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I've considered this a bit intuitively, but I'm not sure how to model it mathematically.

A thought:

1. It seems that if your bicycle is really efficient (here I just mean that it doesn't lose much energy to friction), hills might be easier. You could theoretically spend only one meter going forward, gain a little elevation, and then coast down for the remaining 10 km without using any energy. But if your bicycle is that efficient, then I guess you would also be able to go forward a long ways using little energy on flat ground.

Intuitively, I have a feeling that the same amount of energy should be expended on a flat course as on a hilly one. But I don't know how to justify it mathematically. Thoughts?