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model.
out: vg and v˙g are usually combined with other turbulence velocities and their timederivatives
in a single vector that can be connected on the input side of the aircraft
model (through the uwind port).
Type browse vdryd2 at the command-line for on-line help.
176 Chapter 9. Wind and turbulence block reference
WDRYD1 Main FDC library / Wind and turbulence / Atmospheric turbulence models / WDRYD1
Wind and turbulence library / Atmospheric turbulence models / WDRYD1
Type
Masked subsystem block.
Description
The block WDRYD1 computes the vertical component of the turbulence velocity, which is
aligned along the ZB-axis of the aircraft, together with its time-derivative, using a vertical
Dryden filter with constant coefficients. The user must specify the vertical scale-length of
the turbulence Lwg , the standard deviation swg , and the (expected) mean airspeed of the
aircraft. WDRYD1 does not take into account variations of the filter coefficients with the
airspeed, as the influence of those variations is usually very small; if this limitation is not
acceptable, use WDRYD2 instead.
Equations
For a detailed discussion of the equations from the block WDRYD1 and the underlying
theory, refer to section 4.2.
• Vertical turbulence velocity, [ms−1]:
wg(s) = Hwgw3 (s) w3(s)
where w3 is a white noise signal, that is generated internally by a white-noise generator
within the block WDRYD1, and Hwgw3 is the transfer function of the vertical turbulence
velocity filter.
• Transfer function of the vertical turbulence filter:
Hwgw3 (s) = swg
r
2Lwg
V
1 +
p
3 Lwg
V s
1 + Lwg
V s
2
Note: the value of the airspeed V, used by WDRYD1, is kept constant during simulations.
This value must be specified by the user; obviously, the most realistic result is obtained
by specifying the (estimated) mean velocity of the airplane. If very large variations in
airspeed are anticipated, use the block WDRYD2 instead.
Inputs
None.
Outputs
wg vertical turbulence velocity, wg
w˙ g time-derivative of vertical turbulence velocity, wg dot
Parameters
WDRYD1 does not require any workspace parameters to be specified. The user must
specify the scale length Lwg , the standard deviation swg , and the estimated mean value
of the true airspeed for which the motions are evaluated in the mask dialog, which is
opened after double-clicking the block WDRYD1.
Connections
in: no connections.
out: wg and w˙ g are usually combined with other turbulence velocities and their timederivatives
in a single vector that can be connected on the input side of the aircraft
model (through the uwind port).
Type browse wdryd1 at the command-line for on-line help.
9.1. The wind and turbulence blocklibrary 177
WDRYD2 Main FDC library / Wind and turbulence / Atmospheric turbulence models / WDRYD2
Wind and turbulence library / Atmospheric turbulence models / WDRYD2
Type
Masked subsystem block.
Description
The block WDRYD2 computes the vertical component of the turbulence velocity, which is
aligned along the ZB-axis of the aircraft, together with its time-derivative, using a vertical
Dryden filter with coefficients that will vary with airspeed. The user must specify the
lateral scale-length of the turbulence Lwg and the standard deviation swg , but the filter
coefficients of WDRYD2 are computed ‘on-the-fly’, as a function of the airspeed. Since
the resulting variations in filter characteristics are usually relatively small, the turbulence
library also offers the simplified block WDRYD1, which uses constant filter coefficients.
Equations
For a detailed discussion of the equations from the block WDRYD2 and the underlying
theory, refer to section 4.2.
• Vertical turbulence velocity, [ms−1]:
wg(s) = Hwgw3 (s) w3(s)
where w3 is a white noise signal, that is generated internally by a white-noise generator
within the block WDRYD2, and Hwgw3 is the transfer function of the vertical turbulence
velocity filter.
• Transfer function of the vertical turbulence filter:
Hwgw3 (s) = swg
r
2Lwg
V
1 +
p
3 Lwg
V s
1 + Lwg
V s
2
Note: the filter coefficients are computed ‘on-the-fly’, as a function of the actual value of
the airspeed V. In practice, the transfer-function has been implemented in the form of its
block-diagram equivalent, which was determined using the theory from section 6.4.2; the
gains in this block-diagram are ‘scheduled’ as a function of V.
Inputs
V true airspeed of the aircraft, V
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(86)
