Mass of powder charge generates more recoil than bullet mass?

[labnoti]

Let's say we have two loads:

1.) 158 grain bullet propelled to 1000 fps by 7 grains of powder A
2.) 158 grain bullet propelled to 1000 fps by 14 grains of powder B

We see these kind of results with powders like
Hodgdon Longshot vs. IMR4227 or
Alliant Steel vs. H110

Load 2 will obviously produce more recoil than load 1 because there is 172 grains of solids and gases being ejected whereas with load 1 the mass of ejection is only 165 grains. But why is it that the difference in recoil is even more than that?

The recoil impulse to produce 1000 fps with

158 grain bullet, 7 grains of powder: 0.86 lbs.sec.
165 grain bullet, 7 grains of powder: 0.89 lbs.sec.
158 graim bullet, 14 grains of powder: 1.01 lbs.sec.

Also, how does the % burn of the powder before the bullet leaves the barrel affect this?

 

[labnoti]

I looked into this and determined it is because the velocity of the ejected gas is higher than the velocity of the ejected projectile. I also learned that the velocity of the gas tends to be higher with smaller bores and longer barrels and with different powder types. It's interesting that with some loads more than others we're paying in recoil for ejecting larger masses of gas at higher velocities to obtain the same projectile velocity or we're paying proportionally more to obtain higher velocities. I already gave examples of some powders that might deliver similar projectile velocities with radically different masses of powder charge. Consider also that in order to obtain maximum velocity of a 158 grain projectile in a .357 load, we'd need to eject a large mass of gas at high velocity. A larger diameter, perhaps more massive projectile could be ejected with similar force using a different powder and a lot less mass and velocity in gas, perhaps from a hot .44 Special or .45 LC load. Perhaps even the 9mm will achieve good velocities with 125 grain bullets without blowing out as much gas as .357 with the heavily-deterrent-doped powders.

 

[Infidel]

I have seen the number 7000 fps used as the "muzzle velocity" of the gas. I think that most of the experts just pick a number out of some convenient receptacle and plug it in to calculate recoil, but thousands of fps sounds right to me. ... for the gas.

 

[FROGO207]

Um how does your theory hold up when the gas pressure drops to zero before the bullet exits the barrel. This happens with many loads all the time. The firearm then exhibits no recoil because of no escaping gas? I think not. There are many other factors that produce recoil other than the escaping excess gasses I am afraid.

 

[labnoti]

No it is not the mass times the velocity of the gas alone that is generating recoil. Of course the force acting to accelerate the bullet's mass generates most of it. My point was that using a larger mass of gas to accelerate the same mass bullet to a given velocity will produce more recoil. It produces even more recoil than just the extra mass of the gas, because it is also accelerating that gaseous mass to even higher velocity than the bullet.

The velocity of the gas isn't a constant and it probably varies with factors like the type of powder, the diameter of the bore, the muzzle pressure, etc. But the constant used in most formulas is somewhere between 1.25 and 1.75 muzzle velocity of the bullet.

Let's say I load a 140 grain bullet over 16 grains of H110 and upon firing, it accelerates the 140 grains to 1200 fps as it exits a snubnose barrel. It's also accelerating the 16 grains of H110 to some velocity that for the purposes of calculating recoil impulse is something like 1800fps (1.5 X muzzle velocity of projectile).

If I load the same 140 grain bullet over a few grains of Red Dot, I could theoretically also accelerate the bullet 1200fps without having to also accelerate a large mass of powder to 1800fps. Of course, I would have too much pressure, but the difference in recoil would be substantial, perhaps 20% less recoil impulse. While my hypothetical example may actually be impractical, there are realistic cases where a powder with greater energy-density is going to offer significant reduction of recoil.

 

[Art Eatman]

Within the barrel, the gas cannot travel faster than the bullet. Recoil must consider the sum of the weight of the powder charge and the weight of the bullet. Once the bullet leaves the muzzle, there is nothing against which the gas can react to create additional recoil.

Ergo I disagree with the premise of the opening post.

 

[labnoti]

Then a rocket couldn't be propelled by the gas escaping the nozzle because it can't react against anything to create any propulsion? In fact it does, even in the vacuum of space.

I suppose another way of putting this is that after the bullet leaves the muzzle, the gun becomes a recoil rocket and generates recoil in addition to the force from the ejection of the bullet's mass. A recoil rocket with more propellant mass will have greater impulse than a rocket with a smaller mass of propellant given the same velocity. The force of the additional recoil will be determined by the mass of the propellant times its velocity.

 

[fxvr5]

Um how does your theory hold up when the gas pressure drops to zero before the bullet exits the barrel. This happens with many loads all the time. Incorrect. The firearm then exhibits no recoil because of no escaping gas? I think not. There are many other factors that produce recoil other than the escaping excess gasses I am afraid.

Gas pressure is pretty high when the bullet leaves the barrel. That's what makes compensators and muzzle brakes work.

 

[fxvr5]

Within the barrel, the gas cannot travel faster than the bullet. Recoil must consider the sum of the weight of the powder charge and the weight of the bullet. Once the bullet leaves the muzzle, there is nothing against which the gas can react to create additional recoil.

Ergo I disagree with the premise of the opening post.

The effect of gas pressure contributing to the recoil force is well known.
https://en.wikipedia.org/wiki/Recoil#Including_the_ejected_gas
https://saami.org/wp-content/uploads/2018/07/Gun-Recoil-Formulae-2018-07-9-1.pdf
http://kwk.us/recoil.html

The effect of powder weight on recoil, even when driving the same bullet to the same speed, is measurable and easily demonstrated. Here's an example: http://www.shootingtimes.com/ballistics/compensators-pressure-gas/

And see: https://www.ssusa.org/articles/2017/6/19/gunpowder-selection-for-controlling-recoil

 

[Art Eatman]

With a compensator, the gas has something on which to impinge. Without the comp, the main thrust is "drafting" behind the bullet, just as does your car when behind a semi.

 

[Grumulkin]

Drafting isn't thrust. It's decrease in drag.

The only difference between a bullet in a barrel and a bullet in a compensator is that the compensator leaks most of the gas behind the bullet so there is less thrust on the bullet.

 

[fxvr5]

With a compensator, the gas has something on which to impinge. Without the comp, the main thrust is "drafting" behind the bullet, just as does your car when behind a semi.

Not sure what you're saying. Are you still saying the gas pressure after the bullet leaves the barrel does not contribute to the recoil force (without a compensator)?

 

[higgite]

With a compensator, the gas has something on which to impinge. Without the comp, the main thrust is "drafting" behind the bullet, just as does your car when behind a semi.

Gas doesn't expand in only one direction. Without a muzzle brake, as the expanding gas leaves the muzzle, it pushes back on the muzzle, forward on the bullet and forward and sideward on the surrounding atmosphere. When you add a muzzle brake, the expanding gas still pushes out in all the same directions, but some of it now pushes forward on the brake, which directs some of it outward and backward. Gas impingement on the brake itself, plus the redirection of gas flow to the atmosphere all have equal and opposite reactions that contribute to recoil management.

 

[Art Eatman]

Upon exiting the muzzle, the gas expands in approximately a sphere. But the mass is moving forward at high velocity, right? Seems to me, then, that rearward pressure must be much less than the forward pressure. I see no way that any rearward force from the gas as it exits the muzzle can apply any appreciable force; the impulse causing recoil has already happened. Recoil begins with ignition of the powder.

Separately, with a compensator for muzzle rise, the vents on top mean less pressure above and more pressure on the lower portion. Less muzzle jump on my old 1911, way back when.

 

[fxvr5]

The forward force of the gas is equalled by rearward force as per Isaac Newton's third law.

Even ports, simple holes in the barrel, reduce muzzle rise - and they have no baffle plates for the gas pressure to "push against". Force directed upward by gas escaping the ports is equalled by force directed downward - Newton's third law.

This is not something that is open to debate. It's already known, tested and proven, and easily demonstrated as shown in the links previously posted. You either understand it or you don't. I'd suggest that you read the articles at the Shooting Times and SSUSA links. If the gas had no force, you would not get the results that are shown in those articles.

 

[FROGO207]

So you are telling me that you have to have excess gas pressure pushing the bullet out of the barrel or the bullet will not exit? Not quite the way I learned things.

 

[fxvr5]

The word excess does not apply here. Whoever told you that pressure goes to zero clearly does not understand how guns and ammo work. Look at the pressure curve (Figure 5) at this link: http://www.shootingtimes.com/ballistics/compensators-pressure-gas/

Chamber pressure peaks shortly after the powder ignites. As the bullet travels down the barrel and powder continues to burn - change into gas - gas pressure drops because the space the gas fills increases as the bullet travels forward. Nevertheless, when the bullet exits, pressure is still around 5,000 psi (according to that figure for that caliber, etc.). This gas pressure is the force exiting forward, that is countered by reciprocal force via Newton's third law, which adds to the recoil produced by the bullet's weight and velocity.

Compensators, ports and muzzle brakes harness this gas pressure to push forward on baffle plates (if present) or is redirected upward to reduce muzzle rise.

That author has written other articles on how compensators work, if people want to read more: https://americanhandgunner.com/compensators-do-they-really-work/

Powders that require more weight to push the same bullet to the same speed produce more gas and therefore more gas pressure. This extra gas pressure produces more recoil force, and more muzzle rise, which explains the results in the article at that link. A compensator or port that directs the gas upward, uses the extra gas pressure blasting upward to produce a stronger downward force. That's why people who load ammo for their compensated guns often use a powder that requires more charge weight (usually a slower powder) to maximize the effect of the compensator (Figures 2 and 3 in that article).

Clear as mud?

 

[Stumper]

Art, As these guys are saying, gas acting upon gas (and anything else around it) provides for the equal and opposite reaction. Common example. Blow up a balloon and release it without tying it off. The jet effect of escaping air under mild pressure propels the balloon. No bullet, no comp. just gas impinging gas.

 

[FROGO207]

I guess saying zero (often really 1000 psi or less after a peak pressure of 50,000 psi or more) is actually misleading, sorry there. It will often be so low as to not have a large effect on the already accelerated bullet as it climbs the barrel and exits it. Having the large/long plume of expanding gas follow the bullet out of the barrel does not necessarily equate to a better faster load. It is sometimes detrimental to accuracy as well I find. The biggest contributor to recoil is the inertia of the lead projectile acting against the larger weight of the firearm at the initial expansion of the propellant. Your results may differ from mine though.