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Calculating rifle movement as bullet reaches muzzle

TaperPin

Since google is not as much in the business of providing answers as much as selling products and keywords, it’s surprising difficult to find something as simple as how far a rifle moves before the bullet leaves the barrel. Where I’m going with this is just adding a good, even if rough, value to the movement in discussions - rather than explaining to a kid the gun moves an amount that nobody knows, it would be awesome to be able to say in free recoil it might move .0xx” and with a good two handed hold and shoulder pressure that changes it .00x”.

Engineers among us will find this quite simple, so humor me

From memory of physics 101 years ago (feels like 101 years ago), I’m tending to think it would be a simple conservation of momentum? Roughly, if powder expands equally, would the distance of the center of mass of the powder be about half the barrel length, ignoring volume of cartridge case above and beyond the bore diameter?

mass(gun) x distance(gun) = mass(bullet) x distance(bullet) + mass(powder) x distance(powder)

My gut says that’s the easy part and describes the rifle in free recoil at the moment the bullet exits. Has anyone seen, or wish to take an educated guess, as to what kind of range a two-handed hunter hold combined with pressure from the shoulder adds to the mass of the rifle, reducing movement?

Somewhere, someone has high speed camera footage of free recoil and different holds as the bullet comes out, but I’ll bet it’s been dumbed down into an average fudge factor in an equation in a footnote of a ballistics book.

Thanks for your thoughts! This is one of those things that’s been in the back of my mind for decades and I wait for something to come up, but I was either busy and didn’t notice the conversation, or it was too vague to be of much help.
 
JEFFPPC said:
This is a shooters forum not an engineering forum, maybe your in the wrong place for your skill set.
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I’m just a shooter of hunting rifles - in a group that measures weight to 1/70,000 lb, diameter to .0001”, velocity to single digit sd’s, and can talk at length about a dozen forces on the bullet in flight, I figured someone other than me was curious about how far a rifle moves in recoil? Lol
 
TaperPin said:
I’m just a shooter of hunting rifles - in a group that measures weight to 1/70,000 lb, diameter to .0001”, velocity to single digit sd’s, and can talk at length about a dozen forces on the bullet in flight, I figured someone other than me was curious about how far a rifle moves in recoil? Lol
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Actually groups are measured to three places.
The numbers that you see that are four places are aggregates. Your mention of weight peaked my curiosity and as it turns out a grain is 1/7000 of a pound so if we are talking about hundredths of a grain they would be 1/700,000 lb.!

Generally, before I launch off into an investigation that requires much effort, I need to be convinced that the information that I would be trying to produce would be of some practical use. For matters such as this, there is a good chance (IMO) that the visualization of the problem may not take into account all of the relevant variables, so for that reason I think that an actual test would be the surest way to get an exact value for a particular rifle/caliber/rest/hold situation. If you want to pursue this, I suggest that you contact Bryan Litz.
 
dmoran said:
Are not Internal and External ballistics aspects to Shooting? And aspects that many people here discuss?
Can say, I have on several occasions over the years here with in the forums.
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To me it's about learning better how to hit something with a rifle. Or what is the purpose of a rifle? Or what is the purpose of shooting at a target?. Just go out and pull the trigger to hear it go bang? Seems to work for more and more which is further evidence of the small numbers of those who compete on a regular basis vs those who live vicariously.
 
When shooting off the bench it’s common sense to not let a sling swivel stud contact the front bag and potentially push up on the forend. Is that distance 1/4”, 1/8”, or 1/16”? Seems like something practical to know. No? We just give it plenty of room.

Maybe that’s the easiest way to test this. Put a clamp on the barrel, a stiff metal ramp to bump the clamp into, and reduce the gap until a group goes wonky.
 
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My physics prof would say that the answer is incorrect because I did not consider and measure friction.
So friction can vary with your benchrest setup. It is present and probably negligible but not -0-.
 
BoydAllen said:
Actually groups are measured to three places.
The numbers that you see that are four places are aggregates. Your mention of weight peaked my curiosity and as it turns out a grain is 1/7000 of a pound so if we are talking about hundredths of a grain they would be 1/700,000 lb.!

Generally, before I launch off into an investigation that requires much effort, I need to be convinced that the information that I would be trying to produce would be of some practical use. For matters such as this, there is a good chance (IMO) that the visualization of the problem may not take into account all of the relevant variables, so for that reason I think that an actual test would be the surest way to get an exact value for a particular rifle/caliber/rest/hold situation. If you want to pursue this, I suggest that you contact Bryan Litz.
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An exact measurement isn’t needed.
 
Each action and opposite equal reaction. In shooting, wouldn’t the variables also include barrel torque? And wouldn’t torque offset rearward motion?

And, as torque from mass/velocity varied, wouldn’t rearward motion increase or decrease from its effects.

Asking for a friend. :)
 
For a typical center fire the bullet exit time is around 1.25 milliseconds, too fast to "see". From the vibration perspective and performance on the target the associated muzzle movement is on the order of +/- 0.003". Of course it is easy to import much more movement with poor handling, trigger pull, etc.
 
If an 8-1/2 lb 300 PRC rifle is 59,500 gr.
Base of a 200 gr bullet only travels about 22” in a 24” barrel.
Powder (80gr) starts off with center of mass about an inch from the breach and ends at the 12” mark, so 11” of movement?

Free recoil 300 PRS
59,500 x X = (200 x 22”) + (80 x 11)
59,500 x X = 5,280
X = 5,280/59,500
= .089” (17 lb gun would be half this)

Same rifle weight 6 br 70 gr bullet and 30 gr of powder. The distance traveled for both the bullet and powder is a little different from above because of the shorter case.

Free recoil 6br
59,500 x X = (70 x 22.75) + (30 x 11.5)
59,500 x X = 1592.5 +345
X = 1937.5/59,500
= .033” (a 17 lb gun would be half this)

Since touching a gun to the shoulder and holding it with both hands can only decrease the distance, these values are essentially maximums I’m guessing.

If both hands are gently pulling the stock into the shoulder I’m wondering if they reduce the distance at all since recoil would have to overcome the preload on the hand contact before they would slow anything. Then the only other thing slowing the stock down is friction on the bags, and amount of shoulder mass able to make contact with the recoil pad.

I don’t have any idea if all this is correct, but if someone knows it would be nice to hear.

Watching high speed of guys shooting hunting rifles, it seems there is a sizable amount of squishiness to the human body - maybe all the human squish, plus the squish in the recoil pad means that first .100” movement doesn’t get a lot of resistance?
 
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dryhumor said:
Each action and opposite equal reaction. In shooting, wouldn’t the variables also include barrel torque? And wouldn’t torque offset rearward motion?

And, as torque from mass/velocity varied, wouldn’t rearward motion increase or decrease from its effects.

Asking for a friend. :)
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I thought you were joking, but it just hit me you weren’t, and that it makes sense that if a bullet spins twice going down the bore, the rifle spins the opposite direction matching the momentum. I may have skipped class and went hunting the week we went over angular momentum. That’s a lot harder to figure out for an oddly shaped object.

I don’t know if I can visualize the connection between angular momentum and linear, but that’s not my thing.
 
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