INTERNATIONAL EDITION. Aerodynamics. for Engineers SIXTH EDITION. John J. Bertin Russell M. Cummings

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1 INTERNATIONAL EDITION Aerodynamics for Engineers SIXTH EDITION John J. Bertin Russell M. Cummings

2 This edition of Aerodynamics for Engineers is dedicated to the memory of John J. Bertin Vice President and Editorial Director, ECS: Marcia J. Horton Executive Editor: Norrin Dias Editorial Assistant: Sandra Rodriguez Executive Marketing Manager: Tim Galligan Marketing Assistant: Jon Bryant Permissions Project Manager: Karen Sanatar Senior Managing Editor: Scott Disanno Production Project Manager /Editorial Production Manager: Greg Dulles Publisher, International Edition: Angshuman Chakraborty Publishing Administrator and Business Analyst, International Edition: Shokhi Shah Khandelwal Associate Print and Media Editor, International Edition: Anuprova Dey Chowdhuri Acquisitions Editor, International Edition: Sandhya Ghoshal Publishing Administrator, International Edition: Hema Mehta Project Editor, International Edition: Karthik Subramanian Senior Manufacturing Controller, Production, International Edition: Trudy Kimber Creative Director: Jayne Conte Cover Designer: Bruce Kenselaar Cover Image: EmiliaUngur/Shutterstock Production and Manufacturing: Pat Brown Full-Service Project Management: Jogender Taneja, Aptara, Inc. Cover Printer: Courier Westford Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: Pearson Education Limited 2014 The rights of John J. Bertin and Russell M. Cummings to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act Authorized adaptation from the United States edition, entitled Aerodynamics for Engineers, Sixth Edition, ISBN , by John J. Bertin and Russell M. Cummings, published by Pearson Education All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a license permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6 10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. Microsoft and/or its respective suppliers make no representations about the suitability of the information contained in the documents and related graphics published as part of the services for any purpose. All such documents and related graphics are provided as is without warranty of any kind. Microsoft and/or its respective suppliers hereby disclaim all warranties and conditions with regard to this information, including all warranties and conditions of merchantability, whether express, implied or statutory, fitness for a particular purpose, title and non-infringement. In no event shall Microsoft and/or its respective suppliers be liable for any special, indirect or consequential damages or any damages whatsoever resulting from loss of use, data or profits, whether in an action of contract, negligence or other tortious action, arising out of or in connection with the use or performance of information available from the services. The documents and related graphics contained herein could include technical inaccuracies or typographical errors. Changes are periodically added to the information herein. Microsoft and/or its respective suppliers may make improvements and/or changes in the product(s) and/or the program(s) described herein at any time. Partial screen shots may be viewed in full within the software version specified. Microsoft and Windows are registered trademarks of the Microsoft Corporation in the U.S.A. and other countries. This book is not sponsored or endorsed by or affiliated with the Microsoft Corporation. ISBN 10: ISBN 13: British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Typeset in TimesTen Roman by Aptara, Inc. Printed and bound by Courier Westford in The United States of America The publisher s policy is to use paper manufactured from sustainable forests.

3 Sec. 5.3 / Wing-Geometry Parameters 249 Chord of root section y 0 Vehicle longitudinal axis c /4 (unswept) y (b/2) Chord of tip section Parallel to the vehicle longitudinal axis Figure 5.8 Unswept, tapered wing with geometric twist (wash out). Jackson (2011) ], and are summarized in Table 5.1. Data are presented for four-place single-engine aircraft, commercial jetliners and transports, and high-speed military aircraft. Note how the values of these parameters vary from one group of aircraft to another. The data presented in Table 5.1 indicate that similar designs result for similar applications, regardless of the national origin of the specific design. For example, the aspect ratio for the four-seat, single-engine civil aviation designs is approximately 7, whereas the aspect ratio for the supersonic military aircraft is between 1.7 and 3.8. In fact, as noted in Stuart (1978), which was a case study in aircraft design for the Northrop F-5, the selection of wing aspect ratio represents an interplay between a large value for low drag-due-to-lift and a small value for reduced wing weight. There are other trends exhibited in parameters relating to aircraft performance. Notice the grouping by generic classes of aircraft for the correlation between the powerto-weight ratio and the wing loading that is presented in Fig There is a tendency for airplanes to get larger, heavier, and more complex with technological improvements. The trend toward larger, heavier aircraft is evident in this figure. Note that a fully loaded B-17G Flying Fortess, a heavy bomber of World War II, weighed 29,700 kg (65,500 lb) with a wing span of m ( ft), whereas the F-15, a modern fighter aircraft, has a maximum takeoff weight of 30,845 kg (68,000 lb) with a wing span of m (42.81 ft). However, the successful human-powered aircraft fall in the lower left corner of Fig. 5.9, with wing loadings (the ratio of take-off gross weight to wing area) less than 1 lbf>ft 2. It is in this same region that Lockheed s solar high-altitude powered platform (Solar HAPP) operates.

4 TABLE 5.1 Wing-Geometry Parameters Type (Original and Current Manufacturer Names Are Given) Wing Span [m(ft)] Socata Rallye (France) Ambrosini NF 15 (Italy) Beechcraft Bonanza V35B 9.61 (31.52) 9.90 (32.5) (33.46) Beechcraft Sierra 9.98 (32.75) Cessna (35.83) Piper Commanche (36.0) Bellanca, Model (35.0) Piper Warrior II (35.0) Caravelle 210 (France) 34.3 (112.5) BAC 111 (UK) (88.5) Tupolev 204 (Russia) (137.3) Boeing (93.0) Boeing (195.7) Aspect Ratio, AR Sweep Angle Dihedral Airfoil Section Speed [km/h (mi/h)] a. Four-Place Single-Engine Aircraft None 7 63A414(mod), 63A416, inc ( ) None , inc (202) None at root, at tip, inc. 4 at root, 1 at tip 7.35 None A415, inc. 3 at root, 1 at tip 7.32 None 1 44 NACA 2412, inc at root, at tip ( ) ( ) forward A215, inc (185) 6.70 None 2 NACA , inc None 7 NACA , inc. 2 at root, -1 at tip b. Commercial Jetliners and Transports 211 (131) ( ) ( ) at c >4 3 NACA (490) at c >4 2 NACA cambered section (mod.), t>c = at root, 0.11 at tip, inc at c >4 t>c = 0.14 (inboard) to 0.09 (outboard), inc. twist 815 (507) 850 (528) 25 at c >4 6 t>c = (av.) 848 (527) at c >4 7 t>c = (inboard), (midspan), (outboard), inc (595) 250

5 Type (Original and Current Manufacturer Names Are Given) Wing Span [m(ft)] Aspect Ratio, AR Sweep Angle Dihedral Airfoil Section Speed [km/h (mi/h)] Boeing (212.6) Lockheed C-5A (222.8) McDonnell Douglas (Boeing) C-17 Airbus A310 (International) Airbus A380 (International) SAAB-35 Draken (Sweden) Dassault Mirage III (France) (165) (144.0) (261.8) 9.40 (30.8) 8.22 (27.0) Northrop F-5E 8.13 (26.67) McDonnell-Douglas F (38.4) LTV F (35.7) LTV A (38.75) Mitsubishi T2 (Japan) 7.88 (25.85) General Dynamics (Lockheed Martin) F (30.0) Lockheed Martin F (44.5) Eurofighter (International) Sukhoi Su-27 (Russia) (35.35) (48.2) at c >4 Mach at c >4 Anhedral 5 30 NACA 0011 (mod.) near midspan, inc at c >4 Anhedral 3 30 t>c = (inboard), (outboard) 28 at c > (inboard at the trailing edge) 35 at c >4 (average) c. High-Speed Military Aircraft Central: leading edge 80 outer: leading edge 57 Leading edge t>c = at root, t>c = at tip, inc. 5 3 at root 815 (507) Mach ( ) 5.5 (outboard) 945 (587) t>c = 0.05 Mach Anhedral 1 t>c = Mach at c >4 None 65A004.8 (mod.), t>c = Mach Outer panel 12 t>c = (av.) Over Mach Anhedral 5 Thin, laminar flow section Nearly Mach 2 35 at c >4 Anhedral 5 65A007, inc (698) at c >4 Anhedral 9 NACA 65 series (mod.), t>c = on leading edges 42 on leading edges 53 on leading edges Mach 1.6 NACA 64A-204 Mach Anhedral 3.25 t>c = (inboard) and (outboard); -3.1 at tip 1 Mach NACA 66 (mod.) Mach at c >4 0 t>c = 0.05 Mach 2.35 Source: Data from Jane s All the World s Aircraft (1973, 1966, 1984, and 2011). 251

6 252 Chap. 5 / Characteristic Parameters for Airfoil and Wing Aerodynamics 10 World War II fighters 1.0 Supersonic jet fighters Subsonic jet fighters World War I fighters Powertoweight ratio (hp/lbf) Human powered aircraft Solar HAPPs Wright flyer Solar Challenger Wing loading (lbf/ft 2 ) Jet transports Turboprops General aviation aircraft Figure 5.9 Historical ranges of power loading and wing loading [ from Hall (1985) ]. EXAMPLE 5.1: Aspect ratio of a delta wing Develop an expression for the aspect ratio of a delta wing in terms of the leading-edge sweep angle ( LE ). Solution: Referring to the sketch of the delta wing in Fig. 5.7, the wing area is and the tan LE is given by S = bc r 2 tan LE = c r (b>2) Solving this second expression for c r and substituting it into the expression for the wing area, we obtain: S = b2 4 tan LE Substituting this expression for the wing area into the expression for the aspect ratio gives: AR = b2 S = 4 tan LE (5.1)

7 Sec. 5.3 / Wing-Geometry Parameters 253 EXAMPLE 5.2: Calculate the wing-geometry parameters for the Space Shuttle Orbiter Solution: To calculate the wing-geometry parameters for the Space Shuttle Orbiter, the complex shape of the actual wing is replaced by a swept, trapezoidal wing, as shown in Fig For the reference wing of the Orbiter, the root chord c r is ft, the tip chord c t is ft, and the span b is ft. Using these values which define the reference wing, calculate (a) the wing area S, (b) the aspect ratio AR, (c) the taper ratio l, and (d) the mean aerodynamic chord mac. (a) The area for the trapezoidal reference wing is: S = a c t + c r b b 2 = 2690 ft2 2 2 (b) The aspect ratio for this swept, trapezoidal wing is: AR = b2 S (c) The taper ratio is found from: l = c t c r = = ( ft) ft 2 = ft ft = 0.20 b ft c t ft c r ft Wing glove c r Reference wing area c t b Figure 5.10 Sketch of Space Shuttle Orbiter geometry for Example 5.2.