Precision high-angle shooting is an art form in its own right. High-angle shooting is described as when the rifle is sighted-in (zeroed) on a level or nearly level range, and then it is fired either in an up-hill or down-hill direction, such as from a mountain top or tall building onto a target below.

This effect is common to precision shooters, especially with law enforcement, hunters, and military snipers. Through understanding high angle, we know that the bullet will always impact high. How high the bullet will impact can be determined through precise calculations using mathematical formulas.

To know exactly how high the bullet will impact, we need to revisit “bullet drop” and the “bullet path.” Bullet drop is always measured in a vertical direction regardless of the elevation angle of the bullet trajectory. The bullet drop is expressed as a negative number as the bullet falls away or below the bore line.

The bullet path is measured always in the perpendicular to the shooter’s line of sight through the sights on the gun. The bullet path is where the shooter will visually “see” the bullet pass at any instant of time while looking through the sights of the rifle (if this was even possible). At the rifle’s muzzle, the bullet path is negative because the bullet starts out below the line of sight of the shooter. Near the muzzle, the bullet will follow a path that will rise and cross the line of sight, then the bullet will travel above the line of sight until the target is reached. The bullet path is expressed as positive in this portion of the trajectory/flight. The bullet arc then crosses the line of sight at the zero range, meaning the bullet path is zero at the zero range, and will become a negative as the distance increases past zero range.

Do not let high-angle shooting confuse you, because we can look at it in a very basic way. As human beings, we have all had a chance to throw an object at a distance, may it be a rock, softball, etc. Let’s say you are tossing a rock in an underhand fashion at an object 20 yards away on a flat plain. Through your years of experience of rock throwing, you will naturally throw the rock high to create an arc to compensate for gravity in order for it to reach the target. Now let’s look at the situation, except that the target is on a downhill slope. The ground distance is still 20 yards away, but you’re three stories up on a rooftop. The same arc above the line of sight that allowed your rock to hit the target at ground level, on the flat plain, if applied to the uphill position, will now cause the rock to travel over the target.

The same rule applies to shooting high-angle. When zeroing your rifle at a flat plain, the bullet must create an arc; while shooting at high angle, the arc is slightly different. The effect of this error increases with distance and steepness of an angle to a maximum of 60 degrees. This error applies to both uphill and downhill shooting, meaning that the bullet will always hit above the target, thus you must hold or dial lower than the actual distance to the target.

The greater the angle, the less effect gravity has on the bullet/Shorter gravity distance.

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The mathematics behind figuring out exactly how low we need to hold/dial on the scope are determined by using the Pythagorean Theorem. In mathematics, the Pythagorean Theorem is an equation that is expressed as a² + b² = c² and is relating to the lengths of the sides a,b, and c. For our purposes, the “a” and “b” will represent actual heights/lengths, and “c” is what we need to figure out, also known as the “slope dope.”

pythagoras-theorem

For faster target engagement, we can use another formula that I found to be easier to understand and compute. The equation is simply “actual straight line distance multiplied by the cosine of the angle = slope/corrected distance.” There are many ways to find the cosine of an angle when shooting, but the simplest way that I found to obtain this information, is using an “angle cosine indicator.” An angle cosine indicator simply takes your angle to target (uphill/downhill) and presents you with the cosine of that angle. Once this number is in the equation, you have the data for a shot “corrected for gravity” for a high angle shot. They can typically cost anywhere in the range of $65.00 – 150.00, for a civilian model.

A.C.I. (Angle Cosine Indicator)
A.C.I. (Angle Cosine Indicator)

Let’s take a look at an example of how to properly apply the A.C.I.

Let’s say that you’re shooting off of a mountain top at a target that you laser range find to be a distance of 950 yards. Being that the angle to your target from the mountain is so steep, you look down at your A.C.I. and see that the red line is at the number 77. Now what? You simply take your actual distance to target and multiply it by .77. So, 950 yards multiplied by .77 = 731.50 (732 yards), a 218 yard difference, which would cause a miss if not corrected. The 732 yards is what your corrected elevation is. You then dial in for a 732 yard shot instead of a 950 yard shot.  Sure there are various ways to find the cosine of your angle to target; I simply find this one of the most practical ways, besides the MIL dot Master or Slope Doper.

Below are a few tables that you can also use by simply imputing your ballistic bullet drop data. To find  your up/down compensation, take the Bullet Drop data (which is stated in hundreds of yards) and multiple it by the factors in the accompanying chart, based upon the steepness of angle to your target. For example, your target is 400 yards away, uphill 45 degrees, and you’re firing a .223 Remington, 69-gr. Match round. You already have the data that your Bullet Drop is 36.3 inches at 400 yards. Therefore, you multiply the 36.3 Bullet Drop inches by .293 and find you must hold low 10.63 inches for a perfect hit.

UP / DOWN COMPENSATION FACTORS

5 Degrees: Drop Inches x .004
10 Degrees: Drop Inches x .015
15 Degrees: Drop Inches x .034
20 Degrees: Drop Inches x .060
25 Degrees: Drop Inches x .094
30 Degrees: Drop Inches x .134
35 Degrees: Drop Inches x .181
40 Degrees: Drop Inches x .235
45 Degrees: Drop Inches x .293
50 Degrees: Drop Inches x .357
55 Degrees: Drop Inches x .426
60 Degrees: Drop Inches x .500

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With much credit given to the F.B.I. and A.T.F. snipers with whom I have worked, they introduced a pretty fast method for angle shooting. Here’s how the method works:

You range a target at 500 yards and your slope/angle to target is 30 degrees up or down. You would simply shoot it as if the target is on a flat ground distance, at 90 percent of that distance. This means that you service the target as if it were at 450 yards. You can do this by simply holding under for a 450 yard shot, or dial it on the scope elevation knob.

Basically they have stated that you should engage any 30 degree target (uphill or downhill as if it were 90 percent of its actual distance), well within the danger space.

When shooting a .308 168 grain Match ammo, this method typically has a maximum error of 4 inches at 610 yards, with an average of less than 2 inches at ranges less than 600.

The next method that we have used and tried is the 45 degree method. Basically put, you would shoot a target at a 45 degree angle as you would on a flat plain, except you would engage it with only 70 percent of its actual distance. Meaning that for a target that has a flat line distance of 500, 70 percent of that distance would be 350 yards. Your corrected elevation would be 350 yards instead of 500.

Engage any 45 degree target as if it were 70 percent of its actual distance.

Out to 600 yards, firing .308 Winchester 168 gr. Match ammo, using 70 percent of the distance, the maximum error is 4 inches, with an average error of less than 3 inches.

Please note that this is only to get a firm grasp on high-angle shooting.

 

This article is courtesy of Nick Irving from The Loadout Room.