What is the difference between an air mile and a ground mile?

Imagine that you are a balloon floating around in the air.

Lets say the wind is blowing at 100 miles per hour and you are floating along with the wind.

In this case you will not be travelling any air miles but you will be covering plenty of ground miles.

Because you are not moving through the air.

On the other hand if you are sitting in an airplane that is traveling 100 miles per hour and the wind is blowing at 100 miles per hour. And you are traveling straigh against the wind. Then you will be not be moving from your location and will basically be hovering in place above the spot that you are flying. However you are covering 100 miles of air per hour because you are moving through the air. {1} If TAS + Wd <> 0, AD = (GD x TAS) / (TAS + Wd) {2} If TAS + Wd = 0, AD = infinite AD = Air distance GD = Ground Distance TAS = True Air Speed Wd = Headwind/Tailwind component velocity. >0 if tail wind, <0 if headwind Ground Speed (GS) is equal to TAS+Wd Given a GD to travel: In case (2), GS=0, AD is infinite and you will never get to your destination. If TAS + Wd <0, GS <0 (you go backwards) and you will never get to your destination. In these two cases there is no point in computing air distance.