## Subsystem FMdims

FMdims computes forces in [N] and moments in [Nm] from dimensionless force and moment coefficients, using the dynamic pressure and some geometric properties of the aircraft, see the equations below. In the 'Beaver' model, FMdims is used by the subsystem blocks Aerodynamics Group (Beaver) and Engine Group (Beaver) of the Beaver model, where it is being applied to aerodynamic forces and moments and propulsive forces and moments, respectively. (In those subsystems, the non-dimensional coefficients are computed within the blocks Aeromod and Engmod.)

### Inputvectors: yad1 and Caero or Cprop

      yad1 = [a M qdyn]'                (airdata variables which are
                                      computed in the block Airdata1)

      Caero= [CXa CYa CZa Clt Cma Cna]'   (dimensionless aerodynamic
                                       force and moment coefficients,
                                        computed in Aeromod (Beaver))

      Cprop= [CXp CYp CZp Clp Cmp Cnp]'    (dimensionless propulsive
                                       force and moment coefficients,
                                         computed in Engmod (Beaver))

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

      CXa, CYa, CZa: aerodynamic force coefficients along the
                     aircraft's body-axes
      Cla, Cma, Cna: aerodynamic moment coefficients along the
                     aircraft's body-axes
      CXp, CYp, CZp: engine force coefficients along the aircraft's
                     body-axes
      Clp, Cmp, Cnp: engine moment coefficients along the air-
                     craft's body-axes

The inputvariables which are not actually used by FMdims have been displayed between brackets.

### Outputvector: FMaero or FMprop

      FMaero= [Xa Ya Za La Ma Na]' (vector with aerodynamic forces & moments)
      FMprop= [Xp Yp Zp Lp Mp Np]' (vector with engine forces & moments)

      Xa, Ya, Za: aerodynamic forces along aircraft's body-axes [N]
      La, Ma, Na: aerodynamic moments along aircraft's body-axes [Nm]

      Xp, Yp, Zp: propulsive forces along aircraft's body-axes [N]
      Lp, Mp, Np: propulsive moments along aircraft's body-axes [Nm]

### Equations

The following expressions are used:

      X = CX*qdyn*S,   Y = CY*qdyn*S,   Z = CZ*qdyn*S
      L = Cl*qdyn*S*b, M = Cm*qdyn*S*c, N = Cn*qdyn*S*b

where:

      S        = wing area [m^2]
      c = cbar = mean aerodynamic chord [m]
      b        = wing span [m]

CX, CY, ... , Cn may equal CXa, ... Cna, CXp, ... Cnp, or any other sequence of force and moment coefficients which have been made dimensionless in the same way as the aerodynamic and propulsive forces and moments.

### 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 wing span b, mean aerodynamic chord cbar, and wing area S are extracted from GM1. GM1 can be loaded into the workspace from file by running the utility DATLOAD. Run MODBUILD first if the datafile does not exist.