## WDRYD2: Vertical Dryden filter with non-constant coefficients

The masked subsystem block WDRYD2, which is contained in the library WINDLIB, implements a vertical Dryden filter with coefficients that vary with the true airspeed V.

The user must specify the scale lenght L_wg and the standard deviation sigma_wg. The airspeed V is used as inputsignal to the block WDRYD2. 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 WDRYD1 contains such a filter for vertical turbulence.

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

             b0 + b1*s      a0 = (V/Lwg)^2
    Hwg = ---------------   a1 = 2*(V/Lwg)
          s^2 + a1*s + a0   b0 = sigma_wg*sqrt(Lwg/V)*(V/Lwg)^2
                            b1 = sigma_wg*sqrt(3*Lwg/V)*(V/Lwg)

where:

      V       : true airspeed [m/s]
      sigma_wg: standard deviation of vertical gust
                                                 velocity [m/s]
      Lwg     : scale length for vertical 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 Beaver model, which uses the turbulence velocity ug and its time-derivative as inputsignals!

### Input signal

      V       : true airspeed [m/s]

### Output signals

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

### Block parameters

The following parameters can be specified after double-clicking the block WDRYD2:

      Lwg      = scale length for vertical turbulence [m]
      sigma_wg = standard deviation for vertical
                                         turbulence [m/s]

### More information

While WDRYD1 and WDRYD2 contain vertical Dryden filters, the blocks UDRYD1, UDRYD2, VDRYD1, and VDRYD2 can be used to determine longitudinal and lateral 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.