High-Angle Shooting

Your DOPE assumes a flat, horizontal shot — gravity acting over the full distance the bullet travels. When you shoot at a steep angle, up or down, gravity still pulls straight down, but it only acts over the horizontal component of the flight path, which is shorter than the line-of-sight distance to the target. Less effective gravity drop means the bullet strikes higher than your flat-range solution predicts — and this is true whether you shoot uphill or downhill. The common belief that you hold low uphill and high downhill is wrong; both angled shots impact high relative to line-of-sight DOPE. The steeper the angle, the larger the error.

The key concept: the distance your rangefinder (or reticle) gives you is the line-of-sight (slant) range — straight to the target. But the bullet's drop behaves according to the horizontal range — the distance "along the ground." On a flat shot they're identical. On an angled shot the horizontal range is shorter:

Horizontal range = line-of-sight range × cosine(angle).

A target at 500 yards line-of-sight up a 30° slope has a horizontal range of 500 × cos(30°) = 500 × 0.866 = 433 yards. You must dial/hold for 433 yards, not 500 — using the 500-yard solution would send the round high. The cosine of the angle is always ≤ 1, so the corrected range is always shorter, so you always come down off the slant-range solution.

The practical field technique, the rifleman's rule: measure the line-of-sight range, measure the angle (an angle cosine indicator on the scope/mount, or an inclinometer, reads it directly — many give you the cosine value to multiply by), multiply line-of-sight range by the cosine to get the "shoot-to" horizontal range, and apply your normal DOPE for that shorter range. Reference cosines worth knowing: 15° ≈ 0.97 (small effect), 30° ≈ 0.87, 45° ≈ 0.71 (large effect), 60° ≈ 0.50 (the horizontal range is half the slant range). Below ~15° the correction is often negligible; past 30° it's decisive at distance.

Worked example: 600-yard line-of-sight, 45° downhill. Horizontal range = 600 × 0.71 = 426 yards. Dial your 426-yard elevation, not 600. The difference between a 600- and 426-yard elevation solution at that distance is many feet of vertical — an unmissable miss if ignored.

The basic cosine method corrects the range and works well to moderate angles and distances — it's the right tool for the vast majority of field angle shots. But it's an approximation: at long range and steep angles it slightly over-corrects, because the simple rule applies the cosine to the whole range when, more precisely, the relationship involves the bullet's drop and the trajectory's shape, not just a linear range scaling. More advanced methods (the "improved rifleman's rule," which applies the cosine to the drop/come-up rather than the range, and full trajectory solvers that take the angle as a direct input) are more accurate for extreme-angle, long-range work. A good ballistic solver — including the kind this app uses — can take shot angle directly and give an exact solution. The practical guidance: use the cosine method as your reliable field default, know that it slightly over-corrects at the extremes, and lean on a solver that accepts angle for steep long shots. Either way, the first reflex on any sloped shot is reduce your elevation off the line-of-sight solution.