Originally Posted by
logdrum
The engine of the bike the human body and the mind behind it is a very dynamic system. It's not simply PE and KE physics. Also ascent can be a collection of rise and falls or one great rise and fall AND that one great fall is laid out with lateral elements to it: curves and switchbacks. So will a winding flat course be the same as straight as an arrow course?
Even average power, that is not even a good enough metric. So that is why Coogan and company came up with metrics like IF and TSS. (Intensity Factor and Training Test Scores) and you see why umd makes a big deal out of this when he reports his rides. And everything means nothing unless you graph it over time. You need to trend your own or within a group riding the same roads to come up with generalization what a terrain might do to the speed and power output of cycling entities.
umd would have said FAIL way way back. Again: Average speed does not matter.
Introducing curves is just obfuscating. It doesn't matter whether we're talking about a bike and the human body or an engine, or any other system imaginable, it's less than 100% efficient. And, if it's the same distance and the same power can be applied throughout, yes, a winding flat course is the same as a straight as an arrow course.
This next paragraph is a complete non sequitor. We've made assumptions of constant power for simplicity's sake. If you don't you have entirely too many variables to reach any reasonable conclusion.
Originally Posted by
Pedaleur
This is not exactly true. Any inefficiency whose power loss is proportional to speed (eg, the magical wind in plantrob's bizzarro universe), doesn't count against you. It takes something higher than linear loss.
This is why air resistance, with its cubic power loss, is the fundamental reason hills slow you down. (And braking for corners, and all the other real world things.)
Simply saying the average of 10 and 20 is not 15 begs the question, because even a high-school analysis shows that going downhill speeds you up more than going uphill slows you down.
I don't know what you're trying to say here at all, but even if you neglect air resistance (already putting us in an alternate universe) hills will take longer because friction is proportional to speed, and we've established that the change in speed is greater descending than ascending. Again, that real world less than 100% efficiency applies.
Originally Posted by
plantrob
Pedaleur gets it, and I concede that I should have included the point I made in post 57 in my original post 54. Not that I think it would have avoided the rotten-tomato-pitching that ensued
No, you wouldn't have, because nothing else you typed in post 54 made sense.
Originally Posted by
plantrob
Interestingly, I think I'm the only one in this thread who has conceded a point
That might have something to do with you being the only person in this thread who's been completely, totally wrong.