Wednesday, January 9, 2013

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:

FD is the drag force
ρ is the density of the air
v is the velocity of the bullet relative to the air
Cd 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.

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