If this isn't clear enough for you:

Then I think it's pretty clear where the issue is.

If it's the math that's too complicated for you, well, then there's help for that, too.
If this isn't

In your example (small accelerations with each pedal stroke), the frequency of deceleration is the same as the frequency of acceleration.

The flywheel analogy is fine.

Perhaps, but the bike is accelerating, which is the important, not the coasting.

A bicycle wheel is not a flywheel by any definition; it is not designed as such, does not maintain uniform speed, and is isolated, except in the case of a fixie, from performing as such, by the freewheel. I can go to any dictionary and pull the definition of 'flywheel' and it does not describe a bicycle wheel.

No one in this discussion is talking about coasting besides you.

What we are talking about is the slight variation in speed as you go through a complete pedal revolution. When you're pushing down hard on one of the pedals the bike accelerates slightly. OTOH, when the pedals are at the top&bottom of their rotation you can't apply as much force and the bike decelerates slightly. With light wheels there will be a little more of this periodic variation in speed whereas with heavier wheels the variation will be reduced due to the 'flywheel effect' of the heavy wheels having more angular momentum and maintaining the speed of the bike better during the period that you don't apply quite as much pedal force. Note that while undergoing this periodic acceleration/deceleration cycle while pedaling, the freewheel or freehub mechanism never comes into this since at no point do you let up completely on the pedal force and therefore the ratchet inside those devices never clicks.

How are you calculating this 'little periodic variation in speed' ?

There are lots of calculators for impact of weight on energy expenditure, to which I can provide links, if you're interested.

Anecdotally, this test, if you haven't seen it, is interesting (if not definitive): http://www.training4cyclists.com/how...on-alpe-dhuez/

Similarly, though not addressing inertial weight explicitly: http://middleagecyclist.blogspot.com...ers-study.html

Yes,the extra weight on wheels will increase more drag force,especially on the mountain road.However the bigger tire can load more weight.:lol:

This one is actually interesting.

They put water (1.8 L = 1.8 kg = 4 lbs) in the tires or on the bike (or no where) and climbed Alpe D'Huez.

You see a 1.3% difference between having the water in the wheels than just on the bike. If you take the different power for the run into account, the difference drops to 0.6% (or so).

This is similar to what I suggested by putting weight on the spokes, except that

(1) I wonder how much the water affects rolling resistance (I'm assuming the pumped the tires up to the same pressure) and

(2) since there is air in the tire as well, then the water is sloshing to some degree. I wonder what affect that had.

They didn't state how much the rider and the bike weighed. But given that they added 4 lbs and saw such a minimal difference (call it 1.3% if you don't like the 0.6%), this anecdotal evidence, I think this shows the magnitude of the problem of "heavy tires" (and I'm willing to bet that the combination of this rider and his bike are lighter than probably any of us having this discussion).

This one, not so much. They didn't make sure they had the same tires on both bikes (we know rolling resistance makes a big difference), nor make sure they had the same aerodynamic profile (depending on rider speed, this could be pretty much the biggest difference we're going to see).

There's no coasting.

A flywheel is an energy storage device; in this scenario, the bicycle wheel is storing energy. That energy is not being released to the drive train, but it does go back into the system.

Do an energy balance over one pedal cycle. If the speed of the bike is the same at the start and end, then there is no net change in kinetic energy. When the cyclist puts in energy, the energy is either lost (eg, to wind) or converted to potential energy. The minor variations in speed over on cycle are negligible in terms of energy lost; therefore, regardless of the location of the mass (wheels or bike), the increase in potential energy is the same; therefore the speed is the same.

Interesting in that almost the entire difference (well within the experimental error, I'd guess) between weight in the wheels and weight on the bike is explained by variations in applied power.

Doesn't look like it helps your case much. Comparing the two runs with the same total weight but one having it on the bike and the other with the weight in the tires they observed a difference of 27 sec. out of a total time of about 52 min. or 0.9%. But the run with the weight in the tires also had a lower average power input (275 W vs. 277 W), which amounts to a difference of 0.7%. Those two figures (.7% and .9%) are within the bounds of accuracy of the reported results, so the experiment is entirely consistent with the claim that during a continuous climb there is no difference in the speed whether added weight is in the rotating tires&wheels on in the fixed components of the bike and rider. [I'd also note that rotating weight would have a minor extra effect during the initial acceleration at the start of the climb, and I agree with cplager's concern that putting water inside the tire may affect rolling resistance.]

Also interesting comparing the normal bike to one with reduced tire pressure (runs 3 and 4). The run with reduced pressure (only 3 bar) was slower by 58 sec. or 1.9%, but this run was done with even lower average power, 273 W vs. 278, or 1.8% less. So the reduced pressure appears to also not affect the speed under these conditions.