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This is a relatively simple question. Rather than saying that the bore points up relative to the sights it may be better to visualize this as being two lines which when projected to any distance from the muzzle will converge at a specific point which is usually referred to as zero. If the line of the bore and line of sight were parallel or divergant then the bullet would never be able to strike at the point of aim but would always be below by at least the difference between these lines. No matter what the situation, the up/down relationship applies only to thr bore/sight relationship, not actual up or down relative to our position from the target

There are actually two situations which occur. The first being a shoulder fired gun such as a rifle, and the second being a handgun. I'll try to explain the difference and the why, and in doing so will seem to contradict my statement above.

Let's approach the rifle first. Typically the bore and sight lines will converge in this scenario. A rifle will move very little in recoil except straight back aproximately along the bore line before the bullet leaves the muzzle. Due to gravity the bullet begins to fall immediately on leaving the muzzle and to hit a target at any distance the bore must be elevated relative to the line of sight to start the bullet upward at such an angle that the bore will be pointed at a place above the intended impact (zero) equal to the total drop for that range. If you refer to any of the loading manuals which have ballistic data you will see the total drop listed for a specific bullet/range/muzzle velocity, this figure is from the bore line.

The second situation is the handgun, and it makes no difference if it is a revolver, automatic or single shot. In this case the bore line usually points away from the line of sight. This is because of the dynamics involved. A handgun, being much lighter than a rifle, will start to recoil both to the rear nad at the same time the muzzle will begin to rise. There is actually quite a bit of verticle component which occurs before the bullet leaves the muzzle. Handgun sights will be adjusted so as to cause the muzzle to be pointed below the intended point of impact before discharge. As the gun recoils and the muzzle rises the bore line will rise to point somewhat above the intended point of impact by trhe time the bullet exits.

To simplify this whole thing, to account for the dynamics of the gun/cartridge combination on firing the line of bore in a rifle will converge with the sight line (rear sight higher than front relative to bore line) and with a handgun the lines of bore and sight will diverge (front sight higher than rear relative to bore).

Either case results in the bullet, called a projectile while in flight, being launched from a bore which is pointed slightly above the intended point of impact at the moment when the bullet exits the muzzle. The amount high the bullet must be directed is directly proportional to the time of flight from muzzle to target. A pistol bullet taking x-time to reach its target at 900 f.p.s. will drop exactly the same distance from the bore line as a rifle bullet will at 2700 f.p.s. will in going three times the distance in the same x-time.

I hope this helps.
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