First, remember that bullet drop at any given range is independent of firing elevation angle. So, if bullet drop at 200 yards is measured when the gun is fired on a level range and again at a slant-range distance of 200 yards, the bullet drop will be almost identical whether the barrel is angled up or down and regardless of the degree of the angle.

This is because gravity is a constant 32 feet per second, per second and acts on the bullet throughout its time of flight. Some other constants are range, which never changes regardless of angle; time of flight, which is almost exactly the same since the range is constant; drop, because time of flight and gravity are constant; and velocity.

The only factor that isn't constant is the perspective of the target from the shooter's vantage point. It may not seem like a big deal, but that different perspective is why steep angles cause shots to go high. The reason is that sight adjustments are made in a plane perpendicular to your line of sight. When steep angles come into play, the target is not in a plane perpendicular to your line of sight. Consequently, your correction is incorrect.

Here's how you can visualize it. Let's say you're shooting a .30-06 with a 150-grain bullet at 2700 fps. You're zeroed at 200 yards. You want to shoot something at 500 yards, so according to the ballistic tables, you have to hold 36.69 inches high. Now go downrange, drive a stake in the ground in front of the target, and tie a marker on it at 36.69 inches above the bullseye. Return to the bench, forget about the target, aim at that marker, and shoot. "Bullseye!"

Now go back downrange and tip that target back 30 degrees. Go back to the bench, aim at that marker--which you have not moved--and shoot again. You'll find that your shot went high. Why? Because your holdover was in a plane perpendicular to the line of sight, but the target wasn't in that plane.

Now look through your scope without moving anything and put the crosshair on that marker. See how much more over the angled target you're aiming than you were when it was perpendicular? Well, depending on how good a shooter you are, that is probably the amount you just overshot the angled target.

Figure 3.3-1 from the Sierra manual shows how this happens. Ordinarily, a shooter will sight-in his gun on a fairly level range. To zero his rifle, the shooter adjusts his sights so that the line of sight intersects the trajectory at the range where he wants his gun zeroed. Ro is the zero range for level fire. The vertical distance between the line of departure (extended bore line) of the bullet and the point where the bullet passes is the drop (do). This symbol is used to denote the drop at the range where the gun is zeroed.

Note that the angle between the bullet's line of departure and the line of sight is slight. Even at 1,000 yards, the angle A is much less than one degree and is typically less than 10 minutes of arc for sporting rifles and handguns.

Shooting at steep angles changes everything. The author took this fine Dall sheep at 488 yards, but he held for 300 yards because of the angle.