Dryden Wind Turbulence Model (Aerospace Blockset)

Generate wind turbulence with the Dryden velocity spectra

Library

Environment/Wind

Description

The Dryden Wind Turbulence Model block uses the Dryden spectral representation to add turbulence to the aerospace model by passing band-limited white noise through appropriate forming filters. This block implements the mathematical representation in the Military Specification MIL-F-8785C [1].

Turbulence can be considered as a stochastic process defined by velocity spectra. For an aircraft flying at a speed V through a "frozen" turbulence field with a spatial frequency of radians per meter, the circular frequency is calculated by multiplying V by . The appropriate component spectra for the Dryden model of turbulence are shown here.

Longitudinal:

Lateral:

Vertical:

b is the aircraft wingspan, are the turbulence scale lengths, and _u, _v, _w are the turbulence intensities.

To generate a signal with the correct characteristics a unit variance band-limited white noise signal is passed through appropriate forming filters that are derived by taking the spectral square roots of the spectrum equations. The resulting transfer functions are shown here.

Longitudinal:

Lateral:

Vertical:

The turbulence scale lengths and intensities are functions of altitude, and there are two distinct regions.

Low-Altitude Model (Altitude < 1000 feet)

In [1] the turbulence scale lengths at low altitudes are as given below, where is the altitude in feet.

The turbulence intensities are given below, where is the wind speed at 20 feet (6 m). Typically for "light" turbulence the wind speed at 20 feet is 15 knots, for "moderate" turbulence the wind speed is 30 knots, and for "severe" turbulence the wind speed is 45 knots.

Medium/High Altitudes (Altitude > 2000 feet)

For medium to high altitudes the turbulence scale lengths and intensities are based on the assumption that the turbulence is isotropic. In reference [1] the scale lengths are as given below:

The turbulence intensities are determined from a lookup table that gives the turbulence intensity as a function of altitude and the probability of the turbulence intensity's being exceeded.

At altitudes between 1000 feet and 2000 feet, the turbulence scale lengths and intensities are determined by interpolating between the value from the low- altitude model at 1000 feet and the value from the high-altitude model at 2000 feet.

Dialog Box

Units of Velocity

Define the units of wind speed due to the turbulence.


	Wind Velocity	Altitude	Air Speed
`Meters/second`	Meters/second	Meters	Meters/second
`Feet/second`	Feet/second	Feet	Feet/second
`Knots`	Knots	Feet	Knots

Wind speed at 20 ft (6 m) defines the low altitude intensity

The measured wind speed at a height of 20 feet provides the intensity for the low-altitude turbulence model.

Probability of exceedance of high altitude intensity

Above 2000 feet, the turbulence intensity is determined from a lookup table that gives the turbulence intensity as a function of altitude and the probability of the turbulence intensity's being exceeded.

Scale length at medium/high altitudes

The turbulence scale length above 2000 feet is assumed constant, and from reference [1] a figure of 1750 feet is recommended.

Wingspan

The wingspan is required in the calculation of the turbulence on the angular rates.

Band-limited noise sample time (seconds)

The sample time at which the unit variance white noise signal is generated.

Noise seeds

There are four random numbers required to generate the turbulence signals, one for each of the three velocity components and one for the roll rate. The turbulences on the pitch and yaw angular rates are based on further shaping of the outputs from the shaping filters for the vertical and lateral velocities.

Turbulence on

Selecting the check box generates the turbulence signals.

Inputs and Outputs

The first input is altitude, in units selected.

The second input is aircraft speed, in units selected.

The first output is a three-element signal containing the turbulence velocities, in the selected units.

The second output is a three-element signal containing the turbulence angular rates, in radians per second.

Examples

See the aeroblk_HL20.mdl example included with the blockset.

References

Military Specification MIL-F-8785C, 5th November, 1980.

See Also
Discrete Wind Gust Model

Wind Shear Model

Discrete Wind Gust Model Euler Angles to Direction Cosine Matrix