Originally Posted by
Broctoon
On anything more than a moderately steep descent, your pedaling effort will be wasted. This is because aerodynamic drag (and therefore power required to increase speed) goes up by the square of your speed increase.
Going up a hill, obviously you must pedal to keep moving. It's okay, because at speeds below 10 or 15 mph, air drag is by far the smallest component of the total formula you have to overcome to maintain or increase speed. In other words, your effort is not wasted, because increasing power by 20% will bring an increase in speed of nearly 20%
On flat ground, pedaling is again required, obviously. At speeds of 15 to 20 or 22 mph, air drag starts to take over as the major component. Within this range, any increase in speed will require a progressively greater effort--actually, this is always the case, but in this range it becomes a significant factor.
When you're coasting downhill at 25, 30, 35 mph or higher, you might as well rest and enjoy the free propulsion from gravity (technically, withdrawing potential energy you put in the bank while climbing earlier on your route, or if your descent is at the beginning of the route, going in debt by using energy you haven't banked yet). To increase your speed, you'll have to exert a disproportionately greater effort. Spending any energy here does little to increase speed, therefore it's better saved for a time when it will make a bigger difference.
The one point I'd make here, though, is that if you come over the top of the hill at 10 mph, and then start the descent by spinning up to a decent speed, like 25 or 30, if that's less than your terminal velocity on that hill.