Drag Coefficients

The topic on CD and KD defined the equations of motion for the bullet in common aerodynamic terms, CD, the drag coefficient, and KD, the older BRL nomenclature for the drag coefficient. The drag coefficient, although available for a limited few (e.g. Lapua), is not generally available. Additionally, it is usually a table of values as a function of mach number (speed in terms of the speed of sound) which makes it harder to use -- do you really want to have to remember 30 values, their mach numbers and enter these values? I didn't think so.

Drag Functions

Drag functions were introduced to simplify matters. They have been called a "trick" or an approximation, but if done correctly, they are no less accurate than using drag coefficients as a function of mach number.

A drag function is tabulated for a standard bullet of known shape. This is done by measuring the drag of the standard bullet. This standard bullet has a ballistic coefficient (BC) of 1.0. Other bullets of the same shape but different size have different ballistic coefficients. The drag function and BC are then used to calculate the drag coefficient and therefore the drag on a bullet of similar shape to the standard bullet as a function of velocity.

The drag function is not a simple, single value. It is a table of values as a function of velocity or mach number (depending on the derivation) like the CD. A short discussion on drag functions and their relation to BCs is found here. The difference is that the drag functions are known values that can be built into ballistics software without any knowledge of the bullet's BC which then requires the user to only enter a single value, the BC. [Tabulated values for the common drag functions are here]

Ballistic Coefficients

This gets us to a (usually) single number, called the ballistic coefficient. In theory, this single number is all we need to know and can be used to compare bullets. The one with the higher BC is better, right? No so fast. It is important to know the drag function that the BC is calculated with and how well the drag function fits the bullet. If the drag function is a good model, the BC is relatively constant over the range of useful velocities and we can use a single BC value. If it is not constant, the BC changes and a single number is not good enough. This is why Sierra publishes multiple BCs for many of their bullets. Is this wrong? Not really, but it is not as convenient as a single number.

How do we get to a single BC that is usable? We use the "correct" drag function for the bullet shape. How do we define "correct"? It is the drag function whose BC varies the least over the range of velocities we are shooting.

Most of the BCs published today use the G1 drag function. This is not the ideal drag function for many long range bullets. Unfortunately, the industry is somewhat reticent to adopt other drag functions. When compared to a G7 BC, the G1 is typically higher. This is because the G1 drag function values are higher -- the ratio of the G1 drag function and G1 BC should be the same as the ratio of the G7 drag function and the G7 BC (it depends on the velocity at which the BC is measured). The problem is that many people do not understand the difference between the two drag functions and look at only the values of BC. Since the G7 BC is typically half the G1 BC is does not look as attractive to the marketing department even though it may provide better answers. Additionally, manufacturers can be tempted to inflate the values for ballistic coefficients. This makes a bullet more appealing than other bullets with lower BCs. What is needed is a single comprehensive measurement of long range bullets using the same techniques.

Bryan Litz the ballistician for Berger Bullets, has recently published his book, Applied Ballistics for Long Range Shooting. It provides a single source of highly accurate (+/-1%) measurements for more than 175 bullets from different manufacturers. These measurements were made using the same techniques for all bullets and provide BCs using both the G1 and G7 drag functions.

The BCs measured by Bryan have been entered in the JBM Bullet Library using the G7 ballistic coefficients.

References

Applied Ballistics for Long Range Shooting Bryan Litz, Applied Ballistics LLC, 2009.