📄 uvwdot.htm

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      FDC help: uvwdot
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    <h2>
      Subsystem <i>uvwdot</i>
    </h2>
    <p>The block <i>uvwdot</i>, which is contained
    in the subsystem <i><a href="moreouts.htm">Additional Outputs</a></i> from
    the <i><a href="beaver.htm">Beaver</a></i> model, computes time-derivatives of the body-axes velocity components <i>u</i>,
    <i>v</i>, and <i>w</i>.</p>
    <p><i>uvwdot</i> is an additional output block, which is
    <i>not</i> needed to solve the state equations themselves, because the true airspeed <i>V</i>, angle of attack <i>alpha</i>, and sideslip angle <i>beta</i> have been used as state variables for the aircraft model, instead of <i>u</i>, <i>v</i>, and <i>w</i>! Nowhere in the <i>Beaver</i> model time-derivatives of the body-axes velocities are sent through an integrator
    block or used by other blocks which are necessary to solve the equations of
    motion; therefore, <i>uvwdot</i> can be deleted from the <i>Beaver</i> model without affecting the solution of the equations of motion.</p>
     <p><b>Note:</b> contrary to <i>uvwdot</i>, the block <i><a href=
    "uvw.htm">uvw</a></i> which is contained in the subsystem <i><a href=
    "eqmotion.htm">Aircraft equations of motion</a></i> may <i>not</i> be
    removed from the system, because the outputs from that block (<i>u</i>,
    <i>v</i> and <i>w</i>) are needed in order to compute the aircraft&#39;s
    coordinates.</p>
     <p>The equations in <i>uvwdot</i> are, of course, closely related to the
    time-derivatives of the other state variables. See therefore the
    descriptions of the subsystems <i><a href="eqmotion.htm">Aircraft Equations
    of Motion</a></i>, <i><a href="12odes.htm">12 ODEs</a></i>, <i><a href=
    "vabdot.htm">Vabdot</a></i>, <i><a href="pqrdot.htm">pqrdot</a></i>, <i><a
    href="eulerdot.htm">Eulerdot</a></i>, and <i><a href=
    "xyhdot.htm">xyHdot</a></i> for more information. </p>
    <h3>
      Inputvectors: <i>x</i>, <i>xdot</i>, and <i>yhlp</i>
    </h3>
<pre>
  x    = [V alpha beta p q r psi theta phi xe ye H]&#39;     (states)

  xdot = dx&#39;/dt                 (time derivative of state vector)

  yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
          ... tan(beta) sin(psi) cos(psi) sin(theta) ...
          ... cos(theta) sin(phi) cos(phi)]&#39;
          (frequently used sines and cosines, coming from <a href=
"hlpfcn.htm">Hlpfcn</a>)


 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 inputvariables which are not actually used by <i>uvwdot</i> have been
    displayed between curly braces. Of the vector <i>xdot</i>, the time
    derivatives of <i>V</i>, <i>alpha</i>, and <i>beta</i> are used; from
    <i>yhlp</i>, <i>cos(alpha)</i>, <i>sin(alpha)</i>, <i>cos(beta)</i>, and
    <i>sin(beta)</i> are extracted.</p> 
    <h3>
      Outputvector: <i>yuvw</i>
    </h3>
<pre>
  yuvw = [udot vdot wdot]&#39; = d/dt([u v w]&#39;)

  u    : velocity component along the XB (body-) axis [m/s]
  v    : velocity component along the YB axis [m/s]
  w    : velocity component along the ZB axis [m/s]
</pre>
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