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$10 chrono

A place to ask general spud cannon related questions.
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Unread postAuthor: homedepotpro » Mon Oct 01, 2007 11:27 pm

well it seems like all of you understand it. its pretty simple. I can draw you a diagram but i'm a total noob in that area.
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Unread postAuthor: TechnoMancer » Tue Oct 02, 2007 7:37 am

photo transistors should be this symbol!!!!!
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photo transistor.png
this is the symbol for a photo-transistor the base is usually not used because the light is used to vary the conductivity of the semiconductor. the arrow can also point outwards and then the transistor would be the other type. they are either pnp or npn.
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Unread postAuthor: homedepotpro » Tue Oct 02, 2007 8:33 am

TechnoMancer wrote:photo transistors should be this symbol!!!!!

thanks techno
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Unread postAuthor: iknowmy3tables » Tue Oct 02, 2007 11:29 am

oh, now I see why its cheaper nice
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Unread postAuthor: jimmy101 » Tue Oct 02, 2007 12:14 pm

Homedepotpro: What you built is good, I wasn't (well maybe I was) trying to be a jerk.

Some comments. The wiring shown for the phototransistors (PTs) only works for certain types of MIC inputs. You are using the power the soundcard provides to the Microphone to operate the PTs. Some MIC inputs put the power on the tip of the plug and the Mic uses the same connection to transmit the signal. Other soundcards put the power on the ring of the plug and expect the audio signal on the tip. Usually, the plug is actually a "stereo" plug, that is, it has three contacts. It is used as a mono source and the extra contact is used for the power.
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The accuracy of the chrono should be pretty good. To estimate the accuracy just write down the equation used and then figure out how accurate the various parts are. For the chono;
muzzle velocity = (dt)/(gate separation)
Delta time (dt) is the time difference between the two signals. The accuracy of dt depends on the sample rate of the sound card. If you are recording at 44.1KHz (the standard top recording sample rate, equivalent to CD quality audio) then the time resolution is 1/44100 seconds (22.7 microseconds). To get the dt accurate to +/- 1% then you need at least 100 sample points between the peaks, which works out to 2.27 milliseconds. The time base of the soundcard, that is the circuitry that calculates time, should be very accurate, I would expect that it is good to better than 1% accuracy, and probably more like 0.01% accuracy.

The other measurement in the equation is the distance between the gates. How accurate can you measure that? Over the distance of say 3 feet you should be able to measure the distance to an accuracy of say 1/16". That is an error of 1 part in (3feet * 12"/' * 16) = 576. One part in 576 is ~0.2%.

Combining the timing error from the sound card with the distance error for the gates, for a 3' gate separation and a projectile moving at 300 FPS;
3' at 300 FPS = 0.01 seconds
In 0.01 seconds the sound card took 44,100*0.01=441 samples
So the accuracy from the sound card is +/-1 in 441. The distance error we estimated at 1 part in 576. The total error range is the sum of the individual errors;
1/441 + 1/576 = 0.4%

That is really pretty damned good. 0.4% at 300 FPS is just ~1 FPS. Of course, there may be some other errors, for example the beams might not be parallel, or the projectile might not be traveling perfectly perpendicular to the beams. But even taking those other types of errors into account I would think you rig is accurate to better than plus or minus a percent or two.

From the above, you can see that for velocities below ~300 FPS the gates can be much closer together and still get accurate results. If your gates were 1 foot apart instead of 3 then the error would only increase to ~1.2%.

Of course, as the velocity of the projectile gets higher then you probably want more distance between the gates. For a modern rifle that fires at 2000 FPS you probably would want the gates 3 feet apart. If you can get everything lined up well enough, the error for 3' at 2000 FPS would be about 2%.

The other thing to take into account is the width of the peaks. The peaks must be at least one sample point wide to be able to recorded by the sound card. A big round like a 2" long spud moving at 500 FPS takes;
(2")(1'/12")(seconds/500') = 330 microseconds
to pass over one of the PTs. That corresponds to ~15 sample points at 44.1KHz. Easy to see a peak that is 15 data points wide.

For a 0.5" long bullet moving at 2000 FPS the time to cross a single gate is;
(0.5")(1'/12")(seconds/2000') = 21 microseconds
That corresponds to about 1 data point at 44.1KHz. So, for a real bullet, at real bullet speeds, it looks like it might be hard to see the bullet with the PTs given the maximum sample rate of the sound card. Off hand though, I would expect that it would still work, but just barely.

The other main error would be the projectile slowing down between the two gates. A nerf dart traveling 3' probably slows quite a bit. The chono will give you the average velocity between the gates. Putting the gates closer togther will minimize this error and get you closer to the muzzle velocity.

Overall, pretty darn good for a couple bucks worth of stuff from RadioShack and an old PC.

If people want to get really anal about the accuracy it is possible to check the time base of the sound card. Just point one of you PTs at a 120V/60Hz light. Record the signal with audacity. You should get a 120Hz sine wave with both incandescent and fluorescent lights. Measure the time it takes for 120 cycles. It should be 1 second. Any deviation from 1 second will be a combination of the error in the time base of the sound card and your ability to exactly locate the center of the peak in the recording of the light from the light bulb.
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The above is what a 120V incandescent looks like to the PT/soundcard combination, recorded with a freebie osciloscope progam for the PC.
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