Originally Posted by duhon19
I am half way through a BS in mechanical engineering and hope to work in the firearms design industry when I finish school. I was trying to gain a better understanding of a gas operated reloading system and have run into a problem with my math. If the pressure produced from the volume expansion of the powder is constant and
D1=length of the barrel from cartridge position to gas port
D2=length of the barrel from gas port to end of barrel
M=mass of the projectile/round
SA=surface area of the projectile facing the inside of cartridge
P=pressure of powder expansion
T1=time interval for projectile to travel through D1
T2=time interval for projectile to travel through D2
Ff=force of friction that will oppose motion of the projectile
Fp=force from pressure that will drive the projectile=(P*SA)
A=acceleration of the projectile =(Fx/M)
Then using kinetics
And the velocity of the projectile as it passes the gas port=V0=(Fx/M)*T1
Then T2 could be found by solving the quadratic (Fx/2*M)*T2^2 +V0*T2 –D2=0
T2 would be the amount of time that the reloading mechanism is exposed to force from (P). I was trying to solve the problem of timing (setting the position of the gas port) so that the reloading mechanism dose not begin to extract the casing before the projectile leaves the barrel and I can’t figure it out. D2 would have to be zero? Wouldn’t the reloading mechanism begin to move the instant after the projectile passes D1? What causes the delay?
I am not an expert by any means, but I'll offer up my 2 cents worth.
It seems to me that the delay would be cause by the gas passing from the barrel to the gas port accumulation area (gas block). This can be changed by changing either the size of the accumulation area or by the size of the gas port hole in the barrel. Either a larger gas block or a smaller hole will increase the time of delay in the reloading mechanism because it will take longer for the gas pressure to build to the point that it overcomes the inertia of the recoil/buffer spring. Glancing over your equations, I didn't see anywhere you accounted for the difference between the barrel diameter and the gas port diameter, which would affect how much force is available to cycle the reloading mechanism.