It's commonly established that the braking power scales with rotor size, and an optimal braking technique is to provide enough force for the rear wheel just to lift up. However, my question is wouldn't that be fundamentally limited by the friction between the ground and the rider? Thus, when would increasing rotor size STOP increasing braking power, and we should focus on widening the tire/use tires with more sliding friction instead?
"wouldn't that be fundamentally limited by the friction between the ground and the rider" - no. The most common limit is the rotational force from the torque generated between the ground/tire and hub center, resulting in the lifting the rear wheel. If this is exceeded, the rider goes over the bars. The requirement for maximum braking is to be able to control the brake so the bike is 'balanced' on the front wheel with no weight on the rear wheel, but the rear wheel still on the ground. This maximizes the torque provided by the rider/bike weight to counter the torque from the tire/hub. As soon as the rear wheel lifts, the torque countering the 'over bars' is reduced, and if braking is not reduced accordingly, over the bars will occur. The braking action 'loads' the front wheel dynamically, meaning frictions forces are increased compared to riding with no brakes. In a straight line, surface has to be surprisingly slippery before traction loss occurs before rear wheel lifts. (Any side force/cornering action changes the dynamics quickly).
Increasing rotor size beyond your theoretical maximum has benefits that it increases fine control of braking forces (all else equal). With this fine control, the rider can have the bike closer to the limits of tire/ground traction and front hub centered rotation without exceeding them. At some point, diminishing returns on braking, with increase weight, cost and risk of disc warping/bending mean a practical maximum rotor size is occurs, currently around 200mm for DH MTB and 140 road.
While other answers are correct in their assessment of peak braking power and its limits, that's not the most significant reason for fitting bigger rotors in many cases. Sustained braking power is a big deal too, for example maintaining control on long descents. Stopping once is comparatively easy.
Bigger rotors can absorb more heat, for several reasons:
- The heat goes into a larger thermal mass, scaling with the radius. Note that this means slower heating, but the heat produced in sustained braking would be enough to do damage if it couldn't be dissipated from the rotor.
- For the same pad size, a bigger rotor has a greater proportion of the surface losing heat, and a smaller proportion being heated. The heat loss is both convective and radiative. Convective dissipation should scale with the area convecting, while radiation is increased in proportion to the area, but reduced significantly by a cooler surface.
- A bigger rotor is moving faster through the air, again increasing convective cooling, in rough proportion to the diameter.
All these interlinked effects mean a segment of rotor is cooler when it comes back round to the pads, reducing pad (and fluid in the case of hydraulics) heating.
This is why light road bikes often have 140mm rotors, but tourers are more likely to have 160mm - they're heavier so need to deal with more energy on the same descent, even if they do the same speed (and in practice braking when heavier means slowing down a bit, braking sooner for bends).
Overall, because heat dissipation reduces as the rotor gets cooler, the returns diminish, but a bigger rotor will always run cooler for the same sustained braking (assuming all other variables are unchanged).
Just as a foundational thing, brakes work by applying a torque to the wheel, which is defined as the applied force multiplied by the distance to the pivot point. The pivot in this case is the wheel hub. The applied force is a function of the braking system (as in the lever, caliper, hose, pads, mounts) and is independent of the rotor size. Hence, as we know, changing the rotor size will proportionally change the braking torque. Since your wheel size is (hopefully) a constant, this braking torque converts back into a linear force at the point of ground contact.
You're right that the limit of friction is indeed when the tire loses grip with the ground. Given a static scenario, this would occur at a certain braking torque (equivalent to linear force at the ground). The question is: how much effort from the cyclist is needed to reach this value? A larger rotor reduces the amount of lever force (and thus rider effort) needed to achieve a given braking torque. Given that we currently aren't supporting robotic answers on this site, your (ostensibly) human hand is only so strong.
Ultimately, the answer to your question lies in whether you define "braking power" as your rate of deceleration/energy loss, or in terms of the hand force multiplicative effect. You're absolutely correct that larger rotors won't necessarily slow you down faster. Tire setup and braking technique might matter more there. However, if you generally aren't braking near the traction limit though (as in, you have untapped braking potential), then larger rotors may help you achieve that. Given a constant lever force, you'll get more braking force at the tire.
Physics says "never" - the larger the rotor the less force you need to stop the wheel. So a rotor the size of the wheel would have the most braking force (ie, require the least hand pressure to stop the wheel)
But, modern brakes can lock a wheel already. Being able to do that with less input-pressure isn't really gaining anything.
Instead the control comes from being able to "modulate" the brake effectively through a range of resistance. A brake that is hard on-or-off is worse than a brake that can gradually apply through a range of input-pressure.
Ultimately, your front brake should be at the limit of almost-locking the front wheel, and your hand should be pushing it just beyond that then backing off subtly, resulting an ABS-like pulsing.
Thus, when would increasing rotor size STOP increasing braking power, and we should focus on widening the tire/use tires with more sliding friction instead?
It's quite rare to be limited by the rotor braking power. It is more a question of comfort and ease: larger rotor lets you brake with less hand gripping force and perhaps control the braking better.
But while other answers are correct that balance limits before friction in typical road conditions, that's not always the case. In snow or muddy conditions, improving friction helps braking - and these are typically the conditions where fatbikes and wide tire MTBs excel.
You can observe what is the limit in a hard braking:
- If your rear wheel lifts up, you are limited by balance. You can improve braking by practicing technique.
- If your front wheel stops spinning and slips on the ground, you are limited by friction. Wider tires or more grippy tire pattern can help.
- If your front wheel keeps spinning but rear wheel doesn't lift, you are limited by brake power. Readjusting your brakes or switching components can help.
The grumpy old man in me is obsessed with the misuse of power in disk brake puffery. Disk brakes are demonstratable less powerful.
As suggested, there is a limit on the amount of torque which can be applied to a bicycle wheel before it either skids or pitches the bike over. Any brake system that can achieve this provides all the braking possible. It is only a question of how much grip is required and how far the lever must be depressed. People are more sensitive to grip than travel, but the combination of the two determines the work needed to stop. I don't know biophysics so do not know the optimum combination, but gripping harder longer will be more fatiguing.
The brake system is a lever pulling a spring (with friction in there too). The lever is absolute. If the lever is 5:1 10 pounds of force at the lever will result in 50 pounds at the pads. The lever travel, however, will be the mechanical advantage x the spring factor. The stiffer the system, the less lever travel required.
A 160mm disk starts off requiring four times the clamping force of a rim brake to achieve the same torque. This can be reduced by using more aggressive fricative materials, but less than half. So, the lever must have more mechanical advantage to produce this torque, but the travel can be reduced by using a stiffer system. The smaller calipers on a disk brake are inherently stiffer. Hydraulics are not only stiffer, but can easily engineer the higher mechanical advantage required, that is difficult to do with a cable. Both these advantages are possible with rim brakes. For example, Mathauser hydraulics or brake boosters. But while each has enthusiast users, neither has become de rigueur. There are other claimed advantages for disk brakes. There is modulation which appears to me to be totally subjective and an interpretation of the longer (and slower) lever travel. That leaves performance in the wet, which I cannot evaluate, but will note that an experienced cyclist will periodically squeegee their rims, and braking is done by sensory feedback, not muscle memory.
Well, I hope I provided enough answer to justify the rant!-)