If a is the velocity of the aircraft relative to the air (air velocity), and w is the wind velocity, that is, the velocity of the air relative to the ground, then the velocity of the aircraft relative to the ground is the sum of the two vectors, .
Click on the checkbox to show an example of an airplane flying through the air. Click and or drag on the graph to change the air velocity (a) and/or wind velocity (w). Click "Show Ground Velocity" to show the ground velocity (). Click "Fly" to watch the airplane fly. Notice that the plane does indeed move toward the point in the sky that it is pointing at (the tip of the red vector), even though this point is moving relative to the ground (because of the wind).