Originally Posted by HeskethPritchard
Surely you should just get the scope as low as possible?
This is of course driven by the bell housing diameter (driven by the type of scope you want/need for the work your gonna do) that ultimately drives the height you want to know.
There are good reasons not to mount a scope as low as possible. The reasons I can see for keeping a scope as low as possible above the bore include minimizing the torque on the rings when the gun is fired, making the scope less likely (maybe) to get caught on brush while being carried, and perhaps to keep the shooters head as low as possible on a battle rifle.
The main concern as to how high a scope should be mountd in my opinion is that the scopes optical axis should be comfortable for the shooter. Either too low or too high will be uncomfortable and won't give a proper "cheek weld" . If "tight to the barrel" is the most comfortable position maybe the rifle's stock needs a higher comb. Obviously the shape of the stock's comb relative to the bore matters. So does the relative shape of the shooter's face, neck, and shoulders, so there's no "right" answer to the exact distance a scope should be mounted from the barrel. On certain classes of firearms a scope needs to be mounted beside the barrel, not above it. An example is a shoulder fired recoilless rifle, or grenade launchers like the M70 and M203.
Reasons for raising the scope include the fact that if a rifle is set up to maximize the "point blank" range such that from zero out to some maximum distance a bullet will fall in a given diameter circle if the sights are aimed at the center of the circle, then the scope height above the bore should be equal to the radius of that circle. That could be rediculous if a very large or very small point blank error diameter is desired but it makes sense for a 5 or six inch diameter circle.
Mounting a scope high also puts the bore lower relative to the shoulder, and assuming the stock is designed for it, reducing the rotational recoil moment when a gun is fired. That helps reduce muzzle flip. The AR-15 is an example of a rifle designed with this and the previous reason in mind. The M14 and M1 were not.
Another reason to keep the scope high is that thermal distortion from warm air rising off a heated barrel is more likely to miss being in the line of sight the higher the scope is mounted if there is any crosswind.
There is a slight increase in sensitivity to canting by mounting a scope higher. On the other hand it's easier to notice that a rifle is canted with the scope mounted higher.