Body mass scaling of projected frontal area in competitive cyclists

Abstract.

The primary purpose of this study was to evaluate the scaling relationship between body mass (m _b) and projected frontal area (A _P) of competitive male cyclists whilst allowing statistically for the influence of bicycle geometry. A group of 21 cyclists [mean m _b 74.4 (SD 7.2) kg, mean height 1.82 (SD 0.06) m, mean age 23.6 (SD 5.1) years] volunteered to have A _p determined from photographs at three trunk angles (TA: 5°, 15°, 25°) for each of three seat-tube angles (STA: 70°, 75°, 80°) using a modified cycle ergometer. Using multiple log-linear regression analysis procedures, the following equation was developed: Body A _p (meters squared)=0.00433×(STA^0.172)×(TA^0.0965)×(m _b ^0.762) (r²=0.73, SEE=0.017 m²) (n=183 images total). This equation indicates that after allowing for the independent influence of STA and TA on A _p, A _p was proportional to m _b raised to the +0.762 power (i.e. A _p∝m _b ^0.762). The 95% confidence interval for this exponent (0.670–0.854) barely included the theoretical two-thirds value but not the +0.55 value for A _p or the +0.32 value for submaximal metabolic power ($\dot W_{\rm s}$ ) of outdoor cycling reported in the literature. Further analysis of wind tunnel data reported in the literature suggests that the coefficient of drag (C _D) is proportional to m _b raised to the –0.45 power. When combined with the present study findings, it is suggested that the drag area (C _D×A _P), which should be proportional to $\dot W_{\rm s}$ at submaximal cycling velocities, is proportional to m _b to the +0.312 power (i.e. C _D×A _p∝(m _b ^–0.45)×(m _b ^+0.762)=m _b ^+0.312), which is consistent with the +0.32 exponent for $\dot W_{\rm s}$ in the literature.