AIRCRAFT DRAG REDUCTION THROUGH A DISSERTATION dp147ff0571/thesis- aircraft drag reduction

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    S. Andrew Ning

    August 2011


    This dissertation is online at:

    © 2011 by Simeon Andrew Ning. All Rights Reserved.

    Re-distributed by Stanford University under license with the author.

    This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License.


  • I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

    Ilan Kroo, Primary Adviser

    I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

    Juan Alonso

    I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

    Sanjiva Lele

    Approved for the Stanford University Committee on Graduate Studies.

    Patricia J. Gumport, Vice Provost Graduate Education

    This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives.


  • Abstract

    While the early pioneers of flight looked to birds to learn how to fly, the early aero-

    dynamicists looked to birds to learn how to fly more efficiently. Among the many

    insights gleaned from nature, was the observation that migratory birds often flew

    together in formation. As aerodynamic theory developed, it was shown that forma-

    tion flight could be used to increase range. Despite an understanding of the physics,

    technological challenges have prevented aviation from benefitting from the energy left

    behind in an aircraft’s wake. However, advances in precision navigation and control

    over the last few decades have brought renewed attention to formation flight of air-

    craft. Past published studies have focused on close formation flight, but the hazards

    of flying in close proximity are unacceptable in commercial aviation. This research

    explores a more practical approach, which we term extended formation flight. Ex-

    tended formations take advantage of the persistence of cruise wakes and extend the

    streamwise spacing between the aircraft by at least five wingspans.

    Classical aerodynamic theory suggests that the total induced drag of the for-

    mation should not change as the streamwise separation is increased, but the large

    separation distances of extended formation flight violate the simple assumptions of

    these theorems. At large distances, considerations such as wake rollup, atmospheric

    effects on circulation decay, and vortex motion become important. This dissertation

    first examines the wake rollup process in the context of extended formations and

    develops appropriate physics-based models. These simple models compare well with

    higher-fidelity Navier-Stokes solutions, as well as with experimental data.

    The wake model is then used to investigate the induced drag savings of forma-

    tions of aircraft in the presence of uncertainty in model parameters, variation in


  • atmospheric properties, and limitations of positioning accuracy. Extended formation

    flight is found to only be practical in low to moderately low turbulence conditions

    with streamwise separation distances less than about 40 to 50 wingspans. Tracking

    error is found to be the largest source of variation in the induced drag savings. At

    typical conditions, a 2-aircraft formation achieves a maximum reduction in induced

    drag of approximately 30 ± 3%, while a 3-aircraft formation achieves a maximum reduction of 40± 6% (95% confidence intervals).

    High-fidelity analyses are utilized to help understand the impact of compressibility

    while flying in formation. An Euler solver is modified to allow the use of the wake

    vortex model. This solver is then used to analyze the inviscid aerodynamic forces

    and moments of transonic wing/body configurations flying in a 2-aircraft extended

    formation. By slowing down by about 2%, a formation can achieve large induced drag

    reductions with little compressibility penalties. Flying further from the center of the

    vortex can allow for slightly higher cruise speeds in exchange for higher induced drag.

    Finally, the methodology is applied to studying formations of non-identical air-

    craft. Fundamental considerations in optimally arranging the formations are iden-

    tified. Choosing a proper formation arrangement can have a significant impact on

    the fuel burn. Simple guidelines for choosing the arrangement of the formation are

    found to often coincide with the optimal arrangement. Re-arranging the formation

    en-route, in order to minimize fuel burn, is shown to be generally unnecessary, and

    even in the best cases can only provide fuel savings on the order of half a percent.


  • Acknowledgements

    I am very fortunate to have had Professor Ilan Kroo as my PhD advisor. Although

    I came to Stanford already possessing a general interest in the field of aerospace en-

    gineering, Professor Kroo’s course on aircraft design truly inspired me and changed

    the direction of my graduate studies. His enthusiasm for everything related to flight

    is contagious, and the depth of his insightfulness is always astonishing. Under his

    guidance I have developed greater ability to carefully articulate my thoughts, learned

    to dig deeper until an understanding of the underlying physics illuminates the re-

    sults, and rediscovered the joys of interesting research. Along with Professor Kroo, I

    thank Professor Juan Alonso, and Professor Sanjiva Lele for serving on my reading

    committee and providing helpful feedback and suggestions.

    There are too many professors and instructors here at Stanford who have greatly

    contributed to my education to name them all. The courses here at Stanford have

    been excellent, and I have learned much. My wife would joke that the day the new

    course catalog came out was like Christmas for me. That may be an exaggeration, but

    I have truly enjoyed the learning opportunities afforded me both inside and outside

    of the classroom here at Stanford. I am also thankful for those who have taught and

    mentored me as an undergraduate at Brigham Young University. The availability

    of research opportunities for undergraduates, and the generosity of faculty members

    with their time were simply outstanding.

    I am grateful for the many interesting conversations and good company I have

    enjoyed with my colleagues of the Aircraft Aerodynamics and Design Group. In

    particular, I would like to thank Geoff Bower, Emily Dallara, Tristan Flanzer, and

    Jia Xu for the opportunity we had to work together on the Airbus’ Fly Your Ideas


  • competition. I am always amazed by what can be accomplished when a team works

    well together. The time spent together researching, making a movie, and presenting

    our findings in France, was definitely one of the highlights of my time at Stanford.

    Mathias Wintzer has been a resource to many in our research group as he possesses

    an amazing depth of understanding in anything computer-related as well as a breadth

    of experience in aircraft configuration design. I have benefited from his help in many

    ways. Dev Rajnarayan and Brian Roth, both former members of our group, also gave

    me encouragement and direction as a new researcher in the group, for which I am


    I am thankful for the larger community of the Aero/Astro department with whom

    I have enjoyed playing soccer and basketball, and from whom I have learned about

    the other interesting work being done in the department. I am also thankful for the

    many friends from school, the courtyard, and church who have enriched my life.

    In this past year I have been blessed to have the opportunity to work with Michael

    Aftosmis, Marian Nemec, and James Kless of NASA Ames Research Center. I want

    to thank Mike for not only opening the door to the expertise and computational

    resources of NASA, but also for being an incredible mentor to me. Along with Mike,

    Marian Nemec and James Kless have provided invaluable feedback and direction in

    studying the compressibility effects of formation flight. The work on compressibility

    has been a very satisfying and enjoyable piece of my dissertation, and would not

    have been possible without the contributions from the people and resources of NASA


    I am very grateful to have received the thr

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