Working the Angles for Long Range Shooting
For shooting long range in the mountains, you need to understand how angles play into the equation.
As soon as a bullet leaves the barrel, gravity is trying to make it hit the ground. The majority of our corrected trajectory is aimed at overcoming that. The amount of influence that gravity has changes as the shot angle increases. Unless you’re really going long, angles less than five degrees or so don’t matter. But like all things long range, the farther you shoot and the steeper the angle, the more you’ll have to account for it.
When it comes to bullet drop from gravitational pull, the bullet only cares about the horizontal distance, but we still have to account for drag and time of flight.
The easiest way I’ve found to explain this is to hold out your hand and make the letter “L” with your thumb and forefinger. Imagine you’re shooting from the top of your finger at a target on the end of your thumb. The distance from the web of your hand to the end of your thumb is the horizontal distance. That’s the distance where gravity affects the trajectory. The distance from your finger to the thumb is the line of sight (LOS) distance. The bullet still has to travel the LOS, fighting the drag from the air’s resistance. You can’t simply input the horizontal distance and expect to make an accurate long range shot. Again, shot angle and distance will dictate what you can get away with.
As an example, I shot a wolf a couple of years ago. I was on top of a cirque looking down onto an old lake bed. I ranged the wolf at 771 yards, but the angle was 28 degrees. If you plug that into a math geek calculator, you get a cosine of .882. That means the horizontal distance of the shot was only 88% of the line of sight distance…680 yards. That’s big! A zero degree (flat ground) shot from the 338Edge +P at 771 yards, calls for 15 MOA up. A 28 degree shot at the same distance calls for 12.8 MOA up, a difference of over 17 inches at that distance. I had about a 1 MOA target to shoot at, so without accounting for the steep angle I would have shot quite a bit over his back. That would have resulted in a very alive, very educated wolf. If I had used the cosine of the distance as the direct range input, I would have dialed 12.3 MOA up and maybe creased his brisket instead of anchoring him.
Did I do all of that math in my head? Hell, no. I ranged him, figured the angle and wind, input my variables, and let my solver tell me what to dial. That’s what they’re for.
How to measure and apply angles to get a corrected drop formula.
For a lot of hunting situations, the human eye is precise enough to estimate shallow angles. With practice, an accurate long range shot can be taken with nothing more than quick look from behind the scope. However, to build good habits that enable me to make the tough shots, I try to measure the angle every time I shoot.
There are a variety of tools available to measure angles. I’ve used three of them. The fastest and most convenient one is my Leica 1600-B laser rangefinder. With the push of a button it gives me station pressure, temperature, and shot angle in degrees.
The second tool is my iPhone 6. The Compass App on the phone has an inclinometer. With KAC’s BulletFlight (M) ballistic solver on the phone, I can manually input the angle in degrees, or simply place the phone on the scope while aiming at the target and press the “GET” button to automatically populate the input. This is what I used for the shot on the wolf. When using my Kestrel 4500AB or K5700 Elite, I use the inclinometer screen on the phone, then manually input it to the meter.
The third tool is a mechanical device called an Angle Cosine Indicator (ACI). Mounted to the side of the rifle’s scope, it allows the shooter to see how much the rifle is tilted. Instead of degrees, cosine of the angle is used as an input. The cosine is simply the ratio of horizontal distance to slope distance, expressed as a percentage. Programs such as Exbal use cosine, rather than degrees for the angle input. There are also indicators that show degrees if you want to go that route.