SUMMARY: 6 dof, C*, basic texts...

From: (Robert Dorsett)
Organization: UTexas Mail-to-News Gateway
Date:         14 Jan 93 22:57:31 PST
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A few days ago, I posted a message asking for references on 6dof flight 
models and C*.  Several people replied with suggestions; a couple replied
with questions.  This is an attempt to summarize all the responses, and
to answer a couple of the questions.

"What is a 6 dof flight model?":

A 6 degree of freedom flight model provides for a fairly accurate
modelling of the motion and flying characteristics of an airplane.  It 
is generally used when the airplane is to be modelled 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.

Other models exist: 4 dof and 3 dof models are in use, depending upon the
type of airplane it is desired to simulate.  

Personal computer flight simulator publishers tend to ignore these models 
altogether, instead relying on point-space "performance" based models.

On C*:

Two respondents contributed an old Boeing report: "New Short Period 
Handling Quality Criterion for Fighter Aircraft," September 1965, by 
Malcom & Tobie, Report D6-17841 T/N.  This seems to be a "first 
instance," and is widely quoted by other sources.  

Dan Sharpes also noted that "The C* time history boundaries were 
developed from the data on page 63 of the Mil F 8785B Background 
Information and Users Guide (BIUG).  Page 64 of the 8785C BIUG 
gives the definition of C* and talks about its history and early 
applications.  Neal, Smith, and Brulle found C* was lacking when 
correlating it with pilot opinion ratings."

A fourth person noted that C* is also summarized in the Stevens book 
(see below).

On 6 dof models:

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:

 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

 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.

A description of DATCOM, again from Dan Sharpes:

  The Datcom is the short-hand title for the "USAF Stability and Control
DATCOM."  It contains methodologies for determining the S & C derivatives
for just about any type of configuration.  It does NOT contain the S & C
derivatives of aircraft (popular misconception!).  Here's what the Guide
to Datcom says:

  "Fundamentally, the purpose of the Datcom (Data Compendium) {OK, I was
wrong.  Flame me!} is to provide a systematic summary of methods for
estimating basic stability antd control derivatives.  ...  For any
given flight condition and configuration the complete set of
derivatives can be determined without resort to outside information.
The book is intended to be used for preliminary design purposes before
the acquisition of test data.  ... there are many cases where the
Datcom can be used to advantage in conjunction with test data.  For
instance, if the lift-curve slope of a wing-body combination is
desired, the Datcom recommends that the lift-curve slopes of the
isolated wing and body, respectively, be estimated by methods
presented and that appropriate  wing-body interference factors (also
presented) be applied.  If wing-alone test data are available, it is
obvious that these test data should be substituted in place of the
estimated wing-alone characteristics ..."

  The Datcom has nine sections:
    1) Guide to Datcom and Methods Summary
    2) General Information (notation, parameters of wing, body, section,
and planform)
    3) Effects of External Stores
    4) Characteristics at Angle of Attack (static derivatives in alpha)
    5) Characteristics in Sideslip (static derivatives in beta)
    6) Characteristics of High-Lift and Control Devices (section and wing
forces and moments, including hinge moments)
    7) Dynamic Derivatives (in p, q, r, alpha-dot, and beta-dot)
    8) Mass and Inertia
    9) Characteristics of VTOL-STOL Aircraft (thrust characteristics)

The methods are a mixture of theoretical and emperical equations.  Each
section starts with a description of the aerodynamics that contribute to
the derivative as appropriate to the configuration.  The methods are then
discussed with sample problems following.  Next are the references, the
tables showing accuracy of the methods, and finally, the charts.  You'll
probably recognize these - several authors use them liberally in their texts.

Where to get DATCOM:

It's $175.  It's distributed in four binders, is 3,200 pages, and can be 
ordered from:

	Global Engineering
	7730 Carondelet Ave. #407
	Clayton, Missouri  3105

Lastly: on learning how to use all this:

Berndard Etkin's books on flight control were highly recommended; _Dynamics 
of Flight_ was re-published in 1982, and is an update of the 1959 edition.  
Also, _Dynamics of Atmospheric Flight_ (Wiley, 1972, ISBN 0-471-24620-4).

_Airplane performance stability and control_, by Courtland D. Perkins and 
Robert E. Hage (Wiley, 1949).

_Modern Aircraft Flight Control_, by M. Vukobratovic and R. Stojic, in 
_Lecture Notes in Control and Information Sciences #109 (Springer-Verlag, 
1988).  A monograph: very readable, and of likely interest to those 
approaching the problem from a more traditional CS perspective.

Many thanks to Dan Sharpes, Bruce Jackson, Mary Shafer, Michael Jones, and
anyone else I've missed, for their contributions and suggestions.

Robert Dorsett