I know the guy who wrote this. He's both a great guy and WAY smarter than me. =-)
F = A*P, so A = 1.063*pi = 3.34 sq in, P = 250 psi, so F = 834 lbs. With that and a 1" stroke you can fiddle with the geometry quite a bit and still have some impressive hitting power.
The volume of gas per shot is PI*r^2*h, or .884 cu in, times P/1 ATM. P = 250 and 1 ATM = 15 so you use 250/15*.883 or 14.71 cu in of CO2 (at STP) per shot.
So, how much gas is in a 16g cartridge? 16g of CO2 becomes .302 cu ft at STP, or .302*1728 = 521.8 cu in. 528/14.71 yields ~35 shots.Of course, it isn't that simple...