Quote:
Originally Posted by reuben
Well, yeah. You slipped in 2N less air resistance. Now run the numbers with the same resistance.
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You missed the point (perhaps on purpose). The exercise was to show that lighter bikes won't always accelerate faster. If the difference in air resistance was omitted, then you get back to simplistic question of whether lighter bikes perform better, all else being equal, which we all agree was true. That would be true whether the weight difference was rotational or non-rotational.
But if we want to see what happens if there was no difference in air resistance, then maybe we should use a more realistic difference in weight. The 1 kg (2.2 lb) difference in the exercise is a huge difference in wheel weight. When we talk about the differences between "light" and "heavy" wheels, we're usually talking about differences of only 200 grams or so. So let's see what happens in this case.
Because air resistance increases non-linearly with speed, doing the true calculation would require non-linear differential equations. But for simplicity, we can get a ballpark figure by holding the drag constant during the acceleration. The distance traveled D from an intial speed V0 over an amount of time T is:
D = V0*T + (A*T^2)/2
Acceleration is F/M (force over mass), so the equation becomes
D = V0*T + (F/M)*(T^2)/2
Over a 30 second acceleration with the lighter wheels:
D = (9m/s)*(30 s) + (30 N/90 kg) * ( (30 sec)^2)/2 = 420 m
With the heavier wheels over the same 30 second acceleration
D = (9m/s)*(30 s) + (30 N/90.2 kg) * ( (30 sec)^2)/2 = 419.67 m
So, the lighter wheels come out 1/3 m ahead after 30 seconds of acceleration. Given all the other variables that affect bicycle performance, that's pretty small. Other factors will be more important. (Note: The video didn't say changes in rotational inertial will produce no difference at all, it said they will be relatively insignificant).
So, if a rider has a choice between two wheel sets, where one is has less air drag but more rotational inertia, the choice is clear - the aero set will be better in just about all cases (including climbing and accelerations).
Edit: After pondering a bit more, I realize the simplifications in the calculations above exaggerate the difference in distance traveled. In reality, air resistance will increase as the bike speeds up, and pedal force delivered to the road (for a constant power output) will decrease as the bike speeds up, so the actual acceleration rate will decrease as the bicycles go faster. So in this example, the actual difference in distance traveled will be a bit less than 1/3 me.