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I Physics of firearm recoil

  1. Jul 27, 2017 #1
    In this post I want to address some very controversial issues among the professional sport shooting world, and try to answer these questions with basic physics. Bear with me as it does require some introduction!

    Below is an animation of the gas impingement system typical of a modern semi-automatic rifle: (animation)

    For those not familiar:
    1) The spring on the left is the "buffer spring"
    2) The reciprocating mass consists of the Bolt Carrier Group (BCG) is the gray thing as well as the Buffer (the yellow part in the spring)
    3) There is often an adjustable valve that controls how much gas is allowed back into the system to reciprocate the BCG.

    In modern professional 3-gun competitions, the standard practice to reduce felt recoil during rapid firing is to do the following things:
    1) Reduce the internal reciprocating mass (BCG and Buffer) by as much as 50%
    2) Because reciprocating mass is now lower, also reduce the flow of gas from the adjustable gas block so that the BCG reciprocates at approximately the same speed as originally.
    3) Because reciprocating mass is now lower, also reduce the buffer spring tension so that BCG returns to battery at approximately the same speed as originally.

    The conventional wisdom or explanation for these changes is that by reducing the internal reciprocating mass, the overall felt recoil of the gun will be less. The fact that by restricting the gas port, more of the gas pressure will exit from the barrel of the gun rather than being directed back through the impingement system, is typically ignored -- though I don't think that's a safe assumption (more on that later).

    If one consider the imaginary limit in which one continuously reduces the weight of the reciprocating mass, you eventually end up with a rifle that has no reciprocating mass -- in other words, a bolt action rifle. It is widely agreed that a bolt action rifle has larger felt recoil than a semi-auto rifle. The physics explanation is that the reciprocating action of the BCG absorbs some of the momentum. In other words, the momentum of the reciprocating mass is subtracted from the momentum of the ejected bullet+gas to get at the remaining felt recoil.

    At this point, it is tempting to conclude that the professional 3-gun shooters are full of BS. The fact they have a lower reciprocating mass necessarily means that their guns must have more felt recoil. Or does it?

    This is not quite the end of the story, because It is standard practice to put a compensator at the end of the barrel, which is basically a series of open-air baffles that reflect as much of the gasses coming out of the barrel back in the direction of the shooter as possible, with a hole just barely large enough to allow the bullet to continue moving forward. It has been found that an effective compensator can reduce overall linear motion of the rifle by as much as about 75%.

    So, while it is true that a rifle with low reciprocating mass will have less rearward momentum from the movement of internal parts, it will have MORE gas pressure reflected back towards the shooter at the end of the barrel by the compensator.

    At this point, my arm-chair analysis of the problem escapes me. I'm not sure how effective recoil mitigation in the form of reflected gas pressure would be in comparison to reciprocating mass. I'm interested in trying to get a better understanding of this question from an intuitive/theoretical (arm-chair) perspective...but how to even begin?
  2. jcsd
  3. Jul 28, 2017 #2
    For simplicity, let's assume that the compensator is 100% effective. In other words, 100% of the excess gas coming out of the muzzle will be reflected straight back at the shooter.

    Before reaching the end of the barrel, some fraction of the gas is redirected via the gas tube back in the direction of the shooter -- and this is used to push the BCG. According to the law of conservation of momentum, the rearward force of any gas used to push the BCG must be equal to the force of the BCG itself. Either way, this is force that's NOT being applied to the gun.

    Thus, it seems that the net recoil force of the gun must be equal to the force of the bullet, minus the force of any excess gas not used to power the bullet...and entirely unaffected by mass of the BCG. The only effect that changing the mass of the BCG would have is changing the fraction of rearward force that was due to reciprocating BCG vs. rearward gas pressure.

    So..does this mean that using a lightweight BCG has NO EFFECT on recoil?

    No...because the above is neglecting any timing information. In reality, there is going to be some initial rearward recoil force applied to the gun equal to the total amount of gas force....then the recoil force will be somewhat reduced by the force of gas that enters the gas block and reverse direction...and then reduced more significantly when the gas at the muzzle reflects back off the compensator baffles....and again reduced when the BCG finally starts moving rearward.

    Because the BCG is the last thing to move rearward, using a heavier BCG effectively means that you have to wait longer before recoil of the gun starts being counteracted. Or in the other words, the lighter the BCG is, the more gas will be quickly reflected back at the compensator, which means that the felt recoil impulse of the gun will last for a shorter duration of time.
    Last edited: Jul 28, 2017
  4. Jul 28, 2017 #3


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    A complicating factor is that the reduced recoil might just reflect a reduced bullet velocity. It seems as though a very light BCG might do that. For a fair comparison, suppose the bullet velocity is a constant. Then conservation of momentum says that the backward momentum equals the forward momentum of the bullet and gas combination. So the only variables would be in how the gas is directed and the time profile of the recoil force.
    So it seems to me that the only effects would be due to one of 3 variables (or a combination of them):
    1) Decreased bullet velocity
    2) Redirection of the gas
    3) The time profile of the recoil force.

    Beyond that, I can not follow all the details of the mechanism that you have described, so I can't add anything.
  5. Jul 28, 2017 #4
    Here is a more complete animation:

    As you can see here, the BCG doesn't even start moving until after the bullet has left the barrel -- so the weight of the BCG cannot possibly have an effect on muzzle velocity directly. If anything, a lightweight BCG would increase bullet velocity by a very small factor, because one would typically reduce the amount of gas that is redirected for cycling the BCG, resulting in slightly higher gas pressure for the last few inches of the barrel.
  6. Jul 28, 2017 #5


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    Good video. It's not clear to me how they stop the BCG from being pushed back as soon as the bullet fires, but I'll take their word for it. That seems to leave us with the principle of conservation of momentum. I can only think that the recoil might seem different because of a different force time profile. But one way or another, conservation of momentum must apply.
    Last edited: Jul 28, 2017
  7. Jul 28, 2017 #6
    Good question! That is the "rotating bolt" -- basically, the bolt has a bunch of locking teeth on it that slip through matching teeth on the back of the barrel. At the very end of its travel, it is forced to rotate so that the teeth are locked into the barrel. This prevents the bolt from recoiling and presents a solid surface for the gasses to push off from. You can better see from this animation here:

    Yes, conservation of momentum must apply...and if we assume that the compensator is 100% efficient, then what this means is that the final forward momentum of the bullet must be equal to the final rearward momentum of the gun, excess gasses, and BCG.

    However, I've had another epiphany...

    In my previous post, I argued that it made no difference (other than time) if rearward momentum was conveyed through the BCG vs. excess gasses. However, upon further consideration, any rearward momentum that is initially absorbed by the BCG will then be transferred into the recoil spring, and then released from the recoil spring...giving all this forward momentum back to the BCG, and giving an equal amount of momentum rearward in the gun itself.

    So in other words, when momentum is transferred to the BCG, this results in a delayed counter-recoil of the gun, followed by an even more delayed giving back of recoil to the gun in the original amount. In other words, any momentum initially taken up by the BCG doesn't reduce the net rearward momentum of the firearm one iota. In contrast, momentum that is put into rearward gas pressure is a permanent reduction in the final rearward momentum of the gun...so by using a lighter weight BCG, we funnel more gas down the barrel, hence more gas is reflected by the compensator, hence the final rearward momentum of the gun itself is reduced.

    Impulse force is the change in momentum over time, so if we've concluded that the lower BCG configuration results in less rearward final momentum, then by definition the "impulse force" (aka recoil) of the gun over the recoil duration is reduced.
  8. Jul 28, 2017 #7


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    I'm afraid that I can't help much, but what you say sounds plausible. The redirection of some of the gas backward (or even sideways) would reduce the recoil. Also, the spring actions may spread out the force over a longer time and that may make it easier to resist the recoil even if the total impulse is the same.
  9. Jul 29, 2017 #8
    Well, what would you actually 'feel' as a reduction in recoil? Because you can impart equal momentum by either a short high force or a long low force. Maybe the whole mechanism of the recoiling mass is to spread out the imparted momentum onto the shooters hand over time? (as FactChecker also pointed out) At the point in time where BCG starts moving it does absorb energy and stores it first as kinetic energy of the moving BCG (this will take away of the reaction force at that time instance) and then gradually as potential energy into the spring, which, indeed later will given back to the gun.

    This would however not explain the reduction of recoil due to limiting the weight of the BCG. In fact, it would argue that it increases. Since a lighter BCG, at equal velocity contains less kinetic energy. And you said they decrease the buffer spring tension such that the capacity of the spring to store potential energy is lower. So, I agree with you that the adaptation of the BCG by itself cannot explain the reduction of the recoil felt.

    So, well then, the only thing that indeed might happen is that more gas is accelerated backwards by the compensator as you explained. Because the reduction of gas flow means that more gas will have to move out of the front end.

    This last thing makes me wonder, because this also means that the bullet may in fact have a higher exit velocity. Isn't that a benefit as well?
    (Says me, who has no experience with nor knowledge about guns and anything around it in any appreciable way.)
  10. Jul 29, 2017 #9


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    It's definitely a benefit in lethality, accuracy, and range, but it increases the momentum in the forward direction and therefore the recoil.
  11. Jul 29, 2017 #10
    Indeed, and thanks for joining the conversation. I agree, a short high force is certainly going to contribute to more felt recoil and loss of accuracy than a long drawn out long force, because your muscles will be able to react and control the firearm.

    As explained in my "thesis" above, I think this is false -- but I don't blame you for not following my long drawn out logic :)
    Let me see if I can explain it more concisely:

    The BCG is pushed rearward by gas pressure that was already moving rearwards through the gas tube. All the momentum of this gas was already subtracted from the rearward momentum (recoil) of the gun at the point in time when the gas reflected off the gas valve and changed direction, when it had to push forward on the gun in order to do a 180 degree turn. If the BCG were removed entirely, that gas would just continue to shoot out rearward out of the ejection port and would not have any further impact on the gun's momentum. However, if you keep the BCG in the rifle, then the momentum of this rearward moving gas will be converted into rearward momentum of the BCG, which is then put into the buffer spring, and then re-emitted as FORWARD momentum of the rifle when the spring releases its tension and pushes the BCG forward into battery. Therefore, momentum carried by the BCG is not "momentum subtracted from the gun's recoil"...rather, it is momentum that had already been subtracted from recoil that is going to be ADDED BACK into the gun's recoil with a delay!

    In summary, the momentum was subtracted from the gun's recoil by opening the gas valve (which would shorten the primary recoil impulse of the gun on its latter weaker stage)...and added back into the gun's recoil via the BCG (as a secondary recoil impulse).

    Now, one might argue that you can't simply open the gas valve more without putting in a heavier BCG (it would result in various failures and unreliability if the gas pressure was too much for a light BCG). So in that sense, using a heavier BCG "allows" you to open up the adjustable gas port, and this subtracts from the primary recoil impulse in exchange for a secondary delayed recoil impulse.

    However, this tradeoff only makes sense if you DON'T have a compensator...because when you have a compensator, all the excess gas is reflected back to the shooter (reducing primary recoil impulse) anyway. Therefore, if you are using a compensator, you'd be better off reducing recoil by letting the compensator reflect all the excess gas, rather than trying to redirect it via the gas tube -- because that momentum is just going to come back with a delay.

    I disagree with all of this for the same reason as above.

    Yes, that would be another slight advantage. Higher exit velocity would yield slightly flatter trajectory and increased resistance to wind, making longer range shots more accurate.
    Last edited: Jul 29, 2017
  12. Jul 30, 2017 #11
    Ah, so we agree that if the force is spreaded over time, the felt recoil is less?

    Well, that's interesting. It seems that I'm the one who has the long drawn out logic, because everything you are saying next, is pretty much what I wanted to say as well, only in different words... So it seems we agree :). Let me explain:

    Now, that delay, that was exactly my point! Indeed, I think the BCG works to delay the recoil, but also spread it over time. Because at the instance the BCG starts to move it 'absorbs' kinetic energy, this energy is not converted at this time to a recoil force, so at this instance in time the felt recoil is less. Of course, then the spring starts tensioning and slowing down the BCG, i.e. converting its kinetic energy to its own potential energy (or spring energy). This already increases the backward force, but the spring will keep on pushing until the BCG is back in its original position. So this whole reciprocating move of the BCG is about spreading the recoil over time.

    That was exactly my point when I said that "This would however not explain the reduction of recoil due to limiting the weight of the BCG". It seems here that you agree with me that a heavier BCG would reduce primary recoil in return for a secondary delayed recoil. This would spread the total recoil over time and reduce the felt recoil as we seem to agree upon.

    So indeed, we end up at the same conclusion. Decreasing weight of the BCG doesn't decrease the recoil on itself (it may even increase it), it is because there is more exit gas to return via the compensator that this trade off works :)

    Nice to know!
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