Well, The PSI I have on the poster has Standard Pressure added, sonit was really only about 2 PSI after the calculation, which seemed low, also, the flow rate was only marginally greater than the actual barrel volume, so it seemed to me like it wouldn’t actually push the shirt out the barrel at any real speed.
Our coach will not OK a cannon design unless it has a range of 50’ or less due to safety concerns.
That sounds a lot easier than our math homework way of doing it.
Right or wrong (and it doesn’t look “that wrong”), there is still a value to attempting to solve these problems using the math. Even if the error is 50%, it is still getting to within an order of magnitude of the right answer, so it has some value.
If your barrel was filled with 16 psi air, and you were able to flow air at a great enough rate to maintain 16psi throughout the full travel of the shirt down the barrel, despite it “sounding low”, it is imparting a decent force on the shirt. That 16 psi is working against ~4 square inches so you have 60pounds of force on a reasonably low mass. Additionally, you are saying your barrel has a volume of 2.1L and your fill rate is ~35 actual L/s, so your shirt is travelling the length of the barrel (2.5 ft) in 0.06sec, for an average velocity of 41ft/sec or an exit velocity of 82 ft/sec assuming constant acceleration.
I say all this not because it’s strictly right, but your math probably isn’t that far off.
So back to reality, the issue is that 35 actual L/s (which at 16psi is ~73 standard L/sec or ~150 SCFM of air. That is a LOT of air, enough that to transmit it without extreme pressure drop. Even with a 1" line, if you start at 16psi, you are losing ~0.2psi per foot of travel. At 0.5", you are losing 6.6psi per foot! Couple that with the fact that fittings, valves, regulators, and other restrictions are often much greater than your piping.
So the tl;dr on how to make a pneumatic cannon is that you need to design for higher flow, and have a nice accumulator to hold that flow really close to your barrel to minimize pressure drop. A typical design is something like a 1" solenoid right on the barrel, with an accumulator tank of sufficient volume right at the barrel. You fill it to whatever PSI you want (set with a regulator), and then fire the solenoid to shoot the T-shirt. You can test it with your teacher to determine what pressure is “safe” on the accumulator and then handle it administratively by saying “never set the regulator higher”, or adding something like a analog pressure switch and doing it in code, or adding a mechanical safety relief or even a burst disk, depending on how robust you need your safety to be.
Keep one other thing in mind though, even low pressures of air (10-20psi) can be dangerous in plastics that fail in a brittle manner (PVC) so you should aim to build as much out of more ductile metal as possible, and shield any plastic parts. I would encourage you to develop a design and come back to CD for input on ways to keep it safe.