Originally Posted by
prathmann
The energy required to move something against a resisting force is equal to the size of the force times the distance that the object is moved. The simplest example is lifting a weight - say you lift a 10 lb weight up a 100' cliff. The energy required is then 1000 ft-lbs. Similarly, the energy required to overcome air resistance would be the drag force due to the air times the distance you are moving against that force. Power is energy per unit time, so the power needed is the drag force times the distance traveled divided by the time. But distance divided by time is just your ground speed. So the power is the drag force times your ground speed.
And yes, greg is correct the speed should have been 20.8 mph w/o wind as equivalent to 10 mph into a 20 mph headwind. (I was looking at 20 mph into a 10 mph wind.)
It seems most things have been covered by the excellent analysis of prathmann. I can think of one more thing. An exact head- or tailwind is unlikely. As soon as the wind is coming from the side, you are losing speed by lateral turbulence.
I once read a study that compared speeds on a closed loop trajectory on windy and windless days and the conclusion was that no wind is always better for the average speed, which bears out what you seem to have noticed.