The maximum distance that a gun will shoot in some direction and the barrel elevation angle necessary for the bullet to reach that maximum distance are questions that arise often when an outdoor shooting range is being designed, particularly in an urban or suburban area. The maximum ranges can be more than a mile for some handgun bullets and more than 4.5 miles for some rifle bullets. It is necessary quite often to place barriers forward and above the firing lines to block bullets accidentally discharged from elevated guns from traveling far downrange to threaten inhabitants, homes, or business establishments.

Infinity will calculate the maximum range distance for any cartridge, either horizontally or along any reference slope with either a positive or negative inclination angle, together with the bore elevation angle of the gun necessary for the bullet to reach that maximum range. A reference slope is an upward or downward slope along which the maximum range must be calculated. This feature is incorporated in Infinity because shooting ranges are often located on a hillside or in a valley, and the maximum range in an upward or downward direction is needed. The maximum range of any particular cartridge of course varies with shooting conditions, especially with altitude of the firing point and with the inclination angle of the reference slope and also with atmospheric conditions at the firing location.

The maximum range computation capability in Infinity is reached by selecting the “Maximum Range” entry in the “Operations” dropdown menu. For the cartridge, load and shooting conditions of interest, a reference trajectory need not be calculated. However, those conditions must be entered in the “Trajectory Parameters” and Environment Parameters” lists in the sidebar that appears on the monitor screen in the “Trajectory” operation. After those conditions are entered, the user can proceed directly to the “Maximum Range” operation. Key parameters for the “Maximum Range” operation appear in a sidebar in this mode and can be changed to examine the effects of varying any of these parameters.

The examples calculated below show the surprising maximum range of just a single handgun cartridge, the 45 ACP loaded with Sierra’s 230 grain Full Metal Jacket Match bullet to a muzzle velocity of 850 fps under several variations of firing conditions. All these examples are calculated for standard atmospheric conditions, of course adjusted for altitude automatically within Infinity.

Firing Pt. Reference	Maximum	Bore Elevation
Altitude Slope	Range	Angle
500 ft. 0 deg.	2096.3 yds.	+ 33 deg

500		+ 15		1851.0		+ 42
500		- 15		2450.4		+ 23
5000		0		2265.7		+ 33
5000		+ 15		1992.7		+ 43
5000		- 15		2663.0		+ 24

It is evident that the maximum horizontal range of this cartridge is well over a mile (1760 yards) and that it varies significantly with the altitude of the firing point. It is also quite apparent that the reference slope angle has a large effect on the maximum range.

Note also that the bore elevation angle is with respect to the local level at the firing point, not with respect to the reference slope. A common misconception among many shooters is that the bore elevation angle that maximizes the horizontal range is 45 degrees. It may be seen that for this 45 ACP cartridge that angle is 33 degrees. A 45 degree bore elevation angle would maximize the range if the gun were fired in a vacuum. Air drag, however, changes the physics of the trajectory dramatically. It turns out that the bore elevation angle for maximum horizontal range is around 30 degrees for all small arms bullets fired on the surface of the earth.