Optimal power-to-mass ratios when predicting flat and hill-climbing time-trial cycling

The purpose of this article was to establish whether previously reported oxygen-to-mass ratios, used to predict flat and hill-climbing cycling performance, extend to similar power-to-mass ratios incorporating other, often quick and convenient measures of power output recorded in the laboratory [maximum aerobic power (W_MAP), power output at ventilatory threshold (W_VT) and average power output (W_AVG) maintained during a 1 h performance test]. A proportional allometric model was used to predict the optimal power-to-mass ratios associated with cycling speeds during flat and hill-climbing cycling. The optimal models predicting flat time-trial cycling speeds were found to be (W_MAPm^-0.48) ^0.54, (W_VTm^-0.48)^0.46 and (W_AVGm^-0.34)^0.58 that explained 69.3, 59.1 and 96.3% of the variance in cycling speeds, respectively. Cross-validation results suggest that, in conjunction with body mass, W_MAP can provide an accurate and independent prediction of time-trial cycling, explaining 94.6% of the variance in cycling speeds with the standard deviation about the regression line, s = 0.686 km h^-1. Based on these models, there is evidence to support that previously reported V̇O-to-mass ratios associated with flat cycling speed extend to other laboratory-recorded measures of power output (i.e. Wm^-0.32). However, the power-function exponents (0.54, 0.46 and 0.58) would appear to conflict with the assumption that the cyclists' speeds should be proportional to the cube root (0.33) of power demand/expended, a finding that could be explained by other confounding variables such as bicycle geometry, tractional resistance and/or the presence of a tailwind. The models predicting 6 and 12% hill-climbing cycling speeds were found to be proportional to (W_MAPm^-0.91)^0.66, revealing a mass exponent, 0.91, that also supports previous research.