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Airplane

Design

Manual

FREDERICK K^TEICHMANN

Professor of Aeronautical Engineering

Assistant Dean, Day Division

College of Engineering, New York University

FOURTH EDITION

PITMAN PUBLISHING CORPORATION

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NEW YORK TORONTO LONDON

Engin. Library

TL

G7/.2

3 SB Copyrioht, 1939, 1942, 1950, 1958

BT

PITMAN PUBLISHING CORPORATION

All rights reserved. No part of this book

may be reproduced in any form without

the written permission of the publisher.

4.1

cop. 2.

Associated Companies

Sir Isaac Pitman a Sons, Ltd.

London Melbourne Johannesburg

Sir Isaac Pitman & Sons (Canada), Ltd.

Toronto

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Printed in the United States of America

Preface to the Fourth Edition

This book grew out of notes prepared for airplane design courses at the

Daniel Guggenheim School of Aeronautics, College of Engineering, New

York University more than twenty years ago. The field of airplane design

has undergone enormous changes in these years and will continue to do so.

Thus the book has been expanded to encompass recent developments,

thereby making it more effective and meaningful to the present-day

student.

In addition, an attempt has been made in this revision to amplify the

analytical approach to design problems as well as the purely empirical

approach. The student of airplane design is in this way offered a deeper

appreciation of the interplay of aerodynamics, structural analysis, human

considerations, and other such factors.

Although practical necessity restricts the treatment that can be given

to each of the various fields, it is hoped that the student may be stimulated

to refer to literature that is available elsewhere.

The objectives of aircraft design work in the college classroom are:

(1) To offer an integration of or focal point for applying the various

principles included in aerodynamics, structural design, installation require-

ments, and application of materials. If time permits, economics, perform-

ance calculations, and allied problems continue the understanding of the

design concept.

(2) To afford a basis for stress analyses.

(3) To provide some drafting experience.

(4) To develop an "engineering sense" in the student, enabling him to

evaluate various requirements, judge the necessity of compromise, and

know the amount of time needed to achieve a given objective.

This book has been designed to aid both the teacher and student of

airplane design to effectively meet and fulfill these important goals.

Frederick K. TeichmaHn

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vii

viii

AIRPLANE DESIGN MANUAL

Preface to the Third Edition

Although airplane design has progressed tremendously since this book

was first published, the fundamental approach to the problem of airplane

design has not changed. However, the possibility of attaining transonic

and supersonic speeds with aircraft, a hope seemingly very remote only a

few years ago, has introduced additional considerations in designing even

the smallest detail. The student may not find all the needed answers in

the new edition but the way to his desired goal is indicated. It is up to

him to make the best use of material at hand, either in this book or col-

lateral reading.

The author greatly appreciates the work in redrawing and preparing

new sketches done by Messrs. Dong, Waxman, and Wood, his former

students.

Frederick K. Teichmann

Preface to the First Edition

This book has been written to fill what appears to the author to be a

gap in aeronautical literature, an introduction to the art of airplane de-

sign, with the needs of the student, the young engineer, the draftsman and

the student working on his own especially in view. While aerodynamics,

stress analysis and other aspects of airplane design have been covered many

times, experience in dealing with senior aeronautical students has shown

that such men experience considerable difficulty in coordinating their

knowledge and efforts in approaching the difficult problem of actually

beginning the design of a new machine, and carrying on the work system-

atically. From time to time notes have been prepared for student use

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and these have gradually evolved into the present work.

PREFACE

ix

In view of the rapid growth and complexity of the subject, it is too much

to hope that the entire field has been adequately covered; still teaching

experience indicates that such a manual is helpful to instructors and stu-

dents alike.

It is of course expected that the student shall supplement the present

text by investigations of his own, by studying the latest designs at the

airport, or from descriptions in the technical press, or by study of the

numerous research publications published by the Government Printing

Office and the great engineering societies, even though an attempt has

been made to make each chapter of the book as complete in itself as

possible.

The author wishes to thank the following companies (among others) for

permission to use illustrations: The Pratt & Whitney Aircraft Co., Pioneer

Instrument Co., R.C.A. Manufacturing Co., Inc., The Cleveland Pneu-

matic Tool Co., The Goodyear Tire & Rubber Co., The B. F. Goodrich

Rubber Co., The Firestone Tire & Rubber Co., Bendix Products Corpora-

tion, Harrison Radiator Corporation, Eclipse Aviation Corporation, Kolls-

man Instrument Co.

Thanks are also due to Mr. Robert Boyer and Mr. Leonard Mihalov-

sky, N.Y.U.'37, who kindly permitted the use of their class designs, and

to Professor Alexander Klemin, who established the course in airplane de-

sign in 1924, in a form which has stood the test of time, for many valuable

suggestions and criticisms.

Frederick K. Teichmann

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June, 1939

Contents

Prefaces

, Chapter I. Procedure in Design

Selecting Type of Airplane .

Power Plant

Payload and Crew

Performance Requirements

Step-by-Step Procedure .

Nomenclature

References

i Chapter II. Types of Airplanes

The Biplane

The Sesquiplane

The Multiwing Airplane .

The High-Wing Monoplane .

The Low-Wing Monoplane

Special-Purpose Airplanes

Factors Affecting Choice

Performance

Landing-Gear Retraction .

Structure

Special Features

Sample Airplane Data Sheets

Empirical Data

Airplane Data

8 Chapter HI. Airfoil Selection .

The Airplane in Rectilinear Flight

Horizontal Flight

Gliding Flight

The Dive

The Climb

Range

Other Airfoil Characteristics

Structural Considerations

Recapitulation

Aspect Ratio Corrections

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Aerodynamic Section Characteristics .

Airfoil Construction

Sweepback for High-Speed Airplanes

Laminar-Flow Airfoils .

Compressible-Flow Airfoils

xi

xii AIRPLANE DESIGN MANUAL

Chapter IV. External Loads on an Airplane in Flight .... 50

Load Factor 50

The Airplane in a Maneuver 51

The Airplane in a Gust 52

Experimental Determination of the Load Factor .... 55

Airplane Categories 57

Empirical Load Factors 57

The Flight Envelope 58

Reference Axes 59

Generalized System of Forces 61

Other Dynamic Loads 63

Chapter V. Materials of Construction 64

Application of Available Materials 64

Aluminum and Aluminum Alloys 65

Classification and Nomenclature 66

Sheet 67

Tubing 68

Extruded Shapes 68

Forgings 68

Castings 70

Wire, Rod, and Bar 70

Rivets and Screw-Machine Products 70

Airframe Fabrication 71

Cutting and Blanking 72

Forming 72

Magnesium Alloys 74

Castings 74

Forgings 74

Extrusions 74

Sheet 74

Steel 74

Titanium Alloys 75

Hardware and Other Items 76

Chapter VI. Detail Design Considerations 81

Design Philosophies 81

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Margin of Safety 81

Maintenance Requirements 82

Fool-Proof Operation 82

The "Fail-Safe" Principle 82

Safety 82

The "One-Horse Shay" Principle 83

Strength of Metal Aircraft Elements 84

Structural Behavior . . 84

Stiffeners or Stringers 86

Panels under Load 88

CONTENTS xiii

Panel Sizes 89

Strength of Sheet-Stringer Combinations 92

Equivalent Structure 93

Cut-Outs '94

Riveted and Bolted Joints 95

Fittings 97

Determining Bolt Diameter 99

Determining Thickness of Fitting Lug 99

Determining Value of R 99

Checking whether Dimension R is Sufficient 99

Sandwich Materials 99

Flooring 100

Thermal Problems 102

Miscellaneous 103

Lightening Holes 105

Beading 105

Stiffeners 105

Chapter VII. The Three-View 113 >

Steps in Assembling Preliminary Data for Three-View .114

Estimation of Gross Weight 114

Estimation of Wing Area 116

Determining Length of Span 117

Drawing Up the Wing Planform 118

Determination of the Mean Aerodynamic Chord . .118

Determining Length of Airplane 118

Locating the Engines 119

Planform of Horizontal Tail Surfaces 120

Completing the Top View 120

Completing the Side View 121

Completing the Front View 121

General Notes for Three-View 121

Engineering Studies 122

Final Three-View 122

Chapter VIII. Preliminary Weight Estimate 124

General Procedure 124

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Estimated Weights 126

Calculated Weights .126

Actual Weights 127

Alternate Loads 127

Estimating the Gross Weight 127

Estimation of Structural Weight 128

Recapitulations 128

Form for Preliminary Weight Estimate 128

Variables Affecting Weight Estimation 132

Wing Weight Estimates 132

xiv

AIRPLANE DESIGN MANUAL

Fuselage Weight Estimates 136

Control Surface Weight Estimates 137

Landing-Gear Weight Estimates 138

Power Plant and Power-Plant Nacelle Weight Estimates . . 138

Weight Data Sources 139

Design Control of Weight 139

Empirical Formulas and Data 139

Wing Weight 139

Tail Surfaces 141

Fuselage Weight 142

Landing Gear 143

Total Fabricated Components 145

Weight Empty 146

Engine Nacelles 146

Fuel Weight 147

Oil Weight 147

Power Plant Weights 147

Gross Weight 148

Miscellaneous Weights 149

Propeller Weights 149

Chapter IX. The Balance Diagram 155

General Procedure 155

Center of Gravity Location 157

Practical Solution 160

Center of Gravity Movement 160

The Fuselage and Its Contents 161

The Wing and the Landing Gear 164

Supplementary Calculations 168

Ballast 169

Centers of Gravity of Individual Items ....... 169

Center of Gravity Estimation 170

Error in Balance Calculations 171

Chapter X. The Cockpit 172

Suggested Procedure in Design 174

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General Requirements 175

Windows and Windshields 176

Characteristics of Glass 180

Vision and Visibility 182

Canopies 183

Seating 183

Exits 186

Protection for the Pilot 186

Ejection Equipment 187

Parachutes 188

Controls 188

Instrument Board 189

CONTENTS xv

Chapter XI. Instruments and Equipment 191

Instrument Board 193

Location 194

Grouping 194

Variety of Instruments 194

Selection of Instruments • 197

Electrical Equipment 198

Safety Equipment 199

De-Icing and Anti-Icing 199

Chapter XII. The Passenger Cabin 202

General Considerations 202

Comfort Factors 203

Cabin Dimensions 203

Passenger Seats 205

Seating Arrangements 206

Headroom for Small Airplanes 207

Headroom for Large Airplanes 209

Leg Room 209

Side-by-Side Arrangements 213

Staggered Arrangements 213

Back-to-Back Arrangements 213

Seating Facing Rearward 214

Vision 215

Seating Comfort 215

Seating Accessibility 215

Center of Gravity Considerations 216

Windows 216

Doors and Exits 217

Sleeping Accommodations 218

Lighting .218

Furnishings 218

Provision for Airsickness 218

Flooring 219

Toilets 219

Refreshments 220

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Baggage Compartment 220

Chapter XIII. Air Conditioning 221

Physiological and Psychological Considerations 221

Air Movement for Comfort 222

Air Requirements 223

Pressure Considerations 224

Design Temperature Limits 226

Physical Conditions 226

Air Ducts 227

Boilers and Radiators 229

xvi AIRPLANE DESIGN MANUAL

Heat Sources 229

Pressure Cabin Equipment 229

Calculations 230

Heating Surface 232

Air Conditioning Problems at High Speeds 233

Chapter XIV. Soundproofing 235

Measure of Noise 235

Sources of Noise 236

Effect of Frequency on Soundproofing 236

Soundproofing Materials 237

Application of Materials 237

Noise Due to Jet Engines 239

V Chapter XV. The Propeller 241

General Propeller Characteristics 241

Aerodynamic Effects of Propeller 243

Gyroscopic Effect 243

Propeller Pitch 244

Number of Blades 245

Propeller Influence on Aircraft Configuration 247

Propeller Clearance 247

Asymmetrical Conditions 249

Effect of Engine Torque 250

Tandem Engines 251

Pusher Installations 252

Tail Installation 253

Spinners and Cuffs 254

Propeller Selection 254

Empirical Formulas 258

Chapter XVI. The Power Plant 263

General Considerations 263

Location 264

Submerged Engines 264

Number of Engines 265

Engine Rating 267

Engine Selection 268

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Engine Nacelles 268

Fuel Consumption 268

Engine Mount—Non-Jet Engines 269

Firewall 272

Cowling • 273

Exhaust Manifolds—Reciprocating Engines 276

Carburetor Scoop Design 277

Fuel Systems 278

Pumps 279

Tanks 279

CONTENTS xvii

Lubricating Systems 280

Tanks 281

Air Inlet System—Turboprop Engines 281

Induction System Configuration 281

Design Considerations 281

Inlet Losses during Ground Operations 286

Engine Inlet Anti-Icing Provision 286

Anti-Icing Water Runback into Engine Inlet 286

Air Inlet Systems—Turbo-Jet Engines 287

The Wing-Root Inlet 289

Nose Inlet in the Fuselage or Nacelle 290

The Nacelle or Pod-Type Installation 290

The Annular Inlet 292

The External Scoop 292

The Flush Inlet 294

Rockets .298

Chapter XVII. Design of the Wing 299 1

General Considerations 303

Wing Layout Procedure 304

Mean Geometric Chord 306

Planforms and Taper Ratios 310

Sweepback for High-Speed Airplanes 313

Effect of Wing Sweepback 317

Dihedral 317

Combination Dihedral and Sweepback 318

Angle of Incidence 319

Wing Loading 320

Aspect Ratios 320

Airfoil Thickness and Thickness Ratios 321

Wing-Fuselage Configurations 323

Metal Wing Construction 323

Spars and Their Location 327

Spanwise Stringers and Their Location • 330

Ribs and Their Location 331

Wing-Fuselage Attachments 334

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Fabric-Covered Wing Construction 337

Ailerons 341

Lift-Increase Devices and Spoilers 347

Wing Fences 354

Effect of Wing Mass Distribution 354

Effect of Wing Loading 355

Flutter Prevention 355

xviii AIRPLANE DESIGN MANUAL

Chapter XVIII. The Landing Gear 357

General Considerations 357

Dynamic Loads 358

Means for Landing-Speed Reduction 359

Dissipation of Energy 361

Shock Absorbers 362

Classification by Landing Contact 364

One-Point Contact 364

Two-Point Contact 364

Three-Point Contact 365

Four-Point Contact 365

Landing Gear—Tail-Wheel Type 365

Landing Gear—Nose-Wheel Type 367

Track-Type Landing Gear 370

Tandem Gear 371

Cross-Wind Landing Gear 371

Shimmy and Shimmy Dampers 373

Tread 375

Wheel and Tire Size 375

Size of Tail or Nose Wheel 376

Wheel Position 376

Retraction of Landing Gear 376

Special Problems 380

Chapter XIX. Tail Surfaces 382

Longitudinal Stability Considerations 382

Definitions 382

Preliminary Calculations for Static Longitudinal Stability . . 384

Adequacy of Static Stability 384

Flight Criteria for Stability and Controls 385

Longitudinal Stability and Control 385

General Requirements 386

Control Surfaces 387

Airfoil Sections 388

Aerodynamic Balance 389

Trailing-Edge Tabs and Other Devices 391

r

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Static Balance 391

Dynamic Balance 392

Flutter Prevention 393

Construction 394

Horizontal Tail Surfaces 395

Location 395

Angular Deflection 397

Adjustable Stabilizer 397

Aspect Ratio 398

Angle of Incidence 398

Sweepback 400

CONTENTS xix

Dihedral 401

Area 401

Construction 401

Planform .401

Other Solutions 402

Clearances 403

Vertical Tail Surfaces . . - 403

Directional Stability and Control 404

Location 405

Angular Deflection 406

Aspect Ratio 406

Area 407

Planform 408

Sweepback 408

Tail Length 409

Butterfly or Vee Tail 409

Chapter XX. Control Systems 412

Typical Systems 412

Pulleys 414

Cables 414

Fairleads 415

Stops 415

Differential Ailerons 419

Adjustable Stabilizer 419

Tab Controls 420

Flap Controls 420

Wing Flaps 422

Tabs 422

Hinges 422

Flap- and Tab-Control Loads 423

Hydraulic and Pneumatic Systems 423

Travel of Controls 425

Irreversible Controls 426

Detail Requirements 427

Controls 427

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Engine Controls 427

Electrical Systems 429

Chapter XXI. The Fuselage 430

General Considerations 430

Wing-Fuselage Considerations 430

Shape of Fuselage 432

Fuselage Length 435

Determining Fuselage Lines 435

Use of the Mockup 436

Analytical Studies of Fuselage Structure 437

XX

AIRPLANE DESIGN MANUAL

Frames and Their Location 440

Longitudinal Stringers and Their Location 444

Fuselage Skin 446

Windows 447

Pressurized Cabins 447

Flooring 449

Doors and Exits 449

Access Doors 449

Baggage Compartments 450

Twin Fuselages 450

Tail Booms 450

Alternate Type Structures 451

Effect of Fuselage Mass Distribution 453

Chapter XXII. Preliminary Performance Calculations. . 454

Source of Data 454

Calculations for Horsepower Required 455

Altitude Corrections 459

Arbitrary Standard Atmosphere 459

Parasite Resistance Data 460

The Engine 461

Horsepower Available 462

Maximum Speed 466

Rate of Climb 468

Absolute and Service Ceilings 468

Range 468

Performance Requirements 470

Take-off Performance with All Engines Functioning Normally . 470

Performance in Air with All Engines Functioning Normally . 471

Performance in Air with One Engine Dead 472

Landing 473

Empirical Formulas 474

Maximum Speed 474

Minimum or Stalling Speed 475

Rate of Climb at Sea Level 475

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Absolute Ceiling 476

Range 476

Index 479

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AIRPLANE DESIGN MANUAL

CHAPTER I

Procedure in Design

No task can be intelligently executed unless a definite goal has been set

and a line of attack or orderly form of procedure has been adopted. There

may be different ways of obtaining the same objective, but mistakes and

unnecessary work will be avoided if a definite plan is made before any real

work starts.

The responsibilities of the designer are many. Not only must he meet

the structural requirements, but also, by proper design, the operational

and performance specifications, and he must be able to produce an air-

plane that is economical and safe. For example, it is claimed that two

thirds of the responsibility for aircraft accident prevention lies within the

job of the aircraft designer. Such responsibilities require constant vig-

ilance in checking all phases of the design and in keeping abreast of all

the latest developments.

SELECTING TYPE OF AIRPLANE

It is not sufficient to say "Let's build an airplane." The question is:

What kind of airplane—an open or a closed type, a sleek racing mono-

plane, or a large flying boat? The first thing to be done is to write down

a set of such definite specifications that any designer who receives them

may be able to design an airplane which meets the original design pro-

poser's intentions. The procedure is much the same as that of buying a

family car. The term "family car" immediately sets one specification:

the buyer knows that he is not going to get a truck, or a roadster, or a

racing car. The price that the buyer can meet will set another specifica-

tion automatically, and so it goes.

Specifications for an airplane are far more comprehensive. Consider,

for example, the type of airplane it may be. The airplane to be designed

may be one of two conventional types, a monoplane or a biplane. If it is

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3

4

AIRPLANE DESIGN MANUAL

a monoplane, the wing may be unsupported externally, in which case it

is known as a full cantilever monoplane; or the wing may be externally sup-

ported either by struts or by wires, in which case it is known as a semi-

cantilever monoplane. Moreover, the wing may be placed at the bottom

of the fuselage, when it is known as a low-wing monoplane; or the wing may

be placed halfway between the top and bottom of the fuselage, so that the

airplane is a midwing monoplane; or again, the wing may be at the top or

above the fuselage, in which case the airplane is known as a high-wing or a

parasol monoplane, respectively.

The same variables apply to a biplane. The two wings may not have

the same areas, or the same planform, or the same airfoil. There may be

large forward or positive stagger of the upper wing relative to the lower,

and perhaps more dihedral for one wing than for the other. The com-

binations are almost infinite especially when one considers that changes

may be made in structure, in materials, in planform, in stagger, in angle

of incidence, in airfoil sections, in decalage, in gap-chord ratios, in wing

placement relative to the fuselage, in distribution of wing areas, and a host

of other variables.

The variables just noted apply only to the wing. Consider the fuselage.

It may be round, oval, square, elliptical, rectangular, or a combination of

these cross sections. It may be shallow or deep; it may be wide or nar-

row; it may have an open cockpit or an enclosed cabin; it may be con-

structed of almost any material and in an infinite number of ways. For

each material and specific function, there is a definite, desirable shape of

fuselage.

The landing gear also offers enormous latitude in design. It may em-

ploy a landing gear having two wheels forward with a tail wheel rearward;

or the reverse order with a front or nose wheel and two wheels slightly

rearward, popularly known as the "tricycle" landing gear. The landing

gear may have a through-axle of the type used during the early period of

airplane design, or a split-axle type developed later. Moreover, it may

be nonretractable or retractable.

These are just a few indications of what the design trend might be.

Familiarity with different types of airplanes will help the potential designer

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in determining the type best suited to a specific duty. The designer will

find it decidedly advantageous to read as widely as possible in the various

technical aeronautical publications and to collect, study, and correlate

design details. Thereby his facility in adaptation will be improved.

POWER PLANT

The power plant will be discussed in detail in a subsequent chapter.

However, a brief discussion of the place the power plant takes in the origi-

nal specifications may not be amiss here. In many cases, operating com-

PROCEDURE IN DESIGN

5

panies of aircraft may specify the type and number of engines—either be-

cause of known fuel economy, or efficiency and dependability under certain

operating conditions, or because of possible interchangeability with exist-

ing equipment.

An airline accustomed to maintaining and operating radial air-cooled

engines will be loath to use turboprop engines, for example, since its

personnel may not be trained or sufficiently experienced to handle the

new type of engine.

The reasons for choosing a certain engine may be many, and the section

on power plants should be studied before writing the specifications. The'

specifications may designate a particular engine, although it is more likely

that the number of engines will be designated, for it is quite possible to

obtain one engine or two engines delivering the same total horsepower.

PAYLOAD AND CREW

The payload includes all load from which revenue is obtained. It in-

cludes passengers, mail, baggage, and express. The crew includes pilot,

co-pilot, mechanics, navigators, radio men, stewards, and any other em-

ployee required for specialized work.

Military airplanes have a different type of payload, usually called fixed

equipment or disposable load, as the case may be. This consists of guns,

ammunition, bombs, and other military equipment. Special provision

must be made for these; therefore, these items have a definite bearing on

the airplane type as well as the weight permitted.

The gross weight of the airplane is largely dependent upon the require-

ments for payload and crew. It should be quite obvious that if a crew of

three (a pilot, a co-pilot and a radio man, for example) is required, some

provision must be made for it, and such provision will affect the size of

the cockpit as well as the fuselage and eventually the gross weight. Like-

wise, provision for mail and express will be entirely different from provi-

sion for passengers.

The larger the aircraft becomes, the larger the crew is likely to be.

Some indication of the eventual size of the airplane to be designed can be

gained by looking at the size of crew required. In the same way, the

number of passengers carried has a direct bearing on the size of the fuse-

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lage and the gross weight: the greater the number of passengers to be car-

ried, the larger and wider and higher the cabin, and therefore the fuselage

will be larger. Not only does the increased number of passengers increase

the weight, but the structure will also weigh more because of increased size.

Actually, the gross weight of the airplane can be estimated if the weight

of the payload, crew, fuel, and oil are known since an analysis of a large

class of airplanes shows that there is a definite relationship between the

two weights.

6

AIRPLANE DESIGN MANUAL

It is very important to know as much as possible about the load the

airplane is to carry because these are the items for which the designer has

to make proper provision although he may have little or no control over

their weight, size, or location in the airplane.

PERFORMANCE REQUIREMENTS

Unless the airplane is designed for private use, the performance require-

ments are set by the ultimate purchaser. It takes but little thought to

realize that the keen competition among American airlines requires the

speed of the airplane to be as high as possible in order to obtain attractive

schedules. But where there is less competition, a far slower airplane

may be desirable because of the smaller horsepower and less fuel required

to carry practically the same load.

Likewise, an airplane operating over mountainous territory will need a

high service ceiling in order to clear the mountains, whereas a low service

ceiling would do over low level country.

The performance required for the airplane will have a direct bearing on

the number, type, and horsepower of the engines, as well as the type and

design of wing, fuselage, and perhaps landing gear. The ultimate criterion

of a good airplane is its performance in relation to the load carried and the

conditions to be met.

STEP-BY-STEP PROCEDURE

The foregoing discussion deals with specifications which are only part

of the work to be considered in designing the airplane. From the moment

a new design is contemplated until the final drawing leaves the drawing

board, a definite plan is followed in evolving the design. The individual

steps of the plan may not always be clear-cut, and sometimes several

phases are carried along in parallel sequence. The following procedure

may be gainfully employed.

1. Study of specifications to fix the more important items having im-

mediate import in the preliminary design steps.

2. Study of similar purpose airplanes to determine the possible types

which may be considered as meeting the over-all specifications.

3. Power plant survey for the selection of the likely engine or engines

to be used in the design.

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4. Preliminary three-view, or views, to narrow down the number of

possible solutions and to present a framework on which the work that fol-

lows will depend.

5. Preliminary weight estimate based upon the data and information

obtained in the first four steps.

6. Airfoil selection to obtain the ultimate performance desired.

PROCEDURE IN DESIGN

7

7. Balance diagram to fix the items of equipment and structure in

proper relation to each other for purposes of design, stability, and effec-

tiveness.

8. Inboard profile to check upon installation of equipment and to pro-

vide studies of interior arrangement.

9. Structural layout (work on the various units usually carried on

simultaneously in order to take proper care of the interrelation of the

component parts) somewhat in the following order.

(a) Wing with reference to fuselage.

(b) Landing gear with reference to wing or fuselage.

(c) Tail surfaces with reference to fuselage.

(d) Fuselage.

(e) Power plant with reference to wing or fuselage, or both.

10. Final three-view from data obtained in the course of working on

balance diagram, inboard profile, and structural layouts.

11. Preliminary longitudinal, directional, and lateral stability calcula-

tions performed at time of airfoil selection, balance calculations, and three-

view conception.

12. Preliminary control calculations made along with preliminary sta-

bility calculations.

13. PreUminary performance calculations carried along simultaneously

with other calculations.

14. Preliminary stress analysis according to military or civil require-

ments.

15. Revised structural drawings with added information for the prepa-

ration of detailed design drawings.

16. Check all parts of the design and revise where necessary.

These steps are discussed in considerable detail in subsequent chapters.

More familiarity with the problem of airplane design will often suggest

alternative procedures.

In practice, practically all these steps are carried along simultaneously

because a number of men may be employed on the project, but even so the

initial work is usually done by one man. In practice, too, a mock-up of

the proposed design is made so that many design studies may be made on

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the mock-up rather than on paper. In the classroom, suitable compro-

mises must be made.

NOMENCLATURE

In any discussion, it is necessary to understand the words used. Ordi-

narily, it would be assumed that the student is familiar with the names of

all the parts of the airplane; certainly he should be reasonably well in-

formed on matters dealing with aerodynamics and the internal-combustion

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PROCEDURE IN DESIGN

9

engine. However, it may be that he is not too well informed on names of

structural details. Figure 1-1 will be useful for reference and in establish-

ing some standardization of terms.

REFERENCES

Much research and design material may be found in technical reports,

memoranda, and notes issued by the National Advisory Committee for

Aeronautics (NACA) and published by the Government Printing Office

in Washington, D. C.

Young engineers should become familiar with the current literature to

be found in various trade journals of the industry and in the journals of

the several engineering societies.

Much of airplane design is empirical, at least in the project stage, so that

all the research that may be brought to bear on the design will be particu-

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larly fruitful.

CHAPTER II

Types of Airplanes

Many considerations enter into the selection of a particular type of

airplane to meet a given specification, and, therefore, it is well to know

the characteristics of each type before deciding definitely on any one type.

Airplanes may be classified in various ways, according to structure, meth-

od of construction, number of engines, type of landing gear, weight,

purpose, and any other variation which an airplane may have.

In the specific descriptions given here, it should be borne in mind that

the advantages and disadvantages indicated for the various types have to

be properly evaluated since, in all, certain compromises must be made.

In some cases the advantages, when properly considered, are more impor-

tant than any possible disadvantage. In many cases, the general "eye

appeal" is also a deciding factor in the selection of the final design. Any

statements made in the discussion that follows should not, therefore, be

applied immediately to any existing design.

THE BIPLANE

Historically the multibay biplane was favored because the art of aero-

dynamics had not yet progressed to the point where the thick airfoil was

favored, much less visualized. Economical and light design indicated the

truss as the most convenient type of structure, although the multibay lift

truss eventually gave way to the single-bay lift truss. In a few cases, even

the bracing between the upper and lower wing became more and more sim-

plified so that either only the interplane strut remained or none at all.

The biplane lift truss makes for efficient structural design, small over-all

dimensions, and lends itself to a variety of solutions as well as permitting

the use of relatively thin airfoil sections.

Even though the braced biplane may permit use of thinner and lower

drag airfoils, still the resistance offered by the additional bracing and in-

terferences may more than offset the lesser wing drag.

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10

TYPES OF AIRPLANES

11

The biplane is open to an almost infinite number of variations since any

or all of the following geometric arrangements are possible.

1. Different airfoils for the upper and lower wings.

2. Varying decalage, that is, the upper wing at a different angle of in-

cidence than the lower.

3. Different dihedral for the upper and lower wings.

4. Different aspect ratios for the two wings.

5. Any degree of positive or negative stagger.

6. Varying gap-chord ratios.

7. Different planforms for the two wings.

8. Ailerons on either upper or lower wing, or on both.

9. Different sweepback for the two wings.

10. Various possible bracing arrangements.

Figure I1-1. A typical biplane is shown. The crossed single lines represent the

lift and landing wires. The over-all dimensions of the airplane are smaller than for

the monoplane and there are more design variables to consider. Generally, the biplane

has more parasite and interference drag than a monoplane designed for the same purpose

All these variations, however, can also introduce a great amount of

work in preparing the design and in the process of manufacture, so that

the more variations the design has, the more expensive it is likely to be.

THE SESQUIPLANE

A biplane that has a lower wing considerably smaller than the upper

is called a sesquiplane. The reverse order in the size of the two wings

has also been used. Such a design may be resorted to in order to provide

adequate landing-gear attachments and to afford an opportunity to in-

crease the tread of the wheels. Bracing between wings may be employed.

Such a design may be of particular usefulness in rugged terrain where

ground stability in landing and taxying is particularly important, and

where the high wing will be out of the way of underbrush and other

obstructions.

THE MULTIWTNG AIRPLANE

As the number of wings is increased, the less aerodynamically efficient

the airplane becomes. Although multiwing airplanes, such as triplanes,

have been built, they may be considered as curiosities rather than as sound

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designs to be critically considered.

12

AIRPLANE DESIGN MANUAL

THE HIGH-WING MONOPLANE

The design that became popular after the biplane was the externally

braced high-wing monoplane. When externally braced, the wing is said

to be semicantilever. (See Figure II-2.) The lift strut supports the

wing and thereby reduces the bending moments sufficiently to make for a

lighter structure. A thin airfoil, although somewhat thicker than an air-

foil employed on a biplane, still offers less resistance and permits reason-

ably high-speed performance.

The struts are attached (as all external bracing should be) by a single

bolt at each end (with the head of the bolt facing forward), so that the

normal loads, acting either upward or downward, will impose bending

moments and shear on the wing structure proper but induce only axial

loads in the struts or wires.

Fig. II-2 Fiq. II-3

Figure II-2. A semicantilever high-wing monoplane braced by a V strut. This

arrangement permits a simplified fitting design at the apex of the V. The arrangements

of the struts may be varied. Such bracing permits use of thinner airfoils and efficient

structural configurations.

Figure I1-3. A full cantilever high-wing design with a power-plant installation in

the tail where the effect of propeller interference and slip stream do not affect the

aerodynamic qualities of the wing.

In order to reduce the column length of the external struts, so-called

jury struts are interposed between the wing and the lift strut, just below

the upper end of the lift strut. The juncture of the jury and the lift strut

is a hinge or pin joint, and the upper end of the jury strut is also a pin-

connected fitting attached to the wing spar.

The chord loads are applied to the internal drag structure of the wing

and are assumed not to act on the lift bracing.

The lift struts may be placed parallel to each other in the most common

arrangement, although carrying the lift struts down to the fuselage to

form a V is often done to eliminate one fitting and perhaps to offer better

access to the door which may be located at the rear strut.

The V may be so arranged also that the apex of the V is at the rear-

strut fitting instead of the front-strut fitting. There are also other pos-

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sible variations with the struts both carried farther forward to a point of

TYPES OF AIRPLANES 13

attachment on the fuselage. The advantage of this arrangement lies in

the possibility of combining lift-strut fittings with landing-gear strut fit-

tings, or in the possibility of applying reactions to the wing-drag truss to

counteract the chord force components exerted on the drag truss.

Fig. II-6 Fig. II-7

Fiqure II-4. A low-wing monoplane with a twin vertical tail surface arrangement

which may be used to reduce the over-all height of the airplane; or, to operate more

effectively in the slip stream of a twin-engine design; or, to avoid the "blanketing"

effect of the fuselage. Twin vertical tail surfaces may help to increase the "apparent"

aspect ratio of the horizontal tail surfaces.

Figure II-5. A midwing design with a jet-engine installation. The dihedral in-

corporated in the horizontal tail surfaces installation brings these surfaces into a more

uniform downwash distribution across the span. The air scoops of the jet engines are

in the jet engine nacelle, with the exhaust in the rear.

Fiqube II-6. A so-called butterfly tail combines the functions of the vertical and

horizontal tail surfaces in this midwing monoplane, thereby simplifying the empennage

structure.

Fiqube II-7. The inverted gull wing designed to raise the propeller axis of the

centrally located engine while still bringing the wing down to permit a landing gear

with short members suitable for retraction. Acute angles are also avoided at the inter-

section of the wing with the fuselage, thus eliminating need for fillets. The dotted lines

show the position of the wing when partially folded for stowage purposes.

The cross sections of these lift struts are usually symmetrical airfoils of

small thickness ratio and large fineness ratio. It is possible to envelop

both lift struts in an airfoil in order to add to the lift, but such additional

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lift is comparatively small in usual designs.

14

AIRPLANE DESIGN MANUAL

Figure II-8. A jet engine design

with air inlets along the fuselage. A

single nose inlet in the fuselage is also

used. The exhaust is in the extreme

end of the fuselage tail. The wing-tip

fuel tanks are droppable although their

expense may prohibit such procedure,

and are so located to reduce aerody-

namic resistance; they may affect the

stability of the airplane because of in-

creased moments of inertia about the

axes of the airplane.

Figure II-9. A high-wing mono-

plane with a pusher-type engine install-

ation designed to reduce noise in the

cabin, to obtain a more favorable center

of gravity location for certain designs,

and, perhaps primarily, to afford the

best possible view forward.

Figure 11-10. A small pusher air-

plane with twin booms supporting the

tail surfaces. The booms help to iso-

late the engine but are brought about

primarily by the engine location.

Figure 11-11. A canard pusher-

type airplane of unusual design with

the horizontal tail surfaces ahead of

the wing and the vertical tail surfaces

at the wing tips.

The high-wing monoplane affords excellent vision downward, which is

v especially useful in landing. Vision upward and toward the sides is, of

course, impeded.

It is difficult to obtain a wide tread for the landing gear unless a long

supporting strut is carried to the wing, or a sturdy structure is built to

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support the landing gear.

The retraction of the landing gear becomes particularly difficult in this

type of design because the wheels cannot easily be retracted into wells

located in the fuselage. It is even more difficult if the landing gear is

retracted into the wings because the struts would have to be retracted as

well.

The incorporation of flaps and, in general, various lift-increase devices

is made easier in the high-wing design since ground clearance with de-

TYPES OF AIRPLANES

15

Figure 11-12. A proposed design

with a jet actuated propeller. Since

the blade tips operate at rather high

speeds, a jet engine may attain a rea-

sonable efficiency at the propeller tip

location. The air scoops for the jet

engine are in the leading edge of the

root section of the wing.

Figure 11-13. A multi-engine

monoplane incorporating a triple ver-

tical tail surface arrangement in order

to obtain the necessary directional con-

trol, especially when one or more en-

gines fail.

Figure 11-14. This multi-engine

design uses a pusher installation in or-

der to obtain a more favorable center

of gravity location, to keep the plane

of propeller rotation clear of personnel

in the cabin, to simplify the engine

nacelle construction and engine ar-

rangement by placing the units in a

straight row, and to move the control

cabin as far forward as possible for

visibility.

fleeted or extended flap does not become one of the primary design con-

siderations.

As far as wing locations on the fuselage are considered, the high wing is

aercdynamically superior, for it has both greater lift and less aerodynamic

resistance than if the same wing were placed at the bottom of the fuselage.

While the internally braced wing or full cantilever wing is aerody-

namically better because of the absence of lift struts (see Figure 11-13), the

landing gear offers a special problem in obtaining an adequate tread and

suitable shock-absorbing qualities. A wide tread would mean long land-

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ing-gear struts at a shallow angle to the ground so that the shock-absorbing

medium is likely to function unsatisfactorily.

Struts may be carried from the landing gear to the wing to serve merely

as a support for the gear in order to obtain a reasonably wide tread.

Another variation of the high-wing monoplane is the parasol type where

the open cabane is interposed between the fuselage and the wing. Such

an arrangement is particularly suitable for an open cockpit airplane where

vision forward for the pilot, especially if he happens to be seated quite far

back, is desired.

Open cockpit airplanes do not have the general all-weather utility that

enclosed cockpits have and so are seldom seen, although there is a place

for them for special purposes.

16

AIRPLANE DESIGN MANUAL

Fig. 11-15

Fig. 11-17

Fig. 11-16

Fig. 11-18

Figure 11-15. A cargo airplane with twin booms supporting the tail surfaces high

and clear of the rear loading area of the fuselage.

Figure 11-16. A twin fuselage monoplane which makes use of twin-engine nacelles

and twin booms. It also suggests the possibility of coupling two monoplanes. Such

a design permits separate functions in the two fuselages without interference.

Figure 11-17. A twin fuselage design with a special compartment for personnel.

Figure 11-18. A monoplane with an unusually wide fuselage of airfoil cross section

designed to obtain certain flying wing advantages with more or less conventional air-

plane design.

The low-wing monoplane has variations similar to the high-wing mono-

plane. The design is excellent for short landing-gear structures, and also

affords a ready means for landing-gear retraction. Vision upward and

toward the sides is excellent, but poor down at the sides. It is often

claimed that low-wing monoplanes are not so stable as high-wing mono-

planes, but a properly designed airplane always has sufficient stability.

Struts may be replaced by wires but this requires a set above and below

the wing. In some racing designs for low-horsepower engines, such de-

signs have been used since the use of thin airfoils would offset, to some

degree, the resistance of the wires which offer less resistance than struts

do. The wires, of course, cause complications in rigging and mainte-

nance, and, therefore, are not considered favorably by the private flyer.

In general, external bracing, whether used for a biplane or a monoplane,

should not form too acute an angle at the intersection with the top or bot-

tom surface of the wing since it not only offers more aerodynamic re-

sistance when so located, but also is likely to affect adversely the airflow

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THE LOW-WING MONOPLANE

TYPES OF AIRPLANES

17

over the wing and may, therefore, affect the longitudinal control and sta-

bility of the airplane.

To reduce the aerodynamic resistance resulting from the configuration

offered by the juncture of the wing and the fuselage, filleting is resorted to

in certain cases. However, filleting increases production complexity and

costs. Another solution to this problem is the so-called inverted gull

wing.

A gull-wing monoplane is one that has the root section of the wing

inclined at an angle to the fuselage so that the outer panels of the wing

are raised above the fuselage. (See Figure II-7 for example.)

The gull wing eliminates acute angles of intersection between the wing

and the fuselage and thus helps to reduce the parasite resistance. How-

ever, the design has some structural difficulties in that the construction

of the spars becomes complicated. Such a design improves the vision

upward and sideward over that of the conventional high-wing mono-

plane. In the case of multi-engine designs, when used for seaplanes and

flying boats, the wing is sufficiently raised to obtain propeller clearances.

For the low-wing monoplane, the inverted gull wing permits the fuselage

to be raised above the ground for a single-engine design in order to pro-

vide propeller clearance with the ground. This solution also has the

advantage of reducing the length of landing-gear supports so that re-

traction of the landing gear becomes unnecessary.

The midwing arrangement for the monoplane has definite aerodynamic

advantages in that its aerodynamic resistance is usually the lowest of the

various possible wing and fuselage arrangements. Structurally the design

offers complications because the spars should have "carry-through" mem-

bers in the fuselage. Such members interfere with the internal arrange-

ments. This design may also be braced externally, but because the

shallow angle between external struts and the wing causes large axial

loads in the spars, such bracing is usually not considered very desirable.

SPECIAL-PURPOSE AIRPLANES

Recent efforts have been directed toward developing aircraft requiring

short take-off and landing runs. Such aircraft are known as VTOL (for

vertical take-off and landing) and STOL (short take-off and landing).

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VTOL aircraft must get off the ground without any roll and clear a 50

foot obstacle in 250 feet. STOL aircraft are allowed ground roll, but

must be able to clear a 50 foot obstacle 500 feet from the starting point.

Designs known as convertiplanes employ such means as (1) the com-

bination of helicopter rotors and normal wings, (2) tiltable wings with

counter-rotating propellers, (3) multi- or "Venetian-blind" flaps and

powerful slipstream effects, and (4) multi-purpose wings which when

18

AIRPLANE DESIGN MANUAL

rotating act as a helicopter and when stationary act as ordinary wings.

There are special craft such as "piggy-back," parasite, drone, and

towing, the names of which designate their respective functions.

FACTORS AFFECTING CHOICE

The discussion thus far has been primarily with reference to the lift truss

of the airplane because it is usually the first in the list of considerations in

choosing the type of airplane. However, the discussion has been general.

The student should not overlook the specific considerations entering in the

choice and in the design of the power plant, the landing gear, the fuselage

structure, the interior arrangements, and the wing. Each of these may

have a bearing on the whole.

In determining a suitable type of airplane, the factors affecting the final

design should be listed and then carefully considered with reference to per-

tinent parts of the airplane. Some of these factors will now be considered.

Performance

A high speed requires an aerodynamically "clean" airplane with the

minimum of struts and lifting surfaces. A monoplane seems to be the

answer.

A rapid-climbing airplane requires either a relatively lowipower or low-

> thrust loading, or wing loading, or both. If a low-power loading—is.se-

lected, then an externally-braced monoplane or biplane is desirable.

High ceiling may be obtained by a low-wing loading and a high aspect

ratio. A semicantilever monoplane may be the solution.

^ Low landing speeds may be obtained by means of low-wing loading or a

high maximum lift coefficient, or both. The lift coefficient may be con-

siderably increased by means of flaps or other lift-increase devices. A

high-wing monoplane can incorporate these better than a low-wing mono-

plane, but a low-wing monoplane may be a better solution in spite of that,

because of other considerations.

Landing-Gear Retraction

If the landing gear is to be retracted, an internally braced, low-wing de-

sign offers the best solution. The struts are shorter, the mechanisms sim-

pler, and in case of a forced landing due to impossibility of lowering the

landing gear caused by some mechanical difficulty, the low wing offers the

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best protection.

Structure

^ Some types of structures are better adapted to one kind of airplane than

to another. A tubular steel fuselage is more efficient structurally for a

small airplane than for a very large one. A fabric covering may be satis-

TYPES OF AIRPLANES

19

factory for externally braced wings and for wings of airplanes whose top

speed is not much greater than 150 miles per hour.

Special Features

To help in deciding what type is best suited for your design, it is well to

list the special features the airplane may have, and then study them in the

light of a particular design being considered. Such features might be:

Engines

Air cooled or liquid cooled Pod installation

Radial or in-line Tractor or tandem

Single or multiple Cowled or concealed

Jet-propulsion type Maintenance requirements

Landing gear

Conventional or tricycle Fully cowled, partially cowled,

Retractable or nonretractable or uncowled

Full cantilever, split axle, or other Land or water type

Type of tires Maintenance requirements

Fuselage

Open cockpit or cabin Location of doors

Reinforced monocoque or tubular Type of cargo

steel Maintenance requirements

Wing

Performance requirements Space for landing gear

Fabric or metal covered Location of engine nacelles

Wood or metal spars High or low aspect ratio

Internally or externally braced Thickness ratio of airfoil

Lift-increase devices Maintenance requirements

Space for fuel tanks

Tail surfaces

Single or multiple surfaces Operating controls

Location above or below fuselage Maintenance Requirements

Tab controls

SAMPLE AIRPLANE DATA SHEETS

The design of airplanes is largely empirical. Thus it is advisable to

study as many airplanes as possible, catalog them under different cate-

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gories, and collect as much data as possible on performance, weights,

structure, power, and all other items that may be useful as reference

material in future work. Data collected for a number of airplanes in the

20

AIRPLANE DESIGN MANUAL

same category may then be averaged to give empirical values for de-

termining ratios of power or thrust loadings, wing loadings, etc.

The following condensed airplane data sheet may be taken as a guide

to the type of information that should be collected. It may be expanded

to suit individual needs.

Airplane Data Sheet

Name of Company:

Name of Type:

Price:

1. Power Plant

Engine: Horsepower: Rev. per min.: Altitude:

Starter:

Design of exhaust:

Other engine accessories:.

Fuel, gallons:.—

Oil, gallons: —

Location of tanks: -

Type of engine controls:

Propeller—Make:

Material:

Type:

Diameter:

Number of blades:

Angular range:

2. Wing1

Airfoil section—Root:

Midspan:

Tip:

Wing area (including ailerons), Sw:

Span, b:

Chord—Root, Cr\

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'If biplane statistics are to be listed, repeat these entries for lower wing.

TYPES OF AIRPLANES 21

Tip, CT: p

Taper ratio, RT:

Aspect ratio, AR:

Mean aerodynamic chord, MAC:

Dihedral:

Sweepback:

Incidence—Root:

Midspan:'

Tip:

Length of cantilever tip:

Length of outer bay:

Length of inner bay:

Length of center section:

Location of wing spars in per cent of chord—Front:

Rear:

Maximum rib spacing: —-

Aileron area, Sa:

Flap area, S/r.

Location of center of gravity when fully loaded, in per cent of mean

aerodynamic chord: .'

3. Tail surfaces

Stabilizer area, S,:

Elevator area, Sr:

Total horizontal tail surface area, Sh:

Distance from center of gravity loaded to elevator hinge:

Fin area, S/:

Rudder area, . + DP)00^; (5)

The power available is

Pa = 77BHP; (5a)

and since at maximum speed,

Pa = Pr (5b)

or,

rjBHP = (Z>„ + DP)00^0 0 (5c)

This relationship can be obtained from equation (2), for, again assuming

(a + 1) small and |3 = 0, then

- T + Dp + Dw = 0, (2a)

°r' T = DP + Dw (2b)

and multiplying both sides by v/550,

But, TV/550 is the thrust horsepower available, or

«S> = "bhp (6a)

where r) is the efficiency of the propeller and BHP is the brake horsepower

of the engine delivered to the propeller at the given airplane speed, and

the power required is given in equation (5) as

Pr = (DP + IWJL,

but

Dw = yiPv2cDs

Dp = y2Pv2cDrs,

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where Co is the drag coefficient of the wing,

AIRFOIL SELECTION

33

CDp is the parasite resistance coefficient of the airplane (less the

wing) referred to the wing area.

Then,

Pr = P0 = „BHP = (CD + GDp), (7) .

or, \

T = p-f- (CD + CDp), (7a) V

and for any given lift coefficient the speed v can be determined from equa-

tion (3), the corresponding Cd of the wing will be known and the Cd, for

the airplane may be calculated,1 so that the horsepower required of the

engine-propeller combination can be determined. Then, if the horsepower

available is a certain value, it is obvious that the maximum speed that can

be obtained for a given airplane (whose Cd, is fixed) is one whose wing air-

foil has a minimum value of Cd0 0 It is important, therefore, to compare

the minimum values of the drag coefficients of a series of airfoils.

Since the range of speeds obtainable is determined by the values of the

maximum value of Cl (minimum speed) and of the minimum value of Cd

(maximum speed), then the ratio of CLm., to Co,,, is of importance and is

known as the speed range ratio.

Case 2. Gliding Flight. Again, assuming that the lift on the horizon-

tal tail surfaces is small and the angle (a + i) small, but that 0 is not un-

appreciable, equation (1) becomes Lw = W cos 0, and equation (2) be-

comes Dt — T = W sin 0.

Dividing the first equation by the second,

^Ty = cOt 0, (8)

when there is no thrust (that is, when the engine fails)

cot 0 - ^. (8a)

or the angle of glide is a function of the aerodynamic characteristics of the

airplane. This relationship may be rewritten

Lw qClS Cl Cl . a ,suN ('

-d• = WnTs = c7, = cTfcZ = cot * (8b) A

Again, considering an airplane for which the parasite resistance can be

assumed constant for any angle of attack, the angle of glide /? will be

flattest for that airplane whose L/D for the airfoil alone is the largest.

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1 See Chapter X XII, Preliminary Performance Calculations.

34

AIRPLANE DESIGN MANUAL

Also, the circle determined from

K = ffcot0 = ff(^. (9)

where R is the radius of the circle, and H the altitude from which the

glide takes place, is largest for the largest value of cot 13. The airfoils

should, therefore, be compared on the basis of the maximum L/D.

Case 3. The Dive. In this case, the angle /3 becomes 90 degrees, so

that equation (1) now becomes Lw + Lt = 0, assuming (i + a) is small.

Equation (2) becomes

- T + Dp + Dw - W = 0

when there is no thrust,

Dt = W

where

DP + DW = Dt!

or

WCDJ5 = W,

from which

/W

v V HpCdJS'

The maximum speed will then be obtained in the dive, unless the drag

coefficient is unusually large, and will be determined by the minimum

total drag coefficient of the airplane. This speed is of importance in con-

sidering local pressures on engine cowls and windshields which may be

pulled off the airplane by the "suction" pressure. The leading edge of

the wing would then be subjected to enormous pressure that would tend

to buckle it. Also, the highest load factor in flight is encountered when

pulling out of a dive. The higher the diving speed, the higher the load

factor encountered in the pull-out. (See Chapter IV, External Loads on

Airplane in Flight.) If the speed were to be limited, then means would

have to be provided to increase the drag.

Case 4. The Climb. In the case of the climb, equation (2), as derived

for the general case, is of importance. The angle /3 is now a negative

angle and the equation in question becomes, upon making the same as-

sumptions as to a and i,

T - Dt = W sin 0. (11)

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But, sin /3 = a/v where v is the velocity along the flight path and a is

the vertical component of this velocity, or the rate of climb in feet per

second.

(10)

AIRFOIL SELECTION

35

Then, equation (11) becomes T — Dt = W(a/v), and by multiplying both

sides of the equation by v/550,

550 550 550' 1 J

But !Ty/550 = horsepower delivered by the propeller, or the horsepower

available = Pa. Therefore Tv/550 = 17 BHP where t] is the propeller effi-

ciency and BHP is the brake horsepower of the engine. Dtv/550 is the

horsepower required to overcome the total drag of the airplane at ve-

locity v and may be designated PT.

Rearranging terms

550(Pa - PT)

a= W'

W cos 0 = Lw = y2pv?SCL

or

(lib)

4.

y2pscL {10)

where ve is the velocity along the climb path.

Examination of equation (lib) indicates that the airplane which requires

the least amount of horsepower to overcome aerodynamic resistance will

have the greater climb. Since

Pr = (Dw + DP)(»/550),

then if the parasite resistance is kept constant, Pr is piimarily a function

of Dwv, but

Dwv = (y2PcDSv*)v = y2pcDSv\

and since

so that

or

Dwv

cD

Clw'

CD

Clw

also Cd/Cl*12 should be a minimum, or Clw/Cd a maximum in order to

maintain PT at a minimum. This ratio is sometimes called a "power co-

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efficient" for the airfoil and is calculated for those angles of attack in the

region where the minimum drag coefficient Cj> and the maximum L/D of

the airfoil occur.

36

AIRPLANE DESIGN MANUAL

Case 5. Range. One of the simpler formulas for determining the range

of an airplane is the so-called Breguet's formula for weight with respect to

distance, which is derived from the differential expression,

dW = - TVc ± - WVc (13)

dt 375tj 375(L/D)i7'

which, integrated between the limits of Wo and W„ gives

4*to*.S (13a)

where

R, range in miles = 863 ^ - logw

L Cl Cl

D CD, Cd + Cdf

r) = average propeller efficiency at cruising,

c = average fuel consumption in pounds per brake horsepower per

hour for the average cruising rpm,

Wo = gross weight in pounds at start of flight,

We = weight at end of flight after fuel has been consumed.

It will be noted that, all other things being equal, the higher the value of

the L/D, the longer the range. Therefore, if the parasite resistance of the

airplane is constant, the maximum value of the L/D = Cl/Cd of the airfoil

would be of interest.

This formula can be made to apply to jet engines by dropping the term

7j for propeller efficiency and considering c as the average fuel consumption

in pounds per pound of thrust per hour for cruising conditions.

Other Airfoil Characteristics

The slope of the lift curve, dCiJda, is one of the more important quan-

tities to know since it has an important bearing on the stability of the

airplane.

The angle at which zero lift curve occurs is also important since the

diving speed occurs very close to this angle.

The center of pressure movement over the normal flying range, between

the angle at which the minimum drag coefficients occur and the angle at

which the maximum lift coefficient occurs, is usually of interest since the

greater the movement the greater the load that will fall on the front spar

at high angle of attack, with very little load on the rear spar; the condi-

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tions are reversed at low angle of attack.

Some data may not include the center of pressure but may give the mo-

ment coefficient, Cm., about the aerodynamic center instead. In such a

case a small value of Cm, is considered desirable, since

c

CP = a - ^

CV (14)

AIRFOIL SELECTION

37

v.

"I

©

16

*.

ft

"I

a

4 +.020

00

-.020

ae

420-

0=

~2°— | | I I I | | I I | I

0 20 40 60 80 100

Per cent of chord

cL

CP.

L-

0

4 8 12 16 20

Anqle of attack

(in degrees)

1.4 o

%

1.2 \ .24

00

10 $.20

%

0.8

16

25

0.6

35

0.4

.08

45

0.2

.04

ft 2

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.12

rag eoeffieiem

1:

is the total drag coefficient for the airfoil used, while Cd, is the

profile drag, independent of the aspect ratio and constant for the airfoil.

The induced drag is expressed

€..-%. . CM)

As an example, to calculate the drag coefficient for aspect ratio 8 when

the characteristics for aspect ratio 6 are known, the following formula may

be derived:

where R = 8. Corrections for low values of d may be ignored. The

angle of attack must be corrected also for aspect ratio

= (16)

where clr and ao are in radians; or

57.3 Cl/1

where aK and a6 are in degrees and the known characteristics are for aspect

ratio 6. If the known characteristics are for infinite aspect ratio, then 6

is replaced by oo and l/oo becomes equal to zero. The lift coefficient, the

center of pressure, and the corrected drag coefficient correspond to the

corrected angle of attack. Table III-2 has been set up to expedite the

aspect ratio calculations. The various terms are self-explanatory. The

calculations are usually carried out in the form of such a table.

When an airfoil section used for the tip of a wing is different from that

used at the root, it is necessary to make wind-tunnel tests on a model of

the actual wing. Reasonably close approximation for preliminary cal-

culations may be obtained by averaging the characteristics of the root and

tip airfoils.

AERODYNAMIC SECTION CHARACTERISTICS

At the present time, much of the airfoil data such as the lift, drag, and

moment coefficients, the angle of attack, and the center of pressure, are

presented corrected to infinite aspect ratio. Such data are referred to as

section coefficients for infinite aspect ratio. To distinguish them from

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similar coefficients obtained or given for airfoils of finite aspect ratio, the

42

AIRPLANE DESIGN MANUAL

coefficients are designated with lower-case letters (cj, ca, Cm..,., etc.) for

the infinite aspect ratio case and the upper-case letters (Cl, Cd, Cm...., Cd„

etc.) for finite aspect ratio.

These section characteristics are particularly useful in obtaining the

spanwise lift distribution as outlined in ANC-1 (1) Spanwise Airload

Distribution, a small volume obtainable from the U. S. Government Print-

ing Office, Washington, D. C. It is beyond the scope of this book to

discuss or to indicate the procedure in calculating the spanwise lift distri-

bution. However, for stress analysis purposes, and for more refined calcu-

lation of performance, the spanwise as well as the chordwise distribution

(the latter especially for wings equipped with flaps) should be carefully

calculated.

To obtain the necessary data for preliminary design purposes, the fol-

lowing discussion will indicate a practical procedure. When the design

of the wing is well advanced, more elaborate and refined calculations as

set forth in a number of textbooks on aerodynamics should be made.

The pertinent data of use at this stage are the variation of the lift and

drag coefficients with the angle of attack, and the moment coefficient re-

ferred to the aerodynamic center of the mean aerodynamic chord. As

pointed out elsewhere, the mean geometric chord may be taken as the

mean aerodynamic chord for practical purposes.

A wing having no aerodynamic twist2 would have its section angles for

zero lift arranged so that all sections would have no lift when the root sec-

tion was at zero lift. If aerodynamic twist were not zero, then the angles

of zero lift for the various sections spanwise would not be the same as for

the root. The root section is usually selected for reference. In order to

obtain its position when the lift coefficient of the wing is zero, it will be

necessary to determine when

The section angles corresponding to the section lift coefficients will then

make it possible to find the value of am for the root section.

To simplify the discussion and the presentation, a wing of zero aero-

dynamic twist will be considered. It is a comparatively easy matter to

work out the procedure for a wing with aerodynamic twist.

The equation of the lift curve (Cl versus a) at low values of the lift co-

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efficient is

where the various terms have the significance indicated as follows:

Ci = the lift coefficient of the wing of finite aspect ratio, or may be

assumed equal for a wing of zero aerodynamic twist, as the aver-

age of the section lift coefficients, for the tip and root airfoils,

* For definition of this term, see under Airfoil Construction in this chapter.

ZCiCdy = 0.

(17)

CL = a(aR — ecu),

(18)

AIRFOIL SELECTION

43

a = the slope of the finite aspect-ratio wing,

«k = the angle of attack in degrees of the finite aspect-ratio wing at

which the lift coefficient Cl occurs,

c*lo — the angle of zero lift for the finite aspect-ratio wing; or may be

assumed equal to the average of the section zero-lift angles or

to the average for the root and tip airfoil; or may be determined

for the mean geometric chord assuming a linear variation span wise

of the section zero-lift angles.

The lift coefficient is usually considered the independent variable, and

the angle of attack as the dependent variable. It would, therefore, be

easier to use equation (18) in the form

aR = + (18a)

= KCL + «lo. (18b)

The slope a may be calculated from

a = i= 9.KB + 3)' (19)

where R is the aspect ratio of the wing and the other constants account for

planform and wing-tip corrections. These corrections vary for each type

of planform and wing tip, but the values given are sufficiently accurate

for preliminary work.

The maximum lift coefficient is not so easy to predict for the finite

aspect-ratio wing, but it may be assumed to be about the same as for in-

finite aspect ratio without incurring an error of more than from 3 to 7

per cent.

To determine the desired drag coefficient Cd for the corresponding lift

coefficient Cl, the following relationship is useful:

Ci}

Cd = Cd° + «00«(lp.5 - 0.322) (20) v

= CD, + KiCi? (20a)

where Cb0 is the average spanwise of the section drag coefficients Cd, or,

for a wing of zero aerodynamic twist, may be assumed to be the average

of the section drag coefficients of the tip and root airfoils. To make the

calculated values agree with experiment, the factor (10.5 — 0.3i?) has

been introduced to allow for planform variation and for tip effects.

The moment coefficient about the aerodynamic center of the mean aero-

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dynamic chord may be calculated by means of the following equation:

Cm. = tt^ 2(cm.c2dy + ciXa.c.cdy), (21)

44

AIRPLANE DESIGN MANUAL

where the various terms have the significance indicated as follows:

Cm.„. = theoretically, the mean aerodynamic chord, but for practical

purposes, the mean geometric chord (preferably stated in

inches);

S = wing area, in square inches if the linear dimensions are expressed

in inches;

C = chord, in inches, of the section under consideration;

dy = the span, in inches (usually one inch) of the section under con-

sideration;

Ci = the section-lift coefficient;

xa.c. = the distance, in inches, of the aerodynamic center behind the

leading edge of the section.

Instead of the aerodynamic center, the quarter-point on the chord may

be used, in which case the moment coefficients are about the quarter-point

of the chord.

Table III-3.

Section characteristics

Airfoil (or wing) characteristics

Root section

Tip section

'

where D = 10.35 feet (say, 10 feet, 6 inches). The blade angle at 75 per

cent of the radius is about 30 degrees.

The critical propeller-tip speed is about 1000 feet per second and it

should not be exceeded if serious reduction in propeller efficiency is to be

avoided. The critical propeller-tip speed, Vc, may be calculated from

the following formula: & - 6 lf"

v. - VC^r25)' + ^

For the propeller diameter just calculated Ve becomes equal to

- (1000^1634) 2 + (227 X 1.467)2 = 960 feet per second.

The propeller should, therefore, give excellent performance at sea-level

conditions. If best cruising speed is desired at another altitude, say that

to which the engine is supercharged, then the corresponding values of

brake horsepower and air density must be substituted in the equation

given for calculating the value of the power coefficient C,.

Figure XV-9 represents propeller characteristics when the propeller

is placed in front of a cowled radial engine located in the leading edge of a

moderately thick wing. These characteristics depend upon obstructions

in the propeller slipstream. If more accurate values for efficiency and

blade angles are desired, pertinent NACA reports should be consulted.

If a 2-bladed propeller has too large a diameter so that the tip speed is

too high, or there is insufficient ground clearance, or other factors prevail-

ing which make it necessary to choose a smaller diameter, a 3-bladed pro-

peller may be required.

For the conditions set forth, again assuming an initial efficiency of 80

per cent:

c- - (mi%w»*°^* = °000086Fp.

For 222 miles per hour:

C, = 1.91.

The corresponding maximum efficiency as found before was 86 per cent.

This efficiency is for a 2-bladed propeller whereas a 3-bladed propeller is

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to be used, the maximum efficiency of which would be reduced from 86 to

83 per cent, which is still higher than initially assumed.

258

AIRPLANE DESIGN MANUAL

After successive trials, it is found that maximum speed is closer to 224

miles an hour, for which the value of C, = 1.92, and the propeller efficiency

for a 2-bladed propeller is about 86 per cent, or 83 per cent for a 3-bladed

propeller.

For this value of C„ the corresponding V/nD, determined as before, is

1.15:

V— _ 224 X 100467

nD ~ (1634/60)Z)'

/ evaluating D = 10.47 (say, 10 feet, 6 inches). The blade angle at 75

/ per cent of the radius is approximately 29.5 degrees. Again this value

\ is for a 2-bladed propeller since all values have been based upon those

) obtained from Figure XV-9, which is for a 2-bladed propeller. However,

i these same values may be used, and the diameter so found may be re-

duced 7 per cent to obtain the corresponding diameter of a 3-bladed

propeller, if pertinent data for a 3-bladed propeller is not at hand. The

diameter of the 3-bladed propeller is then 10.5 feet less 7 per cent, or 9 feet

1^ 9 inches, roughly.

Alternative Method of Determining Propeller Diameter. The diameter

required for the 2-bladed propeller may be calculated directly by means

of the formula:

propeller diameter

For the example cited:

The same formula may be used to calculate the 3-bladed propeller by

using only 70 per cent of the value for the brake horsepower in the formula.

EMPIRICAL FORMULAS

Various empirical formulas may be devised, based on various parameters,

for the determination of propeller diameters. In all cases, D is the di-

ameter in feet, P is the rated horsepower, V is the maximum speed in

miles per hour, and N is the number of revolutions per minute of the

propeller.

K = 67 for a two-bladed propeller,

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K = 47 for a three-bladed propeller.

THE PROPELLER 1 1 1

_l I Z-i I I L

0.8 0.9 1.0 1.1 1.2 1.3

Airplane Mach number

Figure XV-10. Propellers for turboprop engines.

2. For a single- or twin-engine design:

2 blades.

3. For a 4-engine design:

3 blades.

40 0 ° = V(l^) (OTo) Xl^)'

2 or 3 blades.

A—

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Figure XV-11. Typical propeller-blade shapes for high-speed applications.

260

AIRPLANE DESIGN MANUAL

100 h

Figure XV-12. Variation of the propulsive efficiency of a propeller with airplane

Mach number. Further reductions for the various Mach numbers may be expected due

to installation, number of blades, and other possible variations.

5. For horsepowers between 2,000 and 0,000:

K = 11.5 for 3-bladed propeller,

K = 9.5 for 4-bladed propeller,

K = 8.0 for G-bladed propeller.

»-«(V£)(Vi>

For wooden propellers:

K = 48 for 2 blades,

K = 51 for 3 blades,

K = 49 for 4 blades.

For metal propellers:

K = (34 for 2 blades,

K = 01 for 3 blades,

X = 57 for 4 blades.

7. For horsepowers up to 3,000:

D = 480

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2 or 3 blades.

THE PROPELLER

261

Table XV-4. Propeller data.

Num-

Maxi-

Maxi-

Material

ber

Diameter

mum

mum

Weight

of blades

of

Pitch

in inches

hp

rpm

in

blades

rating

rating

pounds

1. Wood

2

Fixed

63

40

2800

6

2. Wood

2

Adjustable

84

50

14

2

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3. Al. Allov

Adjustable

84

54

41

4. Wood

2

Fixed

70

65

2800

10

5. Wood

2

Fixed

70

75

2600

9

6. Wood &Plastic

2

Variable

85

76

2800

25

7. Wood

2

Fixed

72

90

2700

11

262

AIRPLANE DESIGN MANUAL

Table XV-4. (Continued). Propeller data.

Num-

Maxi-

Maxi-

Material

ber

Diameter

mum

mum

Weight

of blades

of

Pitch

in inches

hp

rpm

in

blades

rating

rating

pounds

49. Al. Alloy

4

Controllable

151

2300

1520

494

50. Steel

3

Controllable

150 to 181

2500

1225

3

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51. Al. Alloy

Controllable

114 to 180

2500

1430

52. Al. Alloy

(i

Dual-rotation

157

2700

1400

757

53. Al. Alloy

6

Dual-rotation

144

2700

1400

712

54. Hollow Steel

4

Variable

134

2800

1470

485

55. Hollow Steel

4

Variable

158

2800

1470

509

CHAPTER XVI

The Power Plant

The power plant consists of the engine, propeller, starting system, cool-

ing system, fuel and oil systems, cowling, engine mount, and miscellaneous

accessories. Each item requires a considerable amount of design study, for

the ultimate success of the airplane depends upon the proper selection and

proper functioning of every part of the power plant.

GENERAL CONSIDERATIONS

Suppose an engine is to be selected. There are air-cooled and liquid-

cooled engines, either radial or in-line, or inverted in-line, or Vee, as well

as a few others. If the horsepower required is rather large, the elimination

of a few types may be possible since there may be engines having a partic-

ular cylinder arrangement that do not develop the required horsepower.

Again, the air-cooled type may be preferred to a liquid-cooled type due to

less complications in the installation since no cooling system is required

for the former, yet the liquid-cooled engine may be preferred for its lesser

frontal area or greater reliability. The line of demarcation in considering

the advantages between air-cooled and liquid-cooled engines may be fine,

and one cannot say arbitrarily that one engine is better than the other

until all the facts have been considered.

The different possible arrangements of engines are to be considered also,

so that a complete book instead of this short chapter could be written on

the power plant alone. The engines may be tractors or pushers; that is,

they may be placed with the propeller in front of the engine, meeting the

air before the engine; or the propeller may be placed behind the engine.

Such arrangements are sometimes desired for compactness and, as in the

case of tailless airplanes, to obtain a center of gravity location reasonably

far back and relative to the fuselage length.

There are also tandem arrangements, or combinations of tractor and

pusher arrangements. These are to be considered especially when the

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263

264

AIRPLANE DESIGN MANUAL

number of engines becomes so large that it may be desirable to concentrate

the engines as much as possible in order to reduce the length and complica-

tion of fuel, oil, and control lines.

The selection of the engine and the arrangement of a group of engines by

no means ends the problem, for even the best engine cannot function prop-

erly unless attention has been paid to proper installation of the cooling

system (whether it be the NACA cowl for air-cooled engines, or radiators

and pipe lines for liquid-cooled engines); to the correct installation of the

fuel and oil systems with special reference to the size of pipes or tubing; to

the location of pumps and relief valves; and, to the numerous little items

that go to make up the whole.

In the preceding paragraphs a brief survey of a few of the factors affect-

ing the power plant selection and design has been made. The following

material outlines the considerations to be taken into account in greater

detail.

LOCATION

.> To affect least the aerodynamic characteristics of the wing, it would be

desirable to locate the nacelle below the wing. To reduce torsional loads

imposed on the wing structure by the eccentric thrust-line position, it

would be desirable to locate the nacelle more or less with its axis in line

with the chord line. Usually, however, the governing condition for the

low-wing monoplane is the required propeller clearance with the ground.

For jet engines, the pod installation is preferred in this country. Since

the fuel is carried in the wing, the location of the jet pod below the wing

is a primary safety consideration. The torsional moment imposed on the

wing is desirable to offset the wash-out of the wing occurring at high

angles of attack and under accelerating conditions.

Unless the spar structure is cut away, the most rearward position usu-

ally possible is to have the engine as close to the front face of the front

spar as clearances for accessories will permit.

SUBMERGED ENGINES

Considerable attention has been devoted to enclosing engines within

the wing structure or within the fuselage. The chief reason for wanting

to enclose the engine within the wing is aerodynamic. Although this

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arrangement eliminates the engine nacelle, which interferes with the air-

flow around the wing, there is still the possibility of increased resistance

caused by ducts within the wing. For the propeller-type engine, this

increased resistance may be partially offset by extending the propeller

shaft. Then, the propeller may work more efficiently because it is not

operating directly in front of a thick body. Such extensions, however,

have inherent disadvantages such as increased weight and vibration.

THE POWER PLANT

265

Engines located within the fuselage permit the placing of the pilot ahead

of the engine, giving the best possible vision forward. It is also possible

to obtain a better structural arrangement and center of gravity location.

Adequate air intakes may be provided by means of ducts whose open-

ings are located just at the leading edge of the wing where their position

causes the least effect upon the aerodynamic qualities of the wing, espe-

cially at very high speeds.

NUMBER OF ENGINES

Assuming that a certain horsepower is required for a given design, should

this horsepower be provided by one or more engines? Obviously, it is

simpler and cheaper to have only one engine since there is only one set of

controls, one engine mount; in short, one installation and all that it entails.

However, the one engine centrally located in the nose of the fuselage is a

source of undesirable noise, heat, and reduced vision. Moreover, in case

of engine failure due to any reason, the airplane must land immediately.

The other alternatives are two, three, or four engines, so that in case of

one engine quitting, the flight may be continued, provided that this is pos-

sible with the remaining engine or engines.

If flight is to be maintained with one engine in a twin-engine design,

there may be some penalty in allowable gross weight that the airplane

may carry because it is usually, although not always, difficult to maintain

rectilinear flight when the thrust vectors are not symmetrical and espe-

cially if the horsepower loading for the two engines is already initially

heavy. It may be possible to dump the fuel load in order to lighten the

load, but if the airplane is over rugged terrain it may not be advisable to

do so since the required landing might be dangerous if attempted immedi-

ately (as the loss of fuel would dictate).

The three-engine design, then, has the advantage over the twin-engine

design in such a case, since, with one engine not operating, it is usually still

possible to maintain rectilinear flight without loss of altitude with two

engines functioning. Moreover the power loading is increased only 50

per cent instead of 100 per cent.

The use of four or more engines may be necessary for large airplanes,

especially when the number of large capacity engines is limited.

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Opposed to the safety factor of multi-engine design in possible engine

failure it is to be remembered that multi-engines offer many more com-

plications and require at least one co-pilot, in addition to the chief pilot,

to operate. In many cases, additional members are required in the crew

that is responsible for power plant operation.

In attempting to work out the best combination of engines from the

point of view of maintaining flight with one or more engines not operating,

266

AIRPLANE DESIGN MANUAL

it is possible to arrive at a mathematical analysis by means of the prob-

ability theory. If the probability of any engine failure is independent of

any other and is the same for every engine (as would be likely when the

engines have the same manufacturing and operating characteristics) then

the relative probability of 0, 1, 2 • • • failures is given by the successive

terms of the binomial

(5 + P)\

where p = the probability of a failure,

q — 1 — p, where q is the probability that this failure will not occur,

k = the number of engines involved.

The value of p may be assumed if no data are available, or may be based

upon existing flight data, and may then be calculated as follows:

P

/number of failures in annual number\ ,average j th of x

of miles flown H individual trips /

\ annual number of miles flown /

For example, if it is assumed that there were 10 single-engine failures in

1,000,000 miles flown and that the average trip length was 2,000 miles,

then from these data.

'= (imm)2'000 = 002'

q = l - p = l - 0.02 = 0.98.

An example will help to illustrate the calculation procedure and to inter-

pret the algebraic terms involved: for a three-engine airplane, expanding

(q + p)8 yields q* + Zq2j>1 + 3 g'p2 + P30 0 Each term of the expanded

binomial indicates the nonfailing and failing engine combination of the

three engines; for example, the exponent of q indicates the number of non-

failing engines of that combination and the exponent of p indicates the

number of failing engines in that combination. The term dqpp1 indicates

the number of failing and nonfailing combinations when any one of the

three engines may fail. The calculations for the three-engine design for

the values of p and q as determined, are tabulated in Table XVI-1.

Table XVI-1.

1.

Term of binomial

3?'p

2.

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q*

Number of possible en-

gine failures

0

1

2

3

3.

Number of no engine

failures

3

2

1

0

4.

Evaluation of binomial

term (Probability of

number of no engine

failures indicated in

10,000 trips)

9,411.92 X 10-*

576.24 X 10—
f today locate the tail surfaces about to 3

chord lengths (mean geometric chord of the wing) behind the center of

gravity so that the observance of this rule will assure reasonable static

longitudinal stability.

The horizontal tail surfaces may be ahead of or behind the vertical tail

surface or somewhere between these two extreme positions, as shown in

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Figure XIX-15.

396

AIRPLANE DESIGN MANUAL

Figure XIX-14. Layout of the horizontal tail surfaces showing cut-out of elevators

to prevent interference with the movement of the rudder. Each movable surface should

be supported by at least three hinges.

For the small airplane, because of structural and dimensional considera-

tions, the rear stabilizer spar and the rear fin spar usually intersect and

are built in integrally with the fuselage frame at that station unless either

or both the fin and stabilizer are adjustable in flight or on the ground.

A position of the horizontal tail surfaces ahead of the vertical tail

surfaces may be considered if it results in less complication of the control

system. One disadvantage of such a location is the blanketing of the

vertical tail surfaces at high angles of attack.

Figure XIX-15. Location of horizontal tail surfaces. They may be located ahead

or behind the vertical tail surfaces. or located vertically anywhere between the two

extremes of the vertical tail surfaces at the bottom of the fuselage or at the top of the

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vertical tail surfaces.

TAIL SURFACES

397

A position of the horizontal tail surfaces behind the vertical tail surfaces

would clear both, so that neither would be blanketed by the other.

Vertically there may also be some choice of location. The lowest

position would probably be determined by the ground clearance of the

deflected elevator, whether or not the nose-wheel or tail-wheel type landing

gear is used.

The location of the horizontal tail surfaces where they can be securely

attached to the fuselage structure is advantageous from the structural

point of view.

For the higher-speed airplanes, especially those having the exhaust

duct or ducts of the jet engines in .the tail of the fuselage, the horizontal

tail surfaces have to be located above the fuselage. Thus the horizontal

surfaces have to be secured to the vertical tail surfaces. Under asym-

metrical conditions, the aerodynamic load on the horizontal tail surfaces

produces a torsional moment upon the vertical tail surfaces. It there-

fore becomes necessary for those surfaces to be constructed more rigidly,

thereby entailing greater weight.

Consideration has been given to the use of a biplane set of horizontal

tail surfaces, whereby the smaller elevator could, in its operation, be used

as a booster control for the larger surface through suitable linkage.

A design used occasionally is the so-called canard type, which locates

the horizontal tail surfaces ahead of the wing. In that position, the

surfaces are acting in the up-wash, rather than the down-wash of the

wing. For this reason, the horizontal tail surfaces are apt to stall before

the wing, so that sufficient control may not be available at a critical time.

However, this feature has been considered an advantage since the tail

surfaces could act as a stall-warning for the wing. The location of the

tail surfaces ahead of the wing may interfere with the vision forward.

It is considered psychologically bad to be able to see the deflection of the

surfaces at practically all times. Another advantage, in addition to the

stall-warning device, is that the arrangement of the surfaces forward may

serve as a suitable crash-absorber in case of an accident.

Angular Deflection

Elevators are designed to have an equal angular movement up and

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down from neutral. About 30-degree movement is considered maximum,

and, with efficient design, a 25-degree deflection up and a 25-degree

deflection down should be sufficient.

Adjustable Stabilizer

The stabilizer may be adjusted through a small angular displacement

either on the ground or in the air from the cockpit (usually the latter, if at

all, since trimming tabs are displacing adjustable stabilizers).

398

AIRPLANE DESIGN MANUAL

If an adjustable stabilizer is used, a total of 6- to 8-degree movement

(about 5 degrees up and 3 degrees down) is usually used.

The adjustable stabilizer is used to change the trim angle of the air-

plane without displacing the elevator. The elevator can then operate

from the new neutral position determined by the stabilizer. In the first

prototype to be flown, the range of angles provided may be greater than

is absolutely necessary until flight tests have determined the desirable

range.

For high-speed airplanes operating through the transonic regime, the

adjustable stabilizer is preferred over the elevator trim tab, since the trim

drag is becoming an important factor in the performance of the airplane.

Where power operation has been provided, a one-degree-per-second rate

of change through 11-degree travel has been used.

On small airplanes it has been customary to make the stabilizer adjust-

able through a limited angular range, about 3 degrees up and 3 degrees

down. This adjustment has been possible either on the ground or in the

air by means of a control located in the pilot's cockpit. The adjustment

in the air is preferable. On the large transport airplanes, variations in

trim (the object of the adjustable stabilizer) are obtained by means of

trailing-edge tabs.

Aspect Ratio

The aspect ratio of the tail surfaces should be as high as possible (usually

from 3 to 5) in order to avoid blanketing of the structure to which they

are attached. Aspect ratios greater than 6 are seldom used unless ttyey

can be adequately braced.

In proportioning the tail surfaces, it is not desirable to start with the

aspect ratio because the fuselage section increases the span of the tail sur-

faces seemingly beyond the desirable limit.

For correcting airfoil data from the given aspect ratio to that of the tail

surfaces, the aspect ratio is calculated on the basis of the square of the span

length from tip to tip divided by the area including that covered by the

fuselage. In other words, exactly the same procedure is followed as in

calculating the aspect ratio of the wing.

Angle of Incidence

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The incidence of the horizontal tail surfaces is determined by the amount

of downwash from the wing, its relative location with respect to the wing,

and the moment required to obtain the required trim angle.

The angle of trim of the airplane is denned at that angle at which the

sum of the pitching moments about the center of gravity of the airplane is

zero. Normally, it is expected that the elevator be in the neutral position,

that is, undeflected for that attitude of the airplane or angle of trim for

TAIL SURFACES

399

which the flying time is the greatest. This attitude is usually for cruising.

In order to determine this angle, it would be desirable to have calculated

the preliminary performance. In lieu of the necessary data from such

calculations, it may be assumed that the desired angle of trim lies between

the angle of the wing at which the minimum drag coefficient occurs, and

the angle at which the maximum ratio of lift to drag occurs.

Once the angle of trim has been decided upon, the angle of incidence (or

setting) of the horizontal tail surfaces can be determined for at trim by:

Cjfw. = 0 = Cm. + Cm a or Cm, = —Cm.;

but

or

-0.8yi CL, f*.

— Cm.

— -0.8yASt/SK)&ttTim> (2)

where Cm. has been calculated for that angle of attack of the airplane cor-

responding to the angle of trim.

Once the lift coefficient of the tail surfaces at trim condition has been

determined, the required angle of attack of the tail surfaces can be deter-

mined from the aerodynamic characteristics of the tail surface airfoil.

Since the tail surfaces are affected by the downwash of the wing, correc-

tion for this downwash must be made not only to determine the angle of

incidence of the tail surfaces, but to determine the angle of attack of the

tail surfaces corresponding to the angle of attack of the wing.

The downwash angle is given sufficiently accurately by the following

modified Diehl's equation:

e = ^a^»ir*» (3)

where e is the downwash angle in degrees,

Cl is the lift coefficient of the wing,

R is the aspect ratio of the wing, "u0

0

x is the number of mean aerodynamic wing-chord lengths that

V the 20 per cent pomt of the mean geometric chord of the hori-

zontal tail surfaces is behind the aerodynamic center of the

wing, and

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y is, similarly, the number of chord lengths the horizontal tail

surfaces are above or below the mean aerodynamic chord of the

wing.

For any given design, equation (3) could be written in terms of the angle

of attack of the wing since Cl — aa*, where aa is so measured that a = 0

when Cl = 0, and a is the slope of the lift curve. By further evaluation,

the formula would finally take the form

400 AIRPLANE DESIGN MANUAL

e = kaa, (3a)

where

0.40a

£-0.25 y-0.7I_

Then, if the wing has an angle of incidence measured with relation to a

fixed reference line on the fuselage, the effective angle of downwash meas-

ured with relation to this reference line would be e + iw. The angle of

Figure XIX-16. Reference diagram for angles referred to in equation (4a).

attack of the horizontal tail surfaces, when placed at zero angle of incidence

to the fuselage reference line, would be — (« + ij). Should the horizontal

tail surfaces have an angle of incidence of its own, the angle of attack of

the horizontal tail surfaces would be it — (« + i«).

Recapitulating,

at = -(« + (4)

or

OLt = it — (e + im), (4a)

depending upon whether the horizontal tail surfaces have an angle of inci-

dence or not. This angle of incidence can now be determined for the re-

quired at, for Cl [as obtained from equation (2)] at trim gives the neces-

sary information. For subsequent calculations, it would be desirable to

determine at from a modified form of equation (4a) such as at = fca„ —

i* + it0

0

Sweepback

Normally, any sweepback that the horizontal tail surfaces may have is

due to the trapezoidal planform. However, just as sweepback has been

employed for the wing as speeds approach M = 1, so sweepback has to be

applied to the horizontal tail surfaces. The discussion relating to sweep-

back in Chapter XVII, Design of the Wing, is applicable to the design of

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the horizontal tail surfaces.

TAIL SURFACES

401

In order to obtain relatively uniform down-wash conditions on the

horizontal tail surfaces, some sweepback may be employed to compensate

for the sweepback of the wing.

Dihedral

Normally horizontal tail surfaces are not given any dihedral, but it has

been found that the effectiveness of the horizontal tail surfaces can be in-

creased considerably, particularly at high angles of attack, by incorporat-

ing some dihedral in the horizontal tail surfaces. How large the dihedral

angle should be depends upon the down wash of the wing; for purposes of

symmetry, the span line of the tail surfaces may be made parallel to the

span line of the wings.

Area

Examination of airplanes of all sizes reveals that the jpatio of the hori-

zontal tail surfaces to the effective wing area varies from'20xo 25 per cent.

The greater the tail length is, in terms of the wing chord, the smaller per-

centage area is required. Wings equipped with lift-increase device usually

require that the percentage area of the horizontal tail surfaces be greater

than if the wings were not so equipped.

The elevator area varies from 35 to 45 per cent of the horizontal tail sur-

face area.

Construction

For ease in assembly and disassembly, the horizontal tail surfaces are

attached to the top of the fuselage, especially if tubular steel construction

is used for both the tail surfaces and the fuselage. When reinforced metal

monocoque construction is used, the horizontal tail surfaces may be located

nearer the longitudinal centerline of the rear portion of the fuselage and

still obtain the necessary rigidity.

Planform

Some indication of planforms used for horizontal tail surfaces may be

obtained from those shown in Figure XIX-17. Since the aspect ratios

are about the same for the horizontal tail surfaces as for the wing, and

some other considerations of design are similar, the planforms of the

horizontal tail surfaces look very similar to the wing planforms. Some

modification may be made due to the greater role that the movable sur-

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face, which takes up almost half of the total area, plays in the design of

the structure.

402

AIRPLANE DESIGN MANUAL

Figure XIX-17. Typical planforms of horizontal tail surfaces. Only one half of

the surfaces are shown. Vertical tail surface planforms are similar.

Other Solutions

For some aircraft, especially those of the flying-wing type, the horizontal

tail surfaces disappear as separate entities, but their function is taken

over by trailing-edge flaps or wing-tip surfaces. The high-speed transonic

and supersonic designs employing the delta wing should be studied, es-

pecially with reference to the means employed in obtaining longitudinal

stability and control through flaps and other similar devices.

For other high-speed designs, there may be no elevator as such, but the

entire horizontal tail surface may be deflected angularly in order to elim-

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inate the increase in drag caused by the deflected flap.

TAIL SURFACES 403

Figube XIX-18. Two illustrations showing the application of moveable wing tips

that, freely floating, would operate as an aileron on a normal wing, as in (A); or, for a

tailless airplane the tip surfaces could be operated differentially for aileron action or

unidirectionally for elevator action, as shown in (B).

Clearances

When the horizontal tail surfaces have been positioned on the fuselage

or some other component of the airplane structure, the student should

check allowable clearances with the ground when the elevator is deflected,

and with the vertical tail surfaces, especially the rudder.

VERTICAX TAIL SURFACES

The vertical tail surfaces consist of the fixed surfaces (the rudder), the

movable surface (the elevator), and the trim tab.

The function of these surfaces is to obtain the necessary directional

stability and control in flight.

Figure XIX-19. A "canard-type" airplane with the horizontal tail surfaces located

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ahead of the center of gravity. The vertical tail surfaces are located at the wing tip.

404

AIRPLANE DESIGN MANUAL

Directional Stability and Control

Straight flight should be attainable at any speed above 140 per cent of

the minimum speed by sideslipping without the use of the rudder and with

a single engine (of a multi-engine design) being inoperative.

The yawing moment in a sideslip should be such that right-rudder de-

flection would be required for a sideslip toward the left, and left-rudder

deflection toward the right. For small angles of sideslip, the sideslip angle

should be proportional to the rudder angle.

The airplane should always tend to return from a sideslip without the

use of the rudder regardless of the angle of the sideslip.

Rudder control should be such that:

1. A control force of not more than 180 pounds is required to maintain

the airplane in rectilinear flight with one engine inoperative and the other

or others at full rated power at all speeds above the minimum take-off

speed;

2. To meet the spin recovery requirements of the airplane;

3. To overcome the adverse yawing moment caused by aileron deflec-

tions at any speed.

When all controls are released in flight, lateral oscillations of the air-

plane should always damp to one half amplitude within two complete

cycles. When the ailerons or rudder are moved and released quickly,

they should return to their neutral position and damp any oscillations of

the airplane in one cycle.

Both rudder and aileron may employ trimming systems. They should

be:

1. Used if the control forces for level flight are 10 per cent greater than

80 pounds for the aileron control wheel or 30 pounds for the aileron control

stick, or 180 pounds for the rudder pedals for any speed between the maxi-

mum speed and 120 per cent of the minimum speed;

2. Powerful enough to maintain rectilinear flight with one engine inop-

erative (for a multi-engine airplane) at speeds 140 per cent of the minimum

or above.

Further, the approaching stall of the airplane should develop gradually

and make itself felt by increasing "pull force" on the control column, and

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by evidence of buffeting of the airplane. Recovery, after complete stall

has been attained, should be possible by normal use of the controls.

Rolling or yawing moments of the airplane at less than 2 degrees above

the attitude required for a 3-point landing should not cause the airplane to

stall.

TAIL SURFACES

405

From the flight criteria mentioned, the designer is able to work back to

the detail design so that the airplane will incorporate the characteristics

desired. Many features are arrived at through past experience or from

examination of existing designs. Other features are subject to research

in the wind tunnel, for there may be a number of variables that require

proper proportions to obtain the desired effect.

Location

The location of the vertical tail surfaces depends upon the type and

speed range of the aircraft. For the small, single-engine private airplane,

the vertical tail surfaces are, almost without exception, located above the

horizontal tail surfaces in order to centralize control systems and simplify

the supporting structure contained in the fuselage.

It is desirable to locate about half of the rudder below the axis of sym-

metry of the fuselage, but this may not be possible because of required

clearance with the ground.

Large airplanes employ multiple vertical tail surfaces (see Figure

XIX-20) for several reasons, although the primary one is to obtain the

advantage of slipstream effect over one of the surfaces when an engine of a

multi-engine design quits. The increased slipstream velocity helps in pro-

viding the greater yawing moment necessary to overcome that produced

by the offset thrust.

In large designs, it is often difficult to

prevent blanketing of the vertical tail

surfaces by the large fuselage so that

dividing the area into several smaller

ones and placing them at the ends of the

horizontal tail surfaces increases their

relative efficiency.

Where the required area is very large,

three instead of two sets of vertical tail

surfaces are used. This reduces the tor- Figure XIX-20. Arrangements

sional load imposed by the outrigger type of twin vertical tail surfaces.

of vertical tail surfaces which also complicates the control-system design.

The extension of the fin area ahead of the middle fin in triple vertical

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tail-surface design has often been added after flight tests indicated that

additional vertical tail area was necessary. While inefficient aerodynami-

cally, such extensions do not impose very much additional torsion on the

fuselage.

To a less extent, multiple vertical tail surfaces are used in order to re-

duce the over-all height of the aircraft structure, especially in those designs

for which hangar door clearances are the determining factors.

406

AIRPLANE DESIGN MANUAL

For high-speed aircraft, the vertical tail surfaces may be displaced at

the wing tips of the swept-back wing, where they obtain a sufficiently long

moment arm to produce a satisfactory yawing moment.

The placing of the vertical tail surfaces at the end of the horizontal tail

surfaces helps, although to a very small degree, to increase the effective

aspect ratio of the horizontal tail surfaces.

In some cases the vertical tail surfaces are slightly tilted from the ver-

tical. This is usually the result of the dihedral incorporated in the hori-

zontal tail-surface design where dihedral is employed to account for the

downwash of the wing.

Angular Deflection

The rudder has an angular movement of a maximum of 30 degrees each

side of neutral. It is generally desirable to have all primary control

surfaces operate through the same angular range so that a pilot transferring

from one airplane to another is at least likely to be familiar with the

amount of control to be expected for the control-stick or rudder-pedal

movement.

The fin may be adjustable to offset the yawing moment induced by the

means used to produce a rolling moment of the wing to offset the torque

of the reciprocating engine.

Aspect Ratio

The aspect ratio of the vertical tail surfaces may be somewhat restricted

by the possible torsional moment imposed upon the fuselage structure

since the vertical tail surfaces are usually asymmetrical about the longi-

tudinal axis. Since the tail surfaces are at zero angle of attack throughout

the flight regime, aspect-ratio effects play a very small part, if any, in

Figure XIX-21. For aspect-ratio calculations, the surface area represented by the

side of the fuselage aft of the dotted line is included in the total area; but it is not con-

sidered as part of the vertical tail surface area in the evaluation of the ratios of tail

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surface area to wing area—which ratio may vary from .08 to .12.

TAIL SURFACES

407

the over-all aerodynamic drag of the airplane. The main consideration

for the vertical tail surface is to locate it so that it is not made ineffective

by blanketing of the fuselage or horizontal tail surfaces. To minimize

such blanketing, a higher aspect ratio for the vertical tail surfaces often

becomes necessary.

The aspect ratio of the vertical tail surfaces should be between 2 and 4.

It is difficult to state exactly what the aspect ratio of the vertical tail sur-

faces may be, because the rear portion of the fuselage influences the vertical

tail surface effectiveness.

Area

The size of the tail surfaces is dependent upon the location; the greater

the distance between the center of gravity of the airplane and the center

of pressur^of the vertical tail surfaces in terms of the mean^ierodynamic

chord^ofThe wing^the smaller the area needs to be. Where the vertical

tail surfaces are attached to the wing tips, the relative distance is likely

to be smaller, so that the area would have to be proportionately greater

in order to obtain the same degree of directional stability and control.

The area of the vertical tail surfaces ranges from !10jto 15 per cent of

the wing area, with about 30 to 50 per cent of the area devoted to the

rudder. An exception is provided by those designs where dorsal or

ventral fins are employed, in which case the movable portion of the vertical

tail surfaces is likely to be no more than 30 per cent of the total area.

The dorsal fin (see Figure XIX-22) may be used to increase the fin area

in order to (1) increase the directional stability if the original surface

Figure XIX-22. The dotted lines show various ways of increasing the fin area.

The top diagram illustrates a dorsal fin, while the two bottom diagrams illustrate the

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vertical-type fin.

408

AIRPLANE DESIGN MANUAL

proves inadequate, (2) transmit the loads on the fin to a greater number

of fuselage frames, (3) reduce the torsional moment about the longitudinal

fuselage axis, (4) reduce the over-all height dimensions of the vertical tail

surfaces, and (5) obtain a possible weight saving, although the total fin

area is likely to be greater for a dorsal fin than for a normal fin-type

surface.

The ventral fin (See Figure XIX-22) is another solution to increasing

the fin area. Since it is located below the fuselage, it is not blanketed

by any of the aircraft structure and is likely to be even more effective

than the dorsal fin.

Planform

The vertical tail surfaces have a variety of planforms, depending some-

what upon their location. A few likely designs are illustrated in Figure

XIX-23.

Figure XIX-23. Typical planforms of vertical tail surfaces.

Sweepback

For transonic and supersonic designs, the vertical tail surfaces must

incorporate sweepback. For lower-speed aircraft, on the other hand,

the sweepback observed in the design of the vertical tail surfaces is a result

of other design considerations such as planform, appearance, and position

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of the fin-post.

TAIL SURFACES

409

Tail Length

For subsonic designs of conventional layout, the tail surfaces have been

so located that the distance from the center of gravity of the airplane to

the estimated center of pressure of the horizontal or vertical tail surfaces

is from 2.5 to 3.25 times the mean geometric chord of the wing.

As speeds approach the supersonic, the "trim drag", especially with

deflected surfaces, becomes an appreciable portion of the total drag of

the airplane. To ameliorate this condition, the tail length is made as

long as possible, so that smaller areas may be employed for the tail sur-

faces and relatively little deflection is necessary for the desired amount

of control. Both are attempts to reduce the drag. However, there is a

point of diminishing return in that a longer fuselage also implies a greater

skin drag, and thus a gain in one may be offset by a loss in the other.

|- A M

Figure XIX-24. The distance A for conventional airplanes should be from to 3

times the mean aerodynamic chord of the wing. The angle B, corresponding to the

maximum deflection of the elevator, should permit the tailing edge of the elevator to

clear the ground comfortably.

BUTTERFLY OR VEE TAIL

This type of tail surface combines the vertical and horizontal tail

surfaces in one, as shown in Figure XIX-25. The vertical component of

the lift corresponds to the normal tail-surface load, while the horizontal

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Figure XIX-25. A "Vee" or "Butterfly" tail.

410

AIRPLANE DESIGN MANUAL

component of lift when both halves of the surfaces are neutral is zero,

unless both surfaces are at an angle to the normal direction of flight

when the horizontal component of lift produces the necessary yawing

moment to weather-cock the airplane.

The movable trailing-edge flaps act as elevators when both are deflected

in the same direction, and as rudders when operated in the opposite

direction. It is also possible to operate them in a combination of the two

motions so that simultaneous pitching and yawing moments are obtained.

The movable surfaces are called either ruddervaters or elerudders.

The cockpit controls are the same as for the normal type of rudders and

elevators, although the control mechanism from the cockpit to the tail

surfaces is a little more complicated.

The advantages claimed for such an arrangement are:

1. A saving in weight due to its simplicity of construction, its fewer

elements, and the smaller total area possible.

2. Higher maximum speed, due to less area and consequently less pro-

file drag as well as less interference drag.

3. Better spin recovery due to less blanketing of the tail surfaces.

The detailed design information is to be found in an NACA report.

For preliminary design purposes, the following relationships may be

considered:

The effective horizontal tail surface area

SH = S cos 0; (1)

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