Calculating rifle movement as bullet reaches muzzle

[wwbrown]

At risk of wanting to pull more of my hair out I will try to add something to the discussion:

If what you want to know is how much the barrel moves AND you want a solution that does not rely on some simplifications of the physics at hand that may cause large errors in the final, measure it.

With high speed computers and sensors this is a category of problem that is much easier to measure than probably is to calculate. It could be measured in a variety of ways:

1. High speed video photography where the camera is perpendicular to linear scale.
2. High speed linear recorders and associated ADCs
3. Lasers reflected off of linear scales read by a photocell.

Are just the 3 that come to mind.

What would not work is a using a high speed accelerometer as Physics and Math rear their ugly head and the errors from the accelerometer grow huge by the second integral.

Now to possibly rain on some parades.

If we realize the that the motion that impacts the impact on the target is not the motion parallel to the barrel or bullet's path recoil ... but the motion transverse to the bore axis, We then realize that the conservation of momentum while is a tool that can help us quantify recoil but will tell diddley squat about the impact of the accuracy of the system. Accuracy as I understand it is measured at the target because the measurements at the target are all transverse to those quantities that conservation of momentum helped us understand.

The transverse motion largest contributor is probably barrel whip, and to state for the last time conservation of momentum as discussed will not get any information about barrel whip.

To bring it to boys and boats system which seem so popular the barrel whip is analogous to the motion caused by the boy if he jumps up and down and has nothing to do with a leisurely stroll down the boat.

Added in the Edit: Modeling the barrel whip makes the recoil calculations trivial and the solution is not in modeling and sim but measuring it as I started this post off with.

Like I said this was against my better judgement,
wade

 

[RegionRat]

And to add to the misery....

It is the non-repeatability of what wwbrown said that matters.
The general principal holds true, light gun with big recoil opens the door to problems since the amplitude of everything is exaggerated.

Magnum sporting guns with light profile barrels represent the biggest challenge in the labs or models. They have the worst combination of recoil displacement amplitudes and secondary mode shapes that affect the outcome.

I remember trying to collect baseline modeling data that we later used for thermal weapon sight design. The management humored me while I collected parallel data for the rifle designers. The rifles looked like they were going bungee jumping with all the wires coming off them.

 

[TaperPin]

If what you want to know is how much the barrel moves AND you want a solution that does not rely on some simplifications of the physics at hand that may cause large errors in the final, measure it.

Brian Litz has done that with a number of different rifles using high speed photography at the muzzle. He also has a formula for estimating rifle travel while the bullet is in the bore - I haven’t seen it yet, but look forward to reading what he has on it - I don’t know if it’s a momentum based calculation, or an equation that describes the results of his tests.

 

[TaperPin]

If we were to hang a gun on strings and fire it, the boundary supports will affect the answer.

The mass and air resistance of a few filaments of carbon fiber to suspend the rifle would be so small, even without an engineering degree I could estimate the error from that would be quite small, not zero, but quite small.

I will add that to the list of reasons the gun displacement can’t be calculated.

”He who is good with a hammer thinks everything is a nail.”
Engineers seem to be wired to think in terms of work and energy in dynamic systems, and desperately want to use those skills to solve this problem, no matter how much the question is paired down and simplified. Every other post goes outside of the original question of rifle displacement at a single point in time when the bullet has traveled a known distance, and I have to wonder why it’s so pervasive to want to complicate the question.

 

[TaperPin]

Those web based recoil estimators are basics for putting a perspective on various rifles and cartridges, not ones for solving where a bullet will land on a target due to the displacement of the gun.

My question has nothing to do with solving anything related to bullet travel or external ballistics - it’s a simple question of the linear distance the rifle moves while the bullet is still in the bore.

 

[TaperPin]

I have an honest question about the mindset of an engineer.

Instead of a rifle and bullet, what if the client wants to know how far the body of a free floating servo will recoil backward when the plunger is extended, ignoring resistance of the wires or friction of what it’s sitting on.

We know the stroke is 10mm.
Is this how it would be figured out?
10mm x mass(piston) = displacement(body) x mass(body)

 

[dryhumor]

Why not determine by peak pressure how much velocity is generated in moving a given mass of projectile. And apply the same math to moving the mass of the rifle.

It’s apparent that the many variables involved are in flux, why not distill it down to a viable “generally, for X grain projectile weight at X PSI, moving at a speed of X, a rifle of X mass will move X amount”.

That posted video of brake testing would be a decent example. There was a stated FPS and projectile weight. There was a peak pressure involved, that could be determined. The un braked shot demonstrated linear gas flow out of the muzzle. The shot produced on video demonstrated the linear reaction of the rifles mass on the carriage. The rifle moved X amount in X seconds. All the “general” requirements are there to determine an answer.

There are already numerous tables of felt recoil out there. Those same principles should be able to determine rifle mass movement based on the velocity/peak pressure correlation.

 

[RegionRat]

I have an honest question about the mindset of an engineer.

Instead of a rifle and bullet, what if the client wants to know how far the body of a free floating servo will recoil backward when the plunger is extended, ignoring resistance of the wires or friction of what it’s sitting on.

We know the stroke is 10mm.
Is this how it would be figured out?
10mm x mass(piston) = displacement(body) x mass(body)

View attachment 1502918

Here is my mindset.

Why don't you order one of those and compare your math to some simple tests?

If you do a good job, I'll proffer your resume and get you a job as a dynamicist at the national labs.

 

[Varminterror]

@davidjoe - remaining, you absolutely miss what is happening in both the video you watched with your own eyes and what would happen in a rifle with a plugged barrel.

When the boy stops walking, he ceases his momentum, and that of the board, by pressing FORWARD on the board. Exactly the same as he generated his relative movement by pressing REARWARD on the board, there was an equal and opposite reaction. When he starts walking from a stop, he also starts the board moving. When he stops himself, he also stops the board.

Equally, when you fire that 1000 foot long barrel, the bullet will start moving one direction and the rifle will start recoiling in the opposite direction. When the bullet hits the plug and is caught, it will stop again, relative to the barrel, and the rifle will also stop. The center of mass will not have moved, but the rifle WILL have moved towards its buttstock - it WILL have recoiled, until it was stopped by the bullet stopping in the plug. Firing another bullet would do exactly the same thing. But the sum of the displacements of the rifle relative to the center of mass will never actually displace the rifle farther than the relative displacement of the bullet masses - in other words, the center of mass will always remain within the bounds of the rifle, so the rifle can’t actually move farther than the length of its own barrel (or even that far, just using this as an absurd and unattainable maximum).

So a normal rifle fired in space, would fire a bullet which would travel forever, and the rifle would recoil rearward forever. BUT… a rifle with a plugged muzzle which catches the bullet (neglecting the applications problem of how to move the gases from in front of the bullet(s) to behind) could never, even with infinite shots, actually ever move its center of mass in space. The rifle would move towards its buttstock slightly - less than the length of its own barrel - but could never actually move farther than the bounds of its own length.

 

[davidjoe]

@davidjoe - remaining, you absolutely miss what is happening in both the video you watched with your own eyes and what would happen in a rifle with a plugged barrel.

When the boy stops walking, he ceases his momentum, and that of the board, by pressing FORWARD on the board. Exactly the same as he generated his relative movement by pressing REARWARD on the board, there was an equal and opposite reaction. When he starts walking from a stop, he also starts the board moving. When he stops himself, he also stops the board.

Equally, when you fire that 1000 foot long barrel, the bullet will start moving one direction and the rifle will start recoiling in the opposite direction. When the bullet hits the plug and is caught, it will stop again, relative to the barrel, and the rifle will also stop. The center of mass will not have moved, but the rifle WILL have moved towards its buttstock - it WILL have recoiled, until it was stopped by the bullet stopping in the plug. Firing another bullet would do exactly the same thing. But the sum of the displacements of the rifle relative to the center of mass will never actually displace the rifle farther than the relative displacement of the bullet masses - in other words, the center of mass will always remain within the bounds of the rifle, so the rifle can’t actually move farther than the length of its own barrel (or even that far, just using this as an absurd and unattainable maximum).

So a normal rifle fired in space, would fire a bullet which would travel forever, and the rifle would recoil rearward forever. BUT… a rifle with a plugged muzzle which catches the bullet (neglecting the applications problem of how to move the gases from in front of the bullet(s) to behind) could never, even with infinite shots, actually ever move its center of mass in space. The rifle would move towards its buttstock slightly - less than the length of its own barrel - but could never actually move farther than the bounds of its own length.

You are simply picking the option, one of two laid out, more than two years ago, that bullet exit is required for true recoil, above and beyond recentering.

You do realize, don’t you, that your analysis of limited motion is not a new unforeseen outcome, right? That I cast it as one of the “two horns of a dilemma” should be a tip off that no, I haven’t “missed” it.

The reason this hypothetical was devised more than two years ago, was to draw out that recoil, all but that smallest component of it, IS EXIT DEPENDENT. Did you ever read my thread about a magnum not being inherently less accurate, which thread’s thesis is that the disturbance of magnum recoil occurs mainly after exit, when the bullet is already gone? This hypothetical was developed in an organic discussion after I opined about walking on a trailer, and that slight effect on it, not being speed dependent, it’s all there, 2021, deja vu.

Please tell me that you can see why the hypothetical was devised in the first place. It was devised to force deep thinking about bullet exit being needed for true recoil to occur, or else you are stuck with an impossible rocket.

On the one hand, I thank you for supporting the thesis, on the other hand my brows are furrowed at you. Even if you blew past my references here to see my older thread, I’m calling it an impossible rocket as I pose to you the horns of the dilemma. This means it cannot work.

Thank you for describing further why it cannot work, an already stipulated conclusion implied in calling it an impossible rocket, before it was posed, that was by no means stumbled upon, but distilled from much thought on the subject, preceding my bringing it up originally.

But now you have sided firmly with my older thread thesis, and described for yourself exactly why all of recoil that is not displacement limited - that vast majority of it, exists only post-bullet exit, meaning a magnum’s accuracy is not held back by pre-exit recoil relative to other cartridge choices.

You think you are telling me I’m wrong, but you are telling me the opposite. I do hope and trust that you appreciate that in the video, the boy traversing the board analogizes only to recentering balance, that period while the bullet remains in the barrel, and that only if he leapt off of the board, and it careened back, (recoil) would that system replicate the analog of a bullet leaving the barrel of the gun, and it would reset the system, which is a gut feeling problem I felt with you saying that a plugged barrel still serves as a vent, when exit does matter.

And I hope you appreciate that the video experiment was performed on water because recentering is a weak force to overcome. All statements that say only that the rifle recoils while the bullet is in the bore, and leave it at that, mislead people about how weak and easy to stop the imbalance is, which no doubt is why so many other close up videos show no movement.

 

[Varminterror]

that bullet exit is required for true recoil

Absolutely not.

The only way you could possibly believe that a rifle moving rearward in response to being fired is NOT recoil, then you are concocting some nonsense definition of the word, “recoil,” which does NOT correspond to “a rifle moving rearward in response to being fired.”

 

[Bottom Fodder]

I would really like to watch this debate on live streaming TV. Complete with illustrations and demonstration, they mite turn it in to a weekly podcast

 

[davidjoe]

Absolutely not.

The only way you could possibly believe that a rifle moving rearward in response to being fired is NOT recoil, then you are concocting some nonsense definition of the word, “recoil,” which does NOT correspond to “a rifle moving rearward in response to being fired.”

I take it you don’t refute anything else I said, and that’s progress.

You, as I have already mentioned, use the word “recoil” to encompass literally all, or nearly every generic motion there is, even though the context is firing a bullet, on a gun forum, which tends to merge distinct forces.

There is no doubt in my mind, that if we were not thinking about a bullet zipping out of a rifle, we would not use the word recoil to describe imbalance in an object, rifle or not. Me sliding the gun to its stop in the rest generates multiple recoil events by your usage which is at least doubly complicated but isn’t 1/10 as interesting, to anyone.

For this reason, to me, it makes ever so much sense in a gun forum to use “recoil” for what’s unique to a bullet firing and “recentering or unbalanced” as descriptions of the generic motion of all things sharing contact where one moves.

I’ll use your own analysis to support my argument of a terminology distinction, imbalance is inherently limited by displacement. Recoil from exit is not.

The board will never move more than it’s length while the boy is on it, but when he leaps pushing against it, there is no predetermined limit to how hard he can push off and fling it. Did they use the word recoil in the board on water video? Our language incorporates different words for far less reason than this.

 

[dgeesaman]

I have an honest question about the mindset of an engineer.

Instead of a rifle and bullet, what if the client wants to know how far the body of a free floating servo will recoil backward when the plunger is extended, ignoring resistance of the wires or friction of what it’s sitting on.

We know the stroke is 10mm.
Is this how it would be figured out?
10mm x mass(piston) = displacement(body) x mass(body)

Engineering is largely about knowing when a quantity matters, and when it does, how much it matters (accuracy) and whether to use analysis or experimental measurement, or both. Some engineers enjoy the convenience of doing business in just one realm of design method, but the reality is that all of them play an important role.

Unless someone has both a good friction model and pressure curve for 22LR, I agree that experimentally measuring rifle recoil is the smart way to go. The pressure profile is anything but constant, and the friction of the bullet during the early moments of ignition and bullet movement are not easy to predict. (Note that in Quickload, there are a few fudge factors.)

FWIW I found a slide presentation that quoted some muzzle time data (this poster started a similar sh*tshow on rimfirecentral, demanding that the rest of us produce data and advanced calculations to retort his f=ma recitations. I'm not surprised to see the same thing happening here). Here are some stats:
- a 19" barrel shooting 22LR has a dwell time of .0015sec.
- a 28" barrel shooting 22LR has a dwell time of .0023 sec.
Assuming match ammo shooting at 327m/s from the 19" barrel, you can estimate average accelerations for these cases. But the numbers don't work out using basic equations of motion, because the acceleration in the barrel is not constant. We need both better data about the internal pressure and better math (Calculus) to properly account for what's happening.

That said, playing with those equations does suggest a bullet acceleration of 22,000-43,000 g's depending on which motion equation you plug in. That means a 10lb rifle would travel back about .008" during the .0015 dwell time. You'd want to use measuring equipment that is plenty sensitive in those ranges to build a successful experiment. A high speed camera can probably do it, if there is a way to capture the bullet initial movement.

 

[sjoliat]

I may have missed it if anyone posted in the previous eight pages, but here is some super high speed video of firearms recoiling after ignition. Recoil begins at moment of ignition, not the moment the bullet exits the barrel.

 

[davidjoe]

I may have missed it if anyone posted in the previous eight pages, but here is some super high speed video of firearms recoiling after ignition. Recoil begins at moment of ignition, not the moment the bullet exits the barrel.

problem solved. lol.

(Do read those other pages . )

 

[TaperPin]

Here is my mindset.

Why don't you order one of those and compare your math to some simple tests?

If you do a good job, I'll proffer your resume and get you a job as a dynamicist at the national labs.

I’ll add your sentiment to the list of reasons why this can’t be computed.

 

[TaperPin]

But the numbers don't work out using basic equations of motion, because the acceleration in the barrel is not constant.

I’m definitely not the same guy who posted on rimfire central, but it’s good to hear someone else asked he question and nobody could produce an answer why a rifle and bullet supposedly violate one of the most basic laws in physics, but simple tests in physics labs do not.

The latest video has two toy cars on a track. The track is supported at one point in the middle like a teeter totter. A spring pushes the cars apart and they travel in opposite directions. The track stays evenly balanced no matter what weights are used for the cars, because the center of mass of this closed system doesn‘t change. The acceleration is proportional between the two cars - if one car accelerates faster than the other, the equal and opposite reaction still maintains the overall center of mass, or center of gravity in this case. The acceleration is highest as the spring is most compressed and decreases to zero acceleration as the cars leave contact with the spring, so it seems a basic test shows constant acceleration isn’t required for this principle.

There’s definitely disagreement on the basic physics involved - it’s as if conservation of momentum of a closed system is a crazy idea.

After listening to a few more physics lectures about closed systems and non-moving center of gravity/center of mass, I was surprised to learn the two objects don’t even have to be in direct contact for this principle to hold true. Two planets separated by some distance have an initial center of mass, and as gravity draws them together the center of mass of the system doesn’t change, as long as the force that draws them together is from within the system.

Another physics lecture gave an example of a rifle in space and the center of mass/center of gravity before the rifle is fired remains stationary even a year after the bullet and gases have left the barrel. Of course after the bullet leaves the barrel it’s no longer a simple calculation. It also seems reasonable in normal air pressure once the bullet and powder leave there is a lot of air friction on both, and the common equations for total recoil energy attempt to quantify what’s going on.

 

[TaperPin]

FWIW I found a slide presentation that quoted some muzzle time data (this poster started a similar sh*tshow on rimfirecentral, demanding that the rest of us produce data and advanced calculations to retort his f=ma recitations. I'm not surprised to see the same thing happening here). Here are some stats:
- a 19" barrel shooting 22LR has a dwell time of .0015sec.
- a 28" barrel shooting 22LR has a dwell time of .0023 sec.
Assuming match ammo shooting at 327m/s from the 19" barrel, you can estimate average accelerations for these cases. But the numbers don't work out using basic equations of motion, because the acceleration in the barrel is not constant. We need both better data about the internal pressure and better math (Calculus) to properly account for what's happening.

That said, playing with those equations does suggest a bullet acceleration of 22,000-43,000 g's depending on which motion equation you plug in. That means a 10lb rifle would travel back about .008" during the .0015 dwell time.

If
10lb rifle x distance = bullet weight x 19” + powder weight x 9.5”
x = .011”

I assumed bullet weight of 40gr and powder weight of 1.5gr

It only took 15 seconds to rebalance the center of mass so It equals the initial location.

 

[TaperPin]

Acceleration cannot create or destroy mass.