## Subsystem Vabdot

Vabdot computes time-derivatives of the true airspeed, angle of attack, and side-slip angle. It is contained in the block 12 ODEs of the subsystem Aircraft Equations of Motion in the Beaver model. The remaining nine differential equations are stored in the subsystems pqrdot, Eulerdot, and xyHdot, which are all contained in 12 ODEs.

Note: the time-derivative of the sideslip angle beta that leaves Vabdot does not take into account the influence of beta-dot itself upon the aerodynamic force along the YB-axis. This contribution was neglected in the block Aeromod and has therefore not been included in the computed side-force. The resulting error to the time-derivative of the state vector, xdot, has been corrected later in the system, by means of the block xdotcorr.

### Inputvector: uvab

      uvab = [x' Ftot' Mtot' yhlp'],

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

      Ftot = [Fx Fy Fz]'           (total forces along the body-axes,
                                        computed in the block FMdims)

      Mtot = [L M N]'             (total moments along the body-axes,
                                        computed in the block FMdims)

      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 & 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]                           }

      Fx, Fy, Fz: total forces along the aircraft's body-axes [N]
     {L, M, N   : total moments along the aircraft's body-axes [Nm] }

The inputvariables which are not actually used by Vabdot have been displayed between brackets. Of the inputvector yhlp, cos(alpha), cos(beta), sin(alpha), sin(beta), and tan(beta) are used.

### Outputvector: yvab

      yvab = [Vdot alphadot betadot]'

      Vdot    : dV/dt [m/s^2]
      alphadot: d(alpha)/dt [rad/s^2]
      betadot : d(beta)/dt [rad/s^2]

Note: the beta-dot equation in Vabdot does not take into account the contribution of beta-dot itself to the sideforce Fy. Corrections are made in xdotcorr.

### Parameters to be defined in the Matlab workspace

- GM1: vector with some important geometrical properties of the 'Beaver' aircraft, and the mass of the aircraft (which is assumed to be constant during the motions of interest). Here, the mass of the aircraft is extracted from GM1. GM1 can be loaded into the Matlab workspace by calling the routine DATLOAD. If the necessary datafile with aircraft model parameters does not yet exist, run MODBUILD first.