The aim of this study was to determine if it is possible to measure braking power in bicycle disc brakes in field conditions. A device was developed to calculate brake power by measuring torque and angular velocity as the brake pads interacted with the brake rotors of each brake on a mountain bike. It was hypothesised that total energy removed from the bicycle-rider system would be equal to the change in kinetic energy of the bicycle-rider system given Equation 5.3. The main findings show that torque and angular velocity sensors on disc brakes of a bicycle are valid means of calculating brake power on road and dirt surfaces.
In this study, the majority of braking events were completed on a flat, tar-sealed road, which was chosen due to the predictability of the riding surface. The flat terrain was chosen because it allowed the calculation of energy losses without needing to account for changes in potential energy due to undulating elevation. While the present study did not account for energy losses outside of estimates of rolling resistance (Equation 5.4) and aerodynamic drag (Equation 5.5) such as sound, work of fracture associated with damage to the tyres or surface, or displacement of the surface in the off road test (among other factors), we were able to explain a large portion of the energy lost while riding the bicycle (Bertucci et al. 2013). Estimating these energy losses and adding them to measurements of brake work demonstrated a strong linear relationship (Figure 5.3A) with the change in kinetic energy of the bicycle-rider system during the 348 braking events completed on the tar-sealed road. A similar significant relationship was determined for 60 braking
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events on the dirt path (Figure 5.3B). These correlations highlighted the goodness of fit for energy calculations on both surfaces, whereby braking events had linearly increasing estimates of energy loss and change in kinetic energy.
The slopes of regression analyses were 1.01 and 1.06 for the dirt path and tar-sealed road, respectively (Figure 5.3A-B), which supported strong linearity of energy loss equations. However, the y-intercepts varied according to the surface ridden, which may be indicative of error from energy loss estimations. The positive sign of the y-intercept on the tar-sealed road (35.94) indicates that the total energy removed is being overestimated, while the negative sign for dirt road trials (y-intercept=-22.67) indicates that the total energy removed is underestimated. These errors may have been introduced through the calculation of rolling resistance (Equation 5.4), which assumes that energy lost does not change with respect to velocity nor account for the different surfaces. Similarly, it is possible that error may have been introduced to the change in kinetic energy (Equation 5.7) given the calculation of the moment of inertia (Equation 5.8), which could not account for the dynamic distribution of the mass of the spokes, rim, tube and tyre.
Despite the potential errors introduced by estimates of rolling resistance and the moment of inertia, the strong linear relationships between energy calculations were corroborated by t-test results that highlighted no difference between total energy and the change in kinetic energy on the tar-sealed road. Therefore, these results indicate the validity of brake work calculations from brake power during 348 on-road braking events. Similarly, t-test
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results indicated no difference between energy loss calculations on the 60 dirt path braking events. While there was a greater mean of differences between values on the dirt path (2.46%) than on the tar-sealed road (0.23%), this may be attributable to energy lost from additional tire deformation on the uneven surface and movement of the dirt underneath the tyres, though this was not specifically investigated in the present study. Nevertheless, brake power measurement appears robust in the field given these results.
For brake power measurement to be easily adopted in cycling, it is important to display this type of information in a manner that is easily adaptable to other cycling analyses. Figure 5.4 and 5.5 (A-F) demonstrate the readings of torque, angular velocity and brake power in one braking event. In these figures, brake work was done in a relatively short period of time, yet highlights the extent to which even a small braking event can reduce velocity. With brake power readings presented graphically as in Figure 5.4 and 5.5 (E-F), the viewer is shown braking data in a similar manner as readings of propulsive power in cycling analysis software (e.g. TrainingPeaks) and practitioner publications (Allen & Coggan, 2010), which could prove to be useful in future research.
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Figure 5.4. Braking example using both front and rear brakes highlighting
measurements of brake torque (A-B), angular velocity of the brake rotor (C-D) and resultant brake power (E-F). Initial velocity was 3.7 m/s slowing a combined mass of 79.2 kg (rider plus cycling gear and bicycle) to 2.6 m/s. Sample duration was 0.9 s with a total brake work of 231 J. Mean brake power was 166 and 106 W for the front and rear brakes, respectively.
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Figure 5.5. Braking example using front brake only. Mean power was 105 and 6 W for the front and rear brakes, respectively. Sample duration was 2.9 s with a total brake work of 322.0 J. Initial velocity was 3.63 m/slowing a 79.2 kg mass to 1.7 m/s with subsequent ∆EK estimated at 316.8 J.
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All braking events in this study were completed between 0.5 and 10.3 m/s (1.8 to 37.1 km/h), which supports brake power measurements within a moderate range of cycling speeds. In the context of racing speeds, the fastest athletes at XCO-MTB races have recorded average speeds of 21.4 km/h (Abbiss et al. 2013), though downhill riders travel considerably faster (Hurst et al. 2013). The present study did not investigate braking measurements above 37.1 km/h, and despite the strong validity of measurements presented, warrants investigation into the validity of braking variable measurements at higher speeds. A limitation to the present study is the high mass of the devices used to calculate and record brake power, which may affect speed. In building the device, the magnitude of values that would be seen during field riding was not well understood. As such, the device was overbuilt, and increased the total mass of the bicycle to over 17 kg, which is substantially heavier than many racing bicycles. While the current device is therefore not ecologically valid for competitive use, this configuration will allow the quantification of braking data during simulated racing, which remains unexplored.
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