Now consider what happens when a shooter fires his gun uphill at a steep angle, as shown in Figure 3.3-1 (b), with no changes in the sights. Since bullet drop changes very little, at a slant-range distance Ro from the muzzle, the bullet has a vertical drop nearly equal to do. However, the line of sight at Ro still is located a distance do in a perpendicular direction away from the line of departure. Because of the firing angle, the trajectory no longer intersects the line of sight at the slant range Ro. In fact, the bullet passes well above the line of sight at that point--Figure 3.3-1 (b). In other words, the bullet shoots high from the shooter's viewpoint. The effect is almost exactly the same firing uphill and downhill.

A careful look at Figure 3.3-1 (a) or (b) reveals that the amount the bullet shoots high at the slant-range distance Ro is nearly equal to the perpendicular distance do from the line of sight to the extended bore line, minus the projection of do on that same perpendicular line. From plane trigonometry, the distance by which the bullet shoots high at Ro is determined by this formula: Amount by which the bullet shoots high = do [1.0 - cosine A], where A is the elevation (or depression) angle.

Consider taking a shot with a scoped rifle zeroed for 300 yards on a level range at a 300-yard target. With a slope angle of 30 degrees, the cosine is .87, which means you should hold for 261 yards (300 x .87) to hit the target.

This explanation of uphill and downhill shooting was given specifically for a slant-range distance equal to the zero-range distance for level fire for convenience's sake. However, the result applies for all slant-range distances. At any range distance from the muzzle, the amount by which the bullet will shoot high at any elevation or depression angle A is nearly equal to the drop for level fire at that range distance multiplied by the quantity [1.0 - cosine A].

Now, a smarter guy than me could go on and on, but there are simpler solutions for solving angled shooting. At home, you can make charts using software like Sierra's Infinity or Load from a Disk. In the field, the Slope Doper, which is a simple, mechanical device, and Leupold's RXII, RXIII, or RXIV rangefinders, which automatically compute corrections and angles on the spot, are two excellent choices. All are preferable to stumbling through the trigonometry I so doggedly avoided in school.