📄 blwind.htm

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      FDC help: BLwind
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    <h2>
      Subsystem <i>BLwind</i>: wind in Earth&#39;s boundary layer
    </h2>
    <p><i>BLwind</i> is a masked subsystem block, contained in the FDC
    blocklibrary <i><a href="windlib.htm">WINDLIB</a></i>. It calculates
    velocity components of a horizontal wind along the body-axes of the
    aircraft, where the wind velocity and direction may change along the flight
    path as a function of altitude. By default, the wind profile is valid in
    the <u>B</u>oundary <u>L</u>ayer of the Earth. However, <i>BLwind</i> can
    easily be altered in order to implement wind shears at different
    altitudes.</p>
     <p>The user can specify the wind profile by means of three functions:</p> 
    <ol>
      <li>
        wind velocity function; expresses <i>V<sub>w</sub></i> as a function of
        the altitude <i>H</i>,
      </li>
      <li>
        function for the horizontal wind angle; expresses <i>psi_w</i> as a function of
        <i>H</i>.
      </li>
      <li>
        function for the vertical wind angle; expresses <i>gamma_w</i> as a function of
        <i>H</i>.
      </li>
    </ol>
    <p>where <i>V<sub>w</sub></i> is the wind velocity [m/s], <i>psi_w</i> represents the wind direction in a horizontal plane[rad], and <i>gamma_w</i> expresses the wind direction in a vertical plane that is aligned with the projection of the wind-vector on the horizontal line. Notice that <i>psi_w</i> should be equal to <i>pi</i> rad if the wind is blowing <i>to</i> the North and that <i>gamma_w</i> is positive for upward blowing wind! In the default setting, the following expressions, taken from <a href="#References">ref.[1]</a> have been used:</p> 
<pre>
  Vw(H) = (H^0.2545 - 0.4097)/1.3470     0 &lt;= H &lt;= 300 m
  Vw(H) = 2.8658 m/s                     H &gt; 300 m

  psi_w   = 180 rad for all altitudes
  
  gamma_w = 0   rad for all altitudes
</pre>
    <p>(The <i>V<sub>w</sub></i> function in <i>BLWIND</i> is automatically truncated above 300 m and below 0 m, which means that the user can only specify the function for altitudes between 0 and 300 m above the Earth's surface.)</p>
    <p><b>Note:</b> if you want to implement a constant wind, use the block <i><a href="cwind.htm">Cwind</a></i> instead.</p>
    <h3>
      Inputvector: <i>x</i>
    </h3>
<pre>
  x = [V alpha beta p q r psi theta phi xe ye H]&#39;        (states)

 {V    : airspeed [m/s]                                         }
 {alpha: angle of attack [rad]                                  }
 {beta : sideslip angle [rad]                                   }
 {p    : roll rate [rad/s]                                      }
 {q    : pitch rate [rad/s]                                     }
 {r    : yaw rate [rad/s]                                       }
  psi  : yaw angle [rad]                                        
  theta: pitch angle [rad]                                      
  phi  : roll angle [rad]                                       
 {xe   : x-coordinate in Earth-fixed reference frame [m]        }
 {ye   : y-coordinate &#39;&#39;     &#39;&#39;          &#39;&#39;      &#39;&#39;  [m]        }
  H    : altitude above sea-level [m]
</pre>
    <p>The variables which are not actually used by <i>BLwind</i> have been
    displayed between curly braces.</p>
    <h3>
      Outputvector: <i>ywind</i>
    </h3>
<pre>
  ywind = [uw vw ww]&#39;

  uw   : wind velocity component along XB-axis [m/s]
  vw   : wind velocity component along YB-axis [m/s]
  ww   : wind velocity component along ZB-axis [m/s]
</pre>
    <h3>
      <a name="References">References</a>
    </h3>
    <ol>
      <li>
        Approach and Landing Simulation, AGARD report 632, Ames, 1975.
      </li>
    </ol>
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