A variable drag coefficient, spatially extended numerical model of hammer throws and new wind tunnel data on current hammers

Abstract

The maximum distance a hammer can be thrown depends on its mass, length and aerodynamic drag, meaning that record hammer throws performed before and after a rule change (for example, if the minimum mass is changed) cannot be compared directly. However, if all factors affecting the flight of a hammer are fully understood, and the range travelled by a hammer thrown with a given initial speed, angle and release height can be predicted, records thrown under different rules can be compared. In this work, a numerical model is developed, which includes the effects of atmospheric pressure, altitude, Coriolis Effect, gravitational variation, wind speed, ambient temperature, linear drag, torsional drag, hammer size and hammer orientation. It is based on the model of Mizera and Horvath (J Biomech 35:785–796, 2002). Two refinements are made: the drag coefficient varies with Reynolds number, and the hammer is represented as a spatially extended object with nonzero moment of inertia. New wind tunnel data on the drag of the three main components of the hammer (ball, cable and handle) are presented. This data are incorporated into the model which is then used to predict throws made at the IAAF 2011 World Athletics Championships (Daegu, Korea). The model is shown to be capable of predicting to within 1 % the distance of hammer throws where the air density, latitude, release height, release angle and release velocity are known. It is more accurate than numeric and analytic models which assume a constant drag coefficient. This may be because it does not require the user to choose the drag coefficient and automatically uses an appropriate drag coefficient regardless of conditions. With a good biomechanical model or good assumptions about release speeds, throws with different implements can be compared to compare records thrown before and after rule changes. Further work is needed to develop a biomechanical model capable of predicting the release speed an athlete can achieve with a range of different implements.