of jnterest: No. 11
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:
- 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.
- 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.
- A rifle zeroed
in at level range will shoot higher when shooting uphill or downhill.
- 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
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.
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
Watch our web
site for the next topic of interest. Until then, shoot safely and
know where your bullets are going.