Rolling Resistance

Tyre rolling resistance is the second highest contributor of resistance to motion, and decreases as a function of cycling speed, tyre material, tyre pressure, tyre diameter, tyre width, surface roughness, steering angle, temperature and total load. At 40kph, rolling resistance accounts for 10% of total resistance to forward motion [Atkinson et al., 2003]. Rolling resistance is usually expressed in terms of the coefficient of rolling resistance, Crr, which is equal to the friction force divided by the load on the tyre. Reported values of the

coefficient of tyre rolling resistance vary fromCrr = 0.002for tyres on a smooth, hard surface toCrr = 0.010

for tyres on an uneven, soft surface [Wilson, 2004, p211]. For track cycling the coefficient of rolling resistance will be on the lower end of this scale, as the surface of velodromes used for major competitions is often made from timber, the bikes are lighter than road bikes, and the bicycle tyres are narrower and inflated to a high pressure; an increase in tyre pressure reduces the coefficient of rolling resistance regardless of the size of the wheel [Kyle, 2003a]. Martin et al. [2006] measured the global coefficient of friction on a velodrome, which included tyre and bearing resistance, and found the mean value to beCrr = 0.0025. As expected, this value

was slightly higher than previously reported values for the friction coefficient on a velodrome due to the inclusion of bearing resistance. Most mathematical models generate equations, albeit different, which include a term for the coefficient of rolling resistance, and then use reported values in the literature close to race conditions or valid assumptions from previous tests to determine the coefficient of rolling resistance to validate the models [Martin et al., 1998, Olds et al., 1993, 1995, Candau et al., 1999, Lukes et al., 2006]. Grappe et al. [1997] calculated the rolling resistance for four different positions (upright, dropped, aero, and Obree) from

plots of total resistance, RT, against velocity squared for a cyclist performing trials on a velodrome. The

results showed that the rolling resistance was 2.79N, 1.25N, 2.51N and 1.24N for the upright, dropped, aero and Obree positions respectively, which gave an average coefficient of rolling resistance ofCrr = R_mgT = 0.003.

Groot et al. [1995] obtained data for seven cyclists in the dropped position using coast down tests on a flat, asphalt surface. The deceleration due to rolling resistance,ar, was found to be between0.035< ar<0.040,

and assuming ar = Crrg, the coefficient of rolling resistance found to be between 0.0036< Crr <0.0041.

A summary of values of the coefficient of rolling resistance for low-drag tyres typically used for modelling cycling at an elite level is shown in Table 3.4. Table 3.4 shows that the values for the coefficient of rolling resistance in the literature varies between 0.0016 and 0.00563.

Crr Description

0.0016 - 0.0032 sew-ups on linoleum 0.0023 - 0.0029 clinchers on linoleum

0.0017 track sew-up on concrete 0.0016 - 0.0026 track sew-up

0.0028 Moulton clincher

0.0033 - 0.0037 road sew-up

0.0039 road clincher

0.0039 - 0.0049 road tyres (120psi) 0.0016 - 0.0042 road tyres (120psi)

0.0043 top 700C clincher, 100psi 0.00563 linoleum flooring [Candau et al., 1999]

0.0025 on velodrome (includes bearing resistance) [Martin et al., 2006] 0.0036 - 0.0041 asphalt surface [Groot et al., 1995]

0.003 on velodrome [Grappe et al., 1997] Table 3.4: Values forCrr for low-drag tyres [Wilson, 2004, p230]

Few models take into account the increase in rolling resistance due to the steering angle. This is significant for track cycling as the track is always banked, even on the straights, so the rider must steer in order to keep the bike straight. Kyle [2003a] measured the steering angle of a bike on a 250m velodrome track during constant pedalling at 48kph. The results showed a variation in steering angle by 2.5°with every pedal stroke, and that on the straights a steering angle of 1°was required to keep the bike straight, and on the bends the steering angle increased to 4°. This corresponds to an increase in rolling resistance of 4.1% in the straights and 28.6% in the bends. Wilson [2004, p211] states that a slope of even 0.001 can increase the tyre coefficient of rolling resistance by 10-50% due to scrubbing. Only those models created by Bassett Jr et al. [1999] and Lukes et al. [2006] include a factor for the increase in rolling resistance due to steering, using those results published by Kyle [2003a].

In addition to tyre rolling resistance, bearings also resist forward motion. According to Martin et al. [2007] bearing resistance accounts for only 2-5% of power, but Wilson [2004, p215] states that bearing resistance is negligible compared to 1-3N tyre rolling resistance. Martin et al. [1998] states that the total power lost due to bearing friction can be calculated from Equation 3.9, where V is the velocity (m/s).

Wilson [2004, p214] states that the coefficient of bearing resistance is close to 0.001, and this value can be used to determine an expression for the bearing friction in a similar way to tyre rolling resistance. Bassett Jr et al. [1999] included all losses due to bearing friction in a constant value for dynamic rolling resistance (0.00775W.kg−2_h−2_{) which also included losses due to dynamic tyre deformation and windage of the spinning}

wheel. Although this model allows a correction factor to be applied for different external conditions, it is not possible to change actual values for tyre diameter, pressure etc.