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.

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

“…However, the theoretical parameter 0.33 is based on the assumption that the cyclists are performing in windless conditions, where the cyclists' ground speed 's' is equal to the air speed 'v'. The power expended against aerodynamic resistance, normally expressed as P=k a Av 2 s, can be simplified under still-wind conditions as P=k a Av 3 , where 'k a ' is the form drag coefficient and 'A' the frontal surface area (Di Prampero et al 1979). However, in the presence of a tailwind (t), 'v' is less than 's' and hence the power required to maintain a given speed will either become less, given by P=k a A(sÀt) 2 s, or the speed of a cyclist will increase at a rate greater than that implied by the cuberoot relationship 0.33, possibly approaching the 0.5 value reported in the present article.…”

Optimizing the breakaway position in cycle races using mathematical modelling

“…We take the system parameters to be values we would typically expect in a race [1,3,16], and assume that the solo rider has the same mass as the mean, M . This gives the dimensionless parameters and scaling factors to be m = 1 , F 0 ≈ 0.028 , L ≈ 510 m, and T ≈ 7.2 s. We also take the initial velocity to be v i = 0.16 (corresponding to about 40km/h or 11m/s, a typical cycling speed).…”

Sport Aerodynamics: on the Relevance of Aerodynamic Force Modelling versus Wind Tunnel Testing.

“…However, whether cycling, speed skating, skiing, given optimal physical capabilities, it has been shown that the main parameters that can decreased the race time considerably is the aerodynamic behaviour of the athlete and/or his equipment. Indeed, in cycling, the aerodynamic resistance is shown to be the primary force impeding the forward motion of the cyclist on a flat track (Kyle et al, 1973;Di prampero et al, 1979). At an average speed close to 14 ms -1 , the aerodynamic resistance represents nearly 90% of the total power developed by the cyclist (Belluye & Cid, 2001).…”

“…If C D varies for law speed values (Spring et al, 1988), in most of the sports considered in this chapter, it can be considered as constant (Di Prampero et al, 1979 ;Tavernier et al, 1994). In fact, the athletes never reach the critical speed which cause the fall in C D due to the change from laminar to turbulent regime.…”