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Wave drag due to lift for transonic airplanes

Cole, Julian D. and Malmuth, Norman D. (2005) Wave drag due to lift for transonic airplanes. Proceedings of the Royal Society A: Mathematical, physical, and engineering sciences, 461 (2054). pp. 541-560. ISSN 1364-5021.

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Lift–dominated pointed aircraft configurations are considered in the transonic range. To make the approximations more transparent, two–dimensionally cambered untwisted lifting wings of zero thickness with aspect ratio of order one are treated. An inner expansion, which starts as Jones's theory, is matched to a nonlinear outer transonic theory as in Cheng and Barnwell's earlier work. To clarify issues, minimize ad hoc assumptions existing in earlier studies, as well as provide a systematic expansion scheme, a deductive rather than inductive approach is used with the aid of intermediate limits and matching not documented for this problem in previous literature. High–order intermediate–limit overlap–domain representations of inner and outer expansions are derived and used to determine unknown gauge functions, coordinate scaling and other elements of the expansions. The special role of switchback terms is also described. Non–uniformities of the inner approximation associated with leading–edge singularities similar to that in incompressible thin airfoil theory are qualitatively discussed in connection with separation bubbles in a full Navier–Stokes context and interaction of boundary–layer separation and transition. Non–uniformities at the trailing edge are also discussed as well as the important role of the Kutta condition. A new expression for the dominant approximation of the wave drag due to lift is derived. The main result is that although wave drag due to lift integral has the same form as that due to thickness, the source strength of the equivalent body depends on streamwise derivatives of the lift up to a streamwise station rather than the streamwise derivative of cross–sectional area. Some examples of numerical calculations and optimization studies for different configurations are given that provide new insight on how to carry the lift with planform shaping (as one option), so that wave drag can be minimized.

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Additional Information:© 2004 The Royal Society. Received 4 June 2004. Accepted 23 June 2004. This work was jointly accomplished by the two authors, the first of which, Professor Julian D. Cole, has sadly died. This paper was therefore written by Dr Norman D. Malmuth, who takes full responsibility for views here expressed and dedicates this work to Professor Cole. He is also indebted to Elwood Bonner (also deceased), formerly of North American Aviation Inc., for valuable discussions and support, and is grateful for the constructive comments of Katerina Kaouri (Oxford Centre for Industrial and Applied Mathematics (OCIAM), Mathematical Institute, Oxford University) (who also provided typographical corrections), Professors Oleg Ryzhov, U. C. Davis and Zvi Rusak (Rensselaer Polytechnic Institute) and Alexander Fedorov (Moscow Institute of Physics and Technology). This effort was supported by Rockwell North American Aircraft, Air Force Office of Scientific Research, Air Force Materials Command, Grant 88-0037 and Contract No. F49620-92-C-0006, F49620-96-C-0004, F49620-99-C-0005 and F49620-02-C-0024. The US government is authorized to reproduce and distribute reprints for government purposes, notwithstanding any copyright notation thereon. The views and conclusions herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research or the US government.
Funding AgencyGrant Number
Rockwell North American AircraftUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)88-0037
Air Force Office of Scientific Research (AFOSR)F49620-92-C-0006
Air Force Office of Scientific Research (AFOSR)F49620-96-C-0004
Air Force Office of Scientific Research (AFOSR)F49620-99-C-0005
Air Force Office of Scientific Research (AFOSR)F49620-02-C-0024
Subject Keywords:asymptotic expansions; transonic flow; slender body theory; mixed type
Issue or Number:2054
Record Number:CaltechAUTHORS:20200929-143506669
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Official Citation:Cole Julian D. and Malmuth Norman D. 2005 Wave drag due to lift for transonic airplanes Proc. R. Soc. A. 461:541–560
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105644
Deposited By: George Porter
Deposited On:30 Sep 2020 16:11
Last Modified:30 Sep 2020 16:11

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