You seem to think that simply keeping the brakes constantly applied will always result in a large amount of heat to be generated. Causing the drag braking technique to always out-heat the pulse technique. "Because it never has a chance to cool".
Not necessarily a large amount of heat but more heat than if you didn’t apply the brakes at all…or even intermittently. Yes, continuous braking is
continuously pumping heat into the rims. Pulse braking is pumping heat into the rims intermittently with periods of cooling. The temperature the rim reach with continuous braking is also dependent on the speed you are trying to keep the bike at. The slower the speed, the more braking is needed, the more friction generated, and the higher the rim temperature.
The gap in your science knowledge is in not understanding that the amount of heat is not solely based on brake on vs brake off, but also related to how hard the brake is being applied when it IS on. In middle school or high school physics you should have been taught, assuming your state's curriculum is similar to that of other regions, that frictional force = coefficient of friction x normal force. The important factor here is the normal force. If you keep the normal force very small, the friction force will also be very small. That means the amount of heat generated will be very small.
You don’t have to be insulting. I have a degree in chemistry and it came with a whole bunch of instruction on heat and heat management. I spent 40 years doing bench chemistry including designing reactors. I had to learn how to deal with heat a whole lot so I know how heat works.
Additionally, again, I also have decades of mountain riding including mountain biking, loaded touring, and loaded mountain bike touring. And, because I don’t drag brakes, I have
no experience with over heated-rims and melted brakes. I don’t consider that to be a bad thing.
There isn’t a “gap in [my] science knowledge”. Yes, you’ve stated frictional force before. I’m well aware of it. The part you are missing is the effect of time. Yet again, constant braking results in constant heat being poured into the system. Granted the system isn’t adiabatic so there is heat loss at the same time as heat is being added but while heat is being added not all of it can go away. If no heat is being added…i.e. the brakes aren’t being applied…, the overall effect is cooling of the rim more than if the brakes are being constantly applied. Since the system isn’t adiabatic, the rim also loses heat and, since no heat is being added, the overall loose of heat is greater.
The other factor to consider is that anything you do with constant braking, I can do with pulse braking. I don’t have to brake hard all the time or even that often. Your examples keep suggesting that I would have to slow more for a corner than you would under constant braking. But if you can go around a corner at 35 mph, for example, I can only have to slow to your speed. If I’m going down the hill at 40 mph and have to slow 5 mph, that’s not much of a braking demand. On the other side of the equation, I remove the friction after the corner and take full advantage of the cooling available without heat input. The overall effect is that the pulsed rims stay cooler.
Additionally, how much normal force is need is dependent on the speed you want to maintain. If the normal force is kept small like you maintain, you can’t keep the speed down. The magnitude of the normal force as well as the friction generated, is going to be proportional to the speed. The lower you keep the speed, the higher the normal force and the more friction that is generated. That is why Wilson’s graph shows higher heat generated at lower speed. As the speed approaches terminal velocity, the normal force, and the friction, decrease to the point where the brakes aren’t being applied and the rims have no heat going into them.
Here the question is not "but why would a rider only drag brake by 0.5 mph?" The question is, "what would happen if he simply chooses to do it?" The answer is that the heat put into the rims would be very small, with the graph eventually converging on zero as the normal force is infinitely reduced.
I object less to the argument than to the absurdity of a speed reduction. No one who practices constant braking is doing so to keep the speed down by 0.5mph. In your
Altyn-Tagh example, you use your brakes because you fear letting the bike hit terminal velocity. That means slowing more than 0.5mph…reducing speed that much would make little difference in the event of having to avoid a collision or to reduce the risk of injury in a crash.
It’s a silly argument.
It should be obvious to most people by now that drag vs pulse braking is not the determining factor on how much heat is retained in the rim. You can drag brake in a way that ends with cooler rims, just as you can pulse in a way that ends in cooler rims. The rider's action determines the temperature result, it is not fixed to "drag always hotter no matter what".
Dragging the brakes could only end up with a rim as cool as pulse braking if you use the 0.5mph argument above or if you measured the temperature immediately after the brakes have been pulsed hard for control.
Additionally, if you can drag brake in a way that ends up in cooler rims, why do you need to stop in the middle of a hill to let the rims cool?
I apologize for being sarcastic in my previous post, but until you catch up on this part of basic physics, you're simply not going to understand how this works. Maybe give that book another read. Not sure if this is covered or if he just assumes you already know. Good luck!
Even a cursory reading of my posts would indicate that I know at least a little about physics and heat (which isn’t just in the purview of physics, by the way).
I
have read the book…have you? Wilson
only addresses constant braking. And from the paper I linked to above, his only experience is with constant (and hard) braking on downhills. He does not consider what the effect of intermittent braking would have on the rim temperature.