Doping The Slope
January 04, 2011
We'd spotted the blocky, white Dall rams on the face below earlier in the day.
We tried to get closer, but it was too steep and slippery to descend with any degree of stealth. While we were discussing our options, the rams got up to feed. I dropped prone and eased a round into the chamber of my .257 Weatherby, but they were still too far.
I watched them in my Leica Geovid rangefinding binocular, checking the range periodically with a touch of the button. The rams worked their way quickly from 1,100 to 700 yards, feeding steadily. At 670 yards, they turned broadside and began feeding up the face to our right.
At 582 yards, they stopped. I considered the extreme downhill angle, took note of the wind, and calculated my hold. I stuck the scope's 300-yard dot low on the ram's shoulder and squeezed the trigger, sending the ram into overdrive.
"You hit just in front of him," Eric exclaimed, "but your elevation was perfect."
I struggled to find the now-running ram in my scope and settled on its shoulder. Soon, the pair stopped to feed again. The distance was 488 yards. I calculated the angle and then held the 300-yard dot just below the ram's chest, slid into the wind, and squeezed the trigger. At the shot, the ram collapsed and careened down the hill.
That shot helped me realize my lifelong dream of taking a Dall sheep. Although it happened quickly, making the shot took a bit of mental gymnastics. Doping the wind was easy once I figured out the direction was different down below my position. The hard part was figuring out my elevation hold due to the steep downhill angle.
There is a ton of bad information on shooting uphill and downhill. I've seen Internet forum posts advocating holding high on uphill shots and low when shooting downhill, and I've seen gunshop know-it-alls espousing equally idiotic tripe. The truth is you shouldn't give angles a second thought unless the range is long and/or the angle is very steep. Just hold dead on and shoot. But when you reach out to 300 yards and beyond and/or your angle goes to 30 degrees or more, you'd better know what you're doing, or you are sure to miss or wound your target.
There are few absolutes in shooting, but here's one: Whether shooting uphill or down, if the angle is enough to matter, you should hold lower than you would at the same range on level ground. I've seen many explanations of why bullets strike high on steeply angled shots, but the Sierra manual has the best explanation so, with Sierra's permission, I have borrowed heavily from it here.
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.
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.