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FDC help: WDRYD2
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<h2>
<i>WDRYD2</i>: Vertical Dryden filter with non-constant coefficients
</h2>
<p>The masked subsystem block <i>WDRYD2</i>, which is contained in the library
<i><a href="windlib.htm">WINDLIB</a></i>, implements a vertical Dryden filter with
coefficients that vary with the true airspeed <i>V</i>.</p>
<p>The user must specify the scale
lenght <i>L_w<sub>g</sub></i> and the standard deviation
<i>sigma_w<sub>g</sub></i>. The airspeed <i>V</i> is used as inputsignal to
the block <i>WDRYD2</i>. Often, the changes in <i>V</i> due to atmospheric
turbulence are not very large, which means that it may be more
straightforward to use a Dryden filter with constant coefficients, computed
under the assumption that <i>V</i> is constant and equal to a
user-specified value. The block <i><a href="wdryd1.htm">WDRYD1</a></i>
contains such a filter for vertical turbulence.</p>
<p>The vertical gust velocity <i>w<sub>g</sub></i> is obtained by passing white noise through
a Dryden filter, which is defined by the following transfer function:</p>
<pre>
b0 + b1*s a0 = (V/Lwg)^2
Hwg = --------------- a1 = 2*(V/Lwg)
s^2 + a1*s + a0 b0 = sigma_wg*sqrt(Lwg/V)*(V/Lwg)^2
b1 = sigma_wg*sqrt(3*Lwg/V)*(V/Lwg)
</pre>
where:
<pre>
V : true airspeed [m/s]
sigma_wg: standard deviation of vertical gust
velocity [m/s]
Lwg : scale length for vertical gust [m]
</pre>
<p>Here, <i>V</i> is the <i>input</i> signal to the masked subsystem block.
<i>V</i> itself has to be obtained from the aircraft model considered,
e.g., <i>V</i> may be an outputsignal from the <i><a href="beaver.htm">Beaver</a></i> model, which uses the turbulence velocity
<i>u<sub>g</sub></i> and its time-derivative as inputsignals!</p>
<h3>
Input signal
</h3>
<pre>
V : true airspeed [m/s]
</pre>
<h3>
Output signals
</h3>
<pre>
wg : vertical gust velocity [m/s]
d(wg)/dt: time derivative of wg [m/s^2]
</pre>
<h3>
Block parameters
</h3>
<p>The following parameters can be specified after double-clicking the block <i>WDRYD2</i>:</p>
<pre>
Lwg = scale length for vertical turbulence [m]
sigma_wg = standard deviation for vertical
turbulence [m/s]
</pre>
<h3>
More information
</h3>
<p>While <i>WDRYD1</i> and <i>WDRYD2</i> contain vertical Dryden filters, the
blocks <i><a href="udryd1.htm">UDRYD1</a></i>, <i><a href=
"udryd2.htm">UDRYD2</a></i>, <i><a href="vdryd1.htm">VDRYD1</a></i>, and
<i><a href="vdryd2.htm">VDRYD2</a></i> can be used to determine
longitudinal and lateral turbulence (the suffix 1 denotes filters with
constant coefficients and 2 denotes filters with velocity-dependent
coefficients).</p>
<p>These Dryden
filters have been combined in the subsystems <i><a href="turb1.htm">Turbulence Group 1</a></i>
and <i><a href="turb2.htm">Turbulence Group 2</a></i>. Those subsystems combine the
turbulence velocity-components and their time-derivatives into a single vector
<i>uwind</i>, which can be connected to the <i><a
href="beaver.htm">Beaver</a></i> model.</p>
<p>All wind and turbulence systems have been gathered in the blocklibrary
<i><a href="windlib.htm">WINDLIB</a></i>.</p>
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