An angular velocity profile in cycling derived from mechanical energy analysis

The contributions of this article are twofold. One is procedure for determining the angular velocity profile in seated cycling that maintains the total mechanical energy of both legs constant. A five-bar linkage model (thigh, shank, foot, crank and frame) of seated (fixed hip) cycling served for the derivation of the equations to compute potential and kinetic energies of the leg segments over a complete crank cycle. With experimentally collected pedal angle data as input, these equations were used to compute the total combined mechanical energy (sum of potential and kinetic energies of the segments of both legs) for constant angular velocity pedalling at 90 rpm. Total energy varied indicating the presence of internal work. Motivated by a desire to test the hypothesis that reducing internal work in cycling will reduce energy expenditure, a procedure was developed for determining the angular velocity profile that eliminated any change in total energy. Using data recorded from five subjects, this procedure was used to determine a reference profile for an average equivalent cadence of 90 rpm. The phase of this profile is such that highest and lowest angular velocities occur when the cranks are near vertical and horizontal respectively. The second contribution is the testing of the hypothesis that the reference angular velocity profile serves to effectively reduce internal work for the subjects whose data were used to develop this profile over the range of pedalling rates (80-100 rpm) naturally preferred. In this range, the internal work was decreased a minimum of 48% relative to the internal work associated with constant angular velocity pedalling. The acceptance of this hypothesis has relevance to the protocol for future experiments which explore the effect of reduced internal work on energy expenditure in cycling.