Figuring Out Acceleration on a Potato Gun

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.

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jkerksiek7 years ago
So the idea of shooting the gun straight into the air and timing the event will never lead to vary accurate results. I have built numerous potato guns and have since switched to air canons. With an air canon you can control the inputs a lot better. Even with a potato gun the potato is leaving the barrel at relatively very fast speeds much greater than the terminal velocity of the potato as it returns to earth. The effects of drag and the Reynold's number are very great. Basically unless you shape the potato into an aerodynamic shape such as a bullet the potato will rapidly decelerate and will actually start spiral and travel in a path similar to a corkscrew. The other problem is the muzzle velocity is much greater than the terminal velocity so its speed going up will be much faster than its speed going down.

I personally built the exact device you are talking about to measure it very precisely using IR LEDs and photo transistors. One thing that you have to be careful of is choosing the proper transistor. The projectile is traveling so fast that unless the rise and fall time of the transistor is very short ~ 5 - 10 nS the transistor will not actually shut off. When I first built the timer I did not know C++ so I found a "pinewood derby timer" program online that I was able to use and capture the events and time them. Since then I have learned C++ and Assembly and have developed a program that allows you to input all of your cannon criteria (sensor location, chamber size, chamber pressure, barrel length, barrel diameter, projectile size and weight). Then the computer will tell you the theoretical muzzle velocity and then measure the actual velocity when you fire the gun.

One of my favorite things to shoot is ping pong balls and golf ball cores. You would be amazed at the damage that a ping pong ball will cause when leaving the barrel at speeds in the neighborhood of 450 mph. I can put a ping pong ball through an orange box.

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.
intoon (author)  Oorspronklikheid10 years ago
Thanks! I'll have to try that.
ewilhelm11 years ago
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.
ewilhelm ewilhelm11 years ago
Also - turn off superscript with a closing carrot.
= V2
Lotus14 ewilhelm11 years ago
Or you can shoot a carrot rather than a potato
chase!! ewilhelm11 years ago
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.
ewilhelm chase!!11 years ago
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.
chase!! ewilhelm11 years ago
Actually, what I was really calling attention to was the lack of density. Without it you can't get the right units for force.
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