Shooting accuracy question

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This is for physics geeks. lol. I want to understand the effect instability of the shooter has on bullet trajectory. This is not about technique, it's only about the effect of the muzzle not being perfectly still when the bullet leaves the bore. I think it's fun to think about this stuff, but due to my intellectual laziness I usually only take it so far, so then I ask you guys instead of researching the answer, lol. Take the green pill and save yourself the time, or take the red pill and we'll see just where the rabbit hole goes. What you may find is that I took 5 minutes of your time to ask a simple question with an obvious answer. :D

This is about shooter induced movement of the muzzle, not barrel harmonics, etc. If I mounted a rifle to a moving train to shoot perpendicular to the tracks I think everyone would agree when the bullet emerged from the muzzle it's velocity would include the lateral movement of the train as well. Assuming there was a wall 50 yards from the tracks (and all other variables are inconsequential of course), the point of aim at the instant the bullet left the muzzle would not be the point of impact, but the bullet would impact the wall at some point further down the tracks in the direction the train was heading. Exactly where would depend on the velocity of the train, the muzzle velocity of the bullet, and the distance to the wall, the last two giving the time of flight. Now let's hopefully agree that the same thing would happen if the rifle was on a turntable spinning around, it just might be harder to calculate exactly where it would land. :) I think this is closer to what happens when a shooter induces instability at the muzzle.

The wobble. Now unless you're the gun shooting Russian robot they just sent to the ISS you probably can't hold a gun 100% perfectly stable, you induce a "wobble". There are well known causes such as breathing, heartbeat, muscle fatigue or just plain nerves, and maybe others. These can vary in amplitude and frequency. Wherever there is movement there is velocity, which is the result of the amplitude and frequency. Consider a wobble caused by breathing could be rather large (in amplitude) but slow in frequency, whereas a muscle fatigue twitching could be high frequency but short (small in amplitude). A wobble is not a like a square wave but more like a sine wave, the muzzle moves so far in one direction but it slows down and then reverses direction, with every movement it comes out of the last one accelerating, reaching peak speed in the middle and then decelerating before reversing direction and doing it again.

My question is concerning the effect this wobble has on accuracy. I want to know if the movement of the muzzle lateral to the bore direction has an appreciable effect on accuracy beyond the simple changing of the point of aim (POA). Consider a bullet leaving the muzzle at the extreme end of a wobble when the muzzle is stationary. Again assuming all other variables are inconsequential, the impact would be at the POA, even though the POA would be off the target by half the total wobble amplitude. I used to think this is all that happened. So what if instead the bullet left the muzzle in the middle of the wobble (crossing the exact center of the target we assume) but therefore at the highest lateral wobble velocity, would it impact even farther off the target?

I've pretty much convinced myself that the wobble will impart lateral velocity to the bullet, but I doubt I'm good enough at math to determine how much. Is it significant or not? I got to thinking about this one day shooting 22s with a stable rest and decent glass I noticed when I would pull a shot they would impact significantly farther out than I pulled off target but along the same vector that I pulled it. I also had an ATN scope that videoed this effect. This was a year or so ago but I did some 22 shooting today and reminded myself I never got to the bottom of it. Please feel free to share your thoughts.

So if it is significant it's no big epiphany or anything, it just helps me understand why some impacts fall far out of my "wobble amplitude" when I still think they are me and not gun or ammo.
 
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.o1" of a inch at the gun = 1moa past 75yds

Thats about it
That’s the answer to the amplitude question, but what about the velocity question? Assume that a shot breaks at exactly the right time, but the barrel is moving. Does the momentum imparted to the bullet from that movement cause it to strike off target, and by how much.

My simple guess is that it matters, but not much, and probably less than barrel harmonics. Didn’t mythbusters do an episode on curving a shot, maybe something in there that gets to this point.
 
One factor that few seem to consider is the movement imparted by the recoil of the rifle, and the consistency of the mount. That's on the shooter.

The rifle is in full recoil before the bullet leaves the barrel. It will move up and to the left or right, depending on the direction of the rifling twist. This is the variation that's hardest for us to control and the one that has the greatest potential to throw a shot out of the group.

Does the momentum imparted to the bullet from that movement cause it to strike off target, and by how much.

The Law of Conservation of Momentum says that it must. An object in motion tends to remain in motion until an outside force is brought to bear on it.

The bullet won't curve laterally, but it will continue to move in the direction that it was moving when it left the barrel of a laterally moving rifle. How far off target it strikes depends on a number of factors like velocity, distance to target, how fast the rifle was moving laterally when the bullet exited, the shape of the bullet and even the shooter's body mass come into play.
 
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I've pretty much convinced myself that the wobble [of the shooter] will impart lateral velocity to the bullet, but I doubt I'm good enough at math to determine how much. Is it significant or not?
It is not significant.

The very low frequency of your wobble means that the barrel is essentially not moving at all, in the instant that the bullet fires. The barrel may not be pointed where you want it, but with respect to the bullet, it is stationary.
 
I think a good "wake up" is to put a laser or boresight laser on your gun and point it at a target
10 yards away.
The first time I used one I was in shock at how it was all over the place. It is not like you see on TV, that's for sure.
 
If you were on train, didn't move and pressed trigger.....if you remain still and looking through glass you would see the bullet impact at your point of aim on the wall at 50 yards, no?
Certainly is interesting to think about it.
 
Shooting from a train is a different matter... 45 mph or more is significant, although small, relative to the bullet's velocity. The bullet would impact beside the point of aim, because there would be a 45 mph or greater vector perpendicular to the bullet's main vector out the barrel.

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If you were on train, didn't move and pressed trigger.....if you remain still and looking through glass you would see the bullet impact at your point of aim on the wall at 50 yards, no?
Certainly is interesting to think about it.
Eliminate wind resistance as a variable, and assume that you normally shoot to point-of-aim, then yes.

I think wobble is largely irrelevant because the lateral velocity is so low. Say you wobble .5” at 100 yards, 4 times per second. So 2” per second. Assume bullet travels at 1,500 fps time to impact is .2 sec, so wobble induced error is max .4”.

Assume that I’m right, and I may not be, but either way you can cut this at least in half by always shooting from the same side of the wobble. I always approach the target from the lower left. By doing this I have built the wobble error into my dope, which tends to cancel it out.
 
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JimB, your approach corrects Aim because of the wobble.
The OP suggested that a lateral vector is induced because of the wobble motion.
You are correct, the lateral velocity is very low, so low that it's movement approaches zero during the time it takes the bullet to depart.
 
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Eliminate wind resistance as a variable, and assume that you normally shoot to point-of-aim, then yes.

I think wobble is largely irrelevant because the lateral velocity is so low. Say you wobble .5” at 100 yards, 4 times per second. So 2” per second. Assume bullet travels at 1,500 fps time to impact is .2 sec, so wobble induced error is max .4”.

Assume that I’m right, and I may not be, but either way you can cut this at least in half by always shooting from the same side of the wobble. I always approach the target from the lower left. By doing this I have built the wobble error into my dope, which tends to cancel it out.

Wouldn't that .4" be in addition to as much as .25" (half the .5" wobble) in POA shift off the target? The .4 is due to the lateral velocity and the .25 is simply the amount off you could have been aiming at the time.

I was trying to plug in some numbers too and you and I aren't too far off. Another way to think about it I think might be valid is whatever speed and direction you see your reticle traversing the target when the shot breaks, just imagine it continuing across the target until time of impact. It's probably not that significant but kinda interesting to think about, and regardless, the remedies are the same.
 
Wouldn't that .4" be in addition to as much as .25" (half the .5" wobble) in POA shift off the target? The .4 is due to the lateral velocity and the .25 is simply the amount off you could have been aiming at the time.

I was trying to plug in some numbers too and you and I aren't too far off. Another way to think about it I think might be valid is whatever speed and direction you see your reticle traversing the target when the shot breaks, just imagine it continuing across the target until time of impact. It's probably not that significant but kinda interesting to think about, and regardless, the remedies are the same.
When you say it, it seems wrong, because I was wrong, here’s why.

At the 100 yard target you’re wobbling .5” so working back 100 yards to the muzzle and you’re wobbling is .005”.
So the max lateral velocity of the bullet as it leaves the barrel is .005”x4 per sec = .02”
Now that’s as fast as it goes sideways, so when it hits the target .2 sec later, max deviation from POA is .04”

If you could ignore recoil and watch, the bullet would strike closer to the POA that where your sight is at impact. My earlier thoughts were based on a faulty assumption that angular velocity was constant, but it isn’t for the bullet because the lateral force stops when the bullet leaves the barrel.

This is different that when shooting from the train, the barrel isn’t pivoting so it strikes where you’re looking assuming no wind resistance.

I feel better about this math.
 
And sorry, yes I ignore the wobble error in the calculation because I assume that the shot breaks when the barrel is perfectly on target just to eliminate a variable.
 
This is different that when shooting from the train, the barrel isn’t pivoting so it strikes where you’re looking assuming no wind resistance.
I don't think so. The bullet, rifle and shooter are all moving with the train, and the fired bullet carries momentum in the direction the train is moving, after leaving the muzzle. If you aim well out a right side window 90 degrees to the direction of travel, and the train is moving at 88 fps, and you shoot at a distant stationary target, and it takes the bullet a quarter second to get there... then the bullet will hit 22 feet to the left of your target.
 
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I don't think so. The bullet, rifle and shooter are all moving with the train, and the fired bullet carries momentum in the direction the train is moving, after leaving the muzzle. If you aim well out a right side window 90 degrees to the direction of travel, and the train is moving at 88 fps, and you shoot at a distant stationary target, and it takes the bullet a quarter second to get there... then the bullet will hit 22 feet to the left of your target.
If the target is stationary while the train and gun are moving, exactly right. The original question was about shooting a wall and if you don’t move the gun would the bullet hit the wall where the gun is pointing at the moment of impact. The answer is yes it will, and using your math the bullet will impact the wall 22 feet from the original point of aim, but that will be where the gun is pointing at the moment of impact.
 
This is all very interesting in the world of classical physics but, soon we will have laser beams. At this point, even if your train were to approach the speed of light, it would have no bearing on the trajectory of your beam. In fact at some point, possibly this already exists,sharks with laser beams.

next-time-just-go-sharks-laser-beams-heads.jpg
 
Now that’s as fast as it goes sideways, so when it hits the target .2 sec later, max deviation from POA is .04”
So basic math is killing me, .2sec x .02inch per sec = .004” max deviation at target.
 
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