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Bullet Drag Coefficient; Bow Wave, Base & Skin Friction in Small Arms & Artillery

The ballistic coefficient is the drag model used in small arms and artillery. Any coefficient compares two quantities, a known standard vs. a tested quantity. In the case of small arms this is a standard bullet and the tested bullet. In most cases this value is between zero and one and usually below one. A few bullets even outperform the standard. There are two models used. G1 is the standard flat base projectile and G7 used to model low drag and boat tail bullets. The sectional density is the weight of the bullet divided by the square of diameter of the bullet.
SD = W/7000 ∙ d^2
Where SD = Sectional Density W = bullet weight in grains d = bullet diameter
The 7000 converts the weight to pounds (7000 grains/pound)
BC = SD/F
With BC = Ballistic Coefficient and SD = Sectional Density and F = to the form factor.
The form factor was taken from a series of charts, but now the BC is determined using doppler radar or another test procedure. The BC for anyone bullet varies according to velocity. Sierra bullets is one of few that list multiple BC’s for multiple velocity ranges for the bullet. G1 standard is 3.28 calibers (diameters) long with a 2-caliber tangent radius ogive and comes to a point defined by Krupp in 1881. The G7 is much more complicated. Drag has three components.

Bullet Bow Wave

As a bullet moves through the air it is pushing the air to the side as it compresses it to the ogive or curved area of the bullet. At subsonic velocities the pressure wave travels to the front of the bullet. At supersonic velocities the bullet is moving faster than the air can move around it. This creates a compression shockwave and the reason bullet ‘crack’ as they pass by you, a mini-sonic boom. Contributes about 60% to the total drag.
o The bullet efficiency drops as the drag increases.
o Sharp points reduce the bow wave drag.
o Subsonic velocity the drag increase at the square of the velocity.
o Supersonic velocities produce drag at a higher than the square of the velocity.
o Bullet yaw, the turning of the bullet increases drag.

What is Base Drag?

As the laminar air flows around the bullet it comes to the base of the bullet the surface rips apart creating turbulence that produces a low pressure or partial vacuum behind the bullet. The pulls on the bullet and contributes to drag. Base drag’s contribution is about 30% of the total drag.
o Boat Tail or taper base bullets smooth the airflow transitioning from the bearing surface to the base. The taper also reduces the base area and lowering the effects of base drag.
o The low pressure on the bullets base, increases the pressure on the ogive and thus increasing drag.

Skin Friction Drag

This is caused by the friction of the air as the laminar flow breaks up further from the bullet. It contributes less than 10% of the overall drag.
o Bullet coatings do nothing to reduce drag.
o Cannelures and rings increase skin drag.
• Total drag is the total of all the drag components.
Drag is of concern only for the long-range shooter. At normal hunting ranges it is of little consequence. But for the 1000-yard or 1000-meter bench rest competitor it is or primary importance. The bullet is pulled down by gravity. Range is determined by how fast the bullet can cover ground, as all bullets drop at a rate of 32 feet per second^2. As drag slows the bullet it shortens the effective range.

NOTE: Yaw is the ‘wobble’ of the bullet. The ideal is the bullet spin would be on its axis in line with the trajectory. The reality is that the point proscribes a small circle in respect to bullet trajectory always being out of alignment, creating a tiny wobble. In fact yaw is reduced at range, the reason many accuracy and precision fires are at a minimum of a 100 yards, takes that long for the bullet to stabilize its stability.