It's a great analogy. You just didn't get it, I'm sorry. The same way you're not getting how it works with the rims. I tried to make it easier to understand but it didn't help.
There is no need for an analogy when you have a real world example. Your analogy isn’t easier to understand because it is wrong.
"With pulse braking, the same amount of heat put into the rim..."
Wrong. With pulse braking, it's NOT the same amount of heat being put into the rim. You are squeezing the brake lever WAY harder during pulse braking, compared to someone drag braking.
Your examples have been predicated on the idea that the conversion of kinetic energy of the bicycle/rider system is the same in pulse braking and in continual braking (drag braking). So have mine. Yes, someone practicing pulse braking squeezes the brakes WAY harder during the braking phase but they are not squeezing the brakes at all when the brakes aren’t applied. During the time when no braking is being done, the heat input is negative. If both bikes travel the same distance to the same final speed (stopped or some other speed), the conversion of the kinetic energy is the same. The one caveat is that with pulse braking, the time of travel is likely shorter due to the higher average speed and the air flow is higher due to that higher average speed so more heat is lost in pulse braking.
When you pulse brake you squeeze the brake HARD but leave gaps in time. Someone else who is drag braking leaves no gaps in time, but they are LIGHT on the brakes.
Hard braking force = more friction = more heat per second put into the rims (but with gaps in time)
Light braking force = less friction = less heat per second put into the rims (but with no gaps in time)
It balances out, you see? Why is this simple concept so difficult to understand?
You are so close to getting it. It is the gaps in time during pulse braking that you aren’t understanding. During those gaps, the heat input is negative. More friction with periods of no friction results in a higher heat transfer
away from the rims than if you have constant friction at a slightly lower friction input. It’s the higher negative bits that changes the balance. You have the same heat input but you have a higher heat
outflow with pulsed braking.
You're pulse braking alternating between 25 and 40 mph. Every time you need to slow down you give your brakes a firm application. A large burst of heat enters your rims. Then you're off your brakes for a while. You repeat the cycle while always keeping your max heat under a limit. Ok.
You can’t definitively say what speeds pulse braking is alternating between. That depends on how much speed you are willing to carry through corners or how much you are slowing down. Some corners are may need to slow that much but some may not.
And, again, you are missing how much impact the “off [the] brakes for a while” has. Yes, you repeat the cycle while keeping the heat from building in the rim too much.
Someone else is drag braking maintains a constant 35 mph. They're not squeezing their lever the same way you're squeezing your lever. They're only slowing themselves by 5 mph compared to natural speed. They have a casual one finger lean on that brake lever. They are NOT gushing heat into their rims like you are during one of your pulses. Whatever small feathering amount of heat they generate continuously, that heat dissipates in the 35 mph wind. They ALSO keep their max heat under a limit.
If someone is traveling at 35 mph and they only have to slow to 30mph to go around a corner, why does the rider at 40 mph have to slow to 25mm? Why can’t they take the same corner at the same speed as the 35mph scenario? If you can corner at 30mph, I could corner at the same speed, thus the heat input on at higher speed isn’t much different.
But you are wrong on the 35mph scenario keeping their heat “under a limit”. That’s the point. The heat dissipates some but not nearly as much as during pulse braking for two reasons. The first is that the airflow is higher so the heat lost at higher speeds is greater. Second, there are periods when there is no heat going into the rim while at the same time heat is being lost. In the end, the pulse braking ends up losing more heat without putting in a whole lot more heat than constant braking.
I got it before. You are just wrong on your assumptions.
Yes, pro cyclists don't overheat because they only use their brakes momentarily.
In other words, they practice “pulse braking”.
If you add up the amount of seconds they brake on an entire descent, you'll realize that summed up, they didn't really use their brakes much. That's EXACTLY my point! Pro cyclists don't use their brakes. So OF COURSE they won't over heat! Their gravitational potential energy dissipates into the air, not their brakes.
Um…same thing occurs during pulse braking. Higher speed, some air resistance braking, shorter periods of brake application, more time for the rims to cool. If you don’t use your brakes, you aren’t putting heat into the system. If you use your brakes constantly, you aren’t allowing heat to dissipate away at the same rate and thus end up with hotter wheels.
Again, I do mountain riding. I do mountain bike riding with rim brakes. I’ve done mountain riding on tandems with rim brakes. I have never…in 40+ years of mountain riding…cooked a rim brake. I’ve never even come close. I’m unfamiliar with the sound change you describe because I’ve never experienced brakes hot enough to make that sound. It’s not because I don’t go down hills…I do at that highest possible speed I can…but because I know how to manage the heat input to avoid cooking brakes.