Optimum take-off angle in the long jump

In this study, we found that the optimum take-off angle for a long jumper may be predicted by combining the equation for the range of a projectile in free flight with the measured relations between take-off speed, take-off height and take-off angle for the athlete. The prediction method was evaluated using video measurements of three experienced male long jumpers who performed maximum-effort jumps over a wide range of take-off angles. To produce low take-off angles the athletes used a long and fast run-up, whereas higher take-off angles were produced using a progressively shorter and slower run-up. For all three athletes, the take-off speed decreased and the take-off height increased as the athlete jumped with a higher take-off angle. The calculated optimum take-off angles were in good agreement with the athletes' competition take-off angles