Ballistic Coefficient Variations with Muzzle Velocity near the Speed of Sound
There is one velocity region within which the ballistic coefficient of every bullet we have tested exhibits dramatic, radical changes. This velocity region is from about 900 to around 1200 fps, which includes the speed of sound (approximately 1129 fps in Sierras test range). The purpose of this section is to describe then bullets by simply loading and firing many rounds for each bullet type within the 900 to 1300 fps velocity range.
The three bullets chosen were the .355 diameter 115 gr FMJ, the .410 diameter 220 gr FPJ, and the .4295 diameter 240 gr JHC. The test results are shown in
. Each dot in each figure denotes the measured ballistic coefficient for one fired round. The title line in each figure calls out the total number of rounds fired for the test bullet. If the reader counts the dots and finds a discrepancy between the count total and the title line, the reason is that a few dots overlap very closely.
The ballistic coefficient values in the three figures exhibit strikingly similar behavior with abrupt changes near the speed of sound. Perhaps the data in
for the .44 caliber 240 gr JHC best illustrate this characteristic. If the bullet starts at a velocity near 1300 fps, the ballistic coefficient is nearly constant until the bullet slows to about 1160 fps. At this velocity the ballistic coefficient rises abruptly as the bullet slows to about 1140 fps. Then the ballistic coefficient falls precipitously to a minimum value which occurs near 1100 fps. The ballistic coefficient then rises dramatically to a second peak value which occurs near 1050 fps. As the bullet slows below 1050 fps, the ballistic coefficient decreases in value, but in a less dramatic manner.
If we look at the other two figures, we see that the ballistic coefficient behavior is nearly identical to
. The velocity points where abrupt changes take place are nearly the same for all three bullets. This strong similarity exists even though the three bullets are different in shape as well as caliber and weight.
Two questions arise from the behavior shown in the three figures. First, what accounts for the systematic ballistic coefficient variations exhibited by the three bullets? Second, with such radical changes in ballistic coefficient between 900 and 1200 fps, how can we calculate accurate ballistics for bullets with velocities in this transonic velocity range?
Considering the first question, an evident conclusion from the data in the three figures is that the
drag model does not match the true drag of any of these three bullets in the transonic velocity range. Furthermore, because the behavior is systematic for three handgun bullets which differ in shape, caliber, and weight, an interesting hypothesis is that this same behavior may be a characteristic of all bullets in this velocity range. We have not conducted enough tests to verify this behavior for all Sierra bullets used in the transonic velocity range (this includes a large number of rifle bullets as well as all handgun bullets). It is clear, however, that if further testing verifies this systematic ballistic coefficient behavior for all (or most) types of bullets, a change in
for the transonic velocity range could be recommended.
Considering the second question about calculating accurate ballistics for bullets which travel with velocities in the transonic range, we have found that the following method is satisfactory. We use one value of ballistic coefficient for each bullet at velocities above 1200 fps (up to 1600 or 1800 fps). A second value is used for velocities below 900 fps. For velocities between 1200 and 900 fps, a ballistic coefficient value which represents an average for this transonic range is used.
Although this method is less than elegant, it provides trajectory data with acceptable accuracy, but only for the following two reasons. The first reason is that in the subsonic and transonic velocity ranges the total drag on a bullet is much less than it is in the supersonic velocity range. Consequently, trajectory accuracy is less strongly dependent on ballistic coefficient accuracy. The second reason is that the maximum ranges of interest for bullets traveling at transonic and subsonic velocities are much less than maximum ranges of interest for high powered rifles, typically 200 to 250 yards compared to 600 to 1000 yards. Consequently, errors made in calculating drag do not propagate over very long ranges.
A principal conclusion from these investigations is that much more testing is required to resolve the questions which these results have raised. As time, personnel resources, and financial resources permit, Sierra may undertake such tests.