Dammit asked about energy turned into heat, and i gave a slightly trolling answer. The key bits were assuming negligible pedalling, and 'on average'. The average is taken over the whole descent, including the bits where the riders aren't braking...
In more detail:
mass - the MTB is heavier, but both bikes are light compared to their rider, so the difference in total mass is small.
energy - i'm assuming no pedalling, just looking at the gravitational potential energy, so with a bit more mass the MTB has a bit more energy to get rid of, but it's close.
Rolling resistance - the sum of all the non-braking constant forces that resist motion. The MTB has more, but the work done against it is resistance force x distance travelled against it. With the road bike's much longer path length of descent, it's not clear which will loose more energy this way.
Drag force - air resistance and any other forces that go roughly with the square of speed. To calculate the work done against it you can integrate it over the path length of the descent. It will be much larger for the road bike because even though it's more aero, it goes much faster and further.
Brake heat energy - what's left of the starting potential energy after the above have been accounted for. It's clear the MTB will have more.
You're answering a more relevant but slightly different question about how hard the brakes have to work.
I don't have an understanding of physics capable of properly discussing this I guess.
I was working on the assumption that you could ascribe (say) 600W to each rider as the acceleration they gain from going downhill.
The MTB rider is going to put a lot of that into rolling resistance, the suspension, the air resistance of being in a upright position and so forth.
The rider is still going to be hitting 65km/h I would think, for brief periods, but the rider will take much longer (proportionally) than the roadie to get there.
The roadie is going to be more "efficient" in using the 600W to go faster- they'll lose a lot less, essentially.
They're also likely to be adding significant power of their own, especially out of hairpins.
They'll be hitting ~90km/h, frequently.
I suppose, thinking as I write this, that the MTB will quite possibly brake for much more of the descent than the road bike, putting a lot of constant heat into the brakes whereas the road bike will put a much larger amount of heat in, more infrequently.
So I suppose the question is of the two which would exceed the brake systems ability to shed heat before the rider gets to the bottom- i.e. which one goes over the edge when the brake fluid boils.
I don't have an understanding of physics capable of properly discussing this I guess.
I was working on the assumption that you could ascribe (say) 600W to each rider as the acceleration they gain from going downhill.
The MTB rider is going to put a lot of that into rolling resistance, the suspension, the air resistance of being in a upright position and so forth.
The rider is still going to be hitting 65km/h I would think, for brief periods, but the rider will take much longer (proportionally) than the roadie to get there.
The roadie is going to be more "efficient" in using the 600W to go faster- they'll lose a lot less, essentially.
They're also likely to be adding significant power of their own, especially out of hairpins.
They'll be hitting ~90km/h, frequently.
I suppose, thinking as I write this, that the MTB will quite possibly brake for much more of the descent than the road bike, putting a lot of constant heat into the brakes whereas the road bike will put a much larger amount of heat in, more infrequently.
So I suppose the question is of the two which would exceed the brake systems ability to shed heat before the rider gets to the bottom- i.e. which one goes over the edge when the brake fluid boils.