Helicopters - Calculation and Design - Aerodynamics

7/28/2019 Helicopters - Calculation and Design - Aerodynamics

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Y NASATTF-494v.1C . 1c .

T E C H N I C A L N A S A T T F - 4 9 4T R A N S L A T I O N c ,/

AND DESIGNI . Aerodynamics

M . L , Mil et al.ashinostroyeniye Publishing Hoasecow, 1966

AERONAUTICS AND SPACE AD MINISTR A TION WA SHINGTON, D. C . 0 SEPTEMBER 1 9 6 7


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NASA TT F-494

HELICOPTERSCALCULATION AND DESIGN

Vol. I . Aerodynamics

By M. L . Mil', A. V. Nekrasov, A. S. Braverman,L. N. Grodko, and M. A. L eykand

Translation of "Vertolety . Raschet i proyektirovaniye. 1.Aerodinamika."Izdatel'stvo Mashinostroyeniye, Moscow, 1966.

NATIONA L AERONAUT ICs AND SPACE ADMlN ISTRAT ION.~- ~ ~.

For sa le b y t he C lear i nghouse for Fed era l Sc ien t i f i c and Techn ica l I n fo rm at ionSpr ingf ie ld, V i rgin ia 22151 - CFSTI p r i c e $3.00


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ANNOTATION

The work ffHeli copters (Calculation and Design)" i s published i n threevolumes. V01.1 - Aerodynamics;Vol.11 - V ibrations and Dynamic Strength;Vol.111 - Design.The first volume i s devoted to ways of developing helicopters, the basicprinci pl es of thei r design, and the posi ti on occupied by hel icopters among othermeans of aviation not requiring airf i elds. Various theori es of rotors and corresponding methods of determining thei r aerodynamic character i sti cs are presented: the cl assi cal theory of a rotor wi th hinged blades i n the general caseof curvi l inear f l i ght of the hel icopter; the momentum theory of an i deal rotorand i ts appl ication to the energy method of calculation; the cl assi cal theorywhen using methods of numerical quadrature; the vortex theory and methods ofexperimental determination of rotor performance i n f l i ght tests and i n windtunnels. Various methods of aerodynamic calcul ation of a helicopter and thetheory of blade f l ut ter are presented i n detai l . T h i s volume gives an accountof methods of calculating f l ut ter i n hovering and i n forward fl i ght. Particularattention i s devoted to consideration of f r i ct i on i n the axial hinges of the huband to the transfer of blade vibrati ons through the automatic pi tch controlmechanism. Experimental investigations of f l utter are described.The book i s intended f or engineers of design of f ices, sci enti f i c workers,graduate students, and teachers of higher i nsti tutes of learning. It might be

useful to engineers of helicopter manufacturers and to students f or furtheringthei r knowledge of the aerodynamics and mechanical strength of hel icopters.Maqy secti ons of the book wi l l be a useful tool also to f l i ght and technicalstaff s of heli copter f l i ght units.

Numbers i n the margin indicate pagination i n the original foreign text.ii


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PREFACE L2The present book general izes the experience of the sci enti f i c work andpracti cal design acti vi ty of engineers of one of the Soviet teams working on thedevelopment of hel icopters.Twenty years ago, when the team had j ust set out on thei r work, everythingi n this f i el d seemed to have been already long discovered and invented.Those to whom belongs credi t f or the origi nal i deas and designs of rotary-wing ai rcraft - Leonard0 da Vinci , M.V.Lomonosov, N.Ye .Zhukovskiy (J oukowski),B.N.Yurtyev, and others - had long ago proposed al most al l of the exi sti ng designs of hel icopters. Designers, sci enti sts, and inventors i n various countriesbuilt dozens of helicopter models which successfully rose i nto the air. However,

not one of these rotocraft was suitable for practi cal use, large-scale production, or regular service.A very di f f i cul t problem that required considerable and tedious work remained unsolved, namely, the problem of developing hel icopters which would f indpracti cal use i n everyday l i f e.To solve this problem we had at our disposal an important sci enti f i c basisi n the form of cl assical works, the studies of the Central Aero-QdrodynamicI nsti tute (TsAGI), and of foreign sci entists. However, testi ng of each new ai r craf t confronted design engineers with new acute problems and forced them towork out many theoreti cal problems t o f i nd the proper method of sol vi ng specificdesign problems.Thi s volume discusses the basic problems of the theory, calculation, anddesign of helicopters worked out by the team and representing the vital i nterestsof i ts design activity.The fact that some of the authors had occasion to parti ci pate i n applyingthe cl assical rotor theory t o the calculation and design of the f irst autogiros,i n the ori gi nal experimental work on models and on ful l -scale rotors i n windtunnels, i n developing methods of aerodynamic calculation of helicopters, andthen - f or more than Pj years - i n designing an enti re family of hel icopters ofthe same configuration i n al l weight classes, offers an opportunity to elucidatethe basic problems of the theory and calculation of heli copters that have b een hchecked out by practice.A s early as 1948 there was not a single heli copter i n servi ce i n ourcountry. Now thousands of such machines created by various design teams assistpeople i n many areas of thei r l i f e and acti vi ty.Engineers and designers working on the design or construction of helicopters, pi l ots and technicians, students of ai r academies who are studying orar e i nterested i n hel icopters w l l find useful information i n this book.

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Engineering, especiall y ai rcraf t engineering, i s rapidl y becoming obsolete.However, i t i s hoped that the general methods of approach to the development ofa new type of aircraf t, as presented i n this book, W i l l outli ve todayts hel icopter models.M . M i l t

1L

Chapter I of Vol . 1, Sections 1and 2 of Chapter 11, and Section 2 of Chapter I 11 were written by M . L . M i l t ; Chapter I V and Secti on 5 of Chapter I1werewri tten by A.V.Nekrasov; the remaining Sections of Chapters I 1 and I11and alsoSubsections 19-28 of Section 2 of Chapter I 1 were wri tten by A.S.Braverman.I n preparing the manuscript, the authors were assi sted by engineers F.L.Zarzhevskaya, R. L.Kreyer, and L.G.Rudnitskiy.Reviewer R.A.Mikheyev made many valuable coments.The authors express thei r sincere grati tude to these coworkers.

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TABLE OF CONTENTS PagePreface .......................................................... iii Notations ........................................................ xi i i CHAPTER I EVOLUTION HISTORY OF HELICOPTERS AND BASICDESIGN PRINCIPLES ..................................... 1

Section 1.Evolution of the Helicopter I ndustry ............... 1 1.Development of Heli copters i n Size .............. 3 2.Qualitative Development of Helicopters .......... 8 3. Special-Purpose Helicopters ..................... 13 4. Compound Helicopters wi th Additional Engines .Rotocraft ............................. 15 Section 2. The Helicopter Compared to Verti cal Takeoff and Landing and Short Takeoff and Landing A ircraft ........................................... 16 1.Tacti cal and Technical Requirements for VTOL and STOL M i l i tary Transport A ircraft of the West .. 17 2.Means for I ncreasing the Flying Range of Helicopters ..................................... 21 3.Heli copter wi th Takeoff Run ..................... 23 4. Takeoff Distance of Helicopter .................. 255. Cri terion for Estimating the Economy of Various Transport A ircraft ...................... 27 6. Possibilities of I ncrease i n M&mm FlyingSpeed ........................................... 31 Section 3. Basic Principles of Design ......................... 33 1. Selection of Engine Horsepower and Rotor Span ... 33

r 2.Analysis of Multi rotor Configurations ........... 39 CHAPTER I1 ROTOR AERODYNAMICS ................................... 45

Section 1.Development of Rotor Theory and Methods of Experimental Determination of i ts Characteristics ... 451. Classi f i cation of Rotor Theories ................ 54 2.Development of Experimental Methods ............. 54 Section 2. Classical Theory of a Rotor with Hinged Blade Attachment; General Case; Curvilinear Motion ....... 56Rotor Theory i n Curvilinear Motion ............................ 57 1. Coordinate System and Physical Schemeof the Phenomenon ............................... 57 2. I nerti a Forces Acting on the Blade .............. 593.Aerodynamic Forces Acting on the Blade .......... 65 4.Equation of Moments Relative t o F lapping Hinge ........................................... 665.Physical Meaning of the Obtained Result ......... 70 6.Equation of Torque .............................. 72

V

I11.119.1.1............ -"--I I - 1 1 1 1 I 111 I I I I


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Page7. Rotor Thrust and Angle of Attack ............... 748. L ateral Force .................................. 759. L ongitudinal Force ............................. 7710. Consideration of the Change i n the Law ofInduced Velocity Distribution duringCurvilinear Motion ............................. 78Analysis of Obtained Results ................................. 8311. Blade Flapping ................................. 8312. Effect of Curvilinear Motion at Autorotationof the Rotor ................................... 8613. Behavior of the Resultant of AerodynamicForces i n Curvil inear Helicopter Motion ........ 88Effect of Rotor Parameters and Hub Design on Flappingand Damping of the Rotor ..................................... 91

14. Rotor with a Prof i le Having a VariableCenter of Pressure ............................. 9115. Effect of Blade Centering ...................... 9216. Rotor with Flapping Compensator ................ 94Rotor F lapping i n Curvi l inev Motion of the Rotor Axisat Variable Angular V elocity ............................o...o 9617. Uniformly Accelerated Rotation of theRotor Axis ..................................... 9618. Harmonic Osci l lation of the Rotor Axis ......... 100Characteristi cs of Rotor Aerodynamics Determined byHinged Blade Attachment ...................................... 10219. Physical Meaning of Blade Flapping ............. 103X). Redistribution of Aerodynamic Forces over

the Rotor Disk due to Flapping ..................21 Approximate Derivation of Formulas forFlapping Coefficients ........................... 10722. E ffect of Nonuniformity of the InducedVelocity Field on the Flapping Motion ........... 109Method of Calculating the Aerodynamic Characteristi cs ofa Rotor for Azimuthal V ariation of Blade Pitch ................ 11423. Equivalent Rotor Theory ......................... 111524 Derivation of Formulas for a Rotor withFlapping Hinges as for a Rotor without Hinges.Conditions of Equivalence of Hinged andRigid Rotors .................................... 12325. General Expressions for Determining the Components of Blade Pitch Changew, (pl, and ..... 13226. Determination of F lapping Coefficients ofRotor with Flapping Compensator ................. 13827. Determination of the Components of BladePitch Change (pl and af ter Deflection ofthe Automatic Pi tch Control ..................... 1402. Sequence of Aerodynamic Calculation................. ... .f aRotor with Variable Pi tchSection 3. Momentum Theory of Rotor . . . . . . . . . . . . . . . . . . . .o..o.~o1. Theory of an I deal Helicopter Rotor .............

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Page2. Derivation of the Expression for the TorqueCoefficient of a Real Rotor .....................3. Rotor Prof i le Losses ......................o..oo.4. Certain Considerations i n Selecting BladeShape and Prof i le ...............................5. Approximate Determination of Rotor Prof i l eL osses ..........................................6. Effect of A i r Compressibility of RotorProf i le Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .O..7. Induced Losses of a Re a l Rotor ..................8. Determination of Angle of A ttack andPitch of Rotor . . . . . . . . . . . . . . . . . . . . . . .o~..o...o~.Section 4. Classi cal Rotor Theory. Method of NumericalI ntegration .. .. .. .. ... .. .. .. ... .. .. ..o~~.~.. .o~~o1. Formulas for Calculating Forces and Moments

of a Rotor ......................................2. Method of Calculation ...........................3. Aerodynamic Characteri stics of Profi lesfor Rotor Blades ................................4. Distribution of Aerodynamic Forces overthe Rotor Disk ..................................5. Aerodynamic Characteristi cs of Rotor ............6. Aerodynamic Characteristi cs of Rotor i nAutorotation Regime .............................7. L i m i t of Permissible Helicopter FlightRegimes ( Fl ow Separation L i m i t ) .................8. Distribution of Prof i le Losses over Rotor Disk.Dependence of Prof i le Losses on AerodynamicCharacteri stics of Blade Prof i les ...............Section 5. Vortex Theory of Rotor .............................1. Problems i n Vortex Theory .......................2. Theoreti cal Schemes for the Vortex "heory of aRotor wi th a F ini te Number of Blades ............3. Form of Free V ortices ...........................4. Determination of the Induced V eloci ties bythe Biot-Savart Formula .........................5. Use of the Biot-Savart Formula i n Developingthe Vortex Theory of a Rotor ....................6. Axial Component of Induced Velocity fromBound V ortices ...............................o.7. Axial Component of Induced Velocity fromSpi ral (L ongitudinal) V ortices ..................8. Axial Component of Induced Velocity fromRadial (Transverse) V ortices ....................9. I ntegrodi f ferential Equation of the VortexRotor Theory ....................................10. Constancy of Circulation of T rai l ing V orticesalong Straight Lines Parallel to the h i s ofthe I ncl ined Vortex Cylinder and PossibleSimplifications .................................

156160164169170178183184185193195200206

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2182222222%226227228230230232232

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Page11 Characteri stics of Using the L ifting-L ine Scheme and Scheme of a Vortex L i f ti ng Surface .... 23612. Division of V ortices i nto Types Close to and Remote from the Blade; Use of "Steady-Flow Hypothesis" ................................ 237 13. Instantaneous and Mean Induced Velocities and Generation of Variable Aerodynamic Loads on the Blade .............................. 238 14. Characteri stics of the Extri nsic Induced Velocity Field .................................. 238 15. Vortex Theory of a Rotor with an I nf i ni teNumber of Blades ................................ 239 Vortex Theory of Wang Shi-Tsun ................................ 240 16. Rotor Scheme .................................... 240 17. Determination of Induced V eloci ties ' ............. 241 18. Calculation Formulas f or Induced Velocity Determination ................................... 241 19. Application and Evaluation of the Possi bi l i ti esof the Wang Shi-Tsun V ortex Theory .............. 243 Vortex Theory of V.E.Baskin ................................... 24-420. Scheme of Rotor Flow ............................ 245 21. Determination of Induced V eloci ties from the Dipole Col.umn ............................... 246 22. Fluid Fl ow Induced by a Disk Covered wi th Dipoles ......................................... 247 23. Boundary Conditions ............................. 24924. Transformation of Eq.(5.67) to the Rotor Axes;

Use of the Theorem of A ddition of Cyl indri cal Functions ...................................... 249 25. Determination of the Total Velocity Potential from the Enti re Dipole Column .................. 25026. Determination of Induced V elocities ............ 252 Section 6. Experimental Determination of Aerodynamik Characteristics of a Rotor ........................ 253 1. Fl ight Tests for Determining the Aerodynamic Characteristics of a Helicopter ................ 254 2. Wind-Tunnel Tests f or Determining theAerodynamic Characteristi cs of a Rotor ......... 257 Methods of Converting the Aerodynamic Characteristi cs of a Rotor .................................................... 261 3. Conversion of Aerodynamic Characteristi cs t o a Di fferent Rotor Sol idi ty Ratio ................ 261 4. Conversion of Aerodynamic Characteristi cs on V ariation i n Minimum Prof i l e Drag Coefficient of the Blade Sections exPo ...................... 265 5. Conversion of Aerodynamic Characteristi cs on V ariation i n the Peripheral Speed of the Rotor (M o Numbers) .............................. 2666. Conversion of Angle of Attack and Rotor Pi tch

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Pageon V ariation i n I ncl ination of the AutomaticPitch Control, Flapping Compensator, and MassCharacteristic of the Blade ..................... 267 7. Examples of Using the Conversion Formulas ....... 268 Section 7. Performance and Propulsive Efficiency Coeffi cient of a Rotor ................................... 270 1. Performance and Efficiency of RotorProposed by K.Khokhenemzer ...................... 271 2. Determination of Performance and PropulsiveEfficiency of a Rotor ........................... 273 3. Performance and Efficiency of a Rotor, ...... ..........btained from Fxperimental Data 277 4. Performance and Efficiency of a Rotor,Obtained from Calculated Graphs ................. 279 5. Conversion of Performance and Efficiency onV ariations i n Rotor Parameters .................. 282 6. General Comments on Rotor Effici ency andPerformance ..................................... 283Section 8. Calculation of Rotor C haracteri stics i n Hovering and V ertical.......................,......,.... .scent (Momentum Theory of Propellers) 2841. Brief Review of the Momentum Theory ofPropellers ...................................... 284 2. Results of Calculating the Characteri sticsof a Rotor ...................................... 2863. Approximate Method of Determining theDependence of mt on t ........................... 2924. Conversion of Aerodynamic Characteristi cs on V ariation i n the Rotor Sol idity Ratio ........... 295 5. Determination of Optimal Aerodynamic Parametersof a Rotor with Consideration of the Dependenceof Characteri stics on Mo ........................ 296

CHAPTER I 11 AERODYNAMIC DESIGN OF A HELICOPTER .................. 301 Section 1. Basic Equations f or Aerodynamic Design ofa Helicopter ....................................... 301 1. Aerodynamic Design Princi ple of a Helicopter .... 301 2. Equation of Motion of a Helicopter .............. 301 3. Various Methods of Determining Aerodynamic

Rotor Characteristi cs and Methods ofAerodynamic Design .............................. 3034. Calculation of Composite and MultirotorCraft ........................................... 304 5. I nduction Coefficients of Two-Rotor Heli coptersand Helicopters with a Wing ..................... 308'Section 2. Aerodynamic Helicopter Design by theMil?-Y aroshenko Method ............................ 315 1. Equations of Motion and Design Pri nciples ....... 315 2. Determination of Aerodynatnic Rotor Characteristi cs . 318


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Page3. Calculation of Flight Data ...................... 3a4. L imits of A ppli cabil i ty of the Method ........... 322 Section 3. General Method of Aerodynamic Design for Rotary Wing A ircraft ............................... 3231. Construction of Auxil iary Graphs for Helicopter Performance Data ................................ 324 2. Determination of Helicopter Performance Data .... 331 3. Graphs for Determining Optimum HelicopterAerodynamic Parameters .......................... 342 Section 4. Aerodynamic Design of a Helicopter Based on Concepts of Rotor Performance and Effici ency ....... 3461. Helicopter Performance .......................... 34.72. Performance of M ulti rotor and Composite Helicopters ..................................... 348 3. Determination of Helicopter F l ight Data ......... 357 4. Calculation of a Helicopter with a Tractor Propeller ....................................... 363 5. Comparison of Helicopter and A irplane ........... 364 6. Power of Front and T a i l Rotors i n a Helicopter of For e-and-Aft Configuration ................... 3667. Retraction of Landing Gear on Helicopters ....... 368 Section 5. Aerodynamic Calculation of a Helicopter by the Power Method ................................... 369 1. Determination of Required Power i n Horizontal Helicopter Flight ............................... 370 2. Determination of Helicopter Performance Data .... 375 3. Relation between N P r , N in d , and Npar duringHorizontal Flight of a Single-Rotor Helicopter ,... 376 . CHAPTER I V ROTOR FLUTTER ....................................~.... 379

Section 1. Basic Assumptions and Characteristi cs of anApproach t o F lutter Calculation .................... 380 1. Bending and Torsional V ibrations of the Blade. Possible Cases of Stability L oss ................ 380 2. Effect of Blade Attachment to Hub and the Possibi l i ty of Theoretical I nvestigation of F lutter of an I solated Blade .................... 381 3. Di fferent Types of F lutter Di ffering with Respect t o Blade V ibration. Flapping and Bending F lutter ................................. 381 4. Characteri stics of the Torsional V ibration Modes of a Blade and Possible Correlated Assumptions ..................................... 3825. Assumptions on Blade Osci l l ations i n the Plane of Rotation ..................................... 383 6. Determination of Aerodynamic Forces Acting ona V ibrating Prof i l e ............................. 384 Section 2. Flapping F l utter of an I solated B la de with Axial Flow past the Rotor .......................... 386

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Page1.Blade Model ................................... 386 2.Derivation of Di f ferential Equations

of Flutter .................................... 387 3.Particular Solution of the Differential Equation ...................................... 391 4.Di f ferential Equation of Disturbed Motion ..... 391 5.Notation of D i f ferential Equations i n Matrix Form ................................... 392 6. Solution of Di f ferential Equations of Blade V ibrations .............................. 392 7.Determination of the C ri ti cal F l utter Rpm ..... 395 8.Blade Divergence .............................. 3969. Parameters Characterizi ng Blade Balance (Effective Blade Balance) ..................... 39610.Dependence of Cri ti cal F lutter Rpm on Blade Balancing and Values of the Flapping Compensator Coefficient ........................... 398 11.Blade Arrangement .............................. 399 12.Effect of Control Rigidity ..................... 400 13. Conditions f or Absence of F lutter .............. 400 14.Mechanism of Generation of Forces Exci tingFlutter ........................................ 401 Section 3. Consideration of Fri cti on Forces during F lutter .... 4061. Character of the Effect of F ri ction Forces during F l utter ................................. 4062. L inearization of F ri ction Forces ............... 407 3.Determination of F lutter Speed with Consideration of F ri cti on ...................... 408 4.Effect of Forced Motion i n the Feathering Hinge .......................................... 409 Section 4.Rotor Fl utter with Consideration of Coupling of Blade Vibrations through the Automatic Pitch Control ..................................... 414 1.Forms of Rotor F l utter Observed i n Helicopter Experiments ......................... 414 2.A nalytical Expression for Cycl ic Modes ofRotor V ibration ................................ w43. Cycli c Vibration Modes i n Specific Casesand Control Loads .............................. 4.164.Di f ferential Equations of Rotor F l utter with Consideration of Coupling of Blade V ibrations through the Automatic Pi tch Control ............ 418 5. Transformation of Eqs.(k.l8) i n Parti cul arCases where Cycl ic Modes are the Solution ofthe Di f ferential Equations of Rotor F l utter ....6.Rotor F l utter i n the Presence of Di fferentR igidi ty of L ongitudinal and L ateral Controls ... 422 Section 5. Flapping F l utter of a Rotor i n Forward Fl ight ..... 424 1. Preliminary Statements ......................... 4242.Di f ferential Equations of B la de Oscillations i n Forward Fl ight .............................. 424 xi


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3. Solution of Di f ferential Equations ............4. Determination of Cri ti cal F lutter Rpmwithout Consideration of Harmonic Componentsof Blade Motion ...............................5. Effect of Flying Speed on Cri ti calF lutter Rpm ...................................Section 6. Calculation of F lutter with Consideration ofBending and Torsion of the Blade .................1. Bending and Torsion of Blade during F lutter ...2. Determination of the Torque from BendingForces on the Blade ...........................3. Di f ferential Equations of B inary Vibration ....4. Solution of Di fferential Equations ............5. Calculation of F lutter with Considerationof Three Degrees of Freedom ...................6. Calculation of F lutter with Three Degreesof Freedom Disregarding Blade Torsion .........7. Calculation Results ...........................$. Bending F l utter ...............................9. Approximate Method of Determining the Modeof Bending V ibrations i n F lutter ..............Section 7. General Method of Calculation of F lutter andBending Stresses i n the Rotor Blade duringFlight ...........................................1. Calculation Method and i ts Possibilities ......2. Basic Assumptions and Suggestions .............

3. Differential Equations ........................4. Boundary Conditions of the Problem ............5. Determination of Equivalent Rigidi ty of theControl System ................................6. Determination of Aerodynamic Forces ...........7. Method of Solving the Di f ferential Equations ...8. Transformation of Part ial DifferentialEquations into Ordinary Di f ferentialEquations .....................................9. Determination of the Magnitude of the Momentof Fri cti on i n the Feathering Hinge of the Hub ..10. Sequence of Performing the Calculation ........Section 8 . Experimental I nvestigations of F lutter ...........1. Ground Tests for F lutter ......................2. F l utter Tests i n Fl ight .......................3. Comparison of Calculation and Experimentunder Conditions of Axial Flow past the Rotor ..4. Comparison of Calculation and Experiment i nFlight ........................................5 . Check for F lutter .............................6. Experimental Determination of Control SystemRigidity ......................................7. Experiments on Dynamically Similar Models .....References ......................................................

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NOTATIONS LzAe-rsyngnic Characteri stics

cy = angle of attack of rotor;a, = angle of attack of blade section;cyo = angle of zero l i f t of blade prof i l e;Acy = downwash angle of flow;

a, = dcv = c; = tangent of angle of slope of the l i f t curveda wi th respect to angle of attack of the prof i l e;CP = tan -x = inflow angle i n blade section;

U Y = ci rculation i n blade section;M = Mach number of blade section;M, = average Mach number with respect to azimuth,i n ti p section of blade (M O = 2%);

M,, = f l i ght Mach number ( M f l =4)CT, t =2 = thrust and coefficient of thrust of rotor0 / T ) *(t = Q POTPw R ) ~ sCH, h =2 = longitudinal force and coeff ici ent of longi0 Htudinal force of rotor (h = Q ~ ~ I T R ~ ( U I R ) ~

S , s =-, = l ateral force and coefficient of l ateral force0 Sof rotor (s = -2 ponR2(wR) );-mM ,, m, =2= torque and torque coeff i ci ent of rotor0 Mt N = power of motor (of rotor i n Chapt.11);

CY , t, =2= l i f t and l i f t coefficient of rotor0 Y \( t Y = 5 ~ T T R ~ ( W R )

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X, t, =-X =propulsive force and coefficient of pro- /6(5pulsi ve force of rotor \ t, = $ ~O -TTR~(W R)~1 X -);\

cy, cX p=coefficients of l i f t and prof i l e drag ofblade section (ai rf oi l ) referred to dynamicpressure pv2;B = coeff icient of t i p losses;V eloci ties

wR = angular veloci ty;V, (7 = -)VWR / = path velocity of hel icopter fl i ght;\

V,, V, V, = horizontal , vertical , and l ateral componentsof f l i ght velocity;v, (7=2)OR = induced veloci ty;

I- =, : U =u\ rel ati ve veloci ty of flow past a blade/ wR element;- u x - u \U, U, (u. =-, U =A)= horizontal and verti cal components of relawR wR ti ve veloci ty of flow past a blade element;h = coefficient of f law;p, = characteristic (coefficient) of rotor perf ormance.

Geometric Characteri sti csD = diameter of rotor;R = radius of rotor;F = disk area;r = radius of rotor blade section i=2) -R /

I b - b = blade chord ,b =- 9 ==); bz b = number of bl ades;z , = number of rotors;

o = zbb0*7 = load factor of rotor;TTRth.h, t V e h = distance from axis of rotati on of rotor tothe horizontal (f lapping) and verti cal(drag) hinges, respectively; c = thickness of prof i l e section, c =2;.~ b$ = f lapping angle of blade;


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a,, b, = coefficients of flapping;cp, cpo = blade angle (pi tch); angle between chord of bladeprof i l e and plane of rotation;N , 11 = angles of defl ection of automatic pi tch controlmecha

nism; N with index = mutual i nfl uence coeff icient ofl i f ti ng elements;lo = blade angle at F = 0.7 f or @ = N = 7 = 0;I1, l a = components of change of blade angle relati ve to theplane of rotation, due t o defl ection of the automaticpi tch control mechanism;v = change of blade angle due t o el asti c deformation ofblade.


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HELICOPTERS; CALCULATION AND DESIGN. V0L.I: AEEODYNAMICS L2M. L.Mlt, Editor

ABSTRACT. A review of the hi stor i cal development of Russianand Western hel icopters, i n si ze and l i f t capacity, f or ci v i land mil i tary purposes i s followed by detailed discussions onrotor aerodynamics for various angles of attack, blade setting,flapping angle, center-of-pressure position, blade vibration(natural , forced, harmonic, etc ), and other rotor parametersi n thei r infl uence on rotor rpm and craf t stabi l i ty. Formulasare given for the forces and moments of rotor damping i n hoveri ng and forward f l i ght; f or the redi stri buti on of aerodynamicforces over the rotor disk due to flapping; f or cycli c pitchchange of rotors wi th variable and constant pi tch. The theoryof an i deal hel icopter i s developed on the basis of optimumblade prof i l e, prevention of rotor prof i l e losses, and properbalancing. F l utter i n hovering and forward f l i ght i s calculated, wi th emphasis on f r i ct i on i n the axial hub hinges andtransfer of xibrations through the automatic pi tch control .CHAPTER I

EVOLUTIONAL HISTORY OF HELICOPTERS AND BASICDESIGN PFUNCIPUS(Selection of Parameters and Configuration)Section 1. Evolution of the Heli cmter I ndustry

Designing i s always directed toward the future. However, f or a betterpi cture of the potenti al i ti es of the future development of hel icopters i t i suseful t o attempt to understand the basic trends of thei r evolution from pastexperience. Naturally, we are not interested here i n the prehistory of hel i copter construction, which we w i l l only bri ef l y mention, but i n i ts history fromthe t i m e when the hel icopter as a new type of ai rcraf t became useful f or practi cal appl ication.The writings of Leonard0 da V inci going back to l.483 contained the f irstmention of an apparatus wi th a verti cal rotor, a helicopter. The first stage ofevolution ranges from the model of a hel icopter developed by M.V.Lomonosov i n17% through a l ong series of designs, models, and even ful l -scale apparatuswhich were not destined to rise i nto the air, to the construction of the worldtsfirst hel icopter which, i n 1907, was able to become airborne. T h i s four-rotorhelicopter was constructed by the French designers Breguet and Riche. I n 1923,a passenger became airborne f or the first time i n the USA i n a helicopter designed by de Bothezat. The f irst world al ti tude record of a helicopter of 18 mwas set i n 1930 on the I tal i an coaxial hel icopter by dtdscanio.

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I n Russia, a single-rotor helicopter was built i n 1911, on the basis ofthe sci enti f i c research by N.Ye.Zhukovskiy devoted t o hel icopter rotors, by agroup of his students headed by B.N.Y ur'yev. The configurations of this machinerepresent the basic scheme of the single-rotor heli copters used widely atpresent. B.N.Yurtyev was able to resume this work only i n 192.5. I n 1932, agroup of engineers headed by A.M.Cheremukhin constructed the hel icopter TsAGI1-EA (Fig.l.1) which reached an al ti tude of 600 m and stayed i n the air f orl e min, which - f or that time - was an outstanding achievement. It suff i ces tosay that the of f i ci al al ti tude record establi shed three years l ater on Breguettsnew coaxial hel icopter was only 180 m.

A t this time there was a pause i n the development of helicopters. A newbranch of rotary-wing ai rcraf t came to the forefront, known as autogiros. Theidea of the autogiro, as an ai rcraft with a rotary wing ( f reely rotating airf oi l ) never l osi ng speed, occurred to the young Spanish engineer J uan de l aCierva i n the 1920s. A t that time, conventional ai rcraf t whose development hadbeen vigorous during the years of World War I and which, by then, carriedarmament and thus had greater wing loading were troubled by a new problem of /8spin, i.e., stalling. It appeared simpler to develop a safe and suff i ci entlyperfected autogiro than to build a helicopter. The rotor, freely rotating dueto the relati ve flow, el iminated the need for complex reduction gearing andtransmissions. The hinged attachment of the rotor blades to the hub used onautogiros gave far greater strength to the blades and higher stability to theautogiro. Final&, engine failure ceased to be a threat, as had been the casei n t he first hel icopters; the autogiro, wi th autorotating blades, had no di f f i cul ty i n landing at low speed.

.-_ -. . . . ..... .. . . . - .. .

Fi g. l . l Helicopter TsAGI 1-EX.Cierva, working i n England, created several autogiro designs, the bestknown of which was the C-30 autogiro which was produced as a pi lo t series.Autogiros were also bui l t i n the U SA by the Pi tcai rn and K ell ett Companies andi n the Soviet Union at TsAGI by the designers I.P.Bratukhin, V.A.Kuznetsov,N.I.Kamov, ,N.K .Skrzhinskiy, ML.Ml ,, and others.The f lyi ng speed of Soviet autogiros i n 1937 reached 260 km/hr. The A-7autogiros designed by N.I.Kamov were used at the front during the first year ofWorld War 11.

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The great l i f t capacity of the rotati ng rotor gave the autogiro a shortground run. Even though, a mechanical drive from the engine, f or spinning therotor before takeoff, was used i n this design to f urther shorten the takeoffrun. I n the design of the Bri ti sh C-4.0 autogiro the rotor was given a spin-upbefore f l i ght t o an rpm such that, at the instant of disengagement from theengine - which, i n forward f l i ght, rotated the propell er - the machine, due tothe marked increase i n pi tch, took of f without a run, ri sing vertical l y i nto theair.

Only one step remained f or the development of a true helicopter. And thisstep, as i s always the case i n technology, was made almost simultaneously i nvarious countries. T h i s was the beginning of the present development stage ofhelicopters. It was started by flights'of the FW61 helicopter designed byProfessor Focke i n Germany (1937), the VS-300 hel icopter designed by Sikorskyi n the USA (1939), and the Wmegalf helicopter designed by 1.P.Bratukhin i n theUSSR (1940). Al l three of these helicopters used a hinged rotor capable ofautorotation, which had already become standard f or autogiros.Worl d War I1somewhat delayed the development of hel icopters. They werest i l l unsuitable f or practi cal use, and the ways and means f or experimentalstudies were limited. After the end of the war (1946 and 1947), large numbersof designers and inventors invaded this new and promising area of development ofavi ation engineering. Wi thin a short time, l i teral l y dozens of new hel icopter Lpdesigns were created. T h i s was a contest of the most di verse schemes and conf igurations, generally of the single- or two-seater type and used mainly f orexperimental purposes. M i l i tary agencies were the only users of this expensiveand complex equipment. The f irst hel icopters i n various countries were used asl i ai son and reconnaissance mil i tary ai rcraf t.I n the development of hel icopters, j ust as i n many other areas of tech

nology, one can cl earl y disti ngui sh two trends of development: the quantitativetrend concerned wi th si ze of the machine and the almost simultaneous qual i tati vetrend concerned with improvement of the craf t wi thin a certai n size or weightclass. The former trend represents development with respect t o l i f t capacityand the second wi th respect to improvement of the tacti cal or economic featuresof helicopters.1.Development of He-licapters i n Si ze

A study of foreign hel icopters indicates that the use of helicopters f orlanding Marines from ships was the determining f actor i n the f urther developmentof mi l i tary hel icopters as troop carri ers. The American landing of troops i nS-55 helicopters at Inchon during' the Korean War (1951) was a typical exampleof this trend.The si ze range of the assault helicopters was predicatedon bulk and weightof ground transportation means used by the troops and to be dropped by air. Iti s a known fact that conventional weapons - mainly artillery - transported byprime movers are close i n weight to the weight of the prime movers themselves.Thus, the l i f t capacity of the first transport hel icopters i n armies of othercountries was 1200 - 1600 kg ( the weight of a l ight military truck used as

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prime mover together with the respecti ve weapons). Subsequently, the requiredl i f t capacity of helicopters was increased to 6 - 8 tons which, i n accordancewith military technique, was based on automobile carri ers with a l i f t capacityof 3 - 4 tons. Sti l l later, for example i n proj ects developed by Sikorskg Aircraft, the l i f t capacity of hel icopters rose to 20 - 25 tons and fi nal l y to36 - 40 tons. Such weights correspond to the weight of l i ght and medium tanksor of self-propelled landing craf t. Whether.this development trend i n si ze increase wi l l ever come to an end depends on the constantly changing mi l i taryplanning. A rtil lery systems are being largel y replaced by missiles, f or whichreason the foreign press of ten mentions the need to transport missi les or missi lesystems, the prime f actor i n determining the si ze of modern helicopters.I n the attempt to single out the main trend of future helicopter development, af ter successively outl ining the creation of new types of machines i n thef ew designer firms that have been successful i n developing experimental modelsi nto practi cal prototypes and i n starti ng pi l ot seri es, i t wi l l be found that

increase i n the l i f t capaci ty ofhe maj or development was toward an helicopters.

U S A-Char acteri sticsM i - 1 --.. .

Y ear of production 1948 1962 Pr ojectL i f t capacity, i n 0.3 5-6 20ton- forceI ncrease over previous 4 3modelF lyi ng weight, 2.3 17.0 -

ton- force

TABLE 11. -.. - -

HelicoptersUSSR

~

M i-4 M i-6 S-51 S-58_.. 1 . .1952 1957 1946 19561.2-1.6 8-12 0.3 1.24 7 3

7.2 39-41 2 6

Table 1.1gives data characteri zi ng the development of the l i f t capacityof single-rotor helicopters of the same confi guration by two ai rcraf t constructi on departments - helicopters M i - 1 (Fi g. l .2), Mi-& (Fi gol . 3), Mi-6 (Fig.l.&),Mi-10 (Hg.l .5), S-51 (Fig.l.6), S- 58 (Fig.l.7), and S-64 (figal*8).A s we see from Table 1.1, the l i f t capacity increases severalf old witheach prototype.However, i t i s easy to show that an increase i n si ze and weight of heli copters i s impossible without a qual i tative improvement of the engines used /10(reduction i n weight per unit horsepower and increase i n econony, i .e., decreasei n f uel consumption).Actually, an increase i n fl yi ng weight i s possible ei ther by increasing therotor span or the i nstal l ed power, or both factors

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G=T= (kqND)" ..The weight of the engine i s proportional t o the first power of i ts output,w h i l e the weight of the machine itsew increases only i n proportion t o the 2/3power.

Fig.l.2 M i - 1 Helicopter.

Thus, a helicopter with a l arger power-to-weight rati o wi l l have a relati vely greater design weight, owing to the power plant.I n l i ke manner the weight of the blade and, accordingly, the weight of thel i f ti ng system change i n proportion t o the thi rd power of the diameter, whereasthe weight of the heli copter again changes only i n proportion to the 2/3 power.Here also, the weight of the l i f ti ng system of a l arger hel icopter proves to berelatively greater. Thus, on increasing the size of a helicopter i ts loadratio, i.e., the rati o of useful load to f lyi ng weight, should be decreased, i fthere i s no weight improvement i n engines, blade design, reduction gears, ortransmissions. Actually, i n the 1930s papers were published that demonstratedthe uselessness of developing helicopters with a power greater than 500 hp,since an increase i n power would not lead to an increase i n useful load. /13According to technical speci f ications of that time, the weight of rotors, reducti on gears, and of the enti re machine as a whole increased with increasing powermore rapidly than the l i f t .However, i n developing a new mi l i tary - and especially a new general-purpose - helicopter, the designer wi l l not tol erate a lowering of the achieved

level of load rati o.Thus, a quantitative ^ development with respect t o si ze i s impossible without a quali tative development; i n fact, it always i s concurrent with the qualitati ve advance of technology.The development of helicopters l arger than the first two- or three-placemodels took place i n a comparatively short time, since the unit weight of pistonengines always decreased wi th an increase i n power. But i n 1953, af ter develapment of the l3-ton Sikorsky S-56 helicopter (Fig.l.10) wi th two 2300-h~ pi ston

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F'ig.l.3 Mi-4 Helicopter.

Fig.l.4 Mi-6 Helicopter.

F'ig.l.5 M-10 Helicopter.

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fig.l.6 S-5l Helicopter.

Fig.l.7 S-58 Helicopter.

Fi g. l . 8 S-64. Helicopter.

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engines, the si ze series of hel icopters i n the West was discontinued and onlyi n the USSR was i t possible, i n 195'7, to develop the Mi-6 helicopter with af l yi ng weight of 40 tons by using turboprop engines.2. Qualitative DeveloDmenLof Helicopters

I n the middle of the 1950s , the rel i abi l i ty of hel icopters became appreciably greater so that also thei r use potenti al i ti es for the national economy increased. T h i s moved problems of economy i nto the foreground.The operating cost per hour of a helicopter plays a decisive role i nwhether to use them f or geological surveys, i n agri culture, or f or transportingpassengers. Amortization, i.e., the pri ce of a hel icopter divided by i tsservice l i fe, consti tutes a large porti on of the cost. The service l i f e of thehelicopter i s determined by the durabi l i ty of i ts components. The problem of

increasing the fatigue strength of blades, shafts, transmissions, rotor hubs,and other units of the helicopter became a prime problem, which hel icopter designers are st i l l studying atpresent. Today, a l i f e of 1000hours i s no longer a rari ty forseries-produced hel icopters andthere are no grounds to doubt i tsfurther increase. When usinghel icopters i n transportation,the concepts of cost per ton-mileof the transported load and thecost per passenger-mile becomedecisive. T h i s i s the hourly operati ng cost divided by hourlyproductivity, i .e., by the productof the weight of the payload andthe crui sing speed.

Since the construction weightlargely determines the pri ce of ahelicopter, the direct relationbetween economy and load rati o ofthe hel icopter i s obvious. Flyingspeed al so acqvilres a new role.1945 1950 1955 1960 1965 " h i s automaticallS. leads toFig.l.9 Size Evolution of Helicopters. the idea of developing heli copterswi th higher economic indexes. Thedevelopment of turboprop engineswi th an appreciably smaller uni t weight than piston engines made i t possible toproduce helicopters with a larger load rati o w h i l e retaini ng, i n each weightcategory, the rotor dimensions.

GeneralQ, replacement of pi ston engines by turboprop engines not odyresults i n a decrease i n rel ati ve weight of the power plant but also i n someincrease i n power; produces a dual effect and al so leads to an appreciable8


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increase i n cruising speeds.I n the diagram (F ig.l .9) we traced these quanti tative and qual i tati ve development trends of the most common hel icopters produced by the three designengineering departments. Given are the single-rotor hel icopters designed bySikorsky A ircraft (USA), the single-rotor Soviet hel icopters, and the fore- &and-aft hel icopters of the Piasecki A i rcraft Corporation, which subsequentlybecame the Vertol LEV. of Boeing.

-@ > . * .Fig.l.10 S56 Helicopter.

Thus, the si ze development trend on the basi s of piston engines ( sol i dl i nes i n F'ig.l.9) was terminated as early as 1953. Then, as turboprop enginesof the necessary si ze were developed over a period of f i ve to ten years, second-generation hel i copters appeared (points referri ng to these i n the diagrams areconnected with the origi nal models by the broken l i ne of qual i tati ve development).Thus, the helicopters S-55, S-58, and S-56 wi th piston engines servedas prototypes, ectively, f or the turboprop machines S-61 (Fi g. l . l l ) , s-62 /16and S-65 (Fig.l:;3. The same holds f or the fore-and-aft hel icopters of theV ertol Div. of Boeing V-lO7 and vBl& 1tChinook" (F ig.l .13).The Soviet turboprop helicopters Mi-2 (f igel .& ) and M i - 8 (Fig.l.15) al soconstitute a further development of the well-known hel icopters M i - 1 and Mi-&.The unusually long service l i f e of hel icopters i s striking i n comparisonwith airplanes. Almost al l pi ston heli copters shown i n the diagram (wi th.theexception of the experimental helicopters XL16 and S-56) were i n production andservice before the appearance of thei r second turboprop generation, and the M-1helicopter has managed t o stay i n production f or 15 years and i s approachingthe record longevity of the E-2 airplane.We can assume that the weight categori es of helicopters indicated i n

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l l l l l l l l I l l 1 I I I I

Fig.1.U S- 61 Helicopter.

Fig.1.12 ,%65 Helicopter.

. . , ....I Fi g. l . 13 Chinook Helicopter.

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Table 1.2 have become establ ished by now.What w i l l be the future development of helicopters? /18The process of developing a new generation of helicopters, on the basis ofimproved turboprop engines, i s now being completed i n the l i ghtest category ofhelicopters. The l ag i n this weight category can be attributed to di f f i culti es

Fig. l e& Mi-2 Helicopter.

Fig.l.15 Mi-8 Helicopter.

i n developing a l i ghter and simultaneously more economic low-power turbopropengine i n comparison wi th pi ston engines. I n the end, such an engine was developed i n the USA by the A l l ison Company - this was the T-63 weighing only174 l bs at a power of 315 hp and a consumption of 280 gm/hp-hr. The award i nthe competition for a l ight three- or four-place mil i tary heli copter i n the USAwas made to the Hughes A ircraft Compaw, which created the UH-6A helicopter(Fi g. l . 16) weighing only 2680 l bs at an empty weight of about 1340 lbs; this i s11


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Fig.l.16 Hughes Helicopter UH-6A.

8ip.lOl7 Fairchild Hiller Helicopter FH-ll00.an appreciable techni cal achievement which required a number of new design sol utions, i n parti cular the use of a rotor with an elasti c spring retention of theblades instead of the conventional hinge attachment. T h i s hel icopter has a highload rati o (50%) combined with a high cruising speed (213 kmhr), f or a l ightmachine. The Fairchi ld K U er F H- l lOO i s also i n this cl ass (Fig.l.17). It i sobvi ous that these hel icopters considerably outstri p the l i ght l i aison reconnaissance ai rcraf t of World War 11 both with respect to speed and l i f t capacityand, furthermore, have the great advantage of verti cal takeoff and l andi ng.Thus, the deci sion made i n a number of countries t o replace l i ght reconnaissanceaircraft by hel icopters i s not surprising.12


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TABLE 1.2~ - _._-

Char acteri stics L ight L ight Medium1.iai son 1 Multi- 1 T>:i:rtTransport IpurposeL i f t capacity or 2-4 per- 1 ton o r I 3 ton o r 6-8 ton 20 ton 40 tonnumber of places 10-12 per- '25 30 persons [ - sonsFI i ght weight 1.5-2 ton 3.5-4 ton 10-12 ton 20-40 to]

Of course, a new generation of l i ght heli copters Wl l also be developed i nother countries of the world. I n France, this i s being done on the basis of the3.50-hp Turbomecca-Oredon-I11 engine. I n West Germany, the %&ow Conipaqy i sworking on such a machine.Thus, i n speaking of the qual i tati ve development trend of helicopters, i ti s obvious from the foregoing that each new generation of engines gives rise toa new generation of heli copters i n al l weight categories, simultaneously havinggreater econow and better f l i ght performance data. T h i s l i ne of developmentprobably has no upper limit.As regards the si ze evolution of hel icopters, no machine with a l i f t capacity of 20 tons (see Table 1.2) has been developed as yet.According to a request f or proposals, announced i n the USA, firms such asWan, Fairchild Hiller, and Sikorsky A ircraft are working on the development ofa helicopter with a l i f t capacity of 20 tons. I n West Germany, the BzlkowCompany i s working on a helicopter with a 40-ton l i f t capacity. Below, we wi l lreview the possi ble ways of developing heavy and superheavy hel icopters.

3. Speci=al-Pumose Helicopters /19It i s necessary to mention al so the development of various models ofspecial-purpose heli copters wi thi n the indicated weight categories. I n thisconnection, l et us make a brief remark on the new concept of using hel icopters

i n the Army which has recently developed i n the West - especiall y i n the USA nameb, the creation of so-called airborne mobile troops.I n this instance, hel icopters are used i n place of motorized transport f oral l types of troop movement. The B e n 11Iroquois11 hel icopter UH-ID (Fig.l.l8) i sparti cul arl y adapted for transporting troops by platoons (11-12men).Zght reconnaissance three- or four-place armed hel icopters (Hughes helicopters OH-6A); f l ying i n front of battle formations, are also a necessity.Finally, regular troop-carrier hel icopters of various classes, supplying the

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II IIIIIIII I

means of ground f i r e support such as arti l l ery, rockets, and tanks, take overthe task of troop movements.Al so used i n real i zation of this concept are helicopters f or ai r support ofinfantry, constituting a unique type of assault hel icopters. Ordinary hel icopters armed wi th radio-control led missiles and weapons are presentl y used f orthis purpose.

Fig.l.18 Bel l llIroquois11 Helicopter UH-LD.Such an airborne mobile divi sion i s suppli ed from the air by airplanes andhelicopters of the Ai r Force Materiel Command.It i s not di f f i cul t to detect behind this concept past mil i tary experience,wherein any new type of transportation that became accessibl e engendered a newtype of troops. Beginning with cavalry, we recal l the bicycle and motorcycleunits of World W a r I, and the motorized infantry, motorized divi sions, and airborne troops of World War 11.It i s clear by now that this concept i s f inding fol lowers i n many westerncountriesThus, the 12-place SA-330 (Fig.l.19) hel icopter ordered by the French Armycorresponds to the 11-place I roquois heli copter (USA). A similar machine i s

being designed also i n West Germany.The need to retai n the cl ass of 10-to 12-phce l i ght transport heli coptersi s confirmed also by the practi cal experience with the 12-place Mi-4 helicoptersi n the national economy. It i s obvious that the development of more economic( f o r ai rl i nes) 30-place Mi-8 helicopters does not i nterfere wi th the advantageof using the 10-place heli copters i n the national economy f or geology and otherpurposes.


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-.c

4. Compound Helicopters wi th Additional Wines_ - Rotocraft /20Of considerable i nterest was the appearance of compound hel icopters which

use propel lers for forward f l ight, as autogiros did earlier. Such are theRotodyne Ferry designed by Hislop and especiall y the rotocraft of the Sovietdesigner N.I.Kamov.In 1964, world records f or machines of this type were set on the rotocraftKa-22: speed 360 kmhr, l i f t capacity 16 tons.focused attenti on of the helicopter world, after 20 years, on the side-by-sideN.I.Kamov*s rotocraft againconf iguration which had been successful ly developed by Focke i n Germany and by1.P.Bratukhin i n the USSR. T h i s machine recal led the great advantages of theside-by-side configuration i n f lyi ng range and l i f t capacity with a runningtakeoff which must be accounted f or i n a successful design.

fig.l-19 SA-330 Heli copter.A further development of compound helicopters wi th propeller i s representedby the hel icopter prototype wi th additi onal turboj et engines now being proposedi n the West f or mil i tary purposes.An interesting rototype of an assault helicopter i s the Lockheed compositehelicopter (fig.l.207 . T h i s two-place experimental machine, i n addition to themain 55C-hp turboshaft engine dri vi ng a four-blade ro tor with el astic blade retention, uses a turbofan engine mounted on a small wing and permitting rev-upto 426 km/hr when brief ly cut i n during f l i ght.The successful development of dual-flow turbofan engines, especi alb witha large bypass rati o, may lead t o the development of models which, at cruisingspeed, would have a speci f i c consumption of the order of C, = 0.5 kg/kg hr.Since c,= 75rlv R

it i s not di f f i cul t t o calculate that, i n this case, the consumption per horsepower of an equivalent propel ler engine at a propeller efficiency of 0.75 and af l yi ng speed of 150 m/sec i s only about 200 gm/(hp hr) .15


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I f we also take i nto account the small weight of such a motor i n comparisonwith the weight of a turboprop engine, i t becomes clear that the use of turbofanengines of this type can be economics- advantageous even at l ower cruising &speeds and may lead to the development of compound hel icopters with an auxiliarythrust engine and Wing for passenger transport between urban centers at cruisingspeeds of the order of 350 - 4.50 kmhr. A t the same time, such helicopters mayfi nd mi li tary use as fi re-support craft for troops.

Fi g. 1. 20 Lockheed Helicopter S 5 l A .In analyzing the ways and means of hel icopter development, one cannot sidestep the question of verti cal takeoff ai rcraf t. W i l l the development trend anduse of hel icopters come to an abrupt end wi th the appearance of such craf t, ashad been the case wi th autogiros when helicopters came into being?

Section 2. The Helicopter C gr i peV - er tL cal Takeoffand LandinR and Short Takeoff and LandingA ircraftWhen tal king of the prospects of hel icopter engineering development, onemust study the problem of the possi bi l i ty of coexistence of helicopter and

vertical takeoff aircraft. Do helicopters have a future? O r are the potentialities of the helicopter exhausted? Can the helicopter successfully competewith vertical takeoff aircraf t? W i l l thei r development trend terminate, as wasthe case wi th autogiros which ceased to exist with the appearance, i n 1940, ofthe first successful helicopt,ers? A comparative investi gation of hel icoptersand VTOL or STOL craft as means i n transport avi ation not requiring an ai rf i el dwi l l enable us to answer these fundamental problems.It i s known that recently the matter of verti cal takeoff ai rcraft ( i nEnglish, VTOL) and short-run ai rcraf t ( i n Engli sh, Sn>L) has become urgent-.(For footnote, see follow5ng page)

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Actually, the present f l yi ng speed of fighters, reaching 2500 - 3000 km/hr,requires such high-power engines that very l i t t l e remains to add f or thei rverti cal takeoff. Therefore, judging by the literature i n other countries wecan assume that f i ghters and f i ghter bombers W i l l be developed mainly asVTOL ai rcraf t not requiring the use of an ai rf i eld. The di rection of develop- /22ment of transport ai rcraf t, whose power pl ant i s l imited by considerations ofeconomics or quite simply by f uel consumption, tends toward STOL ai rcraf t.

Some propose that the future development of hel icopters w i l l offer a bettersol ution to transport problems f or a range up to 600 km than do VTOL aircraftor special STOL transport ai rcraft.I n examining the possible development trend of avi ation, we cannot limitthe study to an analysi s based on the present state of the art i n science andtechnology.By using such methods, many sci enti sts have repeatedly arrived at erroneousconclusions concerning the l l l i m i t s 1 1 i n the development of various ai rcraf t orhelicopters, since they did not provide for the development of parameters' characteri zing the weight and economic perfection of engines or perfection of designand materials used. I t i s necessary to extrapol ate thei r development somehow tothe future.Leaving room i n the future for such an investigation, we w i l l estimate thesituation at hand. We Wl l compare hel icopters with VTOL and STOL ai rcraf t,using data of the best helicopters that have been bui lt as w e l l as of aircraftbeing i n the design or construction stage.

1. Tackical and Technical Reqr&rements f or V E L and STOLM iE tary Tra-nsport A&raft of the WestThe tacti cal and technical specifications f or VTOL transport ai rcraf t,worked out i n the USA, cal l for a f lying range of 550 - 700 km, a l i f t capacity'of 3600 kg or 32 troops, and a crui sing speed of 450 - 550 km/hr at a grossweight of not more than 16,000 kg. A t the same time a very long delivery range,of the order of 4000 km, i s required, which i s probably intended f or the possibi l i ty of ferrying ai rcraf t from the USA over the ocean.I n studying STOL transport ai rcraf t, one comes across ordinary cl assi calpropel ler transport planes such as, f or example, the British-Canadian De Havilland llCaribourl (Eg.l .21).By STOL transport ai rcraf t we mean ai rcraf t that use engine power f or /23reducing the takeoff and landing runs. T h i s i s useful and necessary.A study of STOL ai rcraf t must include one of the first aircraft of thistype, the French ai rcraf t Breguet-941 (Fig.1.22). On this air craft the entirewing area i s i n the zone of propel l er sl ipstream. A l l propellers are inter-

VTOL - verti cal takeoff and landing; STOL - short takeoff and landing.17


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connected by a transmission which provides safe takeoff or landing i f one ortwo of i ts four engines fai l . The propel ler sl ipstream, deflected downward bya double-slotted f l ap, produces addi ti onal lift, which reduces takeoff speedand shortens the run. However, these qualities are achieved at the expense ofan increase i n empty weight and shorten the range of this STOL aircraft. Helicopters can operate successful ly at such a range.

Fig.l.21 British-Canadian Transport PlaneDe Havilland IICaribouIl.

Fig.1.22 French STOL A ircraft Breguet-941.Despite the great type di versi ty of VTOL and STOL aircraft, i t i s not diff i cul t to arrange them l ogicall y i n a general classification of aircraft. Theyshould be placed between hel icopters and airplanes.It i s comonly known that the l arger the area over which ai r flows (i tmakes no di fference whether i t flows through a rotor or the nozzle of a jetengine) or, more precisely, the smaller the veloci ty imparted to the ai r ?assfor producing l i f t i n ai rcraf t or hel icopter, the smaller w i l l be the power required for this per unit weight of machine.Thus, the ordinary hel icopter and the ai rcraf t taking off verti cal l y by thethrust of j et engines are at opposite poles of this cl assif i cation (Fig.1.23).

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, -

I n the pursui t of greater range and probably higher speed, the hel icopterwas provided wi th a wing; as the wing area and hence the l i f t increased further(since the thrust of the rotor at maxi"f lying speed decreases so much that i ti s insufficient for forward f l i ght) , propellers appeared on the wing. Thus arosethe Bri ti sh IIRotodyne" (Fig.1.a) and the Soviet rotocraf t designed by N.I.Kamov(Fig.1.25) - ai rcraft which i n place of one l i f t ing and moving system have two,one being the rotor and wing f or sustenti on and the other being a system oftractor propel lers, incli ned forward to the thrust vector of the rotor, to provide forward propulsion. During verti cal takeoff, the wing and the propellersare useless, and i n horizontal f l i ght the rotor i s sqerf luous. The attempt toavoid such superf luous units whose weight unavoidably reduces the useful loadled to a confi guration wi th a wing and pivoted rotor (Bel l XV-3, Fig.1.26) i n /24.which the rotor i n horizontal f l i ght becomes a propeller, and to a configurationwith a pivoted wing whose propel lers during takeoff - turning together with thewing - act as rotors as, f or example, the XC-l42 ai rcraf t produced by ChanceVought - @-an- Hil ler (Fig.1.2'7).J e t a i r c ra f t t akTgg o f f

t run

Fig.l.23 Classif ication Scheme for VTOL and STOL A ircraft.

F'ig.1.24. Rotodyne Rotocraft.


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!

Passing now to ai rcraf t wi th an engine more powerful than that of the abovetypes of aircraft, the STOL j et aircraft i s provided with means f or downward def l ection of the blast from the jet engines or from various types of auxiliaryturbofan engines.The configuration of the Breguet-941 ai rcraf t (see Fig.1.22) can be regarded as a vari ant of an ordinary airpl ane which, to increase the l i f t coefficient, uti l i zes the ai rf low over the wing created by the propel lers, or else asa variant of an ai rcraf t with a pivoted wing where the thrust of the propellersi s not l i teral l y turned but i s deflected downward by means of the mechanizedwing.

c -7 - u . . /25

Fig.1.25 Rotocraft Designed by N.I.Kamov.

Fig. 1.26 B e l l XV-3 Convertiplane.The diameter of the propel lers of the VTOL ai rcraf t shown i n Fig.1.23(from left t o ri ght) gradually decreases down to the VTOL jet ai rcraft which

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has no propel ler at all. With a reduction i n propel ler diameter, the engine /26power i ncreases per u n i t takeoff weight from 0.25 - 0.3 +/kg f or hel icopterst o 3 - 4 +/kg f or j et ai rcraf t (the values of the equivalent horsepower aretaken here for the aircraf t) .The crui sing speed of these ai rcraft continuously increases along wi th theincrease i n instal l ed horsepower. However, this i s not a decisive factor f orthe problem of a transport air craf t with a range of 800 - 1000 km

T h i s defi nes the scope of VTOL and STOL transport aircraft to be comparedand the f l yi ng range over which they are effective.

Fig.1.27 Chance Vought - &an - Hiller XGG2 VTOLA ircraft with T i l t Wing.

To which of these types of ai rcraf t w i l l belong the f uture i n solving theformulated problem?Before comparing the helicopter wi th i ts competitors with respect to economy, l et us examine the problem of the f l ying range of the helicopter. I n Viewof i ts comparatively short range, can the helicopter enter this competition atal l?Let us first examine and compare the best of the VTOL and STOL transportai rcraf t that have been or are being constructed: the ti l t- wbg WOL air

craft of the type XC-&2; the STOL ai rcraf t of the type Breguet-941; the regular'transport ai rcraf t of the type IICaribouI* HG4; the rotocraft with turbopropengines of the IlRotodyneIl type; and helicopters.2. Means f or Increasing the Flying Range of Helicmters

The hel i copter,has always been regarded as a short-range ai rcraf t; a figureof 400 - 500 km i s usually given as the m a x i " f or i ts normal range. I n ordert o treat the helicopter as a competitive ai rcraft i n this new area of use, the


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range should be almost doubled w h i l e retaining i ts l i f t capacity. How does oneincrease the fl yi ng range?L et us turn to the well-known formula of f lyi ng range: /27

where G = weight of the ai rcraf t (average during f lyi ng the) ;GT = weight of the fuel ;cy/cx = aerodynamic eff iciency of the ai rcraf t (taken to be constant);C, = speci f ic f uel consumption of the engine;5 = a coefficient taking i nto account power losses i n the transmissiondue to cooling, etc.;7 = rotor efficiency.Equation (2.1) shows that the range i s greater, the larger the proportionof fuel i n the all -up weight of the ai rcraf t and the higher i ts aerodynamic eff ici ency, engine econoqy, and efficiency of engine and auxi l iary units.

T h i s formula holds f or aryheavier-than-air craft, including airplanes and hel icopters. Specif icall y,i t follows from this equation that thef lyi ng range of various fl yingmachines, other conditions beingeq-cal, does not depend on thei r crui sing speed.Can a. hel icopter be given a rangeFig.1.28 Product of Aerodynamic suf f ici ent for competing wi th STOLEfficiency and Rotor Efficiency aircraf t?as a Function of Flying Speed. A s indicated i n Fig.1.28, theproduct of aerodynamic eff ici encycy/cx and rotor eff iciency 17 f or a hel icopter with a f ixed landing gear i s lowerthan for a transport airplane by almost a factor of 2. Furthermore, the f uelconsumption of the hel icopter i s somewhat greater than that of the airplanesince the engine characteri stics are inferior at low al ti tudes and f lyi ng speeds.

Thus, a heli copter can be given a range equal t o that of airplanes only by increasing the f uel supply, i.e., the quantity G T/ G . However, i n so doing howdoes one maintain the useful load? T h i s can be done only by increasing thetakeoff weight, but the helicopter W i l l then no longer be able to take offvertically.What happens i f we place these aircraf t under equal conditions, i.e., allowthe helicopter the same takeoff run asanSTOL ai rcraf t, namely 150 - 200 m oreven less? A t a relatively large value of cy, wi l l the helicopter then be ablet o l i f t - at low speed - a much greater weight than an airplane, accomodate


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more fuel , and thus compensate f or i ts lack i n aerodynamic efficiency?

3. -Helicopter wi th Takeoff R unA s shown i n Fig.1.29 which gives the curves of the requi red and availablehorsepower of a llCariboull-type transport airplane and of a modern helicopter, anairplane can be kept i n the air at a speed not below 115 kmhr. A helicopter /28can hover i n the air without moving. I fthe helicopter i s overloaded by 15% aboveNhp the normal takeoff weight Go, i t can nolonger hover and, l i ke the airplane, W i l lonly be able to f l y without dropping i f i t

3006 has some speed - i n this case, a speed ofnot l ess than 50 km/hr. A t a greaterspeed than this, i t wi l l gain alti tude andat a lower speed, lose al ti tude. The dif-ZOO6 ference here i n favor of the hel icopter,i n comparison wi th the conventional airplane, l ies only i n the fact that thehelicopter retains f u l l controllabilityroo0 \ 1 I I at a speed below i ts minimal and that'Required horsepower there i s no danger of separation of flowf o r ai r p 1an e and loss of control labil i ty, both of whichare possible i n the airplane.0 So far as the takeoff distance i sconcerned, assuming that the helicopterFig. 1.29 Required and Available takes off at a speed of V,,, this dis-Power as a Function of Flying tance at some average accelerati on j ,

Speed. W i l l bej f 2 b- 2L L --:-l nr un 2 j (2.2)

Thus, the takeoff run i s shorter, the lower the minimum f lying speed (closeto takeoff speed) and the greater the acceleration.The m i n i " speed i s

where S , = wing area;p = air density.What values of cY maxare available to airpl anes and helicopters?For this, l et Us calcul ate the value of cy that an airpl ane of the l lCariboulltype should have at the same weight as the hel icopter i n order to f l y withoutdescending at speeds less than"m. Figure 1.30 shows the values of cy,

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calculated from the formula

of a hel icopter referred to the wing area of an equivalent airpl ane, which characterizes the l i f t capaci ty of a hel icopter i n comparison with the airplane.The curve cy of the hel icupter i n Fig.l.30 extends to i nf i ni ty. This i s naturalsince the helicopter has a rotor which i n essence i s a rotating wing with apower pl ant suspended from i t and i s capable of producing l i f t at zero forwardspeed of the enti re machine. Here we see that at speeds of 50 - 60 kmhr theavailable values of cy of the hel icopter are several times greater than for anairpl ane of the IlCaribouIl type at a speed of 115 kmhr, which has a highlymechanized wing.Thus, at equal power a greater weight can be l i f ted by the hel i copter /29at low speeds than by an airplane.

However, a greater f l yi ng weightdoes not always mean a greater usefulload.A t equal relative f uel weight(about l o%, the ordi naq ai rplane ofthe IlCaribouIl type has a range of1000 km, i.e., twice that of a helicopter taking off without a run.The Breguet-941 STOL aircraft (ata f uel weight 12 - 13% Qf the fl yingweight) has twice the Tange of thehelicopter or of the XGl4 .2 VTOL aircraft.I f, i n helicopters, the f uel weighti s increased t o 20 ,- 25% of the grossweight, then the range of the helicoptercan be doubled and raised to 1000 km.T h i s value i s already close to thenormal ranges of special ly designedSTOL aircraft.The load rati o of hel icoptersFig.l.30 Dependence of (cyhal l) e q taking off with a run and at increasedon Flying Speed. f uel supply becomes higher than the l oadrati o of comparable ai rcraf t and reaches4!+- 50%. T h i s makes i t possi bl e'to obtain equal productivity at almost the same takeoff weight of airpl ane and heli copter. For example, a transport helicopter of average l i f t capacity, just asa l*Ca,riboull-type airplane, can transport a load of 3.2 tons over a range of1000 Ism. It i s true that the hel icopter, i n so doing, uses 2.5 times more fuel .However, it must be remembered that the airplane needs twice the area f or taking

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off and, what i s quite important, the helicopter after having consumed hal f i tsfuel i s able t o land verti cal l y, whereas the or di nar y airpl ane cannot do so.It must be emphasized that comparable airplanes and helicopters have

practi cal l y the same power supply (0.23 - 0.25 hp/kg). One must al so bear i nmind that pi ston engines, operating on gasol ine, have a lower f uel consumptionat l ow al ti tudes than turboprops, so that the average turboprop helicopter operates under less advantageous conditions than the IICaribouIl ai rcraf t with pi stonengines.Thus, the suggestion to use a takeoff run f or the hel icopter w i l l permitdoubling i ts range at the same useful load.-. Takeoff Distance of Hel i cmterW e have already expressed the takeoff distance i n terms of takeoff speedand acceleration. The takeoff speed, proporti onal t o the mi"m speed at whicha hel icopter can be supported i n the ai r at an overload of 15%as opposed to @the weight wi th which i t can take offwithout a run, i s not more than60 - 70 km/hr. Lst us now define thepossible degree of l i near acceleration, since the takeoff run i s inversely proportional to acceleration.Let us f i nd the possible initial acceleration.

A s agreed, l et the helicopterdevelop a thrust amounting to only0.85 G (takeoff weight) at the takeof f power. Then, allowing f or someFig.l .31 Forces Acting on Helicopter angle of i ncl i nation of the rotorduring Takeoff Run. axis to the verti cal o (here thediff erence i n the compression of thestruts and pneumatic tires of thenose and tai l wheels i s accounted f or) and for the forward deviation of the resul tant owing to def lecti on of the automatic pi tch control mechanism through anangle Dn, according t o F'ig.l.31, we fi nd the in it ial acceleration:

Here, the second term on the right-hand side takes i nto account f r i ct i onof the wheels against the ground, wi th a f ri cti on coeff ici ent f . Adopting theusual notations of of = 6.5O, D% = l oo, T = 0.85, and f = 0.12, we obtainj, = 2.2 m/sec2. PAssuming a relative stat i c propel ler thrust of - = 1.6 kg/hp f or the

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--o=g - N f\=2.5 m/sec2( N O fi.e., a value of the same order as f or the hel icopter.

O f course. the acceleration at the moment of takeoff i s determined by theexcess power, which i s somewhat higher f or the airplane. However, i ts pr-opellerthrust decreases wi th an increase i n speed whereas the rotor thrust increases;

Fig.1.32 Forces Acting on a Helicopterduring Takeoff on Nose Wheel.(5) 1t a ke of f

where x,, i s the di stance from the centermatic pi tch control mechanism at a majdmal

i n fact, the angle of pi tch of thehelicopter, during the takeoffrun, may even increase since,during takeoff, the tai l wheelsare able t o l i f t off the groundat a thrust substantially 1es.sthan the takeoff weight so thatthe takeoff run i s completed.onthe nose wheel.

It i s obvious from Fig.1.32that the thrust-to-weight rati o atwhich the tai l wheels can l i f t offthe ground (disregarding fri cti on)wi l l be

of gravi ty t o the axis of the auto-forward deflection.of this mechanism2 [here i t i s assumed that the quantity I( xmx ) can be neglected f or unity].

. .~ ^ . . . ,. ..... . . _ 4

Fig.1.33 Running Takeoff of Mi-6 Helicopter.26


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With the usual relations, this corresponds to a thrust-to-weight rati o of0.8 - 0.85. Figure 1.33 shows a helicopter during the takeoff run, at a grossweight of G,,, = 1.15 G .An exact calculation of the takeoff run can be carr ied out by the same &method proposed by the author 30 years ago for calculating the takeoff run of anautogiro (Ref .4).Running takeof fs performed i n practice have confirmed that, at a 15%overload of a helicopter as opposed t o the maximal weight w5th which i t can take offwithout a run, the takeoff run amounts to no more than 60 - 100 m i n st i l l air.

5. Crit-e-ri0.nf or Es&.ima$t,ng the Eco~og~yf VariousTransport A ircraftI n any comparison of two transport ai rcraf t, attenti on i s primarily centeredon the l i f t capacity. Sti l l , the speed of transport i s al so important. Actuall y, i f a load can be transported more qui ckl y, then more l oads can be transported i n unit ' t ime over a given distance at a smaller l i f t capacity.T h i s resul ts i n the well-known cr i teri on of hourly productivi ty GlOadVav t o

km/hr (Vav i s the average ground speed).However, at what cost i s the load transported?I f both ai rcraf t have i denti cal eff iciency and range as w e l l as takeoff &and landing properti es sati sfactory for f ul f i l l i ng the mission, which should begiven preference?To answer this question we must know which of the ai rcraf t i s more economical. I n mil i tary use, the advantages of any aircraf t f or solving transportproblems, which sometimes arise at an appreciable di stance from the supplybases, are determined primari ly by cost data. Ekpenditures f or construction ofthe machine itself, incurred i n the past, are no longer of signi ficance and haveno effect on f ul f i l l i ng the immediate task. Under such condi tions, the economyof an ai rcraft i s determined mainly by the amount of f uel consumed. Here, thetransport of f uel constitutes a bottleneck that i s decisive for the abi l i ty tosol ve the stated problems. The cri teri on of economy under such conditions i sconveniently obtained by referring the hourly productivi ty t o the weight of thef uel consumed during that time GThr:

G VL - . . Le.s 'T hr

Since the f uel conswrption per ki lometer i s

it follows that


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The quantity Le e a has the dimension of length, so that we can cal l i t theequivalent speci f i c range of the ai rcraf t. It represents the distance overwhich a given ai rcraf t can f l y i n excess of the design range i f the entire transported load i s replaced by fuel . S t i l l another meaning can be given to thisquantity. It can be regarded as the distance over which an ai rcr af t can carryone ton of cargo after having consumed one ton of fuel . It i s cl ear that thequantity Lees depends on the distance of transportation j ust as productivitydepends on i t. The farther the machine flie's, the more f uel i t needs and thesmaller the cargo it can take at a given f l yi ng weight ( maxi mal ) .

On the other hand, L e a s i s the work expressed i n ton-miles which a givenai rcraf t can perform, having consumed one ton of fuel .The inverse quantity of L ea8 ,


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I.Y

I

0

l i f ti ng engines impairs the aerodynamic eff iciency of a VTOL aircraft. It wasassumed that, at ranges greater than 1000 km VTOL ai rcr af t of the indicated twotypes with a sustainer turbojet W l l f l y at the design al ti tude at m u m erodynamic efficiency, whereas at a reduction i n f w n g range from 1000 to 50 kmthe operational cei l i ng decreases accordingly and any drop i n aerodynamic efficiency l eads to some increase i n f uel consumption. The hovering time thovastaken as 6 min (3 min i n takeoff and 3 min i n l anding).

Table 1.3 gives our calculated data for ai rcraf t of di f ferent f l yi ng rangesand di f ferent forms of takeoff.TABLE 1.3

Type' o f Tak eof f ICharacteri stici With Shor tV erti cal Run

L ,


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where - GTG , =-G i s the rati o of f uel weight to takeoff weight of the ai rcraf t.For VTOL ai rcraft, aircraft with a l arge f uel consumption f or hovering, thereduction i n fl yi ng weight due to the expenditure of f uel f or hovering and i nhorizontal f l i ght was taken into account. Figure 1.35 show the curve of thecorrection coefficients K L as a function of the values of E , .

C k g / t o n - k n~ I 1

Fi g. l . 34 Dependence of CL on Flying Range L.For ai rcraf t with takeoff run, the values of C L at di f ferent f l yi ng rangesare given i n Fig.1.36. The diagram al so shows how the economy of transportmeans can be increased, at a givenrange, by using a takeoff run. The

% - - . longer the takeoff, the larger the take1.J off weight of the ai rcraf t and hence theI greater the weight of transported cargo.Such are the results of investigat-L 2 ing f uel consumption for transporti ngone ton-mile with various types oftransportation means.

1.1 A s regards the cost of operatingairpl anes and helicopters, which naturall y i s determined not only by the cost of100 0.1 112 a3 a4 E , f uel but also by the servi ce l i f e andin i t ia l cost of the machine, we must bearFi g.1.35 Dependence-of Coefficient i n mind that the greater power/weight &KL on G,. rati o of the VTOL ai rcraf t compared tothat of helicopters as w e l l as thepresence of transmissions i n some typesmore or l es s balances this cost. A s f or safety i n the case of engine f ai l ure

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- - -

during takeoff or landing, al l advantages are here on the si de of helicopterssince the propel lers on an ai rcraft with a pivoted Wing are not capable of auto-rotation, and engine failure (depletion of fuel) during landing of an ai rcraf tof the type Breguet-941 may l ead to f low separation and an uncontrollable descent because the Wing i s no longer washed by the propellers. Furthermore,there W i l l always be the di f f i cul ty of providing control l abi l i ty at low speedsi n these machines.

/ ton-km-9t VTOL turbolet'l '' a i r c r a f t ,

'I "' w i t h f a n s 1Range2000-3000k n

a i r c r a f t

L t g h t t r a n s p o r t urbopropCross-Country propel 1 erT r u c k a i r c r a f t . r unspo r t1 I I Truck on highwi r r c r a f t -IOG zoo 300 400 1, mFig.1.36 Dependence of C , on Takeoff Run f orVarious Flying Ranges.

A further reduction i n weight and f uel consumption of turboprop enginesunder development at present W i l l lead t o an increase i n load factor of helicopters. The substantial increase i n servi ce l i f e of rotor blades, reductiongears, and transmissions obtained i n modern prototypes W i l l equalize the amortization cost of airpl anes and hel icopters, af ter which the hel icopter w l l becomea f ul l and equal member of the ai r transportati on system i n i ts most massivearea.6. Possibi l i ti es of Increase i n M a x i " Flying Sp eed

I f the f l yi ng speed of VTOL and STOL aircraft i s considered to be an i rnportant f l yi ng and tacti cal requirement, then the possi bi l i ti es of rotocraft arefar from exhausted With respect t o further increase i n speed.I f we equate the power required f or hori zontal f l i ght and the net power ofthe engine, we can obtain the rel ati on between maximum speed and power/weightrati o of the ai rcraft:

(2.10)


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where N = engine power;G = gross weight of the ai rcraft.It fol lows from eq.(2.10) that the maximum speed i s directl y proportionalto the power/weight rati o N/G of the ai rcraftFigure 1.37 gives the curves of the required power/weight rati o as a functi on of f l yi ng speed for various ai rcraft. The curves for heavy rotocraft showthat, t o i ncrease the f l yi ng speed above 300 - 320 km/hr, i t i s necessary tosqplement the helicopter rotor with a second high-l i ft device - a wing; toreach speeds above 370 km/hr also propellers are needed, which means changingover to a rotocraft. Thus, by formulating the problem of achieving the highestspeed possible at any price, i t becomes possibl e to decide what VTOL aircraftconfi guration to use for di f ferent d u m l ying speeds. However, i t must beremembered that the transi ti on from heli copter to rotocraft involves a l oss i n

l i f t capacity, an increase i n the cost of construction, etc.power/weight rati o of 0.45 hp/kg, which can presentl y be reali zed on rotocraft,Even wi th athe transi ti on from hel icopter t o rotocraft wi l l not produce a gain i n speed bymore than 30 - 40 lan/hr.

05 0.40.3 0.20.1

Fig.1.37 Powerheight Ratio of A ircraft as aFunction of Flying Speed.Final ly, the graph of the required power/weight rati o cl earl y shows thegreat di fference in the power/weight rati o of VTOL ai rcraf t and of rotocraft.A t equalpower/weight ratio, the rotocraft i s somewhat i nf eri or i n speed to thepropeller-driven VTOL airplane with a short range.

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1

-ection 3. Basic Principles of Design1. Selection of Fn,qine Horser,ower-and Rotor %an

I n most cases, the hel icopter designer i s strpplied with the desired l i f tcapacity. KnaJing the requi red speed, he estimates the necessary power/weightratio. After assigning the current percentage of the useful load rati o, he determines the order of magnitude of the f l ying weight and hence the magnitude ofthe i nstal l ed power. Having selected the number of engines i n View of the enduse of the helicopter (one engine f or a l ight military machine, at least twoengines for a passenger craf t, etc.), he can sel ect the most suitable enginesamong existing or scheduled types.Usually, i t W i l l happen that the power of the possible combinations ofengines does not match the desi red power. T h i s necessitates correcting the parameters of the hel icopter i n question, after sel ecti ng the optimum combination of

exi sti ng engines. After this, the main problem facing the designer i s to selectthe rotor span for the speci f i c power plant.How does one sel ect disk loading?It i s known from stati st i cs that disk loading rapidly i ncreases with i kcreasing fl ying weight and varies within 12 - 50 kg/m2 as the weight i ncreasesfrom the l i ghtest t o the heaviest hel icopter.Disk loading, as a function of weight, varies even more than wing load- &i ng of an airplane. T h i s i s of importance since an increase i n wing loading ofan airpl ane can be compensated by an increase i n length of takeoff run whereas,f or helicopters, the takeoff run must always remain zero.The weight of the ro

Helicopters - Calculation and Design - Aerodynamics

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