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 Optimum Take-Off Angle in the Long Jump Introduction One of the best known 'results' of the science of mechanics is that the optimum projection angle for achieving maximum horizontal range is 45°. However, it is also well known that actual performers in projectile-related sports seldom use an angle of 45°. For example, typical take-off angles of world-class long jumpers are around 21°. Some researchers have noted that in long jumping the landing is about 50 cm lower than the take-off. Even so, this produces only a small reduction in the calculated optimum take-off angle (to about 43°) The reason for the discrepancy between theory and practice is that the take-off speed attained by the athlete are not independent of the take-off angle, as is assumed in the conventional calculation of the optimum take-off angle. Experiments have shown that the take-off speed an athlete can generate decreases with increasing take-off angle, and that this substantially reduces the optimum take-off angle. Optimum Take-Off Angle The idea that the optimum take-off angle in the long jump is about 43° may be understood by using the well-known formula for the range of a projectile in free flight. A series of distance versus take-off angle curves may be plotted for selected take-off speeds. These curves suggest that the optimum take-off angle is just under 45°. This set of calculations contain a serious error. The calculations do not include the fact that an athlete cannot jump with the same speed at all take-off angles. The take-off speed an athlete can generate steadily decreases as the athlete tries to jump with a higher and higher take-off angle. The optimum take-off angle for the athlete is obtained by combining the speed-angle relation for the athlete with the equation for the range of a projectile in free flight. The optimum take-off angle for the athlete is not just under 45°, but about 22°. The optimum take-off angle calculated above applies only to the athlete in question. Each athlete has a unique speed-angle relation that depends on their size, strength, and jumping technique. This means that each athlete has their own specific optimum take-off angle. The optimum take-off angle for a world-class long jumper may be anywhere from 15° to 27°. To find out more about the long jump take-off angle study, see: Linthorne, N.P., Guzman, M.S., and Bridgett, L.A. (2005). Optimum take-off angle in the long jump. Journal of Sports Sciences, 23 (7), 703-712. (Publisher) Linthorne, N.P. Optimum angles of projection in the throws and jumps. SweatPit.com. Optimum Projection Angles in Undergraduate Teaching My work on optimum projection angles has been incorporated into my biomechanics classes. I have produced a Microsoft Excel spreadsheet and graphing tutorial to examine the optimum projection angle in shot-putting. This tutorial highlights to the student the fact that the optimum projection angle in sports is not 45°.