adequadamente por eletrónica concebida para o efeito (filtro sintonizado). No final determina-se a medida do fluxo magnético nesse pequeno volume segunda cada eixo. Refira-se que é usada uma excitação alternada da corrente (AC-30kHz) para se poder desprezar a contribuição do campo magnético terrestre e outros campos espúrios e não sendo utilizado nenhum metal nas proximidades que possa alterar a configuração do campo.

A experiência permite configurar o ângulo do observador com o plano dos cabos mais compridos e varrer radialmente segundo o eixo dos ''xx'' a distância a estes. Efetuando vários varrimentos é possível mapear a área em torno dos cabos. Um ângulo de 0º corresponde a posicionar a bobine na vertical (orientada segundo os eixo dos ''zz'') criando um campo maioritáriamente segundo os ''zz'' e a 90º esta fica orientada no eixo dos ''xx''. Na prática é a bobine rodada no eixo dos ''yy'', sendo o deslocamento da micro-sonda sempre segundo o eixo dos ''xx''.

<div class="toccolours mw-collapsible mw-collapsed" style="width:320px">
'''Orientação duma bobine'''
<div class="mw-collapsible-content">
A definição da orientação duma bobine prende-se com o campo de indução gerado por esta segundo a regra da mão direita: assim adoptamos a definição de que uma bobine está alinhada na vertical ─ eixos dos ''zz'' ─ caso as suas espiras estejam bobinadas no plano ''xx-yy''.
</div>
</div>

Realça-se novamente que a micro-sonda desloca-se ligeiramente abaixo (15 mm) do plano médio definido pelos condutores para poder passar por estes ao ser efetuado o varrimento. Este facto tem grande importância no protocolo avançado na zona próxima aos condutores embora não seja relevante para o cálculo do campo longínquo.
----
Um aspeto importante a ter em atenção ''é a possível saturação do sinal na próximidade dos condutores''. Devido a este facto a corrente selecionada deve ser substancialmente reduzida quando se pretenda estudar esta região.
----

==Configuração==
Para executar a experiência o utilizador necessita de definir os seguintes parâmetros:
;Posição inicial:
:Localização da primeira aquisição sendo que a origem é no eixo da bobine;
;Posição final:
:Último ponto a se medido;
;Número de amostras:
:Número de posições onde são medidas as três componentes do campo de indução magnético e a corrente nas espiras;
;Corrente na bobine:
:Valor em percentagem da modulação da corrente por espira que permite seleccionar aproximadamente o valor da corrente em relação ao valro máximo. Para determinar o valor máximo da corrente há que efetuar uma medida com a modulação no ponto médio, a 50% e extrapolar. Este parametro é fundamental para regular a não saturação das medidas na região da bobine.
;Ângulo:
:Este ângulo permite seleccionar a orientação inicial da bobine tal como descrito na fig.1

==Resultados obtidos==
Após o lançamento da experiência é devolvida uma tabela com a data/hora de cada medida e a posição absoluta em ''xx'' seguida dos elementos medidos nesses pontos: as componentes do vetor do campo e a corrente que atravessava a espira nesse instante. Esta última medida permite estabelecer a estabilidade do gerador de corrente.

A aplicação permite ainda visualizar em tempo real os dados que vão sendo recolhidos.

=MEDEA=
Esta experiência é utilizada no projeto [http://medea.spf.pt MEDEA], uma parceria entre a SPF e REN, Redes Energéticas Nacionais. MEDEA É O acrónimo para designar a MEDição dos campos Electromagnéticos no Ambiente, realizado por alunos de várias escolas secundárias e profissionais e que visa medir o campo eléctrico e magnético no meio ambiente.

=Física=
A determinação do campo de indução magnético implica integrar a lei de Biot-Savart segundo o percurso da bobine, somando num ponto do espaço todas estas contribuições infinitésimais de uma forma vectorial.
No entanto a geometria foi seleccionada de forma a permitir usar um formalismo mais simples baseado na contribuição para o campo gerado por condutores infinitos.

==Campo gerado por dois cabos infinitos==

===No plano onde coexistem ambos os cabos===

[[File:DecaimentoMagnetico2Cabos.png|250px|thumb|Decaímento do campo de indução magnético no plano de dois condutores infinitos com correntes anti-paralelas onde se pode verificar que o campo é anulado muito rapidamente para distâncias acima da distância de separação entre os condutores.]]

[[File:MAG_3D_MagneticField_0degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''zz'']]

Se considerarmos dois condutores de diâmetro desprezável separados por uma distancia ''d=2a'' onde o segundo é percorrido pela corrente de retorno do primeiro cabo, apesar do decaímento do campo de indução magnético de um condutor individual depender do inverso da distância (~1/r), ao considerarmos o efeito dos dois em conjunto esse decaímento é muito mais abrupto ficando com uma dependência do inverso do quadrado da distância em zonas distantes.

Isso mesmo pode ser verificado através da expressão simplificada obtida a partir da lei de Gauss e calculada no plano onde existem os dois condutores:

<math>
B_{Total}=B_1+B_2=\frac{\mu _0 i}{2 \pi (r-a)}- \frac{\mu _0 i}{2 \pi (r+a)}\simeq \frac{\mu _0 i a}{\pi r^2}, r\gg d
</math>

onde

<math>
\frac{\mu _0 i}{2 \pi r}
</math>
representa o módulo do campo de indução magnético criado por um condutor linear infinito.

Os valores experimentais obtidos encontram-se na figura seguinte onde se mostram apenas as duas dimensões relevantes (segundo ''yy'' o campo é despresável por uma questão de simetria).

===No plano de simetria entre os cabos ===
[[File:MAG_3D_MagneticField_90degree.png|250px|thumb|right| Componentes segundo os ''zz'' e ''xx'' para o campo criado pela experiência com a espira alinhada no eixo dos ''xx'']]

Nesta situação, o àngulo da bobine com o eixo dos 'xx'' é nulo e por uma questão de simetria, só existe campo segundo ''xx'' nesse eixo ortogonal ao plano definido pelos cabos. Numa região afastada podemos considerar que a distância ''r'' ao plano, dada por <math>\sqrt{a^2+x^2}</math> é próxima da sua ordenada no eixo e ambos os cabos ─ afastados entre si de ''2a'' ─ concorrem para gerarem um campo construtivo com o dobro da intensidade pelo que:

<math>
B_{Total}=B_1+B_2 \approx 2 \times \frac{\mu _0 i}{2 \pi \sqrt{a^2+x^2}} \cdot \frac{a}{\sqrt{a^2+x^2}} = \frac{\mu _0 i a}{\pi (a^2+x^2)}
</math>

e para <math> x \gg a </math> simplifica para:

<math>
B_{eixo}= \frac{\mu _0 i a}{\pi x^2} , x \approx r\gg a
</math>

==Campo gerado por uma bobine retangular==

O estudo generalizado da geometria retangular implica o cálculo do campo de indução magnético através da integração da contribuição dos elementos infinitesimais da corrente sobre a espira<ref>Introdução à Física, Jorge Dias Deus (McGraw-Hill)</ref> cuja contribuição é:

<math>
d{\bf{B}} = \frac{{\mu _0 }}{{4\pi }}\frac{{Id\ell \times {\bf{\hat r}}}}{{r^2 }}
</math>

Esta integração pode ser simplificada considerando que a sonda se desloca apenas segundo o eixo dos ''xx'' para ''z=y=0'' (por razões práticas aproximamos a posição real ''y=-10mm≃0'') e por simetria pode-se estabelecer que o campo segundo os ''yy'' é nulo.

=Estudos experimentais=

==A orientação do campo==

A visualização dum campo vetorial nem sempre é bem conseguida. Na análise deste trabalho a melhor forma de proceder é usar um software que permita visualizar os vetores do campo de indução magnética a cada 10 mm numa projeção tridimensional.
Para tal sugere-se a utilização do Octave, Matemática, Pyton, IDL ou MatLab.
[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Neste link (BiotSavart.ipynb)] poderá encontrar uma simulação efetuada em Jupyter.

==Linhas de campo e curvas de nível==

Obtendo-se várias características fruto da seleção de ângulos diversos, consegue-se mapear numa superfície de simetria no plano ''xx-zz'' valores para o módulo do campo e a sua direção, analisando o seu comportamento espacial.
As linhas de campo, que seguem os vectores espacialmente, permitem identificar facilmente a orientação do fluxo magnético.
As curvas de nível ligam pontos do módulo do campo constante identificando as regiões do espaço onde a sua variação é maior ou menor pelo espaçamento entre elas.

=Bibliografia=

<references />

=Ligações=
*[[ Magnetic_field_created_by_two_wires | Versão em Inglês (English Version)]]
*[https://github.com/bernardocarvalho/life-jupyter/blob/master/BiotSavart.ipynb Python simulation]

Admin

2026-01-15T13:29:06Z

Ist12916: /* Elab1 Network Hosts */

== Links for administrative private pages ==

[[Page Template]]

[[Cluster configuration|Node/apparatus table connections]]

[[dsPic-Raspberry programmer interface]]

[[REC Prototype function]]

[[:File:ReC_Generic_Driver.pdf | REC Generic Driver]]

[[Free Quiz Manual]]

== General info ==
=== Table of nodes ===

{| class="wikitable"
!colspan="6"|Control rooms
|-
| '''Hostname
| '''Experiment
| '''Stream
| '''Watch
| '''Serial
| '''Baud rate
|-
| elab100 -
| radiare
| [rtsp://elabmc.ist.utl.pt/radiare.sdp 5006]
| [http://consum.ist.utl.pt/radiare.html Watch]
| /dev/ttyS0
| 4800
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220m
| 2705mm +/- 0.5mm @23ºC
| 80.5 +/- 1.0 mm
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20m
| 2677mm +/- 0.5mm @19ºC
| 80.5 +/- 1.0 mm
|-
| Maputo
| 25º56'S
| 32º36'E
| 80m
| 2609.8mm +/- 0.5mm @27ºC
| 80.5 +/- 1.0 mm
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50m
| 2756.5mm +/- 0.5mm @29ºC
| 81.8 +/- 0.5 mm
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150m
| 2850mm +/- 0.5mm @25ºC
| 80.15 +/- 0.5 mm
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2756.5mm +/- 0.5mm
| 81.8mm
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40 m
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650 m
| 2815,3mm +/- 0.5mm
| 82.0mm
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552 m
| 2825mm +/- 0.5mm @27ºC
| 81.9mm
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|}

===Glassfish===
* Parar o glassfish:
«glassfishv3/bin/asadmin stop-domain»
* Caso este não pare, ao fim de 3 minutos, fazer mesmo o kill ao processo:
«ps aux | grep java», procurar o processo que está sediado em 'glassfishv3/'
* Ver o PID o processo e
«kill PID»
* Iniciar o glassfish:
«glassfishv3/bin/asadmin start-domain»

===Acesso elab===
O endereço é elab.ist.utl.pt e a PORTA é 22xx.

Maquinas Linux

login: elab
pass: jo......

Maquinas windows ser........

Uma vez no e-lab, para reiniciar, executar:
> /usr/local/ReC7.0/scripts/restartAllElab

(esperar que o script termine, antes de desligar sessão remota/putty))

Antes de reiniciar convém perceber se há alguém a fazer experiências:

> tail -n 100 /usr/local/ReC7.0/multicast/logins.txt

Normalmente para monitorizar e ver se há problema basta
Correr o comando anterior.
Se virem que já há algum tempo ninguém faz experiências, tentar
ligar ao eLab e ver se há realmente problemas.
Se por acaso estiver muita gente ligada e não tiverem sido executadas
experiências nos últimos 10->20 mins, é porque o sistema está ''halted''.

Reiniciar :)

No caso de o e-lab estar a funcionar, mas não aparecerem experiências, fazer:

> ping 192.168.0.121

Se não existir resposta, é porque faltou a electricidade e o cluster tem
de ser reiniciado. Se obtiverem resposta, tentem reiniciar toda a
plataforma.

===Video===
START Video

/home/elab/videos/wp_saotome.start

START Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh start

STOP Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh stop

[[technical pages|e-lab technical pages (connections diagrams, schematics, hardware configurations]]
http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Technical_pages&action=edit&redlink=1

=== Elab1 Network Hosts ===

{| class="wikitable sortable"
! IP atríbuido do DHCP
! IP Address Estático
! VPN IP
! MAC Address
! Hostname
! Experiment
! Location
! Status
! Notes
|-
| 192.168.0.17
| 192.168.0.210
| 10.7.0.23
| b8:27:eb:3f:c7:c0
| plano-inclinado
| Plano Inclinado
| Lisbon
| On
|
|-
| 192.168.0.14
| 192.168.0.211
| -
| b8:27:eb:89:30:7d
| colisione
| colisione
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Campo Magnético 3D
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Light Polarization
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| Sonda de Langmuir
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| elab200
| Lisbon
| -
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| pendulo gravitico
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| -
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Planck
| Lisbon
| On
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Gamma
| Lisbon
| -
|
|-
| 192.168.0.202
| -
| -
| -
| elab202
| -
| Lisbon
| Off
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| elab203
| Lisbon
| On
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| Condensador Cilíndrico
| Lisbon
| On
|
|-
| 192.168.0.250
| 192.168.0.216
| -
| b8:27:eb:ac:8c:3b
| fotovoltaico
| Painel Fotovoltaico
| Lisbon
| On
|
|-
| 192.168.0.100
| -
| -
| -
| elab100
| -
| Lisbon
| Off
|
|-
| 192.168.0.101
| -
| -
| -
| elab101
| -
| Lisbon
| Off
|
|-
| 192.168.0.102
| -
| -
| -
| elab102
| -
| Lisbon
| Off
|
|-
| 192.168.0.103
| -
| -
| -
| elab103
| -
| Lisbon
| Off
|
|-
| 192.168.0.104
| -
| -
| -
| elab104
| -
| Lisbon
| Off
|
|-
| 192.168.0.105
| -
| -
| -
| elab105
| -
| Lisbon
| Off
|
|-
| 192.168.0.106
| -
| -
| -
| elab106
| -
| Lisbon
| Off
|
|-
| 192.168.0.150
| -
| -
| -
| elab150
| -
| Lisbon
| On
|
|-
| 192.168.0.151
| -
| -
| -
| elab151
| -
| Lisbon
| Off
|
|-
| 192.168.0.152
| -
| -
| -
| elab152
| -
| Lisbon
| Off
|
|-
| 192.168.0.153
| -
| -
| -
| elab153
| -
| Lisbon
| Off
|
|-
| 192.168.0.154
| -
| -
| -
| elab154
| -
| Lisbon
| Off
|
|-
| -
| -
| 10.7.0.1
| -
| elab1
| -
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.3
| -
| orionte_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.4
| -
| planetarium_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.5
| -
| espav_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.6
| -
| luanda_vpn
| World Pendulum
| Luanda
| Off
|
|-
| -
| -
| 10.7.0.7
| -
| ccvalg_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.8
| -
| elab_vpn???
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.9
| -
| ecb1_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.10
| -
| puc_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.11
| -
| ccvsintra_vpn
| World Pendulum
| Sintra
| Off
|
|-
| -
| -
| 10.7.0.12
| -
| epm_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.13
| -
| mola_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.16
| -
| saotome_vpn
| World Pendulum
| São Tomé
| Off
|
|-
| -
| -
| 10.7.0.17
| -
| mag3d_vpn
| mag3d
| Remote
| Off
|
|-
| -
| -
| 10.7.0.20
| -
| hidrostat_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.22
| -
| labIE2_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.24
| -
| WP-PRG
| World Pendulum
| Prague
| On
|
|-
| -
| -
| 10.7.0.25
| -
| bsb_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.26
| -
| puq_umag_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.27
| -
| vap_vpn
| World Pendulum
| Valparaíso
| Off
|
|-
| -
| -
| 10.7.0.28
| -
| bog_unad_vpn
| World Pendulum
| Bogotá
| Off
|
|-
| -
| -
| 10.7.0.29
| -
| bog_uniandes_vpn
| World Pendulum
| Bogotá (Uniandes)
| Off
|
|-
| -
| -
| 10.7.0.30
| -
| pty_utp_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.31
| -
| pty_usma_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.32
| -
| WP-BCN
| World Pendulum
| Barcelona
| On
|
|-
| -
| -
| 10.7.0.33
| -
| WP-MRS
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.34
| -
| rio_puc2_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.35
| -
| WP-TAGUS
| World Pendulum
| IST Lisbon Taguspark
| On
|
|-
| -
| -
| 10.7.0.36
| -
| rai_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.37
| -
| scl_vpn
| -
| ?
| Off
|
|-
| 192.168.0.11
| -
| 10.7.0.38
| -
| rpicavidade
| Cavidade
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:62:fe:ab
| WP-DIL
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:f4:7e:32
| WP-TAGUS
| World Pendulum
| Tagus
| On
|
|-
| -
| -
| 10.7.0.40
| -
| tagus_vpn
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.41
| -
| dev_vpn
| -
| Lisbon
| Off
|
|-
| 192.168.0.19
| 192.168.0.217
| 10.7.0.42
| d8:3a:dd:e0:a2:75
| elab
| Multi-Polarizer
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.43
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.44
| -
| -
| -
| -
| Off
|
|-
| -
| 192.168.0.218
| 10.7.0.45
| d8:3a:dd:e0:a2:87
| oeiras-elab
| Multi-Polarizer
| Oeiras
| On
|
|-
| -
| -
| 10.7.0.46
| d8:3a:dd:e3:4d:fe
| ictp
| Multi-Polarizer
| Trieste
| On
|
|-
| -
| -
| 200.128.66.240
| -
| ios
| -
| ?
| On
|
|}

[[MediaWiki:Flash]]
[[MediaWiki:Youtube]]
[[MediaWiki:CaixaLigacoes]]
[[MediaWiki:Links]]

Admin

2026-01-15T13:19:34Z

Ist12916: /* Elab1 Network Hosts */

== Links for administrative private pages ==

[[Page Template]]

[[Cluster configuration|Node/apparatus table connections]]

[[dsPic-Raspberry programmer interface]]

[[REC Prototype function]]

[[:File:ReC_Generic_Driver.pdf | REC Generic Driver]]

[[Free Quiz Manual]]

== General info ==
=== Table of nodes ===

{| class="wikitable"
!colspan="6"|Control rooms
|-
| '''Hostname
| '''Experiment
| '''Stream
| '''Watch
| '''Serial
| '''Baud rate
|-
| elab100 -
| radiare
| [rtsp://elabmc.ist.utl.pt/radiare.sdp 5006]
| [http://consum.ist.utl.pt/radiare.html Watch]
| /dev/ttyS0
| 4800
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220m
| 2705mm +/- 0.5mm @23ºC
| 80.5 +/- 1.0 mm
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20m
| 2677mm +/- 0.5mm @19ºC
| 80.5 +/- 1.0 mm
|-
| Maputo
| 25º56'S
| 32º36'E
| 80m
| 2609.8mm +/- 0.5mm @27ºC
| 80.5 +/- 1.0 mm
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50m
| 2756.5mm +/- 0.5mm @29ºC
| 81.8 +/- 0.5 mm
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150m
| 2850mm +/- 0.5mm @25ºC
| 80.15 +/- 0.5 mm
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2756.5mm +/- 0.5mm
| 81.8mm
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40 m
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650 m
| 2815,3mm +/- 0.5mm
| 82.0mm
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552 m
| 2825mm +/- 0.5mm @27ºC
| 81.9mm
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|}

===Glassfish===
* Parar o glassfish:
«glassfishv3/bin/asadmin stop-domain»
* Caso este não pare, ao fim de 3 minutos, fazer mesmo o kill ao processo:
«ps aux | grep java», procurar o processo que está sediado em 'glassfishv3/'
* Ver o PID o processo e
«kill PID»
* Iniciar o glassfish:
«glassfishv3/bin/asadmin start-domain»

===Acesso elab===
O endereço é elab.ist.utl.pt e a PORTA é 22xx.

Maquinas Linux

login: elab
pass: jo......

Maquinas windows ser........

Uma vez no e-lab, para reiniciar, executar:
> /usr/local/ReC7.0/scripts/restartAllElab

(esperar que o script termine, antes de desligar sessão remota/putty))

Antes de reiniciar convém perceber se há alguém a fazer experiências:

> tail -n 100 /usr/local/ReC7.0/multicast/logins.txt

Normalmente para monitorizar e ver se há problema basta
Correr o comando anterior.
Se virem que já há algum tempo ninguém faz experiências, tentar
ligar ao eLab e ver se há realmente problemas.
Se por acaso estiver muita gente ligada e não tiverem sido executadas
experiências nos últimos 10->20 mins, é porque o sistema está ''halted''.

Reiniciar :)

No caso de o e-lab estar a funcionar, mas não aparecerem experiências, fazer:

> ping 192.168.0.121

Se não existir resposta, é porque faltou a electricidade e o cluster tem
de ser reiniciado. Se obtiverem resposta, tentem reiniciar toda a
plataforma.

===Video===
START Video

/home/elab/videos/wp_saotome.start

START Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh start

STOP Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh stop

[[technical pages|e-lab technical pages (connections diagrams, schematics, hardware configurations]]
http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Technical_pages&action=edit&redlink=1

=== Elab1 Network Hosts ===

{| class="wikitable sortable"
! IP atríbuido do DHCP
! IP Address Estático
! VPN IP
! MAC Address
! Hostname
! Experiment
! Location
! Status
! Notes
|-
| 192.168.0.17
| 192.168.0.210
| 10.7.0.23
| b8:27:eb:3f:c7:c0
| plano-inclinado
| Plano Inclinado
| Lisbon
| On
|
|-
| 192.168.0.14
| 192.168.0.211
| -
| b8:27:eb:89:30:7d
| colisione
| colisione
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Campo Magnético 3D
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Light Polarization
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| Sonda de Langmuir
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| elab200
| Lisbon
| -
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| pendulo gravitico
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| -
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Planck
| Lisbon
| On
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Gamma
| Lisbon
| -
|
|-
| 192.168.0.202
| -
| -
| -
| elab202
| -
| Lisbon
| Off
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| elab203
| Lisbon
| On
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| Condensador Cilíndrico
| Lisbon
| On
|
|-
| 192.168.0.250
| 192.168.0.216
| -
| b8:27:eb:ac:8c:3b
| fotovoltaico
| Painel Fotovoltaico
| Lisbon
| On
|
|-
| 192.168.0.100
| -
| -
| -
| elab100
| -
| Lisbon
| Off
|
|-
| 192.168.0.101
| -
| -
| -
| elab101
| -
| Lisbon
| Off
|
|-
| 192.168.0.102
| -
| -
| -
| elab102
| -
| Lisbon
| Off
|
|-
| 192.168.0.103
| -
| -
| -
| elab103
| -
| Lisbon
| Off
|
|-
| 192.168.0.104
| -
| -
| -
| elab104
| -
| Lisbon
| Off
|
|-
| 192.168.0.105
| -
| -
| -
| elab105
| -
| Lisbon
| Off
|
|-
| 192.168.0.106
| -
| -
| -
| elab106
| -
| Lisbon
| Off
|
|-
| 192.168.0.150
| -
| -
| -
| elab150
| -
| Lisbon
| On
|
|-
| 192.168.0.151
| -
| -
| -
| elab151
| -
| Lisbon
| Off
|
|-
| 192.168.0.152
| -
| -
| -
| elab152
| -
| Lisbon
| Off
|
|-
| 192.168.0.153
| -
| -
| -
| elab153
| -
| Lisbon
| Off
|
|-
| 192.168.0.154
| -
| -
| -
| elab154
| -
| Lisbon
| Off
|
|-
| -
| -
| 10.7.0.1
| -
| elab1
| -
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.3
| -
| orionte_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.4
| -
| planetarium_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.5
| -
| espav_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.6
| -
| luanda_vpn
| World Pendulum
| Luanda
| Off
|
|-
| -
| -
| 10.7.0.7
| -
| ccvalg_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.8
| -
| elab_vpn???
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.9
| -
| ecb1_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.10
| -
| puc_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.11
| -
| ccvsintra_vpn
| World Pendulum
| Sintra
| Off
|
|-
| -
| -
| 10.7.0.12
| -
| epm_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.13
| -
| mola_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.16
| -
| saotome_vpn
| World Pendulum
| São Tomé
| Off
|
|-
| -
| -
| 10.7.0.17
| -
| mag3d_vpn
| mag3d
| Remote
| Off
|
|-
| -
| -
| 10.7.0.20
| -
| hidrostat_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.22
| -
| labIE2_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.24
| -
| WP-PRG
| World Pendulum
| Prague
| On
|
|-
| -
| -
| 10.7.0.25
| -
| bsb_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.26
| -
| puq_umag_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.27
| -
| vap_vpn
| World Pendulum
| Valparaíso
| Off
|
|-
| -
| -
| 10.7.0.28
| -
| bog_unad_vpn
| World Pendulum
| Bogotá
| Off
|
|-
| -
| -
| 10.7.0.29
| -
| bog_uniandes_vpn
| World Pendulum
| Bogotá (Uniandes)
| Off
|
|-
| -
| -
| 10.7.0.30
| -
| pty_utp_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.31
| -
| pty_usma_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.32
| -
| WP-BCN
| World Pendulum
| Barcelona
| On
|
|-
| -
| -
| 10.7.0.33
| -
| WP-MRS
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.34
| -
| rio_puc2_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.35
| -
| WP-TAGUS
| World Pendulum
| IST Lisbon Taguspark
| On
|
|-
| -
| -
| 10.7.0.36
| -
| rai_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.37
| -
| scl_vpn
| -
| ?
| Off
|
|-
| 192.168.0.11
| -
| 10.7.0.38
| -
| rpicavidade
| Cavidade
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:62:fe:ab
| WP-DIL
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:f4:7e:32
| WP-TAGUS
| World Pendulum
| Tagus
| On
|
|-
| -
| -
| 10.7.0.40
| -
| tagus_vpn
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.41
| -
| dev_vpn
| -
| Lisbon
| Off
|
|-
| 192.168.0.19
| 192.168.0.217
| 10.7.0.42
| d8:3a:dd:e0:a2:75
| elab
| Multi-Polarizer
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.43
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.44
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.45
| d8:3a:dd:e0:a2:87
| oeiras-elab
| Multi-Polarizer
| Oeiras
| On
|
|-
| -
| -
| 10.7.0.46
| d8:3a:dd:e3:4d:fe
| ictp
| Multi-Polarizer
| Trieste
| On
|
|-
| -
| -
| 200.128.66.240
| -
| ios
| -
| ?
| On
|
|}

[[MediaWiki:Flash]]
[[MediaWiki:Youtube]]
[[MediaWiki:CaixaLigacoes]]
[[MediaWiki:Links]]

Admin

2026-01-15T13:19:11Z

Ist12916: /* Elab1 Network Hosts */

== Links for administrative private pages ==

[[Page Template]]

[[Cluster configuration|Node/apparatus table connections]]

[[dsPic-Raspberry programmer interface]]

[[REC Prototype function]]

[[:File:ReC_Generic_Driver.pdf | REC Generic Driver]]

[[Free Quiz Manual]]

== General info ==
=== Table of nodes ===

{| class="wikitable"
!colspan="6"|Control rooms
|-
| '''Hostname
| '''Experiment
| '''Stream
| '''Watch
| '''Serial
| '''Baud rate
|-
| elab100 -
| radiare
| [rtsp://elabmc.ist.utl.pt/radiare.sdp 5006]
| [http://consum.ist.utl.pt/radiare.html Watch]
| /dev/ttyS0
| 4800
|-
| UESC/Ilhéus
| 14º47'S
| 39º10'W
| 220m
| 2705mm +/- 0.5mm @23ºC
| 80.5 +/- 1.0 mm
|-
| Lisbon
| 38º41'N
| 9º12'W
| 20m
| 2677mm +/- 0.5mm @19ºC
| 80.5 +/- 1.0 mm
|-
| Maputo
| 25º56'S
| 32º36'E
| 80m
| 2609.8mm +/- 0.5mm @27ºC
| 80.5 +/- 1.0 mm
|-
| São Tomé
| 0º21'N
| 6º43'E
| 50m
| 2756.5mm +/- 0.5mm @29ºC
| 81.8 +/- 0.5 mm
|-
| Prague - CTU
| 50º5.5'N
| 14º25.0'E
| 150m
| 2850mm +/- 0.5mm @25ºC
| 80.15 +/- 0.5 mm
|-
| Barcelona - UPC
| 41º24.6'N
| 2º13.1'E
| 55
| 2756.5mm +/- 0.5mm
| 81.8mm
|-
| Rio de Janeiro - PUC
| 22º54.1'S
| 43º12'W
| 50
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Praia - UniCV
| 14°56'N
| 23°31'W
| 40 m
| 2826,0mm +/- 0.5mm
| 81.6mm
|-
| Bogotá - UniAndes
| 4°36'N
| 74°3'W
| 2650 m
| 2815,3mm +/- 0.5mm
| 82.0mm
|-
| Panama city - UTP
| 9°1.3'N
| 79°31.9'W
| 82 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|-
| Santiago - UChile
| 33°27.5'S
| 70°39.8'W
| 552 m
| 2825mm +/- 0.5mm @27ºC
| 81.9mm
|-
| Valparaiso - UTFSM
| 33°1'S
| 71°37'W
| 30 m
| 2825mm +/- 0.5mm @28ºC
| 81.9mm
|}

===Glassfish===
* Parar o glassfish:
«glassfishv3/bin/asadmin stop-domain»
* Caso este não pare, ao fim de 3 minutos, fazer mesmo o kill ao processo:
«ps aux | grep java», procurar o processo que está sediado em 'glassfishv3/'
* Ver o PID o processo e
«kill PID»
* Iniciar o glassfish:
«glassfishv3/bin/asadmin start-domain»

===Acesso elab===
O endereço é elab.ist.utl.pt e a PORTA é 22xx.

Maquinas Linux

login: elab
pass: jo......

Maquinas windows ser........

Uma vez no e-lab, para reiniciar, executar:
> /usr/local/ReC7.0/scripts/restartAllElab

(esperar que o script termine, antes de desligar sessão remota/putty))

Antes de reiniciar convém perceber se há alguém a fazer experiências:

> tail -n 100 /usr/local/ReC7.0/multicast/logins.txt

Normalmente para monitorizar e ver se há problema basta
Correr o comando anterior.
Se virem que já há algum tempo ninguém faz experiências, tentar
ligar ao eLab e ver se há realmente problemas.
Se por acaso estiver muita gente ligada e não tiverem sido executadas
experiências nos últimos 10->20 mins, é porque o sistema está ''halted''.

Reiniciar :)

No caso de o e-lab estar a funcionar, mas não aparecerem experiências, fazer:

> ping 192.168.0.121

Se não existir resposta, é porque faltou a electricidade e o cluster tem
de ser reiniciado. Se obtiverem resposta, tentem reiniciar toda a
plataforma.

===Video===
START Video

/home/elab/videos/wp_saotome.start

START Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh start

STOP Hardware server
elab@wp_saotome:~ $ /home/elab/rec-deployment/wpilheus/wpilheusDaemon.sh stop

[[technical pages|e-lab technical pages (connections diagrams, schematics, hardware configurations]]
http://www.elab.tecnico.ulisboa.pt/wiki/index.php?title=Technical_pages&action=edit&redlink=1

=== Elab1 Network Hosts ===

{| class="wikitable sortable"
! IP atríbuido do DHCP
! IP Address Estático
! VPN IP
! MAC Address
! Hostname
! Experiment
! Location
! Status
! Notes
|-
| 192.168.0.17
| 192.168.0.210
| 10.7.0.23
| b8:27:eb:3f:c7:c0
| plano-inclinado
| Plano Inclinado
| Lisbon
| On
|
|-
| 192.168.0.14
| 192.168.0.211
| -
| b8:27:eb:89:30:7d
| colisione
| colisione
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Campo Magnético 3D
| Lisbon
| On
|
|-
| 192.168.0.15
| 192.168.0.212
| -
| b8:27:eb:4e:de:b3
| mag3d
| Light Polarization
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| Sonda de Langmuir
| Lisbon
| On
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| elab200
| Lisbon
| -
|
|-
| 192.168.0.200
| 192.168.0.213
| -
| b8:27:eb:f9:5d:c2
| elab200
| pendulo gravitico
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| -
| Lisbon
| -
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Planck
| Lisbon
| On
|
|-
| 192.168.0.201
| 192.168.0.214
| -
| b8:27:eb:45:03:1e
| elab201
| Gamma
| Lisbon
| -
|
|-
| 192.168.0.202
| -
| -
| -
| elab202
| -
| Lisbon
| Off
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| elab203
| Lisbon
| On
|
|-
| 192.168.0.203
| 192.168.0.215
| -
| b8:27:eb:9d:b8:09
| elab203
| Condicionador Cilíndrico
| Lisbon
| On
|
|-
| 192.168.0.250
| 192.168.0.216
| -
| b8:27:eb:ac:8c:3b
| fotovoltaico
| Painel Fotovoltaico
| Lisbon
| On
|
|-
| 192.168.0.100
| -
| -
| -
| elab100
| -
| Lisbon
| Off
|
|-
| 192.168.0.101
| -
| -
| -
| elab101
| -
| Lisbon
| Off
|
|-
| 192.168.0.102
| -
| -
| -
| elab102
| -
| Lisbon
| Off
|
|-
| 192.168.0.103
| -
| -
| -
| elab103
| -
| Lisbon
| Off
|
|-
| 192.168.0.104
| -
| -
| -
| elab104
| -
| Lisbon
| Off
|
|-
| 192.168.0.105
| -
| -
| -
| elab105
| -
| Lisbon
| Off
|
|-
| 192.168.0.106
| -
| -
| -
| elab106
| -
| Lisbon
| Off
|
|-
| 192.168.0.150
| -
| -
| -
| elab150
| -
| Lisbon
| On
|
|-
| 192.168.0.151
| -
| -
| -
| elab151
| -
| Lisbon
| Off
|
|-
| 192.168.0.152
| -
| -
| -
| elab152
| -
| Lisbon
| Off
|
|-
| 192.168.0.153
| -
| -
| -
| elab153
| -
| Lisbon
| Off
|
|-
| 192.168.0.154
| -
| -
| -
| elab154
| -
| Lisbon
| Off
|
|-
| -
| -
| 10.7.0.1
| -
| elab1
| -
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.3
| -
| orionte_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.4
| -
| planetarium_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.5
| -
| espav_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.6
| -
| luanda_vpn
| World Pendulum
| Luanda
| Off
|
|-
| -
| -
| 10.7.0.7
| -
| ccvalg_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.8
| -
| elab_vpn???
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.9
| -
| ecb1_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.10
| -
| puc_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.11
| -
| ccvsintra_vpn
| World Pendulum
| Sintra
| Off
|
|-
| -
| -
| 10.7.0.12
| -
| epm_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.13
| -
| mola_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.16
| -
| saotome_vpn
| World Pendulum
| São Tomé
| Off
|
|-
| -
| -
| 10.7.0.17
| -
| mag3d_vpn
| mag3d
| Remote
| Off
|
|-
| -
| -
| 10.7.0.20
| -
| hidrostat_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.22
| -
| labIE2_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.24
| -
| WP-PRG
| World Pendulum
| Prague
| On
|
|-
| -
| -
| 10.7.0.25
| -
| bsb_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.26
| -
| puq_umag_vpn
| World Pendulum
| Remote
| Off
|
|-
| -
| -
| 10.7.0.27
| -
| vap_vpn
| World Pendulum
| Valparaíso
| Off
|
|-
| -
| -
| 10.7.0.28
| -
| bog_unad_vpn
| World Pendulum
| Bogotá
| Off
|
|-
| -
| -
| 10.7.0.29
| -
| bog_uniandes_vpn
| World Pendulum
| Bogotá (Uniandes)
| Off
|
|-
| -
| -
| 10.7.0.30
| -
| pty_utp_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.31
| -
| pty_usma_vpn
| World Pendulum
| Panama City
| Off
|
|-
| -
| -
| 10.7.0.32
| -
| WP-BCN
| World Pendulum
| Barcelona
| On
|
|-
| -
| -
| 10.7.0.33
| -
| WP-MRS
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.34
| -
| rio_puc2_vpn
| World Pendulum
| Rio de Janeiro
| Off
|
|-
| -
| -
| 10.7.0.35
| -
| WP-TAGUS
| World Pendulum
| IST Lisbon Taguspark
| On
|
|-
| -
| -
| 10.7.0.36
| -
| rai_vpn
| -
| Remote
| Off
|
|-
| -
| -
| 10.7.0.37
| -
| scl_vpn
| -
| ?
| Off
|
|-
| 192.168.0.11
| -
| 10.7.0.38
| -
| rpicavidade
| Cavidade
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:62:fe:ab
| WP-DIL
| World Pendulum
| Remote
| On
|
|-
| -
| -
| 10.7.0.39
| b8:27:eb:f4:7e:32
| WP-TAGUS
| World Pendulum
| Tagus
| On
|
|-
| -
| -
| 10.7.0.40
| -
| tagus_vpn
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.41
| -
| dev_vpn
| -
| Lisbon
| Off
|
|-
| 192.168.0.19
| 192.168.0.217
| 10.7.0.42
| d8:3a:dd:e0:a2:75
| elab
| Multi-Polarizer
| Lisbon
| On
|
|-
| -
| -
| 10.7.0.43
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.44
| -
| -
| -
| -
| Off
|
|-
| -
| -
| 10.7.0.45
| d8:3a:dd:e0:a2:87
| oeiras-elab
| Multi-Polarizer
| Oeiras
| On
|
|-
| -
| -
| 10.7.0.46
| d8:3a:dd:e3:4d:fe
| ictp
| Multi-Polarizer
| Trieste
| On
|
|-
| -
| -
| 200.128.66.240
| -
| ios
| -
| ?
| On
|
|}

[[MediaWiki:Flash]]
[[MediaWiki:Youtube]]
[[MediaWiki:CaixaLigacoes]]
[[MediaWiki:Links]]

Inclined Plane

2025-11-05T20:55:16Z

Ist12916: /* Advanced protocol */

==Experiment description==

The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally used to move heavy loads over vertical obstacles, such as ramps to move cargo.

Moving an object up on an inclined plane requires less force than lifting it vertically, as if we reduced gravity! This mechanical advantage, by which the force is reduced, is equal to the ratio between the length of the inclined surface and the height of the plane.

In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.

However, friction is an integral part of the mechanics of the problem. With this experiment, it is possible to determine the friction function through a multivariate analysis, adjusting a function that depends on the inclination of the rail. For this purpose, the experiment allows changing the descent angle and, through this, separating the frictional forces from the gravitational force, obtaining a value very close to 9,8 ms<sup>-2</sup>.

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: [http://elab.tecnico.ulisboa.pt Básico]
*Control Room: Inclined Plane
*Level: *

</div>
</div>

On purpose, this experiment uses a car equipped with a frontal windshield in order to exacerbate the effect of friction and demonstrate that its motion equation can be determined by multivariate analysis over several rides, for different inclinations.

[[File:PlanoInclinado.png|thumb| Inclined plane experience assembly where is easy to identify the necessary acoustic insulation to avoid spurious echoes that difficult the detection of the position by the sonar.|center|720px]]

===Experimental apparatus===

[[File:Promenor_Sonar.jpeg||thumb|General view of the experiment with the sonar at one end, after the collision collector spring. |right|border|288px]]

The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.

Initially the chute tilts to a position with a negative angle in order to collect and park the car at the origin, about 1.3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and, subsequently, the rail is raised to the pre-selected height. When it reaches that point, the electromagnet releases the car and it moves freely on the rail until it hits the spring. An ultrasonic detector collects position samples as a function of the elapsed time, allowing to trace the vehicle's trajectory during the fall and in its final damping.

==Protocol==
Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data, determine the speed and acceleration graphs. Compare the acceleration obtained value with gravity.

====Determination of speed as a function of distance traveled====
Based on the previous data, determine the speed as a function of the distance traveled eliminating the time in the previous graphs, that is, tracing the curve drawn by the speed pairs, distance for each available time.

====Determination of the spring restitution constant====
Depending on the various parables obtained in the vehicle's damping, determine the relative energy loss in each collision with the spring and determine the spring restitution constant.

===Advanced protocol===
As can be quickly inferred, the adjustment of the parabolic model to the movement produces a deviation that is only possible to understand with the inclusion of a friction term. In effect, the car has a front flap designed to induce a certain aerodynamic friction. By adapting the equations to include a rolling friction term (Cv, viscous, linear with velocity) and aerodynamic (Cx, quadratic dependence with velocity), a more accurate value for the acceleration of the vehicle can finally be determined. Usually the ''Cx'' only significantly influences the movement after 25 km/h.

The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles as the ''b'' term from the Coulomb friction as the same dimensions as gravity.

====Multivariate model====
The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a=b+c*v+d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.

When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.

====Strict determination of the spring restitution constant====
A brief analysis makes it possible to conclude that the spring restitution constant for the various strikes is affected by an appreciable error, which increases with the distance traveled, since the work carried out by the frictional force affects the calculation of the mechanical energy in each section of the movement. However, by calculating the work performed by the frictional force based on the frictional force equation determined by the previously described process, it is possible to correctly infer the mechanical energy before and after each impact, allowing to correctly calculate the spring restitution constant.

==Construction details==
[[File:ElectroIma.png||thumb| Car mooring electromagnet.|right|border|120px]]
The most curious component of this experience is the electromagnet who keeps the car safe in the launch position. This electromagnet can be built by wrapping enameled wire over a soft iron core or using an electromagnet extracted from a simple toaster!

Another innovation is the fact that the assembly is carried out on a tilting chute that simplifies the return of the car to the launch position. As it is necessary a reasonable inclination to overcome static friction, the impact on the fixing electromagnet is significant but can be resolved by placing a self-adhesive foam on both sides, between the mooring iron and the car.

==Links==

*[[Plano inclinado | Portuguese version (Versão em Português)]]

Inclined Plane

2025-11-05T20:46:14Z

Ist12916: /* Experiment description */

==Experiment description==

The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally used to move heavy loads over vertical obstacles, such as ramps to move cargo.

Moving an object up on an inclined plane requires less force than lifting it vertically, as if we reduced gravity! This mechanical advantage, by which the force is reduced, is equal to the ratio between the length of the inclined surface and the height of the plane.

In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.

However, friction is an integral part of the mechanics of the problem. With this experiment, it is possible to determine the friction function through a multivariate analysis, adjusting a function that depends on the inclination of the rail. For this purpose, the experiment allows changing the descent angle and, through this, separating the frictional forces from the gravitational force, obtaining a value very close to 9,8 ms<sup>-2</sup>.

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: [http://elab.tecnico.ulisboa.pt Básico]
*Control Room: Inclined Plane
*Level: *

</div>
</div>

On purpose, this experiment uses a car equipped with a frontal windshield in order to exacerbate the effect of friction and demonstrate that its motion equation can be determined by multivariate analysis over several rides, for different inclinations.

[[File:PlanoInclinado.png|thumb| Inclined plane experience assembly where is easy to identify the necessary acoustic insulation to avoid spurious echoes that difficult the detection of the position by the sonar.|center|720px]]

===Experimental apparatus===

[[File:Promenor_Sonar.jpeg||thumb|General view of the experiment with the sonar at one end, after the collision collector spring. |right|border|288px]]

The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.

Initially the chute tilts to a position with a negative angle in order to collect and park the car at the origin, about 1.3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and, subsequently, the rail is raised to the pre-selected height. When it reaches that point, the electromagnet releases the car and it moves freely on the rail until it hits the spring. An ultrasonic detector collects position samples as a function of the elapsed time, allowing to trace the vehicle's trajectory during the fall and in its final damping.

==Protocol==
Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data, determine the speed and acceleration graphs. Compare the acceleration obtained value with gravity.

====Determination of speed as a function of distance traveled====
Based on the previous data, determine the speed as a function of the distance traveled eliminating the time in the previous graphs, that is, tracing the curve drawn by the speed pairs, distance for each available time.

====Determination of the spring restitution constant====
Depending on the various parables obtained in the vehicle's damping, determine the relative energy loss in each collision with the spring and determine the spring restitution constant.

===Advanced protocol===
As can be quickly inferred, the adjustment of the parabolic model to the movement produces a deviation that is only possible to understand with the inclusion of a friction term. In effect, the car has a front flap designed to induce a certain aerodynamic friction. By adapting the equations to include a rolling friction term (linear with velocity) and aerodynamic (Cx, quadratic dependence with velocity), a more accurate value for the acceleration of the vehicle can finally be determined. Usually the ''Cx'' only significantly influences the movement after 25 km/h.

The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles.

====Multivariate model====
The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a=b+c*v+d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.

When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.

====Strict determination of the spring restitution constant====
A brief analysis makes it possible to conclude that the spring restitution constant for the various strikes is affected by an appreciable error, which increases with the distance traveled, since the work carried out by the frictional force affects the calculation of the mechanical energy in each section of the movement. However, by calculating the work performed by the frictional force based on the frictional force equation determined by the previously described process, it is possible to correctly infer the mechanical energy before and after each impact, allowing to correctly calculate the spring restitution constant.

==Construction details==
[[File:ElectroIma.png||thumb| Car mooring electromagnet.|right|border|120px]]
The most curious component of this experience is the electromagnet who keeps the car safe in the launch position. This electromagnet can be built by wrapping enameled wire over a soft iron core or using an electromagnet extracted from a simple toaster!

Another innovation is the fact that the assembly is carried out on a tilting chute that simplifies the return of the car to the launch position. As it is necessary a reasonable inclination to overcome static friction, the impact on the fixing electromagnet is significant but can be resolved by placing a self-adhesive foam on both sides, between the mooring iron and the car.

==Links==

*[[Plano inclinado | Portuguese version (Versão em Português)]]

Inclined Plane

2025-11-05T20:43:13Z

Ist12916: /* Experiment description */

==Experiment description==

The inclined plane is one of the six [https://pt.wikipedia.org/wiki/M%C3%A1quina_simples classic simple machines]. Inclined planes are generally used to move heavy loads over vertical obstacles, such as ramps to move cargo.

Moving an object up on an inclined plane requires less force than lifting it vertically, as if we reduced gravity! This mechanical advantage, by which the force is reduced, is equal to the ratio between the length of the inclined surface and the height of the plane.

In laboratory experiments that recreate this machine, when an air chute is not used in order to almost eliminate the rolling friction, the plane must have a significant slope so that the gravitational acceleration can be much higher than the friction, making it impossible for this experience to be carried out in a long time, perceptible to human senses.

However, friction is an integral part of the mechanics of the problem. With this experiment, it is possible to determine the friction function through a multivariate analysis, adjusting a function that depends on the inclination of the rail. For this purpose, the experiment allows changing the descent angle and, through this, separating the frictional forces from the gravitational force, obtaining a value very close to 9,8 ms<sup>-2</sup>.

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: [http://elab.tecnico.ulisboa.pt Básico]
*Control Room: Inclined Plane
*Level: *

</div>
</div>

Purposely, this experiment uses a car equipped with a frontal windshield in order to exacerbate the effect of friction and demonstrate that its equation can be determined by multivariate analysis of several rides, for different inclinations.

[[File:PlanoInclinado.png|thumb| Inclined plane experience assembly where is easy to identify the necessary acoustic insulation to avoid spurious echoes that difficult the detection of the position by the sonar.|center|720px]]

===Experimental apparatus===

[[File:Promenor_Sonar.jpeg||thumb|General view of the experiment with the sonar at one end, after the collision collector spring. |right|border|288px]]

The inclined plane of this experiment recreates this "reduction of gravity". It consists of a vehicle that moves on a track with adjustable inclination and that tilts at its midpoint. The height of the chute is measured at 1003 mm from the axis of the experiment.

Initially the chute tilts to a position with a negative angle in order to collect and park the car at the origin, about 1.3 m from the spring that will absorb the energy of its movement. The electromagnet immobilizes the car and, subsequently, the rail is raised to the pre-selected height. When it reaches that point, the electromagnet releases the car and it moves freely on the rail until it hits the spring. An ultrasonic detector then collects position samples as a function of the elapsed time, allowing to trace the vehicle's trajectory during the fall and in its final damping.

==Protocol==
Based on the pre-selected data in the experiment, obtain a graph of the position as a function of the elapsed time. Based on this data, determine the speed and acceleration graphs. Compare the acceleration obtained value with gravity.

====Determination of speed as a function of distance traveled====
Based on the previous data, determine the speed as a function of the distance traveled eliminating the time in the previous graphs, that is, tracing the curve drawn by the speed pairs, distance for each available time.

====Determination of the spring restitution constant====
Depending on the various parables obtained in the vehicle's damping, determine the relative energy loss in each collision with the spring and determine the spring restitution constant.

===Advanced protocol===
As can be quickly inferred, the adjustment of the parabolic model to the movement produces a deviation that is only possible to understand with the inclusion of a friction term. In effect, the car has a front flap designed to induce a certain aerodynamic friction. By adapting the equations to include a rolling friction term (linear with velocity) and aerodynamic (Cx, quadratic dependence with velocity), a more accurate value for the acceleration of the vehicle can finally be determined. Usually the ''Cx'' only significantly influences the movement after 25 km/h.

The adjustment of a friction function for the acceleration in the form ''a = b + c*v + d*v<sup>2</sup>'' allows to extract the local acceleration of gravity when using several sets of data for various angles.

====Multivariate model====
The multivariate analysis used serves to build a model of numerical adjustment for various angles to the various characteristics of the movement obtained. The variation of the angle makes it possible to distinguish the effect of gravity from the effect of rolling friction force, since this is considered independent of the angle. Thus, by making a ''a=b+c*v+d*v<sup>2</sup>'' type adjustment, the parameter ''b'' which implicitly deters the gravity and friction of the bearing (related to the mechanics of the vehicle) can be solved by separating it into ''b =g*sin(θ)+b<sub> friction </sub>''. The remaining parameters result from a model of the dependence of friction with speed. For high values of this (typically greater than 7-10 ms<sup>-1</sup>), friction has a strong quadratic dependence on speed - aerodynamic friction - but, in our case, we also have to consider the dependence on mechanical friction (''b<sub>atrito</sub>+c*v''), since the car departs from rest.

When performing this multivariate analysis, we are considering an independent association between the parameters, a necessary condition for these parameters to be part of a numerical model that will prove correct by the outcome of the adjustment. For this purpose, a numerical solver should be used, interactively adjusting the various covariates, such as that of the MSExcel.

====Strict determination of the spring restitution constant====
A brief analysis makes it possible to conclude that the spring restitution constant for the various strikes is affected by an appreciable error, which increases with the distance traveled, since the work carried out by the frictional force affects the calculation of the mechanical energy in each section of the movement. However, by calculating the work performed by the frictional force based on the frictional force equation determined by the previously described process, it is possible to correctly infer the mechanical energy before and after each impact, allowing to correctly calculate the spring restitution constant.

==Construction details==
[[File:ElectroIma.png||thumb| Car mooring electromagnet.|right|border|120px]]
The most curious component of this experience is the electromagnet who keeps the car safe in the launch position. This electromagnet can be built by wrapping enameled wire over a soft iron core or using an electromagnet extracted from a simple toaster!

Another innovation is the fact that the assembly is carried out on a tilting chute that simplifies the return of the car to the launch position. As it is necessary a reasonable inclination to overcome static friction, the impact on the fixing electromagnet is significant but can be resolved by placing a self-adhesive foam on both sides, between the mooring iron and the car.

==Links==

*[[Plano inclinado | Portuguese version (Versão em Português)]]

Content Management

2025-11-05T20:42:34Z

Ist12916: /* Basic Laboratory */

Welcome to the e-lab wiki. Here you can find all the consolidated documentation on the e-lab experiments.

IMPORTANT NOTE: We plan to migrate all elab laboratory to the new Framework for Remote Experiments in Education (FREE). Experiments will be gradually moved to this platform. The ''FREE experiments'' have a direct link in the list below.



=Introduction=
e-lab platform allows students to perform real experiments through the Internet.

Most the physical setup for the experiments is hosted at [http://www.ist.utl.pt/ Instituto Superior Técnico].
The experiment is controlled by the administrator, who is the top user at the end of the queue of all users. On special occasions the experiment administrator is a granted special rights when controlling an experiment, like a teacher who has booked the lab in advance. On such situations he can direct the experiment and all the students will share the data and graphics simultaneously, despite any physical distance.

The data and video feed from each experiment are captured by sensors and cameras, which are connected to a central server and then broadcasted to the subscribers through the internet.

Each '''control room''' is specific to each experiment and has its own page, where the user can find a protocol, suggestions for variations to the experience, as well as explanations and reviews of the data. There's a chat room in each control room, so that everyone can share and comment information about the experiments and the data analysis (results).

Control room, experimental apparatus, protocol and experimental setup are key concepts in e-lab:

* '''Control Room:''' virtual environment to control a real apparatus belonging to a laboratory.
* '''Experimental apparatus:''' equipment that allows performing certain experiments.
* '''Experimental setup:''' experimental apparatus configuration according to the protocol to be executed.
* '''Protocol:''' steps needed to carry out an experiment with a particular selection and configuration of the apparatus.

Users can send suggestions or reports of their own experiences to [mailto:wwwelab@ist.utl.pt this email].

You can also see the [[Sponsors]] that have made this project possible.

The [[World Pendulum]] project is a good example of our future plans.

=e-lab Experiments=
{{Launch}}
Before trying to launch ReC the application be sure to have installed JAVA and VLC and all security permissions set as state on our [[Add_e-lab_to_Java's_Security_Exception_Site_List | FAQ]]

==Basic Laboratory==
*[[Free Fall (determination of the standard gravity)]]
*[[Liquid Pressure Variation with Depth]]
*[[Inclined Plane]]
*[[Dice Statistics]]
*[[Hooke's law]]
*[[Boyle-Mariotte Law]]
*[[Determination of the Speed of Sound]]
*[[Linear Momentum Conservation]]
*[[Physical Pendulum]]
*[[World Pendulum]]
*[[Photovoltaic_panel|Photovoltaic panel]]

==Intermediate Laboratory==
*[[Thermal Conductivity of Metals]]
*[[Radiation Attenuation over Different Materials]]
*[[Weather Station]]
*[[Damped Pendulum Oscillations | Damped Pendulum]]
*[[Angular Momentum Conservation]]
*[[Pinhole Camera Optics]]
*[[Semi-cilinder Optical Behavior]]
*[[Magnetic field created by two wires]]
*[[Light Polarization]]
*[[Light Polarization with multiple polarizers]]
*[[Determination of Planck's Constant]]

==Advanced Laboratory==
*[[Acoustic Standing Waves]]
*[[Determination of the Adiabatic Constant]]
*[[Propagation of Solitons]] (under construction)
*[[Dielectric effect in a Cilindric Capacitor]]
*[[Paschen Curve]]
*[[Langmuir Probe]]
*[[Microwave plasma cavity]]

=Tools=
[[file: TrackerTrajectoryCapture.png | Exemplo dum ajuste à trajectória de um dos pendulos mundiais efectuado com recurso ao Tracker|thumb|320px]]
*[[FAQ.en]]
*[[Fitteia]]
*[http://www.codecogs.com/latex/eqneditor.php Online LaTeX Editor]
*[http://www.cabrillo.edu/~dbrown/tracker/ Tracking movie software]
*[[Main Page|Experiments list]]

The apparatus videos, in some relevant cases, are streamed at 640x480 resolution in order to allow the analysis of trajectories with appropriate software, for example the [https://physlets.org/tracker/ Tracker].

=Additional info=
*[[Publications]]
*[[Hall of fame]]
*[[Como instalar o Java | How to install JAVA]]
*[[Executar o e-lab a partir da command prompt |e-lab from the command prompt]]
*[[Add e-lab to Java's Security Exception Site List]]
*[[Training]]

=Licensing=
<html>
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Licença Creative Commons" style="border-width:0" src="http://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />This wiki and related material accessed by the e-lab portal has been release by <a xmlns:cc="http://creativecommons.org/ns#" href="www.e-lab.ist.eu" property="cc:attributionName" rel="cc:attributionURL">www.e-lab.ist.eu</a> is licensed under the <a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/">Creative Commons Atribuição-Partilha nos termos da mesma licença 4.0 Internacional License</a>.
</html>

Determination of the Adiabatic Constant

2025-10-22T10:36:38Z

Ist12916: /* Theoretical Principles */

=Description of the Experiment=
The purpose of this experiment is the determination of the ratio between the specific heat of air (constant pressure and constant volume), through the use of adiabatic oscillations of an embolus of known dimensions.

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Video: rtsp://elabmc.ist.utl.pt:554/gamma.sdp
*Laboratory: Advanced in e-lab.ist.eu[http://e-lab.ist.eu]
*Control room: Cp/Cv
*Level: ****

</div>
</div>

{{#ev:youtube|BWd4R-ud81I|Slow motion video of the piston performing the damped oscillation motion.|center}}

=Experimental Apparatus=
The apparatus is composed of a syringe, which embolus weighs 26.4 gram and has a diameter of 18.9 mm. The embolus has reduced friction due to graphite lubrication and the fact that the apparatus is in the vertical position.

=Protocol=
Ruchhardt’s method (see bellow) is a way to determine the specific heat of a gas in a very precise way, but it is very sensitive to the measurement of the oscillations period. Because of this, extra care in this measurement is recommended and thus, two methods are used to determine this quantity: the waveform recorded by the pressure transducer and the average period, digitally determined. The data must be used judiciously, exploring all the information that it can give.
After a reference volume is selected, the embolus is agitated so that it oscillates freely around the equilibrium position.
$ \gamma $ can be inferred from the oscillation period.

=Advanced Protocol=
By redoing the experiment for several volumes, a better adjustment can be achieved between the experimental data and the theoretical function. When adjusting the experimental data, allowing the parameter $ \gamma $ to be free as well as the volume and pressure, the measure precision can be increased, since atmospheric pressure can have variations of up to 1% and because the volume measured will have a systematic error due to the various external connections to the syringe. It should be noted that the piston mass and the diameter have a 0.5% precision.

=Data Analysis=
By using [[Fitteia]], you can plot the experimental results and adjust a theoretical function with certain parameters. This [http://www.elab.tecnico.ulisboa.pt/anexos/2012outros/gamma.sav file] is an example of a fit of this experiment (right-click on the link and "Save As").

=Theoretical Principles=
With this method, it is possible to determine the ration between the specific heat of a gas through experimentation. If the gas in study is the atmospheric air (mostly diatomic), this ratio should be 1.4.

<div class="toccolours mw-collapsible mw-collapsed" style="width:600px">
'''Ruchhardt's Method'''
<div class="mw-collapsible-content">

If we consider a piston without friction, oscillating freely in a cylinder of volume $ V_0 $, with pressure $ p $, then the force exerted upon the piston ( $ m \ddot{y} $ ) equals the force of gravity minus the variation of pressure upon the piston( $ A \Delta p $ ).

<math>
-mg+A \Delta p = m \ddot{y}
</math>

The variation of pressure for small oscillations in volume is:

<math>
\Delta p = \frac{\partial p}{\partial V} | _{V = V_0}\Delta V
</math>

if we consider a fast enough process so that no exchange in heat occurs (adiabatic process)

<math>
pV^{\gamma} = p_0 V_0 ^{\gamma}, \quad p = \frac{ p_0 V_0 ^{\gamma} }{ V^{\gamma} }
</math>

From the above equation we have:

<math>
\frac{\partial p}{\partial V} | _{V = V_0} = - \gamma \frac{ p_0 V_0 ^{\gamma} }{ V^{\gamma +1} } | _{V = V_0} = - \gamma \frac{p_0}{V_0}
</math>

and

<math>
-mg+ A (- \gamma \frac{p_0}{V_0} \Delta V) = m \ddot{y} , \text{ where } \Delta V = Ay
</math>

simplifying

<math>
\ddot{y} + \gamma \frac{p_0 A^2}{m V_0} y+g = 0
</math>

We make

<math>
\gamma \frac{p_0 A^2}{m V_0} = \omega ^2, \text{ so that } \ddot{y} + \omega ^2 y + g = 0
</math>

Changing the point of origin to the equilibrium position of the piston, we can easily see that this is the equation for the motion of a frictionless harmonic oscillator

<math>
\ddot{y}' + \omega ^2 y' = 0 \text{ with } y = y' - \frac{g}{\omega ^2} \text{ and } \omega ^2 = (\frac{2 \pi}{T})^2 = \gamma \frac{p_0 A^2}{m V_0}
</math>

Measuring the oscillation period, $ T $, we can determine $ \gamma $

<math>
\gamma = \frac{4mV_0}{p_0 r^4 T^2}
</math>

where $ r $ is the cylinder radius.
A more precise estimation can be achieved using the differential equation considering the dumping effect caused by friction. Is such a situation you could consider friction being proportional to velocity leading to:

<math>
\ddot{y} + 2\lambda\omega \dot{y}+\omega ^2 y + g = 0
</math>
Considering again the change in the origin, the result of such an equation leads to:

<math>
y' = y'_{0} e^{-\lambda \omega t}cos( \sqrt{1 - \lambda^2}\omega t + \phi)
</math>

where the period leads to a slight correction due to the dumping factor.
</div>
</div>

=Links=
*[[Determinação da Constante Adiabática do Ar | Portuguese version (Versão em Português)]]
*[[Détermination de la constante adiabatique d'air | French version (version française)]]

Determination of the Adiabatic Constant

2025-10-22T10:33:14Z

Ist12916: /* Theoretical Principles */

=Description of the Experiment=
The purpose of this experiment is the determination of the ratio between the specific heat of air (constant pressure and constant volume), through the use of adiabatic oscillations of an embolus of known dimensions.

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Video: rtsp://elabmc.ist.utl.pt:554/gamma.sdp
*Laboratory: Advanced in e-lab.ist.eu[http://e-lab.ist.eu]
*Control room: Cp/Cv
*Level: ****

</div>
</div>

{{#ev:youtube|BWd4R-ud81I|Slow motion video of the piston performing the damped oscillation motion.|center}}

=Experimental Apparatus=
The apparatus is composed of a syringe, which embolus weighs 26.4 gram and has a diameter of 18.9 mm. The embolus has reduced friction due to graphite lubrication and the fact that the apparatus is in the vertical position.

=Protocol=
Ruchhardt’s method (see bellow) is a way to determine the specific heat of a gas in a very precise way, but it is very sensitive to the measurement of the oscillations period. Because of this, extra care in this measurement is recommended and thus, two methods are used to determine this quantity: the waveform recorded by the pressure transducer and the average period, digitally determined. The data must be used judiciously, exploring all the information that it can give.
After a reference volume is selected, the embolus is agitated so that it oscillates freely around the equilibrium position.
$ \gamma $ can be inferred from the oscillation period.

=Advanced Protocol=
By redoing the experiment for several volumes, a better adjustment can be achieved between the experimental data and the theoretical function. When adjusting the experimental data, allowing the parameter $ \gamma $ to be free as well as the volume and pressure, the measure precision can be increased, since atmospheric pressure can have variations of up to 1% and because the volume measured will have a systematic error due to the various external connections to the syringe. It should be noted that the piston mass and the diameter have a 0.5% precision.

=Data Analysis=
By using [[Fitteia]], you can plot the experimental results and adjust a theoretical function with certain parameters. This [http://www.elab.tecnico.ulisboa.pt/anexos/2012outros/gamma.sav file] is an example of a fit of this experiment (right-click on the link and "Save As").

=Theoretical Principles=
With this method, it is possible to determine the ration between the specific heat of a gas through experimentation. If the gas in study is the atmospheric air (mostly diatomic), this ratio should be 1.4.

<div class="toccolours mw-collapsible mw-collapsed" style="width:600px">
'''Ruchhardt's Method'''
<div class="mw-collapsible-content">

If we consider a piston without friction, oscillating freely in a cylinder of volume $ V_0 $, with pressure $ p $, then the force exerted upon the piston ( $ m \ddot{y} $ ) equals the force of gravity minus the variation of pressure upon the piston( $ A \Delta p $ ).

<math>
-mg+A \Delta p = m \ddot{y}
</math>

The variation of pressure for small oscillations in volume is:

<math>
\Delta p = \frac{\partial p}{\partial V} | _{V = V_0}\Delta V
</math>

if we consider a fast enough process so that no exchange in heat occurs (adiabatic process)

<math>
pV^{\gamma} = p_0 V_0 ^{\gamma}, \quad p = \frac{ p_0 V_0 ^{\gamma} }{ V^{\gamma} }
</math>

From the above equation we have:

<math>
\frac{\partial p}{\partial V} | _{V = V_0} = - \gamma \frac{ p_0 V_0 ^{\gamma} }{ V^{\gamma +1} } | _{V = V_0} = - \gamma \frac{p_0}{V_0}
</math>

and

<math>
-mg+ A (- \gamma \frac{p_0}{V_0} \Delta V) = m \ddot{y} , \text{ where } \Delta V = Ay
</math>

simplifying

<math>
\ddot{y} + \gamma \frac{p_0 A^2}{m V_0} y+g = 0
</math>

We make

<math>
\gamma \frac{p_0 A^2}{m V_0} = \omega ^2, \text{ so that } \ddot{y} + \omega ^2 y + g = 0
</math>

Changing the point of origin to the equilibrium position of the piston, we can easily see that this is the equation for the motion of a frictionless harmonic oscillator

<math>
\ddot{y}' + \omega ^2 y' = 0 \text{ with } y = y' - \frac{g}{\omega ^2} \text{ and } \omega ^2 = (\frac{2 \pi}{T})^2 = \gamma \frac{p_0 A^2}{m V_0}
</math>

Measuring the oscillation period, $ T $, we can determine $ \gamma $

<math>
\gamma = \frac{4mV_0}{p_0 r^4 T^2}
</math>

where $ r $ is the cylinder radius.
A more precise estimation can be achieved using the differential equation considering the dumping effect caused by friction. Is such a situation you could consider friction being proportional to velocity leading to:
<math>
\ddot{y} + 2\lambda\omega \dot{y}+\omega ^2 y + g = 0
</math>
Considering again the change in the origin, the result of such an equation leads to:
<math>
y' = y'_{0} e^{-\lambda \omega t}cos( \sqrt{1 - \lambda^2}\omega t + \phi)
</math>
where the period leads to a slight correction due to the dumping factor.
</div>
</div>

=Links=
*[[Determinação da Constante Adiabática do Ar | Portuguese version (Versão em Português)]]
*[[Détermination de la constante adiabatique d'air | French version (version française)]]

Light Polarization with multiple polarizers

2025-08-20T14:51:06Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Trieste (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1
|-
| 2 || 44.3 ± 1 || 33.5 ± 1
|-
| 3 || 34.6 ± 1 || 34.2 ± 1
|-
| 4 || 41.0 ± 1 || 34.9 ± 1
|-
| 5 || 39.2 ± 1 || 35.6 ± 1
|}

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Microwave plasma cavity

2025-07-04T08:01:41Z

Ist12916: /* Spectrometer */

=Description of the Experiment=
[[File:MicrowaveResonantCavity_withCoils.png|229|thumb|Fig. 1 - Experimental setup with the Helmholtz coils assembled]]

Plasmas are inseparable from radio-frequency studies. Effectively the most basic properties of a plasma is derived from its plasma frequency, ''ω<sub>pe</sub>''. As such, combining plasma physics studies with electromagnetic (EM) wave propagation is a challenging matter for physics with great advances achieved last century before space conquest due to the necessity of wave reflections on the ionosphere for long range communication.
An electromagnetic cavity poses a good opportunity to understand the behavior of EM standing waves and how free charges in a plasma affects its resonant frequency and quality factor, interlinking the properties of matter with wave propagation.

<div class="toccolours mw-collapsible mw-collapsed" style="width:380px">
'''Links'''
<div class="mw-collapsible-content">


*Laboratory: Advanced
*Control room: [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/3/3 Microwave cavity]
*Level: ****

</div>
</div>

WARNING: Due to overuse sometimes the experiment can lack on gas. Please be aware that if you can't reach a suitable pressure for a given injection time use a different gas or contact us by email to elab (at) tecnico.ulisboa.pt (if you are human you will find out the email :-).

==Experimental Apparatus==
A microwave cavity refers to a volume enclosed by a conducting surface which can store electromagnetic (EM) energy. It can be thought of as the microwave analog of an LC circuit, albeit with multiple resonance frequencies and much larger quality factors. Three main processes govern the energy losses in a cavity: conduction losses in the cavity walls, conduction loss in the dielectric material filling the cavity, and losses through access ports or holes in the conducting surface. In the first-order approximation, these losses cause the same resonance peak broadening as the resistivity losses in an RLC circuit, causing both a resonance frequency shift and a decrease in the quality factor.

Two types of resonant modes occur in electromagnetic cavities: transverse-electric modes (TE) and transverse-magnetic modes (TM). In the TE (TM) modes, the electric (magnetic) field lines are transverse to the longitudinal direction.

A comprehensive derivation of all the resonant modes of a cavity is available in chapter 6 of the book by David Pozar~\cite{Pozar2011}. In a cylindrical cavity filled by a homogeneous and isotropic medium, the resonant frequencies of the TM modes are:

\begin{equation}
f_{nml}=\frac{c}{2\pi\sqrt{\mu_r\epsilon_r}}\sqrt{\left(\frac{p_{nm}}{a}\right)^2+\left(\frac{l\pi}{d}\right)^2},
\label{eq:resonant-frequency}
\end{equation}

A detailed description of the cavity and all apparatus in place can be found in the paper [[:File:Resonant_cavity_final.pdf | "An accessible microwave cavity experiment for plasma density determination"]].

===Discharge chamber===
The present cavity is made of copper covered with a tiny surface of nickel to protect it against corrosion. A Cold Cathode Fluorescent Light (CCFL) inverter serves as a current source to generate a Penning discharge inside the cavity~\cite{Knauer1962}. The inverter converts a 12~V DC input to 1~kV/50kHz AC output which is applied to both the electrodes inside the cavity. This electrodes are basically an aluminum meshes and are electrically insulated from the cylinder's lateral surface and close the extremes of the cylinder (see figure). This configuration ensures that the discharge permeates the entire cavity uniformly. The CCFL inverter managed to sustain discharges with working gas pressures between ~10 and ~300Pa.
The schematic in figure depicts the resonant cavity used in this experiment. The copper cylinder have a width of 64 mm diameter and 50 mm length. The cylinder bases consist of an aluminum mesh with a spacing inferior to one-tenth of the microwave wavelength used in the experiment. A spring bolted to the opposite side to the vacuum window holds the mesh in place, as shown in next figure. The whole cavity lies between two Helmholtz coils that generate a magnetic field of 1.4~mT per Ampere, up to the~maximum current of ~18A.

Two loop antennas lie in the middle of the cylinder wall opposite to each other. The antennas have a 4~mm radius with their axis coincident with the magnetic field line of highest intensity, the TM<sub>010</sub> mode.
One of the antennas injects the microwaves in the cavity, and the other antenna collects the propagated signal. A observed resonance is expected close to a frequency of 3560~MHz (see figure).

===Vacuum and gas injection setup===
The chamber is kept under vacuum by a rotary pump that can reach pressures of the order of 2 to 5Pa. The pump drives a common-rail primary vacuum distribution system. The rail connection is done by a solenoid valve, allowing for the isolation during the experiment.

The working gas flows into the chamber through another solenoid valve equipped with a capillary injector which allows to save gas usage. It is possible to select a working pressure by adjusting the valve inflow controlling carefully the opening time window. This setup has a injection rail feed by three different working gases: helium, nitrogen and argon.

===Spectrum analyzer===
To generate and receive the microwaves passing through the cavity, we used the
inexpensive ARNIST SSA-TG R2 spectrum analyzer. The device has a frequency
range from 35 to 4500 MHz with the resolution of 200 kHz. The
analyzer sweeps the frequency spectrum measuring the attenuation (in dBm) for each
frequency. As the generated signal for

The required number of spectra are retrieved allowing the identification and changes in the resonant frequency and Q-factor by online visualization .

===Spectrometer===
Spectroscopy is a fundamental tools for diagnosing plasmas. Specifically, optical emission spectroscopy (OES) analyzes the light emitted by excited atoms or ions as they return to lower energy states. Each element emits light at several
specific, well-defined wavelengths, known as spectral lines, which serve as fingerprints for their identification.

The role of spectroscopy in the electromagnetic cavity experiment includes:

• Element identification: Detecting and confirming the presence the selected gas based on their strongest emission lines.
• Impurity detection: Identifying unwanted elements in the discharge (e.g., O, H, or N contamination).

The spectrometer is based on the optical architecture of the Czerny-Turny Monochromator with a diffraction grating with a CCD device in place of the exit slit. It operate in the UV/VIS/NIR allowing users to acquire real-time spectra between density samples. Nevertheless light may be attenuated by the fiber and specially by the plexiglass window.

Note that you have two basic settings: gain and integration time. The first relates to the electronic nature of the sensor device and is basically amplifier gain with direct impact in noise. The integration time must be adjusted to maximize the signal-to-noise ratio of the measurements. By experimenting with different settings, a trade-off between this two settings shall be found based desired signal amplitude, maximizing peaks to the order of 60k. The amplifier gain must be used to make up for the lack of signal (light intensity) in the measurements. Notice once more that increasing the gain also increases the noise floor, which lowers the dynamic range of the sensor. Another aspect related to the CCD device is the existence of a dark current, i.e., a signal that is output even with no light in the input of the device, and phenomena like read-out noise or sensor patterns/artifacts. Dark current in particular must be accounted for so that the faintest signals are separable from noise.

The second noteworthy aspect is the fact that the radiation must go through a series of optical elements before it reaches the CCD device. Therefore, only wavelengths transmitted by all these elements will be able to reach the CCD sensor on the spectrometer. In this particular setup, the transmittance of the acrylic glass the lens looks through is the most limiting factor. Common acrylic glass is opaque to wavelengths lower than ∼400nm, therefore signal level at these wavelengths will be noticeably lower than for the rest of the range (is it verifiable?).

Please refer to NIST database for spectral lines identification.

=Protocol=
This experiment allow to determine the impact on plasma density by: (i) the influence of different atomic and molecular particles structures in the plasma generation, (ii) the effect produced by magnetic confinement and (iii) various background pressure. All this three parameters are prone to be tuned in the experiment interface.
very
''Note that after being not used for a long time, the firsts readings may be misleading due to wall impurities, a few experiments have to be conduced in order to validate the results.''

=Data Analysis=
[[File:Cavity frequency shift.png|240|thumb| Expected drift in frequency when plasma is generated inside the chamber.]]

The experiment return a sequence of power spectra selected by the user, usually around the first cavity's TM mode. Due to noise and because a precise value for the peak frequency is desired, the peak central frequency should be measured taking the half-difference at -3bd. Actually, the imaginary cut at -3db intercepts the spectrum's characteristic in a steeper section of the curve, allowing for a better determination.
As the plasma RF generator induces some noise due to spiky effects on the electrodes (small arching spots), eventually a low-pass data filtering shall be conducted prior to extract the peak and broadness, the later for the quality factor (Q) determination.

Assuming that the resonance frequency shift ''Δf'' caused by the plasma is small with respect to the vacuum resonance frequency ''f<sub>010</sub>'', the plasma electron density with respect to ''Δf'' is given by:

\begin{equation}
n_e = \frac{8\pi^2m_e\epsilon_0}{e^2}f_{010}\Delta f.
\label{eq:freq-shift}
\end{equation}

If an external magnetic field is present, this equation is only valid as long as the electric field of the mode is parallel to the external magnetic field. This approximation further assumes that the plasma does not change the shape of the mode's electric field.

Nevertheless, when an external magnetic field is applied and due to confinement, it is visually clearly seen that the plasma stays aside from the walls leading to a reduced effective chamber diameter filled with plasma. Three values of magnetic field are available to study this effect (0T, 20mT, 25mT).

Expected results are presented in the figure. Several types of experiments can be conducted by selecting different pressures and gases (plasma color should always be checked in the webcam to confirm the correct gas being injected).

=Links=

Microwave plasma cavity

2025-07-03T08:02:03Z

Ist12916: /* Experimental Apparatus */

=Description of the Experiment=
[[File:MicrowaveResonantCavity_withCoils.png|229|thumb|Fig. 1 - Experimental setup with the Helmholtz coils assembled]]

Plasmas are inseparable from radio-frequency studies. Effectively the most basic properties of a plasma is derived from its plasma frequency, ''ω<sub>pe</sub>''. As such, combining plasma physics studies with electromagnetic (EM) wave propagation is a challenging matter for physics with great advances achieved last century before space conquest due to the necessity of wave reflections on the ionosphere for long range communication.
An electromagnetic cavity poses a good opportunity to understand the behavior of EM standing waves and how free charges in a plasma affects its resonant frequency and quality factor, interlinking the properties of matter with wave propagation.

<div class="toccolours mw-collapsible mw-collapsed" style="width:380px">
'''Links'''
<div class="mw-collapsible-content">


*Laboratory: Advanced
*Control room: [https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/3/3 Microwave cavity]
*Level: ****

</div>
</div>

WARNING: Due to overuse sometimes the experiment can lack on gas. Please be aware that if you can't reach a suitable pressure for a given injection time use a different gas or contact us by email to elab (at) tecnico.ulisboa.pt (if you are human you will find out the email :-).

==Experimental Apparatus==
A microwave cavity refers to a volume enclosed by a conducting surface which can store electromagnetic (EM) energy. It can be thought of as the microwave analog of an LC circuit, albeit with multiple resonance frequencies and much larger quality factors. Three main processes govern the energy losses in a cavity: conduction losses in the cavity walls, conduction loss in the dielectric material filling the cavity, and losses through access ports or holes in the conducting surface. In the first-order approximation, these losses cause the same resonance peak broadening as the resistivity losses in an RLC circuit, causing both a resonance frequency shift and a decrease in the quality factor.

Two types of resonant modes occur in electromagnetic cavities: transverse-electric modes (TE) and transverse-magnetic modes (TM). In the TE (TM) modes, the electric (magnetic) field lines are transverse to the longitudinal direction.

A comprehensive derivation of all the resonant modes of a cavity is available in chapter 6 of the book by David Pozar~\cite{Pozar2011}. In a cylindrical cavity filled by a homogeneous and isotropic medium, the resonant frequencies of the TM modes are:

\begin{equation}
f_{nml}=\frac{c}{2\pi\sqrt{\mu_r\epsilon_r}}\sqrt{\left(\frac{p_{nm}}{a}\right)^2+\left(\frac{l\pi}{d}\right)^2},
\label{eq:resonant-frequency}
\end{equation}

A detailed description of the cavity and all apparatus in place can be found in the paper [[:File:Resonant_cavity_final.pdf | "An accessible microwave cavity experiment for plasma density determination"]].

===Discharge chamber===
The present cavity is made of copper covered with a tiny surface of nickel to protect it against corrosion. A Cold Cathode Fluorescent Light (CCFL) inverter serves as a current source to generate a Penning discharge inside the cavity~\cite{Knauer1962}. The inverter converts a 12~V DC input to 1~kV/50kHz AC output which is applied to both the electrodes inside the cavity. This electrodes are basically an aluminum meshes and are electrically insulated from the cylinder's lateral surface and close the extremes of the cylinder (see figure). This configuration ensures that the discharge permeates the entire cavity uniformly. The CCFL inverter managed to sustain discharges with working gas pressures between ~10 and ~300Pa.
The schematic in figure depicts the resonant cavity used in this experiment. The copper cylinder have a width of 64 mm diameter and 50 mm length. The cylinder bases consist of an aluminum mesh with a spacing inferior to one-tenth of the microwave wavelength used in the experiment. A spring bolted to the opposite side to the vacuum window holds the mesh in place, as shown in next figure. The whole cavity lies between two Helmholtz coils that generate a magnetic field of 1.4~mT per Ampere, up to the~maximum current of ~18A.

Two loop antennas lie in the middle of the cylinder wall opposite to each other. The antennas have a 4~mm radius with their axis coincident with the magnetic field line of highest intensity, the TM<sub>010</sub> mode.
One of the antennas injects the microwaves in the cavity, and the other antenna collects the propagated signal. A observed resonance is expected close to a frequency of 3560~MHz (see figure).

===Vacuum and gas injection setup===
The chamber is kept under vacuum by a rotary pump that can reach pressures of the order of 2 to 5Pa. The pump drives a common-rail primary vacuum distribution system. The rail connection is done by a solenoid valve, allowing for the isolation during the experiment.

The working gas flows into the chamber through another solenoid valve equipped with a capillary injector which allows to save gas usage. It is possible to select a working pressure by adjusting the valve inflow controlling carefully the opening time window. This setup has a injection rail feed by three different working gases: helium, nitrogen and argon.

===Spectrum analyzer===
To generate and receive the microwaves passing through the cavity, we used the
inexpensive ARNIST SSA-TG R2 spectrum analyzer. The device has a frequency
range from 35 to 4500 MHz with the resolution of 200 kHz. The
analyzer sweeps the frequency spectrum measuring the attenuation (in dBm) for each
frequency. As the generated signal for

The required number of spectra are retrieved allowing the identification and changes in the resonant frequency and Q-factor by online visualization .

===Spectrometer===
Spectroscopy is a fundamental tools for diagnosing plasmas. Specifically, optical emission spectroscopy (OES) analyzes the light emitted by excited atoms or ions as they return to lower energy states. Each element emits light at several
specific, well-defined wavelengths, known as spectral lines, which serve as fingerprints for their identification.

The role of spectroscopy in the electromagnetic cavity experiment includes:

• Element identification: Detecting and confirming the presence the selected gas based on their strongest emission lines.
• Impurity detection: Identifying unwanted elements in the discharge (e.g., O, H, or N contamination).

The spectrometer operate in the UV/VIS/NIR allowing users to acquire real-time spectra between density samples. Nevertheless light may be attenuated by the fiber and specially by the plexiglass window.

Please refer to NIST database for spectral lines identification.

=Protocol=
This experiment allow to determine the impact on plasma density by: (i) the influence of different atomic and molecular particles structures in the plasma generation, (ii) the effect produced by magnetic confinement and (iii) various background pressure. All this three parameters are prone to be tuned in the experiment interface.
very
''Note that after being not used for a long time, the firsts readings may be misleading due to wall impurities, a few experiments have to be conduced in order to validate the results.''

=Data Analysis=
[[File:Cavity frequency shift.png|240|thumb| Expected drift in frequency when plasma is generated inside the chamber.]]

The experiment return a sequence of power spectra selected by the user, usually around the first cavity's TM mode. Due to noise and because a precise value for the peak frequency is desired, the peak central frequency should be measured taking the half-difference at -3bd. Actually, the imaginary cut at -3db intercepts the spectrum's characteristic in a steeper section of the curve, allowing for a better determination.
As the plasma RF generator induces some noise due to spiky effects on the electrodes (small arching spots), eventually a low-pass data filtering shall be conducted prior to extract the peak and broadness, the later for the quality factor (Q) determination.

Assuming that the resonance frequency shift ''Δf'' caused by the plasma is small with respect to the vacuum resonance frequency ''f<sub>010</sub>'', the plasma electron density with respect to ''Δf'' is given by:

\begin{equation}
n_e = \frac{8\pi^2m_e\epsilon_0}{e^2}f_{010}\Delta f.
\label{eq:freq-shift}
\end{equation}

If an external magnetic field is present, this equation is only valid as long as the electric field of the mode is parallel to the external magnetic field. This approximation further assumes that the plasma does not change the shape of the mode's electric field.

Nevertheless, when an external magnetic field is applied and due to confinement, it is visually clearly seen that the plasma stays aside from the walls leading to a reduced effective chamber diameter filled with plasma. Three values of magnetic field are available to study this effect (0T, 20mT, 25mT).

Expected results are presented in the figure. Several types of experiments can be conducted by selecting different pressures and gases (plasma color should always be checked in the webcam to confirm the correct gas being injected).

=Links=

Light Polarization with multiple polarizers

2025-06-17T14:58:45Z

Ist12916: /* Advanced protocol */

=Description of the Experiment=
[[File:CascadePolarizersTopView.jpeg|thumb|Fig. 1 - Experimental setup showing (A) at the bottom the polarized light source, (B) the main body with a set of five cascaded polarizers, (C) on the left and right the servo-motors, and (D) on the top, the photodetector.]]

This experiment allows you to select the orientation up to five polarizers to interact with a source of polarize light from a red LED, ultimately measuring the incident power on a photocell. As such, the cascade of polarizers can be used to demonstrate the Malus law (classical electromagnetic theory) but as well the quantum explanation when it comes to a pile-up of single photons.

Polarizers have the property of absorbing the wave in one direction on that plane and remaining "transparent" in the other direction, such as "Polaroid" lenses. In the quantum interpretation, each polarizers acts as a measuring sensor as a single photon either passes or are absorbed by the medium, as described in the thought experiments of Dirac n-polarizers for the understanding the principle of quantum state superposition.

The aim of this experiment is to demonstrate the effect of light passing through those polarizers by interposing them in the light optical path at various angles defined by the user. For judicious angles, some counter intuitive results emerge...

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Links'''
<div class="mw-collapsible-content">

*Laboratory: Intermediate [http://elab.tecnico.ulisboa.pt elab.tecnico.ulisboa.pt]
*Control Room: Multi-Polarizer
*Grade: **

</div>
</div>

==Who likes this idea==

[[File:IYQST2025 IUPAP Logo.png|border|180px|link=https://quantum2025.org]]
[[File:LogoSPF long.jpg|border|180px|link=https://fisica-materia-condensada.spf.pt/IYQ2025]]
[[File:IUPAP_Logo.png|border|240px]]
[[File:Logo_quantum-uc_azul_n.png|border|180px]]
[[File:Oeiras_Valey_logo_cor_preto.direta.png|border|240px]]
[[File:UESC-logo.jpg|border|111px]]


=Experimental Apparatus=
The apparatus consists on a light source (high bright red LED) passing a collimator, which focuses then the light rays into a parallel beam of light. At the beginning of the optical path, a vertical light polarizer is interposed, creating a source of polarized light.

In the optical path, the light travels through several polarized lenses without graduation, having the angle of the first been preset and being the other one free to rotate around the axis of propagation.

The light is finally collected through a converging lens into a photo-diode that measures the incident radiation intensity. This intensity is obviously the result of attenuation introduced by polarizing systems brought into its optical path.

A detailed description is available on a [[Multiple polarizers experimental apparatus|special page with instructions]] for the construction and assembly of this 3D printed experiment.

=Protocol=
In this control room we can measure the attenuation of a light beam caused by the cross-rotation of up to five polarized lenses. The light source is previously polarized.

The supervisor of the experiment can choose two sweep limits for one polarizer and set the angle of the other polarizers, acquiring the value of the transmitted power in a photo-diode.

The resolution (angle increment between two samples) is given by the step-motor minimum angle (1/200=1.8º) times the de-multiplication factor of the transmission, 1/5, giving 0.36º.

The LED power can be adjusted in order to have a broad resolution, be sure to select the appropriate power in order to avoid the non-linear region of the photo-diode circuit. Sometimes ''less is more''.

= Advanced protocol =
The experience allows to be performed with starting with polarized light. Selecting this option the user can check the Malus's law in which multiple polarizers are used. In such case we need to multiply all the squares of the cosines between themselves, so the final value of the attenuation equation became:

<math>
I_s = I_a \prod cos ^ 2 (\alpha_i)
</math>

were $ \alpha_i $ are the successive polarizers angles and $I_a$ the initial light intensity.

In the case where two of the polarizers are at 90º between them, but the one between them is at an angle α, the sequential application of Malus' law leads to the following:

<math>
I_s=I_a (cos (\alpha_i)cos(90-\alpha_i))^2=I_a (cos (\alpha_i)sen(\alpha_i))^2=\frac{I_a}{4}sen^2(2\alpha)
</math>

A paradox can arise from this, since if we have two polarizers at 90º no light will pass through, but by introducing a third polarizer between them at a proper angle such as 45º we already get light through the system, which will emerge attenuated (by 25% for 45º)!

Nonetheless, the interpretation of this phenomenon of the "repolarization" of light <ref "3Polarizers>https://www.informationphilosopher.com/solutions/experiments/dirac_3-polarizers/ </ref> necessarily has a [[Quantum interpretation of three polarizers | quantum interpretation ]] in the limit of a single photon. In this limit, the proposed experiment of the three consecutive polarizers can lead to a very interesting conclusion.

Note that every polarizer can have a systematic error. In the following table we provide a first clue of such angles, measured during assembly. Nevertheless a proper fit taking in consideration those errors can lead to a better estimation of the results.

{| class="wikitable" style="margin:auto"li
|+ Polarizers calibration angles for maximum transmission
|-
| Polarizer order|| @Lisbon (º) ||@Oeiras (º)
|-
| 1 || 34.9 ± 1 ||30.6 ± 1
|-
| 2 || 44.3 ± 1 || 33.5 ± 1
|-
| 3 || 34.6 ± 1 || 34.2 ± 1
|-
| 4 || 41.0 ± 1 || 34.9 ± 1
|-
| 5 || 39.2 ± 1 || 35.6 ± 1
|}

=References=
<references/>

=Links=
*[[Polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[[多偏振器偏振光 | Chinese version (中文版)]]
*[[Multiple polarizers experimental apparatus]]

Multiple polarizers experimental apparatus

2025-06-11T10:52:56Z

Ist12916: /* Raspberry FREE proxy */

=Apparatus description=

{|
|[[File:exploded_kit_view.png|thumb|x250px|Left|Exploded view of the experimental kit.]]
|[[File:exploded_kit_view_1.png|thumb|x250px|Left|Exploded view of the experimental kit.]]
|}

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a Raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed_.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the pulley.

35. Connect the pulley (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Pulley placement with the belt on]]
|}

36. Tighten the pulley.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the pulley]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, the drivers (1) for the step-motors and the light source and detection (2).

==Electonic component assembly==

1. Select a heat sink.
{|
|[[File:Heat_Sink.jpg|thumb|Heat Sink.]]
|}

2. Remove the paper protection.
{|
|[[File:paper_protection_removal.jpg|thumb|Remove the paper protection.]]
|[[File:paper_removed.jpg|thumb|Remove the paper protection.]]
|}

3. Glue the heat sink to the step-motor driver.
{|
|[[File:heat_sink_placement.jpg|thumb|Heat sink placement.]]
|[[File:heat_sink_placed.jpg|thumb|Heat sink placed.]]
|}

4. Repeat the steps 1, 2 and 3 for the other five step-motor drivers.

5. Place the step-motor driver on the RAMPS 1.4 (RepRap Arduino Mega Pololu Shield)
{|
|[[File:Placa_RAMPS.jpg|thumb|RAMPS 1.4.]]
|[[File:Placa_RAMPS_software.png|thumb|RAMPS 1.4 (software view).]]
|}

6. Check if the step-motor driver is well placed, meaning its ground connection is as shown in the image below and that the bolt (potentiometer) is on the opposite side of the power supply (in the case of the green and red step-motor drivers) or in the side of the power supply (in the case of the purple step-motor drivers).
{|
|[[File:drivers.png|thumb|Step-motor drivers models.]]
|[[File:driver_placement_software.png|thumb|Purple step-motor driver placement (software view).]]
|[[File:driver_placement_green.png|thumb|Purple and green step-motor driver placement.]]
|}

7. Repeat the steps 5 and 6 for the other five step-motor drivers.
{|
|[[File:driver_placement.jpg|thumb|RAMPS 1.4 with the step-motor drivers in place.]]
|}

8. Connect the step-motor wires to the step-motor drivers through the RAMPS 1.4. Check the pinouts connection through its colour and according to the information provided in the subsection [[#Step-motor drivers|Step-motor drivers]].
{|
|[[File:stepper_wires_placement.jpg|thumb|Wires connection in the RAMPS 1.4.]]
|[[File:stepper_wires_placement_software.png|thumb|Wires and switches connection in the RAMPS 1.4 (software view) according to each step-motor.]]
|}

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motor drivers can have multiple design outputs according to the producer. The stepper pin-outs are numbered from 1-6, from left to right from the front view (shaft pointing you, connector downwards).
The driver's location on the arduíno mezzanine relates to the step-motor according to the schema below:

{| border="1" style="width:150px; height:150px; text-align:center;"
|+ Driver to step-motor link
| style="width:66px; height:66px;" | 5
| style="width:66px; height:66px;" | 3
| style="width:66px; height:66px;" | N/A
|-
| style="width:66px; height:66px;" | 1
| style="width:66px; height:66px;" | 2
| style="width:66px; height:66px;" | 4
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Motherboard pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is fed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode. This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present.

As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass through the cascade of polarizers in parallel rays.]]
The optical path consists of a light source (1) (red LED) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light.

Then it is polarized by the fixed polarizer (3) before entering the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and it passes the second lens in order to focus on the detector, a photodiode (6).

Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise. This filter is not damned necessary and can be replaced by red cellophane paper or even absent in case of a fully opaque plastic structure.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays are later focused on the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#First assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for easy observation of such maxima. Consider having it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it until the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in the measured position. Now insert the third polarizer and repeat the procedure for the detection of the maximums and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizer film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

It is provided in the firmware a function able to rotate a set of polarizers in conjunction with each other. With this procedure local maximums can be inferred to confirm the previous determined values. In fact, if a group of the last polarizers are made to rotate in conjunction, the maximum is dictated by the first one to rotate in order to the last one fixed.

Later, when performing the experiments these values of offsets must be considered in order to eliminate the systematic error of the system.

=Software =
To properly use the experiment, commands and data retrieval has to be in place. This can be achieved by two ways acting through the serial connection to the Arduino Mega.

The firmware existing in the Arduido is able to (i) configure the experiment (ii) run and retrieve the generated data and (iii) execute some specialized function in order to test, calibrate and maintain the experiment. To interface with the firmware it can be use (i) a python proxy code (high level software layer) capable to interoperate with the FREE server or a (ii) a terminal emulator like Minicom avaiable for Linux that allows you to send and receive data over the serial connection.

==Raspberry FREE proxy==
The Raspberry Pi is responsible for transmitting the video feed of the experiment and establishing communication with the FREE-Server by using a proxy interface. The FREE hosts the graphical user interface (GUI) to the clients. This section provides a concise overview of the procedure used to control all electronic components via the arduino, as well as the communication protocols between the arduino and the FREE-Server.

===Communication model between the FREE-Server and the Raspberry PI===

The communication between the server and the experiment follows the elab’s structured protocol that enables real-time interaction and data exchange. The central server, Exp Server, acts as an intermediary between users and the experimental apparatus (RPi Server). Users interact with Exp Server via a web interface made with Django, a high-level Python web framework, to configure and control the experiment parameters, while Exp Server which directly relays these commands to the experimental setup. The communication between Exp Server and RPi Server occurs over the internet using JSON-formatted messages, ensuring flexibility across different experimental configurations. Authentication is
performed at the connection stage, where RPi Server transmits an ID and a secret key for verification. Once authenticated, Exp Server sends an experiment-specific configuration file to RPi Server, which then establishes communication with the local controller using the predefined protocol [7]. Through out the experiment, RPi Server continuously exchanges status updates, experimental results, and error messages with xp Server, ensuring synchronized operation and real-time data accessibility for users.

===Communication model between the Raspberry PI and the Arduino Mega===
To enable seamless communication between the Arduino and the Raspberry Pi 4, the protocol ReC Generic Drive 11 was implemented, allowing the external user to have full control over the experiment and its status through a set of commands. The ReC Generic Drive is a generic communication protocol designed for remote laboratories, facilitating interaction between a software driver and experimental hardware. It enables seamless communication over serial ports (RS232), using structured messages where driver commands are in lowercase and hardware responses in uppercase.

The protocol ensures synchronization through message handshaking and timeout handling, supporting functions like identification, configuration, data transmission, experiment configuration, and error reporting.

Fig. 11: ReC Generic Drive State-machine diagram of the driver [7]

By reading the arduino’s serial port at a baud rate of 115200 bits per second, the user sends a bit string (ending with the character ’\r’). The configuration message is defined as:
cfg p0 p1 p2 p3 p4 p5 p6 p7\r
where p0 defines the state of LED (on or off), p1 p2 p3 p4 and p5 define the angle (in steps of 0.36◦) at which the experiment will start the sweep, p6 defines what polarizer will be sweeping
(if do not pretend to sweep then p6 is 0) and p7 defines the limit angle of the polarizer being swept (also in steps of 0.36◦) at which the experiment will stop.

==Firmware==
The programming was done using the C++ language without any external libraries. To declare a component in the code, one simply provides the corresponding input pin and accesses the enable function to initialize it, as well as the
''isTrigger'' function to check whether the logical value read corresponds to the component’s trigger state. In this particular case, the switch is active on a LOW signal. Since all objects and respective components need to be initialized and turned off, each has corresponding enable/disable functions. Components connected to single read pins, declared as ''pinMode'' (such as switches and photodiodes), do not require a disable function since ''pinMode'' does not prevent reading the pins but rather helps define the type of input being processed.

In order to rotate the stepper motors, the operation consists of sending a pulse each time a rotation of 1.8◦ (0.36º effective) is desired.
Since different RPM values require different pulse intervals, the frequency of sent pulses must be calculated accordingly.
To execute a discrete sequence of steps based on a given angle in degrees, the rotate function was implemented. The motor rotates to the low nearest integer multiple of 1.8◦ to the provided angle.

The data acquisition interval is crucial for the final experiment since the goal is to optimize the user experience by minimizing waiting times when retrieving intensity of light and scanning angle data. To address this, a global RPM of 600 revolutions per minute was used. With a scanning limit of 324◦ (as previously mentioned in Section III), the experimentally measured data acquisition time for scanning one or more polarizers simultaneously was approximately 40 seconds.

To further refine the voltage readings from the photodiode, an arithmetic mean of N points was implemented in the photodiode voltage reading function. By computing the arithmetic mean over 13 points of the value being measured, the standard deviation of this mean reduces the original standard deviation in ≈ 27.14%. This reduction was deemed acceptable for the experiment, as the data adjustment performed was successful, as will be observed in Section V).

=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]
*[https://www.printables.com/model/1293618-multi_polarizer_experiment Print your experiment]

Multiple polarizers experimental apparatus

2025-06-11T10:48:49Z

Ist12916: /* Software */

Multiple polarizers experimental apparatus

2025-06-11T10:31:47Z

Ist12916: /* Optical path calibration */

Multiple polarizers experimental apparatus

2025-06-11T07:55:40Z

Ist12916: /* Links */

Multiple polarizers experimental apparatus

2025-05-28T11:12:57Z

Ist12916: /* Optical path */

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode, This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present.

As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]
The optical path consists in a light source (1 - red led) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light.

Then it is polarized by the fixed polarizer (3) before enter the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and the it passes the second lens in order to focus on the detector, a photodiode (6).

Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise. This filter is not damned necessary and can be replaced by a red cellophane paper or even absent in case of a fully opaque plastic structure.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.



=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]

Multiple polarizers experimental apparatus

2025-05-28T10:50:12Z

Ist12916: /* Optical path */

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode, This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present.

As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]
The optical path consists in a light source (1 - red led) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light.

Then it is polarized by the fixed polarizer (3) before enter the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and the it passes the second lens in order to focus on the detector, a photodiode (6).

Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.



=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]

Multiple polarizers experimental apparatus

2025-05-28T10:48:50Z

Ist12916: /* Light source and detection */

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode, This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present.

As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]
The optical path consists in a light source (1 - red led) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light. Then it is polarized by the fixed polarizer (3) before enter the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and the it passes the second lens in order to focus on the detector, a photodiode (6). Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.



=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]

Multiple polarizers experimental apparatus

2025-05-28T10:47:41Z

Ist12916: /* Light source and detection */

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

After passing the cascade of polarizers, the signal is detected by a photodiode, This photodiode is inversely biased with a resistor to ground in order to have a zero signal when no light is present. As the signal is modulated and its frequency has to be removed we use a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]
The optical path consists in a light source (1 - red led) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light. Then it is polarized by the fixed polarizer (3) before enter the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and the it passes the second lens in order to focus on the detector, a photodiode (6). Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.



=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]

Multiple polarizers experimental apparatus

2025-05-28T10:34:56Z

Ist12916: /* Optical path */

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

The detected signal after passing the cascade of polarizers id achieved by a photodiode inversely biased with a resistor to ground in order to have a zero signal when no light is present. The signal is modulated and its frequency has to be filtered by a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x120px|Top|Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]
The optical path consists in a light source (1 - red led) placed in the focal point of a semi-spherical lens (2) where the light rays are collimated in a parallel beam of light. Then it is polarized by the fixed polarizer (3) before enter the cascade of variable tilt polarizers (4). This chain will dim the light according to each polarizer angle and the it passes the second lens in order to focus on the detector, a photodiode (6). Before reaching the photodiode, light may pass a red filter (5) to narrow the bandwidth and limit external noise.

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.



=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]

Multiple polarizers experimental apparatus

2025-05-28T09:38:21Z

Ist12916:

=Apparatus description=

The setup for the construction of the multiple polarizers twin experiment is composed of three main components: (i) the supporting 3D printed plastic parts whose schematics are available here, (ii) a raspberry Pi running the control software over the internet and performing the video streaming and (iii) the low-level slave controller electronics comprising the sensing and the experiment motorisation.

=Mechanical Assembly=

{|
|[[File:Imagem_Experiência_1.jpg|thumb|x250px|Top|Top view of the experiment]]
|[[File:Imagem_Experiência_2.jpg|thumb|x250px|Top|Front view of the experiment]]
|}

In this section, the mechanical assembly of the experiment is explained in detail so that it can be used correctly.

==Order of assembly==

1. Check if all the parts needed to assemble the mechanical structure of the experiment are available.
{|
|[[File:parts_needed.png|thumb|x400px|Top|Parts needed for the assembly]]
|}

2. Peel the supports of the pulleys using pliers or an X-Acto knife.
{|
|[[File:peeled_support_1.jpg|thumb|x250px|Top|Peeling the support]]
|[[File:peeled_support_2.jpg|thumb|x250px|Top|Peeling the support]]
|}

3. Put the belt on the peeled pulleys.
{|
|[[File:belt_on_pulley.jpg|thumb|x250px|Top|Belt on pulley]]
|}

4. Connect the pulleys with the polarizer holders. Make sure to hear a “click” as only one side of the polarizer leads to this firm blockade. Additionally, place the polarizer inside the polarizer holder. (Don't forget to remove the polarizer protection if needed)
{|
|[[File:pulley_polarizer.jpg|thumb|x250px|Top|Pulley and polarizer holder connection position]]
|[[File:pulley_polarizer_connected.jpg|thumb|x250px|Top|Pulley and polarizer holder connected]]
|}

5. Repeat steps 2, 3 and 4 until a complete chain is achieved. You will get a cascaded polarizers set capable to move between each one. Do not forget to put the belts on, as they are not represented in the example picture.
{|
|[[File:pulley_polarizer_chain.jpg|thumb|x250px|Top|Chain of connected pulleys and polarizers]]
|}

6. Cut the thin layers covering the holes of the main plates of the structure.
{|
|[[File:thin_layer_cutting_process.jpg|thumb|x250px|Top|Main plates thin layers cutting process]]
|[[File:thin_layer_cut.jpg|thumb|x300px|Top|Main plates thin layers cut]]
|}

7. Place two of the four pillars together and put the nuts in the specific holes on top of one of the pillars.
{|
|[[File:nuts_on_pillars.jpg|thumb|x250px|Top|Nuts placed on the pillar]]
|}

8. Insert the bolts through the holes and bolt the two pillars together.
{|
|[[File:bolts_on_pillars.jpg|thumb|x250px|Top|Bolts placed on the pillar]]
|[[File:pillars_bolted_together.jpg|thumb|x250px|Top|Pillars bolted together]]
|}

9. Place the main plates next to each other.
{|
|[[File:main_plates_placement.jpg|thumb|x250px|Top|Placement of the main plates (same as shown in the step 1 image)]]
|}

10. Place the bolted pillars on the side of the junction of the two plates.
{|
|[[File:junction_placement.jpg|thumb|x250px|Top|Placement of the pillars]]
|}

11. Place the chain support on the other side of the main plates, so that they are in opposite positions. Check if the chain support is placed on top of the hexagonal holes.
{|
|[[File:chain_support_opposite_to_pillars.jpg|thumb|x250px|Top|Placement of the chain support]]
|[[File:chain_support_in_position.jpg|thumb|x250px|Top|Placement of the chain support]]
|}

12. Place the nuts on the chain support inside the “boxes” closest to the chain support “wall”.
{|
|[[File:nuts_placement.png|thumb|x250px|Top|Chain support nuts placement]]
|}

13. Insert the bolts through the holes on the bolted pillars and bolt the pillars, the main plates and the chain support together.
{|
|[[File:bolts_placement.png|thumb|x250px|Top|Insert the bolts through the highlighted holes]]
|}

14. Insert the nuts inside the other holes of the chain support.

15. Insert the bolts through the main plates and fully bolt the chain support to the main plates.
{|
|[[File:bolt_chain_support.jpg|thumb|x250px|Top|Bolt the chain support to the main plates and the pillars]]
|}

16. Repeat steps 7 and 8.

17. Go to the opposite side of the main plates and place the bolted pillars under the circular holes.

18. Place the nuts inside the top holes of the bolted pillars.

19. Insert the bolt through the main plates and bolt them together with the pillars.
{|
|[[File:bolt_the_other_pillars.jpg|thumb|x250px|Top|Bolt the other pillars]]
|}

20. Connect the chain with the bolted chain support and with the loose one, as well.
{|
|[[File:chain_in_place.jpg|thumb|x250px|Top|Chain structure placement]]
|}

21. Place the nuts inside the specific “boxes” of the loose chain support.

22. Insert the bolts through the holes in the main plates to connect the loose chain support to the main plates.
{|
|[[File:fully_bolted_chain.jpg|thumb|x250px|Top|Bolted chain structure]]
|}

23. Pick one of the pillars and place the nut inside the middle “box”.
{|
|[[File:nut_middle_box.jpg|thumb|x250px|Top|Nut inside the middle "box"]]
|}

24. Place it beneath the main plates in one of the corners.

25. Insert the bolt through the main plates to bolt them to the pillar.
{|
|[[File:corner_placement.jpg|thumb|x250px|Top|Corner placement]]
|}

26. Repeat steps 23, 24 and 25 until the four corners of the structure are supported.

27. Remove the small pillars on the surface facing downwards of the main plate to allow nuts to be inserted into those “boxes.”
{|
|[[File:remove_small_pillars_1.jpg|thumb|x250px|Top|Small pillars removal]]
|[[File:remove_small_pillars_2.jpg|thumb|x250px|Top|Small pillars removal]]
|}

28. Insert the nuts inside those “boxes”.
{|
|[[File:nuts_on_main_plate_1.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|[[File:nuts_on_main_plate_2.jpg|thumb|x250px|Top|Nuts placement on the main plate]]
|}

29. Place the stepper holder above the holes.

30. Insert the bolts through the holes of the stepper holder in order to connect it to the main plates.
{|
|[[File:stepper_holder_placement.jpg|thumb|x250px|Top|Stepper holder placement on the main plate]]
|}

31. Repeat steps 28, 29 and 30 for the other four stepper holders.

32. Place the stepper motor on the stepper holder by first putting the wires through the top and bottom holes. Then, hear a click to ensure the stepper motor is well fixed. NOTE: the cable connection may vary depending on the driver, it is not reliable to use cable colors.
{|
|[[File:wires_placement.jpg|thumb|x250px|Top|Wires entering position]]
|}

33. Repeat step 32 for the other 4 stepper motors.
{|
|[[File:stepper_placement.jpg|thumb|x250px|Top|Stepper motor placement]]
|}

34. Place the belt in the thread.

35. Connect the thread (with the belt) to the stepper motor.
{|
|[[File:motor_placement.jpg|thumb|x250px|Top|Thread placement with the belt on]]
|}

36. Tighten the thread.
{|
|[[File:motor_tightened.jpg|thumb|x250px|Top|Tightening of the thread]]
|}

37. Adjust the stepper holder position to ensure the belt is not loose.
{|
|[[File:adjust_stepper_holder_position.jpg|thumb|x250px|Top|Stepper holder too close to the chain (Belt is loose)]]
|}

38. Tighten the bolts of the stepper holder to fix it.
{|
|[[File:stepper_holder_position_adjusted.jpg|thumb|x250px|Top|Stepper holder in the correct position]]
|}

39. Repeat steps 34, 35, 36, 37 and 38 for the other four stepper holders.

40. Assembly completed.

=Electronic circuit=

The experiment has two main electronic parts, (1) the drivers for the step-motors and the (ii) light source and detection.

==Step-motor drivers==
[[file:StepMotorCable.jpg | Numbering of the step-motor cable connection|thumb|120px]]
The step-motors drivers can have multiple design outputs according to the producer. The steppers pin-out are numbered from 1-6, left-right from front view (shaft pointing you, connector downwards).
The drivers location on the arduíno mezzanine relate to the step-motor according to the schema:
{| border="1" style="text-align: center;"
|+ Driver to step-motor
|-
| #4 || #2 || #1
|-
|N/A||#3 || #5
|-
|}

By using a proper cable the connections should follow the table below:
{| border="1" style="text-align: center;"
|+ Driver to step-motor connections
|-
!Mother board pin-out
!Cable color
!Step-motor pin (A4988)
!Step-motor pin (DRV8825)
|-
|2B
|Red
|
|6
|-
|2A
|Green
|
|3
|-
|1A
|Black
|
|1
|-
|1B
|Blue
|
|4
|-
|}

==Light source and detection==
[[File:NPolarizersElectronicCircuit.png|thumb|Schematic for the LED PWM connection to the A4 pin of the controller board and the filter for the photodiode detection circuit.]]

The red LED is feed by a PWM output pin (A4) from the main controller board, which allows for a variable light intensity. The default PWM from the board has a 490Hz modulation in steps of 1/256, giving a resolution of less than 0.5%.

The detected signal after passing the cascade of polarizers id achieved by a photodiode inversely biased with a resistor to ground in order to have a zero signal when no light is present. The signal is modulated and its frequency has to be filtered by a low-pass first order RC-filter. As the time constant is ~1s, is necessary to delay the first acquisition for the settling of the circuit voltages. Then, as the signal varies smoothly and slowly due to the polarizer rotation, and oversampling is in place, a much lower settling time is needed.

=Optical path=
[[File:Polarizer optical circuit.png|thumb|x250px|Top||Optical path showing the collimating system to let the light pass thought the cascade of polarizers in parallel rays.]]

==Optical path alignment==
The main body of the device has the light propagating in parallel rays through the cascade of polarizers. Those rays later are focused in the sensor (photo-diode). It is crucial for a good signal-to-noise reading to have the system perfectly aligned. For that end, the linear position of the emitting LED and the photo-diode receiver can be adjusted according to the following procedure:

#Firstly assemble the system lens and the light source (LED);
#Energize the LED and follow the emerging circular image from the output, eg. projecting it in a wall a couple of meters apart;
#Move the LED position in order to have an output image the closer to the size of the exit circle (~30mm);
#Install the structure for the cascade of polarizers without any lens or hard film in it;
#Put in place the second collimating lens in order to focus the light in the photo-diode;
#Using a voltmeter for reading the collected light intensity to the photo-diode terminals, move back and forward the photo-diode position in order to maximize the signal;
#Firmly glue the light source and photo-diode positions in their final position.

==Optical path calibration==

Once the support structure is in place, is necessary to calibrate the absolute position of each polarizer; effectively all the polarizers will have a small offset giving a systematic error. It is important to note these angular value that maximizes the transmissivity.

The first polarizer is fixed and shall be positioned with a couple of degrees in order to avoid starting the experiment from a maximum, allowing for an easily observation of such maxima. Consider to have it around ~15º to 30º and well secured, eventually with glue.
Then start the calibration procedure by inserting the second polarizer and rotating it till the maximums are detected and measured (usually two). Take note of their value and leave the second polarizer at rest in one of such that position. Now insert the third polarizer and repeat the procedure for the maximums detection and do this for the rest of them.
Every time a hard film or lens is installed it has to be firmly fixed or glued. If glue is used it ''must not damage the polarizers film''.

You will end up with a table of maximum transmission angles, leading to the reference value of maximum intensity in the cascade of polarizers.

Later, when performing the experiments this values of offsets must be consider in order to eliminate the systematic error of the system.


=Links=

*[[Kit experimental de polarização da luz com múltiplos polarizadores | Portuguese version (Versão em Português)]]
*[https://elab.vps.tecnico.ulisboa.pt:8000/execution/create/33/14 Direct link for the control room]
*[[Light Polarization with multiple polarizers | Reference lesson]]