## WDRYD1: Vertical Dryden filter with constant coefficients

The block WDRYD1 is contained in the block-library WINDLIB. It implements a vertical Dryden filter with constant coefficients.

The user must specify the scale lenght L_wg, the standard deviation sigma_wg and the airspeed V. In reality, V will not be constant, which results in non-constant filter coefficients, but in practice the influence of the change in airspeed upon the gust velocities can often be neglected. Use WDRYD2 instead of WDRYD1 if the airspeed varies so much that the filter coefficients cannot be held constant anymore.

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]

In this case, V must be pre-specified by the user in the dialog-boxes from the block WDRYD1.

### Outputs from the block WDRYD1

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

WDRYD1 has no inputs.

### Block parameters

The following parameters can be specified after double-clicking the block WDRYD1:

      Lwg      = scale length for vertical turbulence [m]
      sigma_wg = standard deviation for vertical
                                              turbulence [m/s]
      V        = value of airspeed, used to determine filter
                    coefficients 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.