I was looking at Steve Gribble's Cycling Calculator , and I noticed that the aero resistance was higher going 40 mph with a 20 mph tail wind than going 20 mph with no tail wind. Why is this? I always thought they should be the same.
Think about the spokes: when you're going 40 mph, the spokes near the tops of the wheels are moving at 80 mph, so moving through the air at 60 mph. Meanwhile, when you're going 20 mph in still air, the spokes near the top of the wheel are only moving through the air at 40 mph. It is true that in the case with a tail wind, the air actually puts a forward force on the spokes near the ground, but it does not fully cancel the extra drag from the the spokes near the top--drag increases faster than linearly with speed.
The drivetrain loss and rolling resistance depend on your speed relative to the ground, and are higher at 40 mph than at 20.
In the calculator, if you set the drivetrain loss and the coefficient of rolling resistance to 0, and a tailwind of 20 mph, you will see that it does calculate that zero power required for a velocity of 20 mph. For velocities less than 20 mph you need to use your brakes, since the wind force is trying to make you go faster not slower.