Rifleman's rule
Rifleman's rule is a "rule of thumb" that allows a rifleman to accurately fire a rifle that has been calibrated for horizontal targets at uphill or downhill targets.
The rule says that only the horizontal range should be considered when adjusting a sight or performing hold-over in order to account for bullet drop.
The slant range is not compatible with standard ballistics tables for estimating bullet drop.
, the rifle sight must be adjusted as if the shooter were aiming at a horizontal target at a range of
The rule holds for inclined and declined shooting (all angles measured with respect to horizontal).
Very precise computer modeling and empirical evidence suggests that the rule does appear to work with reasonable accuracy in air and with both bullets and arrows.
This relationship between the LOS to the target and the bore angle is determined through a process called "zeroing."
The bore angle is set to ensure that a bullet on a parabolic trajectory will intersect the LOS to the target at a specific range.
In general, the shooter will have a table of bullet heights with respect to the LOS versus horizontal distance.
The drop table can be generated empirically using data taken by the shooter at a rifle range; calculated using a ballistic simulator; or is provided by the rifle/cartridge manufacturer.
The drop values are measured or calculated assuming the rifle has been zeroed at a specific range.
Assume that a range finder is available that determines that the target is exactly 300 meters distance.
Apply the rifleman's rule to determine the equivalent horizontal range.
The gun sight is adjusted up by 0.94 mil or 3.2' in order to compensate for the bullet drop.
This section provides a detailed derivation of the rifleman's rule.
be the bore angle required to compensate for the bullet drop caused by gravity.
using standard Newtonian dynamics as follows (for more details on this topic, see Trajectory).
Two equations can be set up that describe the bullet's flight in a vacuum, (presented for computational simplicity compared to solving equations describing trajectories in an atmosphere).
, is important because corrections due to elevation differences will be expressed in terms of changes to the horizontal zero range.
For example, the standard 7.62 mm (0.308 in) NATO bullet is fired with a muzzle velocity of 853 m/s (2800 ft/s).
must also account for the fact that the rifle sight is actually mounted above the barrel by several centimeters.
This fact is important in practice, but is not required to understand the rifleman's rule.
Observe that if the rifleman does not make a range adjustment, his rifle will appear to hit above its intended aim point.
In fact, riflemen often report their rifle "shoots high" when they engage a target on an incline and they have not applied the rifleman's rule.
If the rifleman wishes to adjust his rifle to strike a target at a distance
along an incline, he needs to adjust the bore angle of his rifle so that the bullet will strike the target at
This requires adjusting the rifle to a horizontal zero distance setting of
This expression can be expanded using the double-angle formula for the sine (see Trigonometric identity) and the definitions of tangent and cosine.
Multiply the expression in the parentheses by the front trigonometric term.
The expression inside the parentheses is in the form of a sine difference formula.
