# Help with air pressure/volume in an air cannon

Hey im new here and ive got a small physics problem for you guys (and any gals out there).

I am making an air cannon for use in scenario paintball. The way its set up now is with a small expansion chamber that holds very high pressure air. Im wondering if i can use a much larger expansion chamber and use much lower pressures and still acheive a somewhat decent velocity out of the barrel. If this is possible, are there any equations that i can use to calculate pressure vs volume vs velocity? I know there are many other variables, but im assuming no friction, the valve is 3/4in wide, and the projectile is about 70g. (im doing this so i can charge it with a tire pump rather than expensive compressed co2)

Thanks for the help in advance!

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If you use a lower pressure you will actually lose velocity. Think about this. Pressure is force over an area correct? So if you keep your area the same, the firing chamber, and the force decreases if the pressure decreases. So what is going on is that you are pushing your paintball with a lower force and so it will have a slower speed. What you have done is that you have increased the amount of air you are blowing on it, which might actually help you if you increased the length of your barrel. Basically the more air you have the longer you can blow on the ball down the chamber, but to make this possible you would probably have to make the barrel extremely long.

But. In any air cannon the volume of the tank of compressed air compared to the barrel is always or should be greater.

Here is some math for you, Say you have 100psi in your original tank. and for sake of simplicity lets make your chamber with 1inch. So when you open the valve you will be giving a force of 100(pi)pounds. If you decrease the pressure to say 30? you will have a force of 30(pi)pounds.

To find your velocity i would need to know the length of the barrel and then you would use 2AD=Vf^2 where A is your acceleration found by F=MA, D is the distance of the barrel and Vf is your final velocity(all neglecting friction and such).

In conclusion, The pressure is the only thing that will change the velocity of your ball, that and the barrel but the barrel wouldnt change it as drastically as the pressure. My addvice. Find a tank that can hold close to or higher than the pressure of the compressed co2 and a small air compressor. A tire pump could never get the the pressures of compressed co2.... If i am not mistaken.

How large is the pressure chamber relative to the barrel? If it is large then then the previous post is correct but if your pressure chamber is 5 cubic inches and your barrel is 15 cubic inches then the pressure will most certainly change as the paint ball moves down the barrel and this change needs to be accounted for.