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section 2.4.
• Time-derivatives of the Euler angles y, q, and j, [rad s−1]:
˙y
= q sin j + r cos j
cos q
˙q
= q cos j − r sin j
˙j
= p + ˙y sin q
Inputs
ueul = [ xT Ftot
T Mtot
T yhlp
T ]T input vector to Eulerdot, ueul
where:
x = [ V a b p q r y q j xe ye H ]T state vector, x
Ftot = [ Fx Fy Fz ]T total external forces, Ftot
Mtot = [ L M N ]T total external moments, Mtot
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
yeul = [ ˙y
˙q
˙j
]T time-derivatives of the Euler angles, yeul (part of x˙ )
Parameters
None.
Connections
in: x comes from the block Integrator; Ftot and Mtot come from the block FMsort; yhlp
comes from the block Hlpfcn.
out: yeul 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 eulerdot at the command-line for on-line help.
8.2. The aircraft model block libraries 147
Flpath Beaver level 1 / Beaver level 2 / Additional Outputs / Flpath
Main FDC library / Other (output-) equations
Type
Aircraft-independent masked subsystem block, not essential for solving the equations of
motion.
Description
The block Flpath is used to compute some flight-path (-related) variables. These output
variables are useful for flight path tracking, but are not required to actually solve the
equations of motion themselves.
Equations
The equations used by the block Flpath have been discussed in some more detail in section
3.6.
• Flight-path angle g, [rad]:
g = arcsin
˙H
V
• Flight-path acceleration fpa, i.e. the acceleration in the direction of the true airspeed
vector V, [g]:
fpa =
˙V
g0
with g0 = 9.80665 ms−1 the gravitational acceleration at sea level.
• Azimuth angle c, [rad]:
c = b + y
• Bank angle F, [rad]:
F = arcsin
sin j cos q
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
yfp = [ g fpa c F ]T flight-path variables, yfp
Parameters
None.
Connections
in: x comes from the block Integrator; ˙x comes from 12 ODEs via the correction blocks
xdotcorr (Beaver) and xfix; yhlp comes from the block Hlpfcn.
out: yfp is not used by any other block from the aircraft model.
Type browse flpath at the command-line for on-line help.
148 Chapter 8. Aircraft model block reference
FMdims Beaver level 1 / Beaver level 2 / Aerodynamics Group or Engine Group / FMdims
Main FDC library / Aerodynamics or Engine forces and moments
Type
Aircraft-independent masked subsystem block, essential for solving the equations of motion.
Description
The block FMdims is used to obtain dimensional forces and moments from the dimensionless
force and moment coefficients as determined by the aerodynamic model Aeromod
(Beaver) and the propulsion model Engmod (Beaver). It should be noted that the relation
between the dimensionless coefficients and the corresponding forces and moments
is typical for most aircraft models from the Faculty of Aerospace Engineering of Delft
University of Technology; other sources may apply slightly different definitions.
Equations
The equations used by the block FMdims have been discussed in some more detail in
section 3.3.1.
• Dimensional forces, [N]:
Xa = CXa qdyn S
Ya = CYa qdyn S
Za = CZa qdyn S
• Dimensional moments, [Nm]:
La = Cla qdyn S b
Ma = Cma qdyn S c
Na = Cna qdyn S b
The index a denotes aerodynamic forces and moments, which corresponds to the use of
FMdims in the subsystem Aerodynamics Group; replace this by p for the propulsive forces
and moments, determined in the subsystem subsystem Engine Group.
Inputs
yad1 = [ a M qdyn ]T basic airdata variables, yad1
Caero = [ CXa CYa CZa Cla Cma Cna ]T aerodynamic force and moment coefficients, Caero
or:
Cprop = [ CXp CYp Czp Clp Cmp Cnp ]T propulsive force and moment coefficients, Cprop
Outputs
FMaero = [ Xa Ya Za La Ma Na ]T dimensional aerodynamic forces and moments, FMaero
or:
FMprop = [ Xp Yp Zp Lp Mp Np ]T dimensional propulsive forces and moments, FMprop
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(73)
