One of the stranger Olympic sports is the shot put, an event in which an athlete throws a grapefruit-sized sphere of metal as far as possible, using a strange throwing motion specified by the rules.

Now here’s a curious puzzle of biomechanics: at what angle should the shot be released to maximise the distance of throw?

It’s easy to think this ought to be 45 degrees and a straightforward analysis can indeed suggest this. But measurements of the action of the best putters consistently shows them using a release angle of between 37 and 38 degrees. Why the shallower trajectory?

In the 1970s, biomechanicists realised that the height of release needs to be included because it ensures that the trajectory is not quite symmetrical. When this is taken into account, the optimum angle of release turns out to be 42 degrees, closer to the measured value but still some 4 or 5 degrees out. Nobody since then has been able to figure out where the difference arises

Now Alexander Lenz at the Technical University of Dortmund and Florian Rappl at the University of Regensburg in Germany say they know what’s going on. They point out that there are several other effects that need to be taken into account.

First, the height of release is the height of the athlete’s shoulder plus an additional term that depends on the length of the arm and its angle. When this is taken into account, the optimal angle of release turns out to be up to 1 degree bigger, making the biomechanical puzzle even more acute.

Next, Lenz and Rappl look at the energy the athletes can impart to the shot as they push it at an angle from the shoulder. This can be split into kinetic and potential components. The potential component is related to the height of the shot above the shoulder when it is released.

The German pair point out that the equation that determines the final distance depends on the height but also on the velocity squared. So the athlete is better off imparting more energy in kinetic than potential form. And this lowers the optimum angle of release.

Finally, Lenz and Rappl say it has long been known that world records in bench-pressing are significantly higher than for the clean and jerk. This implies that athletes have greater power at their disposal when the angle of release is 0 degrees compared to other angles. This effect also means that a smaller angle of release could send the shot further.

Putting all that together, Lenz and Rappl create a model of shot putting that predicts that the optimum angle of release is between 37 and 38 degrees, which matches almost exactly the measurements from top athletes.

Puzzle solved!

Ref: arxiv.org/abs/1007.3689: The Optimal Angle Of Release In Shot Put