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Take the case where you have two identical riders, Joe Slo and Billy Whizz. They both weigh 75kg and have identical aerobic threshold power output.

Joe has a 11kg steel audax bike, but Billy likes shiny gear so bought the latest Emonda weighing 5kg.

Physics based calculators (e.g. http://www.analyticcycling.com/ForcesLessWeight_Page.html or http://bikecalculator.com) put Billy about 50m head of Joe after 1km cycling up a 1km hill averaging 5% gradient.

That doesn't sound like much, and not worth spending $5k on.

However, during a hilly sportive the pair will ride 160km including 20km at gradients over 5%, and these are spaced evenly throughout the ride.

Let's assume Billy makes an effort and rides the hills at his aerobic threshold, which is 300watts, and they therefore ride at 20.2kph (http://bikecalculator.com). Joe has to ride at 316watts to keep up (so ~5% above his threshold). That doesn't sound like as much fun.

What would the likely effect on recovery be for the last part of the ride? Does chasing those few additional watts on each climb have a non-additive impact on performance in the final 20km, for example?

I guess my question is, even though Billy would wait for Joe at the top of each hill, does the additional effort required to keep up make this a sufferfest for Joe?

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    It needs to be noted that Joe's "aerobic threshold" may be 300 watts one day and 325 the next. The experiment you propose is not reproducible in real life. – Daniel R Hicks Apr 11 '16 at 17:33
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The physics model of cycling power and speed has been validated in the real world. Two examples are this and this. The model embedded in Analyticcyling.com's online calculator is based on these two papers.

Whether the amount of difference calculated by the validated models is worth it to Joe and Billy is a question that can't be answered by the physics.

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This largely depends on rider goals and finances. Your example clearly highlights the advantage of a light bike (although aero is probably equally important). If Joe and Billy are racing, and they are exactly the same, we can assume Billy is going to win. If Joe can afford it, and wants to stay competitive with Billy, it will likely be worth it for him. If Joe and Billy are non-competitive and just riding for fun, Billy likely isn't going to ride at a high level to make it a sufferfest for Joe (unless Joe is into that sort of thing).

You may also be missing the fact that Billy is recovering (a bit) while waiting. Whether or not this is a "sufferfest" for Joe is sort of irrelevant. Joe may enjoy training pain. Regardless, because of equipment, Joe has a lower level of upper performance than Billy.

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