If you want to go through that you could. But the system isn't a perfect one (i.e. as if you were to take one piston/syringe of a given diameter and hooked it up air/water tight to another one of a different diameter). There are a lot of variables with each setup...and no setup will ever be perfect.
For example, losses of efficiency will be:
- leaks in the piston head, nozzle, hopup rubber
- leaks around the BB (it's obviously not like a bullet that will form/impress to the barrel)
- resistance from the hopup application
And in your calcs you'd need to anticipate the action and delivery of energy from the spring as it expands. The piston is accelerating from a stop to a stop...and the projectile starts to move before the piston is at full speed and is out the barrel before the piston comes to a full stop. I'm no math wiz...that sounds hard to calculate.
What I was trying to say is...don't sweat the "ideal" setup...because it'll never happen. Set it up so that there's more than enough air going down the tube (and manufacturers have already done that with the cylinder ports/barrel lengths)...and adjust muzzle FPS/power with your spring.
Spring powered systems are not a "compressed air" system. Air is not compressed and then released instantaneously. It's inherently a leaky system...the compression parts leak, the projectile does not seal with the barrel. The volume of air in a cylinder is not appreciably compressed when the piston goes forward...there's just a moment of restriction as the BB passes the hopup and then it's simply pushed along until it's speed matches that of the speed of the air moving down the barrel...or it runs out of barrel. A heavier BB is not brought up to air speed as quickly as a lighter one.
As MadMax so eloquently put together in another post...the purpose of the porting in a cylinder is not to reduce the amount of air, but rather to allow some "run up" time for the piston to get up to speed before the BB starts to move.
A great practical example of this is to put a full cylinder and a short (say MP5K) barrel together. You'll get very low FPS' because the BB's out of the barrel before the piston gets up to speed. You'd have to put a retardedly strong spring in there to get any decent speed out of it. Swap that barrel for an AK length and you're back in business.
While much of the parts/pieces are the same with a gas based system...the power source is very different. The liquified gas expands at a rate and the longer/more space it has it will continue to expand. Since the resevoir of liquid gas is "plentiful" for a given shot...the potential expansion is more than sufficient for it to apply power for any barrel length.
Take a gas setup and shoot a given weight of BB through a given barrel length...then swap just the barrel for a longer one. Your FPS will increase...because more gas has been allowed to expand longer. Swap it for a tighter barrel...your FPS will increase...because there is less leakage around the BB.
Take a gas setup and shoot one weight of BB through it. Then swap for a heavier BB. If your barrel length is sufficiently long...your FPS will remain the same....the power of the shot will go up though. Then swap for a lighter BB...again, if your barrel length is long enough...the FPS will stay the same and the power level will go down. You can start to see this effect in "full size" GBB pistols that have tightbores...it's very noticeable in GBBR's, especially those based on the negative pressure system.
If all that sounds like too much bother...you're right, it really is. Just skip back to the italicized part