Airfoil Design and Data

568 Pages·1990·9.929 MB·English

by  Prof. Dr. Richard Eppler (auth.)

Richard Eppler
Airfoil Design
and Data
With 439 Figures
Springer-Verlag Berlin Heidelberg GmbH
Prof. Dr. Richard Eppler
Institut A fUr Mechanik
Universităt Stuttgart
Pfaffenwaldring 9
0-7000 Stuttgart 90
ISBN 978-3-662-02648-9
Ubrary of Congress Cataloging-in-Publication Data
Eppler, Richard.
Airfoil design and data 1 Richard Eppler.
Includes bibliographical references.
ISBN 978-3-662-02648-9 ISBN 978-3-662-02646-5 (eBook)
DOI 10.1007/978-3-662-02646-5
1. Aerofoils.1. Title.
TL514.A4E67 1990
629.134'32--dc20 90-33339
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© Springer-Veriag Beriin Heidelberg 1990
Originally published by Springer-Veriag Beriin Heidelberg New YorK in 1990
Soflcover reprint of the hardcover 1s t edition 1990
The use of registered names, trademarks, etc, in this publiclation does not imply, even in the
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2161/3020-543210 - Printed on acid-free paper
Foreword
This book represents the latest state of my work on airfoils which began more than 30
years ago. The major subject of this work was the continous development of a computer
program which allows to solve the potential flow problem for given airfoils and to design
airfoils from the properties of their velocity distributions. After the solution of these
potential flow analysis and design problems the boundary layers can be computed and the
total lift. drag and moment coefficients can be evaluated. Several short and unpublished
notes on this program were promoted by the US Airforce Academy in Colorado Springs with
the support of R. Gallington and W. Smith. A first complete description was published by
the NASA Langley Research Center. Ref. [1]. after had been invited to visit this center
for four weeks in 1978. This was the beginnning of a very fruitful coorperation with Dan M.
Somers. It led to another visit to the NASA Langley Center in 1979. during which several
new options were added to the program and described in Ref. [2].
The NASA TM [1] contains a listing of the program which invited some smart people to
retype it. Obviously they've been selling it for a lot of money. However. this early 1979
version should not be used anymore. because it's missing ten years of development and
improvements. The latest version of the program is available from Universitat Stuttgart. Inst.
A fUr Mechanik. Pfaffenwaldring 9. D - 7000 Stuttgart 80. It now costs DM 1200.- including
a detailed User's Guide. Ref. [36].
Almost since the publication of [1] and [2] I had been collecting data of airfoils. which
were designed by means of the program that is described in these reports. I intended to
publish a book with many examples for the application of the computer program. My
intention was to name it "Airfoil Data". because I wanted to demonstrate that my work was
a continuation of the famous NACA 824 Report "Summary of Airfoir Data" by Abbott. von
Doenhoff and Stivers. That report has fascinated me from the very beginning and initiated
my own work on airfoils. During the writing of the book it became clear that I had to
extend the description of the fundamental theories and computational methods. Eventually it
became evident that I had to change the title and include the airfoil design. The same
experience was probably made. when the NACA 824 report was replaced by the book
"Theory of Wing Sections" by Abbott and von Doenhoff. This book also contains much more
theoretical fundamentals than the NACA report.
It was a certain risk to write the book in English. But I thaught this is not only the
VI
language of the report and book mentioned above. it is also known to more scientists and
engineers than my German mother tongue. Moreover. all my american friends encouraged me
and offered help. In fact. they really did a tremendous job by "translating·· my English into
the English in which most chapters of the book are written. I must still apologize for many
··bumps" in the text. When I was running out of time and more and more new airfoils and
comments were added I eventually concluded that it would be better to publish the book
earlier with some sentences in poor English rather than later but in excellent English.
In any case I am very grateful to Dan M. Somers. Dr. Mark D. Maughmer and Richard C.
Eklund. They not only corrected my text carefully. they also came up with many suggestions
to improve the content. I also thank J. Miller. C. Marks and M. Routschka who exactly
typed the manuscript. Mainly C. Marks simultanously did a lot of editing which saved some
time to my american friends. Furthermore D. Althaus provided most of the experimental data
in the book for which I thank him very much. Finally. T. Lutz performed the complete
make - up of the pages and. as an aeromodel expert. he checked and corrected the text
and the figures. I also appreciate his help very much.
Last not least I thank the Springer - Verlag. Dr. W. Ludwig. and Mr. A. von Hagen for
accepting and printing the book in the excellent manner that their company is known for.
I hope that their very long and patient waiting for the manuscript will be rewarded by the
content of the book.
Stuttgart. in January 1990 Richard Eppler
Contents
Introduction
2 Potential Flow, Analysis Mode 4
3 Potential Flow, Design Mode 9
3.1 General Considerations 9
3.2 The Complex Planes 10
3.3 The Velocity Specification on the Unit Circle 11
3.4 Specification of the Velocity Distribution in Segments 11
3.5 Main Pressure Recovery Functions 14
3.6 Conditions for Continous Velocity Distributions 17
3.7 The Closure Conditions 18
3.8 The Trailing Edge and the Leading Edge 20
3.9 The Computation of the Airfoil Coordinates 21
3.10 Common Features of the Input Data Lines 22
3.11 The Input Lines for the Airfoil Design 23
3.12 The Trailing Edge Iteration 27
3.13 General Remarks 40
4 Boundary Layer Theory 48
4.1 Fundamentals 48
4.1.1 Nondimensional Variables and Units 48
4.1.2 Similarity ........ . 49
4.1.3 The Boundary Layer Equations 50
4.2 The Computation of Laminar and Turbulent Boundary Layers 55
4.3 Boundary Layer Transition 62
4.4 The Laminar Separation Bubble 68
4.5 Total Lift. Drag. and Moment 76
4.6 The Bubble Warning 81
4.7 Single Roughness Elements 88
5 General Considerations for the Selection of the DesIgn Parameters 90
5.1 The Laminar Region of the Airfoils 90
5.2 The Critical Reynolds Number 110
5.2.1 The Transition Ramp 110
5.2.2 Artificial Turbulators 125
5.3 The Main Pressure Recovery 126
VIII
5.3.1 The Maximum Total Amount of Pressure Recovery 126
5.3.2 The Main Pressure Recovery for Maximum Lift 140
5.3.3 The Main Pressure Recovery for Minimum Drag 152
5.3.4 The Contribution of the Main Pressure Recovery
to the Stall Characteristics 154
5.3.5 The Selection of the Recovery Parameters 155
5.4 Airfoils with Flaps 156
5.5 Profiles for Maritime Applications (Hydrofoils) 160
6 Airfoil Data 163
6.1 Directory 163
6.2 Older. Successfully Applied Airfoils for Different
Reynolds Number Ranges 172
6.3 Airfoils for Low Reynolds Numbers 210
6.4 Airfoils for Manpowered Aircraft 224
6.5 Airfoils without Flaps for the Reynolds Number
Range of Sailplanes 238
6.6 Airfoils with Flaps for Sailplanes (Gliders) 264
6.7 High lift Airfoils 298
6.8 Airfoils for General Aviation Aircrafts 306
6.9 Airfoils for Acrobatic Aircraft 384
6.10 Airfoils for Tailless Airplanes 408
6.11 Airfoils for Vertical and Horizontal Tails 432
6.12 Airfoils for Propellers 458
6.13 Airfoils for Helicopter Rotor Blades 476
6.14 Hydrofoils 500
6.15 Airfoils for Non-Lifting Struts 510
Appendix I: The Mathematics of the Inverse Potential Flow Method 514
Appendix ,,: Airfoil Coordinates 522
Appendix III: Airfoil Input Data 552
References 559
1 Introduction
The publication of an airfoil catalog seems to be not very consequent today. There exist
computer programs which allow the design of airfoils which are very good, if not optimally
adapted to the requirements resulting from certain special applications. It may be better to
design an entirely new airfoil for an application rather than to look for an appropriate one
in some catalog. It is not very likely to find an optimal airfoil there which has the correct
thickness, the correct lift coefficient range and the correct moment coefficient, being tested
for the intended flap arrangement, the right Reynolds number and the right surface rough
ness, to mention only a few criterions for the selection.
For example, the computer code published in [1] and [2] is a very effective tool for the
design of airfoils for special applications, shortly called airfoil tailoring. It contains a simple
solution of the inverse problem, which starts from a prespecified velocity distribution and
one obtains as a result the airfoil, for which that velocity distribution is realised at a cer
tain angle of attack. This way, it is possible to "apply" velocity distributions, which guarantee
a good boundary layer development and low drag.
Moreover this code also allows for prespecified airfoil shapes to compute the velocity distri
butions, the boundary layer developments and the lift, drag and moment coefficients in a ve
ry simple manner. A pre specified or a designed airfoil may be modified by flap defl~ction or
by variable geometry devices. The results are both cheaper and earlier available by a factor
of about 100 compared to wind tunnel experiments, and this factor still has increasing
tendency. Additionally, the amount of information obtained from the computer is much bigger
than that obtained from wind tunnel experiments. For example the boundary layer thicknesses
are directly available from the computer by typing a different number in an input line, while
the corresponding measurement is very expensive and time consuming.
There may be several reasons for the fact that such a tool is not used more widely,
although it is very cheaply available today:
Selecting an airfoil from a catalog is easier than tailoring one. The latter takes some
effort to study the computer code and its input-output-options, and to get experienced
with it.
- Many deSigners still have more trust in wind tunnel tests than in computer results.
2
This last reason provokes som~ comments. Of course, the computations are based upon
some mathematical assumptions. The results should be interpreted carefully. But exactly the
same is true for wind tunnel tests. There are lots of significant differences between a wind
tunnel test and the free flight of a wing. The wind tunnel model has a low aspect ratio,
the tunnel side wall is to produce two dimensional flow, but it has a boundary layer, which
even intersects with the airfoil boundary layer. The effects caused by such wind tunnel
properties are probably higher near the maximum lift of the airfoils. These effects are
merely investigated. One tunnel has a side wall suction, another one does not, one tunnel
gets the lift from pressure measurement at the model [22], another one from the tunnel
wall [21]. the third from force scale. Moreover, D. Althaus [3] recently published
experimental results showing that even the spanwise position of the wake rake for the drag
evaluation can have sensitive influence, as the turbulent boundary layer has in many cases a
distinct longitudinal structure.
How then should computer results be judged? On first sight the best way seems to be to
compare computer results with experimental data from different sources, if possible different
wind tunnels and free flight evaluations. There are a few airfoils which have been experi
mentally tested in different ways. More details will be given in the book. But also the com
parison of many computer results with experiments from one tunnel adds certain experience.
It leads to the following statements:
An airfoil should never be applied without a computer analysis. The analysis is extremely
cheap and always provides additional information.
- It is more reliable to compare two different airfoils by data obtained from the same
computer program than by tests from different wind tunnels.
But this also means that the effect of minor modifications of an airfoil can be studied ea
sily and with good reliability in a computer. This is already the first step to airfoil tailoring.
In a more direct way, the tailoring can be done by using velocity distributions, which have
proved to be satisfactory in theory, wind tunnel and free flight for certain Reynolds num
bers. The angles of attack, at which these well proved velocity distributions really occur,
can be changed without risk. The modification of airfoils and the transfer of velocity distri
butions from one airfoil and one angle of attack to another airfoil and a different angle of
attack can be handled by the design part of the computer code [1], [2] in a very simple
and pleasant way.
The present data collection is hence more than a normal catalog. All airfoils described here
are examples for the airfoil design. Most of them have been tailored for special applications,
3
which will be mentioned in each case, and the design features will be explained. So they
may be used as starting point for modifications, or just their velocity distributions may be
used by transferring them to other angles of attack. To promote this procedure, this data
summary includes the input data for the computer code, and it will be shown how easily
these data can be used in the design of new airfoils.
Beyond that, some of the airfoils may be used directly. The applications for which they have
been tailored may reoccur in a similar fashion. To be careful, it could be said that some of
the airfoils may for some applications be better than others from other catalogs.
In fact, many of the airfoils have been applied in aircraft, gliders and models and not all
applications have been straightforward. If for example an airfoil has been optimized for a
tailless glider, it should not be applied for a tailless model whose Reynolds number is lower
by a factor of 6 to 10. Even if the model enthousiast is convinced that he made an excel
lent choice, I must warn of such off-design applications.
Some knowledge of airfoil aerodynamics and boundary layer theory is necessary for under
standing the airfoil design features. A short guideline of the fundamentals with references
will be given in the next chapters. For entering the field of airfoil tailoring, the report [1J
and the User's Guide [36J must be studied and the program must be adapted to the
computer to which access is available. The computer only must have a compiler for
Standard FORTRAN 77 language. Its memory must cover a FORTRAN-program with about
6000 instructions, and a small plotter or graphics printer with the corresponding control
software should be available.
The report [1] does not consider compressibility. In the meantime, the program system
described in [1J has been extended to compressible subsonic flow by using a good com
pressibility correction. The correction is however only used for a few airfoils of the present
volume. All others are restricted to local Mach numbers below 0.3 to 0.4. This means that
the free stream Mach number must be smaller for high lift coefficients than for lower
ones. The Reynolds numbers for which the program has been successfully applied vary from
30000 to 50 X 106, thus covering at least the range of three different types of wind tun
nels and an additional range for which no tunnel exists yet.