## VDRYD2: Lateral Dryden filter with non-constant coefficients

The masked subsystem block VDRYD2, which is contained in the library WINDLIB, implements a lateral Dryden filter with coefficients that vary with the true airspeed V.

The user must specify the scale lenght L_vg and the standard deviation sigma_vg. The airspeed V is used as inputsignal to the block VDRYD2. 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 VDRYD1 contains such a filter for lateral turbulence.

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

             b0 + b1*s      a0 = (V/Lvg)^2
    Hvg = ---------------   a1 = 2*(V/Lvg)
          s^2 + a1*s + a0   b0 = sigma_vg*sqrt(Lvg/V)*(V/Lvg)^2
                            b1 = sigma_vg*sqrt(3*Lvg/V)*(V/Lvg)

where:

      V       : true airspeed [m/s]
      sigma_vg: standard deviation of lateral gust
                                                velocity [m/s]
      Lvg     : scale length for lateral 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

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

### Block parameters

The following parameters can be specified after double-clicking the block VDRYD2:

      Lvg      = scale length for lateral turbulence [m]
      sigma_vg = standard deviation for lateral
                                        turbulence [m/s]

### More information

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