## VDRYD1: Lateral Dryden filter with constant coefficients

The block VDRYD1 is contained in the block-library WINDLIB. It implements a lateral Dryden filter with constant coefficients.

The user must specify the scale lenght L_vg, the standard deviation sigma_vg 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 VDRYD2 instead of VDRYD1 if the airspeed varies so much that the filter coefficients cannot be held constant anymore.

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]

In this case, V must be pre-specified by the user in the dialog-boxes from the block VDRYD1.

### Outputs from the block VDRYD1

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

VDRYD1 has no inputs.

### Block parameters

The following parameters can be specified after double-clicking the block VDRYD1:

      Lvg      = scale length for lateral turbulence [m]
      sigma_vg = standard deviation for lateral
                                               turbulence [m/s]
      V        = value of airspeed, used to determine filter
                      coefficients 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.