# Discrete Wind Gust Model

Generate discrete wind gust

• Library:
• Aerospace Blockset / Environment / Wind

## Description

The Discrete Wind Gust Model block implements a wind gust of the standard “1-cosine” shape. This block implements the mathematical representation in the Military Specification MIL-F-8785C [1]. The gust is applied to each axis individually, or to all three axes at once. You specify the gust amplitude (the increase in wind speed generated by the gust), the gust length (length, in meters, over which the gust builds up) and the gust start time. For more information on the gust shape, see Algorithms.

The Discrete Wind Gust Model block can represent the wind speed in units of feet per second, meters per second, or knots.

## Ports

### Input

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Airspeed, specified as a scalar, in selected units.

Data Types: `double`

### Output

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Wind speed, returned as a scalar, in selected units.

Data Types: `double`

## Parameters

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Units of wind gust, specified as:

Units

Wind

Altitude

`Metric (MKS)`

Meters/second

Meters

```English (Velocity in ft/s)```

Feet/second

Feet

```English (Velocity in kts)```

Knots

Feet

#### Programmatic Use

 Block Parameter: `units` Type: character vector Values: ```'Metric (MKS)'``` | ```'English (Velocity in ft/s)'``` | ```'English (Velocity in kts)'``` Default: ```'Metric (MKS)'```

To apply a wind gust to the u-axis in the body frame, select this check box. Otherwise, clear this check box.

#### Programmatic Use

 Block Parameter: `Gx` Type: character vector Values: `'on'` | `'off'` Default: `'on'`

To apply a wind gust to the v-axis in the body frame, select this check box. Otherwise, clear this check box.

#### Programmatic Use

 Block Parameter: `Gy` Type: character vector Values: `'on'` | `'off'` Default: `'on'`

To apply a wind gust to the w-axis in the body frame, select this check box. Otherwise, clear this check box.

#### Programmatic Use

 Block Parameter: `Gz` Type: character vector Values: `'on'` | `'off'` Default: `'on'`

Model time, specified as a scalar, at which the gust begins, in seconds.

#### Programmatic Use

 Block Parameter: `t_0` Type: character vector Values: scalar Default: `'5'`

The length, in meters or feet (depending on the choice of units), over which the gust builds up in each axis. These values must be positive.

#### Programmatic Use

 Block Parameter: `d_m` Type: character vector Values: vector Default: ```'[120 120 80]'```

The magnitude of the increase in wind speed caused by the gust in each axis. These values may be positive or negative.

#### Programmatic Use

 Block Parameter: `d_m` Type: character vector Values: vector Default: ```'[3.5 3.5 3.0]'```

## Algorithms

This figure shows the shape of the gust with a start time of zero. The parameters that govern the gust shape are indicated on the diagram.

To assess airplane response to large wind disturbances, you can use the discrete gust singly or in multiples.

The mathematical representation of the discrete gust is:

`${V}_{wind}=\left\{\begin{array}{lll}0\hfill & x<0\hfill & \hfill \\ \frac{{V}_{m}}{2}\left(1-\mathrm{cos}\left(\frac{\pi x}{{d}_{m}}\right)\right)\hfill & 0\le x\le {d}_{m}\hfill & \hfill \\ {V}_{m}\hfill & x>{d}_{m}\hfill & \hfill \end{array}$`

where Vm is the gust amplitude, dm is the gust length, x is the distance traveled, and Vwind is the resultant wind velocity in the body axis frame.

## References

[1] U.S. Military Specification MIL-F-8785C, November 5, 1980.