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Old October 19th, 2010, 23:13   #10
Delierious Designer of Dastardly Detonations
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Join Date: Dec 2001
Location: in the dark recesses of some metal chip filled machine shop
You can't have my baby. My wife would be pissed and I wouldn't have an heir to continue my airsoft work.

That calculation is pretty rough. Assuming a constant acceleration is a bit of a whopper of an assumption given that the mainspring will assert a force related to the piston position. I think my calculation stands as a reasonably good "beer coaster" look into what's going in our AEGs, but if you really want a good theoretical explanation, I think one would have to creak open a differential equation textbook and hammer away. I've probably got one somewhere, but I don't have good table data on the force-deflection behavior of our AEG springs and I think our AEGs may have some funny phase of operation that would require a few sequences of equations to properly model. Maybe someone here languishing away in university attaining a math degree might be so inclined to give this one a try. I'd even settle for a pimply Eng Sci looking to codify the world.

In the first phase we'd see a non linear acceleration of the piston as the spring starts from it's fully compressed length. If you have a spring with two more more pitch angles (loose and tighter coils) then you may observe two spring constants if the lower pitch coils start fully compressed against each other. Coils that are crunched together aren't compressible. They may be pushing outwards, but they can't be compressed any closer together. In this situation, your spring behaves like it's got a solid section so it'll have a higher constant. Once these tighter coils open up, suddenly more winds "appear" so the springs constant reduces. I suspect that a spring designer could use this feature to reduce the pick up force that a sector would have to exert to make the first piston tooth engagement to reduce the wear on this crappy initial engagement. This may or may not be effectively done as airsoft designers often tend to be avid hobbyists, but not the greatest at engineering (e.g. poor mat'l selections et al). This first phase is the most simple one as all you've got is a rigid mass (the piston) being accelerated along a stiffer spring constant then a less stiff one. I think it may be ok to neglect pneumatic effects because the air isn't compressing because it's flying out the cylinder side opening.

The second phase is a more complicated one. Once the piston passes the cylinder opening, air begins to compress in the cylinder. I suppose that the pressure will build until it overcomes the detenting effect that the hopup has against a breeched ball. In this phase the initially moving mass of the piston is pushed by a single constant spring (I'm assuming that the tight coils have opened by now) and air pressure starts to rise non linearly in relation to piston movement. The pressure-distance relation would be inverse as each halving of cylinder volume would result in a doubling of pressure. Pressure will rise until the bb pushes past the hopup and things get even more messy.

The third phase is ultra messy because the bb is free to accelerate. Basically you've got two moving masses, piston and bb, with the piston pushed one way by the mainspring, and a squishy nonlinear "spring" pneumatically coupling the piston face to the spring. This is pretty much where I want to get off because I didn't do all that well in differential equations which we ended up calling difficult equations.

Still there are some approximations which might also prove to be fatal. If we were to be concerned with the moving mass of the piston, we should also consider the moving spring which is heavy steel. I suppose it could be approximated by assuming it's centre of gravity would move half the distance and speed of the piston, but it adds yet another term to the chain of crap. We also have to neglect air leakage around the bb as well as friction in the cylinder and barrel because that might be very difficult to model. A constant friction is easy to work with, but in my experience, orings do funny things when they're compressed. Under low pressure, an oringed assembly might slide nice, but when pressurized, round cross sectioned orings squish into an oval cross section so their sides flare more firmly against their sealing surfaces. While this prevents leaks, it increases dynamic friction.

If I really really wanted to know how everything was happening, I'd probably skip most of the hardcore math and put together a P90 build and swap out barrels with a fixed cylinder set. Measure muzzle velocity at varying barrel lengths and make a fudge factor chart to cheat around the whole messy ball of assumptions and math.
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