Why do I push more watts while climbing? - http://forum.slowtwitch.com/forum/Slowtwitch_Forums_C1/Triathlon_Forum_F1/Why_do_I_push_more_watts_while_climbing__P3839309-2

Question from non physicist-friend: 
I've noticed that I can produce 350 plus watts for 15 min at 12 mph on a big climb but only 325 on the flats at 25mph for the same time period. What is it that limits my output on the flats? Is it the added work due to wind resistance being cubed? Has me thinking.... 

Physicist/ crazy fast cyclist friend: 


That’s a great question. I don’t think there is a simple mechanical explanation. Here is one possible idea. When I am mostly working against gravity an increase in Watts of 10% (say from 300 to 330) delivers an increase in speed of 10% (12 to 13.2 mph). That is a fairly noticeable change. By contrast, when I am mostly working against air resistance a 10% increase in wattage delivers only a 3.33% increase in speed (25 to 25.8 mph). This is because of the cubed dependence that you mention. 

A related issue is response time. When I make a sudden increase in power the kinetic energy begins to rise at an initial rate equal to the increase in power. The rate of change in speed corresponding to a given rate of change in kinetic energy is inversely proportional to the speed. This means that for the same increase in power the speed begins rising twice as quickly when the speed is half as much. As a percentage of the current speed the rising rate is 4 times as large at half the speed. 

So… when climbing an increase in power results in a change in speed that is both greater (especially as a percentage of current speed) and much quicker. A decrease in power also results in a much more noticeable change in speed. In short, the biofeedback from power to bicycle motion is much tighter at lower speeds.