Estimating propulsive forces in swimming from three-dimensional kinematic data.

Propulsive forces are important determinants of swimming performance. The aim of this study was to quantify the measurement error (uncertainty) in propulsive forces calculated from kinematic data. Ten operators digitized underwater video recordings of a breaststroke swimmer's right arm action. Four landmarks on the hand were digitized at 50 Hz and their three-dimensional coordinates obtained using a DLT algorithm. Two angles (alpha and psi) defining the orientation of the hand relative to the fluid flow were calculated following the procedures of Schleihauf et al. (1983). The hydrodynamic force acting on the hand (FR) was calculated using the force coefficients of Schleihauf (1979). Errors in single measurements of hand speed, alpha and psi were estimated for each video field analysed. Errors in alpha and psi led to average errors in the lift and drag coefficients of 27 and 20% respectively, which, when combined with an average hand speed error of 6%, produced an average error in FR of 26%. Each of these errors was reduced by a factor of square root 10 when the mean of 10 measurements was used to calculate FR. Researchers should report both the estimated errors in their hydrodynamic data and the procedures used to reduce them.