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# Physics/pumpkin chunkin

Question
I am building an air cannon for pumpkin chunkin. It is for a charity event. The pumpkins will be between 8 and 10 inches in diameter and probably weigh about 10 lbs. The distance I need to reach is 200 foot because we are shooting at a target. I have a 7 foot long 10 inch ID barrel. It will have a 10 inch butterfly valve. What size air tank and what psi will I need to reach that distance. Is a 80 gal tank big enough to reach that distance. Can I use a smaller tank. Can I get that distance on low PSI in the tank.

Terry

I love the chunkin'!  Good luck!

OK, a 10 lb pumpkin.  I'm going to have to assume a few things to help you out here:
1) 8-10" pumpkin...assume on the larger end (see later in this post), gives us about 400 cm^2 of area for the air to push against as it goes up the barrel, or almost exactly 0.05 m^2.
2) It's on the heavy end anyhow, a full 5 kg.
3) It has to go the full 61 meters (you may have noticed that I prefer to work in metric), but that you can turn down the pressure slightly.
4) A fixed angle to fire at, adjusting only the pressure to fire the cannon.  I'll go with 45 degrees.

Your barrel is large, it's 22.5 gallons alone, so the pressure will drop adiabatically (fast process, no chance to exchange heat).  The gamma factor for air (almost pure diatomic molecules O2 and N2) is 1.4, so since PV^gamma = constant, the pressure will drop by 70% by the end.

Now let's talk velocity.  A simple range equation simplifies dramatically under the assumption that initial and final heights are the same, so you need a 24.4 m/s final velocity at the end of the barrel.  Air resistance and the initial height will probably approximately cancel out.  In fact, a lot of these little guesstimates should be left in to cancel with air resistance, and we have absolutely no way to calculate losses from air leaking around the side and friction (idea on that coming up to make your shot way more accurate).  Your barrel is 2.13 m long, so it has to roughly accelerate at an average (we'll approximate at the acceleration in the middle of the barrel, and use that pressure) acceleration of 140 m/s^2, or about 15 g's.  Hopefully it doesn't smash.  With your pumpkin's mass and F=ma you need a force of 700 N over an area of 0.05 m^2, so you need a pressure P=F/A= 14,000 Pa = just 2.0 psi.  So an initial load of about 2.4 psi in the tank.  Seems low, but the math checks out.  80 gal is a huge tank, think of much bigger than a 55 gallon drum.  It's about 50% bigger.  That cannon is long, and a human can simply throw an object that far pretty easily, so you're not talking about huge velocity.  24.4 m/s is 54.6 mph.  A person can throw a shot put 75 feet, and those are 50% heavier than you're talking about.

Now, the idea to increase your range accuracy and distance...a caddy.  Load a rope-tethered caddy into the barrel for the pumpkin to sit on.  Something that will cradle the pumpkin gently, but match up to the barrel the same way every time.  Also called a "sabot" in military terms, but this one will be tethered to not fly off and be re-used every time.  You'll want to shape it and perhaps fill it with gel or water bags to distribute the force.  Air holes to help increase the cushioning effect would help with the release from the sabot as well, and that release is absolutely critical.  Any way you slice it, I'd put some kind of brake or surgical rubber tubing pre-tether to slow the sabot just at the end of the barrel.  I predict that with all the inefficiencies in the system you'll need 3 psi to make this work with a good build, closer to 4 psi with a rickety build.

Post a follow-up with video!  The calculations really do change when you reduce the volume, and I wouldn't go below the volume of the barrel...or even all that close to it.  But if it reduces the cost and bulk of your cannon to do so, focus on safety and proper design of the sabot.  Specifically a cup sabot http://en.wikipedia.org/wiki/Sabot (it will also protect the sides of your pumpkin from getting damaged on the barrel and keep it from exploding before release.

Hah, it was fun just to give you planning advice.  Good luck!

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