Don,
The reason guns don't shoot the same MOA at all ranges is the error, even in zero wind and shooting from a machine rest, is generally caused by some form of slow drift away from the average trajectory path that remains practically constant all the way to the target. With the drift being constant, you would think it would be the same for every hundred yards until you remember that the bullet is slowing down as it flies. That means it takes longer to traverse the second 100 yards than it did the first 100 yards, giving that constant drift more time to move the bullet a larger number of moa away from the average trajectory path. The third 100 yards takes still long to traverse than the second 100 yards did, letting the drift add an even bigger error than it did in the second 100 yards, etc, etc. So the actual drift error has the shape of a brass horn, sort of flaring outward as it goes downrange.
As to guns shooting tighter at a longer range, while it is true that it takes a couple of hundred yards for initial yaw (which varies some from shot-to-shot due to muzzle blast effects on the bullet) to damp down about 80%, most of the error from yawing averages out over a distance. So it doesn't really have much to do with final accuracy. However, with a typical rifle, the boreline is above the line from the center of your shoulder contact with the butt plate to the muzzle. This causes recoil to induce an upward flip of the muzzle that starts when the bullet is still in the barrel and introduces a harmonic wiggle in the muzzle. If your load has just the right barrel time, that wiggle can just compensate for a slower bullet dropping more by the time it gets to the target because the muzzle has risen slightly in the extra time the slower bullet takes to get out of the bore. The compensation will only be perfect at one range. So if you suppose it is perfect at 200 yards, your 100-yard group can have more vertical dispersion than your 200-yard group, but by the time the bullets get to 300 yards, the vertical dispersion will be back.
The first two illustrations in this article are an example of perfect compensation, though it is in the context of getting barrel tuners to make it happen.
Nick
The reason guns don't shoot the same MOA at all ranges is the error, even in zero wind and shooting from a machine rest, is generally caused by some form of slow drift away from the average trajectory path that remains practically constant all the way to the target. With the drift being constant, you would think it would be the same for every hundred yards until you remember that the bullet is slowing down as it flies. That means it takes longer to traverse the second 100 yards than it did the first 100 yards, giving that constant drift more time to move the bullet a larger number of moa away from the average trajectory path. The third 100 yards takes still long to traverse than the second 100 yards did, letting the drift add an even bigger error than it did in the second 100 yards, etc, etc. So the actual drift error has the shape of a brass horn, sort of flaring outward as it goes downrange.
As to guns shooting tighter at a longer range, while it is true that it takes a couple of hundred yards for initial yaw (which varies some from shot-to-shot due to muzzle blast effects on the bullet) to damp down about 80%, most of the error from yawing averages out over a distance. So it doesn't really have much to do with final accuracy. However, with a typical rifle, the boreline is above the line from the center of your shoulder contact with the butt plate to the muzzle. This causes recoil to induce an upward flip of the muzzle that starts when the bullet is still in the barrel and introduces a harmonic wiggle in the muzzle. If your load has just the right barrel time, that wiggle can just compensate for a slower bullet dropping more by the time it gets to the target because the muzzle has risen slightly in the extra time the slower bullet takes to get out of the bore. The compensation will only be perfect at one range. So if you suppose it is perfect at 200 yards, your 100-yard group can have more vertical dispersion than your 200-yard group, but by the time the bullets get to 300 yards, the vertical dispersion will be back.
The first two illustrations in this article are an example of perfect compensation, though it is in the context of getting barrel tuners to make it happen.
Nick