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On Wings of the Minimum Induced Drag: Spanload Implications for Aircraft and BirdsFor nearly a century Ludwig Prandtl's lifting-line theory remains a standard tool for understanding and analyzing aircraft wings. The tool, said Prandtl, initially points to the elliptical spanload as the most efficient wing choice, and it, too, has become the standard in aviation. Having no other model, avian researchers have used the elliptical spanload virtually since its introduction. Yet over the last half-century, research in bird flight has generated increasing data incongruous with the elliptical spanload. In 1933 Prandtl published a little-known paper presenting a superior spanload: any other solution produces greater drag. We argue that this second spanload is the correct model for bird flight data. Based on research we present a unifying theory for superior efficiency and coordinated control in a single solution. Specifically, Prandtl's second spanload offers the only solution to three aspects of bird flight: how birds are able to turn and maneuver without a vertical tail; why birds fly in formation with their wingtips overlapped; and why narrow wingtips do not result in wingtip stall. We performed research using two experimental aircraft designed in accordance with the fundamentals of Prandtl's second paper, but applying recent developments, to validate the various potentials of the new spanload, to wit: as an alternative for avian researchers, to demonstrate the concept of proverse yaw, and to offer a new method of aircraft control and efficiency.

Document ID
Acquisition Source
Armstrong Flight Research Center
Document Type
Technical Publication (TP)
Bowers, Albion H.
(NASA Armstrong Flight Research Center Edwards, CA, United States)
Murillo, Oscar J.
(NASA Armstrong Flight Research Center Edwards, CA, United States)
Jensen, Robert (Red)
(Jacobs Technology, Inc. Edwards AFB, CA, United States)
Eslinger, Brian
(Jacobs Technology, Inc. Edwards AFB, CA, United States)
Gelzer, Christian
(Logical Innovations, Inc. Houston, TX, United States)
Date Acquired
March 22, 2016
Publication Date
March 1, 2016
Subject Category
Aircraft Stability And Control
Report/Patent Number
Funding Number(s)
Distribution Limits
Public Use Permitted.
flight dynamics
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