(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
1. FLIGHT STABILITY AND AUTOMATIC CONTROL.
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
coefficients.
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
footnote:
1. For example Anderson on INTRODUCTION TO FLIGHT and Stevens and Lewis on
AIRCRAFT CONTROL AND SIMULATION. Also FLIGHT DYNAMICS and THE
AERODYNAMICS OF FLIGHT.
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 **2.
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.)
footnotes:
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)
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