## UDRYD1: Longitudinal Dryden filter with constant coefficients

The block UDRYD1 is contained in the block-library WINDLIB. It implements a longitudinal Dryden filter with constant coefficients.

The user must specify the scale lenght L_ug, the standard deviation sigma_ug 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 UDRYD2 instead of UDRYD1 if the airspeed varies so much that the filter coefficients cannot be held constant anymore.

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]

In this case, V must be pre-specified by the user in the dialog-boxes from the block UDRYD1.

### Outputs from the block UDRYD1

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

UDRYD1 has no inputs.

### Block parameters

The following parameters can be specified after double-clicking the block UDRYD1:

      Lug      = scale length for longitudinal turbulence [m]
      sigma_ug = standard deviation for longitudinal
                                               turbulence [m/s]
      V        = value of airspeed, used to determine filter
                 coefficients 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.