I wrote another article for RECOIL magazine – this one covers how to calculate and compensate for shooting at angles. They’ve posted the entire article on their site – please go check it out!
Shooting Ranges Are Almost Always Flat. Real Life Isn’t.
In the real world, it’s likely that your target may be above or below your location. If the target is far enough away and the angle is steep enough (high or low), you might just completely miss it if you don’t compensate for the angle and adjust your normal elevation settings on your scope or sights.
The longer a bullet flies through the air, the further it falls from its original path. To compensate for this increased drop at further distances, we must increase the angle of our barrel upward.
The good news is that a bullet’s drop due to gravity, and the corresponding elevation compensation across flat ground, are fairly consistent. Of course, different environmental conditions and different bullets and/or velocities affect how much a bullet drops and how much elevation compensation is needed (see “A Funny Thing Happened on the Way to the Target,” RECOIL Issue 22).
However, for the purposes of this article, let’s focus only on angle and assume that all other conditions are exactly the same. Therefore, once you know exactly how much elevation adjustment on your scope or sights is needed in order to hit a target at a certain distance across flat ground in certain environmental conditions, you can use that elevation adjustment again in the future when you want to shoot another target across level ground in front of you at the same distance and in the same conditions. Easy, right?
But, if the target is above or below your position, the corresponding angle that you’re shooting (up or down) may well require a change to your typical “flat-ground” elevation adjustment for a target at that distance in those conditions. When shooting at an angle, the bullet won’t fall as far off of its original path. Therefore, less elevation adjustment is needed in order to hit a target at an angle than a target directly in front of you. Remember it this way — if you ignore the angle, your bullet will impact high. How high depends on the degree of the angle and the target’s distance. This is true whether the target is above or below you — don’t believe me? Let’s do that math!
First, a thought exercise. Imagine laying on the edge of a 500-yard cliff and shooting at a target (target #1) directly below you against the base of the cliff on the ground. How far will the bullet deviate off of its original path due to gravity? You’re right; it won’t deviate at all! It’ll fly straight down to the target.
This is the steepest angle we can shoot, i.e. 90 degrees (any more than 90 degrees is really just less than 90 degrees facing the other way). Now imagine a target (target #2) that’s almost directly below you. Let’s say it’s 25 yards away from the base of the cliff on the ground.
The further out the target gets from the base of your cliff, the more gravity will affect the bullet off of its original path. For example, a bullet will fall further off of its original path on its way to a target 200 yards away from our cliff’s base (target #3) than it would for target #2 only 25 yards away. From this we know that gravity pulls a bullet off of its original path most at a 0-degree angle (straight out) and least at a 90-degree angle (straight up or down). Now, we’re not saying that gravity doesn’t have an effect on bullets at certain angles — gravity is pulling on a bullet regardless of what angle you’re shooting. Rather, gravity pulls the bullet off of its original path different amounts depending on the angle of the original path.
Interestingly, there’s an easy way to figure out gravity’s effect on the bullet’s path — simply focus on the horizontal distance the bullet must travel (rather than the total distance from your position to the target) and pretend that the target is that far away, directly in front of you. When we shoot at target #2, which is 25 yards away from the base of our cliff, the bullet is only traveling horizontally 25 yards. And when we shoot at target #3, which is 200 yards away from our cliff’s base, the bullet travels horizontally only 200 yards. Therefore, the bullets will deviate off of their paths the same as if we were shooting at targets directly in front of us 25 yards and 200 yards away.
So, how do you figure out the horizontal distance a bullet will travel for an angled target? Trigonometry! (Your suspicion that snipers were kinda nerdy might just be true.) If we know the angle we’re shooting and the distance to the target, we can calculate the horizontal distance the bullet is travelling. We do this by visualizing a right triangle (one with a 90-degree corner) to represent the various measurements. In the diagram on page 104, you can see that our height above the target is the vertical side of the triangle (X), the view from our position to the target is (Z), and the horizontal distance that the bullet covers is (Y). Note that (Y) will always be shorter than (Z).
I like to refer to the actual distance to the target as the “true distance” and the shorter distance that we’re going to pretend the target is from us to compensate our elevation adjustment for the angle as the “angle distance.” After you know the true distance to your target, the first step in finding the angle distance is determining the angle of the target from your position. One rule of trigonometry is that alternate angles are equal. For our purposes, that means angle B in the diagram is the same as angle A.
There are a few ways to measure the angle to a target. Basic methods include using a card (homemade or a MilDot Master) with a weighted string (1) or a compass with an angle finder built-in. Chances are your smartphone also has the ability to measure angles. You can either look down the edge of these devices to the target or rest them against the edge of your elevation turret as you look through your scope. You can also mount purpose-built devices to your rifle/scope like an Angle Cosine Indicator (2), saving a step in this process by giving you the cosine of the angle instead of the angle itself.
Modern laser rangefinders often have a feature that not only tells you the true distance to the target, but also the angle to the target and, even better, some can do all the math for you and just give you the angle distance. Similarly, the MilDot Master can be used to calculate the angle distance (3). Just as I’d warn you to learn to read a map and compass before relying solely on a GPS, I’m warning you now to learn to calculate the angle distance by hand before relying on a fancy laser rangefinder. . . .