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x = [ V a b p q r y q j xe ye H ]T state vector, x
Parameters
Integrator reads the vector xinco from the MATLAB workspace; xinco contains the initial
value of the state vector. A steady-state initial value can be computed using the aircraft
trim routine ACTRIM (see section 11.1), or it can be loaded into the MATLAB workspace
from file, using TRILOAD (see section 12.4.2). Of course, it is also possible to manually
enter the elements of xinco, if required.
Connections
in: ˙x comes from the block xdotcorr.
out: x is connected to most other blocks in the aircraft model.
See the SIMULINK block-reference in the ‘MATLAB helpdesk’ documentation for more information
about the Integrator block.
8.2. The aircraft model block libraries 155
Power (Beaver) Beaver level 1 / Beaver level 2 / Engine Group / Power (Beaver)
Main FDC library / Engine forces and moments
Type
Aircraft-dependent masked subsystem block, essential for solving the equations of motion.
Description
The block Power (Beaver) is used to compute the engine power P and the dimensionless
increase in total air pressure, measured across the working plane of the propeller, dpt. The
equations are valid for the Beaver aircraft, but the structure of these relations is probably
typical for piston-powered aircraft, driven by a constant-speed propeller; see also ref.[34].
Power (Beaver) needs to be updated if one wishes to implement a model of a different
aircraft within the FDC framework. Thanks to its black-box structure, it is relatively easy
to change the structure of the equations if necessary, e.g. to incorporate look-up table
functions.
Equations
The equations used by the block Power (Beaver) have been discussed in more detail in
section 3.3.2.
• Dimensionless increase in air pressure, measured across the working plane of the propeller,
[–]:
dpt = Dpt
12
rV2
= C1 + C2
P
12
rV3
!
with P
12
rV3 measured in [kW kg−1 s3], and: C1 = 0.08696, C2 = 191.18, see ref.[34].
• Engine power P, [Nms−1]:
P = 0.7355
−326.5 +
0.00412(pz + 7.4)(n + 2010) + (408.0 − 0.0965n)
1.0 −
r
r0
Inputs
x = [ V a b p q r y q j xe ye H ]T state vector, x
uprop = [ n pz ]T external propulsion inputs, uprop
yatm = [ r ps T μ g ]T basic atmospheric properties, yatm
Outputs
ypow = [ dpt P ]T engine power related variables, ypow
Parameters
All parameters for Power (Beaver) have been defined within the block itself; the block
does not use any parameters from the MATLAB workspace.
Connections
in: x comes from the block Integrator; uprop is an external input vector with control inputs
for the engine; yatm comes from Atmosph.
out: ypow is connected to Engmod (Beaver).
Type browse power at the command-line for on-line help.
156 Chapter 8. Aircraft model block reference
pqrdot Beaver level 1 / Beaver level 2 / Aircraft Equations of Motion / 12 ODEs / pqrdot
Main FDC library / Equations of motion
Type
Aircraft-independent masked subsystem block, contains three (out of twelve) state equations.
Description
The block pqrdot computes the time-derivatives of the roll rate p, pitch rate q, and yaw
rate r. These three variables form a subset of the twelve state variables of the nonlinear
aircraft model.
Equations
The equations used by the block pqrdot have been discussed in some more detail in section
2.1.4.
• Time-derivatives of the angular velocities around the body-axes, [rad s−2]:
p˙ = Ppp p2 + Ppq pq + Ppr pr + Pqqq2 + Pqrqr + Prrr2 + PlL + PmM+ PnN
q˙ = Qpp p2 + Qpq pq + Qpr pr + Qqqq2 + Qqrqr + Qrrr2 + QlL + QmM+ QnN
˙ r = Rpp p2 + Rpq pq + Rpr pr + Rqqq2 + Rqrqr + Rrrr2 + RlL + RmM+ RnN
The coefficients Ppp, Ppq, Ppr, ... , Rm, and Rn are inertia coefficients, see the definition in
table 2.2.
Inputs
upqr = [ xT Ftot
T Mtot
T yhlp
T ]T input vector to pqrdot, pqr
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
ypqr = [ p˙ q˙ r˙ ]T time-derivatives of the angular velocities
around the body-axes, ypqr (part of x˙ )
Parameters
The block pqrdot needs the parameter matrix GM2 to be present the MATLAB workspace,
in order to extract the inertia coefficients (the moments and products of inertia have been
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FDC 1.4 – A SIMULINK Toolbox for Flight Dynamics and Contro(76)
