Equation of motion of a cyclist

Abstract

Tractional resistance (RT, N) was determined by towing two cyclists on a racing bike in "fully dropped" posture in calm air on a flat track at constant speed (5--16.5 m/s). RT increased with the air velocity (v, m/s): RT = 3.2 + 0.19 V2. The constant 3.2 N is interpreted as the rolling resistance and the term increasing with v2 as the air resistance. For a given posture this is a function of the body surface (SA, m2), the air temperature (T, degree K), and barometric pressure (PB, Torr). The mechanical power output (W, W) can then be described as a function of the air (v) and ground (s) speed: W = 4.5.10(-2) Ps + 4.1.10(-2) SA (PB/T)v2 s, where P is the overall weight in kg. With a mechanical efficiency of 0.25, the energy expenditure rate (VO2, ml/s) is given by: VO2 = 8.6.10(-3) Ps + 7.8.10(-3) SA (PB/T)v2 s (1 ml O2 = 20.9 J). As the decrease of VO2max with altitude is known from the literature, this last equation allows the calculation of the optimal altitude for top aerobic performance. The prediction derived from this equation is consistent with the present 1-h world record.