The speed of an aircraft or other airborne object relative to the ground, or a point on the ground. The speed of an aircraft through the air is its airspeed. If the air is absolutely still then ground speed=airspeed (in the direction of the airspeed). If the air is moving, i.e. there is wind, then ground speed of the aircraft will be the vector sum of the aircraft's airspeed and direction of travel plus the air's ground speed and direction of travel.

For example, a plane flying due North at 80 knots in still air will have a ground speed of 80 knots. If there is a 20 knot wind coming from the North then the plane will have a ground speed of 60 knots, even though it is traveling at 80 knots through the air. If the same wind is coming from the South, then the plane will have 100 knots of ground speed. Flying upwind and downwind require only simple addition and subtraction.

If the previously mentioned plane were flying through an area with a wind from the East at 20 knots and kept its nose pointed straight North it would travel North at 80 knots and West at 20 knots, with a ground speed of 82.4 knots since the direction of travel is the hypotenuse of a right triangle
(square root of (80^2)+(20^2))
For winds at other than right angles to the plane's direction of thrust, the wind is resolved into a headwind component and a crosswind component. The headwind will be
airspeed+(windspeed*cos(theta))
where
theta=direction of wind relative to the plane's direction of thrust
and the cross component will be
airspeed+(windspeed*sin(theta))
The overall grounspeed will be the length of the hypotenuse as previously shown.

If the example plane were encountering a 20 knot wind from 45 degrees (NE) it would face a 14.14 knot headwind component
20*cos(135)
yielding 65.86 knot North ground speed, and a 14.14 knot crosswind component
20*sin(135)
yielding 14.14 knots West ground speed. The resultant ground speed would be 67.35 knot and its direction of travel would be 12.1 degrees West of North (347.9 degrees)
sin-1(67.35/14.14)


In order to actually travel directly North in the previously given conditions the plane would have to establish a crab angle, where it was pointed some angle into the wind so that the East component of its thrust equalled the West component of the wind. In this case, the West component of the wind is 14.14 knots, so if the plane flies at 10.18 degrees
sin-1(80/14.14)
then it will have zero East-West drift and will arrive at the airport directly North of its position.

The crabbing airplane will only have a North component of 78.7 knots due to the angle, so its ground speed will be 64.6 knots (78.7 - 14.14).

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