Engineers/Math People- a question

[Precision Underground]

I know I’ve seen this info and/or how to determine it but can’t find it now. The question is, what’s the relationship between movement at the muzzle vs impact on target at 100 yards? So if my barrel moves .01” up from POA how much movement does that translate to POI on target at 100? @Rocketmandb ?

 

[godofthunder]

I’m on my phone and don’t feel like doing math this early, but you just need to use the Pythagorean theorem to get the angle of that movement and then use that with the 100 yard distance and there you have it.

 

[C.R. Adams]

.01/distance from butt to muzzle = X/distance from butt to target.............. solve for x

the two "distances" have to be in the same units of measure. this will be good enough for government work to get you what you're looking for.

so let's say it's 36" from butt to muzzle (im just pulling that 36" out of my ass). .01/36=x/3636.................. .01x3636=36x.................... 36.36=36x....................... 36.36/36=x................ 1.01=x................... so, .01 at the muzzle is approximately 1.01" at 100 yards.

 

[1moaoff]

Are you talking constant pressure and fixed stock location....?
Example. Secured test action locked down. Then tie a string to the ceiling and pull on muzzle until it holds it to the desired offset?

That may be a repeatable test but there's more than just the math for the physical offset.
When fired normally where in the barrel movement does bullet normally leave the barrel. Harmonics would be changed. Recoil impulse would be changed.

 

[Precision Underground]

Are you talking constant pressure and fixed stock location....?
Example. Secured test action locked down. Then tie a string to the ceiling and pull on muzzle until it holds it to the desired offset?

That may be a repeatable test but there's more than just the math for the physical offset.
When fired normally where in the barrel movement does bullet normally leave the barrel. Harmonics would be changed. Recoil impulse would be changed.

I’m talking purely hypothetical for the sake of illustration. @C.R. Adams answer above was in the ballpark of what I was thinking.

 

[C.R. Adams]

I’m talking purely hypothetical for the sake of illustration. @C.R. Adams answer above was in the ballpark of what I was thinking.

BTW, love your ELR bag.

 

[Precision Underground]

.01/distance from butt to muzzle = X/distance from butt to target.............. solve for x

the two "distances" have to be in the same units of measure. this will be good enough for government work to get you what you're looking for.

so let's say it's 36" from butt to muzzle (im just pulling that 36" out of my ass). .01/36=x/3636.................. .01x3636=36x.................... 36.36=36x....................... 36.36/36=x................ 1.01=x................... so, .01 at the muzzle is approximately 1.01" at 100 yards.

Perfect, thanks. How much change if you go with something like 55”? Somewhere just under 2” or am I confused?

edited, 1.5”. Apparently I don’t know how many inches are in 100 yards.

 

[C.R. Adams]

Perfect, thanks. How much change if you go with something like 55”? Somewhere just under 2” or am I confused?

edited, 1.5”. Apparently I don’t know how many inches are in 100 yards.

somewhere there's an error in your calculation. it should be .67". see pic for a short cut formula that's more clear.

 

[Rocketmandb]

I know I’ve seen this info and/or how to determine it but can’t find it now. The question is, what’s the relationship between movement at the muzzle vs impact on target at 100 yards? So if my barrel moves .01” up from POA how much movement does that translate to POI on target at 100? @Rocketmandb ?

Depends on the distance from the fulcrum point, as that will determine the angle. Assuming the fulcrum point is your shoulder, and using a 48" total length rifle.

Image exaggerated for illustration purposes EDIT: Note that the image shows a .1" barrel rise, which is a typo.

Your POA is rising .01" per 48". As @C.R. Adams mentions the formula is rise at muzzle/distance to muzzle = POA rise at target/distance to target

For your example with my assumption of a 48" rifle: .01"/48" = .00021

So, POA rise = .00021 x distance to target

At 100 yards = .00021 x 100 yards = .021 yards or .756"

Actual POI will be altered by the drop over 100 yards - likely 0 since you'd probably be zeroed at 100, but not always the case.

 

[UpSideDown]

This is a super incomplete question. You need to answer way more questions to get a useful answer out of this. Where is the gun supported (pivoting), how far from there is the muzzle rise, is the gun moving linearly as well as rotationally, wheeeeee I love questions like this because there's so many variables that people don't want to answer that the actual answer is totally pointless because we aren't talking about fixed naval guns.

 

[Precision Underground]

This is a super incomplete question. You need to answer way more questions to get a useful answer out of this. Where is the gun supported (pivoting), how far from there is the muzzle rise, is the gun moving linearly as well as rotationally, wheeeeee I love questions like this because there's so many variables that people don't want to answer that the actual answer is totally pointless because we aren't talking about fixed naval guns.

Thanks for the input. You have absolutely zero idea why I even asked the question so how the hell could you know if the answer is pointless? (it’s not and it achieved what I needed) Anything else to add?

 

[UpSideDown]

Thanks for the input. You have absolutely zero idea why I even asked the question so how the hell could you know if the answer is pointless? (it’s not and it achieved what I needed) Anything else to add?

I'm glad you got what you needed. The info in your first question was so minimal that it seemed like it was going to be another one of those threads. Not that you don't know what you're doing.

 

[Precision Underground]

Depends on the distance from the fulcrum point, as that will determine the angle. Assuming the fulcrum point is your shoulder, and using a 48" total length rifle.

View attachment 7517151
Image exaggerated for illustration purposes EDIT: Note that the image shows a .1" barrel rise, which is a typo.

Your POA is rising .01" per 48". As @C.R. Adams mentions the formula is rise at muzzle/distance to muzzle = POA rise at target/distance to target

For your example with my assumption of a 48" rifle: .01"/48" = .00021

So, POA rise = .00021 x distance to target

At 100 yards = .00021 x 100 yards = .021 yards or .756"

Actual POI will be altered by the drop over 100 yards - likely 0 since you'd probably be zeroed at 100, but not always the case.

Got it. Saying it rises .01 for every rifle length to the target makes it make sense in my head. Thank you sir!

 

[Precision Underground]

somewhere there's an error in your calculation. it should be .67". see pic for a short cut formula that's more clear.

View attachment 7516870

Yep that makes more sense. I was trying to decipher your calc and got one of the numbers wrong apparently

 

[Jack Master]

When shooting I'm not to worried about the movement of the muzzle but rather the movement of the stock at the rear support, because that is what I can control. Here is the match that I worked out of it. Looks like you might has got this number already but here is a visual representation.

 

[Precision Underground]

When shooting I'm not to worried about the movement of the muzzle but rather the movement of the stock at the rear support, because that is what I can control. Here is the match that I worked out of it. Looks like you might has got this number already but here is a visual representation.

View attachment 7518368

Thanks Jack. Picturing the answer and the real world application I had the same thought - that the error would be magnified by movement at the stock with the stock to bipod distance being the multiplier. Correct?

 

[C.R. Adams]

When shooting I'm not to worried about the movement of the muzzle but rather the movement of the stock at the rear support, because that is what I can control. Here is the match that I worked out of it. Looks like you might has got this number already but here is a visual representation.

View attachment 7518368

Jack, why doesn't setting up two fractions, making them equal to each other and solving for the unknown change at the target, not work? Where is the mistake in the logic that it doesn't provide a 'good enough for gov't' number?


Change in elevation at muzzle/distance from butt to muzzle = unknown change at target/distance from butt to target


or is the difference, because the example you provided, places the 1" of change at the butt rather than at the muzzle?

nothing malicious intended, just curious if I made an error.

 

[Precision Underground]

Jack, why doesn't setting up two fractions, making them equal to each other and solving for the unknown change at the target, not work? Where is the mistake in the logic that it doesn't provide a 'good enough for gov't' number?


Change in elevation at muzzle/distance from butt to muzzle = unknown change at target/distance from butt to target

The way I’m understanding it you are both correct. It’s just a matter of where the movement happens. If the stock sinks into the bag Jack’s calc applies. If the bipod hops and the stock stays put your calc applies. I asked the question from a purely academic standpoint so both answers are useful and hearing both makes me understand what’s happening.

 

[Rocketvapor]

You could use the barrel length to range ratio if you were looking for POI due to barrel whip.
Or maybe even half the barrel length assuming if flexes around the midpoint.
Could actually be down if bullet exited at that point.

Another metric is scope base flex. A problem when someone mounts a scope with a 4 inch ring to ring distance and the scope mount moves. Like when someone mounts a scope on the recoil cover on an SKS.
The ratio is 4"/3600". A 0.001" movement of the cover could be almost an MOA at 100 yards.
0.010" movement is @ 100yards.

 

[Jack Master]

Jack, why doesn't setting up two fractions, making them equal to each other and solving for the unknown change at the target, not work? Where is the mistake in the logic that it doesn't provide a 'good enough for gov't' number?


Change in elevation at muzzle/distance from butt to muzzle = unknown change at target/distance from butt to target


or is the difference, because the example you provided, places the 1" of change at the butt rather than at the muzzle?

nothing malicious intended, just curious if I made an error.

Your way of doing it totally works too. The only difference between yours and mine is probably the length used in the equation. Full Rifle length vs rear bag to bipod length. Both of them are so close we still came to the same conclusion.

Plus I've had this visual for awhile and it was a fitting place to put it.

 

[seansmd]

This all makes sense if we are predicting, if we are measuring, I would expect the muzzle will still rise after the bullet has left. This would affect the numbers, correct?

 

[Lowlight]

The difference if you subtract the front from the back of a 20MOA Base is .112”.

So .11 give the shooter 20 Inches at 100 yards... that means about .0056” is 1 Inch back at the trigger

I would go with Jack Masters numbers, but a little goes a long way.

 

[seansmd]

From a purely analytical view, it would be great to see data from a 3-axis sensor line up with the barrel that also measured acceleration.

Ideally you would see barrel orientation (jack's picture), cant, and then where it moved and in what magnitude under recoil.

Then many of these techniques could validated and the results seen in data. I thought someone was attempting a date collection devices like this.

 

[AccuSol-ERN]

Ok stupids.......don't you know dialing in scope elevation is so last year.......cool people crank in elevation with the barrel.....duh.

For the mathematically challenged.....just use a laser boresighter.

I used to do an in-shop demonstration to show the importance of fixturing during precision TIG welding. I strapped a laser pointer to the material and taped a bullseye to the wall and introduced heat to different areas on the material and the students could watch the red dot move around......it worked really well to get the point across.

 

[Lowlight]

Ask everyone to post their group photos where they blew a shot, you know a group image that says I would put it on the refrigerator but for that one shot,

Kinda like this image, decent group but that one damn round drops outside the rest.

We don't really try to throw stuff and when it goes a distance beyond our expectation that sounds like .000" of a inch because many times we don't even realize it happens because so much of this subsconscious

take Ballistic X, (I am too lazy) measure the group center to the flyer, we often look at the edges, but look the middle of each and measure the group.

 

[308pirate]

I know I’ve seen this info and/or how to determine it but can’t find it now. The question is, what’s the relationship between movement at the muzzle vs impact on target at 100 yards? So if my barrel moves .01” up from POA how much movement does that translate to POI on target at 100? @Rocketmandb ?

Do you even Pythagoras theorem bro?

 

[Macht]

None of the answers given so far are complete. Taken as stated, there isn't enough information to answer the question. If we only consider the vertical plane, there are three values that control the offset between POA and POI (jump): deflection, angle, and lateral velocity.

Excluding everything else, a vertical deflection of 0.01" at the muzzle translates to exactly 0.01" of deflection at the target. That is the only thing you can be sure of with the information given. The other answers assume that the barrel stays perfectly straight (not realistic) and then calculate the angle based on that assumption. Note that due to certain combinations of rigid body motion and barrel curvature it is possible to have a vertical deflection that raises the point of impact while having a muzzle angle that lowers it. Beyond that, for the above configuration it is possible to have either a negative or a positive lateral velocity. You then need to calculate how the three factors interact. A book like McCoy's Modern Exterior Ballistics has equations which will do exactly that.

As a rough rule of thumb, if you isolate the factors:

	Deviation at Muzzle	Deviation at 100 Meters [mm]
Deflection	10 [micron]	0.01
Angle	0.1 [mrad]	10.0
Velocity	0.1 [m/s]	12.4

 

[Precision Underground]

There are likely 1000 answers depending on 100 variables. The first two answers cured my curiosity and gave me what I needed. I knew a small amount of movement at the rifle would translate to a large move on target I just wanted a ballpark for reference. It confirmed my suspicion that the fact that we can shoot 1/2 MOA is absolutely incredible if you think about how small the window is.

 

[DaleAGribble]

When shooting I'm not to worried about the movement of the muzzle but rather the movement of the stock at the rear support, because that is what I can control. Here is the match that I worked out of it. Looks like you might has got this number already but here is a visual representation.

View attachment 7518368

.010" or 10 thousands is actually the thickness of about 2-3 human hairs. I have beard hairs that measure 6 thousands

 

[AccuSol-ERN]

We haven't even began to talk 70s wolf pussy vs the coveted Red Cunt Hair.........there may indeed be a general tolerance (+/- .003") ........"unless otherwise specified"........ha ha.

Ern