# Ground Speed Calculator

Created by Mehjabin Abdurrazaque
Reviewed by Dominik Czernia, PhD and Steven Wooding
Last updated: Oct 09, 2022

You've come to the right place if you are looking for a comprehensive ground speed calculator! Let's quickly tell you what our ground speed calculator can do.

Using this tool, you can calculate an aircraft's ground speedthe velocity we use to calculate its flight duration, as well as the wind correction angle and heading. This calculator also explains what ground speed is and the difference between ground speed and true airspeed. Further, we provide the wind correction angle, heading, and ground speed formulae the aviation industry uses.

## What is the ground speed of a flying object?

The ground speed of any flying object is its horizontal velocity relative to the earth's surface or the ground.

Do you enjoy watching buildings and trees moving backward while traveling by train? We know that how fast they shift away from us, while we don't move inside the train, is actually the speed of our vehicle relative to the ground. Similarly, you can estimate how fast your aircraft is moving through the air relative to the ground or what its ground speed is by comparing it with stationary objects on the ground, if you can see them.

## True airspeed vs. ground speed

Here are the major differences between ground speed and true airspeed:

1. An aircraft's true airspeed tells us how fast it moves relative to the surrounding air, while the ground speed is its horizontal speed relative to the earth's surface. In still air, an aircraft's ground speed is equal to its true airspeed.

🙋 A usually has no ground speed as it is held on the end of a string. Yet, it has a true airspeed which is always equal to the wind speed.

1. True airspeed tells the pilots whether the plane is moving fast enough to take off or continue in the air. Ground speed informs the pilots how long they have to fly to reach their destination.

2. True airspeed increases with altitude - drag equation tells us that drag decreases proportionally to air density, which lowers as you move up. Meanwhile, ground speed does not depend upon how high a plane flies. In the true airspeed calculator, you can see the relationship between this quantity and the vertical displacement.

💡 A by Heide and Mohazzabi, 2013, shows that our vehicle's speed relative to the ground has little influence on its fuel consumption unless they are traveling in still air! The study states that a vehicle's fuel economy depends on its airspeed.

## How do I calculate ground speed from true airspeed?

The ground speed formula in aviation is the following:

$\scriptsize v_g = \sqrt{v_a^2 + v_w^2 - (2 v_a v_w \cos (\delta) - \omega + \alpha)}$

where:

• $v_g$Ground speed – Aircraft's speed relative to the ground;
• $v_a$True airspeed – Speed of the aircraft relative to the surrounding air;
• $v_w$Wind speed – Speed of the wind relative to the ground;
• $\delta$Course – The desired trajectory of the flight measured clockwise from the North;
• $\omega$Wind direction – The direction the air is blowing; and
• $\alpha$Wind correction angle – The angle between the course and the heading.

The above equation is a simple vector addition of the aircraft's true airspeed and wind speed. You can obtain it using law of cosines formula.

⚠️ The wind direction ω is not the direction the wind is coming from. If the wind is coming from the north, the wind direction would be south, and the angle is 180 degrees. If the wind is coming from the south, the angle is 0 degrees.

## How do we find the wind correction angle of an aircraft?

We don't throw an arrow parallel to the ground if you want it to hit the target. We throw it at an angle from the ground to counteract the gravity's pull. To know how projectiles move, check our projectile motion calculator.

Similarly, the wind correction angle helps the pilot keep the airplane non-deviated in the desired course in the presence of wind. When the wind flows to the right, the aircraft also drifts in the same direction away from its course. To bring the plane back to its course, the pilot heads to the left. The wind correction angle is how much the pilot shifts the aircraft to the left.

We estimate the wind correction angle, ⍺ as:

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

In our wind correction angle calculator, you can learn more about how the wind changes an aircraft's course and how to calculate wind correction angles.

## How to use ground speed calculator

Let's see how to use this tool to calculate wind correction angle, heading, and ground speed from true airspeed:

1. Select the desired units for each quantity from the drop-down list near them.
2. Enter the true airspeed of the aircraft. To know the difference between ground speed and true airspeed, view the true airspeed vs. ground speed section above 👆
3. Enter the wind speed.
4. Specify the course.
5. Input the wind direction.

That's all! The ground speed calculator displays the wind correction angle, heading, and ground speed.

## FAQ

### What is the difference between an aircraft's course and its heading?

The course of an airplane is its route to reach the destination in still air. The heading is the direction the aircraft is pointing as it flies to counteract the wind's effect.

### How do I find an aircraft's heading?

The heading ѱ is the direction a pilot points the aircraft's nose to prevent any displacement from its course due to wind. It is the sum of course δ and wind correction angle ⍺:

• ѱ = δ + ⍺

### What is the ground speed for 80-knot TAS and 20-knot wind?

The ground speed of this aircraft depends on the wind direction. The answer is:

1. 100 knots if the wind is blowing in the same direction you're moving;

2. 60 knots if the wind is blowing from the opposite direction; and

3. Between 60 and 100 knots in other cases. To find the exact answer, add the true airspeed (TAS) and wind speed vectors using the law of cosines.

### Is ground speed faster than airspeed?

The vector addition of airspeed and wind speed gives the ground speed of an aircraft: vg = √(va2 + vw2 - (2vavw cos θ). Thus, for a given airspeed, the ground speed becomes greater than airspeed when the angle between airspeed and wind speed is lower. Hence, the ground speed becomes greater than airspeed when there is a strong tailwind.

Mehjabin Abdurrazaque
True airspeed
mph
Wind speed
mph
Course
deg
Wind direction
deg
Wind correction angle
deg
deg
Ground speed
mph
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