In my learning I questioned what is the lowest pressure need to propell a paintball to 280 fps in 10 inches? Now granted this is the inital baby-step in coming up with a more complex answer. So imagine a system that is open at one end for the paintball to leave and a the PSI level that is constant through acceleration. I haven't figured in friction of gelatin on aluminum/steel/brass. If you happen to know the frction coefficient (u) of gelatin on one of these combinations I would appreciate it if you let me know. I just don't happen to have a block of gelatin and aluminum handy. If I did it's a simple test to gather the friction number.
Onto the fun stuff..... *Note: all numbers are in metric.
t = 0.254000508001 / 85.3444 = 0.002976196 seconds for the ball to travel 10 inches and peak at 280 fps.
a = 85.344 / 0.002976196 = 28675.53078 m/s^2 acceleration for 10 inches
F = 0.003188 * 28675.53078 = 91.41759212 newtons
A = 4(PI)(r^2) / 2 = 0.000468603 m^2 ; this is area (standard .68 ball)
P = 91.41759212 / 0.000468603 = 195085.3753 pascals
195085.3753 pascals = 28.294743 PSI
If this is correct, then this is extremely interesting. If I'm correct we can't supply a constant flow of ~28 PSI for 10 inches against an area of 0.000468603 m^2 for 0.002976196 seconds. So the next thing to figure in the PSI volume expansion ratio. That should bump this up to ~100 psi.