## Drag Functions

I receive a number of questions about what drag function one should be using. The typical answer is that it depends on what drag function the ballistic coefficient (C) was calculated with. What does that mean? It means that the ballistic coefficient and the drag function go hand in hand. You cannot use a C calculated for the G1 drag function with the G7 drag function. You will not get sensical answers.

Drag functions are a measure of the drag of a "standard" bullet. This standard bullet has a C of 1.0. Bullets of the same shape typically have a drag curves (drag as a function of speed) that are the same or very similar. This similarity led to the idea of defining the standard bullet and then related other bullets of the same shape, but different size to the standard bullet. This is where the ballistic coefficient comes into play. It relates a bullet to the standard bullet. Since we know the drag of the standard bullet, we can, with the C, define the drag of a non-standard bullet.

Bullets of different shape such as round nose bullets, boattail bullets hollow points would all have different drag curves and therefore different drag functions. Because the relation between the standard bullet and other non-standard bullets is not perfect, some manufacturers define multiple ballistic coefficients as a function of velocity to better fit the drag model. This is especially true when most of the industry uses the G1 drag function for almost all bullets, whether or not the drag function is a good fit (the G7 is a better fit for boattail bullets). Further more, some manufacturers (Lapua) are skipping the ballistic coefficient and drag function all together and releasing tables of drag coefficient versus mach number.

### Drag Force

The relationship between different drag functions and their ballistic coefficients can be shown using the following equations.

The drag force on the bullet is proportional to the following quantity

Gi(M)/Ci

where G is the drag function [which is not constant and changes with the speed of sound denoted by the (M)] and i is a designator for the drag function, such as 1, 2, 5, 6, etc, denoting the drag functions G1, G2, G5, G5, etc. C is the ballistic coefficient for the chosen drag function. The formulas for the drag function as a function of the drag coefficient can be found here.

For any bullet, the drag force must be the same no matter what drag function is chosen since the drag force is physical and depends on the shape of the bullet. This means that the following equation must be true

Gi(M)/Ci = Gj(M)/Cj

where j is a different drag function than i. This means that it is the ratio of the drag function and ballistic coefficient that model the drag of the bullet. For different drag functions, the Cs will be different, but with properly chosen Cs and drag functions, the same trajectory will be calculated because the drag force is the same. For example, the value of the G7 drag function is typically half that of the G1 drag function. That means that for the drag to be the same, the G7 C is going to be half of the G1 C. This does not mean that the G1 is better because it is higher, it is just a different model for the drag.

One can also use the formula above convert from one C to another. Just divide both sides by Gi(M) and invert:

Ci = CjGi(M)/Gj(M)

The ballistic coefficient, C, is obviously a function of the speed of sound, M. This same formula is used in the Drag Function conversion program. The speed of sound is found from the input velocity and the speed of sound at standard conditions.

### Variables

 C Ballistic Coefficient G "G" Function M Speed of Sound

### References

The Effect of Wind on Flat-Fire Trajectories, Robert L. McCoy, BRL Report Number 1900, Ballistic Research Laboratories, Aberdeen Proving Ground, Maryland, August 1976, [ADB012872]