Performance and Stability of Aircraft

317 Pages·1996·13.17 MB·English

by  J. Russell

Performance and
Stability of Aircraft
This Page Intentionally Left Blank
Performance and
Stability of Aircraft
J. B. Russell
MSc, MRAeS, CEng
Centre for Aeronautics
City University
London
~ E ! N E M A N N
OXFORD AMSTERDAM BOSTON LONDON NEW YORK PARIS
SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO
Butterworth-Heinemann
An imprint of Elsevier Science
Linaere House, Jordan Hill, Oxford OX2 8DP
200 Wheeler Road, Burlington, MA 01803
First published 1996
Transferred to digital printing 2003
Copyright © 1996, J. B. Russell. All rights reserved
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Whilst the advice and information in this book is believed to be true and accurate
at the date of going to press, neither the author not the publisher can accept any
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Library of Congress Cataloguing in Publication Data
A catalogue record for this book is available from the Library of Congress
ISBN 0 340 63170 8
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Contents
Preface xi
List of symbols and abbreviations Xleele l
Note to undergraduate students xxii
1 Introduction 1
1.1 The travelling species 1
1.2 General assumptions 1
1.3 Basic properties of major aircraft components 2
1.3.1 Functions of major aircraft components and some definitions 2
1.3.2 Lift characteristics of wing sections and wings 4
1.3.3 Maximum lift and the characteristics of flaps 7
1.3.4 Estimation of drag 10
1.3.4.1 Effect of compressibility on drag 12
1.3.4.2 Drag polars 13
1.4 Engine characteristics 13
1.5 Standard atmospheres 14
1.5.1 Pressure and density in the troposphere 18
1.5.2 Pressure and density in the stratosphere 19
Student problems 20
Background reading 21
2 Performance in level flight 22
2.1 Introduction 22
2.2 The balance of forces 22
2.3 Minimum drag and power in level flight 23
2.4 Shaft and equivalent powers for turboprop engines 26
2.5 Maximum speed and level acceleration 27
Worked example 2.1 28
2.6 Range and endurance 29
2.6.1 General equations for range and endurance 30
2.6.1.1 Application of general equations 32
Worked example 2.2 32
Worked example 2.3 33
2.6.2 Cruise in the stratosphere 35
Worked example 2.4 35
2.6.3 Range-payload curves 36
2.7 Incremental performance 36
Student problems 38
vi Contents
3 Performance- other flight manoeuvres 41
3. I Introduction 41
3.2 Steady gliding flight 41
3.3 Climbing flight, the 'Performance Equation' 42
3.3.1 Climb at constant speed 45
3.3.1.1 Propeller-driven aircraft 45
Worked example 3.1 47
3.3.1.2 Jet-driven aircraft 47
Worked example 3.2 49
3.3.2 Climb with acceleration 5O
3.3.3 Ceiling 51
3.3.4 Time to height 52
3.3.5 Energy height methods 52
3.3.6 Standardized performance 54
3.4 Correctly banked level turns 56
Worked example 3.3 59
3.4.1 Turns at constant throttle 59
3.5 Take-off and landing 60
3.5.1 Landing 65
3.5.2 Balanced field length 66
3.5.3 Reference speeds during take-off 66
Student problems 67
4 Introduction to stability and control 71
4.1 Aims of study 71
4.2 First thoughts on stability 71
4.2.1 Choice of axes 71
4.2.2 Static and dynamic stability 72
4.2.3 Approximate treatment of response to gusts 73
4.2.4 The natural time scale 74
4.2.5 Simple speed stability 75
4.3 Controls 76
4.3.1 Flap type controls 76
4.3.2 Balancing of flap type controls 77
4.3.3 Spoilers 79
Student problem 80
5 Elementary treatment of pitching motion 81
5.1 Introduction 81
5.2 Modelling an aircraft in slow pitching motion 81
5.2.1 Centre of pressure and aerodynamic centre 81
5.2.2 The reference chord 83
5.2.3 The aircraft-less-tailplane 84
5.2.4 The pitching moment equation of the complete aircraft 85
5.2.5 Tailplane contribution to the pitching moment equation 86
5.2.6 The pitching moment equation, 'stick fixed' 88
5.3 Trim 88
5.3.1 Trim, 'stick fixed' 89
5.3.2 Trim, 'stick free' 90
5.3.3 Trim near the ground 91
Worked example 5.1 92
Contents vii
5.4 Static stability 93
5.4.1 Static stability, 'stick fixed' 93
5.4.2 Static stability, 'stick free' 95
Worked example 5.2 96
Worked example 5.3 97
5.5 Actions required to change speed 97
5.5.1 Stick movement and force to change speed 98
5.6 Manoeuvre stability 99
5.6.1 The pullout manoeuvre 99
5.6.2 Manoeuvre stability, 'stick fixed' 101
5.6.3 Manoeuvre stability, 'stick free' 102
5.7 The centre of gravity range and airworthiness considerations 103
5.8 Some further matters 104
5.8.1 More accurate expression for the cg margin, 'stick fixed' 105
5.8.2 Canard aircraft 106
5.8.3 Effects of springs or weights in the control circuit 108
Student problems 108
6 Lateral static stability and control 112
6.1 Introduction 112
6.2 Simple lateral aerodynamics 112
6.2.1 Aileron and rudder controls 112
6.2.2 Sideslip 113
6.2.3 Effect of rate of yaw 116
6.3 Trimmed lateral manoeuvres 117
6.3.1 The correctly banked turn 117
6.3.2 Steady straight sideslip 119
6.3.3 Minimum control speeds 120
6.4 Static stability 120
Student problem 121
7 Revision and extension of dynamics 122
7.1 Introduction 122
7.2 Some simple aircraft motions 122
7.2.1 Pure rolling 122
7.2.2 Pitching oscillation 125
7.2.3 The phugoid oscillation 126
7.3 'Standard' form for second-order equation 128
7.4 Dynamics using moving axes 129
7.4.1 Equations of motion for a system of particles 130
7.4.2 Equations of motion for a rigid body 131
7.4.3 Moving frames of reference 133
7.4.4 Equations of motion of a rigid body referred to body fixed axes 134
7.4.5 Example of use of equations 135
7.5 State-space description 136
7.5.1 Example of state-space description 137
7.5.2 Analytical solution of state-space equations 138
7.5.2.1 Time domain solution 138
7.5.2.2 Frequency domain solution 139
7.5.2.3 Numerical example 141
viii Contents
7.5.3 Step-by-step solution of state-space equations 142
Student problems 143
Background reading 144
8 Equations of motion of a rigid aircraft 145
8.1 Introduction 145
8.2 Some preliminary assumptions 145
8.2.1 Axes and notation 145
8.2.2 Plan of action 146
8.3 Orientation 146
8.3.1 Relations between the rates of change of angles 148
8.4 Development of the equations 149
8.4.1 Components of the weight 149
8.4.2 Small perturbations 150
8.4.2.1 Stability derivatives 151
8.4.2.2 Linearized equations of motion 151
8.4.3 Symmetry 152
8.5 Dimensional stability equations 153
8.6 Concise, normalized and nondimensional stability equations 154
8.6.1 Concise stability equations 157
8.6.2 Dynamic-normalized equations 157
8.6.2.1 The motion of the centre of gravity of the aircraft 160
8.6.3 Stability equations in American notation 161
Student problems 164
9 Longitudinal dynamic stability 165
9.1 Introduction 165
9.2 General remarks on stability derivatives 165
9.2.1 Derivatives due to change in forward velocity 167
9.2.2 Derivatives due to downward velocity 169
9.2.3 Derivatives due to angular velocity in pitch 171
9.2.4 Derivatives due to vertical acceleration 172
9.2.5 Derivatives due to elevator angle 174
9.2.6 Derivatives relative to other axes 174
9.2.7 Conversion of derivatives to concise forms 174
9.2.8 Conversions to derivatives in American notation 174
9.3 Solution of the longitudinal equations 175
9.3.1 Solution of the equations of free motion 176
9.3.2 Stability of the motion 178
9.3.3 Test functions 179
9.3.4 Iterative solution of the characteristic quartic 182
Worked example 9.1 183
9.3.5 Relation between the coefficient E, and the static stability 184
9.3.6 Relation between the coefficient C, and the manoeuvre stability 185
9.4 Discussion of the longitudinal modes 186
9.4.1 The phugoid mode 186
9.4.2 The short period pitching oscillation 188
9.4.3 The effects of forward speed and cg position 189
Appendix" Solution of longitudinal quartic using a spreadsheet 191
Student problems 193
Contents ix
10 Longitudinal response 195
10.1 Introduction 195
10.2 Response to elevator movement 195
10.2.1 Response using Laplace transform 195
10.2.2 Frequency response 197
10.2.3 Response using numerical integration of state-space equations 198
10.2.4 Typical response characteristics of an aircraft 200
10.2.5 Normal acceleration response to elevator angle 201
10.3 Response to gusts 204
10.3.1 Response to discrete gusts 204
Worked example 10.1 207
10.3.2 Introduction to random variable theory 209
10.3.3 Application of random variable theory, the 'PSD method' 214
10.3.4 Statistical discrete gust method 217
10.3.5 Pilot opinion, handling and flying qualities 218
Student problems 220
11 Lateral dynamic stability and response 222
11.1 Introduction 222
11.2 Lateral stability and derivatives 222
11.2.1 Derivatives due to slideslip velocity 222
11.2.2 Derivatives due to rate of roll 223
11.2.3 Derivatives due to rate of yaw 223
11.2.4 Estimation of the lateral derivatives 223
11.2.5 Control derivatives 224
11.2.6 Conversion of derivatives to concise forms 225
11.2.7 Conversions to derivatives in American notation 225
11.3 Solution of !ateral equations 225
11.3.1 Solution of the equations of free motion 227
11.3.2 Iterative solution of the characteristic quintic 228
I 1.3.2.1 The large real root 228
I 1.3.2.2 The small real root 228
I 1.3.2.3 The complex pair 229
Worked example 11.1 229
11.4 Discussion of the lateral modes 230
I 1.4. l The zero root 230
I 1.4.2 The spiral mode 231
I 1.4.3 The roll subsidence mode 232
I 1.4.4 The dutch roll 235
I 1.4.4.1 The directional oscillation 236
11.4.4.2 The directional oscillation with lateral freedom 237
I 1.4.4.3 Conventional dutch roll with large damping in roll 239
I 1.4.4.4 Conventional dutch roll with large inertia in roll 240
I 1.4.4.5 The rolling oscillation 241
I 1.4.4.6 The rolling oscillation with lateral freedom 242
11.4.4.7 Discussion of dutch roll characteristics 244
I 1.5 Effects of speed 245
I 1.6 Stability diagrams and some design implications 245
I 1.7 Control and response 248
11.7. l Response to control action 249
I 1.7.2 Typical results 250