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implemented as parameters, i.e. they are assumed to be constant during the relative short
time intervals considered). The definition of this matrix can be found in appendix C. GM2
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; Ftot and Mtot come from the block FMsort; yhlp
comes from the block Hlpfcn.
out: ypqr is muxed together with the time-derivatives of the other state variables into a
single vector ˙x (not corrected for the implicit nature of the ˙b-equation). This timederivative
of the state vector x is then connected to the block xdotcorr.
Type browse pqrdot at the command-line for on-line help.
8.2. The aircraft model block libraries 157
uvw Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / uvw
Main FDC library / Equations of motion
Type
Aircraft-independent masked subsystem block, essential for solving the equations of motion.
Description
The block uvw is used to compute the body-axes velocity components, using the angle of
attack a, sideslip angle b, and true airspeed V. These velocity components are required
to determine the coordinates xe and ye and the altitude H of the aircraft.
Equations
The equations used by the block uvw have been discussed in some more detail in section
2.2.2.
• Velocity component u, directed along the XB-axis, [ms−1]:
u = V cos a cos b
• Velocity component v, directed along the YB-axis, [ms−1]:
v = V sin b
• Velocity component w, directed along the ZB-axis, [ms−1]:
w = V sin a cos b
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
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
ybvel = [ u v w ]T body-axes velocity components, ybvel
Parameters
None.
Connections
in: x comes from the block Integrator; yhlp comes from the block Hlpfcn.
out: ybvel is connected to xyHdot.
Type browse uvw at the command-line for on-line help.
158 Chapter 8. Aircraft model block reference
uvwdot Beaver level 1 / Beaver level 2 / Additional Outputs / uvwdot
Main FDC library / Other (output-) equations
Type
Aircraft-independent masked subsystem block, not essential for solving the equations of
motion (the block does not contain any state equations).
Description
The block uvwdot computes the time-derivatives of the body-axes velocity components
u, v, and w. It should be noted that these body-axes velocity components are not state
variables, and therefore, their time-derivatives do not represent state equations (the state
equations have been based on the airspeed, angle of attack, and sideslip angle, instead of
the body-axes velocity components, as explained in section 2.2).
Equations
The equations used by the block uvwdot have been discussed in some more detail in section
3.6.
• Time-derivative of the velocity component along the XB-axis, [ms−2]:
˙ u = ˙V cos a cos b − V(˙a sin a cos b + ˙b cos a sin b)
• Time-derivative of the velocity component along the YB-axis, [ms−2]:
˙ v = ˙V sin b + V˙b cos b
• Time-derivative of the velocity component along the ZB-axis, [ms−2]:
˙ w = ˙V sin a cos b + V(˙a cos a cos b − ˙b sin a sin b)
Inputs
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
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
yuvw = [ u˙ v˙ w˙ ]T time-derivatives of body-axes velocities, yuvw
Parameters
None.
Connections
in: x comes from the block Integrator; ˙x comes from the block xfix; yhlp comes from the
block Hlpfcn.
out: yuvw is not used by any other block from the aircraft model.
Type browse uvwdot at the command-line for on-line help.
8.2. The aircraft model block libraries 159
Vabdot Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / 12 ODEs / Vabdot
Main FDC library / Equations of motion
Type
Aircraft-independent masked subsystem block, contains three (out of twelve) state equations.
Description
The block Vabdot computes the time-derivatives of the true airspeed V, angle of attack a,
and sideslip angle b. These three variables form a subset of the twelve state variables of
　
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