## The turbulence block Turbulence Group 1

Turbulence Group 1 is a Simulink subsystem which is contained in the Atmospheric Turbulence sublibrary of the library WINDLIB. It contains the Dryden filters UDRYD1, VDRYD1, and WDRYD1 for longitudinal, lateral and vertical turbulence, respectively.

The filters have been implemented in masked subsystem blocks, in which the user must specify the scale lengths L_ug, L_vg, and L_wg, the standard deviations sigma_ug, sigma_vg, and sigma_wg, and the velocity V (for each of the three masked subsystem blocks!). The coefficients of the Dryden filters are determined for the value of the airspeed V which is specified in the dialog boxes from the blocks UDRYD1, VDRYD1, and WDRYD1, i.e., V is assumed to be constant during the simulations.

In cases where the airspeed changes over a very large range, it is recommended to use the Turbulence Group 2 instead, because it takes into account variations of the filter coefficients due to changes in the true airspeed V during the simulations (using the more sophisticated UDRYD2, VDRYD2, and WDRYD2 Dryden filter implementations).

### Outputvector

      uwind = [uw vw ww uwdot vwdot wwdot]'

(Actually, this vector should have been called `ugust = [ug vg wg ugdot vgdot wgdot]'`, since the wind velocities and their time-derivatives from the subsystem Turbulence Group 1 represent gust-velocities only; contributions due to steady wind or windshear still have to be added to this vector! See Cwind and BLwind for more information on the implementation of constant wind and a wind-profile in the Earth's boundary layer, respectively.)

     uw   : wind (gust-) velocity along XB-axis of aircraft [m/s]
     vw   : wind (gust-) velocity along YB-axis of aircraft [m/s]
     ww   : wind (gust-) velocity along ZB-axis of aircraft [m/s]

     uwdot: time-derivative of uw [m/s^2]
     vwdot: time-derivative of vw [m/s^2]
     wwdot: time-derivative of ww [m/s^2]

Turbulence Group 1 does not have any input signals.

### Block parameters

Before starting a simulation of a system in which the subsystem Turbulence Group 1 is involved, the parameters of the masked subsystem blocks UDRYD1, VDRYD1, and WDRYD1 have to be defined by double-clicking these blocks and entering the correct values in their dialog-boxes. These parameters are:
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]

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]

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]