From the aircraft, the ground will appear to move aft at some velocity called the ground speed . Again this is a vector quantity. The air in which the aircraft flys can move in all three directions. In this figure, we are only considering velocities along the aircraft's flight path and we are neglecting cross winds which occur perpendicular to the flight path but parallel to the ground and updrafts and downdrafts which occur perpendicular to the ground. From the aircraft, we can not directly measure the wind speed, but must compute the wind speed from the ground speed and airspeed.
Wind speed is the vector difference between the airspeed and the ground speed.
On a perfectly still day the wind speed is zero and the airspeed is equal to the ground speed. If the measured airspeed is greater than the observed ground speed, the wind speed is positive. Now suppose we had a day in which the wind was blowing 20 mph towards the West. Since a positive velocity is defined to be toward the tail, a headwind will be a positive wind speed. This gives a negative wind speed.