## UDRYD2: Longitudinal Dryden filter with non-constant coefficients

The masked subsystem block UDRYD2, which is contained in the library WINDLIB, implements a longitudinal Dryden filter with coefficients that vary with the true airspeed V.

The user must specify the scale lenght L_ug and the standard deviation sigma_ug. The airspeed V is used as inputsignal to the block UDRYD2. Often, the changes in V due to atmospheric turbulence are not very large, which means that it may be more straightforward to use a Dryden filter with constant coefficients, computed under the assumption that V is constant and equal to a user-specified value. The block UDRYD1 contains such a filter for longitudinal turbulence.

The longitudinal gust velocity ug is obtained by passing white noise through a Dryden filter, which is defined by the following transfer function:

                   K
      Hug  =  -----------       K   = sigma_ug * sqrt(2*Lug/V)
               1 + tau*s        tau = Lug/V

where:

      V       : true airspeed [m/s]
      sigma_ug: standard deviation of longitudinal gust
                                                velocity [m/s]
      Lug     : scale length for longitudinal gust [m]

Here, V is the input signal to the masked subsystem block. V itself has to be obtained from the aircraft model considered, e.g., V may be an outputsignal from the non-linear aircraft model (such as the Beaver model), which uses the turbulence velocity ug and its time-derivative as inputsignals!

### Input signal

      V       : true airspeed [m/s]

### Output signals

      ug      : longitudinal gust velocity [m/s]
      d(ug)/dt: time derivative of ug [m/s^2]

### Block parameters

The following parameters can be specified after double-clicking the block UDRYD2:

      Lug      = scale length for longitudinal turbulence [m]
      sigma_ug = standard deviation for longitudinal
                                             turbulence [m/s]

### More information

While UDRYD1 and UDRYD2 contain longitudinal Dryden filters, the blocks VDRYD1, VDRYD2, WDRYD1, and WDRYD2 can be used to determine lateral and vertical turbulence (the suffix 1 denotes filters with constant coefficients and 2 denotes filters with velocity-dependent coefficients).

These Dryden filters have been combined in the subsystems Turbulence Group 1 and Turbulence Group 2. Those subsystems combine the turbulence velocity-components and their time-derivatives into a single vector uwind, which can be connected to the Beaver model.

All wind and turbulence systems have been gathered in the blocklibrary WINDLIB.