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Optimum Take-Off Angle in the Long Jump


Introduction    Optimum Take-Off Angle    Undergraduate Teaching


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°.