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Wind and turbulence library / Atmospheric turbulence models / VDRYD1
Type
Masked subsystem block.
Description
The block VDRYD1 computes the lateral component of the turbulence velocity, which is
aligned along the YB-axis of the aircraft, together with its time-derivative, using a lateral
Dryden filter with constant coefficients. The user must specify the lateral scale-length of
the turbulence Lvg , the standard deviation svg , and the (expected) mean airspeed of the
aircraft. VDRYD1 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 VDRYD2 instead.
Equations
For a detailed discussion of the equations from the block VDRYD1 and the underlying
theory, refer to section 4.2.
• Lateral turbulence velocity, [ms−1]:
vg(s) = Hvgw2 (s) w2(s)
where w2 is a white noise signal, that is generated internally by a white-noise generator
within the block VDRYD1, and Hvgw2 is the transfer function of the lateral turbulence
velocity filter.
• Transfer function of the lateral turbulence filter:
Hvgw2 (s) = svg
r
2Lvg
V
1 +
p
3 Lvg
V s
1 + Lvg
V s
2
Note: the value of the airspeed V, used by VDRYD1, 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 VDRYD2 instead.
Inputs
None.
Outputs
vg lateral turbulence velocity, vg
v˙g time-derivative of lateral turbulence velocity, vg dot
Parameters
VDRYD1 does not require any workspace parameters to be specified. The user must specify
the scale length Lvg , the standard deviation svg , 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 VDRYD1.
Connections
in: no connections.
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 vdryd1 at the command-line for on-line help.
9.1. The wind and turbulence blocklibrary 175
VDRYD2 Main FDC library / Wind and turbulence / Atmospheric turbulence models / VDRYD2
Wind and turbulence library / Atmospheric turbulence models / VDRYD2
Type
Masked subsystem block.
Description
The block VDRYD2 computes the lateral component of the turbulence velocity, which is
aligned along the YB-axis of the aircraft, together with its time-derivative, using a lateral
Dryden filter with coefficients that will vary with airspeed. The user must specify the
lateral scale-length of the turbulence Lvg and the standard deviation svg , but the filter
coefficients of VDRYD2 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 VDRYD1, which uses constant filter coefficients.
Equations
For a detailed discussion of the equations from the block VDRYD2 and the underlying
theory, refer to section 4.2.
• Lateral turbulence velocity, [ms−1]:
vg(s) = Hvgw2 (s) w2(s)
where w2 is a white noise signal, that is generated internally by a white-noise generator
within the block VDRYD2, and Hvgw2 is the transfer function of the lateral turbulence
velocity filter.
• Transfer function of the lateral turbulence filter:
Hvgw2 (s) = svg
r
2Lvg
V
1 +
p
3 Lvg
V s
1 + Lvg
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
Outputs
vg lateral turbulence velocity, vg
v˙g time-derivative of lateral turbulence velocity, vg dot
Parameters
VDRYD2 does not require any workspace parameters to be specified. The user must specify
the scale length Lvg and the standard deviation svg in themask dialog, which is opened
after double-clicking the block VDRYD2.
Connections
in: the airspeed V is usually extracted from the state vector x of the nonlinear aircraft
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(85)
