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

where

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.

The Effect of Air Density on Ammunition Performance

A couple of months ago, we'd discussed how temperature affects ammunition performance. In this post, we will study the effect of air density on ammunition.

When a cartridge is fired, the bullet travels through the air and is slowed down by air resistance. This force acting on the bullet is called aerodynamic drag. The equation to compute drag force is:

where:
F_D is the drag force
ρ is the density of the air
v is the velocity of the bullet relative to the air
C_d is the the drag coefficient (a dimensionless constant for an object of a given shape)
A is the cross sectional area of the bullet.

As we can see from the above equation, the drag force depends on cross-sectional area of the bullet, the velocity of the bullet and the air density. Of these, we are mainly concerned with the air density in this article. If the air density decreases, the drag forces decrease and therefore the bullet can move faster through the air. If the air density increases, the drag forces on the bullet increase and the bullet slows down quicker. This makes sense as there is less air to slow down the bullet. Air density decreases as we go higher in altitude, this means that bullets travel further when we are at higher altitudes.

At this point, it may be a good idea to introduce a term: ballistic coefficient. Briefly, the ballistic coefficient of a bullet is its ability to resist the aerodynamic drag. The ballistic coefficient of bullets are measured under standard conditions and available from most manufacturers. If the ballistic coefficient at standard conditions is known and the velocity of the bullet and current air density are known, it is possible to predict bullet performance under any conditions.

There are two different standards that ammunition manufacturers use to measure ballistic coefficient. Some use the Standard Metro conditions where the temperature is 59 degrees Fahrenheit, 78% humidity, 29.5275" (750 mm.) of mercury pressure and altitude of sea level. This standard is used by some manufacturers such as Sierra and Hornady. Some other manufacturers, such as Speer and Nosler, use the International Civil Aviation Organization standard (ICAO), which defines the standard conditions to be 59 degrees Fahrenheit, 0% humidity, 29.921" (760 mm.) of mercury pressure and altitude of sea level. The difference between the values of ballistic coefficients obtained by these two standards is less than 2% though.

Air density depends on three factors: air pressure, air temperature and relative humidity. Of these three, relative humidity has the least effect on ballistic coefficient -- the difference between the ballistic coefficient values of a bullet at 1% relative humidity and 100% relative humidity is about 1%. Therefore the effect of relative humidity can be ignored for most practical purposes. The other two factors (i.e.) air pressure and air temperature have much more to do with air density. A decrease in air pressure results in a decrease in air density. On the other hand, a decrease in air temperature results in an increase in air density. However, as we go up in altitude, the decrease in air density due to air pressure is far more than the increase in air density due to the temperature drop. As a result of this, the density of air decreases as we go to higher altitudes.

On the other hand, if we were to stay at the same altitude, but the air temperature decreases (say between summer and winter), then the effect of temperature decrease is an increase in air density and therefore an increase in the drag forces. This is why bullets will slow down faster in winter than in summer and the bullet trajectory changes.

Some bullet manufacturers have handloading manuals that list formulae to recalculate the ballistic coefficient for different air densities. With the aid of a barometer, the formula and a ballistic coefficient under standard conditions, it is possible to calculate the performance at current conditions.