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FDC library (shown in figure 7.7 of chapter 7) by double-clicking the ‘Wind and
turbulence library’ button, or by typing windlib in the MATLAB command-window.
WINDLIB itself consists of two sublibraries: WNDLIB1, which contains the deterministic
wind models, and WNDLIB2, which contains the stochastic turbulence models.
These sublibraries have been shown in figures 9.2 and 9.3.
Figure 9.1: Wind and turbulence library WINDLIB
166 Chapter 9. Wind and turbulence block reference
Figure 9.2: Sublibrary with wind-models
Figure 9.3: Sublibrary with turbulence models
The remainder of this chapter (pages 167 to 177) provides detailed descriptions
of the individual blocks from the wind and turbulence library. The blocks have
been listed in alphabetical order; their locations have been referenced in relation
to the main FDC library and the wind and turbulence library.
9.1. The wind and turbulence blocklibrary 167
BLwind Main FDC library / Wind and turbulence / Wind models / BLwind
Wind and turbulence library / Wind models / BLwind
Type
Masked subsystem block.
Description
The block BLwind calculates components of the wind velocity along the aircraft’s bodyaxes
in the boundary layer of the Earth (‘BL’ stands for ‘Boundary Layer’), which ranges
from ground level to a height of about 300 m. The wind velocity and direction (both in the
horizontal plane and the vertical plane) can be freely defined as a function of the altitude.
By default, a wind velocity function according to ref.[1] is used, the wind direction is
assumed to be constant, and the vertical wind component is set to zero.
Equations
For a detailed discussion of the equations from the block BLwind, refer to section 4.1.
• Total wind velocity in the boundary layer of the Earth, according to ref.[1], [ms−1]:
Vw = Vw9.15
H0.2545 − 0.4097
1.3470
(0 < h < 300m)
Vw = 2.86585Vw9.15 (h 300m)
where Vw9.15 is the wind velocity at a height of 9.15 m.
• Horizontal and vertical components of the wind velocity, [ms−1]:
Vwhor = Vw · cos gw
Vwvert ww = −Vw · sin gw
where gw is the ‘vertical wind direction angle’, i.e. the angle between the wind vector
and the horizontal plane.
• Horizontal components of the wind velocity, aligned along the Earth-fixed reference
frame, [ms−1]:
uw = Vwhor · cos(yw − p)
vw = Vwhor · sin(yw − p)
where yw is the ‘horizontal wind direction angle’, i.e. the direction from where the horizontal
component of the wind (Vwhor ) emanates, measured relatively to the magnetic
north (yw is measured in [rad]; it equals zero when the wind is blowing from the north,
and p when the wind is blowing to the north).
• Wind components, measured along the body-axes of the aircraft, [ms−1]:
VBw
= (TF · TQ · TY) · VEw where TF, TQ, and TY represent the transformation matrices corresponding to Euler
rotations, and the superscripts denote the applicable reference frame. This transformation
has been written out in more detail in appendix A, equation (A.4).
The angles gw and yw may be defined as a function of the height above ground, similar to
the wind velocity function, but by default the values have been set to 0 [rad] and p [rad],
respectively (no vertical wind component, and the wind is blowing to the north).
Please notice that the thickness of the boundary layer has been hard-wired in the BLwind
structure by means of a Saturation block, which has been hidden beneath the mask interface
of BLwind. The height above ground is extracted from the twelfth element of the
input vector, which has the same definition as the state vector x from the aircraft model.
However, it should be noted that this element actually represents the altitude of the airplane
above sea-level, which means that the equations are only valid when ground-level
and sea-level coincide!
168 Chapter 9. Wind and turbulence block reference
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector from the aircraft model, x
Outputs
[ uw vw ww ]T wind velocities along aircraft’s body-axes, [uw,vw,ww]’
Parameters
BLwind does not require any workspace parameters to be specified. The user may change
the equations for the wind velocity, horizontal wind direction, and vertical wind direction
in the mask dialog, which is opened after double-clicking the block BLwind. In these
equations, u[1] denotes the height above ground-level (which is assumed to be equal to
the altitude above sea-level, as explained above).
Connections
in: x is usually extracted from the nonlinear aircraft model (type browse outputs at
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(81)
