When you shoot uphill, you aim over the target, and if the target is downhill, you hold low. Or is it the other way around? Or does it make any difference? Shooters love to argue this, but seldom do we hear a convincing argument or explanation. The answer is easy once you understand the principle. Before getting into reasons why, let me promise you that the point of aim does indeed change if you shoot at a target either above or below you. Also, as the uphill or downhill angle increases, so does on-target bullet displacement.
Let's say you're going after a mountain goat with your new rifle in .270 Winchester caliber. You adjust the riflescope so that the bullet hits dead center at 200 yards. This means that the point of impact is 1 1/2 inches high at 100 yards, about 6 1/2 inches low at 300 yards and 19 1/2 inches low at 400 yards. In the mountains, you get a shot at a big billy at what you and your guide estimate to be close to 400 yards. It's a longish shot, but you roll your down vest into a rifle cushion and, taking a solid rest, settle the crosshairs a few inches over the goat's back. Allowing for the 19 1/2 inch drop at 400 yards, you hold high and figure that the bullet's trajectory will curve right into the goat's boiler room. But you have forgotten something.
The goat is 45 degrees above you. What a difference will that make in the bullet's flight in respect to the line of sight? Do you need to aim higher, perhaps? Or lower?
If you aimed at the goat the same way that you would over level ground, the old billy would live to see another winter because the bullet would zip harmlessly over its back. At an upward angle of 45 degrees, the bullet would only fall 8 1/2 inches in respect to line of sight, less than half as much as it would drop when shot horizontally. Exacly the same would be true if you were shooting downhill at a 45 degree angle.
By now, we're very much aware that gravity causes the path of the bullet to curve downward. But let's put gravity to work another way. Imagine, if you will, a rifle held perfectly perpendicular so that when it is fired, the bullet goes straight up. If there were no wind or other variables to disturb the bullet's flight, the projectile would go straight up until it ran out of momenum. Then, gravity would pull it straight back down again, base first.
Here's where you need to use your imagination. This time, we'll tilt the rifle slightly, say 1 degree off plumb. This time, the bullet's flight is almost straight, but not quite. As it nears the apex of its trip, it begins to curve ever so slightly. So, let's keep shooting (and using our imaginations). Each time we fire, we tilt the muzzle another degree from the vertical, and the bullet path of each succeeding shot is progressively more curved. At last, we come to 90 degrees (horizontal), and the bullet follows its normal curved trajectory.
By now, I'm sure that you're getting the picture. we know that our logic is sound, but it must be demonstrated. How? Let's use an ordinary fly rod- the one you take trout fishing! Assuming that the rod is not warped, set the butt on the ground and hold the rod vertically. It remains perfectly straight. Now, holding it by the grip, lower it horizontally. See how it curves downward? (If it is too stiff to bend very much, attach a weight to the tip.) Now, slowly angling the rod from the vertical to dead level, note how gravity causes the curve to increase as the angle nears the horizontal.
Now, let's get down to basics. Realizing that shooting uphill or downhill causes the bullet to strike higher than it would on the horizontal, in respect to point of aim, how can we judge where to aim? The easiest way is to use a cartridge with a flat trajectory. Obviously, if a bullet has a relatively little cuve in its trajectory, that curve will be less affected by variations in shooting angle. For example, let's compare two cartridges with widely different trajectories. One is a 7mm Magnum with a 145-grain pointed bullet loaded to 3,100 fps. The other is a .30/30 Winchester with a 150-grain flat-nose slug loaded to 2,100 fps. Both rifles are scope-sighted, with the scopes 1 1/2 inches above the bore centers, and both are sighted in at 200 yards.
Changing the angle form horizontal to 45 degrees but still shooting at 200 yards, the 7mm Magnum hits 2 32/100 inches above the point of aim, and the .30/30 is all of 5 65/100 inches high. Now you see why a cartridge with a flat trajectory elimnates some of the guesswork when shooting uphill or downhill.
Another way of "guesstimating" where to hold on angle shots is my rule of thumb. For many years, I've reasoned that a bullet fired at an upward or downward angle will hit very close to where it would hit if fired over the horizontal leg of the angle-the horizontal distance to a vertical line running through the target.
A triangle is formed by the horizontal line, the steep (angled) line from rifle to target, and the vertical line from the horizontal distance up to the target. In any such triangle, the horizontal line is shorter than the uphill (or downhill) line. Gravity affects the bullet's flight only for as long as the projectile is in the air - along the shorter, horizontal line.
By Jim Carmichel from the 1991 Outdoor Life Deer Hunter's Yearbook
I'm real tired-a bit old-and didn't take physics---but if you can shoot under a target 2-300 yards out and hit it that bullet has one hell of a trajectory-and gravity pulls down not up-I didn't get aim low from that writing-did you?
For those of you whom enjoy seeing what bullets actually do down range, you might want to buy a software package called "Ballistic Explorer" by Oehler. It is a super good program where you can use standard factory ammo or plug in your own reloads to see such things as trajectory, wind drift, energy, velocity, etc. You can change nearly all shooting parameters such as scope height, up hill/down hill, temperature, barometric pressure, etc.
I ran a chart on a 30-'06 just because that is usually what everone uses for compairisons. With a 165 gr factory load, the point of impact doesn't change more than an inch when shooting 30 degrees up hill or down hill vs level out to 200 yards. After that, the POI stays a bit higher on up or down hill than if the muzzle were level.
For all practical purposes, when shooting level, up hill, or down hill, just put the cross hairs on the mark and pull the trigger.