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due to the propeller slipstream. This is done in the masked subsystem block Engmod
within the subsystem Engine Group.
Equations
The aerodynamic force and moment coefficients of the Beaver are expressed in terms of
nonlinear polynomial functions of the state variables and aerodynamic control inputs.
The model includes longitudinal-lateral cross-coupling effects, as well as unsteady aerodynamics,
but it does not take into account the influence of compressibility, as airspeed is
assumed to be low [34]. The equations have been described in more detail in section 3.3.1.
• Coefficients of the aerodynamic forces and moments, measured in the body-fixed reference
frame:
CXa = CX0 + CXaa + CXa2 a2 + CXa3 a3 + CXq
qc
V
+ CXdr dr + CXd f
df + CXad f
adf
CYa = CY0 + CYb b + CYp
p b
2V
+ CYr
rb
2V
+ CYda da + CYdr dr + CYdra dra
+CY˙b
˙b
b
2V
CZa = CZ0 + CZaa + CZa3 a3 + CZq
qc
V
+ CZde de + CZdeb2 deb2 + CZd f
df + CZad f
adf
Cla = Cl0 + Clb b + Clp
p b
2V
+ Clr
rb
2V
+ Clda da + Cldr dr + Cldaa daa
Cma = Cm0 + Cmaa + Cma2 a2 + Cmq
qc
V
+ Cmde de + Cmb2 b2 + Cmr
rb
2V
+ Cmd f
df
Cna = Cn0 + Cnb b + Cnp
p b
2V
+ Cnr
rb
2V
+ Cnda da + Cndr dr + Cnq
qc
V
+ Cnb3 b3
The coefficients of the polynomials represent the stability and control derivatives of the
Beaver; they have been listed in table B.3 of appendix B. A closer look at the internals of
the block Aeromod (Beaver) reveils that the polynomial evaluation has been implemented
in practice by means of a multiplication of the vector:
1 a a2 a3 b b2 b3 pb
2V
qc
V
rb
2V de da dr adf adr ada deb2 0
T
with the constant parameter matrix AM in which the stability and control derivatives of
the Beaver are contained.
Notice that the direct contribution of the time-derivative of the sideslip angle ˙b to the
aerodynamic side-force coefficient CYa has not been taken into account in this block: the
8.2. The aircraft model block libraries 129
last element of the multiplication vector equals zero instead of ˙b b/2V, i.e. the bracketed
term in the CYa equation is neglected by Aeromod (Beaver)! This was necessary in order to
prevent the ˙b equation from becoming implicit, which would have yielded an algebraic
loop in the simulation model (see section 6.4.1). The error which results from neglecting
this term is corrected in the separate block xdotcorr.
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
uaero = [ de da dr df ]T aerodynamic control inputs, uaero
ydl = [ pb
2V
qc
V
rb
2V ]T dimensionless angular velocities, ydl
Outputs
Caero = [ CXa CYa CZa Cla Cma Cna ]T aerodynamic force and moment coefficients, Caero
Parameters
The block Aeromod reads the parameter matrix AM from the MATLAB workspace. AM
contains the stability and control coefficients of the Beaver; see appendix C for its exact
definition. This matrix can be loaded from the file AIRCRAFT.DAT, using the utility DATLOAD
(see section 12.4.2). If this datafile has somehow inadvertently been deleted, it can
be re-created by running the program MODBUILD (see section 12.6.1).
Connections
in: x comes from the block Integrator; uaero is an external input vector, containing the
aerodynamic control inputs; ydl comes from Dimless.
out: Caero is connected to FMdims.
Type browse aeromod at the command-line for on-line help.
130 Chapter 8. Aircraft model block reference
Aircraft Equations of Motion (Beaver) Level 1 / Level 2 / Aircraft Equations of Motion
Main FDC library / Equations of Motion
Type
Aircraft-independent subsystem, except for the block xdotcorr (Beaver), essential for solving
the equations of motion. The subsystem is not masked.
Description
The subsystem Aircraft Equations of Motion (Beaver) contains the generic nonlinear sixdegree-
of-freedom rigid-body equations of motion. It determines the time-derivatives of
the state variables from the aircraft model, and the time-trajectories of the state variables
themselves. Aircraft Equations of Motion (Beaver) contains one aircraft-dependent element:
the block xdotcorr (Beaver) is needed to correct the time-derivative of the sideslip angle
for the implicit nature of the sideforce equation in the aerodynamic model. Because of
this, this subsystem is not entirely aircraft-independent; the current implementation has
been tailored to the DeHavilland DHC-2 Beaver.
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(64)
