Modelling the effect of curves on distance running performance

Background: On a curve, the average axial leg force (F a ) of a runner is increased due to the need to exert centripetal force. The increased F a presumably requires a greater rate of metabolic energy expenditure than straight running at the same velocity. We propose a model that explains the velocity reduction on curves, compared to straight running, assuming that runners maintain a constant metabolic rate. Methods: We combined published equations to estimate the change in the rate of gross metabolic energy expenditure as a function of F a , where F a depends on curve radius and velocity, with an equation for the gross rate of oxygen uptake as a function of velocity. We compared performances between straight courses and courses with different curve radii and geometries. Results: The differences between our model predictions and the actual indoor world records, are between 0.45 % in 3000 m and 1.78 % in the 1500 m for males, and 0.59 % in the 5000 m and 1.76 % in the 3000 m for females. We estimate thata 2:01:39 marathon on a 400 m track, corresponds to 2:01:32 on a straight path and to 2:02:00 on a 200 m track. Conclusion: Our model predicts that compared to straight racecourses, the increased time due to curves, is notable for smaller curve radii and for faster velocities. But, for larger radii and slower speeds, the time increase is negligible and the general perception of the magnitude of the effects of curves on road racing performance is not supported by our calculations.