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Applied Ballistics For Long Range Shooting
Step 2: Turn the raw uncertainties into inches of deflection at the target range.
This can easily be done with the included software. We’ll do the vertical plane first. Using all of the pertinent variables, calculate the drop at 500 yards for the average muzzle velocity. The 185 grain bullets at 2850 fps will have about 49” of drop at 500 yards from a 100 yard zero. Now add ˝ of the extreme spread to the muzzle velocity to see what the difference in drop is. An additional 30 fps in muzzle velocity would cause a round to hit about 1.2” higher at 500 yards, so you can expect +/- 1.2”, or 2.4” of vertical spread in addition to the 5.7” inherent precision of the rifle at 500 yards.

Now here comes a little twist. In order to quantify the total vertical dispersion, you can’t simply add the 5.7” and 2.4”. The likely magnitude of multiple random errors is quantified using the RSS method which stands for Root Sum Squares. Mathematically, the sum is written as:
Applied Ballistics For Long Range Shooting
Where a and b are the two components being added. In this case, the total likely vertical dispersion is:
Applied Ballistics For Long Range Shooting

Applied Ballistics For Long Range Shooting
So the likely total vertical dispersion from the rifles inherent precision and the velocity variation is 6.2” total.

Now let’s consider the horizontal plane.

We have estimated +/- 2 mph of crosswind uncertainty for this example. Again, using the ballistics program, convert this wind uncertainty to inches of deflection for the pertinent variables. In this case, a 2 mph crosswind will result in +/- 3.1” of wind deflection at 500 yards, a total horizontal error of 6.2”. The RSS of the horizontal components of dispersion yields:
Applied Ballistics For Long Range Shooting

Applied Ballistics For Long Range Shooting
So the likely total horizontal dispersion is +/- 4.2 inches, or 8.4 inches total at 500 yards with the non-deterministic variables we’re using in this example. This information is best represented visually. Refer to Figure 15.1 for an illustration of the expected cumulative dispersion.

Notice how the muzzle velocity variation adds some uncertainty to the vertical shape of the group, and the wind uncertainty adds some uncertainty to the horizontal shape. The probability contour in the bottom right corner of Figure 15.1 shows the regions and associated probability of impacts. For example, there is a 67% chance the rounds will strike the inner ring (2.1 inches tall by 2.8 inches wide), a 95% chance that the rounds will strike in the next biggest ring (4.1 inches tall and 5.6 inches wide), and a 99% chance the rounds will strike in the largest ring (6.2 inches tall by 8.4 inches wide).
Publisher's Note: The book can be purchased at the LRH Gear Shop
Applied Ballistics For Long Range Shooting
Figure 15.1. Cumulative effects of non-deterministic variables on a 500 yard target.


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