Is precision linear? What say the masses?

[slow is slow]

So while reading threads here and elsewhere I continue to come across posts that insinuate or outright say that precision isn't linear. And by that I mean an average 1/2" group at 50 yards equates to a 1" group at a hundred under the same conditions (unchanging wind) and for argument's sake we'll say that the stabilized bullet does not go through a transonic phase between the two distances. It's either already subsonic or supersonic throughout. I can't see what would make the precision of the round non linear, but I continue to see posts about a gun/ round that can hit tiny targets at 50, but opens up tremendously at 100. What say the learned gurus of trajectory?

 

[NCLivingBrit]

I think errors and offsets magnify at range and not always in a linear fashion.

 

[Bunsen]

So while reading threads here and elsewhere I continue to come across posts that insinuate or outright say that precision isn't linear. And by that I mean an average 1/2" group at 50 yards equates to a 1" group at a hundred under the same conditions (unchanging wind) and for argument's sake we'll say that the stabilized bullet does not go through a transonic phase between the two distances. It's either already subsonic or supersonic throughout. I can't see what would make the precision of the round non linear, but I continue to see posts about a gun/ round that can hit tiny targets at 50, but opens up tremendously at 100. What say the learned gurus of trajectory?

Specifically only speaking in regards to rimfire ammo: as your distance increases, so does your vertical dispersion as a result of differences in muzzle velocity. Velocity variances that have a small or negligible impact on group size at 50yds will have a greater impact at 100yds and beyond. Rimfire ammo is nothing like centerfire ammo where you can tune your load and drop your ES and SD into the teens or single digits. Considering that most match rimfire ammo is only leaving the muzzle at around 1080fps a 20fps+ SD will have an impact downrange.

 

[NCFubar]

In a controlled environment maybe but for me once I cross say 300 yards the wind or should I say winds mess me up. I’ve seen 1,000 yard matches with flags indicating 4 different wind vectors as you go down range. Each effects the round at different velocities as the round drops velocity as it travels farther.

 

[slow is slow]

Specifically only speaking in regards to rimfire ammo: as your distance increases, so does your vertical dispersion as a result of differences in muzzle velocity. Velocity variances that have a small or negligible impact on group size at 50yds will have a greater impact at 100yds and beyond. Rimfire ammo is nothing like centerfire ammo where you can tune your load and drop your ES and SD into the teens or single digits. Considering that most match rimfire ammo is only leaving the muzzle at around 1080fps a 20fps+ SD will have an impact downrange.

I see nothing that would keep the spread from being roughly double from one distance to the next. Sure, it affects it less at fifty yards, but just because something is smaller and harder to measure doesn't mean it's not there. As for the winds, yes longer flight time means more effect, as the bullet is slower between 50 and 100, wind will be able to move it more than it did during the first 50 yards (even if the wind is the same from muzzle to target. I guess my question is if we were shooting indoors and at 50 yards we were shooting through a square that sensed shot lovation without affecting flight and the bullet passed through it out to 100 yards, would our group size be exactly double from 50 to 100? This is strictly a theoretical question and not a question of real world application.

 

[Catfish]

Well first you would need to identify 1) all the potential errors and deviations and then 2) all the forces acting on and within the bullet after it leaves the muzzle and then evaluate each of them over both flight paths.

 

[slow is slow]

Assuming no wind, you have gravity, corialis, spin drift, and velocity deviation . The best I can calculate, precision should be linear along two distances, as well as along two flight times. Really, these play no role in precision at all as they remain relatively constant across all shots in a group. The only variable among those that could change would be velocity (thereby affecting spin drift), but you would expect to see it have double the effect (as would any variable I can possibly come up with) when you double the distance or flight time, given a large enough sample size.

 

[J R Green]

In a vacume it would be linear but for all the factors listed plus a few others it would be hard to keep to that metric. Depending on the scope the reticle will cover more and more of the target and there you will have more room for error. There is also a psychological factor involved, you would forgive yourself more error on the farther targets.

 

[mikep7m10]

Gravity is not linear. The rate of falling increases with time & distance. A vertical spread of 1/2" at 50 yards is not 1" at 100 yards because the bullet is falling faster further out.

 

[GymB]

Gravity is not linear. The rate of falling increases with time & distance. A vertical spread of 1/2" at 50 yards is not 1" at 100 yards because the bullet is falling faster further out.

Gravity is constant, what you describe is correct, but it’ll happen the same for each bullet with the same initial velocity and mass so the spread should only double.

I was thinking air resistance because it is not linear with a change in velocity, but this effect is also constant for each bullet with the same initial velocity and mass.

If the deviation is purely a result of inaccurate aim, then the group will double. But if it is in part a result of different initial bullet velocity or bullet mass then I think the effects of both gravity and wind resistance will cause the group to more than double.

 

[slow is slow]

Gravity is constant, what you describe is correct, but it’ll happen the same for each bullet with the same initial velocity and mass so the spread should only double.

I was thinking air resistance because it is not linear with a change in velocity, but this effect is also constant for each bullet with the same initial velocity and mass.

If the deviation is purely a result of inaccurate aim, then the group will double. But if it is in part a result of different initial bullet velocity or bullet mass then I think the effects of both gravity and wind resistance will cause the group to more than double.

This is the point i've been trying to completely wrap my head around, I agree with your initial velocity or weight of a bullet being different, which is why i referred to a large sample size. 100 shots fired at each distance from the same batch of ammunition at random, should double the group size at double the distance OR flight time either one. Reticle and person firing the shot are irrelevant

 

[Spartan]

In theory, yes, it should be linear.

However, even under ideal conditions, you still are dealing with incalculable variables that will tend to make the correlation exponential:
Miniscule differences and imperfections in the bullets,
miniscule differences in powder charge,
miniscule differences in burn rate or complete burn,
the barrel's own temperature,
carbon and copper buildup in the barrel,
The receiver's own heat, causing micro shifts in how everything fits and works together.

While gravity is a constant, these micro differences would be effected at greater and greater values as velocity decreases.

 

[NKD]

Gravity is not linear. The rate of falling increases with time & distance. A vertical spread of 1/2" at 50 yards is not 1" at 100 yards because the bullet is falling faster further out.

Acceleration (edit: I mean speed increases due to acceleration) of the dropping object (bullet) increases as it falls until TV.

Never really thought of that in regards to shooting. But if you were drop a bullet from the top of a tower, and fire one from a rifle horizontally at the exact same instant, both should hit the ground at the same time. I’ve heard this described in regards to shooting but never really thought of the vertical acceleration.

And the further the fired bullet goes, the faster it is falling vertically. Until all forward momentum is lost and it’s just freefalling at terminal velocity. (Would need a super tall tower lol).

 

[Spartan]

Acceleration of the dropping object (bullet) increases as it falls until TV.

Never really thought of that in regards to shooting. But if you were drop a bullet from the top of a tower, and fire one from a rifle horizontally at the exact same instant, both should hit the ground at the same time. I’ve heard this described in regards to shooting but never really thought of the vertical acceleration.

And the further the fires bullet goes, the faster it is falling vertically.

This is true, in theory.
A minor amount of spindrift can create lift and artificially suspend the bullet longer in the air than the dropped bullet.

 

[slow is slow]

Acceleration of the dropping object (bullet) increases as it falls until TV.

Never really thought of that in regards to shooting. But if you were drop a bullet from the top of a tower, and fire one from a rifle horizontally at the exact same instant, both should hit the ground at the same time. I’ve heard this described in regards to shooting but never really thought of the vertical acceleration.

And the further the fired bullet goes, the faster it is falling vertically. Until all forward momentum is lost and it’s just freefalling at terminal velocity. (Would need a super tall tower lol).

That is a correct assumption, ignoring air resistance and curvature of the earth, Gravity is unaffected by speed in another vector.

 

[Catfish]

Acceleration of the dropping object (bullet) increases as it falls until TV..

Nope, acceleration due to gravity is a constant 32 ft/(s^2)

 

[NKD]

Nope, acceleration due to gravity is a constant 32 ft/(s^2)

I meant that “speed increases” not acceleration. I’ll fix it.

 

[slow is slow]

Nope, acceleration due to gravity is a constant 32 ft/(s^2)

This is correct, SPEED at which an object is falling would increase, but not acceleration. But I still think none of this, or changes in anything would keep the groups from being linear. The changes are happening just the same at 50 yards. Call it deviation from point of aim, those same changes that happen at 50 must be doubled at 100 unless something that is acting upon them is changing between the two distances.

 

[NKD]

This is true, in theory.
A minor amount of spindrift can create lift and artificially suspend the bullet longer in the air than the dropped bullet.

I would think it’s just as likely to move it up, right, or left as much as down, no?

Bit spindrift seems pretty minimal compared to he acceleration of the bullet dropping I would think?

Just interested here: full disclosure, I have very little long range experience.

 

[Spartan]

This is correct, SPEED at which an object is falling would increase, but not acceleration. But I still think none of this, or changes in anything would keep the groups from being linear. The changes are happening just the same at 50 yards. Call it deviation from point of aim, those same changes that happen at 50 must be doubled at 100 unless something that is acting upon them is changing between the two distances.

This...
so in theory, if you had a perfect rifle, with perfect rounds, and prefect conditions, and heat and deposits were not a factor then it would be a perfect correlation of distance....
That being said, I am talking about utterly minute variables that a good shooter with a great rifle can compensate for...

 

[Spartan]

I would think it’s just as likely to move it up, right, or left as much as down, no?

Bit spindrift seems pretty minimal compared to he acceleration of the bullet dropping I would think?

Just interested here: full disclosure, I have very little long range experience.

You are correct, but if it is moving left or right then it is not moving down, at least not at the same rate as the dropped bullet...
Then you might also have to take into account the Coriolis effect...
#I'maNERD!!!

 

[slow is slow]

You are correct, but if it is moving left or right then it is not moving down, at least not at the same rate as the dropped bullet...
Then you might also have to take into account the Coriolis effect...
#I'maNERD!!!

Coriolis is unchanging, so is spin drift. All of these things are there at 50, 100 and 1000. Spin drift would change with velocity changes due to a myriad of causes, but if you shot enough rounds at each distance to get a large enough sample size, you should see that precision is completely linear. I just don't buy into the fact that a rifle will shoot tiny holes at one distance, and be disproportionately less accurate at another, unless outside conditions change between the two i.e. shifting or multiple winds, bullet destabilization, etc.

 

[Catfish]

All we have to do is identify one force that is not linear with distance. Gravity clearly is not the one. I can think of two possibilities:

1) Air resistance will cause the rate of spin of the bullet to change as the bullet travels, fastest at the muzzle, slower at the target. As the rate slows down any eccentricity in the center of mass will have a varying de-stabilizing effect on the bullet. Think about how an out-of-balance tire only bounces at a certain speed. If your bullets are made really well, this will be negligible - but are they?

2) Supersonic fluid dynamics is really complex but decelerating forces vary with the square of the velocity, so they are definitely not linear. Air resistance at 100 yds will be less than at 50 yds and the change will not be linear with distance.

 

[NKD]

One thing is apparent.
I need to get a bolt gun and a spendy scope....for nerd research.

 

[slow is slow]

All we have to do is identify one force that is not linear with distance. Gravity clearly is not the one. I can think of two possibilities:

1) Air resistance will cause the rate of spin of the bullet to change as the bullet travels, fastest at the muzzle, slower at the target. As the rate slows down any eccentricity in the center of mass will have a varying de-stabilizing effect on the bullet. Think about how an out-of-balance tire only bounces at a certain speed. If your bullets are made really well, this will be negligible - but are they?

2) Supersonic fluid dynamics is really complex but decelerating forces vary with the square of the velocity, so they are definitely not linear. Air resistance at 100 yds will be less than at 50 yds and the change will not be linear with distance.

All shots in a group would still be acted upon similarly. If you have bullets that are not perfect or varying velocities, you should still see that in your groups at each distance. I think i've came up with a good way to kinda practically test this theory. Something like this:

Indoors, with minimal air movement like the guys who shoot competitive pellet rifles do.
At 25 yards, put up a steel plate with a hole drilled. . Paint the edges to ensure no bullet strikes the plate and fire through said plate. Corresponding group at 50 yards should be no larger than twice the diameter of the hole you drilled. The farther out you put these plates (think 100 and 150) the closer to perfect these would become because it would help to filter out any fliers.

 

[GymB]

@slow is slow I think that you’re thinking about the sample size wrong. Because you’re measuring the size of the group the little differences will tend to cause the group to be more than twice the size, and there is no mechanism that minimizes the fliers in the test you described. If you were to average the results you could say that the calculated center at 100 is XX from the calculated center at 50, but that doesn’t answer the question about group size.

Between the nonlinear forces and the variances in bullet mass and initial velocity, each of which will tend to cause groups to be larger by a nonlinear amount at longer distance, it seems pretty clear that the answer is that it’s nonlinear. The best experiment would probably be a device that accuratly identifies the path of the bullet without affecting that path, maybe some specialized equipment or high speed cameras and an indexed background. To reduce variables gun would be in a fixed rest.

 

[BatteryOaksBilly]

But if you were drop a bullet from the top of a tower, and fire one from a rifle horizontally at the exact same instant, both should hit the ground at the same time. I’ve heard this described in regards to shooting but never really thought of the vertical acceleration.

Go to YT and look for this on Myth Busters. It is a great episode. They use a .45 auto. Yes it IS true.

 

[slow is slow]

@slow is slow I think that you’re thinking about the sample size wrong. Because you’re measuring the size of the group the little differences will tend to cause the group to be more than twice the size, and there is no mechanism that minimizes the fliers in the test you described. If you were to average the results you could say that the calculated center at 100 is XX from the calculated center at 50, but that doesn’t answer the question about group size.

Between the nonlinear forces and the variances in bullet mass and initial velocity, each of which will tend to cause groups to be larger by a nonlinear amount at longer distance, it seems pretty clear that the answer is that it’s nonlinear. The best experiment would probably be a device that accuratly identifies the path of the bullet without affecting that path, maybe some specialized equipment or high speed cameras and an indexed background. To reduce variables gun would be in a fixed rest.

The hole size would be the method to which flyers are minimized. If I'm shooting a .22 through a half inch hole, any flyer would hit or skim paint from your plate. I'm going to cut a plate and give this a go. I'll do it at 25 and 50 to minimize flight time and reduce the effects of wind.

 

[Spartan]

Go to YT and look for this on Myth Busters. It is a great episode. They use a .45 auto. Yes it IS true.

Mmmm...
Their sample size is way too small, and the rounds only went roughly a few hundred yards.
Also, 45 ACP is significantly less aerodynamic than most BTHP sniper rounds,
Both bullets will impact at very similar times, but their is a slight difference

 

[slow is slow]

I think I'm going to test this out in the same style as @FlatFender does his junk science episodes on his podcasts. Maybe try 5 calibers and a few different distances, logging and recording it all.

If it wasn't always so windy at woodys!

 

[GymB]

The hole size would be the method to which flyers are minimized. If I'm shooting a .22 through a half inch hole, any flyer would hit or skim paint from your plate. I'm going to cut a plate and give this a go. I'll do it at 25 and 50 to minimize flight time and reduce the effects of wind.

Give it a shot. So POA will be marked on the 50 years target and you’ll adjust from the shooting position to see it through the hole. Should be interesting.

 

[Spartan]

All shots in a group would still be acted upon similarly. If you have bullets that are not perfect or varying velocities, you should still see that in your groups at each distance. I think i've came up with a good way to kinda practically test this theory. Something like this:

Indoors, with minimal air movement like the guys who shoot competitive pellet rifles do.
At 25 yards, put up a steel plate with a hole drilled. . Paint the edges to ensure no bullet strikes the plate and fire through said plate. Corresponding group at 50 yards should be no larger than twice the diameter of the hole you drilled. The farther out you put these plates (think 100 and 150) the closer to perfect these would become because it would help to filter out any fliers.

The way to do it:
Same as this, but, shoot the first group at 25,
Then whatever size hole that is, say 1”,
Shoot the 50 thru a 1”hole at the 25,
Then the 100 thru a 1” hole at 25, and a 2” hole at 50 etc

This would eradicate flyers and operator error

 

[JohnFreeman]

So if there's no wind, and on a relatively equal temp, gravity works at any distance, it should be linear.

 

[slow is slow]

Yep. That's what I planned, sorry if I wasn't clear. I mean for the plate to be at half the distance as the target.

 

[Spartan]

So if there's no wind, and on a relatively equal temp, gravity works at any distance, it should be linear.

Yes, but that’s assuming perfect projectiles, forex by a perfect rifle, that doesn’t get hot or leave carbon or copper deposits, etc...

 

[Bunsen]

I see nothing that would keep the spread from being roughly double from one distance to the next. Sure, it affects it less at fifty yards, but just because something is smaller and harder to measure doesn't mean it's not there. As for the winds, yes longer flight time means more effect, as the bullet is slower between 50 and 100, wind will be able to move it more than it did during the first 50 yards (even if the wind is the same from muzzle to target. I guess my question is if we were shooting indoors and at 50 yards we were shooting through a square that sensed shot lovation without affecting flight and the bullet passed through it out to 100 yards, would our group size be exactly double from 50 to 100? This is strictly a theoretical question and not a question of real world application.

No, group size/precision will NOT be linear as range increases indoors or outdoors. There are two indoor rimfire ammo testing facilities in the US that routinely have demonstrated precision to be more than linear at range. Lapua in AZ and Eley in TX.

Also, you have posed this question in the RIMFIRE section of the forum, but you and others keep bringing in concepts or variables (specifically Coriolis and spin drift) that have near zero applicability to RIMFIRE. I think you're in the wrong sub-forum for this topic of discussion. If your question is truly exclusive to rimfire precision then I highly suggest you go over to the rimfire forum on Snipers Hide and pose this question as well.

https://forum.snipershide.com/forums/sniper-s-hide-rimfire-section/

If your question is more concerning center-fire ballistics and precision then I suggest reading Brian Litz's Applied Ballistics Books to better understand the theory and answer your questions.

 

[Spartan]

Nice catch @Bunsen

 

[MacEntyre]

Accuracy is how close your shooting gets to the bullseye.
Precision is how repeatable is your shooting.

Nothing about shooting is linear. Most of it is best described by third order differential equations.

 

[slow is slow]

I posted in the rimfire section because it's a pretty active area, and I know some of the people in this area really know their stuff. I don't believe that this is a rimfire or centerfire topic, or that the basics of centerfire and rimfire ballistics are all that different. I am not a learned ballistic expert, but I am a pretty good shot with a rifle at most any distance, and so I'll take your advice to read Mr. Litz's book to heart. As for coriolis and spin drift, they were mentioned as things that affect point of impact. Even if too small to measure (which coriolis most definitely is, and spin drift most definitely is not), these things still play a part in point of impact. I've searched and cannot find anything published by eley or lapua, but I did note that lapua tests "simultaneously at both 50 and 100 meters" so perhaps precision is not linear. I've got an email out to both companies now to try and get an answer. I'm not set on my answer, it's why I asked the question, but as someone who understands physics quite well, I am having a hard time getting my mind to understand what would cause groups to not be linear

 

[Spartan]

I posted in the rimfire section because it's a pretty active area, and I know some of the people in this area really know their stuff. I don't believe that this is a rimfire or centerfire topic, or that the basics of centerfire and rimfire ballistics are all that different. I am not a learned ballistic expert, but I am a pretty good shot with a rifle at most any distance, and so I'll take your advice to read Mr. Litz's book to heart. As for coriolis and spin drift, they were mentioned as things that affect point of impact. Even if too small to measure (which coriolis most definitely is, and spin drift most definitely is not), these things still play a part in point of impact. I've searched and cannot find anything published by eley or lapua, but I did note that lapua tests "simultaneously at both 50 and 100 meters" so perhaps precision is not linear. I've got an email out to both companies now to try and get an answer. I'm not set on my answer, it's why I asked the question, but as someone who understands physics quite well, I am having a hard time getting my mind to understand what would cause groups to not be linear

Yeah...
I kind of got off point there...
My main point is that a bullet, dropped straight down falls a shorter distance than a bullet effected by spin drift causing it to fall at an angular curve, so it falls farther than the dropped bullet resulting in differing impact times.