A symmetric spin stabilized projectile without a dynamic

A symmetric spin stabilized projectile without a dynamic imbalance exhibits what is known as epicyclic motion. In epicyclic motion, the nose of the projectile “cones” around the projectile\'s velocity vector at two distinct frequencies aswhere is the magnitude of the pitching motion, K represents the oscillation amplitude, φ0 represents the phase shift, represents the oscillation frequency, and the subscripts “F” and “S” represent the fast and slow oscillations. The fast oscillation is known as nutation, and the slow frequency is known as precession. Most artillery projectiles have only slight dynamic imbalances, making it possible to accurately model their six degree-of-freedom trajectories using only these two effects (as well as the yaw of repose which affects the trajectory mostly near the maximum ordinate of the trajectory curve). A projectile with a significant dynamic imbalance will exhibit a third frequency of coning motion following cannon launch. This motion is referred to by McCoy [2] as the “tricyclic” arm but will be referred to as “wobble” in this paper, since wobble is defined as a fluctuating state of motion caused by a mass imbalance. The wobble motion occurs at a frequency that is equal to spin-rate of the projectile. This motion is described in Eq. (2),where the subscript w represents the wobble oscillation and p represents the projectile spin-rate. All three “coning” motions rotate the nose of the projectile in the same direction as the spin-rate, which for all U.S. artillery projectiles is clockwise when looking from the Deferoxamine mesylate toward the nose. Illustrations of the initial coning motion are shown in Fig. 1 for a projectile with and without a significant dynamic imbalance.
Test description
Data analysis The launch videos were then analyzed using the automated flight video analysis (AFVA) system [4]. This analysis processes each frame of a launch video to segment the shape of the projectile and identify key points such as the nose, center of gravity (CG) and base locations. The pitching motion history estimated from each camera is then corrected and combined to determine the resolved three dimensional (3D) pitch and yaw motion history for the first ~150 m of flight. A screen shot of the AFVA extracting the projectile shape of an M110A2E1 projectile is shown in Fig. 2. The resolved pitch and yaw histories from AFVA for rounds with (left) and without (right) dynamic imbalances are shown in Fig. 3. The next step in the analysis was to isolate the wobble motion from the resolved pitch and yaw histories. To do this, reasonable estimates for the nutation and precession frequencies were determined. For the M483 projectile (which is a ballistic match to the nominal M110A2E1), those values were roughly 72 Hz for the fast arm, 17 Hz for the slow arm, and a spin-rate of 136 Hz for an average muzzle velocity of 420 m/s. Using these values, only the magnitudes and phase shift angles for both the fast and slow oscillation modes needed to be matched to resulting pitching motion history. This was done by first aligning the fast oscillation and then incrementally adjusting the slow oscillation until the difference between the epicyclic fit and the raw pitch data resembled a steady harmonic oscillation. The final step was to fit a sinusoid oscillating at the spin-rate to the isolated wobble motion. This process is illustrated for one of the imbalanced projectiles (which clearly illustrated wobble) in Fig. 4. The complete results for all eight rounds are shown in Fig. 5. It required several iterations of parameter adjustments to arrive at a best-fit for the epicyclic motion of the projectiles, and dermal system was especially difficult for the projectiles that were restored to normal levels of inertial asymmetry. In addition, all eight of these rounds exhibited a relatively low amount of total pitching motion, making it especially difficult to determine the correct epicyclic parameters. Still, it was possible to isolate the wobble motion for each of the rounds fired. Once isolated, it was clear that the projectiles with mass asymmetries exhibited significantly more wobble motion.