nbra, can you please elaborate on this formula? What is the basis for the math? From my way of thinking the radius of the 1.2 moa ammo capability must be added to each side of the 2 moa rifle capability so the moa values would really just add together.
The math or stats explanation is that they are two "independent, un-correlated error sources". The "square root of sum of squares" is how those sorts of things add up.
A non-math summary of it would be
when the rifle zigs, sometimes the ammo zigs but sometimes it zags. When you are firing a group, the position of each shot depends on where the rifle flings the shot, plus where the ammo flings the shot. "Plus" in this sense is the vector addition of the two errors (not the addition of their radius-of-error). With vector addition, 3 + 1 does not always equal 4, for example:
- 3 North plus 1 South is 2 North
- 3 North plus 1 North is 4 North
- 3 North plus 1 East is 3.2 North-NorthEast
The total group size of the rifle, assumed to be firing perfect ammo, is the maximum amount that it flings shots. Each individual shot in the group will be flung in a random direction, by a some random amount between zero and the maximum. Some shots are flung a bit, some are flung a lot. It is the outlier shots, the ones which are flung the most, which determine the rifle's group size, when "group size" is measured (as we do it) from the furthest two shots in the group.
Similarly, the total group size of the ammo in consideration, if it could be fired from an absolutely perfect rifle, is the maximum amount that the ammo flings each shot. (Also add in all the other factors from the previous paragraph, they are analagous).
Now what happens when you fire your real-world-imperfect rifle, with your real-world-imperfect ammo? How does the rifle's group size
combine with the ammo's group size?
If it happens that on the shot that the rifle happens to fling the most, is also the shot that the ammo flings the most, and these shots are flung in exactly the same direction by the rifle and by the ammo, then the group sizes will add up. A 2 MOA (extreme-spread) group from the rifle, plus a 1.2 MOA (extreme-spread) from the ammo, will form a 3.2 MOA (extreme-spread) group. In this case, what is happening is that the errors are
perfectly correlated, i.e. when the rifle "zigs" so does the ammo, and when the rifle "zags" the ammo also zags. This probably doesn't sound like a very realistic scenario to you, and it is not a very realistic (or likely) scenario.
What tends to happen, is that the amount and direction of a rifle's "zig", is pretty much unrelated to the ammo's "zag" (the technical naming of this being along the lines of "uncorrelated" and "independent"). When the rifle throws a wide shot, there is a 50% chance that the ammo's error will be in the opposite direction, which will act to _reduce_ the amount that that particular bullet is landing from the centre of the group. It is likely that when the rifle happens to throw its widest shot, that the ammo on that particular shot is throwing it in a
random direction, by an
average (not maximum) amount.
If you go through the mathematical derivation of it all, it turns out that the way you correctly "add" random un-correlated "zigs" and "zags" is by the square-root-of-sum-of-squares method.
How is your formula correct and the formula paraphrased from the army doc not correct?
It sounds to me like your square root formula is determining the mean radius and not extreme spread.
Did the Army document say "6 inch rifle+ammo group, minus 3.5 inch group for the ammo, means that the rifle is firing 2.5 inch groups"? Or, was that the conclusion/interpretation of the writer of the post? (an entirely reasonable and intuitive conclusion to make, though in this case intuition can be misleading)
The square-root-of-sum-of-squares should work correctly on the group's extreme spread, and also (though we haven't mentioned it yet) on the group's standard deviation. Both of these are usually "Normal" or "Gaussian" distributions, and so this is the correct way to "add" them. I *think* (but am not positive) that it won't work correctly on "mean radius"; I think that when you calculate "mean radius" you end up throwing a bit of information away (you are combining the x-error with the y-error... so you are crunching two pieces of error information into a single "r-error" value). I think the radius of the shots in a "Normal" or "Gaussian" group end up following a "Rayleigh" distribution, and the mean values of a Rayleigh distribution don't add in this manner. I am already out of my depth here so I better stop...
rone/Sitting/BenchedBags/support/lead sled front or rearBipodHow long you're waiting between shots, cooling etc.Nice thread revival if something comes of this.
