# Crosswind and Headwind calculation^{[PDF]}

## Contents

## Introduction

## Headwind, tailwind and crosswind definitions

### Headwind

If the winds are pure headwinds, the aircraft will face the wind. The crosswind component is null. The direction of travel is the opposite direction of the wind.

### Tailwind

If the winds are pure tailwinds, the aircraft will follow the wind. The crosswind component is null. The direction of travel is the same direction of the wind.

### Crosswind

If the winds are pure crosswind, the direction of travel is perpendicular to the wind direction. The headwind and the tailwind are null. The cross wind can be from left to right (like the example below) or from right to left (opposite direction of the example below)

## Generic wind configuration

The wind flow can be taken from the METAR information.

There are 2 parts in a wind flow:

- a headwind blows against the direction of travel or a tailwind blows in the same direction of travel
- a cross wind blows using perpendicular direction of travel (from the left or from the right)

## Headwind configuration

α is the angle of the wind from direction of travel.

α = (Wind speed heading° - Headwind Heading°)

Headwind heading = Aircraft heading The angle shall be: -90° < α < +90°

## Tailwind configuration

α is the angle of the wind from direction of travel.

α = (Wind speed heading° - Tailwind Heading°)

Tailwind heading = Aircraft heading + 180
The angle shall be: -90° < α < +90°

## Tailwind, headwind and crosswind in function of the runway

Using the same wind, tailwind and crosswind values are different for each runway used! According to the image, the wind direction is coming from the north.

For a take-off, we will have:

- a headwind if aircraft use runway 36
- a tailwind if aircraft use runway 18
- a crosswind from the left if aircraft use runway 09
- a crosswind from the right if aircraft use runway 27

If you have a tailwind for a runway, the opposite runway will have the same wind but in headwind configuration. If you have a headwind for a runway, the opposite runway will have the same wind but in tailwind configuration. If you calculate, the tailwind, headwind and crossing values, you must calculate the values for each runway.

## Calculation

We now calculate the crosswind and headwind (tailwind) speeds using the angle α and METAR information:

- Crosswind speed = wind speed * sin ( α )
- Headwind speed (or tailwind) = wind speed * cos ( α )

As the ‘sine’ and ‘cosine’ mathematical functions are quite complex, here are some conversion tables:

This table below is the conversion of ‘sine’ and ‘cosine’ functions:

α | 0° | 10° | 20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° |
---|---|---|---|---|---|---|---|---|---|---|

sin α | 0 | 0.17 | 0.34 | 0.5 | 0.64 | 0.77 | 0.86 | 0.94 | 0.98 | 1 |

cos α | 1 | 0.98 | 0.94 | 0.86 | 0.77 | 0.64 | 0.5 | 0.34 | 0.17 | 0 |

We can have a simpler table for wind calculation: here we have approximated crosswind and headwind speeds for a wind speed value = 10kt.

α | 0° | 10° | 20° | 30° | 40° | 50° | 60° | 70° | 80° | 90° |
---|---|---|---|---|---|---|---|---|---|---|

Crosswind (kt) | 0 | 0 | 3 | 5 | 6 | 8 | 9 | 10 | 10 | 10 |

Tailwind (kt) | 10 | 10 | 9 | 8 | 7 | 6 | 5 | 3 | 0 | 0 |

## Example

Input data are:

- Wind speed = 8KT
- Aircraft heading = 60°
- Wind speed heading in METAR = 100°

- True mathematical calculation: Crosswind = 8 * sin(40°) = 5.14 KT ; Headwind = 8 * cos(40°) = 6.12 KT
- Calculation with the first table given above: Crosswind = 8 * 0.64 = 5.12 KT ; Headwind = 8 * 0.77 = 6.16 KT : error < 1%
- Calculation with the second table given above: Crosswind = 8 * 6/10 =4.8 KT ; Headwind = 8 * 7/10 = 5.6 KT ; error < 10%

For runway 24, if the headwind is +5KT, then for opposite runway 06, the headwind is transformed into a tailwind. So, for the runway 06, Headwind is -5KT or tailwind is +5KT.

## See also

- none

## Reference

- none

## Author

- VID 150259 - Creation
- VID 150259 - Wiki integration

## DATE OF SUBMISSION

- 00:20, 14 May 2021

## COPYRIGHT

- This documentation is copyrighted as part of the intellectual property of the International Virtual Aviation Organisation.

## DISCLAIMER

- The content of this documentation is intended for aviation simulation only and must not be used for real aviation operations.