X. Miscellaneous

D. Ballistics Information

5. Why Ballistic Coefficients are Important

by Jim Ristow c/o Recreational Software, Inc. (rsi@sedona.net)

This article was edited from software documentation to encourage a discussion about ballistic coefficients and explain why good B.C.'s are crucial to getting accurate results from ballistic software.

A Little History

In 1881 Krupp of Germany first accurately quantified the air drag influence on the travel of a large flat-based blunt-nosed bullet. Within a few years Mayevski had devised a mathematical model to forecast the trajectory of a bullet and then Ingalls published his famous tables using Mayevski's formulas and the Krupp data. Their work has been refined but is still the basis of most computer programs and published trajectory data after more than 100 years.

By the middle of this century rifle bullets had become more aerodynamic and there were better ways to measure air drag. After W.W.II the U.S. Army conducted experiments at their facility in Aberdeen, MD to remeasure the drag caused by air resistance on different bullets. They discovered the air drag on modern boat-tail bullets increased substantially more above the speed of sound than previously understood. They also learned further refinement to the original Ingalls model would better forecast the trajectory of flat-based small arms bullets. In 1965 Winchester-Western published air drag data based on the Aberdeen research for different types of bullets. Included was a modified Ingalls/Mayevski drag model designated "G1" and one for modern boat tail bullets designated "G5". The "G1" drag model has been accepted by ballisticians as the best "all-around" model and is most commonly used to generate published trajectory data. "G5" is primarily used for long range boat tail trajectories (1000 yards or more).

The Problems

Ingalls defined the Ballistic Coefficient (B.C.) of a bullet as it's ability to overcome air resistance in flight indexed to Krupp's data or the "standard reference projectile". Although the Aberdeen study demonstrated the Krupp projectile is not a good standard for modern bullets, the old Krupp bullet is still used in exterior ballistics to calculate B.C.'s. This really complicates matters because few modern bullets will follow a similar trajectory. While B.C.'s were originally intended by Ingalls to be constant throughout a trajectory, we now know they must be adjusted at various velocities to accurately forecast modern bullet flight.

The firearms industry has developed myriad ways to compensate for this problem. Some bullet manufacturers publish trajectory tables that group bullets with similar aerodynamics under an "average" of calculated B.C.'s for "normal" velocities. These published B.C.'s are typically smaller at high velocities and larger at low velocities than the actual B.C. calculated from firing tests. Another way to estimate B.C.'s uses only the form factor of a bullet and a standard industry bullet classification. B.C.'s provided without trajectory data are often calculated using this method. It gives bullet manufacturers who do not know how the bullet will be used a way to compare aerodynamics but is at best an approximation and can be more than 10% off.

Some ballistic programs adjust published B.C.'s for velocities above the speed of sound or use several B.C.'s at different velocities. While these approaches mitigate some of the problem, in the final analysis, published B.C.'s are still not correct unless your gun shoots the bullet at exactly the same velocity used to calculate the coefficient.

There is another problem with traditional ballistics modeling. The change to air drag does not happen abruptly at predetermined velocity zones. Air drag change as a function of velocity is continuous with only small variations immediately above or below any point along a trajectory. Programs that translate Ingalls or 'G1' drag models directly to computer or use several B.C.'s change air drag values abruptly at pre-determined velocity zones and produce discontinuities. The calculated velocities in each zone do not duplicate a "real world" trajectory and is why many ballistic programs are not accurate when transversing the speed of sound.

The Solution

The latest ballistic modeling techniques use a specific air drag model for the bullet's shape and ballistic algorithms developed by government agencies for ICBM's (called aeroballistics). Aeroballistic algorithms eliminate velocity discontinuities, and when combined with the 'G5' drag model for modern streamlined bullets is extremely accurate to distances well beyond 1000 yards.

For Best Accuracy, Calculate Your Own Coefficients!

Accurate B.C.'s are crucial to getting good data from your exterior ballistics software. Of the two methods used for calculating ballistic coefficients, either or both may be included in software. As stated earlier, methods that use a bullet's standard classification and form factor are not reliable and should only be used if actual velocity data is not available or your software is not capable of calculating ballistic coefficients from velocity and range data.

A good ballistic program should be able to use two velocities and the distance between them to calculate an exact ballistic coefficient. This method of calculating a B.C. is much preferred and can be used to duplicate published velocity tables for a bullet when the coefficient is unknown or to more accurately model trajectories acheived from your own firearm. A lot has changed in shooting software. If your software is more than two years old, chances are it does not employ the latest modeling techniques or calculate B.C.'s. You can find both PC & Macintosh software that use the latest exterior ballistic modeling techniques at commercial sites on the Internet.