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Shot Put Projection Angle

Introduction    Optimum Projection Angle    Undergraduate Teaching


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 projection angles of world-class shot-putters are around 37. Some researchers have noted that in shot-putting the landing is about 2 m lower than the launch. Even so, this produces only a small reduction in the calculated optimum projection angle (to about 42)

The reason for the discrepancy between theory and practice is that the projection speed and launch height attained by the athlete are not independent of the projection angle, as is assumed in the conventional calculation of the optimum projection angle. Experiments have shown that the projection speed an athlete can generate decreases with increasing projection angle, and that this substantially reduces the optimum projection angle.

Optimum Projection Angle

The standard view that the optimum projection angle in shot-putting is about 42 may be understood by using the well-known formula for the range of a projectile in free flight.

A series of distance versus projection angle curves may be plotted for selected projection speeds. These curves suggest that the optimum projection angle is just under 45.

This set of calculations contain a serious error. The calculations do not include the fact that an athlete cannot throw with the same speed at all projection angles. The projection speed an athlete can generate steadily decreases as the athlete tries to throw with a higher and higher projection angle.

The decrease in projection speed with increasing projection angle is a result of two factors.

  • When throwing with a high projection angle, the shot-putter must expend a greater effort during the delivery phase to overcome the weight of the shot, and so less effort is available to accelerate the shot (i.e. produce projection speed).

  • The structure of the human body favours the production of putting force in the horizontal direction more than in the vertical direction. Considering just upper body strength, most athletes can lift more weight in a bench press exercise than in a shoulder press exercise.

The optimum projection 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 projection angle for the athlete is not just under 45, but about 34.

The optimum projection 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 throwing technique. This means that each athlete has their own specific optimum projection angle. The optimum projection angle for a world-class shot-putter may be anywhere from 26 to 38.

To find out more about the shot put study, see:

Linthorne N.P (2001). Optimum release angle in the shot put. Journal of Sports Sciences, 19 (5), 359-372. (Publisher)

Linthorne, N.P. Optimum angles of projection in the throws and jumps.

Optimum Projection Angles in Undergraduate Teaching

The 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.