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. Typically, the range of an elevated target is considered in terms of the slant range, incorporating both the horizontal distance and the elevation distance (possibly negative, i.e. downhill), as when a rangefinder is used to determine the distance to target. The slant range is not compatible with standard ballistics tables for estimating bullet drop. The Rifleman's rule provides an estimate of the horizontal range for engaging a target at a known slant range (the uphill or downhill distance from the rifle). For a bullet to strike a target at a slant range of R S {\displaystyle R_{S}} and an incline of α {\displaystyle \alpha } , the rifle sight must be adjusted as if the shooter were aiming at a horizontal target at a range of R H = R S cos ( α ) {\displaystyle R_{H}=R_{S}\cos(\alpha )} . Figure 1 illustrates the shooting scenario. 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.
Background
Definitions There is a device that is mounted on the rifle called a sight. While there are many forms of rifle sight, they all permit the shooter to set the angle between the bore of the rifle and the line of sight (LOS) to the target. Figure 2 illustrates the relationship between the LOS and bore angle.
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. A properly adjusted rifle barrel and sight are said to be "zeroed." Figure 3 illustrates how the LOS, bullet trajectory, and range ( R H {\displaystyle R_{H}} ) are related.
Procedure In general, the shooter will have a table of bullet heights with respect to the LOS versus horizontal distance. Historically, this table has been referred to as a "drop table." 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. The bullet will have a drop value of zero at the zero range. Table 1 gives a typical example of a drop table for a rifle zeroed at 100 meters. Table 1: Example Bullet Drop Table
If the shooter is engaging a target on an incline and has a properly zeroed rifle, the shooter goes through the following procedure:
Determine the slant range to the target (measurement can be performed using various forms of range finders, e.g. laser rangefinder) Determine the elevation angle of the target (measurement can be made using various devices, e.g. sight attached unit) Apply the "rifleman's rule" to determine the equivalent horizontal range ( R H = R S cos ( α ) {\displaystyle R_{H}=R_{S}\cos(\alpha )} ) Use the bullet drop table to determine the bullet drop over that equivalent horizontal range (interpolation is likely to be required) Compute the bore angle correction that is to be applied to the sight. The correction is computed using the equation angle correction = − bullet drop R H {\displaystyle {\mbox{angle correction}}=-{\frac {\mbox{bullet drop}}{R_{H}}}} (in radians). Adjust the bore angle by the angle correction.
Example Assume a rifle is being fired that shoots with the bullet drop table given in Table 1. This means that the rifle sight setting for any range from 0 to 500 meters is available. The sight adjustment procedure can be followed step-by-step. 1. Determine the slant range to the target. Assume that a range finder is available that determines that the target is exactly 300 meters distance. 2. Determine the elevation angle of the target. Assume that an angle measurement tool is used that measures the target to be at an angle of 20 ∘ {\displaystyle 20^{\circ }} with respect to horizontal. 3. Apply the rifleman's rule to determine the equivalent horizontal range.
R H = 300 meters cos ( 20 ∘ ) = 282 meters {\displaystyle R_{H}=300{\mbox{ meters}}\cos(20^{\circ })=282{\mbox{ meters}}}
4. Use the bullet drop table to determine the bullet drop over that equivalent horizontal range. Linear interpolation can be used to estimate the bullet drop as follows:
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