For the average hunter/long range shooter, they will most likely never need to correct for angle of fire. By angle of fire, I mean shooting up or down hill. Because you will be shooting at an angle, even though the target's distance doesn't change, the bullet covers less horizontal ground, and will be exposed to gravity for a shorter amount of time. This means it will have less drop, and we need to calculate for this. This works the same for shooting up or down hill.
Before we get into the calculation, there are a few things that will help you learn to estimate angles.
First, there is an illusion called perspective illusion. When looking at in incline or decline, it can appear significantly more or less steep than it really is. The same is true with distance. Objects uphill can appear to be closer. For example, if an object is 50 feet tall and two feet in front of you, you have to tilt your head way back to see the top edge. So, it appears tall. Now, if you're 50 feet back it will appear smaller because of distance but also, you only have to tilt your head back slightly to see the top edge. This perspective illusion will lead you to believe it's not as tall.
Second is Angle of Repose. This is the natural angle a granular material can be piled relative to the horizon. Think of (on a small scale) a pile of dirt or (large scale) a hill or mountain. This angle is about 35°, but can vary depending on if it's sand, dirt, clay or gravel, as well as moisture content. This is important to be aware of because it's very common to over estimate an angle while looking up or down a hill.
Let's jump right into the formula.
Distance * Cos =
Distance (to target) multiplyed by the cosine of the angle = corrected distance
Example: We are shooting at 700 yards and a 20° angle.
700 * .939 = 657 yards
This means, even though our target is 700 yards, we will dial as if it were at 657 yards.
There are a few ways to calculate for this.
1. A cosines indicator - It works the same way a bubble level works but, it does not give us the angle, only the cosine. This takes out a step of finding the angle to get a relative cosine and that is ultimately what we want to know. The only negative I see to this is you have another piece of equipment on your rifle that you may hardly ever use. If you are shooting at angles a lot, then it's probably the best option in my opinion.
2. Slope Doper - This is just a small plastic card with a metal arm. You point it at your target and the arm will give you your angle and cosine. It's easy to use and no real negative other than it's another piece of equipment to carry around and only does one thing.
3. Mildot Master - The Mildot Master can give you the angle by tying a string on it and pointing it toward your target. The string will lay across the angle mark on the side. The negative part about this is you will need to find the relative cosine. I just use a table printed on my drop table. This is the method I use, mainly because the Mildot Master does multiple things. It can calculate in Mils and MOA, give you distance and give you angles. Also, I hardly ever shoot angles, so I'm not carrying around more equipment than I need that I rarely use. Plus, the fact that it has multiple uses is a plus.
You can buy rangefinders that give you yardage for the corrected angle, but if you forget to turn this option on or off while ranging, you are adding another problem to your already complex calculations. I personally don't like that idea. However, that potential problem is relatively easy to solve by knowing your equipment. So, it's really just personal preference.
Let's look at another scenario where you would need to calculate for an upward or downward angle. A hunter in the mountains spots an elk at 750 yards. He calculates drop and wind and takes aim. With a perfect trigger squeeze the bullet cuts through the air. The hunter watches the vapor trail and sees he missed. But he didn't miss by a little. He missed way over the back of the elk.
Let's break this down. At 750 yards the hunter would need to dial up 4.8 Mils or 130 inches. The elk he spotted is at the top of a hill at about 35°. The cosine for 35° is
.819. If the hunter used the calculation
750 * .819 = 614 he would have only dialed for 614 yards, 3.5 Mils or 77 inches. You can see he missed by 53 inches or 1.3 mils because he did not account for his angle of fire.
To find the cosine, you can use a calculator.
Simply press the cosine button (cos) and enter your angle. You can also print up a table and laminate it and add it to your d.o.p.e book. Listed below are the relative cosines to angles per 5 degrees.
5 - .996
10 - .984
15 - .965
20 - .939
25 - .906
30 - .866
35 - .819
40 - .766
45 - .707
Unless you are training, you may want to reconsider taking shots at extreme angles. Obviously, in a military application you take what you get and make the best of it. In a hunting situation you need to keep in mind you have to climb up there to retrieve the meat and are climbing back down with possibly hundreds of pounds of meat. Either way, have fun, keep shooting and be safe.
The Overwatch
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