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Subsystems and/or blocks
The subsystem Aircraft Equations of Motion (Beaver) contains two blocks:
uvw computes the body-axes velocity components as a function of the true airspeed,
angle of attack, and sideslip angle,
xdotcorr applies corrections to the time-derivatives of the state variables in order to take
into account the implicit nature of the aerodynamic forces and moments model
(the current implementation is valid for the Beaver model, where the timederivative
of the sideslip angle is corrected to account for the contribution of
˙b
to the aerodynamic sideforce Ya).
In addition, Aircraft Equations of Motion (Beaver) contains the subsystem:
12 ODEs contains the state equations, which express the time-derivatives of the state
variables in terms of the external forces and moments, and the state variables
themselves.
An Integrator-block is used determine the time-trajectories of the state variables as a function
of their time-derivatives and initial condition.
Inputs
Ftot = [ Fx Fy Fz ]T total external forces, Ftot
Mtot = [ L M N ]T total external moments, Mtot
uwind = [ uw vw ww u˙w v˙w w˙ w ]T wind velocity components along body-axes
and their time-derivatives, uwind
yatm = [ r ps T μ g ]T basic atmospheric properties, yatm
yhlp = [ cos a sin a cos b sin b tan b sin y cos y sin q cos q sin j cos j ]T
frequently used sines and cosines, yhlp
Outputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
˙x = [ ˙V
˙a
˙b˙ p
˙ q
˙ r
˙y
˙q
˙j
˙ xe ˙ ye ˙H ]T time-derivative of state vector, xdot
ybvel = [ u v w ]T body-axes velocity components, ybvel
Parameters
The block xdotcorr (Beaver) reads the parameter matrix AM and the vector GM1 from the
MATLAB workspace. The subsystem 12 ODEs needs the parameter vector GM1 and the
matrix GM2. The definitions of these variables can be found in appendix C. The variables
8.2. The aircraft model block libraries 131
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). The block Integrator requires the initial value
of the state vector, xinco, which can be computed using the aircraft trim program ACTRIM
(see section 11.1), or loaded from file using the utility TRILOAD (see section 12.4.2).
Connections
in: Ftot and Mtot come from FMsort; uwind is an external input containing wind and turbulence
velocities and their time-derivatives; yatm comes from Atmosph; yhlp comes
from Hlpfcn.
out: x, which leaves the block Integrator, is connected to many other blocks in the aircraft
model; ˙x from xfix is connected to Accel, Flpath, and uvwdot; ybvel from uvw is
connected to xyHdot.
Type browse eqmotion at the command-line for on-line help.
132 Chapter 8. Aircraft model block reference
Airdata1 Beaver level 1 / Beaver level 2 / Airdata Group / Airdata1
Main FDC library / Airdata, atmosphere
Type
Aircraft-independent masked subsystem block, essential for solving the equations of motion.
Description
The block Airdata1 is used to compute some essential airdata variables. This information
is usually required to be able to compute the aerodynamic and propulsive forces and
moments, and hence, to solve the equations of motion. For the Beaver model, only the
dynamic pressure qdyn is actually needed to solve the state equations, but models of faster
flying aircraft usually also require the Mach number M. Other airdata (-related) equations
have been implemented in the blocks Atmosph, Airdata2, and Airdata3.
Equations
The equations used by the block Airdata1 have been discussed in more detail in section
3.5.
• Dynamic pressure qdyn, [kg m−2]:
qdyn = 12
rV2
• Speed of sound a, [ms−1]:
a =
p
gRT
where g = 1.4 is the ratio of specific heats of air with constant pressure and constant
volume, respectively, and R = Ra/M0 = 287.05 JK−1kg−1 is the specific gas constant of
the air (Ra = 8314.32JK−1kmol−1 is the molar gas constant, and M0 = 28.9644 kg kmol−1
is the molecular weight of the air at sea level).
• Mach number M, [ – ]:
M = V
a
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
yatm = [ r ps T μ g ]T basic atmospheric properties, yatm
Outputs
yad1 = [ a M qdyn ]T basic airdata variables, yad1
Parameters
All parameters for Airdata1 are defined within the block itself; Airdata1 does not use any
parameters from the MATLAB workspace.
Connections
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(65)
