Ballistic Coefficient Dependence on Coning Motion
The correct technical term for coning motion is gyroscopic precession. We call this motion coning motion because this name, although not precisely correct in a technical sense, creates a visual image which clearly portrays the motion.
illustrates coning motion. An interesting analogy to the motion of the bullet is the motion of a football thrown by a quarterback. When the bullet is perfectly stabilized in flight, the spin axis of the bullet is almost perfectly tangent to the trajectory, that is, almost perfectly aligned with the velocity vector of the bullet as it flies. We have seen this in football games when the quarterback throws a perfect pass. receiver. This same concept of perfect stabilization applies to the bullet, as illustrated in
Sometimes in a football game we see a quarterback throw a pass which TV commentators described as wobbly, which corresponds to the situation shown in
Figure 4.6-1 (b)
. When a football wobbles, the nations the wobbling bullet will shoot lower than it would if it were perfectly stabilized.
A third type of angular motion is possible with both a football and a bullet. This motion is called nutation or nodding. In thon does not damp out quickly, the bullet, or the football, will tumble in flight.
In the case of a bullet, precessional motion (or coning) and nutational motion may result from tipoff force thround the geometrical axis. The coning motion which results from tipoff forceersist throughout the entire flight of the bullet.
It turns out that coning motions are worse for long, slender, heavy bullets than for lighter and shorter bullets. The reason is that the long, heavy bullets have a large separation distance between the center of mass and center of pressure of the bullet. However, a bullet which undergoes coning motion, and even a little nodding motion at the beginning of its flight, is
unstable, that is, it will not tumble as it flies. The spinning motion of the bullet, which is caused by the rifling in the gun barrel, gyroscopically stabilizes the bullet in flight, although the stabilization is not perfect when the bullet cones. The cone angle is small always, and the nutation angle starts out very small and dies out very quickly.
Coning motion has very important effects on the measurement of ballistic coefficient of the bullet. If the bullet is coning, it presents an effective area which is larger than the true cross sectional area of the bullet, and the drag pressure of the air acts on this larger area to produce a larger drag force on the bullet. This can be seen in
. When the bullet is tipped with respect to the trajectory, as shown in
Figure 4.6-1 (b)
, it clearly presents a larger area for drag to act upon than it does in
Figure 4.6-1 (a)
. This is because drag acts backward along the direction of the bullets velocity vector. The result is an increase in the drag force experieere perfectly stabilized.
How do we know this for sure? Lets look at some measured data.
shows results of two sets of measurements of the ballistic coefficient of the Sierra 910 grain Hollow Point Boat Tail MatchKing bullet. The first set of measurements involved 14 rounds fired, with the ballistic coefficient of each round measured by the three screen method, that is by measuring muzzle velocity and time of flight between the muzzle chronograph and a third screen downrange 50 yards from the first screen of the chronograph. The data are plotted and the statistics are given on the right side of
. The second set of measurements involved 16 rounds fired, with the ballistic coefficient measured by the four screen method, that is with initial velocity measured by a muzzle chronograph, and the final velocity measured by a chronograph set up 250 yards downrange from the muzzle chronograph. The four screen method had to be used for the longer distance because the time of flight to 250 yards exceeded the capacity of the electronic counter used to measure time of flight. The data are plotted and the statistics are given on the left side of
The average values of the measured ballistic coefficient differ by almost 10 percent and the average values of the velocities differ by only 135 fps. From the spreads in the velocities of the rounds shown in the figure, and it is obvious that there is no strong trend in the value of ballistic coefficient with velocity for either set of measurements. Therefore, we attribute the difference in average values of ballistic coefficient to the fact that the bullets were coning, and the coning did not damp out over the 50 yard range, while it damped out well over the 250 yard range.
To support this observation further, look at
which shows the variation of measured ballistic coefficient of the .30 caliber 190 grain Hollow Point Boat Tail MatchKing bullet as a function of twist rate in the test barrel. Six barrels were used in this test, with twist rates varying from one turn in 14 inches to one turn in 8 inches. Fifteen rounds were fired through each barrel at velocities near 2350 fps. The ballistic coefficient for each round fired is plotted in the figure. The figure also lists the average value of ballistic coefficient for the 15 rounds, together with the standard deviation and extreme spread, for each of the six twist rates used. Note that one barrel chambered a .300 Winchester Magnum cartridge, while the other five barrels chambered the .308 Winchester cartridge.
We know from common knowledge that if the twist rate of a barrel is too slow, long and heavy bullets will not be well stabilized. They do not tumble in flight, but the holes in paper targets are elliptical rather than round, indicating that the bullets are coning.
shows what happens to the measured ballistic coefficient in such cases. For the faster twist rates, out through one turn in 11 inches in the case of the 190 grain HPBT MatchKing bullet in this test, the average values of the ballistic coefficients differ very little, and the statistical spreads are tight. When a twist rate of one turn in 12 inches was reached, the average value of measured ballistic coefficient dropped by more than 2 percent, and the spread of the measurements increased substantially. At a twist rate of one turn in 14 inches, the average ballistic coefficient decreased by more than 30 percent, and the spread increased dramatically. We emphasize that none of the test bullets tumbled in flight; all were gyroscopically stabilized, though marginally for the slowest twist rate.
This test dramatically illustrates the effect of coning motion on measured ballistic coefficient.
shows the same test conducted on the .22 caliber 69 grain Hollow Point Boat Tail MatchKing bullet, with the same obvious results. The conclusion is inescapable that coning motion reduces the average measured ballistic coefficient and increases the statistical spread of the measured values.
Another observation we have made is that with long, slender Spitzer and Spitzer Boat Tail bullets the average measured ballistic coefficient at high muzzle velocities is significantly lower than at intermediate velocities, and the statistical spread of the measured values often (but not always) is significantly greater. We believe that this is caused by greater coning motion imparted to each fired bullet at high muzzle velocities compared to intermediate muzzle velocities. We suspect that this results from the larger amounts of powder gases exiting from the bore, resulting from the larger powder charges necessary to obtain higher velocities. This effect is shown for the .375 caliber 250 grain Spitzer Boat Tail bullet in
. The measured ballistic coefficient has an upward trend between the measurements at 1585 and 2240 fps, and then it drops dramatically between 2240 and 2785 fps. We believe this dramatic drop at higher velocities results from greater coning motion at the higher velocities. Note that in this particular case the statistical spread in the measurements at the high velocity level did not increase dramatically. This means that the bullets are coning consistently from round to round.
What have we learned from this experience with coning motions? We now know that ballistic coefficients must be measured downrange from the muzzle at a distance sufficient for the coning motion to have died out. Coning motions are caused by side forces applied to each bullet as it exits the muzzle, but in all but very severe cases the coning motion will damp out within about 100 yards downrange from the muzzle. Consequently, we have set up Sierras underground test range to measure ballistic coehe time of flight screen is positioned about 150 yards downrange from the firing point.