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# Figuring Out Acceleration on a Potato Gun Answered

My newest craze is potato cannons. I built a simple potato cannon powered with hairspray. I didn't plan out ratios of chamber volume to barrel volume, but I must have guessed pretty well because the potatos go far. Really far. I shoot them in an empty bean field and they stay in the air for 10 seconds before hitting the ground at what I guess is 300 yards away. I want to measure it to be sure. I'm probably exaggerating the distance out of sheer amazement. But the potato goes really far.

I got to thinking, though, that I could go beyond just shooting the potatoes, and actually turn this into something useful. If there was a way to determine the acceleration of the potato inside the barrel, that would be super cool. I've had a few ideas on this so far:

The most complicated involves drilling holes on each side of the barrel. The holes would be every inch the entire length of the barrel. On one side led's would be installed and wired in parallel to remain on constantly. On the other side photoresistors would be installed and also wired in parallel with a microcontroller. When the potato traveled down the barrel it would block the light to some of the photoresistors and the microcontroller would get a readout. If there was a way to program this whole system and get a graph on a computer of the acceleration/time curve, that would be awesome!!

Another way would yield a less accurate number. Shooting the cannon straight up and timing how long it takes the potato to hit the ground would give you the initial velocity. Vf = Vi + Gt, so: -2Vi = -9.81t . Once the initial velocity is known, if the time it takes for the potato to leave the barrel can be figured out, the acceleration could be figured out.

Let me know what you think!

Note: I will attach images as they come.

## Discussions

You can measure speed more accurately with two microphones , some paper(soft paper towels work best) and a free ware program called audacity.Heres how to: First put the paper in something like a wooden frame so that the spud can shoot through the frame and tear the paper. Make anther frame like the other one.Put your one of your microphones against each paper frame.Align both frame with the cannon and measure the distance between the frames(Something like 15 cm- 20cm). Start recording on Audacity and shoot through the frames. Measure the last two bit of sound that came through and do some calculation.Now you have an exiting speed.

At the speeds your potato is travelling, air resistance will be significant. Roughly, F_air-resistance = 1/2 C V2, where C is a constant related to the cross-sectional area of the object. Also, remember that air resistance fights your potato on the way up and on the way down making for quite an interesting problem.

Also - turn off superscript with a closing carrot.
`V^2^`
= V2

Or you can shoot a carrot rather than a potato

Close, but you're off. Drag=1/2*density*V2*Cd*A. Where Cd is drag coefficient and A is projected area.
At sea level density is approximately 1.223 kg/m3. A sphere has a drag coefficent of approximately 0.4.

A 3" diameter potato leaving the gun at 45 m/s (in the ball park for a potato traveling 300 yards in 10 seconds experiences a drag force of 2.26 N. Doesn't seem like much, but over the whole flight it adds up and makes the problem a nonlinear system.

In my mind, I had lumped all those into my constant; hence not calling it C_d. But, you're totally right, stating that way was probably not very instructive of me.

Let me take this opportunity to plug my favorite aerodynamics book: Flight Without Formulae.

Actually, what I was really calling attention to was the lack of density. Without it you can't get the right units for force.

So basically you want to construct a simple photogate?

How did you get -2Vi = -9.81t ?

Could you explain the photogate?

The -2Vi = -9.81t becuase if the potato goes straight up, then when it hits its starting position it will be going the same speed as when it left, or the opposite velocity. Therefore Vf = -Vi, and then combining the two Vi's give me -2Vi.
If the potato didn't end up below where it started (because the cannon is held in the air), the equation deltaY = Vi(t) + .5G(t2). The second equation would be more accurate, because it takes into account the change in position (about 1m).

I guess that is true then Vi = 9.8t / 2 .... go do it, and just mark time when it passes the top of the gun barrel again so you don't have to account for deltaY :)

A photogate is just what you describes. It measures velocity / acceleration by comparing the change in position to the change in time by doing what you just described :D

Ok, I guess what I meant was, how do you build a photogate? What are the components?

1. get a light source, a laser, a LED, whatever.

1. Shine it on a phototransister, properly feed the phototransister with power

(http://encyclobeamia.solarbotics.net/articles/phototransistor.html)

3. detect a change in voltage somehow. I've already suggested the parallel printer port on an old PC

4. ???

5. profit

Do you want to measure acceleration in the barrel?

Or do you just want the velocity of teh spud as it leaves your device?

If you just want the velocity, there are things called chronographs for firearms that should work out of the box. Google image search for chronograph skyscreen to see what these things look like.

The skyscreens look like IR emitting diodes at the bottom of the V, and some reflective tape at the bow. There's likely a photo transistor also measuring the reflected light at the bottom of the V, but I want to stress that I've never seen one in real life. They should be homebrewable.

The best chronographs use three skyscreens and average the results.

As for measuring the acceleration in the barrel, you have a number of options that firearm people don't.

First off, you can get clear PVC tubing instead of the white kind. Also, IR light might pass right through normal white PVC tubing. I think your holes idea is a good one, except without the holes.