(extracted from the TAC textbook, Pages 54-57.)

give  a coefficient  that  has not  dimensions, or  dimensionless.  A same procedure is
used on the lift and  drag equations to get Cl and  Cd, for the coefficient of lift and  
coefficient of drag respectively.  Much  of what is needed for back- ground on flight and  
flight dynamics, that is for data analysis, centers  around these three coefficients: Cm,
Cl, and  Cd.

3-1:  Cl,  Cd,  and  Cm on  seleted  Aircraft.

It is necessary to look at some  numbers for these three coefficients in order to  get a  
feel for the  coefficient  of lift,  the coefficient  of drag, and   the moments coefficient;
even  before we look at the equations.   Dr.  Robert C. Nel- son1   has  made  an   
excellent  contribution  in  Appendix  B  in  providing  many detailed specs for specific  
aircraft,  14 specs for the  C coefficients;  but  now we will only compare the three
primary Cs of Cl, Cd, and  Cmalpha  for the follow- ing  aircraft:   the  Jetstar  business
aircraft,  the General Aviation  Navion,  the
Convair 8802,and the Boeing  747.

TABLE 1.  Aerodynamic Coefficients for Aircraft.

NOTE:  For a more structured look at this Table, download a pdf copy of this sample
from th link at the top of the page for Longitudinal Stability with Matlab.pdf


We need one low speed tuboprop aircraft for comparison since another focus of this
book will be on simulation with MATLAB of a transport aircraft and of the F-16.  The
closest spec FS&AC offers us of a jet like the F-16 is the A-4D, which is a ways back in
history before the F-16; but some of the first elogated exper- iment flights at NASA on a
UAV was on an A-4D offered to them by Naval Aviation.

1.  You will come to expect low numbers like .68, .08, and  -.903--all less than 1;
and the why of this will be discussed when we take a look at the equations.

2.   It would  make sense that  the Aerodynamic Coefficients  for the  Boeing  747 would
have higher numbers than for the Convair 880 since it is a much  larger air- craft.   The
weight of the 747 is  636,600  pounds, and  that  of the  Convair  880 was  126,000
pounds.  And  you notice that 2 of the coefficients for the 747 are above 1, Cl = 1.11
and  Cmalpha  = -1.26.

3.  I guess that we are not surprised that the Jetstar has more lift than the 880 and  less
than the 747. If we respectively compare the surface area of the wings respectively of
the Jetstar  at  542.5 square feet,  that  of the  747 at  5,500 square feet,  and   that  of
the  880 at  2,000 square feet,  that  relationship is exactly what we would expect for the

4.   Wow {and not  for Weight on Wheels}, look at the lift of the STOL  transport aircraft,
so we  are not   surprise to see a  wing  area of 945 square feet  and  a weight of only  
40,000  pounds.  The wing area of the transport aircraft we  will simulate in  MATLAB  
has a  weight of 162,000 pounds and  a  wing  area of 2170 square feet.

Please keep in mind that we an only provide in summary form a drop in the bucket of
both basic aerodynamics and  stability and  control dynamics; that only which  is
required for TECHNICAL APPLICATIONS  OF  COMPUTERS, and  in  particular Data  
Analysis, and  such is the way  it  should be lest  we feebly  try  to  compete with  the
recognized  experts like Anderson,  and   Stevens  and   Lewis.    In other words, if  you
want a good,  thorough book  on Flight  and  Flight  Mechanics read a book  like the one
by Anderson or on flight control and  simulation, read the one  by  Stevens  and  
Lewis.    {This  chapter  has  tried  to  cull   some    of  their essentials, by  research
while avoiding plagarism,  combing those  salient  points of stability  and control  
aerodynamics  with  many   other  recognized authorities.

2.  When Lockheed Martin at Fort Worth was still General Dynamics {in one of the
dumbest moves in history the former astronaut Bill Anders sold GDFW to Lockheed
even though it made over 50% of the profit for GD}, the Con- vair 880 made its last flight
to Europe dropping off our F-16 teams at various bases to unground the F-16s.  My
team was dropped at Brussels to go to Beuvechan AFB; and as far as I know was the
first to fly after the world-wide grounding.

For the  purpose of this  book  only  and  in this  one chapter,  we  will do  a  little
Systems  Integration  of our  own,  briefly integrating  the  two  diverse subjects of flight
Aerodynamics with that of Automatic Control, also  in the Transport Aircraft MATLAB
simulation, adding optimization.  Actually the integration will be larger than that
consisting of the bringing together in one  chapter what has generally be called the
disciples of and  the title of books on flight mechanics, aerodynamics, the history of
flight, automatic control, and  flight test and  simulation.  Ambitious yes; but that is far
better than trying in one  book  on DATA ANALYSIS for Systems Integration to attempt
an inclusion of even one  complete chapter on these diverse but closely related sub-
jects. Then except for a few “aero- dynamic moments” in each chapter,  we  will have  
sufficient  background  to proceed into  simulation, automatic control, and  flight itself.  
The challenge of such  integration will be assisted by  a focus on those aspects of flight
aerodynamics and  automatic control that most easily lend  themselves to data analysis.  
As a matter of fact, if  a more scholarly and  longer title  were chosen for this  chapter,  it
could  be “Systems Integration of Flight Aerodynamics and  Automatic Control for
Simulation and  Data Analysis”.  

Fig 3-1:   Flight Test  Parameters.

(For a structured look at typical aircraft parameters, and as given on a diagram of the F-
16 the reader is referred to the online download of the PDF.  See NOTE above for the
link or at the top of this page.)

Never forget  that  when large flight simulators are used like at NASA  Dryden and  
Wright Patterson, the simulator comes first then the simulator data; and  during actual
flight test, that previously collected  and analyzed data  from the  simulation both gives
clues for  flight  test and   gives another standard  for comparison. {That is actual flight  
test  data versus flight simulator data.}   And in this day  and  time of fuel costs and  the
economic crunch, more and  more aircraft and  missile companies are turning to
increased simulation for testing

1.  For example Anderson on INTRODUCTION TO FLIGHT and Stevens and Lewis on

3-2:  Steady State Flight  with  Principles  of Stability and  Control.

(NOTE:  Sect 2.6,  3.6,  and  3.7  of S&L and  chp  7 of Anderson)

We pilots call this flight condition, “straight and  level”:  in aerodynamics the more
acceptable terminology is “Principles of Stability and  Control.”   Airplane control,
according to a recognized authority on Flight1 is defined as:

Deflections of the  flight  control surfaces  like the  ailerons, elevators,  and  rudders to
shift  equilibrium positions  {we  will shortly come  to  the  energy concept and  
equations  for aircraft which   is much  like  the  basic kinetic energy versus potential
energy concepts of physics, K.E. = 1/2 mv^2  and  P.E.  = h g}, or  produce non-
equilibrium accelerated motions called flight manuevers **

For purposes of data analysis, this entails  a measurement of the deflections of these
flight  control surface, generally with  transducers  on motion sensors  con- nected  
physically to  those   control   surfaces;   then   the   data  collected   in  an onboard
computer like in ATIS or  the newer CAIS,  then transmitted to ground for  analysis by  a  
special kind  of radio signal called Telemetry.    So  ultimately designers, and  the pilot  
learning to fly that particular aircraft, must decide what amount of deflection is required
to do what is expected at that time, and  beyond that how much  force is required for that
amount of deflection.  Of course, technically  we  must  have  numbers of the deflection  
and  for the  force.  Remember while the force in such  small aircraft like the Piper
Cherokee Arrow that most of us fly  is  almost directly on the control surfaces {that is  
directly and  physically connected by  a  mechanical linkage},  the  force in aircraft such  
as  the F-16  and newer FBW (Flight By Wire) commercial aircraft is on a transducer.  
That proper... (For continuation read the book TAC on amazon.com or sign up at for the
email correspondence course at sungrist@gmail.com.)

1.  For enjoyable research and reading you can not beat John D. Anderson Jr’s
INTRODUCTION TO FLIGHT.  In this easy to read and understand book, he combines
his knowledge and skill from being a Curator of Aerodynamics at the Smithsonian and
Professor Emeritus at the University of Maryland.
2.  Focus on flight and especially flight test will be on four typical manuvers of flight test:  
the dutch roll, short period, phugoid, roll, and spiral.
An Introduction to Longitudinal
Stability numbers and parameters
from the TAC textbook.

NOTE:  For a more structured look  
download a PDF copy of this sample from
this website, entitled like this web page as

Longitudinal Stability with Matlab
.  (it will be
a pdf file instead of an html fie like this page)

The complete over 400
page book of

Technical Applications
of Computers with
Matlab, FreeMat,
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