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Topic of jnterest: No. 11

Shooting Uphill and Downhill

Shooters are sometimes confused about the bullets path when shooting uphill or downhill. For instance, does the bullet strike high when shooting downhill and strike low when shooting uphill? Sierra and other bullet companies have done extensive testing on shooting uphill and downhill and have found the following to be true for a given cartridge:

  1. The true vertical bullet drop is the same for level fire and uphill or downhill shooting for the same range. See Figure 1. The vertical drop, do, is the same for all three methods of shooting over the same range.
  2. The bullet velocity is the same whether shooting over a level range or shooting uphill or downhill. In other words the bullet does not slow down faster in uphill shooting than with level shooting and the bullet velocity does not increase when shooting downhill.
  3. A rifle zeroed in at level range will shoot higher when shooting uphill or downhill.
  4. For a given angle of fire the bullet will shoot high by the same amount weather shooting uphill or down hill.


    Fig 1- Bullet trajectories for level fire, shooting uphill, and shooting downhill

The theory as to why the bullet always shoots high for uphill and downhill shooting is based on the projectiles path in relation to the pull of gravity. Gravity works perpendicular to the horizontal line. It's the horizontal distance traveled by the bullet that is important rather than the actual linear distance traveled. This is explained by the use of trigonometry and the right triangle shown in Fig. 2.


Fig. 2-Using trigonometry to explain uphill/downhill shooting

According to the rules of trigonometry the cosine of THETA is equal to the horizontal range divided by the slant range (hypotenuse). By rearranging the terms, the horizontal range is equal to the slant range (hypotenuse) multiplied by the Cosine of THETA.

Assume we have zeroed a rifle at 300 yd on a level range and we are shooting at a target on a slant range of 300 yards. Assume the slope angle THETA is 30 degrees. The cosine of 30 degrees is 0.87. The horizontal range for the bullet is only 261 yards (300 * 0.87). In order to hit the target we should hold the gun as if the target were only 261 yards away not 300 yards. If we shoot where the scope crosshairs intersect the target we will shoot over the target. In the field, you probably don't really know the slant range or the slant angle very accurately. Just remember to always aim lower, because any slant range shot, either downhill or uphill, will be higher than if it were a horizontal shot.

Our Load From a Disk ballistics program will allow the user to calculate a level range trajectory or enter the slant angle and slant distance and calculate a completely new trajectory for these uphill/downhill conditions.

Watch our web site for the next topic of interest. Until then, shoot safely and know where your bullets are going.

Sincerely,
The Ballistician

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Last Modified August 18, 2012