08 What is a 6 DOF model? (Flight Simulator Theory)
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This article is from the Flight Simulators FAQ, by with numerous contributions by Bob Wittick rwittick@msu.edu others.
08 What is a 6 DOF model? (Flight Simulator Theory)
Robert Dorsett writes:
A 6 degree of freedom flight model provides for a fairly accurate
modeling of the motion and flying characteristics of an airplane.
It is generally used when the airplane is to be modeled as a "rigid
body." It considers both rotational (yaw, pitch, and roll) and
translational motion, both centered around the center of gravity.
Since there are three axes to consider in each case, this is referred
to as a six- degree-of-freedom model. This model actually considers
twelve variables, since both the instantaneous rate of change *and*
position have to be considered. These are referred to as the state
variables, which are applied to varying matrices of coefficients to
get the desired fidelity.
Several people recommended "Aircraft Control and Simulation," by
Frank L. Lewis and Brian L. Stevens (Wiley Interscience, 1992, ISBN
0-471-61397-5). It is a comprehensive work, using an F-16 model as a
case-study example. It includes FORTRAN code.
A couple of people recommended NASA CR-1756, "The simulation of a
large jet transport aircraft volume I: mathematical model," by C.
Rodney Hanke, March 1971. This deals with the simulation of a Boeing
747. I've found the second half, containing the aerodynamic data, is
all but impossible to find, however.
One of the more accessible references is J. M. Rolfe's _Flight
Simulation_, a survey of the art. It has a bottom-line description
of a 6 DOF flight model, adapted from the Hanke paper. It is more
useful for its insights into other aspects of system and flight
simulation.
One respondent suggested "A review of flight simulation techniques,"
by Max Baarspul, in _Progress in Aerospace Science_, Vol. 27, 1990.
This is a comprehensive monograph (120 pages), detailing the art of
simulation. Portions are reminiscent of Rolfe, but he develops a
flight model for a DHC-2 "Beaver" in much more detail.
Dan Sharpes dug up the following two:
_Aircraft Dynamics and Automatic Control_, by McRuer, Ashkenas, and
Graham, (Princeton University Press, 1973, ISBN 0691080836), which
apparently has a detailed DC-8 model at the end.
_Flight Stability and Automatic Control_, by Robert C. Nelson (McGraw
Hill, 1989, ISBN 0070462186). Dan transcribed the following
derivatives for a 747-100 or -200, on page 260:
Longitudinal
Mach Alt CL CD CLa CDa Cma CLadot CLq
.25 SL 1.11 0.102 5.70 0.66 -1.26 6.7 5.4
.90 40k 0.5 0.042 5.5 0.47 -1.6 0.006 6.58
Mach CMq CLM CDM CmM CL-De CM-De
.25 -20.8 -0.81 0.0 0.27 0.338 -1.34
.90 -25.0 0.2 0.25 -0.10 0.3 -1.2
Lateral
Mach Alt CyB ClB CnB Clp Cnp Clr Cnr
.25 SL -0.96 -0.221 0.150 -0.45 -0.121 0.101 -0.30
.90 40k -0.85 -0.10 0.20 -0.30 0.20 0.20 -0.325
Mach Cl-Da Cn-Da Cy-Dr Cl-Dr Cn-Dr
.25 0.0461 0.0064 0.175 0.007 -0.109
.90 0.014 0.003 0.075 0.005 -0.09
W = 636,600 lb
CG @ 25%MAC
S = 5500 ft sq
b = 195.68 ft sq
c-bar = 27.31 ft
Ix 18.2 E6 slug-ft sq
Iy 33.1 E6 slug-ft sq
Iz 49.7 E6 slug-ft sq
Ixz 0.97 E6 slug-ft sq
All derivatives are per radian.
For more aircraft models, check out the following references:
Robert K. Heffley and Wayne F. Jewell, _Aircraft Handling Qualities
Data_, NASA CR 2144, December 1972, 343 pp. Aircraft described are
NT-33A, F-104A, F-4C, X-15, HL-10, Lockheed jetstar, Convair 880M,
B-747, C-5A, and XB-70A.
G. L. Teper, "Aircraft Stability and Control Data, NASA CR-96008,
1969. Aircraft covered are A-7A, A-4D, F-106B, T-38, F-5A, F-104,
F-105B, B-58, Navion, and DC-8.
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