2.4 Lessons Learned from Ballistic Coefficient Testing
Much has been written in previous editions of Sierra’s Reloading Manuals about our BC measurements. We now have more than 30 years of experience in measuring BC values for Sierra’s line of sporting bullets, as well as some bullets from other manufacturers, and we have learned a great deal. Our observations and lessons learned through this experience are enumerated and summarized below.
1. Ballistic coefficients must be measured by firing tests. We have tried to determine BC values by the method of Coxe and Beugless. We also have tried to determine BC values using bullets of similar shapes to scale the values based on bullet weights and diameters. But we have never been successful in accurately predicting BC values, or determining these values by any method other than firing tests.
2. The ballistic coefficient of each bullet changes with velocity of the bullet as it flies. The ballistic coefficient of a bullet is not constant with bullet velocity. The reason that the BC changes with velocity is that the standard drag function (the G1 drag function) does not characterize the aerodynamic drag on any sporting bullet throughout the full range of its velocity from the gun muzzle to impact. When a bullet is fired with a supersonic muzzle velocity, as its velocity falls there can be a gradual change in ballistic coefficient until the bullet reaches a velocity near 1600 fps (which is in the upper transonic velocity region). When the bullet velocity falls below 1600 fps, radical changes in ballistic coefficient begin to occur. In the next subsection, we will show some examples of this phenomenon for both rifle and handgun bullets.
When the bullet velocity is greater than 1600 fps, the G1 drag function is a reasonable model from which to compute the aerodynamic drag on a bullet. The gradual changes in BC value with velocity can be handled in trajectory calculations by adjusting the BC values used in those calculations by changing the BC stepwise as the bullet traverses four or five velocity regions. The trajectory will start with the bullet velocity in one of those velocity regions. As the bullet velocity decreases and crosses the boundary between that initial velocity region and the next lower region, the BC is changed to the value corresponding to the next lower region. This process is repeated as the bullet velocity falls through successively lower velocity regions.
When the bullet velocity is less than 1600 fps, the G1 drag function just does not characterize the aerodynamic drag on the bullet. This causes the BC values to vary widely as the bullet velocity falls through the speed of sound (about 1120 fps) and to lower subsonic velocities. The step change method of adjusting BC values is, at best, a crude approximation. This situation is mitigated somewhat by the fact that aerodynamic drag on a bullet diminishes dramatically in the lower transonic and subsonic velocity regions. Consequently, the effect of large ballistic coefficient errors on bullet trajectories is much less than when the bullet velocities are above 1600 fps. For handgun bullet trajectories, the effect is also lessened by the fact that ranges to the targets or the game animals are considerably shorter than for rifles. But at the present time, accurate long-range trajectories simply cannot be calculated for bullets that travel at lower transonic and subsonic velocities. This affects the ballistics of rifle cartridges such as the 30-30 Winchester, 35 Remington, 444 Marlin, 45-70, and the “Whisper” class of cartridges, as well as all handgun cartridges chambered in rifles.
This is an area of continuing research for these authors. Ballistic coefficient data have been gathered for a variety of rifle and handgun bullets at transonic and subsonic velocities. Investigations are under way to find modifications to the G1 drag function at velocities below 1600 fps that will enable ballistic coefficients to remain reasonably constant in this velocity region. We hope to be able to report successfully on this research effort at a later date.
3. The G1 drag function is the best standard drag model to use. We have tested several drag functions (G1 for sporting bullets; GL for lead bullets; G5 for boat tail bullets; and G6 for flat base, sharp pointed, fully jacketed bullets). For each drag function we have measured BC values referenced to that function and observed how those BC values change with bullet velocity. We have chosen G1 because the changes in BC values with bullet velocity are least, and because there is a vast database in the literature on BC values referenced to the G1 standard. Also, to our knowledge all projectile manufacturers refer their published BC values to the G1 drag function, which facilitates comparisons among bullets of different calibers, weights, shapes and manufacturers.
4. Any of the firing test methods measures a ballistic coefficient of the bullet as it flies through the air, including effects imparted by the gun, the cartridge, and firing point environmental conditions, as well as imperfections in the bullet. Theoretically, the BC of a bullet depends only on its weight, caliber and shape. But in a practical sense, the measured BC of a bullet also depends on many other effects.
The gun can affect the measured BC value in two important ways: spin stabilization and tipoff moments. A bullet is gyroscopically stabilized by its spin, which is imparted by the rifling in the barrel. If a bullet is perfectly stabilized by its spin, then its longitudinal axis (which is also its spin axis) is almost perfectly aligned with its velocity vector. If a bullet is not perfectly stabilized (which is usually the case), the bullet may not be tumbling, but its point undergoes a precessional rotation as it flies. In previous editions of Sierra’s Reloading Manuals we have described this precessional rotation and have called it “coning” motion to aid in mental visualization of the motion. As the bullet flies, the point rotates in a circular arc around the direction of the velocity vector. Coning motion results in increased drag on the bullet, and any firing test method then yields an effective BC value for the bullet that is lower than the theoretical value. The rifling twist rate in the gun barrel and the muzzle velocity together control the spin rate of the bullet, and therefore control its degree of stability.
When a bullet exits the barrel, it generally has a small angular misalignment, which ballisticians call “yaw.” Yaw is caused by tipoff moments of torque applied to the bullet by powder gases exiting the barrel nonsymmetrically around the bullet, or by barrel whip or vibrations. This angular misalignment will cause coning as the bullet begins to fly downrange. Coning can also be caused by an abrupt exit of the bullet from the barrel into a crosswind, although BC measurements should never be attempted when winds exist at the firing point.
The cartridge used in the firing tests affects the measured BC values mainly through the muzzle velocity it produces. As noted above, muzzle velocity combines with the twist rate in the rifling to produce the bullet spin rate, which in turn controls stability. In addition, BC values change with the instantaneous velocity of the bullet, and so the muzzle velocity directly affects the measured BC value of the bullet. For example, a 180 grain 30 caliber bullet can be fired at a much higher muzzle velocity in the 300 Winchester Magnum than in a 308 Winchester cartridge. The same is true for a 240 grain 44 caliber bullet from a 44 Magnum compared to a 44 Special. So, the measured BC values can be expected to be different just because of the different starting velocities.
Altitude and atmospheric conditions at the firing point affect the mass density of the air through which the bullet flies, in turn affecting aerodynamic drag on the bullet. Measured values of BC will depend on the actual conditions at the firing point, unless special pains are taken to convert those measurements to sea level altitude and standard atmospheric conditions at sea level. Unless this is done, the BC of one bullet cannot be compared to the BC of another, because the test conditions may be different. Measurements of BC values must then be reduced to sea level altitude and standard atmospheric conditions at sea level. Using Sierra’s exterior ballistics software program Infinity in the procedures described in Section 2.3 will perform this reduction to sea level standard conditions automatically. Otherwise, measured BC values at nonstandard conditions must be reduced by manual calculations. Reducing measured values to sea level standard conditions by manual calculations has been described in preceding issues of Sierra’s Reloading Manuals, and these procedures are available from Sierra upon request.
The coning motion caused by the initial yaw of a bullet when it exits the muzzle generally damps out as the bullet flies — that is, it decreases in amplitude as the bullet travels downrange. This is because the causes of initial yaw are transient in nature. In other words, these causes occur only at the muzzle and do not persist as the bullet flies. Also, the aerodynamic forces caused by the coning motion are restoring forces (tend to improve stability of the bullet) as long as the amplitude of the coning motions is not large enough to cause loss of stability (tumbling). This is the fundamental cause of many anecdotes heard by these authors that “my rifle shoots 1.5 MOA groups at 100 yards, 0.8 MOA groups at 200 yards, and 0.6 MOA groups at 300 yards.” However, some causes of coning motion are not transient in nature, and can cause sustained coning motions throughout the flight of the bullet. Any imperfection in bullet structure leading to a small center of gravity offset from the bullet longitudinal axis can cause sustained coning motions of the bullet as it flies. Also, any small aberrations in bullet shape, such as a small imperfection in point shape or tail shape, can cause sustained coning motions as the bullet flies. This a very strong reason to shoot bullets of high manufacturing quality.