[KenWittlief]

the equations you are looking for relate force, mass, acceleration, velocity, distance and time

you need to specify the length of the cylinder-throw, the mass of the ball, and the velocity you desire

the pressure will then fall out as the calculated force divided by the area of the face of the (circular) internal piston plate.

Force = mass times acceleration

distance = 0.5 * acceleration * time^2

velocity = acceleration * time (and you can average the velocity = final speed / 2) to get the time

remember that mass is kilograms and force is newtons. (or slugs and pounds).

something else (that has been discussed in other threads): the flow of air through the valves and hoses in the kit of parts is not that fast - probably not fast enough to laungh a ball. You will most likely need to hold the cylinder back with a release pin (a pin that blockes its forward motion) and precharge the cylinder with air, then pull the pin to fire the launcher. This means if you want a 4" throw you might need an 8" cylinder, with the release trigger pin half way down its travel.

and you might also need to take the fitting off the far end of the cylinder, to allow the air to escape without restriction.