Sprinting with banked turns.

Bank angle effects can attenuate peak running speed on the order of 10%. Experimental and theoretical results are presented here to quantify this phenomenon over a wide range of bank angles theta b and turn radii R. Experimentally, eleven subjects ran on a 34 m long plywood test track with variable radius and bank angle to sample the (R, theta b) space. From another study, ten subjects are borrowed to examine the theta b = 0 degrees case in greater detail. Various gait parameters were measured from high-speed film, and after parallax correction, compared with the theoretical predictions. The theory is a simple two-parameter constant force model requiring only the effective ankle pulley ratio beta and the runner's top speed vm. A closed-form dimensionless solution is presented for the speed ratio (v/vm) as a function of the radius number (Rg/v2) and the bank angle theta b. Agreement between theory and experiment is limited by experimental scatter. For twenty different subjects and twelve different combinations of R and theta b, the apparent ankle pulley ratio is beta = 0.27 +/- 0.22 based on 128 separate trials. Applications are discussed briefly for the design of indoor and outdoor running tracks. The theory allows a calculation of foot force, bone force, and tendon tension for the general case of arbitrary maximum speed, turn radius and bank angle.