Physics of shooting a rifle

[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.

 

[tangolima]

The force that compresses the spring also asserts on the sleeve (action and reaction). It will accelerate backward as the spring is being compressed (F=m x a). The sleeve can't possibly be stationary.

Heavy sleeve/soft spring = slow sleeve/a lot compression. Light sleeve/stiff spring = fast sleeve/little compression. It is also possible that the spring bottoms out during recoil. It becomes a solid steel disc. That may well be the Benelli trick. The sleeve aquires the same speed of the receiver and is further accelerated by the compressed spring.

I think qualitatively we are taking about the same thing. Difference is in the quantities. The video clips are good. But they could be a bit over simplified for marketing purposes.

-TL

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[JohnKSa]

The sleeve can't possibly be stationary.

Yes, of course, there will be some acceleration on the sleeve before the acceleration cycle of recoil finishes because the spring is very stiff, but the point is that the sleeve is propelled by the spring, not by the impulse of recoil. It's absolutely clear in the videos that initially the sleeve stays more or less still (note that I've been saying "more or less still" repeatedly throughout this exchange) during the first part of recoil which is not how a momentum/recoil operated system works.

In a momentum/recoil operated system, the moving parts get all their kinetic energy before the bullet leaves the barrel from conservation of momentum. In an inertia operated system, the moving parts get their kinetic energy mostly after the bullet leaves the barrel from the potential energy of a spring. It's a fundamental difference and it is clearly visible in the videos.

If the gun were recoil operated, the bolt would move with the gun as soon as recoil begins and then continue rearward when the shooter's shoulder decelerated the gun. Instead, it does not move with the gun in recoil, it initially stays more or less still and that inertia compresses a spring which then drives the bolt rearward when it decompresses.

The video clips are good. But they could be a bit over simplified for marketing purposes.

They actually show the system in operation. No way to oversimplify that--you can see what is actually happening as the system operates.

The explanation Benelli gives (and the one I've given) is consistent with physics and with what can be seen visually in the videos. There's no need to try to cast about to come up with some other explanation for how it works--we can see how it works in the video and we can hear how it works from the people who designed the system and worked out the physics to make everything function properly.

I think qualitatively we are taking about the same thing. Difference is in the quantities.

I think that if you can convince Benelli they don't know how their system works, you may be onto something. Until then...

 

[tangolima]

Ok John. Let's set this aside and move on to something else, shall we? Thanks.

-TL

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[tangolima]

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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I'm answering my own question. Hopefully the discussion can be restarted.

The recoil follows the principle of conservation of momentum. The momentum comes from the projectile and the gas existing the muzzle. The mass of the gas equals the powder charge. The speed of gas is generally higher than the projectile, so the gas' momentum is significant part of the equation.

Slower powder requires higher charge for the same MV. It has flatter pressure curve, which often leads to higher muzzle pressure. The gas exits at higher speed as result. That's why slower powder tends to have more recoil force, louder report, and more visible muzzle flash. True that the peak pressure is lower than faster powder, but human body most certainly can't tell the difference for events all happen within a minisecond or two.

Actually I managed to use this mechanism to improve one of my loads. I experimented with .22TCM9R. Found a conversion upper for Glock 23. The recoil spring is very soft, and yet it doesn't cycle reliably, even when the load is maxed with bullseye. The MV is crazily high. But with the light 40gr bullet, the momentum is just not enough. I switched to Ramshot enforcer, and it worked. It is loud with big ball of fire. Basically the slide is rocketed backwards by the hot gas to complete the cycling.

Okay, next rabbit hole is canting of sight and its effects on POI, if there is still interest from the forum.

Before going down the hole, let's take a sidetrack. Why is it dangerous to shoot a gun under water?

-TL

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[tangolima]

I'm compiling a dope chart for my .22LR rifle out to 300yd. I have the elevations from actual test firing. But I need windage dope, assuming 10mph full value cross wind. I can't use ballistic calculator as I don't know the bullet's BC. Well I could, by extracting the bullet's BC, but it is unnecessarily messy.

Here are relevant figures
Distance 200yd
MV 1250fps
Elevation 22MOA
Zero 50yd (It is a first crossing zero)
Sight height 1.5"

I managed to come up with a method that works quite ok. Give it a thought if it interests you. I will post details of my approach later. Hint: flight time is the key.

-TL

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[stagpanther]

I shoot a lot of 22lr out to 200 to 250 yds as well; very interested in your results but perhaps this would be a better topic on a different thread? So far my experience with any velocity 22lr ammo is that a crosswind of 10 mph for long distances shooting is going to scramble the impacts--no matter how fast the bullet is flying given existing 22lr bullet designs. I've shot lots of cartridges at those distances and have yet to come up with any "definitive" correlation between velocity and accuracy. But I keep hoping and trying nonetheless.

 

[JohnMoses]

A couple of points-
1) no one has mentioned secondary recoil. The energy to make all this happen comes from a phase change from solid to gas. This is a constant - powder type does not matter, the solid gunpowder increases its volume by a factor of 7000 ( I think). Thus you need to know powder charge and gun weight to calculate recoil.
2) Bill Davis, inventor of the 'bulletproof' vest, would stand on one leg on a 5 gallon bucket and shoot himself with a 44 mag and eventually a 308 H&K to prove you don't get knocked down. Newton was right.

 

[tangolima]

Finally a reply! Contemplating this sort of topics is part of the reason I enjoy this hobby. I have been trying to keep this thread alive so that we can have enjoyable conversations. The result so far is mixed at best. One more try perhaps.

I totally agree with your observation on .22LR. Its MV and BC are so low that any disturbance in the air will easily push the projectile off course. The windage dope is certainly a bit on the academic side. It assumes consistent wind at all points along the projectile's journey down range, which is of course impossible. However, I have found it quite useful as a starting point from which small adjustments are made on shot-to-shot basis, based on the shooter's ability to detect variations in the wind. On range, before firing, I usually would spend a few minutes to read the several things that tell the wind; flags, grass, etc, paying more attention to locations near me than the target. I try to come up with a figure of "prevailing cross wind". With that I look up the dope and dial it in. Then I fire a few shots on the berm to verify. Adjustments thereafter are mostly made by hold-over with reticle.

All the literatures on external ballistics I have read so far point to one common factor; the projectile's flight time. Less flight time, less error. For that I came up with a figure of merit to gauge performance of a bullet. It is the product MV*BC. Higher the better.

I will write up the details of my method and post it in a few days. Hopefully it will gives interested folks a chance to think about it. I'm delighted to share what I have found, but will be more so if someone can beat me to it.

-TL

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[tangolima]

Got home from a trip. Fighting off jet lag and a bug picked up in flight, I finally can get back to this one.

The dope in my previous post was pulled out of my memory. There are a few errors. Let me restate.

Distance 200yd

MV 1250fps

Elevation 26MOA

Zero 50yd (It is a first crossing zero)

Sight height 1.5"

Here are the steps.

The gun's bore inclines above the horizontal line by an launch angle A.

For 50yd zero, A=1.5/50*100=3MOA

For 200yd zero, A = 3 + 26 = 29MOA

A << 6 degree, so principles of flat firing apply. Flight time can be estimated from bullet drop d.

d=29 * 2 = 58" or 4.8'

Actual flight time

tf = sqrt(4.8 * 2 / 32.34) = 547ms

Flight time in vacuum

to = 200*3/1250 = 480ms

10mph wind is equivalent to 14.7fps.

Following point mass model, the wind deflection at 200yd is

w= (0.547 - 0.48)*14.7 = 0.98' or 11.8" or 5.9MOA

A few points to note
1. This method applies to all similar situations, where actual vertical dopes are known. Handy for cast bullets with unknown BC.
2. Flight time is estimated by gravity only. Actually flight time is always longer, although slightly for short distances.
3. Wind deflection (windage dope) is proportional to the cross wind speed. 5.9MOA @10mph, 3MOA @5mph etc.
4. Putting the equation in spreadsheet can be a useful tool.

Hope you find this interesting.

-TL

PS I'm putting together a spreadsheet of this. PM me if you want a copy.

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[tangolima]

A couple of points-

1) no one has mentioned secondary recoil. The energy to make all this happen comes from a phase change from solid to gas. This is a constant - powder type does not matter, the solid gunpowder increases its volume by a factor of 7000 ( I think). Thus you need to know powder charge and gun weight to calculate recoil.

2) Bill Davis, inventor of the 'bulletproof' vest, would stand on one leg on a 5 gallon bucket and shoot himself with a 44 mag and eventually a 308 H&K to prove you don't get knocked down. Newton was right.

JohnMoses. The discussion has changed topics several times. Please read the early posts. Newton wasn't wrong, but the way we apply his principles may be. Thanks.

-TL

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