3.6
Maximum Horizontal Range of a Gun
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.
