Method
The experimental design to quantify damping of pitch and yaw uses three chronographs simultaneously. We’ve found that CED Millenium chronographs with LED sky screens meet their specification of 0.3% accuracy and can be calibrated by placing all three in a row, with minimal separation, and shooting though them. Each reading of the second and third chronograph is adjusted upward appropriately for the small loss of velocity (< 5 fps) over the two to four foot distance from the closest chronograph. Then the average velocity of ten shots can be compared to determine systematic variations in the readings between the three chronographs. In this manner, the variations between chronographs can be reduced to 0.1%.

After calibration, the three chronographs are placed 10 feet, 160 feet, and 310 feet from the muzzle. Chronograph separations are measured with a tape measure and are accurate within a few inches. With this arrangement, velocity losses are simultaneously determined for each shot over 100 yards, the near 50 yards, and the far 50 yards. This data is then used to determine drag coefficients over the three intervals for each shot. The average and uncertainty of the drag coefficient for each powder charge can then be determined through standard statistical methods. To achieve a range of muzzle velocities from Mach 1.4 to Mach 3.1, 40 grain Nosler Ballistic Tip bullets were loaded in .223 Rem Lapua brass in front of 6, 8, 10, 11, 12, and 14 grains of Blue Dot and 29 grains of CFE 223. Ten shots each were fired for each powder charge except for 6 grains, for which 20 shots were fired. (Earlier work had shown greater shot-to-shot drag variations in this load, so more data points were desired.) The rifle used was a Remington 700 ADL with a 1 in 12 inch twist.

The drag coefficients at different Mach numbers for the complete 100 yard interval were used to establish the curve of drag coefficient vs. Mach number. Using drag coefficients rather than ballistic coefficients is important so that increased drag due to pitch and yaw is not confounded with increased ballistic coefficient due to lower velocity. Since the drag coefficients will decrease as pitch and yaw are damped, the theory of bullets going to sleep (pitch and yaw damping) predicts that the drag coefficients for the near 50 yard interval will tend to be above the curve and the drag coefficients for the far 50 yard interval will tend to be below the curve. (A similar approach is also possible with ballistic coefficients, but one would need to compute the ballistic coefficients over the 100 yard interval, establish a trend line of BC vs. velocity for a range of muzzle velocities, and then see if the near and far ballistic coefficients were below and above the trend line, respectively. Seeing an increase in BC over the far 50 yards with a single muzzle velocity might be suggestive, but is much less definitive.)

Figure 1: The solid line shows the best fit quadratic to drag coefficients over the 100 yard interval. The line of small x's show the G7 drag model. The large x's show drag coefficients determined over the near 50 yards. The diamonds show drag coefficients determined over the far 50 yards.

Results
Figure 1 shows results for drag coefficient vs. Mach number for the 40 grain Nosler Ballistic Tip. All of the drag coefficient measurements above Mach 1.5 for the near 50 yards are above the curve for the 100 yard interval. This indicates support for the theory that increased pitch and yaw cause increased drag early in the bullet's flight. However, note that the error bars of some of the points intersect the curve. This limits the confidence level regarding the definitiveness of this conclusion. It is unclear whether some points are closer to the curve because of smaller initial yaw angles for those loads or because of measurement uncertainties. It is uncertain whether the near drag coefficient at Mach 1.4 is so close to the curve due to the steep transonic drag rise or a small initial yaw angle for the load with 6 grains of Blue Dot.

All the drag coefficient measurements for the far 50 yards are below the curve for the 100 yard interval. This reduction in drag coefficient suggests that the pitch and yaw angles are significantly smaller for the far 50 yards than they were over the near 50 yards. Confidence is limited for data points whose error bars touch the curve. However, the overall trend provides compelling support for smaller drag coefficients over the far 50 yards.