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📄 wdryd2.htm

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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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