Enter the wind speed, true airspeed, and wind angle (relative to the aircraft heading) into the calculator to determine the ground speed of an aircraft.
Ground Speed Formula
The following formula is used to calculate ground speed (speed over the ground) by treating wind as a vector.
V_g = \sqrt{V_{TAS}^2 + W^2 + 2V_{TAS}W\cos(\theta)}- Where Vg is the ground speed (magnitude of the aircraft’s horizontal speed over the Earth)
- VTAS is the true airspeed (airspeed relative to the surrounding air)
- W is the wind speed
- θ is the angle between the aircraft heading (direction of travel through the air) and the wind direction (direction the wind is blowing toward): 0° = tailwind, 180° = headwind, 90° = crosswind
To calculate ground speed, add the wind velocity vector to the true-airspeed vector and take the magnitude of the result. (If the aircraft is climbing/descending significantly, use the horizontal component of true airspeed in place of VTAS.)
Ground Speed Definition
What is ground speed? Ground speed is the magnitude of the horizontal component of an aircraft’s velocity relative to the Earth's surface (i.e., speed over the ground).
Example Problem
How to calculate ground speed?
- First, determine the wind angle.
Measure/estimate the wind angle relative to the aircraft heading. For this example, the wind angle is 45°.
- Next, determine the true airspeed.
For this problem, the true airspeed (TAS) is 100 m/s.
- Next, determine the wind speed.
The wind speed is 5 m/s.
- Finally, calculate the ground speed.
Using the formula above, the ground speed is found to be Vg = √(100^2 + 5^2 + 2·100·5·cos(45°)) = 103.5968 m/s.
FAQ
Is ground speed faster than airspeed? Ground speed can be faster than true airspeed when there is a tailwind, and it can be slower than true airspeed when there is a headwind.
Can ground speed be negative? Ground speed is normally reported as a non-negative magnitude. However, the along-track component of ground velocity (relative to a chosen direction) can be negative if the headwind component exceeds the aircraft’s airspeed component, meaning the aircraft is moving backward relative to the ground in that direction.
Does ground speed increase with altitude? Not necessarily. Ground speed depends on true airspeed and wind. True airspeed may increase with altitude if you hold indicated airspeed (or lift/angle of attack) roughly constant, but it will not automatically increase in all cases. Winds also vary with altitude and can increase or decrease, so ground speed can rise, fall, or stay similar as altitude changes.
