## Subsystem Additional Outputs

The subsystem Additional Outputs of the Beaver model computes a number output signals that were not needed for solving the equations of motion, and which could not logically be placed in one of the other subsystems (i.e. Airdata Group, Aerodynamics Group, Engine Group, or Aircraft Equations of Motion). Deleting Additional Outputs from the system Beaver will not affect the solution of the equations of motion. It is easy to add more output equations to the list that is currently contained in this subsystem.

Since the outputs from this subsystem are not involved in the actual solution of the state equations, the outputs may depend not only upon the state-vector x and the inputvectors uaero, uprop, and uwind, but also upon the time-derivative of the state vector, xdot. If the outputs from the subsystem Additional Outputs would have been needed for solving the state equations, this would not be possible (or at least undesirable), because it would yield an algebraic loop and it wouldn't have been possible anymore to delete the subsystem Additional Outputs without affecting the solution of the state equations.

By default, Additional Outputs contains masked subsystem blocks Accel, Flpath, and uvwdot, which determine accelerations and specific forces, flightpath variables, and time-derivatives of the velocity components u, v, and w, respectively (note: u, v, and w are not state variables!). More output equations may be included in this subsystem if desired.

### Inputs: x, xdot, yhlp, Ftot, Fgrav

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

      xdot = dx/dt = [Vdot alphadot betadot pdot qdot rdot ...
                      ... psidot thetadot phidot xedot yedot Hdot]'
                                    (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) ]'
                      (sines & cosines, computed in the block Hlpfcn)

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

      Fgrav= [Xgr Ygr Zgr]'         (gravity forces along body-axes,
                                       computed in the block Gravity)

      V        : airspeed [m/s]
     {alpha    : angle of attack [rad] or [deg]                      }
      beta     : sideslip angle [rad] or [deg]
     {p        : roll-rate [rad/s] or [deg/s]                        }
     {q        : pitch-rate [rad/s] or [deg/s]                       }
     {r        : yaw-rate [rad/s] or [deg/s]                         }
      psi      : yaw-angle [rad] or [deg]
      theta    : pitch-angle [rad] or [deg]
      phi      : roll-angle [rad] or [deg]
     {xe       : X-coordinate in Earth-axes [m]                      }
     {ye       : Y-coordinate in Earth-axes [m]                      }
     {H        : altitude [m]                                        }

      Vdot     : time-derivative of airspeed [m/s^2]
      alphadot : time-derivative of alpha [rad/s] or [deg/s]
      betadot  : time-derivative of beta [rad/s] or [deg/s]
     {pdot     : time-derivative of p [rad/s^2] or [deg/s^2]         }
     {qdot     : time-derivative of q [rad/s^2] or [deg/s^2]         }
     {rdot     : time-derivative of r [rad/s^2] or [deg/s^2]         }
     {psidot   : time-derivative of psi [rad/s] or [deg/s]           }
     {thetadot : time-derivative of theta [rad/s] or [deg/s]         }
     {phidot   : time-derivative of phi [rad/s] or [deg/s]           }
     {xedot    : time-derivative of xe [m/s]                         }
     {yedot    : time-derivative of ye [m/s]                         }
      Hdot     : time-derivative of H [m/s]

      Fx       : total external force along XB-axis [N]
      Fy       : total external force along YB-axis [N]
      Fz       : total external force along ZB-axis [N]

      Xgr      : gravity force along XB-axis [N]
      Ygr      : gravity force along YB-axis [N]
      Zgr      : gravity force along ZB-axis [N]

The variables which are not actually used by any of the masked subsystems within the subsystem Additional Outputs have been bracketed between curly braces. Of the vector yhlp, only sin(alpha), cos(alpha), sin(beta), and cos(beta) are used within Additional Outputs.

### Outputs

      yfp  = [gamma fpa chi Phi]'             (flightpath parameters)

      yuvw = [udot vdot wdot]'  (time-derivatives (!) of u, v, and w)

      yacc = [Ax Ay Az axk ayk azk]'    (specific forces and accele-
                                                             rations)

      gamma    : flightpath angle [rad] or [deg]
      fpa      : flightpath acceleration [m/s^2]
      chi      : azimuth angle [rad] or [deg]
      Phi      : bank angle [rad] or [deg]

      udot     : time-derivative of u [m/s^2]
      vdot     : time-derivative of v [m/s^2]
      wdot     : time-derivative of w [m/s^2]

      Ax       : specific force along XB-axis [g]
      Ay       : specific force along YB-axis [g]
      Az       : specific force along ZB-axis [g]
      axk      : kinematic acceleration along XB-axis [g]
      ayk      : kinematic acceleration along YB-axis [g]
      azk      : kinematic acceleration along ZB-axis [g]

Note: the time-derivatives of the body-axes velocity components, udot, vdot, and wdot, are not needed for solving the equations of motion, because the true airspeed V, angle of attack alpha, and sideslip angle beta have been used as state variables instead of u, v, and w.

### Parameters to be defined in the Matlab workspace

- GM1: Vector which contains some basic geometrical properties of the aircraft, as well as its mass (which is considered to be constant during the motions of interest). Here, the value of the mass is needed by the masked subsystem block Accel. GM1 can be loaded to workspace from file by means of the routine DATLOAD. Use MODBUILD first if the datafile does not yet exist.