How hot does a bicycle disk get? I’ve been working on heat rejection for auto/truck disk brakes with some success. But the disk temperature needs to reach 700 degrees to be effective. This seems a bit toasty for a bicycle disk. Any thoughts?
To simplify this a bit, I'm going to ignore rolling resistance and aerodynamic drag, so all the work is done by braking. Also, when you brake hard, the front brake does almost all the work, so ignoring the rear brake to simplify the scenario.
Mass of bike + rider = 100kg
Speed = 10 m/s (36km/h, about 22.4mph)
kinetic energy = 0.5 m v^2 = 5000J
A basic 180mm steel brake rotor weighs about 150g and the specific heat of steel is about 0.5 J/gK (Joules per gram-degree), so converting 5kJ of kinetic energy into heat in the rotor should increase the rotor temperature by 67 degrees (C), assuming none of the energy is absorbed by the brake pad, caliper body or brake fluid (not realistic, but useful to identify an upper bound for the rotor).
To maintain constant speed on an even slope, the change in gravitational potential energy must equal the heat energy extracted by braking (plus other sources of friction and drag that we're ignoring).
Descending a 1 in 10 slope for a 100m distance gives a height change of 9.95m (not 10m, because the distance is along the hypotenuse).
Gravity on earth is about 9.8 m/s^2.
Energy change = m g h = 100 * 9.8 * 9.95 = 9751J
This would increase the rotor temperature by 130 degrees.
Heat Dissipation and the limits of my knowledge
The two calculations above don't have a duration because I haven't allowed for heat loss during the event; here are some of the complicating factors:
- The friction creates a film of pad material on the rotor. This film insulates the rotor, but also is necessary for cohesive friction, which generates heat without consuming the pad material, but gives way to destructive friction as pressure increases.
- The heat is generated at two patches on either side of the rotor, not uniformly throughout the rotor material, so as the rotor turns through the contact patch, heat penetrates from the surface to the core of the rotor, then as the rotor leaves the contact patch, the surface is cooled proportionally to the surface-air temperature difference, and once the surface is colder than the core, heat moves from core to surface. Heat is also conducted parallel to the surface, from hotter to colder parts of the core.
- The airflow path length across the rotor is not consistent.
- The airflow around the rotor is turbulent due to the disruption caused by the leading part of the wheel and, for the upper aft part of the rotor, the fork leg and brake caliper.
Modelling heat in rotors is sufficiently complicated that it is a topic used in Engineering project assignments for university students, and the software typically used to perform the calculations is very expensive.
"Experimental and Numerical Thermal Analysis of Formula Student Racing Car Disc Brake Design", Manthan Vidiya1 and Balbir Singh, Manipal Institute of Technology. Published in Journal of Engineering Science and Technology Review 10(1)(2017)138-147
Example model "Heat Generation in a Disc Brake" for COMSOL Multiphysics: