The puzzle of whip cracking – uncovered by a correlation of whip-tip kinematics with shock wave emission

Abstract.

During whip cracking the whip-tip reaches a supersonic velocity for a period of about 1.2 ms, thereby emitting a head wave with a parabolic-shaped geometry. A detailed study of this mechanism which encompasses the motion analysis of the whip-tip as well as the determination of the local origin of the shock emission requires a sophisticated recording technique. A pre-trigger framing high-speed video camera system was used which was triggered by an acoustical sensor and synchronized with a pulsed copper-vapour laser. The phenomena were visualized by the direct shadowgraph method and recorded cinematographically as digital images at a frame rate of 9 kHz using a CCD-matrix with $256{\rm (H)}\times 128{\rm (V)}$ pixels. The resulting series of frames allowed, for the first time, (i) a reconstruction of the whip-tip trajectory, (ii) a determination of the tuft velocity and acceleration, (iii) a correlation of whip-tip kinematics with shock wave emission, and (iv) a motion analysis of the turning and unfolding mechanism of the tuft. The tuft at the whip-tip was accelerated within a distance of about 45 cm from a Mach number of $M=1$ to a maximum of $M=2.19$, thereby reaching a maximum acceleration of 50,000 g. The shock is emitted at the moment when the cracker, arriving at the turning point of the lash, is rapidly turned around. After emission of the shock wav $M<1$ within a short distance of only 20 cm.