Wednesday, January 16, 2013

The Effect of Wind on Ammunition Performance

In our last post, we discussed the effects of air density on ammunition performance. In this post, we will study the effects of wind on performance.

In practical outdoor shooting, especially at longer ranges, there is a good chance that wind may be present and this could affect the ballistics of the bullet. Therefore, it is a good idea to study exactly how it affects bullet trajectory.

The effect of wind on the bullet trajectory depends on the direction of the wind and the speed that it is blowing. It is easy to compensate for wind if it is blowing at a steady rate in a fixed direction. It is much harder to compensate for wind if it is sporadic and blows in gusts of differing velocities. At longer ranges (say 1000 meters), the wind may also blow in different directions along the path to the target.

There are four types of winds we need to concern ourselves with:

  1. Headwind - This is wind that is blowing from the target to us.
  2. Tailwind - This is wind that is blowing from behind us towards the target.
  3. Crosswind - This wind blows from right to left or left to right across the line between the firearm and the target.
  4. Vertical wind - This is usually encountered in mountainous areas and is caused by the wind bouncing off the side of a hill or mountain. This wind moves in a vertical direction (blowing up or down) and pushes the bullet higher or lower on the way to the target.
The first three types of wind are considered to be horizontal winds and the last one is a vertical wind. The headwind and tailwind are easy to account for. Recall that in our previous article, we discussed a term called "drag force", which serves to slow down a bullet horizontally, as it travels through the air. As was discussed in the previous article, drag force is proportional on the velocity of a bullet through the air. Therefore, if a bullet is fired through a headwind, it is moving faster relative to the air than if it were to be fired with no wind. Therefore, this causes an increase in drag forces and the bullet travels slower. Similarly, if a bullet is fired through a tailwind, it is moving slower relative to the air, than if it were to be fired with no wind. Therefore, this causes a decrease in the drag forces and the bullet travels faster. This means that when firing into a headwind, it is necessary to slightly raise the angle of the barrel and when firing into a tailwind, it is necessary to slightly lower the angle of the barrel to compensate.

The famous English author W.W. Greener cites the following formula to calculate how much to compensate for headwinds or tailwinds:
R = V * D/4

R = range distance to compensate by (in yards)
V = velocity of the wind (in miles per hour)
D = distance to the target (in hundreds of yards)

Say we are shooting at a target 300 yards away and there is a tailwind of 10 miles/hour blowing behind us. Then we calculate:
R = 10 * 3/4 = 7.5 yards

This means that if the target is 300 yards away, we should really treat it as though it is 300 - 7.5 = 292.5 yards away and adjust our sights accordingly. If this was a headwind instead of a tailwind, we would treat the sights as though the target was 300 + 7.5 = 307.5 yards away. If you remember our discussion on Minutes of Arc (MOA) from a few months ago, the range adjustment translates to a 1/4 MOA adjustment for this distance (usually one or two clicks on the scope, depending on model). While this seems like a small adjustment amount, the compensation amount increases with distance to target. If we were shooting at 900 yards instead of 300 yards, then the same 10 miles/hour wind will require 1.75 MOAs correction.

A crosswind causes a bullet to move in a large deflection horizontally and also causes a small vertical deflection. A vertical wind causes a large deflection in the vertical direction and a small horizontal deflection. We can easily understand the large deflections, but why are the small deflections caused? The reason for these small deflections is because a spinning bullet tends to turn to face the wind, due to spin stabilization and the resulting torque causes a small deflection.

In reality, we often do not get a true headwind or tailwind, but rather a wind that blows at an angle to the shooter. Therefore, we must break this wind up into (1) headwind or tailwind component (2) crosswind component and (3) vertical wind component. In this case, we must compute the effects of each of these components separately and then add the results in horizontal and vertical directions to figure out how much to compensate for.

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