Physics of shooting a rifle

[Hawg]

I have read that a .58 minie ball has twice the knockdown power of a 30-06. It has been documented that soldiers shot during the civil war with .58's fell forward.

[tangolima]

Physics is study of energy transfer. When there is enough energy, it is possible. The question is how to direct the energy to the right place. I'm holding on to the hope. Experiments fail to make it happen. It is just that. They fail to make it happen. Not a proof to the impossibility.

Before this discussion cork screws into a philosophical debate. Let's go back to muzzle climb.

Shoulder on the butt stock. Average force on the stock 50lbf for 2ms. Center of butt stock is 5" below bore axis. The torque to raise the muzzle is 250 inch-lb. It is being countered by the weight of the rifle. The CG is usually right at the chamber about 24" from the butt stock. 7.5lb gives rise a torque of 180 inch-lb. The net torque to rotate the rifle is 70 inch-lb or about 6 ft-lb.

It doesn't take much to significantly change POI. For a 40" long rifle, the muzzle just needs to rise by 0.01" to move POI by 1" at 100yd.

There are actually ways to totally eliminate muzzle rise. The above calculation gives a few hints.

-TL

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[stagpanther]

Grip on the foreend as well as the pull in would counteract some of that muzzle rise, I guess it really depends on how much rise there before the bullet clears the muzzle. The big magnums I shoot--especially ones without a muzzle device--repressing that muzzle lift is going to be hard to do (and transfer more felt recoil). It seems to me the muzzle lift is just another vector of recoil force resulting from a lever moment due to the off-centerline contact point of the shoulder.

[JohnKSa]

Physics is study of energy transfer. When there is enough energy, it is possible. The question is how to direct the energy to the right place.

The answer is that even when using tremendously more energy than conventional hunting rifle rounds, there's still just not enough energy applied in such a way as to make it happen. The problem is that a huge amount of the energy is used up doing things other than moving the target downrange. Any bullet deformation, any noise from the impact, any heat from the impact, any deformation of the target, any force applied other than directly downrange, all of that uses up energy. Just like the water balloon, there's a lot of motion at impact, but very little of the resulting motion is actually in the downrange direction.

Experiments fail to make it happen. It is just that. They fail to make it happen. Not a proof to the impossibility.

If experiments using projectiles with far more energy and momentum than conventional rifle rounds, hitting targets that deform/yield far less than human tissue still fail to make it happen, what possible reason could there be to expect that far less energy and momentum with a far more yielding target could make it happen?

If 1000 + 1000 << desired result then how could 50 + 50 somehow provide the desired result?

Go shoot a prairie dog with a .338 Lapua and see what happens. It will get blown apart, but pieces will go in all directions with a center hit. Very little of the prairie dog will get moved directly downrange. Look at the old bowling pin matches. Even with high-momentum bullets, it was not a simple task to knock the bowling pins back off the edge of the tables and they are much tougher than flesh and blood and far, far smaller and lighter than humans.

Look at the results of the crash test dummy shot with a .50BMG at arm's length without the bullet exiting the dummy. It hardly moved backwards at all.

Physics is about observation, not about making wishes come true. Science is looking at the outcomes of experiments and accepting the reality of what they tell you.

There are actually ways to totally eliminate muzzle rise.

The Russians came up with a machinegun that did it. The action reciprocated straight backwards so that the next round was fired with no muzzle rise. Eventually the muzzle rose, but not appreciably until the 3 round burst was complete.

So that's one way, set up the action/barrel to reciprocate straight backwards until the bullet is out of the barrel.

A lot of recoil operated autopistols function like this. The coupling of the slide/barrel to the frame is loose enough during the period that the bullet is in the barrel that there is very little muzzle rise. Not until the unlocking process is significant recoil force first applied to the frame resulting in muzzle rise and, by design, the bullet is out of the barrel by then. Revolvers are much different. Since the coupling of the barrel to the frame is completely rigid, muzzle rise begins the instant that recoil motion starts.

Another way is to set up the stock and action so that the geometry results in recoil straight back into the shooter's shoulder so that the muzzle doesn't rise appreciably due to torque. The Chiappa revolver is an example of a design that tries to alter the relationship of the bore axis to the point where recoil is resisted by the shooter in such a way as to minimize muzzle rise.

[stagpanther]

Hmmm...I've seen videos of animals doing flips and wild jumps upon projectile impact--could be autonomic nerve system shock response?

[JohnKSa]

Right. Animals have the ability to move their bodies voluntarily or reflexively. If someone is stuck with a pin and jumps into the air, we don't attribute that motion to the energy imparted by the pin because we can stick inanimate objects with a pin and they don't move.

Same with bullets. The bullet strike may cause an animal to react by jumping/flipping, but unless the animal is very small and the bullet is quite energetic, that's a reaction, not the actual bullet imparting sufficient momentum to drive the animal into the air.

[jrothWA]

We have TOO much time, on our hands!

Should have used SI and drop some calculations.

[JohnKSa]

Yes, it's simpler in that unit system, but people seem more comfortable talking about pounds and foot pounds than about joules and Newtons.

[tangolima]

SI at school and imperial at work. I can go back and forth. Like telling the same story in different languages. None is better than the other.

Upward torque to raise the muzzle, and downward torque vise versa. No force on the stock butt or no distance between the barrel's axis and the center of the stock, there will be no upward torque. Theoretically possible but neither is practical. There will always be such upward torque the way we shoot. However the weight of the rifle and the position of the CG gives rise the ever present downward torque. As long as the upward torque doesn't exceed the downward torque, the muzzle will not rise during the barrel time. Note that the force between the stock and shoulder is never constant. It peaks after the bullet exits the muzzle so the muzzle may still climb. But that doesn't affect POI.

Not leaning too hard on the stock reduces the said force. Gun designs with low bore axis, such as AR, help shorten the moment arm. Long range shooters added weight to the forend to increase the weight and to move the CG away from the shoulder. Of course extra downward torque can be applied to the rifle by...slinging up tight.

Those are examples of methods to eliminate muzzle climb. There are a few more.

BTW, the force can really go to zero if the rifle is let free recoil. The ransom mega 2 rifle rest is such device. This leads to another rabbit hole for later.

-TL

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[tangolima]

We learned at gunsmithing school that American and European shoot their rifles differently. American firmly grabs hold of the forend, whereas the European rests the forend on their palm. One tries to eliminate or reduce the muzzle climb, and the other just lets the recoil do its thing. I asked my European coworkers, French, Finnish, Swedish, British etc, about it but it was inconclusive. They didn't remember exactly as they hadn't thought much about it.

My shooting is mostly on front rest and rear bag, either on bench or prone, with my left hand squeezing the rear bag. Effectively it is "European". The rifles I shoot are mostly milsurps with medium weight and steel plate on heel of the butt stock. POI elevation varies quite noticeably with loads. I'm pretty sure muzzle climb due to recoil plays a significant role.

I have been considering letting go of the rear bag and holding the forend with my left hand, pulling the rifle down on to the front rest. It will reduce, if not eliminate, the muzzle climb. I will give it a serious try.

-TL

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[mehavey]

High/mass recoil and/or snapshot -- Forearm hold
Offhand at targets -- from 5.56 through Garand -- flat palm/hand under forearm at/near balance point.
`59 Sharps and other carbines? Forearm hold.

Hunting? Any support I can get.

[tangolima]

The strongest kicking caliber I load and shoot is 8mm Mauser, which is really not bad. So I rest the forend on palm for offhand. POI elevation does change quite a bit if I change the load or my posture. Never really like slinging up. Maybe I should give it a serious try. Matching-winning-record-breaking people do that, do they not?

There is another very effective method to eliminate muzzle. Didn't know that till I started using bipods. Friend competes in PRS (precision rifle series). He demonstrated that with proper pre-loading the bipod, there could be no muzzle climb (they call that bipod hop) at all. I tried that and it was true. I couldn't understand how pushing the rifle forward could also keep it down. He has no clue either, only knows that it works. I finally figured out the mechanism. It is the downward torque created by the preloading force and the height of bipod.

That really got me thinking. I didn't care about bipod and vertical forend grip, as they are too tacticool. Now I want to put one on each of my rifles. Well one thing to watch out, only rifles with free floating barrel, or the cons will out weigh the pros.

-TL

PS I repaired a couple of 12 gauge auto shotguns with forends broken off. Shooters all held on to the forend tight while firing magnum rounds. The wood got torn off. I glued it back with epoxy. I had the same talk with owners to persuade them to perhaps let the recoil do its thing. I shouldn't mind the repeated business.

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[tangolima]

One more rabbit hole. Will stop if there is no interest. Don't intend to have monologue.

The recoil force is between the heel of the butt stock and the shooter's shoulder. It can be tapped off to cycle the action on auto loaders, as JohnKSa described in his post. Such designs are called short-recoil or long-recoil. Such designs, although simple, have one drawback. It can be limp-wristed or limp-shouldered, that the recoil force is inadequate to complete the cycling of the action.

Gas operated action is another kind of auto loading. Can gas operated actions be limp-wristed or limp-shouldered?

-TL

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[Bart B.]

I've coached team matches where 4 people shoot the same rifle and ammo. A couple MOA spread in sight zeros was normal. Both bolt action and semiautomatic.

[JohnKSa]

The recoil force is between the heel of the butt stock and the shooter's shoulder. It can be tapped off to cycle the action on auto loaders, as JohnKSa described in his post.

There are also actions, like Benelli employs in some of their shotguns, that exploit the inertia of a heavy bolt vs the force of acceleration of the rest of the action/firearm generated by recoil. That acceleration of recoil compresses a spring against the inertia of the heavy bolt and when the acceleration of recoil stops (and the force also therefore stops--remember zero acceleration means zero force) the spring then expands to operate the bolt and perform the extraction/ejection operations cycle with a conventional recoil spring in the stock then returning the bolt to battery, feeding a new shell in the process.

We know that conventional recoil operated systems work better the more rigidly the action is restrained from recoiling and will tend to malfunction if insufficient constraint is applied with a loose hold.

So does an action like the inertial action cycle more effectively when the firearm is rigidly constrained?

[tangolima]

Let me answer my own question first. I don't think one can out limp-wristing / limp-shouldering a gas operated action. After firing a shot, both the bolt and the receiver move backward due to recoil. The bolt needs to move faster enough than the receiver for the unlocking/extraction/ejection to work correctly. It is the relative speed that counts. In a gas gun, the bolt is always faster than the receiver (rifle) by the same amount, regardless the receiver's absolute speed. It works even when it is free recoiling. You can't out limp-wristing/limp-shouldering free recoiling.

Recoil operated and inertia operated sound similar, but they are indeed different. Instead of jumping neck deep into the minutiae, I just cut to the chase. We can discuss the details if there is enough interest shown.

Recoil operated. Free recoil: doesn't work. Butt stock against solid wall: works.

Inertia operated. Free recoil: doesn't work. Butt stock against solid wall: doesn't work either. The receiver (rifle) needs to be moving backwards and then be stopped abruptly. You need to have certain cushioning between the stock heel and shoulder, recoil pad, clothings, muscle etc, and yet you need to lean into the stock.

I was a bit surprised to learn our military chose an inertia operated shotgun. The design is on the finicky side. Shooting from hip, or any positions without firmly mounting on shoulder, could lead to unreliable cycling.

-TL

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[JohnKSa]

I don't think one can out limp-wristing / limp-shouldering a gas operated action.

I agree. The gas creates the velocity difference between the bolt and the action required to perform extraction/ejection/feeding and that's not going to change if the action is allowed to recoil freely.

Butt stock against solid wall: doesn't work either.

Correct. If the action doesn't recoil, it doesn't experience acceleration and that acceleration is what generates the force necessary to compress the inertia spring.

Inertia operated. Free recoil: doesn't work.

The key to the extraction/ejection function is the acceleration of the action and that is maximized if the gun recoils freely. The bolt's inertia is the same in free recoil as it is whether the action is partially or fully restrained so the inertia spring will get maximum compression when the action recoils as freely as possible. On the other hand, if the action is completely unconstrained I suppose it's possible that the recoil spring that returns the bolt to battery and feeds the next shell may not have anything to "brace" against to push the bolt back to battery and that may result in insufficient force to complete the feeding cycle.

[tangolima]

When the action is closed, the bolt is locked on to the barrel (or something similar) to contain the chamber pressure. After the projectile exits the muzzle, something comes along to unlock the bolt and move it back to extract and eject. That "something" differentiates one working mechanism for the other.

In a gas gun, that something will be powered by the gas from the gas port, which is straightforward.

In recoil operated action, that would be barrel and the bolt themselves. Driven by the reaction force that accelerates the bullet, they accelerate backward together. After the bullet exits the muzzle, one of them stops and they unlock and separate. Whichever still in motion will complete the rest of the cycling. Newton's 3rd law is the working principle.

The inertia operated action is a bit more convoluted. It involves something like a sliding hammer, with name like inertia sleeve or the sort, usually sprung by light spring. When shaking the gun hard enough it may even rattle. Upon firing the whole gun, including the inertia sleeve, accelerates backward. Then the rifle stops, and the inertia sleeve continues on. The kinetic energy of the inertia sleeve will complete the rest of the cycling. The working principle is Newton's 3rd law and 1st law.

-TL

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[JohnKSa]

Upon firing the whole gun, including the inertia sleeve, accelerates backward. Then the rifle stops, and the inertia sleeve continues on.

That would be a "momentum sleeve" and more or less recoil operation.

Upon firing, the inertia sleeve (Benelli calls it a bolt) stays stationary due to its inertia (thus inertia operated), and the acceleration/force of the action against that inertia compresses the "inertia spring". When the acceleration of recoil on the action stops there is no longer any force against the spring (F=m x a and when a is zero, F is also zero) and, the inertia spring decompresses, driving the inertia sleeve backwards with respect to the action at high velocity. That unlocks the bolt (Benelli calls the bolt a "locking head"), performing the extraction/ejection operation. At the end of rearward bolt travel, a recoil spring (independent of the inertia spring) drives the bolt/inertia sleeve back forward completing the feeding cycle.

In a recoil (momentum) operated firearm, the recoil (momentum) from firing drives parts backwards while the shooter holds other parts more or less still. The velocity (kinetic energy) of the parts moving backwards with respect to the frame/stock/action held in place by the shooter is used to perform extraction/ejection with a recoil spring performing the feeding/return to battery function.

In an inertia operated firearm, the recoil from firing drives the whole gun backwards while inertia holds one particular part more or less still. The acceleration of the gun with respect to the inertia part that stays still compresses a spring and the potential energy in that spring is then converted to kinetic energy to perform extraction/ejection with a recoil spring performing the feeding/return to battery function.

[stagpanther]

Much appreciate this knowledgable dialogue.

[cdoc42]

This thread has been supremely enjoyable by this 80-year retired pharmacist and physician who flunked physics in Pharmacy school because he didn't like the professor.
I read through it quickly only to justify why I flunked physics but massaged my ignorance by bringing to mind that I shot a nice 8-point buck at 9:45 a.m. today, dressed it, dragged it to my car, mounted it on the rear car rack, and responded to club members who advised they would take help take care of it for me it with, "Never say never to an old man."

[tangolima]

Physician flunked physics? Ha!

Newton's 1st law of motion is also called law of inertia.

"An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Same speed, zero (at rest) or non-zero (in motion). Unbalanced force. Those are the key phrases.

The action's operation has 2 phases; during the 2ms of recoil and after. During recoil, the inertia sleeve is under unbalanced force, either by direct contact to the receiver or via the inertia spring. It is being accelerated backwards. After the bullet exits the muzzle, the rifle is supposed to stop, and the inertia sleeve will be on its own continuing its backwards journey by its..inertia. I think the 2nd phase fits the concept of inertia better.

The inertia spring in Benelli is a supplement to optimize the operation. In geeky talks, it turns a 1st order system into a 2nd order one. Right at the end of recoil, the inertia sleeve moves and the spring is compressed. The total energy captured is the sum of the sleeve's kinetic energy and the potential energy stored in the spring's compression.

The spring comes with its Hooke's constant K. One extreme case is K being infinite, a very stiff spring or a steel disc if you will. This is the same as direct contact, like the system I have described in previous post. The capture energy is the sleeve's kinetic energy only. The other extreme is K being zero, a very soft spring or even air gap between the receiver and sleeve. Obviously it won't work, as sleeve has no kinetic energy and hardly is there any energy stored in compression.

I remember solving such problem in applied mathematics during my matriculation (It is a British thing. Last 2 years of high school is matriculation, or 1st year college equivalent). It involves solving differential equation. Maybe I will give it a crack during the weekend if I get bored. If I remember correctly there exists a combination of K and the mass of the sleeve that gives maximum captured energy.

Without the spring (direct contact), the sleeve can never be faster than the receiver, so the action won't work unless the receiver stops abruptly enough. With the spring it is possible that the sleeve travels faster than the receiver. However, I'm pretty sure Beneli can't be limp-shouldered, meaning it most probably won't work free recoiled.

Inertia action tends to be finicky. It needs good acceleration of the gun, and yet the gun needs to stop abruptly. These are seemingly contradictory. The general advice is to install recoil pad and lean into the butt stock. A saw-off Beneli with just the pistol grip will probably be problematic.

-TL

PS The force asserted by the shooter's shoulder on the heel of the butt stock probably doesn't form much of a constrain to the rifle's acceleration. In the early posts, we established that the reaction force on the rifle is about 1000 lbf, whereas the force on the shoulder is about 50 lbf, or 5%.

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[JohnKSa]

The inertia spring in Benelli is a supplement to optimize the operation.

The inertia spring is what operates the action for extraction and ejection.

During recoil, the inertia sleeve is under unbalanced force...

The inertia sleeve is more or less stationary during the acceleration phase of recoil during which time the inertia spring is compressed. As soon as the acceleration phase of recoil ends, so does the force against the inertia spring--no acceleration, no force. At that point, the inertia spring's potential energy (stored during the acceleration phase) is converted to kinetic energy to drive the inertia sleeve backwards to operate the action.

Right at the end of recoil, the inertia sleeve moves and the spring is compressed.

Right at the beginning of recoil, during the acceleration phase, the spring is compressed. As soon as force against the spring ends (as soon as the bullet exits the barrel and the acceleration phase of recoil ends), it decompresses and at that point it drives the inertia sleeve backwards to operate the action.

However, I'm pretty sure Beneli can't be limp-shouldered, meaning it most probably won't work free recoiled.

The extraction/ejection works best with free recoil because that maximizes the acceleration and therefore the amount of potential energy stored in the inertia spring which operates the action. There can be problems with the feeding stage if the gun is moving backwards too freely at that point and not providing a solid platform for the recoil spring to push against to return the inertia sleeve/bolt to battery.

The action you are describing is a momentum/recoil operated action where the parts are driven backwards by recoil/momentum and then continue moving backwards to operate the action while the rest of the firearm is stopped by the shooter.

In the inertia system, the inertia spring is compressed by the acceleration of recoil acting against a part that stays more or less still during the acceleration phase of recoil. When the bullet exits the barrel and recoil acceleration stops, at that point the inertia spring begins to decompress to drive the inertia sleeve backwards relative to the rest of the gun.

In a momentum/recoil operated firearm, the parts that operate the action are put in motion instantly by recoil and their momentum operates the action.

In an inertia operated firearm, the parts that operate the action are more or less stationary for the initial part of recoil and their inertia relative to the rest of the firearm is used to compress a spring which then operates the action.

Don't take my word for it. See what Benelli says.

[tangolima]

Well, John, I guess we have different takes on the system. It is quite alright. Let's shift gear to something else, shall we?

When I first started handloading (I prefer that to reloading), I had a mentor. He quite liked using slower powders for pistols. The recoil is milder. Instead of snappy shove, it would be a gentler push, so he told me. So I started with just that, slower burning powders.

However I found it was quite the opposite. The recoil with faster powders, similar bullets and MVs of course, is actually more agreeable.

How so?

-TL

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[JohnKSa]

Here's a link to a video. At about 1:03, you can see that the inertial sleeve actually appears to move forward during the initial phase of recoil. That is because it stayed still (inertia) while the gun accelerated backwards.

https://www.youtube.com/watch?v=XgMaOdkQCkU

Furthermore, as the recoil continues, you can see that the bolt/inertial sleeve, after the inertia spring is compressed and decompresses, are moving backwards faster than the gun is due to the inertia spring's force.

Here's a closeup showing that at the initial moment of recoil, the inertial sleeve stays still (appears to move forward relative to the rest of the recoiling firearm). This demonstrates that the gun is not momentum operated. The sleeve doesn't recoil with the gun, it stays still initially while the gun recoils. It doesn't move backwards until after the inertia spring decompresses and drives it backwards.

https://www.youtube.com/watch?v=TvgtB2hTWaI

Here's a video from Benelli explaining how the system works.
https://www.youtube.com/watch?v=hLro9wdHq44

The explanation is completely consistent with the description I provided above.