## Subsystem Engine Group (Beaver)

The subsystem Engine Group (Beaver) of the Beaver model is used to compute the forces and moments which arise due to the operation of the engine. These include slipstream effects, induced by the propeller. In the case of the 'Beaver', this is done by first computing the engine power and the closely related increase of pressure across the propeller, then using this result for determining the magnitude of non-dimensional force and moment coefficients, and finally computing the forces and moments in [N] and [Nm], respectively. A similar sequence will usually be followed for other piston-engined aircraft.

Engine Group (Beaver) consists of three blocks: Power (Beaver), Engmod (Beaver), and FMdims. Power computes the engine power and pressure increase across the propeller, Engmod contains the actual engine model according to ref.[1] which determines the dimensionless force and moment coefficients, and FMdims computes the forces and moments in N and Nm.

The block Power uses the state vector x, the vector with external inputs to the engine uprop, and the outputvector yatm from the block Atmosph in the subsystem Airdata Group as inputs. Engmod uses x and the outputvector ypow from the block Power, hence, Engmod has been placed on the lower right side of Power. Finally, FMdims uses the outputvector of the block Engmod, Cprop, and the outputvector yad1of the block Airdata1 in the subsystem Airdata Group. Hence, FMdims is located on the right side of the block Engmod. Power, Engmod, and FMdims have also been shifted vertically with respect to each other, in order to make it possible to connect their outputs to the Outport blocks on the right side of the subsystem Engine Group (Beaver).

### Inputs: x, uprop, yatm, yad1

      x    = [V alpha beta p q r psi theta phi xe ye H]'    (states)
      uprop= [n pz]'           (external engine inputs (propulsive))
      yatm = [rho ps T mu g]'    (atmosphere variables, computed in
                                       the masked subsystem Atmosph)
      yad1 = [a M qdyn]'        (airdata variables, computed in the
                                          masked subsystem Airdata1)

      V    : true 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, relative to Earth-axes [m]               }
     {ye   : Y-coordinate, relative to Earth-axes [m]               }
     {H    : altitude above sea level [m]                           }

      n    : engine speed [RPM]
      pz   : manifold pressure ["Hg]

      rho  : air density [kg/m^3]
     {ps   : static pressure [N/m^2]                                }
     {T    : air temperature [K]                                    }
     {mu   : dynamic viscosity [kg/(m*s)]                           }
     {g    : acceleration of gravity [m/s^2]                        }

     {a    : speed of sound [m/s]                                   }
     {M    : Mach number [-]                                        }
      qdyn : dynamic pressure [N/m^2]

The variables which are not actually used by any of the blocks from the subsystem Engine Group (Beaver) have been put between curly braces.

### Outputs (prop = 'propulsive'): ypow, Cprop, FMprop

      ypow  = [dpt P]'
      Cprop = [CXp CYp CZp Clp Cmp Cnp]'
      FMprop= [Xp Yp Zp Lp Mp Np]'

      dpt  : dimensionless pressure increase across the propeller [-]
      P    : engine power [Nm/s]

      CXp, CYp, CZp: propulsive force coefficients along body-axes [-]
      Clp, Cmp, Cnp: propulsive moment coefficients along body-axes [-]

      Xp, Yp, Zp: propulsive force components along body-axes [N]
      Lp, Mp, Np: propulsive moment components along body-axes [Nm]

### 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, it is needed by FMdims in order to extract geometrical data for the determination of dimensional forces and moments from the non-dimensional force and moment coefficients.
- EM: matrix with stability and control derivatives of the 'Beaver' (valid only for the nonlinear engine forces and moments model of the DHC-2 'Beaver', see ref.[1]). This matrix is needed by Engmod (Beaver).

EM and GM1 can be loaded into the workspace from datafile by running the utility DATLOAD. Run MODBUILD first if the datafile does not yet exist.

### References

1. R.T.H. Tjee and J.A. Mulder. Stability and Control Derivatives of the De Havilland DHC-2 "Beaver" aircraft. Report LR-556, Delft University of Technology, 1988.