## The subsystem uvw

The block uvw computes the body-axes velocities u, v, and w. The body-axes velocity components must be known to solve the state-equations for the coordinates xe, ye, and the altitude H, so even though u, v, and w have been replaced by the true airspeed V, angle of attack alpha, and sideslip angle beta as state variables, it is not allowed to delete this block from the aircraft model!

The outputs from uvw are used by the block xyHdot in the subsystem 12 ODEs. uvw is included in the subsystem Aircraft Equations of Motion of the Beaver model.

Since u, v, and w are not state variables, their time-derivatives do not have to be known to solve the equations of motion. However, for some purposes, knowledge of these time-derivatives still may be useful; therefore, a separate block uvwdot has been included in the subsystem Additional Outputs within the Beaver model.

### Inputvectors: x and yhlp

      x    = [V alpha beta p q r psi theta phi xe ye H]'     (states)

      yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
              ... tan(beta) sin(psi) cos(psi) sin(theta) ...
              ... cos(theta) sin(phi) cos(phi)]'
              (frequently used sines and cosines, coming from Hlpfcn)

     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 ''     ''          ''      ''  [m]        }
    {H    : altitude above sea-level [m]                           }

The inputvariables which are not actually used by the block uvw have been displayed between curly braces. From yhlp the signals cos(alpha), cos(beta), sin(alpha) and sin(beta) are used.

### Outputvector: ybvel (bvel = 'body-axes velocities')

      ybvel = [u v w]',

      u     : component of the true airspeed V along XB-axis [m/s]
      v     : component of the true airspeed V along YB-axis [m/s]
      w     : component of the true airspeed V along ZB-axis [m/s]