## The turbulence block Turbulence Group 2

Turbulence Group 2 is a Simulink subsystem which is contained in the Atmospheric Turbulence sublibrary of the library WINDLIB. It contains the Dryden filters UDRYD2, VDRYD2, and WDRYD2 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, and the standard deviations sigma_ug, sigma_vg, and sigma_wg.

In Turbulence Group 2, the coefficients of the Dryden filters vary with the true airspeed V, which enters this subsystem through an Inport block. The value of the true airspeed must be obtained from the non-linear model of the aircraft under consideration, e.g., V may be extracted from the outputvector of the non-linear aircraft model Beaver, which itself uses the outputs of Turbulence Group 2 as input signals.

In many cases, the variations of V due to atmospheric turbulence are not very large, so the resulting changes in filter coefficients may be neglected. In such cases, it is recommended to use Turbulence Group 1 instead of Turbulence Group 2, thus eliminating the feedback-loop of V from the aircraft model to Turbulence Group 2 within the resulting Simulink system. Turbulence Group 1 uses the simpler Dryden implementations UDRYD1, VDRYD1, and WDRYD1.

### Inputsignal

      V = true airspeed [m/s]

### 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 wind (-shear) 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]

### Block parameters

Before starting a simulation of a system in which the subsystem Turbulence Group 2 is involved, the parameters of the masked subsystem blocks UDRYD2, VDRYD2, and WDRYD2 have to be defined by double-clicking these blocks and entering the correct values in their dialog-boxes. These parameters are:
UDRYD2:

      Lug      = scale length for longitudinal turbulence [m]
      sigma_ug = standard deviation for longitudinal
                                               turbulence [m/s]

VDRYD2:

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

WDRYD2:

      Lwg      = scale length for vertical turbulence [m]
      sigma_wg = standard deviation for vertical turbulence [m/s]