I have been thinking about accuracy lately, specifically: things that affect how far from where you are aiming at a given long distance.

For simplicity, assume the gun shoots a consistent 1 MOA. 1 MOA is 1.0472" at 100 yards.

So, all other things being exactly "on", this would be 2.09" at 200 yards, or generally 1.0472" * ( R / 100 ).

Now assume you have a long-range scope (eg. Leupold Long Range M1 3.5X-10). It has 1/4 MOA "clicks" - the quantum of elevation adjustment is 0.25 MOA. They way you figure out what elevation adjustment to set the scope on for a certain range is to:

1. zero the rifle at 200 yards (example, I will use it)
2. measure the muzzle velocity
3. for the bullet mass & B.C., look up the trajectory in a ballistics book

   This will yield point-of-impact distance measurements above the point of aim, for the 200y zero. So you get something like this (example):

       0     100  200  300    400     500    yards
      -1.5   2.1  0    -8.8   -25.5   -51.9  inches
   

   Negative values mean the bullet is below the ray of aim at that distance. It starts off negative because the bore is below the scope.

4. Now you map that distance measurement (d) in inches to MOA at that range (r). MOA = -d/r * (100/1.0472) = -95.493 * d/r

   For the example above, you get

      0     100    200     300    400     500    yards
     -1.5   2.1      0    -8.8   -25.5   -51.9   inches
           -2.01     0     2.80    6.0     9.91  MOA
   

This means that if your scope is zerod at 200 yards, and you want to hit a target at 500 yards, you need to adjust the point of impact UP 9.91 MOA with respect to the point of aim.

But the scope has an elevation quantum of 0.25MOA. So you would round 9.91 MOA up to 10MOA, or forty full "clicks."

What is the maximum error introduced by this rounding? It's half the quantum (1/4 / 2 = 1/8 = 0.125 MOA). At 500 yards, this adds 0.125 * 5 * 1.0472 = 0.654".

So if we are using elevation knobs to adjust the zero for the range, an error of 1/8 MOA (in this case) is introduced.

The other factor is how differences in muzzle velocity change the point of impact at long range.

At close range, a change in muzzle velocity does not affect the point of impact much. For a sample load from my Hornady ballistics book (.308, 165gr BTSP, BC 0.435, 2500 - 2800 fps), it changed about 0.1" per 100 fps. This comes to about 0.000955 MOA/1fps.

If I do a comparison at 500 yards, a change in muzzle velocity makes a much larger difference in point of impact. For the same bullet used above, if I linearly model the change in point of impact as muzzle velocity goes from 2500 - 2800 fps, it averages about 0.00877 MOA/1fps.

This is about an order of magnitude more effect than at the short range. And it is magnified by the range, since it is an angular measurement.

For a +/-  5 fps load, that's 0.0438 MOA, 0.229" at 500 yards
For a +/- 10 fps load, that's 0.0877 MOA, 0.459" at 500 yards
For a +/- 20 fps load, that's 0.1750 MOA, 0.916" at 500 yards

1. 1/8 MOA from elevation quantum.
2. +/- 10 fps muzzle velocity. My handloads have a std dev of about 10-15 fps, and Federal Gold Match was about 12fps in my FAL. That's 0.0877 MOA.
3. the rifle is 1 MOA at 100 yards.

So the rifle that started out a 1 MOA is now 20% worse at 500 yards.

If I do the same exercise for 1000 yards, I get about 0.0345 MOA / 1fps. Or +/- 10 fps -> 0.345 MOA at 1000 yards. This is 3.61" at 1000 yards.

If I do the same calculation, (1 + 1/8 + 0.345) * 1.0472 * 10 = 15.4".

Now our 1MOA rifle at 100 yards is 1.47 MOA rifle at 1000 yards! That's almost 50% worse!

If you start off with a 0.25MOA rifle.. which you can buy for $4000 or $5000, you get: (0.25 + 1/8 + 0.345) * 10.472 = 7.54".

If you can get your handloads down to a 10 MOA variance (+/- 5fps):

(0.25 + 1/8 + 0.172) * 10.472 = 5.73".