Potential of Multi-Winglet Systems
to Improve Aircraft Performance
vorgelegt von
Diplom-Ingenieur
Martin Berens
von der Fakultät V - Verkehrs- und Maschinensysteme -
der Technischen Universität Berlin
zur Erlangung des akademischen Grades
Doktor der Ingenieurwissenschaften
- Dr.-Ing. -
genehmigte Dissertation
Promotionsausschuss:
Vorsitzender: Prof. Dr.-Ing. W. Nitsche
Gutachter: Prof. Dr.-Ing. J. Thorbeck
Prof. Dr.-Ing. F. Thiele
Tag der wissenschaftlichen Aussprache:
28. März 2008
Berlin 2008
D 83
Preface
The work documented in this thesis was mainly performed during my job as an assistant
lecturer in the Aircraft Design and Aerostructures Group at the Institute of Aeronautics
and Astronautics at the Technical University Berlin.
I would like to express my gratitude to my supervisor, Prof. Dr.-Ing. Jürgen Thorbeck,
for giving me the opportunity to freely work on the ideas that finally culminated in the
present document. Also I would like to thank for his valuable advice which was not
limited to technical matters and last but not least his patience.
Furthermore, I am grateful to Prof. Dr.-Ing. Frank Thiele, who did not hesitate to accept
to become second examiner. I also appreciate that Prof. Dr.-Ing. Wolfgang Nitsche
agreed to take the chair of the examination board, who succeeded in strengthening my
personal interest in the field of aerodynamics in the years of my studies.
I would also like to thank Prof. Dr.-Ing. Karl Heinz Horstmann of the Institute of
Aerodynamics and Flow Technology of DLR Braunschweig for the valuable advice on
lifting line and vortex lattice methods. Thanks also to Prof. Dr.-Ing. Dietrich Hummel of
the Institute of Fluid Mechanics of the Technical University of Braunschweig for
recollecting details on the multi-winglet experiments conducted back in the 1970s
including an excursion to the loft of the institute building to take some photos of the
wind-tunnel model, which were helpful for designing of a CAD model of the
configuration. The next person to thank is my colleague Johannes Hartmann for
sketching the CATIA model. It is with regret in this context, that I had finally to curtail the
project scope and abandon the attempt to analyse the multi-winglet configuration by
means of RANS simulations.
Finally I am indebted to Michael Stache for the demonstration of experimental set-ups
for the analysis of non-planar wing concepts, the willingness to share ideas and the
experience gained in the course of many years of research on multi-winglet
configurations at the Institute of Bionics and Evolutiontechnique of the Technical
University Berlin.
I could extend the list of persons to whom I am grateful, but it would become too lengthy
and it would be extremely difficult not to miss someone. Hence, I prefer to thank groups
of persons, the secretariat staff for their patient advises on and practical help in
administrative matters, the workshop staff who's assistance I merely requested for non-
scientific efforts but who were enduringly interested in the finalisation of my thesis, of
course, my direct colleagues and last but not least the students of the KATO team, who,
due to their enthusiasm, took a lot of work off my hands and thus indirectly also
contributed to the present work.
Furthermore I am indebted to Dipl.-Ing. August Kröger of Airbus Deutschland for his
gentle but sustained pushing to bring the project finally to an end.
Last but not least I have to address my special thanks to my parents, my sister Monika
and my brother Thomas for their continuing encouragement. Anke, the person who
deserves my greatest gratitude coined the working title of the thesis and had to put up
with a sometimes less than balanced private life, but also never lost confidence that the
project will finally have a happy end.
Martin Berens Hamburg, June 2008
i
Contents
ABSTRACT V
ÜBERSICHT VI
NOMENCLATURE VII
1 INTRODUCTION 1
2 NON-PLANAR CONFIGURATIONS FOR LIFT PRODUCTION 4
2.1 Lift, Induced Drag and Related Phenomena 4
2.1.1 The Concept of the Lifting Line 4
2.1.2 Induced Drag of Non-Planar Lifting Systems 8
2.1.3 Classification of Non-planar Lifting Systems According to their Wake Shapes 15
2.1.4 Aircraft Wake Vortices and Associated Effects 22
2.1.5 Design and Off-Design Characteristics of Non-planar Lifting Systems 25
2.2 Further Aspects for the Design of Optimum Lifting Systems 26
2.2.1 Profile Drag 27
2.2.2 Effect of Wing Splitting on Profile Drag 28
2.2.3 Effect of Induced and Profile Drag on Aircraft Performance 30
2.2.4 Compressibility Effects 32
2.2.5 Wing Structure Mass 33
2.3 Multiwinglet Systems in Nature - Outer Primaries of Birds 34
2.3.1 Wing Morphology 35
2.3.2 Correlation of Wing Loading and Aspect Ratio with Fan-Out 39
2.3.3 Functions of Slotted Outer Primaries in Flight 40
2.4 Non-Planar Aircraft Wing Concepts 47
2.4.1 Technically Prevailing Winglet Systems 48
2.4.2 Attempts of Technical Adaptation of Multiwinglet Systems 53
2.5 Synopsis of Trends Affecting Planar and Non-Planar Wing Efficiencies 58
3 NUMERICAL MODEL 61
3.1 Aerodynamics 64
3.1.1 Vortex Lattice Method 64
3.1.2 Profile Drag Estimation 74
3.1.3 Interference Drag Estimation 82
3.1.4 Minimum and Maximum Section Lift Coefficients 84
3.1.5 Non-Linear Lift Effects 86
3.1.6 Cascade Effects 94
3.1.7 Aggregation of Integral Forces and Moments 108
3.2 Structures 109
3.2.1 Simplified Dimensioning of Wing Box 109
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