Validated biomechanical model for efficiency and speed of rowing

Abstract

The speed of a competitive rowing crew depends on the number of crew members, their body mass, sex and the type of rowing-sweep rowing or sculling. The time-averaged speed is proportional to the rower's body mass to the 1/36th power, to the number of crew members to the 1/9th power and to the physiological efficiency (accounted for by the rower's sex) to the 1/3rd power. The quality of the rowing shell and propulsion system is captured by one dimensionless parameter that takes the mechanical efficiency, the shape and drag coefficient of the shell and the Froude propulsion efficiency into account. We derive the biomechanical equation for the speed of rowing by two independent methods and further validate it by successfully predicting race times. We derive the theoretical upper limit of the Froude propulsion efficiency for low viscous flows. This upper limit is shown to be a function solely of the velocity ratio of blade to boat speed (i.e., it is completely independent of the blade shape), a result that may also be of interest for other repetitive propulsion systems.

Keywords: Allometric scaling; Froude propulsion efficiency; Geometric scaling; Kleiber׳s law; Similarity; Speed of rowing; Theoretical upper limit for repetitive motion.