By Elya R. Courtney,1 Amy C. Courtney,1 and Michael W. Courtney2 1BTG Research, P.O. Box 62541, Colorado Springs, CO, 80962 2United States Air Force Academy, 2354 Fairchild Drive, USAF Academy, CO, 80840
A bullet can leave the barrel with a significant yaw angle (or tip off rate leading to pitch and yaw) and then pitch and yaw in an oscillatory manner as the peak pitch and yaw angles slowly decrease as the bullet flies downrange. This paper presents an experimental design for detecting the in-flight damping and test results which support the theory of damping of pitch and yaw. Three chronographs were employed simultaneously to determine drag coefficients of bullets over near and far intervals 50 yards long for bullets fired at Mach 1.4 to Mach 3.1. Drag coefficients for the complete 100 yard interval were used at different Mach numbers to establish the curve of drag coefficient vs. Mach number. Since the drag coefficients will decrease as pitch and yaw are damped, the theory of bullets going to sleep predicts that the drag coefficients for the near 50 yard interval will be above the curve and the drag coefficients for the far 50 yard interval will be below the curve. This is, in fact, observed for Mach numbers above 1.5, so the theory of bullets going to sleep is supported in this case. Between Mach 1.0 and Mach 1.5, the damping of pitch and yaw may be obscured by the steep transonic drag rise.
There are a lot of hand waving explanations of bullets going to sleep being bandied about at shooting ranges and internet discussion forums, but Bryan Litz has a pretty good description of the more rigorous theory in the article at the Applied Ballistics, LLC, website on “Epicyclic Swerve.” (Litz, 2012) Bryan also describes the effect of pitch and yaw increasing drag in the article “Accurate Specifications of Ballistic Coefficients” originally published in Varmint Hunter Magazine and also available at his web site. (Litz, 2009a) Bryan has also published a great video entitled “Pitching and Yawing of a Bullet” on YouTube. (Litz, 2009b) While these resources do a great job explaining the theory elucidated by numerical solutions to Bryan’s six degree of freedom model (which is built on Robert McCoy's techniques), to our knowledge, actual observation of these effects has been limited to extremely specialized test equipment and facilities such as spark photography at the BRL free flight aerodynamics range. (Braun, 1958; McCoy, 1988; McCoy 1990) Consequently, detecting pitch and yaw requires expensive equipment that is unavailable at most facilities. The technique presented here requires only three optical chronographs and can be implemented at almost any 100 to 200 yard shooting range.
Previous attempts to demonstrate the damping theory with more common equipment (for example, Halloran et al., 2012) may have failed to detect pitch and yaw damping because they were looking for a decrease in ballistic coefficient with range, and this approach is confounded with possible variance of the actual drag curve from the predicted drag curve of the G1 or G7 drag model used to determine the ballistic coefficient. Drag on the bullet might be varying with range due to the decrease in velocity AND possible damping of pitch and yaw, so that the two effects might be obscuring each other. It is also possible that the cases tested previously might have simply not had significant yaw angles (or tip off rates) when they left the barrel, as this possibility is suggested from the high-speed video failing to show the expected yaw angles. Multiple, precision triggered high speed video cameras have the potential to detect pitch and yaw damping, but this equipment is very expensive and replicates (using more modern equipment) the essential elements of spark photography technique.