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Good answer, thorpie. For biking, muscles are probably most efficient at a low power level, like about 1/4 horsepower or less. I'm pretty sure that it is more efficient to keep putting out 1/4 horsepower than to make 1/2 HP half the time and rest the other half of the time. Also, you don't get twice the speed when you double the power, you only get about 1.26 (the cube root of 2) times the speed, since the vast majority of the power is used to overcome wind resistance. Doubling the speed requires 8 times the power (2 cubed). If I remember correctly, you can go about 20 MPH on a level road when using 1/4 HP on a good ten speed bike.
My strategy for biking is to just go at the highest comfortable speed on level roads. I coast down most hills without pedaling and when I have to climb a hill I use a little extra effort, since extra power on a hill will significantly improve the average speed.
Glee17, you remind me of some of my biking when I was a kid. The steepest hill I rode was Tyringham mountain road heading north from Monterey. I had a speedometer on my bike and I'm pretty sure I exceeded 40 MPH pedaling down that hill. I had to pedal really fast even in the highest gear of my ten speed bike. The water would run out from the corners of my eyes. There was a bump in the road that caused me to take a little jump. Then at at the bottom of the hill there was a fairly sharp right turn. I would sit straight up before the turn to catch some air and slow down before the turn.
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