The Anatomy of L.R. shooting. So...err...what is it?
- Thread starter Pond James Pond
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Jim Watson
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Bart and Kraig have a lot more experience than me, so I will just say that with the gear you ALREADY OWN, I would go with a 155 gr bullet, the Lapua Scenar or a Sierra Palma or other similar. That will get you the highest BC in that weight and a relatively light bullet will moderate the recoil in a light sporting rifle.
Pond James Pond
New member
Thanks for the endorsement of bullet choices!!
I called the Sierra Palma supplier: sold out until the end of the month, but then I'm not buying before then, anyway. I'll check out the Lapua options, although it seems the local shop only stocks the Scenar in 167gr, so I may opt for the 150gr Lockbase, if Lapua ends up as my choice: that seems to have a healthy BC, too!
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It's been my experience with the .308 Win. barrels I've worn out that all the 30 caliber Sierra HPMK bullets as well as several of their hunting bullets all shot sub 1/2 MOA at 100. These are weights from 150 to 200 grains. 'Course the HPMK's were more accurate, but those barrels "liked" all of them. Perhaps the reason is all those Sierra's were all the same diameter; .3082" except for the 155's that were.3084" but they shot very good, too.
That is correct if we consider only a single shot.
However, it's important to understand that both the rifle and shooter errors are random so they don't always end up pointing in the same direction. The rifle's error for a particular shot might be in the 5 O'Clock direction while the shooter's error for that same shot might be in the 11 O'Clock direction (opposite the rifle's error) from the aiming point. The effect on the target in that case would actually be a shorter distance from the center than either of the errors ALONE would have caused.
In fact, the odds that both errors will end up pointing in exactly the same direction (or in exactly opposite directions) are vanishingly small.
So when you try to calculate the group sizes generated by a 1MOA shooter and a 2MOA rifle you have to consider that both the magnitude of the error (distance from the aiming point) and the angle of the error (direction of the error from the aiming point--say 10 O'Clock or 6 O'Clock) are random.
For the expected group size to be generated by a simple addition of 1MOA and 2MOA, the angular error for the rifle and the shooter would have to line up for each shot which is impossible in any practical sense. To calculate the actual expected group sizes of a 1MOA shooter using a 2MOA rifle, one must use techniques for adding random variables.
John, I understand your reasoning.
My point is, the accuracy of a rifle and its ammo is the largest group they shoot. Half its size is the furthest a bullet will strike from where the rifle's aimed. If the rifle's aimed somewhere inside a 1 MOA circle 'cause that's the area it moves around in when held by a shooter, the furthest a shot will land from the edge of that circle is half the size of the rifle and ammo's accuracy.
So, a shooter aiming at a point on the target holds within 1/2 MOA of that point; his area where the sights align is 1 MOA. His desired impact point's in the middle of it. His rifle and ammo's largest groups are 2 MOA. The furthest a bullet will strike from where it's aimed is half that amount; 1 MOA.
Therefore, the resultant group on target should the shooter fire many shots will be 1 MOA of holding plus 2 MOA of accuracy and that's 3 MOA. The shooter's shot will land somewhere between his desired impact point and 1-1/2 MOA away from it. The fewest number of shots will be at the outside edge, but they're still gonna be there. They have to be counted in the measurement of the group he shoots. Most of the shots will be inside about 2 MOA, but not all of them. About one third will be in the 2 and 3 MOA range.
In talking with ballistic folks at Lake City Army Ammo Plant on their 7.62 NATO match ammo tests, I've gained some insight on the realities of accuracy tests. They would shoot a couple hundred shots per test group and they told me the following. It's been their observations for a "rule of thumb" that about 10% of the shots fall in the outer 10% of the group radius, 20% in the next inner 20%, 30% in the next on and finally 40% in the inner 40% of the group's radius. Which correllates well with the mean radius (their standard measurement of accuracy) covering about 70% of the bullet holes; inner 40% and 30% of the shot holes and about 70% of the group's radius. Oft times there would be 5 or 10 holes by themselves at the outer edge of a 200-shot cluster typically about 6 to 11 inches in diameter depending on the quality of the ammo lot tested. Yet those outliers very precicely represented the furthest a bullet would strike from group center or where the rifle was aimed and have to be counted as part of the group. I've seen a couple of their test targets and it's hard, but one can fairly easy identify each bullet hole for measuring its location with reasonable accuracy. They're fired at 600 yards.
Where the rifle's aimed about a desired point for bullet placement by the shooter, any error in that has to be added to the radius of the shot group to determine the maximum miss distance from the desired point of impact.
My point is, the accuracy of a rifle and its ammo is the largest group they shoot. Half its size is the furthest a bullet will strike from where the rifle's aimed. If the rifle's aimed somewhere inside a 1 MOA circle 'cause that's the area it moves around in when held by a shooter, the furthest a shot will land from the edge of that circle is half the size of the rifle and ammo's accuracy.
So, a shooter aiming at a point on the target holds within 1/2 MOA of that point; his area where the sights align is 1 MOA. His desired impact point's in the middle of it. His rifle and ammo's largest groups are 2 MOA. The furthest a bullet will strike from where it's aimed is half that amount; 1 MOA.
Therefore, the resultant group on target should the shooter fire many shots will be 1 MOA of holding plus 2 MOA of accuracy and that's 3 MOA. The shooter's shot will land somewhere between his desired impact point and 1-1/2 MOA away from it. The fewest number of shots will be at the outside edge, but they're still gonna be there. They have to be counted in the measurement of the group he shoots. Most of the shots will be inside about 2 MOA, but not all of them. About one third will be in the 2 and 3 MOA range.
In talking with ballistic folks at Lake City Army Ammo Plant on their 7.62 NATO match ammo tests, I've gained some insight on the realities of accuracy tests. They would shoot a couple hundred shots per test group and they told me the following. It's been their observations for a "rule of thumb" that about 10% of the shots fall in the outer 10% of the group radius, 20% in the next inner 20%, 30% in the next on and finally 40% in the inner 40% of the group's radius. Which correllates well with the mean radius (their standard measurement of accuracy) covering about 70% of the bullet holes; inner 40% and 30% of the shot holes and about 70% of the group's radius. Oft times there would be 5 or 10 holes by themselves at the outer edge of a 200-shot cluster typically about 6 to 11 inches in diameter depending on the quality of the ammo lot tested. Yet those outliers very precicely represented the furthest a bullet would strike from group center or where the rifle was aimed and have to be counted as part of the group. I've seen a couple of their test targets and it's hard, but one can fairly easy identify each bullet hole for measuring its location with reasonable accuracy. They're fired at 600 yards.
Where the rifle's aimed about a desired point for bullet placement by the shooter, any error in that has to be added to the radius of the shot group to determine the maximum miss distance from the desired point of impact.
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Look at it this way,
When I say "out shoot the rifle" I mean if you have a 2 MOA rifle and constantly shoot that rifle at 2 MOA, then its time to move up in equipment.
When I first got my M1A (1977) it was a standard grade. I reached a point in High Power where I could shoot certain scores and could not improve. I could outshoot the rifle.
I gave my rifle to the All Guard Armors at the Wilson Matches (National Guard Championships) who converted it to a Super Match. Only then could I improve to the point I could shoot master scores and get my Distinguished Rifle badge.
You can add 2 MOA plus 1 MOA and get 3 MOA all you want. There comes a point where it is time to move on, or move up rifle wise if you want to improve.
When I say "out shoot the rifle" I mean if you have a 2 MOA rifle and constantly shoot that rifle at 2 MOA, then its time to move up in equipment.
When I first got my M1A (1977) it was a standard grade. I reached a point in High Power where I could shoot certain scores and could not improve. I could outshoot the rifle.
I gave my rifle to the All Guard Armors at the Wilson Matches (National Guard Championships) who converted it to a Super Match. Only then could I improve to the point I could shoot master scores and get my Distinguished Rifle badge.
You can add 2 MOA plus 1 MOA and get 3 MOA all you want. There comes a point where it is time to move on, or move up rifle wise if you want to improve.
Kraig, I agree with you. When you can hold better than the rifle and ammo shoots, then you need to get better ammo and rifle. Your rifle and its ammo needs to shoot better than you can hold if best accuracy's the goal. The better that "hardware" is the smaller your groups will be, the higher your scores will be and you'll miss your desired point the least amount.
There are exceptions but I'll not address them here. There's been National champions who've picked a less accurate firearm than what was available because they shot it more accurate than what the could do with the more accurate ones.
There are exceptions but I'll not address them here. There's been National champions who've picked a less accurate firearm than what was available because they shot it more accurate than what the could do with the more accurate ones.
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Again, the only way that they will add up to 3 MOA is in the extremely improbable case where the vector angle of the errors lines up perfectly on two shots that go in opposite directions on the target and the magnitudes of all the errors are at their maximums.
Each shot has a random error associated with it. That error has both a magnitude and an angle. If you consider that the shooter contributes some error and the rifle contributes some error, now each shot is the vector sum of two random errors. That is the combination of two random magnitudes and two random angles.
To get a group of 3MOA, you'd first need a shot where the random error magnitudes of both shooter and rifle are essentially at their maximums and the random error angles of both the shooter and the rifle are lined up in the same direction. Then you need a SECOND shot where both random magnitudes are again essentially at their maximums and the two random angles are lined up with respect to each other but in the OPPOSITE direction of the two random angles of the other shot where everything lined up.
So you need two shots in your group where all of the following are true.
- All four random magnitudes are at or very near their maximums.
- One of the shots must have two random angles line up very closely.
- A second shot must have two random angles that line up very closely and that are opposite or very nearly opposite the other two random angles from the other shot.
The bottom line is that a X MOA shooter with a Y MOA rifle will shoot groups that are larger than the larger of the two accuracy figures but smaller than X+Y MOA.
Absolutely, a 1 MOA shooter + a 2 MOA rife will produce, on average, a 2.24 MOA group.
And the biggest group will be 1 + 2 = 3. 3 MOA. This happens when all the errors or variables add up directly.
If all the errors for a given bunch of shots cancel each other out, the smallest groups will be zero MOA. Or close enough to not matter.
Ain't math great?
And the biggest group will be 1 + 2 = 3. 3 MOA. This happens when all the errors or variables add up directly.
If all the errors for a given bunch of shots cancel each other out, the smallest groups will be zero MOA. Or close enough to not matter.
Ain't math great?
Indeed -- as number of groups goes to infinity, the outliers will be 3MOA and 1MOA, but the average "should" be as stated. This thread is a fascinating example of everybody being right, but in different ways, and talking "past" each other.
All of that, of course, assumes that the deviations are truly random (and thus, evenly distributed). They probably aren't, since there are certain phenomena that create these deviations. The result will likely not be random. I would guess that some of the deviations, such as a wobbling hold or inconsistent cheekweld, "tend" to produce linear deviations (rather than "planar", if that distinction communicates) such that you might well approach the "extreme case" of 3MOA more often than root-mean-square indicates.
Nevertheless, 3MOA is a "worst case" given the conditions. Math IS awesome, especially since it includes probability and statistics
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All of that, of course, assumes that the deviations are truly random (and thus, evenly distributed). They probably aren't, since there are certain phenomena that create these deviations. The result will likely not be random. I would guess that some of the deviations, such as a wobbling hold or inconsistent cheekweld, "tend" to produce linear deviations (rather than "planar", if that distinction communicates) such that you might well approach the "extreme case" of 3MOA more often than root-mean-square indicates.
Nevertheless, 3MOA is a "worst case" given the conditions. Math IS awesome, especially since it includes probability and statistics
.Sent from my ASUS Transformer Pad TF300T using Tapatalk 2
Correct.
Assuming that the 1 and 2 MOA figures are hard limits--no shots ever go larger than those limits for the shooter and rifle respectively. (This isn't really a good assumption. In reality the figures aren't hard limits, they are a very simplified representation of the probability distribution of the shots on the target. That's why the MOA figures for 10 shots groups is larger than that obtained shooting 3 shot groups. The more shots you get, the better the representation of the probability distribution you get and the farther the extreme shots are likely to be from each other. But the math gets complicated and I don't want to mess with it so I'm going to assume these are hard limits. It will serve to illustrate the probabilities that explain why it's problematic to think about it in terms of straight addition of accuracy figures.)
AND
Assuming the shot distribution over the magnitude limits are uniform. (This isn't really a good assumption either but it will suffice for illustration. The shot distribution would probably be better modeled with a normal (Gaussian) distrubition but I don't want to fiddle with the math.)
AND
Assuming that we accept magnitudes that are 95% or greater as being sufficiently large.
Then you'd need a group containing about 400 shots in order to get JUST the magnitudes to line up so you'd have a really good chance of getting a group that was 2.9MOA or greater.
That completely ignores the error angles which would also have to line up just right to get a group that large. So...
Making the same general assumptions as above and assuming that the error angles have to line up within 18 degrees (5%) to make everything work, then you'd end up again needing a group with maybe 400 shots before you'd have a really good chance of having JUST the angles lined up just right.
If we assume that the magnitude and angle errors are independent of each other and independent from shot to shot.
Then, to get the magnitudes AND angles to line up just right all at the same time--based on the above assumptions, we would need a group with something like 160,000 shots in it to have a really good chance of getting everything to line up just right.
That's why it's much better to talk about averages when we combine accuracy figures than to try to define maximums. Averages provide useful information. If you talk about maximum group sizes instead of averages, the resultant figures aren't very representative of what is likely to be encountered in the real world.
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Pond James Pond
New member
I want to learn to shoot long range. I really do... but that really is more reloading than I'd had in mind.
John, how many call vs. impact plots for 20-shot groups have you made with 1/2 moa gear fired hand held?
And isn't the average of 2 3 4 5 6 7 & 8 the same as 4 4 5 5 5 5 6 & 6? If these are groups fired with two systems, one is more accurate than the other in spite of having the same average.
And isn't the average of 2 3 4 5 6 7 & 8 the same as 4 4 5 5 5 5 6 & 6? If these are groups fired with two systems, one is more accurate than the other in spite of having the same average.
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Corrected my post above. Got a 4 where there should have been a 2 and since it was an exponent, it really made a difference.
So if you're getting a wide variance across your groups (as with the first system in your example)--especially with a relatively small number of groups then you won't be able to provide a representative accuracy figure and the combination won't be representative either.
To have any chance of providing a reasonable answer when combining accuracy figures, the figures need to actually be representative accuracy figures.
So if you're getting a wide variance across your groups (as with the first system in your example)--especially with a relatively small number of groups then you won't be able to provide a representative accuracy figure and the combination won't be representative either.
While the odds of both sources of variables adding to the maximum is one in a huge number, nobody can predict the shot it will happen on. Might be in the last thousand, middle hundred or the first ten. Therefore I'll include it in the accuracy measurement of the shooter and his equipment.
PS
Mean radius of a many shot group is better than the average of several few shot ones.
PS
Mean radius of a many shot group is better than the average of several few shot ones.
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Sure, it won't hurt anything. On the contrary, you'll be pleased to find that the groups shot will be always be significantly smaller than the accuracy measurement you've chosen to espouse would suggest they should be. It'll be like Christmas every time you measure a group. 
I believe the military uses Mean Radius rather than extreme spread because they are less interested with how far the farthest two shots are from each other and more interested in how far the shots land, on average, from the aim point.
Group size is a convenient measurement and that's why it's used. There are certainly better ways to characterize accuracy.
I believe the military uses Mean Radius rather than extreme spread because they are less interested with how far the farthest two shots are from each other and more interested in how far the shots land, on average, from the aim point.