# Ground Speed Calculator

Created by Davide Borchia
Last updated: Aug 06, 2022

Measuring the speed of a plane is not as easy as measuring the one of a car: our ground speed calculator will explain to you how to find how fast an aircraft travels, the quantities involved in the calculations, and much more.

• What is the ground speed of an airplane;
• The difference between true airspeed and ground speed of a plane;
• How to calculate the ground speed of an aircraft;
• How a jumbo jet broke the sound barrier without breaking the sound barrier.

While in the air, the Earth curvature calculator can help you determine the distance to the horizon and how much an object is obscured. It's certainly worth trying it!

## What is the ground speed of an airplane?

When flying on a plane, you can identify different characteristic speeds.

The true airspeed is the plane's speed with reference to the surrounding air mass. You can measure it on board the plane using simple instruments called Pitot tubes: they are the tiny straws poking out of the aircraft's nose. The airspeed, however, doesn't factor in the wind speed: a tailwind (wind blowing in the direction of travel) adds to the airspeed, while a headwind subtracts, slowing you down.

The airspeed doesn't always give you information about the airplane's speed along its route — i.e., the time needed to reach your destination. The relevant quantity, in this case, is the ground speed. By calculating the plane's speed relative to the ground level on a known route, we can easily estimate the time necessary to reach your destination.

🙋 Rockets have an extremely high airspeed when climbing in the first phases of the launch while at the same time maintaining a relatively small ground speed. This is common to every quick climb.

To calculate the ground speed from the true airspeed, we need a simple formula. Let's check it out!

## How to calculate the ground speed of a plane

Calculating the ground speed of a plane requires you to know a set of quantities associated with the aircraft's motion and the wind. Let's first check the formula for the ground speed of a plane:

$\footnotesize v_{\text{g}} = \sqrt{v_{\text{a}}^2\! +\! v_{\text{w}}^2\! -\! (2\!\cdot\! v_{\text{a}}\!\cdot \!v_{\text{w}}\!\cdot\! \cos{(\delta \!-\! \omega\! +\! \alpha)})}$

Here we can identify:

• The ground speed $v_{\text{g}}$, the speed of the aircraft relative to the ground;
• The true airspeed $v_{\text{a}}$, the speed of the aircraft relative to the air it's traveling in;
• The wind speed $v_{\text{w}}$;
• The course $\delta$, the planned direction of the plane.
• The wind direction $\omega$; and
• The wind correction angle $\alpha$, the correction to the course to remain on route.

Together, course and wind correction angle define the heading of the plane, the **true angle at which the aircraft is traveling. We calculate the heading with the formula:

$\psi = \delta + \alpha$

The formula for the ground speed of an airplane is, mathematically speaking, the square root of the square of the sum of the air speed and the wind speed in vector form. Learn how to calculate it with our vector addition calculator.

## How to measure angles in the ground speed calculations?

Measuring angles (in particular directions) is slightly more complicated than, for example, measuring distances. We need to set a reference for three of the angles introduced above:

• $\delta$, the course;
• $\omega$, the wind direction; and
• $\psi$, the heading.

We choose north as a reference for all of them, with value $0\degree$. Going south would mean that your course is $180\degree$, and so on.
For the windspeed, however, there is a catch: we consider the direction the wind is pointing at. To have $\omega=0\degree$, then we should have a wind coming from the south and pointing toward the north.

#### The wind correction angle

When calculating the speed of an airplane, we need to compensate for the effect of the wind on the aircraft's course. For this purpose, we compute the wind correction angle $\alpha$:

$\alpha = \sin^{-1}[\frac{v_w}{v_a} \sin(\omega - \delta)]$

## Interpretation of the calculation of the ground speed

Angles and true airspeed can be computed and measured easily. Once you know their values, you can calculate the ground speed.

The true airspeed increases with altitude: a reduced drag allows to achieve the maximum possible thrust. The McDonnell Douglas F15 fighter can fly at a maximum speed of Mach 2.5 at high altitude, while it can "only" reach Mach 1.6 at sea level. The same holds for your average passenger jet: that's why it climbs quickly, just to remain high above the ground for most of the flight.

The wind speed can contribute greatly to the travel time. In February 2020 — right before the pandemic broke — a British Airways B747 flew from the JFK airport in New York to London Heathrow in a mere four hours and 56 minutes. The average flight on the same route lasts around seven hours. How come? The jet flew right inside an exceptionally strong jetstream clocked at $230\ \text{knots}$ (or $426\text{ km}/\text{h}$: learn how to convert between those two units with our speed converter).

Here you can see the difference from true airspeed to ground speed: the BA jet traveled at $1,330\ \text{km}/\text{h}$, well into the supersonic regime: the jet, however, never crossed the speed of sound. Flying at its cruise speed of around $900\ \text{km}/\text{h}$, it simply hitched a ride!

Davide Borchia
True airspeed
mph
Wind speed
mph
Course
deg
Wind direction
deg
Wind correction angle
deg
deg
Ground speed
mph
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