Shoe weight effect on pedaling force?

[DeeCeeMTB]

Cut/Re-posted from general Physics because I only skimmed the FAQ. my bad.

Hi everyone, and thanks so much in advance for any help given. I'm hoping you guys can help me come to a conclusion (and settle a friendly wager) over an applied physics problem. I took general physics and biomechanics in my undergrad but am pretty rusty.
This is not 'homework'. Unfortunately I can't get it off my mind and can't seem to work it out on my own. Time to turn to the experts.

A mountain biking friend and I were discussing cycling footwear recently, and the subject of shoe weight came up.
The pedal/shoe combo in question are 'platform' pedals, and MTB-specific 'flat' shoes...something like Vans. Not the clipless shoes that are cleated and attach to the pedal.

He commented that 'X' shoe was nice but that it was heavy and would make it harder to pedal than wearing a slimmer (lighter) shoe. The difference is a few ounces per shoe. He further proposed that they're also rotational mass the same as wheels and tires and would account for more effect than 'static' weight of the same amount. He was adamant that a lighter shoe was desirable, and that effort to pedal would suffer noticeably.

I disagreed, and contended that in the above scenario that shoes (not formally affixed to the pedal, but worn on the foot) were NOT rotational weight in the same sense as wheels, and additionally, even though they are traveling in a circle, the angular velocity is very slow and the inertia is low.

My feeling, though I can't work out the math, is that any increase in mass of a shoe will contribute to the force on the pedal in an exceedingly minuscule amount, but be totally countered by the opposite shoe 'riding' the pedal upwards on the non-force side. At steady-cadence pedaling, it might actually be infinitesimally easier due to a 'flywheel' effect.
My gut says that if I were wearing lead boots, of course accelerating the pedals would be very difficult, but the difference of even 8 ounces per shoe would be all but undetectable.

So, assuming nothing in the system changes except a small amount of weight per shoe, and disregarding any possible changes in power transfer/force production by shoe construction (e.g. stiffer sole/ankle support) are either of us even close?

BTW, I've lurked here before and you've answered several questions or helped me work it out, so for that I'm thankful and want you all to know it.

 

[NascentOxygen]

While you could allow the powering leg to raise the "idle" leg and its shoe, I think the rider himself contributes to raising the idle leg using its own muscles. So a heavier shoe would afford a slightly greater downward driving force, and the rider would perform a little more work with the idle leg to raise the idle foot's now heavier shoe. The net result: potentially faster, but possibly a little more tiring over time.

 

[yasmin1369]

I got a little confused by this question, i got to say. I mean sure pedaling with a heavier shoe would be more tiring but does it contribute to the force? I mean its trivial to see that if you had no weight on your feet to hold you back, you can go as fast as you can, but if you like, attach 10kg weights to your feet you won't be pedaling as fast because something is taking your extra strength. I just don't understand the question, can you be more specific?

 

[Quantum Defect]

Road racers wear very light shoes because of the reasons raised by NascentOxygen above. Also, mass is mass. If you have it on you, you have to move it up every slight hill that you encounter. Why spend kaboodles of money buying a bike frame made of fantastically-expensive, ultra-light-weight materials only to strap on a pair of heavy clod-hoppers?

In the Tour de France, the guys who wear the polka-dotted jerseys are often the little guys. None of those very tall Dutchmen have ever been the "king of the mountains."
Here are the two most recent winners:
2013: http://en.wikipedia.org/wiki/Nairo_Quintana (58 kg)
2014: http://en.wikipedia.org/wiki/Rafał_Majka (62 kg)