Originally Posted by FBinNY

What everyone here is forgetting is that in the example given of riding 10mph against a 20mph wind is that the total distance covered is 1/3rd what would be ridden if doing 30mph is still air. I tried o give Sreten the clue in my first post (#2). So while the resistance is comparable to 30mph, the work done is one third.

So using 10mph as a base line, and discounting mechanical and tire resistance for the moment) the drag in a 20mph headwind would be 9 times what it would be in still air (3x air speed, squared). But since the distance is only 1/3rd we divide that by 3 and can compare it to 3x drag, and take the square root to convert air drag back to speed and find that riding 10mph against a 20mph wind is comparable to riding 17.3mph in still air.