Is precision linear? What say the masses?

[MacEntyre]

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

I think what you are getting at might be this... we think of precision in a linear way, and it works for the most part, because we are not being rigorous. We are just tweaking things and seeing results directly.

However, it's no different from the way one might approach making a mathematical model in physics. First, you try a linear model, and it works but it has limitations. Then, you make a non-linear model, and it starts fitting reality better.

Remember, Newton invented The Calculus in order to be able to describe motion, because Linear Algebra was not working.

As I said, nothing about shooting is linear. That's because nothing about motion is linear.

 

[JohnFreeman]

I think what you are getting at might be this... we think of precision in a linear way, and it works for the most part, because we are not being rigorous. We are just tweaking things and seeing results directly.

However, it's no different from the way one might approach making a mathematical model in physics. First, you try a linear model, and it works but it has limitations. Then, you make a non-linear model, and it starts fitting reality better.

Remember, Newton invented The Calculus in order to be able to describe motion, because Linear Algebra was not working.

As I said, nothing about shooting is linear. That's because nothing about motion is linear.

Sure! Some things about motion are linear ("a body in motion will tend in the same motion, unless acted on by another force", etc). But you're absolutely right in that bullet drop is non linear.

Maybe the discussion has mixed accuracy and bullet drop. Accuracy depends on lots of things
that can't be calculated (a fleck of dirt in the barrel that's not there the next time, the difference in seating depth from one cartridge to another, etc). Bullet drop is very predictable

Gravity works by accelerating a body at 32ft/sec^2 . You're right in that the ^2 means the effect is non linear. The way it appears linear ( 1/2 MOA at 50 yrds =1 MOA at 100) is that the time part of that equation is REALLY tiny , especially when you square it.

The difference in time between 50 yards and 100 yards (~150 ft) at 2000 feet/sec is a small number. Square that small number and it gets REALLY small between 50 and 100 yards anyway!

distance traveled = V0 + 1/2 at^2

In the vertical dimension (bullet drop) V0 (initial vertical velocity =0) so we can ignore that

Distance= 1/2 32ft/sec^2 * t^2


Lets say it's a slow 22 and that velocity remains constant between 50 and 100 yrds (it doesnt and it's gonna get tricky calculating the negative acceleration of the bullet due to air resistance and ballistic coefficient etc. It too is non-linear, you're right. That pesky t squared!!)

Since the diff in velocity towards the target (not in "y" towards earth) between 0-50 yards and 50 -100 yards is pretty small, the error between the the two "y" dimension calculations is pretty small if we assume the same velocity in the two calculations. It's pretty close to linear here, but you're absolutely right...as the velocity gets lower the assumption gets less accurate.

Accuracy is subject to a host of unpredictable variables caused by randomness in the real world

Bullet drop and bullet impact position due to gravity and/or inaccurate aiming are very predictable (but not linear as I said). What did I goof up this time ?

 

[GymB]

So, take it like a high school physics problem.

Will two identical bullets fired identically from the same origin at the same point of aim in a vacuum with no gravity that pass through the same point in space 50 yards from the origin also pass through a single point in space at 100 yards?

The answer is, Yes. You can even replace the simplifying assumption about gravity being zero with an assumption that it is constant and still answer yes. But beyond that, the question gets far more difficult as you start eliminating simplifying assumptions. What is clear is that the answer immediately becomes No.

The testing should be interesting, but I don’t expect it to be conclusive because it won’t control all the variables, but it’ll be fun and I look forward to the results.

 

[MacEntyre]

Precision is repeatability.

Ya'll are talkin' about Accuracy, which is something else.

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[slow is slow]

Precision is repeatability.

Ya'll are talkin' about Accuracy, which is something else.

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I don't believe anyone is talking about accuracy, or that accuracy has anything to do with this question. We're strictly talking about group sizes and how/if they correlate to distances in a linear fashion. Which is why nothing about the variances in bullet or powder or anything else really come into play. If you shoot enough of them, it will even your groups out at all ranges. A 100 round aggregate at two distances should
even out when it comes to variances in ammunition.

 

[MacEntyre]

What I mean is that it doesn't sound like ya'll are differentiating between accuracy and precision, in this discussion about whether precision i shooting is linear.

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[slow is slow]

If that seems that way, then I apologize. I specifically used precision in the title to stray away from accuracy talks. The difference in the two is the exact reason why i don't believe that all of these variations such as velocity, weight variances and "carbon deposits" will play much of a role. If you shoot enough at each distance, those small variances will become evident at both distances.

 

[MacEntyre]

First you have to know what affects repeatability.

 

[MacEntyre]

Sure! Some things about motion are linear ("a body in motion will tend in the same motion, unless acted on by another force", etc).

Newton's rule does not illustrate or define a linear relationship.

Some motion can be described by Algebra, like billiard balls, but little of it is linear. Usually, one assumes that a system is linear, when the non-linear components can be ignored without a large error. The rest is best described by Calculus, and usually involves changes to rate of change variables.

Anyway, Precision is a statistical term meaning repeatability. That would be group size. Accuracy is proximity to the bullseye you are aiming at.

You can't just mix in all the forces acting on a bullet and attribute them to Precision. Has anyone figured out which characteristics of shooting affect Precision, and which affect Accuracy?

 

[doose]

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.

There can be a linear progression where the grouping does not double at double the distance. That is a 1:1 linear progression. There may be a 1:2 linear progression, and it would still be linear. 1 inch group at 50, 4 inch group at 100 for instance...

But there would need to be data points at multiple distances to determine an approximated mathematical relationship. What appears linear at close range could be parabolic with more data points at longer and longer distance.

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[GymB]

There can be a linear progression where the grouping does not double at double the distance. That is a 1:1 linear progression. There may be a 1:2 linear progression, and it would still be linear. 1 inch group at 50, 4 inch group at 100 for instance...

But there would need to be data points at multiple distances to determine an approximated mathematical relationship. What appears linear at close range could be parabolic with more data points at longer and longer distance.

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The OP is asking about precision in shooting where the paths of the bullets are parabolic and precision is determined by group size. I think maybe you’re answering an as yet unasked question about POI vs POA at different distances. Either that or I don’t understand your point.

 

[MacEntyre]

I think he's saying that group size at multiple distances might look linear with a small data set, when it is actually non-linear. The true relationship will show up when you have a good data set, such as group size vs distance with groups shot at 25, 50, 100, 150, 200, 250, 300, 350 yards. That would be 8 data points, which is not very many, statistically speaking. You could shoot that sequence several times, I suppose.

You would have to use a bench rest clamp to eliminate the shooter from the results.

 

[doose]

Newton's rule does not illustrate or define a linear relationship.

Some motion can be described by Algebra, like billiard balls, but little of it is linear. Usually, one assumes that a system is linear, when the non-linear components can be ignored without a large error. The rest is best described by Calculus, and usually involves changes to rate of change variables.

Anyway, Precision is a statistical term meaning repeatability. That would be group size. Accuracy is proximity to the bullseye you are aiming at.

You can't just mix in all the forces acting on a bullet and attribute them to Precision. Has anyone figured out which characteristics of shooting affect Precision, and which affect Accuracy?

You exspressed what I was trying to express much more.... precicely.

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[MacEntyre]

I feel like we've beat this topic to death, but has anyone decided to collect data? We won't know until someone choots their rifle in a benchvise ten shots at each of 8 distances, out to 350 yards. Without doing that, we're jus' speculatin' an' paintin' pictures!

 

[GymB]

Unfortunately, you can’t just lock the gun in a vise, the barrel harmonics would be too weird. Maybe a lead sled?

I like the idea of having the POA at 50 yards and a 1/2” or 3/8” hole (or better a length of pipe) to shoot through at 25. Those 2 points would define a line, so the rifle and shooter would need to be pretty consistently positioned to fall on that line. If they don’t, then the shot won’t make it cleanly through the first hole.

If the group at 50 is larger than 2x the hole/pipe, then the test is done, no need for longer range.

 

[MacEntyre]

Linear doesn't mean double the distance and expect to double the group size. You could double the distance and triple the group size and still be linear.

Anyway, if you only get two data points, your data will always be linear.

 

[GymB]

Linear doesn't mean double the distance and expect to double the group size. You could double the distance and triple the group size and still be linear.

Anyway, if you only get two data points, your data will always be linear.

You are generally correct about the broad definition of linearity, but you’re not reading the more specific definition of “linear” as the OP proposed, specifically

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...

His language seems more precise than most on the internet.

I also believe that the OP proposes to effectively measure at 3 points, at the muzzle (one point), at 25 yards (1/2”), and at 50 yards (x). If x is greater than 1” then the precision of the system is not linear as defined in the hypothesis.

All that said, I highly doubt that he’ll find it to be linear even at 50 yards, but I’ve never seen this specific test and am curious about the outcome.

 

[doose]

You are generally correct about the broad definition of linearity, but you’re not reading the more specific definition of “linear” as the OP proposed, specifically


His language seems more precise than most on the internet.

I also believe that the OP proposes to effectively measure at 3 points, at the muzzle (one point), at 25 yards (1/2”), and at 50 yards (x). If x is greater than 1” then the precision of the system is not linear as defined in the hypothesis.

All that said, I highly doubt that he’ll find it to be linear even at 50 yards, but I’ve never seen this specific test and am curious about the outcome.

I propose, as has been presented already, that no definitive answer can be determined with respect to linearity at two data points (distances). A minimum of three would be required and ideally more. The more data points gathered, the more accurate the mathematical model.

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[slow is slow]

I propose, as has been presented already, that no definitive answer can be determined with respect to linearity at two data points (distances). A minimum of three would be required and ideally more. The more data points gathered, the more accurate the mathematical model.

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I agree with this, and am going to try to make this test happen one day late next week or Christmas week. Perhaps I'll set up plates at 25, 50, and 75 with corresponding size holes, and my final target at 100 yards, then fire 100 rounds, noting after every 10 how many struck plates before hitting the 100 paper. It'll take a while to set it up because I'll have to set up one plate at a time, and then fire 20 rounds or so through that hole, then center the next plate's hole in that ones group, but I suspect I'll have a pretty good idea after the first plate if the theory is plausible or not.

 

[slow is slow]

Update: I received a response back from lapua about my question. I asked him if precision was linear and if the lots of ammo that do the best at 50m are the lots that do the best at 100m. Here is his response:

Jamie,




That is a good question. I have thought about it some and I would say that most of the time, if a lot does noticeably well at 50M it will also at least do OK at 100M as well. Sometimes the opposite is true and a good lot at 50M can be quite unusable at 100M. I would say slightly more often than not, if a lot is worth its salt at 50, it will at least be decent at 100 as well. I don’t think that I could give you a % breakdown (like 75% good at both and 25% opposite performance) but I feel that it is definitely better than half of them are going to do well at both but there is a non-insignificant amount of lots that just do well at one distance only.



Hope this helps,



Dan.

Seems to me that this pokes a hole in my theory. I'm still going to try my test and report back.