Ballistic coefficient

From Wikipedia, the free encyclopedia

The ballistic coefficient (BC) of a body is a measure of its ability to overcome air resistance in flight. It is inversely proportional to the deceleration—a high number indicates a low deceleration.

It is given by the mass of the object divided by the diameter squared that it presents to the airflow divided by a dimensionless constant i that relates to the aerodynamics of its shape.

Ballistic coefficient has units of lb/in² or kg/m².

The formula for calculating the ballistic coefficient is as follows:

$C = \frac{SD}{i} = \frac{w}{i*d^2}$

where:

C = ballistic coefficient
SD = sectional density
i = form factor
w = Mass of object, lb or kg
d = diameter of the object, in or m

Alternately:

$C = \frac{M}{Cd*A} = \frac{d*l}{Cd}$

where:

C = ballistic coefficient
M = Mass
A = cross-sectional area
Cd = Cd factor
d = average density
l = body length

1 Bullet Performance
2 Reentry vehicles
3 References
4 Notes

[edit] Bullet Performance

A bullet with a high BC will travel further than one with a low BC. Since dense materials give more mass for a given volume or cross-section, bullets often employ lead in their construction and some military weapons use depleted uranium.

When hunting with a rifle a higher BC is desirable for several reasons. A higher BC results in a flatter trajectory which in turn reduces the effect of errors in estimating the distance to the target. This is particularly important when attempting a clean hit on the vitals of a game animal. If the target animal is closer than estimated, then the bullet will hit higher than expected. Conversely, if the animal is further than estimated the bullet will hit lower than expected. Such a difference in bullet drop can often make the difference between a clean kill and a wounded animal.

This difference in trajectories become even more critical at longer ranges. For some cartridges, the difference in two bullet designs fired from the same rifle can result in a difference between the two of a foot or more at 500 yards. The difference in impact energy can also be great because kinetic energy depends on the square of the velocity. A bullet with a high BC arrives at the target faster and with more energy than one with a low BC.

Ammunition makers often offer several bullet weights and types for a given cartridge. Heavy-for-caliber pointed (spitzer) bullets with a boattail design have the highest BC, whereas lighter bullets with square tails and blunt noses have lower BCs. 6mm and 6.5mm cartridges are probably the most well known for having high BC bullets and are often used in long range target matches of 600-1000 meters. The 6 and 6.5 have relatively light recoil compared to larger calibers with high BC bullets and tend to take matches where accuracy is key. Examples include the 6mm PPC and the 6.5 Grendel The 6.5mm is also a very popular hunting caliber in Europe but not so much in the United States. In the larger caliber category, the .338 Lapua Magnum, .50 BMG are popular with very high BC bullets for shooting beyond 1000 meters. A new competitor in the the larger caliber category is the .408 Cheyenne Tactical.

Since the higher BC bullet gets to the target faster, it is also less affected by the crosswinds.

[edit] Reentry vehicles

The ballistic coefficient of an atmospheric reentry vehicle has a big impact on its behaviour. A very high ballistic coefficient vehicle would reduce velocity very slowly and would impact the Earths surface ("auger in") at supersonic speeds. A low ballistic coefficient vehicle would slow at high altitude in thin air and would experience less heating.