Elevation

This example shows how to find a bullet's trajectory at atmospheric conditions different from the zero conditions. For this example, it is assumed that the shooter is zeroing at some atmospheric conditions and then hunting at different atmospheric conditions. The idea is to find the elevation angle for zero conditions and apply this angle to the hunting conditions. For this example, the standard (not simplified) trajectory calculation is used. This is required because the basic trajectory does not have an elevation angle input.

Conditions at Zero Range

The first calculation finds the values of interest at the zero conditions. For this example, assume that the shooting conditions are as follows:

Ballistic Coefficient:0.5
Bullet Weight:220 grains
Caliber:0.308
Muzzle Velocity:2600 f/s
Sight Height:1.5 in
LOS Angle:0 deg
Cant Angle:0 deg
Wind Speed:10.0 mph
Target Speed:10.0 mph
Minimum Range:0
Maximum Range:1000 yd
Range Increment:50 yd
Zero Range:200 yd
Temperature:80°F
Pressure:29.92 in Hg
Relative Humidity:30%

Additionally, only the boxes "Corrected Pressure", "Elevation Correction for Zero Range" and "Drop and Windage Relative to Target" are checked. These atmospheric conditions are typical Fall conditions in Southern New Mexico. All other values are the default.

This gives the following trajectory:

RangeDropDropWindageWindageVelocityMachEnergyTimeLeadLead
(yds)(in)(moa)(in)(moa)(ft/s)(none)(ft·lbs)(s)(in)(moa)
0-1.5***0.0***2600.02.2833301.70.0000.0***
1002.22.10.70.72429.02.1332881.70.11921.020.1
200-0.0-0.02.91.42264.51.9882504.60.24743.520.8
300-9.0-2.96.82.22106.31.8492166.80.38567.721.5
400-25.8-6.212.53.01954.71.7161866.20.53393.722.4
500-51.8-9.920.33.91810.31.5901600.70.692121.823.3
600-88.4-14.130.34.81673.91.4701368.40.864152.124.2
700-137.4-18.742.85.81546.41.3581168.01.051185.025.2
800-201.0-24.058.06.91429.21.255997.61.253220.526.3
900-281.6-29.976.18.11323.91.162856.01.471258.927.5
1000-382.1-36.597.29.31232.11.082741.41.706300.328.7

Additionally, the calculated elevation is 6.10 MOA. This calculated value is shown above the trajectory table in the output of the calculation. This is the important part. The elevation is the angle between the line of sight (the axis of the sights/scope) and the barrel. This does not change so long as the sights are not adjusted.

Hunting Conditions

For the hunting trajectory assume that we are going hunting later in the year in much colder conditions (changed values are in red):

Ballistic Coefficient:0.5
Bullet Weight:220 grains
Caliber:0.308
Muzzle Velocity:2500 f/s
Sight Height:1.5 in
LOS Angle:0 deg
Cant Angle:0 deg
Wind Speed:10.0 mph
Target Speed:10.0 mph
Minimum Range:0
Maximum Range:1000 yd
Range Increment:50 yd
Zero Range:200 yd
Temperature:0°F
Pressure:29.92 in Hg
Relative Humidity:30%

With the same 6.10 MOA elevation angle. The difference is that for the hunting trajectory, we are going to input this elevation angle and not have the calculation find a new elevation angle for us, so uncheck "Elevation Correction for Zero Range". The difference in muzzle velocity is due to the change in powder temperature (and could be greater than this).

The calculated trajectory for these new atmospheric conditions with the rifle zeroed at the old atmospheric conditions is then:

Range Drop Drop Windage Windage Velocity Mach Energy Time Lead Lead
(yds) (in) (moa) (in) (moa) (ft/s) (none) (ft·lbs) (s) (in) (moa)
0 -1.5 *** 0.0 *** 2506.5 2.385 3068.4 0.000 0.0 ***
100 2.0 1.9 0.8 0.8 2316.4 2.204 2620.8 0.125 21.9 20.9
200 -1.0 -0.5 3.5 1.7 2134.8 2.031 2225.9 0.259 45.7 21.8
300 -11.7 -3.7 8.3 2.6 1961.3 1.866 1878.7 0.406 71.5 22.7
400 -31.4 -7.5 15.3 3.7 1796.2 1.709 1575.8 0.566 99.6 23.8
500 -62.0 -11.8 25.0 4.8 1640.4 1.561 1314.2 0.741 130.4 24.9
600 -105.5 -16.8 37.7 6.0 1495.0 1.422 1091.6 0.932 164.1 26.1
700 -164.5 -22.4 53.7 7.3 1361.8 1.296 905.8 1.143 201.1 27.4
800 -242.4 -28.9 73.2 8.7 1243.0 1.183 754.6 1.373 241.7 28.9
900 -342.8 -36.4 96.5 10.2 1141.0 1.086 635.9 1.626 286.1 30.4
1000 -470.0 -44.9 123.6 11.8 1058.3 1.007 547.0 1.899 334.3 31.9

For most people and most hunting scenarios, this example shows that we don't have to worry about the change in atmospheric conditions. The second trajectory is no more than 2.7" different from the zero trajectory from 0 to 300 yards.

The longer ranges though, the trajectories do not line up so well and an error is introduced. The following table shows the differences in the trajectories and shows that we would be shooting low at farther ranges.

Range Drop Drop Windage Windage
(yds) (in) (moa) (in) (moa)
00.00.00.00.0
100-0.2-0.20.10.1
200-1.0-0.50.60.3
300-2.7-0.81.50.4
400-5.6-1.32.80.7
500-10.2-1.94.70.9
600-17.1-2.77.41.2
700-27.1-3.710.91.5
800-41.4-4.915.21.8
900-61.2-6.520.42.1
1000-87.9-8.426.42.5

A common mistake is to use the hunting conditions to calculate a new trajectory, but not input the elevation angle for the zero conditions or an adjusted muzzle velocity. This yields a trajectory with the following values (use the hunting conditions with 2600 f/s muzzle velocity and check "Elevation Correction for Zero Range"):

Range Drop Drop Windage Windage Velocity Mach Energy Time Lead Lead
(yds) (in) (moa) (in) (moa) (ft/s) (none) (ft·lbs) (s) (in) (moa)
0 -1.5 *** 0.0 *** 2606.6 2.480 3318.6 0.000 0.0 ***
100 2.2 2.1 0.8 0.8 2412.1 2.295 2841.6 0.120 21.1 20.1
200 -0.0 -0.0 3.3 1.6 2226.2 2.118 2420.6 0.249 43.8 20.9
300 -9.3 -3.0 7.8 2.5 2048.6 1.949 2049.7 0.390 68.6 21.8
400 -26.9 -6.4 14.5 3.5 1879.1 1.788 1724.6 0.543 95.5 22.8
500 -54.3 -10.4 23.6 4.5 1718.5 1.635 1442.4 0.709 124.9 23.8
600 -93.6 -14.9 35.5 5.7 1567.6 1.491 1200.2 0.892 157.0 25.0
700 -147.0 -20.1 50.6 6.9 1428.0 1.359 995.9 1.093 192.4 26.2
800 -217.5 -26.0 69.1 8.2 1301.5 1.238 827.4 1.313 231.1 27.6
900 -308.6 -32.7 91.3 9.7 1190.7 1.133 692.4 1.554 273.6 29.0
1000 -424.3 -40.5 117.3 11.2 1097.9 1.045 588.8 1.817 319.8 30.5

The differences between this trajectory and the hunting trajectory just above are shown below:

Range Drop Drop Windage Windage
(yds) (in) (moa) (in) (moa)
00.00.00.00.0
1000.20.20.00.0
2001.00.5-0.2-0.1
3002.40.7-0.5-0.1
4004.51.1-0.8-0.2
5007.71.4-1.4-0.3
60011.91.9-2.2-0.3
70017.52.3-3.1-0.4
80024.92.9-4.1-0.5
90034.23.7-5.2-0.5
100045.74.4-6.3-0.6

Again, for short ranges, it probably won't make any difference. For longer ranges, we would be shooting low. For example, at 500 yards, we would use a holdover of 10.4 moa, but the actual (from the hunting trajectory) holdover is 11.8 moa which would give us an error of 7.7 inches low, because we didn't holdover high enough.

The errors introduced by zeroing at different atmospheric conditions can be minimized by zeroing in conditions that are as close as possible to the shooting conditions. If this is not possible, the elevation angle should be used from the zero conditions to accurately calculate a trajectory at the hunting conditions.

This example focuses primarily on the influence of the change in elevation angle, but one should remember that the muzzle velocity was changed which can have a large affect also.