Helicopters. Calculation and Design. Volume I. Aerodynamics

506 Pages·2016·27.29 MB·English

by  Mil' M.L.

NASA
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N A S A T E C H N I C A L NASA TT F-494
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HELICOPTERS
CALCULATION AND DESIGN
Volume I. Aerodynamics
by M. L, Mil’ et al.
‘Mashinostroyeniye” Publishing Hoase
Moscow, 1966
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION WASHINGTON, D. C. SEPTEMBER 1967
0
NASA TT F-494

HELICOPTERS
CALCULATION AND DESIGN
Vol. I. Aerodynamics
By M. L. Mil', A. V. Nekrasov, A. S. Braverman,
L. N. Grodko, and M. A. Leykand
.
Translation of "Vertolety Raschet i proyektirovaniye. 1. Aerodinamika."
Izdatel'stvo Mashinostroyeniye, Moscow, 1966.
NATIONAL AERONAUT ICs AND SPACE ADMlN ISTRAT ION
. ~- ~ ~-.
For sale by the Clearinghouse for Federal Scientific and Technical Information
Springfield, Virginia 22151 - CFSTI price $3.00
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ANNOTATION
I
f
The work ffHelicopters (Calculation and Design)" is published i n three
volumes.
-
V01.1 Aerodynamics;
-
Vol.11 Vibrations and Dynamic Strength;
-
Vol.111 Design.
The first volume is devoted to ways of developing helicopters, the basic
principles of their design, and the position occupied by helicopters among other
means of aviation not requiring airfields. Various theories of rotors and cor­
responding methods of determining their aerodynamic characteristics are pre­
sented: the classical theory of a rotor with hinged blades i n the general case
of curvilinear flight of the helicopter; the momentum theory of an ideal rotor
and its application to the energy method of calculation; the classical theory
when using methods of numerical quadrature; the vortex theory and methods of
experimental determination of rotor performance i n flight tests and i n wind
tunnels. Various methods of aerodynamic calculation of a helicopter and the
theory of blade flutter are presented i n detail. This volume gives an account
of methods of calculating flutter in hovering and i n forward flight. Particular
attention is devoted to consideration of friction i n the axial hinges of the hub
and to the transfer of blade vibrations through the automatic pitch control
mechanism. Experimental investigations of flutter are described.
The book is intended for engineers of design offices, scientific workers,
graduate students, and teachers of higher institutes of learning. It might be
useful to engineers of helicopter manufacturers and to students for furthering
their knowledge of the aerodynamics and mechanical strength of helicopters.
Maqy sections of the book will be a useful tool also to flight and technical
staffs of helicopter flight units.
Numbers i n the margin indicate pagination i n the original foreign text.
ii
PREFACE L2
The present book generalizes the experience of the scientific work and
practical design activity of engineers of one of the Soviet teams working on the
development of helicopters.
Twenty years ago, when the team had just set out on their work, everything
i n this field seemed to have been already long discovered and invented.
Those to whom belongs credit for the original ideas and designs of rotary-
-
wing aircraft Leonard0 da Vinci, M.V.Lomonosov, N.Ye .Zhukovskiy (Joukowski),
-
B.N.Yurtyev, and others had long ago proposed almost all of the existing de­
signs of helicopters. Designers, scientists, and inventors in various countries
built dozens of helicopter models which successfully rose into the air. However,
not one of these rotocraft was suitable for practical use, large-scale produc­
tion, or regular service.
A very difficult problem that required considerable and tedious work re­
mained unsolved, namely, the problem of developing helicopters which would find
practical use in everyday life.
To solve this problem we had at our disposal an important scientific basis
i n the form of classical works, the studies of the Central Aero-Qdrodynamic
Institute (TsAGI), and of foreign scientists. However, testing of each new air­
craft confronted design engineers with new acute problems and forced them to
work out many theoretical problems to find the proper method of solving specific
design problems.
This volume discusses the basic problems of the theory, calculation, and
design of helicopters worked out by the team and representing the vital interests
of its design activity.
The fact that some of the authors had occasion to participate in applying
the classical rotor theory to the calculation and design of the first autogiros,
i n the original experimental work on models and on full-scale rotors in wind
tunnels, i n developing methods of aerodynamic calculation of helicopters, and
- -
then for more than Pjyears i n designing an entire family of helicopters of
the same configuration i n all weight classes, offers an opportunity to elucidate
the basic problems of the theory and calculation of helicopters that have b e e n h
checked out by practice.
As early as 1948 there was not a single helicopter i n service i n our
country. Now thousands of such machines created by various design teams assist
people i n many areas of their life and activity.
Engineers and designers working on the design or construction of heli­
copters, pilots and technicians, students of air academies who are studying or
are interested i n helicopters will find useful information i n this book.
iii
Engineering, especially aircraft engineering, is rapidly becoming obsolete.
However, it is hoped that the general methods of approach to the development of
a new type of aircraft, as presented i n this book, Will outlive todayts heli­
copter models.
M .Milt
1L

Chapter I of Vol.1, Sections 1and 2 of Chapter 11, and Section 2 of Chap­
ter I11 were written by M.L.Milt; Chapter IV and Section 5 of Chapter I1 were
written by A.V.Nekrasov; the remaining Sections of Chapters I1 and I11 and also
Subsections 19-28 of Section 2 of Chapter I1were written by A.S.Braverman.
In preparing the manuscript, the authors were assisted by engineers F.L.
Zarzhevskaya, R. L.Kreyer, and L.G.Rudnitskiy.
Reviewer R.A.Mikheyev made many valuable coments.
The authors express their sincere gratitude to these coworkers.
iv

I
TABLE OF CONTENTS
Page
..........................................................
Preface iii

........................................................
Notations xiii

CHAPTER I EVOLUTION HISTORY OF .H..E.L.I.C.O..P.T.E.R..S. A..N.D. .B..A.S.I.C. .
..........
DESIGN PRINCIPLES 1

. ...............
Section 1 E.volution of the Helicopter Industry .............. 1

1. Development of Helicopters in Size .......... 3

2 . Qualitative Development of Hel.i.c.o..p.t.e..r.s. .......... 8

3 . Special-Purpose Helicopters 13

4 Compound Helicopters w.it.h. .A..d.d.i.t.io.n..a.l .
..............
. Engines .Rotocraft 15

Section 2 The Helicopter Compared to Vertical Takeoff

and Landing .a.n.d. ..S.h.o.r.t. .T.a.k.e.o.f.f. .a.n.d. .L.a.n.d.i.n.g. .
...........
A.ir craft 16

1 Tactical and Technical Requirements for VTOL
..
.and STOL Military Transport Aircraft of the West 17

2 Means for Incre.a.s.i.n.g.. t.h..e. F..ly..in..g. R..a.n.g.e. .o.f.
..........
. Helicopters ..................... 21

3. Helicopter with Takeoff Run .................. 23

4. Takeoff Distance of Helicopter 25

5 Criterion for Estimating the E..c.o.n.o..m..y. .o..f. .
.......
. Various Transport Aircraft 27

6 Possibil.i.t.i.e.s. .o.f. .I.n.c.r.e.a.s.e. .i.n.. M..&.m.m.. ...F.l.y.i.n.g. ......
. Speed ......................... 31

Section 3 B.as ic Principles of Design ... 33

1.Selection of Engine Horsepower and Rotor .S.p.a.n. ...... 33

r 2 Analysis of Multirotor Configurations 39

...................................
CHAPTER I1 ROTOR AERODYNAMICS 45

.
Section 1 Development of Rotor Theory and Methods of
...
E.xp erimental Determination of its Char.a.c.t.e.r.i.s.t.ic.s. ..... 45

1. Classification of Rotor Theories ............. 54

. 2 Development of Experimental Methods 54

Section 2 Classical Theory of a Rotor with Hinged Blade
.......
Attachment; General Case; C..u..r.v.i.l.i.n.e..a.r. .M...o.t.io..n. ..... 56

Rotor Theory .i n Curvilinear Motion 57

1 Coordinate System and. .P..h.y.s.i.c.a.l .S.c.h.e.m.e. .
.............
.of the Phenomenon .............. 57

2.Inertia Forces Acting on the Blade .......... 59

3 .Aerodynamic Forces Acting on the Blade 65

4 Equation .o..f. .M..o.m..e.n.ts. .R..e.l.a.t.i.v..e. .t.o.. F..la..p.p.i.n.g..
.....
. Hinge ......... 66

5.Physical Meaning of th.e.. O..b.t.a.in.e.d. .R..e.s.u.l.t. ........... 70

6 Equation of Torque 72

V

............
I11.119.1.1. -"--I -I -1111 I 111 I I I I
Page
...............
7. Rotor Thrust and .A..n.g..le.. .o.f. .A..t.t.a.c.k.. .............. 74
8. Lateral Force ............................. 75
9. Longitudinal Force 77
10. Consideration of the Change in the Law of
Induced Velocity Distr.i.b..u.t.i.o..n. .d..u.r.i.n..g. ..........
Curvilinear Motion.. ............................... 78
Analysis of Obtained Results ................................. 83
11. Blade Flapping 83
12. Effect of Curvi.l.in.e.a.r. .M..o.t.i.o.n .a.t. .A..u.to..ro.t.a..ti.o.n. ......
of the Rotor 86
13. Behavior of the Resultant of Aerodynamic ........
Forces in Curvilinear Helicopter Motion 88
Effect of Rotor Parameters a.n..d. .H.u.b. ..D..e.s.i.g.n. .o..n. .F.l.a.p..p.i.n.g.. .....
and Damping of the Rotor 91
14. Rotor with a Profile H..a.v..in..g. .a.. .V..a.r.i.a..b.l.e. .......
Center of Pressure ...................... 91
15. Effect of Blade Centering ................ 92
16. Rotor with Flapping Compensator 94
Rotor Flapping in Curvilinev Motion of the Rotor Axis
............................o...o
at Variable Angular Velocity 96
17. Uniformly Acc.e.l.e.r.a..te..d. .R..o.t.a.t.i.o..n. .o.f. ..t.h.e.. .......
Rotor Axis ......... 96
18. Harmonic Oscillation of the Rotor Axis 100
Characteristics of Rotor A.e.r.o.d.y.n.a.m..i.c.s. .D..e.t.e.rm..i.n.e.d.. .b.y. .........
Hinged Blade Attachment ............. 102
19. Physical Meaning of Blade Flapping 103
X). Redistribution of Aerodynamic Forc.e..s .o.v..e.r ..........
the Rotor Disk due to Flapping
21. Approximate Derivation of. .F.o.r.m..u.l.as. .f.o..r .............
Flapping Coefficients 107
22. Effect of Nonuniformity of the Induced ...........
Velocity Field on the Flapping Motion 109
Method of Calculating the Aerodynamic Characteris.ti.c.s. .o.f. .........
a Rotor for Azimuthal Variation of Blade .P..it.c.h. ................... 114
23. Equivalent Rotor Theory 1115
24. Derivation of Formulas for a Rotor with
Flapping Hinges as for a Rotor without Hinges.
Conditions of E.q.u.i.v.a..l.e.n.c.e.. .o.f. .H..i.n.g.e.d.. .a.n.d.. ......
Rigid Rotors 123
25. General Expressions for Determining the Com­ .....
ponents of Blade Pitch Change w,(pl, and 132
26. Determination of Flapping Coefficie..n.ts. .o.f. ..........
Rotor with Flapping Compensator 138
27. Determination of the Components of Blade
Pitch Change (pl and after D.e..f.l.e.c..t.i.o..n. .o..f. ....
the Automatic Pitch Control 140
2. Sequence of Aerodynamic Calc.u.l.a.ti.o.n. .o.f. .a. ..... ... .
Rotor with Variable Pitch
Section 3. Momentum Theory of Rotor .............
....................o..o.~o
1. Theory of an Ideal Helicopter Rotor
v i
Page
2. Derivation of the Expression fo..r. t.h.e. .T..o.rq.u..e ........
Coefficient of a Real Rotor 156
3. Rotor Profile Losses 160
......................o..oo.
4. Certain Consideration..s. .i.n.. .S..e.l.e.c..t.i.n.g.. B..l.a.d..e. ....
Shape and Profile 164
5. Approxima.te.. .D..e.te..r.m..in..a.t.io..n. .o.f. .R..o.t.o.r. .P..r.o..f.i.le.. ...
Losses 169
6. Effect of A i r Compressibility of Rotor
Profile Losses ..............................................O..... 170
7. Induced Losses of a Real Rotor 178
8. Determination of Angle of Attack and
Pitch of Rotor 183
.......................o~..o...o~.
Section 4. Classical Rotor Theory. Method of Numerical
..........................o~~..~....o~~o
Integration 184
1. Formulas for C..a.l.c.u..l.a.t.i.n.g. .F..o.r.c.e.s. .a..n.d. .M..o.m..e.n.t.s ...
of a Rotor ........................... 185
2. Method of Calculation 193
3. Aerodynamic Charact.e.r.i.s.ti.c.s. .o.f. .P.r.o..fi.l.e.s. ............
for Rotor Blades 195
4. Distribution of A.e.r.o.d.y..n.a.m..i.c. .F.o..r.c.e.s. ..o.v.e.r. .......
the Rotor Disk ............ 200
5. Aerodynamic Characteristics of Rotor 206
6. Aerodynamic Characteri.s.t.ic.s. .o.f. .R..o.to..r .i.n.. ...........
Autorotation Regime
7. Limit of Permissible Helicopter Fli.g.h..t .............
Regimes (Flow Separation Limit) 212
8. Distribution of Profile Losses over Rotor Disk.
Dependence of Profile Losses on Aerod.y.n.a.m..ic. ........
Characteristics of Blad..e. .P..r.o.f..i.l.e.s. ............... 218
Section 5. Vortex Theory of Rotor ....................... 222
1. Problems in Vortex Theory 222
2. Theoretical Schemes for the Vortex "heor.y. .o..f .a. .....
Rotor with a Finite Numb.e.r ..o..f. .B..l.a.d..e.s. ........... 2%
3. Form of Free Vortices 226
4. Determination of the Induce.d.. .V..e..l.o.c..i.t.i.e.s. .b..y.....
the Biot-Savart Formula 227
5. Use of the Biot-Savart Formula i..n.. D...e.v..e.l.o.p..i.n.g...
the Vortex Theory of a Rotor 228
6. Axial Component of Induced Velocity from
...............................o.
Bound Vortices 230
7. Axial Component of Induced Veloci.ty. .f.r.o.m. ...........
Spiral (Longitudinal) Vortices 230
8. Axial Component of Induced Velo.c.i.ty. .f.r.o.m. ...........
Radial (Transverse) Vortices 232
9. Integrodifferen.t.i.a.l. .E..q.u..a.t.io..n. .o..f. .t.h.e.. .V..o.r.t.e.x. ...
Rotor Theory 232
10. Constancy of Circulation of Trailing Vortices
along Straight Lines Parallel to the h i s of
the Inclined Vortex.. .C.y..l.in..d.e.r. ..a.n.d. .P..o.s.s..i.b.l.e. .....
Simplifications 234
Page
11. Characteristics of Using the Lifting-Line
....
Scheme and Scheme of a Vortex Lifting Surface 236

12. Division of Vortices into Types Close to

and Remote from the .B..l.a.d.e..; ..U..s.e. .o.f. ..".S.t.e.a.d..y.-.
....
Flow Hypothesis" 237

13. Instantaneous and Mean Induced Velocities

and Generation of Var.ia.b..le. .A..er.o.d.y.n.a.m..ic. .
............
Loads on the Blade 238

14. Characteristics of. ..t.h.e. .E..x..tr..i.n.s.i.c.. I.n..d.u.c.e..d.
......
Velocity Field 238

15. Vortex Theory of a R..o.t.o.r. ..w..i.th.. .a.n.. .I.n..f.i.n..i.t.e. ....
Number of Blades ................................ 239

Vortex Theory of Wang Shi-Tsun. ................................... 240

16. Rotor Scheme ............. 240

17. Determination of Induced Velocities 241

'
18. Calculation Form.u.l.a.s. .f.o..r. .I.n.d..u.c.e.d.. .V..e.l.o.c.i.t.y..
....
Determination 241

19. Application and Evaluation of the Pos.s.i.b.i.l.i.ti.e.s. ....
of the Wang Shi-T.s.u.n.. .V..o.r.t.e.x. .T..h.e.o..ry.. ............. 243

Vortex Theory of V.E.Baskin ............................ 24-4

20. Scheme of Rotor Flow 245

21. Determination of Indu.c..e.d. .V..e..l.o.c.i.t.i.e..s. .f.r.o.m.. .
.....
the Dipole Col.umn 246

22. Fluid Flow .I.n..d.u.c.e.d.. .b.y. .a.. .D.i.s.k.. .C.o..v.e.r.e.d. .w..i.t.h.
....
Dipoles ............................. 247

23. Boundary Conditions 249

24. Transformation of Eq.(5.67) to the Rotor Axes;

Use of the Th..e.o.re.m.. .o..f. .A..d.d.i.t.i.o.n. .o..f ..C..y.l.i.n.d.r.i.c..a.l

Functions 249

25. Determination of the Total Veloc.i.ty. .P..o.t.e.n.t.i.a.l.
....
I
from the Entire Dipole Column ............ 250

26. Determination of Induced Velocities 252

Section 6. Experimental Determination of .A..e.r.o..d.y.n..a.m..i.k. .
.......
Characteristics of a Rotor 253

1. Flight Tests for Determining the A.e.ro.d.y.n.a.m..ic. .
.....
Characteristics of a Helicopter 254

2. Wind-Tunnel Tests for Determining the .........
Aerodynamic Characteristics of a Rotor 257

Methods of Co.n.v.e..rt.i.n.g. .t.h..e. .A.e.r.o.d..y.n.a.m..ic. .C..h..a.r.a.c.t.e.r.i.s.t.i.c.s. .
......
of a Rotor 261

3. Conversion of Aerodynamic Character.i.s.ti.c.s. .t.o..
......
a Different Rotor Solidity Ratio 261

4. Conversion of Aerodynamic Characteristics on

Variation in Minimum Profile D..ra.g. .C..o.e.f.f.ic.i.e.n.t. .
.....
of the Blade Sections exPo 265

5. Conversion of Aerodynamic Characteristics on

Variation in the Perip..h.e..r.a.l. .S..p.e.e.d.. .o.f. ..t.h.e..
.....
Rotor (Mo Numbers) 266

6. Conversion of Angle of Attack and Rotor Pitch
v i i i

I
Page
on Variation in Inclination of the Automatic
Pitch Control, Flapping Compen..s.a.t.o.r.,. ..a..n.d.. .M..a.s..s
Characteristic of the Blade ....... 267

7. Examples of Using the Conversion Formulas 268

Section 7. Performance and Pro.p.u.l.s.i.v.e.. .E.f.f.i.c.i.e..n.c.y.. .C..o.e.f.f.i.­
.....
cient of a Rotor 270

1. Performance and Efficiency of .R..o..t.o.r. ..............
Proposed by K.Khokhenemzer 271

2. Determination of Performa.n..c.e. ..a.n.d. ..P.r.o..p.u..ls..i.v.e. ...
Efficiency of a Rotor 273

3. Performance and Efficiency of a Ro.to.r.,.
.. ..........
Obtained from Fxperimental Data 277

4. Performance and Efficiency of a Ro.to.r.,. .............
Obtained from Calculated Graphs 279

5. Conversion of Performance and Effi.c.i.e.n.c.y. .o.n. ........
Variations in Rotor Parameters 282

6. General Commen.t.s. .o.n. .R..o.t.o.r. .E..f.f.i.c.i.e.n..c.y.. .a.n.d. ......
Performance 283

Section 8. Calculation of Rotor Characteristics in

.
Hovering and Vert.ic.a..l .A..s.ce.n..t .(.M..o.m.e.n.tu.m. .T.h.e.ory. .
. .... .
of Propellers) , , 284

1. Brief Review o.f. ..t.h.e.. M..o.m..e.n.tu.m.. .T..h.e.o.r.y. ..o.f. ........
Propellers 284

2. Results of Ca.l.c.u..la..t.in..g. .t.h..e. .C..h.a..r.a.c.t.e..r.is..t.ic..s. ...
of a Rotor 286

3. Approximate Method of De.t.e.r.m..i.n.i.n.g.. .t.h.e.. ..........
Dependence of mt on t 29 2

4. Conversion of Aerodynamic Characteristics. .o.n. .
......
Variation in the Rotor Solidity Ratio 295

5. Determination of Optimal Aerodynamic Parameters
of a Rotor with Consideratio.n. .o.f. .t.h.e.. D..e.p.e.n.d.e.n.ce. ....
of Characteristics on Mo 296

..................
CHAPTER I11 AERODYNAMIC DESIGN OF A HELICOPTER 301

Section 1. Basic Equations .f.o..r. .A..e.ro..d.y.n.a.m..i.c. .D.e.s.i.g.n.. .o.f. .........
a Helicopter .... 301

1. Aerodynamic Design Principle of a Hel.ic.o..p.te..r ....... 301

2. Equation of Motion of a Helicopter 301

3. Various Methods of Determining Aerodynamic
Rotor Characteristics ..a.n.d. .M..e..th..o.d.s. ..o.f. ...........
Aerodynamic Design 303

4. Calculati.o.n. .o..f ..C.o.m..p.o.s.it.e. .a.n.d. .M..u.l.ti.r.o.t.o.r. ...........
Craft 304

5. Induction Coefficients of Two-R..o..to..r ...H..e..l.i.c.o..p..t.e rs
and Helicopters with a Wing 308

Section 2. Aerodynamic Helicopter De.s.i.g.n.. b..y. .t.h..e.. ..'. ..........
Mil?-Yaroshenko Method ....... 315

1. Equations of Motion and Design Principles . 315

2. Determination of Aerodynatnic Rotor Characteristics 318

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