Blowback designs: Back of envelope calcs

Picture in your head that you are sitting on a motionless platform in the middle of a perfectly flat, level floor. The platform is resting on ball-bearings. You hold a spud-gun in your arms.

For the sake of simplicity, let us suppose that you, the spud-gun and the platform weigh 222.2 pounds and further, let us suppose that the potato in the spud-gun weighs 2.2 pounds.

For the sake of convenience, we will define the center-of-mass for your universe (everything above the floor) as the "zero" of our coordinate system. No matter how you wiggle-and-jiggle atop the platform, the center-of-mass of that universe does not move from the zero which was the creator (me) painted on the floor.

Getting bored, you raise the spud-gun to your shoulder and launch the 2.2 pound spud horizontally at 100 inches per second. The seconds tick off the clock. The center-of-mass of the system remains stationary while the spud moves off at 100 feet per second and you+platform+empty spud-gun move in the opposite direction at 1.0 feet per second.

Counter-intuitive? There were no external forces exerted on your universe so the center-of-mass which was stationary remains stationary even though the individual pieces are moving through space.

Hold that thought...

The CCArms LGB series PCCs

Rounding up, it might be capable of launching a 147 grain bullet and the gasses produced by 7 grains of powder at 1100 feet per second.

An extreme example of a case that bulged in the region where the barrel was notched out to accommodate the extractor and/or feed-ramp.

The residual pressure in the barrel just before the bullet clears the muzzle will be on the order of 7000psi-to-10000psi so there is still the potential of the brass case rupturing if it is unsupported by the cylinder. The tricky part is that it can be partially unsupported and the thin brass wall will bulge and carry the pressure load in membrane mode but it will rupture if the distance is too much or the pressure is too high.

Another, less severe example of bulging

It is assumed that the pressure of the hot gas in the barrel will evacuate very quickly after the bullet's base clears the muzzle.

Skipping a bunch of math, if the head of the case can only move backwards 1 millimeter (0.40") then the bolt must weigh about three pounds. If it can move backwards 2 millimeters then the bolt must weigh about 1.5 pounds. If it can move back 3 millimeters then the bolt can weigh about 1 pound.

Increasing the barrel length to squeeze out a few more fps forces the designer to use a heavier bolt to meet the (admittedly arbitrary) 3mm extraction criteria. The heavier bolt requires a longer receiver and increases the likelihood of the plastic parts being damaged when the weapon is dropped.

In a similar vein, making the barrel shorter would allow the designer to use a lighter bolt, making a lighter and shorter firearm but at a loss of velocity/energy of the bullet.

Secondary factors:

There will be friction between the case and the walls of the chamber. That might reduce the thrust by 15%...or it might reduce it by 0% or by 50%. Friction is goofy and the wise designer doesn't hang his hat on it being reproduceable.

The 147 grain load is not very common. The most common is 115 grains but many shooters like 124 grains. The lighter projectiles will result in less movement of the bolt as the projectile clears the muzzle.

Back to calcs

You will notice that there has been no mention of springs. That is because of the very small distances traveled.

The energy stored in a spring is 0.5*K*d*d where "K" is the stiffness or spring-rate and "d" is the amount of compression from the free-state.

In theory, you could design a mechanism with the spring at its fully extended, free-length when the bolt has the head of the case fully inserted into the chamber BUT nobody ever does that for various reasons.

So you are looking at an energy formula of  0.5 * K * (d2*d2 - d1*d1) where d1 is the less compressed distance and d2 is the more compressed (bolt back) state.

That energy will equal the kinetic energy of the bolt as the bullet clears the muzzle. In our example that would be 1/2 * mass * velocity * velocity. In metric, that would be 1/2 * 0.5kg * 6.8m/s * 6.8m/s or 11.5 Joules. In our example, the backward speed of the bolt is 1/50th the speed of the projectile by virtue of their relative masses and conservation of momentum. You can pencil it out or you can play around with parts and spacers (to adjust pre-compression of the spring) to make it work.

One of the beauties of a carbine is that you can absorb all (or nearly all) of the recoil in your spring. The packaging and handling constraints make that impossible in a handgun. If you made the spring stiff enough to absorb all of the energy in the limited length of travel, it would be impossible to rack. Consequently, much of the energy is dumped into the frame when the slide hits the stops at the end-of-rearward travel. That impact plays hell on the frame due to the stresses it creates.