OPTIMIZATION OF HANG-TIME TECHNIQUE FOR VOLLEYBALL SPIKE JUMPS Dhruv Gupta 1 , Richard R. Neptune 2 , Jody Jensen 1 and Lawrence Abraham 1 Department of Kinesiology and Health Education, The University of Texas at Austin, Austin, Texas, United States of America 1 Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas, United States of America 2 In a previous study, we found that hang-time can have potential benefits on athlete performance during volleyball spikes, but hang-time usually comes at a cost of decreased peak height. To address this loss in peak height, we tested whether the trajectories of the “non-performing segments” (legs and non-hitting arm) can be modified to maximize the performance of the hitting arm without affecting the hang-time (defined by vertical motion of the head and trunk). The purpose of this study was to present details of an optimizer to facilitate a wide range of future studies aimed at maximizing performance. Using optimization we predict that for males the peak height of the hitting arm and its sagittal plane velocity at its peak can be increased by 52±11 mm (p<0.001) and 3.0±0.6 m/s (p< 0.001) by modifying the trajectories of the non-hitting and hitting side legs respectively. KEY WORDS: “hang”, hang-time, optimization, hitting arm, trajectory, volleyball INTRODUCTION: When athletes are in flight, the only force acting on them is the force of gravity. The center of mass (COM) of the athlete, like any other projectile, will follow a standard parabolic trajectory. If all body segments remain in a fixed configuration during flight (that is, if the body remains in a rigid position), then each of the body segments will follow the same parabolic trajectory. If, however, one or more segments move to follow a lower trajectory, other segments would also change relative position resulting in higher pathways so that their weighted sum, the COM, continues to follow the parabolic trajectory. This is the basic concept, the relative positioning of body segments, that allows athletes to “hang” in the air, or appear to pause their vertical movement near the peak of the jump. Visually, it appears to observers that the laws of physics are violated. However, by manipulating the relative position of limb segments, the athlete’s trunk drops and then rises with respect to the whole body COM that is following a pre-determined parabolic trajectory, resulting in reduced vertical motion of the athlete’s head and trunk. Note that the COM trajectory cannot be affected due to motion of the segments but rather it is the trajectory of head and trunk that changes. The flattened path of the head and trunk is perceived as “hang” (Gupta et al., 2015). In a previous study (preliminary description in Gupta et al., 2015), we studied the mechanisms behind “hang” and how it affects performance. We established that volleyball athletes (n=12) significantly increased (p<0.001) their hang-time when they flexed their knees and then extended them during flight compared to no flexion of the knees during flight. We measured hang-time as the time when the center of mass of the head and trunk combined had a near zero vertical velocity; mathematically, the time when the absolute value of vertical velocity of the center of mass of the head and trunk combined was lower than a threshhold minimum. Extended hang-time was shown to come at a cost of reduced peak height of the head and trunk. A critical finding in that study was that the athletes swung the hitting arm significantly later (p<0.001), with the hitting arm reaching its peak at 58.9% of flight duration when the athletes flexed their knees (and so extended their hang-time) compared to 50.7% flight duration when they did not flex their knees at all during flight. This suggests that athletes can use extra time in the air with a more stable head trajectory to adjust to different sets for the hit or to look at the opponents’ defense and make decisions on how and where to hit. These results raise an additional question. Since contacting the ball higher is an advantage in a spike, is there a way to compensate for the potential loss in peak height of the hitting arm during the hang-time? We hypothesize that the motion of the legs and non-hitting arm could be optimized without affecting the motion of body COM or hang-time (the motion of the