and cheap, yes! river falls, wi october 30, 2010 saint cloud state university, mn

DIY Photogates Made EasyAnd cheap,

yes!

River Falls, WI October 30, 2010

Dr. John LiuSaint Cloud State University, MN

What are photogates?Photogates measure time with millisecond

accuracy.With known distance, photogate timers can

calculate period, speed, angular speed, acceleration, etc.

One can do Newton’s 2nd law, conservation of momentum and energy etc. with photogates.

Photogate systems are carried by all major vendors.

You can DIY a commercial-quality system.You only spend a fraction of the cost.

Comparison

Pasco standalone $400Vernier PC-based $150+softwareDIY less than $60

Works with existing gates

What you need?Parts: Arduino microcontroller development board $25 Photo interrupter modules $2 $4 total Stereo audio jacks 3.5mm $1.5 each $6 total Stereo audio cables 3.5mm $2 $4 total Headers and resistors $2.5 Prototype boards and wires $8 Or PCB (much easier to solder) $20 (cheaper with batch order)

Tools: Basic PC/Mac/Linux computer with USB RadioShack soldering set $8 Cutting tools if you use prototype boards

Total: $50 if you’re good with proto-boards and diagrams or $60 if

you’re not

What is an Arduino?Arduino is an open-source, very easy to

learn/use physical computing platformArduino can sense many types of sensors and

buttons (analog and digital)Arduino can be programmed to sense its

inputs repeatedlyArduino can communicate with a computer

via the serial portArduino has an active online community

Initial tests on breadboard

Breadboard testing

ConnectionsPC interface

Breadboard testing

ConnectionsPC interface

Breadboard testing

Connections

Very simple setup

It is a proof of the concept but is not student-proof!

Switching to PCB

Photogate diagram Photogate PCB

Shield diagram Shield PCB

Arduinospacing

PCB results

PCB

Populated PCB

Connected to photogates

Arduino board

Photogate

10mm

ImprovementsAll parts are safe and secureSoldering is a breezeJumper wires to audio cables and stereo jacksBreadboard-bound gates to standalone gatesGates can stay a few meters away from the

timer and be mountedArduino board can be easily taken out for

repurposing and put back without having to connect a bunch of wires

Program the ArduinoOpen Arduino environment and load source

codeCompile source codeDownload compiled code to Arduino board

The PC programShows live dataOptions of different measurementsSave data automatically

Videos

How long does it take?Programming the microcontroller – 30sSoldering the PCB – 20 minOr using proto-board – 60 min? (I did the

easy way)Running data collection – 30sSecuring photogates – depends on your

setupTesting everything – 10 min

What do you get?You will get one timerYou will get two gatesSame functionality is sold for $400 at Pasco Your system is pin-compatible with Pasco or

Daedalon gates (needs ¼” to 3.5mm converter $2)

You’re very happy You’ll likely make more stuff with the Arduino

boardWho knows? World peace?

How accurate is it?Well, it depends on three things: your picket

fence, the timing accuracy and the speed being measured.

The PC serial limits dt to ~0.1ms timing for two gates

Say you use 1.00±0.01cm picket fence machined with a mill.

For 1.00m/s speed, you get 1.4%.𝑑𝑣 = ඨ൬1𝑡𝑑𝑥൰2 +ቀ

𝑥𝑡2 𝑑𝑡ቁ2 = ඨቀ𝑣𝑥𝑑𝑥ቁ2 +ቆ

𝑣2𝑥 𝑑𝑡ቇ2 𝑑𝑣𝑣 = ඨ൬

1𝑥𝑑𝑥൰2 +ቀ𝑣𝑥𝑑𝑡ቁ2 =ඨሺ0.01ሻ2 +ቆ

1∗10−41∗10−2 𝑣ቇ2 = ඥ10−4 +ሺ10−2𝑣ሻ2 = 1.4% 𝑖𝑓 𝑣 = 1𝑚/𝑠

Boring math:

Update: Physics shield

Connectors:

Proto-connectorBreadboard connector Stereo plug connector

Compatible with all Arduino boardsTwo robust RJ11 connectors for

sensorsLCD and 6 buttons for user

interactionGPS connector for GPS

applicationsReal time clock and EEPROM for

data logging, timing etc.Brings out all Arduino pins

Photogate connector

Future directions:More functions on the PC photogate programSupport more gates (may reduce timing

accuracy)Start a blog liudr.wordpress.com for physics

projectsDevelop more shields for physics prototypingDevelop upper-division electronics class with

Arduino

Thank you!

Care for some details?v (cm/s) dv/v*100% dx(cm) 0.01 10

0 1.0 dt(ms) 0.1 1005 1.0 x(cm) 1 100

10 1.015 1.020 1.025 1.030 1.035 1.140 1.145 1.150 1.155 1.160 1.265 1.270 1.275 1.380 1.385 1.390 1.395 1.4

100 1.4105 1.5110 1.5115 1.5120 1.6125 1.6130 1.6135 1.7140 1.7145 1.8150 1.8

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0 20 40 60 80 100 120 140 160

Per

cen

tag

e er

ror o

f V

Velocity (cm/s)

Relative error vs. V

Just linksArduino official siteArduino forumMy blogPrograms for the photogate shield (on my blog)

Parts:Arduino microcontroller development board $25Photo interrupter modules $2 $4 totalStereo audio jacks 3.5mm $1.5 each $6 totalStereo audio cables 3.5mm $2 $4 totalHeaders and resistors $2.5Prototype boards and wires $8Phi-1 shield (please check my blog)