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NAVAL POSTGRADUATE SCHOOLMonterey, California

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- DTICI1ELECTETHESIS DGUIDE FOR CONCEPTUALHELICOPTER DESIGN

byStephen Glenn Kee

June 1983Thesis Advisor: Donald M. Layton

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1A conceptual helicopter design method utilizing closed formformulas and approximations from historical data is developedfor use in a helicopter design course. The design manualis to be used for the conceptual design of a single mainrotor, utility helicopter. The manual was written principallyfor use in AE4306--Helicopter Design.,

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Approved for public release; distribution unlimited.

Guide for Conceptual Helicopter Designby

Stephen Glenn KeeCaptain, United States ArmyB.S., United States Military Academy, 1973Submitted in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING

from theNAVAL POSTGRADUATE SCHOOLJune 1983

Author:

Approved by: ,- /Th sis AdvisorAOccssion For 1NTIS GRAV n--rman, Dtpartmif of AeronauticsDTIC TAR~ 11UnannouncedJust 4'Dean'of Science and EngineeringDistribiuton/.Availability Codes 90:6 2

Avail and/or -- ow 2Dist Special

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ABSTRACT

A conceptual helicopter design method utilizing closedform formulas and approximations from historical data isdeveloped for use in a helicopter design course. The designmanual is to be used for the conceptual design of a singlemain rotor, utility helicopter. The manual was writtenprincipally for use in AE4306--Helicopter Design.

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TABLE OF CONTENTS

I INTRODUCTION . . . . . . . . . . . . . .. .. .... 5A.* BACKGROUND . . . . . . . . . . . . . . . . . . 5B. GOALS . . . . . . . . . . . . . . . . . . . . 6

II. APPROACH TO THE PROBLEM . .. . ... .. .. .. 7III. THE SOLUTION . . . . o . . . . . . . . . . . . . . 9IV. RESULTS . . . . . . . . . . . . . . . . . . . 11V. CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . 12LIST OF REFERENCES . . .. .. .. .. .... .. .... 13APPENDIX A: HELICOPTER DESIGN MANUAL . . . . . . .* . 14APPENDIX B: HELICOPTER DESIGN COURSE HANDOUTS . . . . 71APPENDIX C: EXAM8PLE OF CONCEPTUAL HELICOPTER DESIGN **84INITIAL DISTRIBUTION LIST ............ . ... .. 122

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.4

I. INTRODUCTION

A. BACKGROUNDThe methods of conceptual helicopter design have changed

dramatically over the past 30 years. Two principal reasonsfor this change are the greatly increased research anddevelopment costs and the scientific advances which have ledto engineering specialization. Today almost all new produc-tion helicopters are to a great extent hybrids of theirpredecessors, with technological advances applied toexisting systems rather than to an entirely new design. Thehelicopters of today are designed by committees composed ofspecialists in various fields who compromise and optimize toreach a final design. As a result the designer of today ispresented with challenges not faced by his predecessors.

Traditionally, design courses have been used to equipthe engineering student with the skills needed to meet thechallenges in the real world of engineering [Ref. 1]. Eventhough the required skills have changed, design courses arestill very important in the education process; however,design is no longer being taught in many aeronautical engi-neering schools [Ref. 2]. In the field of helicopter designthis is due largely to the complexity of the subject matter.

When it was decided to incorporate a helicopter designcourse into the curriculum at the Naval Postgraduate School,

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the search for a design methodology that could be used inthis course led to the discovery that few texts on the heli-copter design process exist. Many manufacturers have theirown methods, but since they rely so heavily on previousin-house designs, they are not suitable for use in an educa-tional framework. It became apparent that a conceptualdesign process for the course would have to be developed.

B. GOALSThe goals of this study were to:

1. provide a simple design process for use in a capstonehelicopter design course,2. provide an opportunity to exercise the skills ofoptimization and decision-making, aot only in

engineering but in managerial areas as well, and3. provide a framework from which further research canbe undertaken.

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II. APPROACH TO THE PROBLEM

The first step in the development of the helicopterdesign course was to analyze the complex nature of heli-copter engineering and to simplify its concepts into aseries of design steps. It became evident that the designmethodology would require an iterative process due to therelationships among the major design variables. A decisionwas made not to use the computer directly to perform theiterations, so that the student, as he performed therequired calculations, would develop a much greater under-standing of the interrelationships of the variables.However, the decision not to utilize a computer increasesthe complexity and length of the process.

It was decided to use a guided design technique ofinstruction, in order to limit the time and complexityfactors.

"Guided design is a relatively recent innovation inwhich students are first presented with a problemsetting. Sequential written instructions . . . arethen used to expose them to desired course materialand to aid them in learning to use rational problemsolving techniques. The guidance feature makes theapproach best suited to elementary courses or forintroductory projects in an advanced course." (Ref. 3]

Another advantage of the guided design process is that itfrees the student from lecture sessions and allows theinstructor to focus on critical areas. A disadvantage of

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this structure is that student creativity and initiative issomewhat inhibited.

The second step was to incorporate the design method-ology into a structure which would guide the student to acompleted project and allow for creativity and initiative.

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III. THE SOLUTION

The design process uses closed form equations to providea numerical analysis of helicopter theory. Where theorydoes not provide an exact solution, historical trends areused to approximate. The historical data that is obtainedfor use in the design process should reflect the type ofhelicopter that is to be designed. Specifications andmission requirements must be provided by the instructor.

The design process was incorporated into a design manual(Appendix A) for student use. Included in Appendix B aresample handouts which provide the specifications and histor-ical data necessary to use this manual. These handoutslimit the design to a single rotor, utility helicopter. Thedifficulty of the design process can be adjusted by varyingthe amount of information provided or the type of helicopterto be designed can be changed through modification of thesehandouts. Additionally, the handouts provide a means bywhich the course can be improved by continued researchwithout the requirement of having to rewrite or modify themanual.

The student is expected to have a basic understanding ofthe theory of helicopter performance. Many of the equationsused in the manual were taken from Helicopter Performance" ,ii9


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[Ref. 4]. Those areas of theory that are not included inReference 4 were covered in greater detail in the manuAl.

During the design process the student is required tomake decisions and optimize several factors. It was decidedto require the student to write several brief discussions atthese steps in the design process so that the instructor canfollow the student's reasoning in the critical decisions.These discussions allow the student an opportunity toexhibit initiative and creativity.

Several hand-held calculator programs [Ref. 5] and acomputer plotting routine (Ref. 6] have been developed foruse in the design process. These programs are mentioned inthe design manual where they are applicable. They havebeen included to reduce the tedium of several repetitivecalculations.

An introduction to cost estimating relationships havebeen included to broaden the student's perspective of realworld considerations and to allow the use of some managerialskills.

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IV. RESULTSThe design process has been included in a design manual(See Appendix A) which is suitable for use in a helicopter

design course.An example design is included in Appendix C. The speci-

fications and historical data used in this example areincluded in Appendix B. The specifications for two addi-tional designs are also contained in Appendix B (See HD-I).

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V. CONCLUSIONS AND RECOMMENDATIONSThe simplification of the field of helicopter engi-

neering into the design process presented in Appendix Anecessitated that some areas be slighted. Several majorareas are either covered only superficially or omitted dueto the time constraint that the student would face in a onequarter design course. Typical of these areas are airframedesign, structural designs, cost, tail rotor and verticalfin effects, and power required to overcome retreating bladestall effects. Other areas which were included must useestimations or historical trends to reach a design due to alack of an adequate theory to predict real world data. Theweight estimating relationships and profile drag computa-tions are examples. Future research in these areas could beincluded in the design manual or the handouts.

Many of the decisions that the student is required tomake using the design process are based on a numerical anal-ysis of the various factors. In the real world, many otherfactors may be present which would necessitate a differentdecision, so that in this sense the process is not a validrepresentation. However, the design process as found in thedesign manual should be useful as an educational tool.

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LIST OF REFERENCES

1. Haupt, Urich, Needs and Challenges in Education forAircraft Design, p. F-I, Naval Postgraduate School,1973.

2. Ibid., p. 4.3. Alic, J. A., "Integrating the Teaching of Design andMaterials", Engineering Education, Vol. 65, No. 7, pp.725-729, April 1975.4. Layton, Donald M., Helicopter Performance, NavalPostgraduate School, 1980.5. Fardink, Paul J. , Hand-Held Computer Programs for Pre-

liminary Helicopter Design, M.S. Thesis, Naval Post-graduate School, 1982.6. Sullivan, Patrick, Helicopter Power ComputationPackage, Term Paper for AE4900, Naval PostgraduateSchool, 1982.

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APPENDIX AHelicopter Design Manual

by

CPT Stephen G. Kee

AE4306Professor Donald M. Layton

Department of AeronauticsNaval Postgraduate SchoolMonterey, California

June 1983114

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ABSTRACT

This design manual is to be used for the conceptualdesign of a single main rotor, utility helicopter. Thedesign method utilizes closed form formulas and approxi-mations from historical data. This manual was writtenfor use in AE4306--Helicopter Design.

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CONTENTS

ABSTRACT . . . . . . . . . . . . . . . . . . . 15Chapter page1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . .21

DESIGN OBJECTIVE .......... . . . . . . .21DESIGN PHASES . . ................ .23PROCEDURE ........................... . . .24APPLICABILITY . . . . .............. 25ASSUMPTIONS . . . . . ............ .25

2. MAIN ROTOR DESIGN ....... .................. 26MAKE A ROUGH ESTIMATE OF THE MANUFACTURER'S EMPTYWEIGHT . . . . ........... ........ 26MAKE A ROUGH ESTIMATE OF GROSS WEIGHT .. ....... .. 26CALCULATE THE MAXIMUM TIP VELOCITY ......... 26DETERMINE THE ROTOR RADIUS ..... ............ ..26DETERMINE A FIRST-CUT ROTATIONAL VELOCITY ... . 27MAKE A FIRST-CUT DETERMINATION OF THRUSTCOEFFICIENT ...... ..... ....... ... . 27DETERMINE THE BLADE SOLIDITY.. .27DETERMINE THE NUMBER OF MAIN ROTOR BLADES*TO BE"USED ............. 28DETERMINE THE CHORD AND TE" SPECT .ATIO. ....... .. 29DETERMINE THE AVERAGE LIFT COEFFICIENT . .... .30CHOOSE AN AIRFOIL SECTION FOR THE MAIN ROTORBLADES .................... 30DETERMINE AVERAGE LIFT CURVE SLOPE AND AVERAGEPROFILE DRAG COEFFICIENT ..... .............. .31

3. PRELIMINARY POWER CALCULATIONS ..... ............ 32MAKE FIRST ESTIMATE OF THE POWER REQUIRED TOHOVER . . .................... .. 32MAKE SECOND GROSS WEIGHT ESTIMATE .. .... .. 32ESTABLISH FIGURE OF MERIT AT APPROXIMATELY 0.75* . .33REFINE SECOND GROSS WEIGHT ESTIMATE . ...... 34MAKE THIRD ESTIMATE OF POWER REQUIRED TO HOVER . . .35REPEAT THE GROSS WEIGHT ESTIMATE AND THE HOVERPOWER REQUIRED ITERATION.. . . . . 35DETERMINE THE POWER REQUIRED TO HOVER IGE, SSL . . .35

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DETERMINE THE PARASITE POWER REQUIRED IN FORWARDFLIGHT . ......... 35DETERMINE MAIN ROTOR POWER REQUIRED*AND'THE'MACHNUMBER OF THE ADVANCING BLADE TIP FOR FORWARDFLIGHT . . . . . . . . . . . . . . . ........ 36

4. TAIL ROTOR DESIGN . . . . . . . ............. 38MAKE PRELIMINARY DETERMINATIONS OF TAIL ROTORGEOMETRY . . . . . . . . 38DETERMINE TAIL ROTOR POWER REQUiRED'AT HOVER OGE,SSL ...... 38DETERMINE TAIL ROTOR POWER REQUiRED'AND'TIP*MACHEFFECTS FOR FORWARD FLIGHT ..... ............. .39

5. POWER CALCULATION REFINEMENTS ............ 41DETERMINE TOTAL POWER REQUIRED FOR HOVER ANDFORWARD FLIGHT .................. 41DETERMINE COMPRESSIBILITY CORRECTION. . .42DETERMINE THE REQUIRED RSHP AT MAXIMUM VELOCITY . .43DETERMINE THE REQUIRED RSHP FOR HOVER (IGE) AT THESPECIFIED CEILING ................... 43DETERMINE THE TOTAL ESHP REQUIRED ... ......... 44

6. ENGINE SELECTION ........ ................... 45SELECT TYPE AND NUMBER OF ENGINES - e . .... .45REVISE GROSS WEIGHT AND POWER REQUIRED-. ........ .48DETERMINE FUEL FLOW RATES AT VARIOUS POWERSETTINGS .......... ...................... 48

7. RANGE AND ENDURANCE CALCULATIONS ..... .......... 50DETERMINE THE SLOPE OF THE FUEL FLOW VERSUS SHPLINE AND THE ZERO HORSEPOWER INTERCEPT ......... .50COMPUTE THE ZERO HORSEPOWER INTERCEPT ATSPECIFICATION CONDITIONS ....... ............ .51DETERMINE THE ZERO HORSEPOWER INCREMENT . . . . . .51DETERMINE THE MAXIMUM RANGE VELOCITY... . . . e.52DETERMINE THE MAXIMUM ENDURANCE VELOCITY AND THEREQUIRED FUEL FLOW RATE AT THIS VELOCITY . . . . . .53DETERMINE THE POWER REQUIRED AT SPECIFICATIONCRUISE VELOCITY AND THE REQUIRED FUEL FLOWRATE AT THIS VELOCITY . ......... . . . .54DETERMINE THE TOTAL FUEL REQUIREMENTS FORSPECIFIED MAXIMUM RANGE ............ 54

8. MISCELLANEOUS CALCULATIONS . . . . . . . . . . . . . .56COMPUTE DESIGN GROSS AND EMPTY WEIGHT . . . . . . .56DETERMINE RETREATING BLADE STALL VELOCITY . . . . .56

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DETERMINE BEST RATE OF CLIMB . . . . . . . . . . . .58COMPUTE MAXIMUM HOVER ALTITUDE (IGE) . . . . . . . .60COMPUTE SERVICE CEILING . . . . . . . . . . . . . .61

9.* FINAL CHECK . . . . . . . . . . . . . *.. .. .. . .62MAKE FINAL CHECK FOR COMPLIANCE WITHSPECIFICATIONS . . . . . . . . . . .. .. .. .. .. 62

AppendixA-i LIST OF HELICOPTER DESIGN COURSE HANDOUTS . . . . . .63A-2 LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . .64A-3 SAMPLE FINAL SUMMARY FORMAT. ....... . . . . .*67LIST OF REFERENCES . . . . . .. .. .. .. .. .. .. .. 69BIBLIOGRAPHY .. ...... ... .... .. ... .. 70

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LIST OF TABLESTable Rae

1.The Phases of the Design Process . . . . . . . . . . 23

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LIST OF FIGURES

Table Page1. Weight Estimation Format ...... . . . . . . . 332. Main Rotor Power Profile Format . .... . . . . 373. Tail Rotor Power Profile Format . .... . . . . 404. Total Rotor Power Profile Format . .... . . . . 415. Engine Selection Format .. .. .. .. .. . . . 486. Zero Horsepower Intercept .. ........ . . . 507. Maximum Range Velocity . .. .. .. .. .. . . . 528. Maximum Endurance Velocity .. ............ 53

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Chapter 1INTRODUCTION

1.1 DESIGN OBJECTIVEThe goal of the design process is to optimize the mission

effectiveness of the design item. There are two groups offactors which determine an item's mission effectiveness.

A) Operational factors.1. Mission readiness which is a measure of the degree

to which an item is operable at the start of arandomly selected mission. Mission readiness ismeasured by an item's availability, reliability,and maintainability.a) Avaiiability is a function of the mean time

between maintenance actions and the maintenancedown time.

b) Reliability is a function of an item's failurerate.

c) Maintainability is measured by the item's meantime to repair.

2. Survivability which is a measure of the item'sability to withstand a hostile man-madeenvironment and still be mission ready.

3. Overall performance which is a measure of how wellan item performs its designated mission.

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B) Economic factors. The principle economic factor iscost, which is a measure in dollars of the amountrequired to design, produce, test, and operate anitem during its life-cycle.

One cost concept generally used to select among competingdesigns is life-cycle cost, which is the sum of all expen-ditures required from design conception to operationalphase-out. The life-cycle cost is comprised of research anddevelopment costs, initial investment, annual operatingcosts, annual maintenance costs, and salvage value. Thereare two major difficulties in using the life-cycle costmethod of economic analysis. First, the task of assemblingsufficient historical data on similar systems to createmeaningful cost estimating relationships is quite large.Second, the various parties involved in the procurementprocess have a different perspective from that of thedesigner. For example, a manufacturer may be more concernedwith an item's initial cost than with the user's maintenancecosts.

Any economic analysis of a design process should containthe following elements:

A) a statement of the design objective and the effec-tiveness measures which will be used to determineif the objective is reached,B) specification of the design choices (alternatives),

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D) a set of relationships (a model) that relates eachchoice to the effectiveness measures, and

E) the criteria or criterion which will be used to selectone of the design alternatives.

There are two major sources of uncertainty in any costanalysis: inadequate or inaccurate specification of thesystem being analyzed, and statistical inaccuracies in thecost estimating relationships.

1.2 DESIGN PHASESThe design process can be divided into five basic phases.

The first phase is a study of the historical data and thetrends in the helicopter design. Second, a conceptual studyis conducted using "rules of thumb" and experience to devel psimple layouts. Third, preliminary designs are drawn whichinclude volumetric sizing, airframe lines, mechanisms, andstructural concepts. Fourth, the design enters a "pror~osalstatus" in which detailed subsystems are developed,structural sizing is refined, and mockups are constructed.Fifth, the final details are completed.

Table 1 shows the design phases in outline form.

TABLE 1The Phases of the Design Process

1. T'end study(a) Provide direction for further study(b) Obtain quick look answers

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2. Conceptual study(a) Compare configuration(b) Estimate size and cost(c) Establish feasibility(d) Recommend follow-on3. Preliminary design(s.) nsure design practicality(b) Develop structural concepts(c) Develop concepts for mechanisms(d) Expand data base4. "Proposal status" design(a) Increase detail of structure, weight, etc.(b) Increased confidence by risk reduction(c.) Support proposal commitment5. Details

1.3 PROCEDUREA design sequence has been delineated in a step-by-step

manner in the subsequent chapters of this manual. Each stepis numbered sequentially within each chapter so that readyreference can be made to any step, when necessary, in otherchapters. Where calculations are required in the designsequence used in this manual, the necessary equations havebeen included for the convenience of the user.

The specifications and historical data required for usein the design sequence of this manual are listed in AppendixA-i. This data is in the form of handouts which should beobtained from the instructor. The symbology used in thismanual has been defined in Appendix A-2.

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1.4 APPLICABILITYBecause this manual has been written for use in the

Helicopter Design Course (AE4306) at the Naval PostgraduateSchool, it presumes a final report will be prepared andprovides sample formats and guidance for the preparation ofthat report (see Step 9.1).

1.5 ASSUMPTIONSThere have been several assumptions made in this manual

in order to limit the scope of the design process which thestudent would have to undertake. These assumptions irementioned as they occur in the design process.

Reference 1 was used as the principle source for thetheories of helicopter performance. Several assumptions aremade in order to quantify the theory. The assumptions madein Reference 1 are not listed in this manual.

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Chapter 2MAIN ROTOR DESIGN

2.1 MAKE A ROUGH ESTIMATE OF THE MANUFACTURER'S EMPTYWEIGHT.

Use the specification maximum gross weight from HD-1 andthe graph of historical weight ratios (HD-2) to estimate themanufacturer's empty weight.

2.3 MAKE A ROUGH ESTIMATE OF GROSS WEIGHT.Begin with an estimated gross weight which is 80% of the

specification value of gross weight.

2.4 CALCULATE THE MAXIMUM TIP VELOCITY.The maximum tip velocity should be calculated a-. he 90

degree point at hover, standard sea le-el. At hover themain rotor tip Mach number should no, exceed 0.65. Calcu-late the maximum main rotor tip velocity using Equations 1and 2.V = M * a (1)a = .y * g ' H * T (2)

2.4 DETERMINE THE ROTOR RADIUS.The selection of a main rotor radius will affect the disk

loading of the blade. The disk loading is a function ofgross weight and main rotor radius. Historically, the valueof disk loading increases with increasing gross weight (HD-3

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shows this trend). Use Equation 3 to calculate a rotorradius which will optimize disk loading for the gross weightestimate. Note that the maximum allowable radius is givenas a specification in HD-1.R = VW / (DL * 7) (3)2.5 DETERMINE A FIRST-CUT ROTATIONAL VELOCITY.

The maximum rotational velocity can be determined sincethe maximum tip velocity and the design rotor radius areknown. Use Equation 4 to calculate the first-3ut rotationalvelocity.Q = V / R (4)

2.6 MAKE A FIRST-CUT DETERMINATION OF THRUST COEFFICIENT.The first-cut value of thrust coefficient should be

determined at the specification density altitude usingEquation 5. The tip velocity is found using Equation 6 withthe main rotor radius found in Step 2.4 and the rotationalvelocity found in Step 2.5. Thrust should be set equal tothe value of gross weight found in Step 2.2.C = T / [A * 0 * V 2] (5)V = Q * R (6)

2.7 DETERMINE THE BLADE SOLIDITY.Equation 7 can be used to find the maximum advance ratio.

The tip velocity was determined in Step 2.6 and the maximumvelocity is given as a specification in HD-i. Once

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the maximum advance ratio has been determined, HD-4 can beused to determine the maximum blade loading. With thismaximum blade loading value and the main rotor thrustcoefficient from Step 2.6, calculate the solidity usingEquation 8.il = V / V (7)a = C / BL (8)

2.8 DETERMINE THE NUMBER OF MAIN ROTOR BLADES TO BE USED.The number of rotor blades to be used is a function of

rotor radius (as it affects solidity), vibration, andweight.

For a given solidity, more blades would be required ifthe radius and chord are to be ke~t small.

.The vibration of the main rotor is a factor in thedetermination of the number of blades to be used. Theairframe can be expected to vibrate at the rotor harmonicfrequency and at integer multiples of the rotor frequency.This integer multiple corresponds to the number of blades.A vibration with a frequency of 1/REV (4 Hz) may occur whichcould be caused by rotor unbalance, a blade out of track,differences between blades, or a combination of thesefactors. A vibration will also occur at the blade passagefrequency (b / REV). Vibrations of the rotor bladesinduce loads which are summed at the hub and passed to theairframe. A perfect rotor with all blades identical will

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act as a filter, so that only the (b / REV) andmultiples of (b / REV) are passed to the airframe [Ref.2]. Therefore, the effect of main rotor vibration on theairframe can be reduced by increasing the number of blades.

Note that the positive effects of reduced vibration andsmaller blades are offset by an increase in weight and hubcomplexity. Select the number of blades for design andinclude a brief analysis of your decision in the finalreport.

2.9 DETERMINE THE CHORD AND THE ASPECT RATIO.The chord can be calculated from Equation 9, since the

solidity (Step 2.7), the number of blades (Step 2.8), andthe rotor radius (Step 2.4) are known.

For a helicopter rotor, the aspect ratio is defined asthe radius divided by the chord. Historically, the mainrotor aspect ratio has been between 15 to 20, The aspectratio can be found using Equation 10 and the radius found inStep 2.4. Adjust the value of rotational velocity (Step2.5) as necessary, in order to obtain an aspect ratio of 15to 20. If the rotational velocity is reduced, then Steps2.6 and 2.7 must be recalculated.c = (a * 1 * R) / b (9)AR = R / c (10)

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2.10 DETERMINE THE AVERAGE LIFT COEFFICIENT.The average lift coefficient is a function of thrust

coefficient and solidity as shown in Equation 11.C = ( 6 * C ) / a (11)2.11 CHOOSE AN AIRFOIL SECTION FOR THE MAIN ROTOR BLADES.

The selection criteria for an airfoil are [Ref. 3]:A) high stall angle of attack to avoid stall on the

retreating side,B) high lift curve slope to avoid operation at high

angles of attack,C) high maximum lift coefficient to provide the neces-

sary lift,D) high drag divergence Mach number to avoid com-

pressibility effects on the advancing side,E) low drag at combinations of angles of attack and Mach

numbers represeating conditions at hover and cruise,and

F) low pitching moments to avoid high control loads andexcessive twisting of the blades.

Historically, the NACA 0012 airfoil has been used most often.The primary sources for making your selection should be HD-5and Theory of Wing Sections [Ref. 4]. Choose one of theairfoils from HD-5 or select one from Reference 4. Yourfinal report should include a brief discussion of the rea-sons for your selection.

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2.12 DETERlMINE AVERAGE LIFT CURVE SLOPE AND AVERAGEPROFILE DRAG COEFFICIENT.

If you selected one of the blades from HD-5, then useHD-5 to determine the profile drag coefficient and the liftcurve slope (C If another airfoil was chosen, then

- use Reference 4 to determine the profile drag coefficientand the lift curve slope. DATCOM [Ref. 5] can also be asedto find the lift curve slope.

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Chapter 3PRELIMINARY POWER CALCULATIONS

3.1 MAKE FIRST ESTIMATE OF THE POWER REQUIRED TO HOVER.The total power required to hover out-of-ground effect

at standard sea level is the induced power (out-of-groundeffect with tiploss) added to the profile power. Computethe power required to hover out-of-ground effect at standardsea level using Equations 12 through 15. An HP-41CV program

entitled HOVER [Ref. 6) can be also used to compute thesevaluesB = 1 - [ v' * C


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defined as the internal load capacity plus the crew weightallowance. Use the format in Figure 1 for your report.

WEIGHT ESTIMATION TABLE---------TERATION----------FIRST SECOND THIRD

SOLIDITY:RADIUS:HOVER POWER:ROTOR - BLADES:HUB/HINGES:TOTAL:PROPULSION:FUSELAGE:FLIGHT CONTROLS:ELECTRICAL:FIXED EQUIPMENT:EMPTY:FUEL:USEFUL LOAD:GROSS:

Figure 1: Weight Estimation Format

3.3 ESTABLISH FIGURE OF MERIT AT APPROXIMATELY 0.75.Historically, a Figure of Merit of 0.75 is considered

average [Ref. 2] . If the induced power is between 70 to 80%of the total power, the Figure of Merit will be approxi-mately 0.75. Recalculate the hover power (Step 3.1)using the new gross weight estimate calculated in Step 3.2.For small gross weight changes the value of disk loading maybe adjusted provided it remains within the limits defined by

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HD-3. If a significant gross weight change occurs, a radiuschange should be made in Step 2.3 to keep disk loadingwithin limits. If the main rotor radius is changed, thenSteps 2.5, 2.6, 2.7, and 2.10 must be recalculated. Verifythat the new value of induced power is between 70 to 80% ofthe new total power. If not, the geometric parameters mustbe changed to obtain that relationship. Hint: If theinduced power is greater than 80% of the total power, thenincrease the chord length. An increase in the value ofchord length increases solidity and decreases blade loading.The maximum value of blade loading was used in Step 2.7 andlower blade loadings are desirable. If the chord length isincreased, Steps 2.7, 2.9, and 2.10 must be recalculated.If the chord length cannot be increased without violatingthe limits of aspect ratio, then the radius or therotational velocity should be changed. If the induced poweris less than 70% of the total power, then reduce therotational velocity. In Step 2.5, a maximum tip velocitywas used which could be lowered slightly. A reduction inthe rotational velocity increases the advance ratio whichdecreases the blade loading (see HD-4).

3.4 REFINE SECOND GROSS WEIGHT ESTIMATE.Since the hover power (and possibly solidity or area) was

adjusted, refine the gross weight using HD-6. List the new

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weight estimates (third iteration) in your report as per theformat of Figure 1.

3.5 MAKE THIRD ESTIMATE OF POWER REQUIRED TO HOVER.Refine the power required to hover out-of-ground effect

(Step 3.2) using the revised gross weight (Step 3.4).:3.6 REPEAT THE GROSS WEIGHT ESTIMATE AND THE HOVER POWER

REQUIRED ITERATION.Repeat the iterations (Steps 3.3, 3.4, and 3.5) until

successive steps converge at less than 10% difference.

:3.7 DETERMINE THE POWER REQUIRED TO HOVER IGE, SSL.The profile power stays the same as for hover OGE (Step

:3.1), but the induced power gets smaller. Calculate thehover power in ground effect using Equations 15 through 17.An HP-41CV program entitled HOVER [Ref. 67 can also be usedto compute these values. Use a hover height of 10 feetabove ground level for your calculations.Pi - (P/P) * Pi (15)P/P = - 0.1276(h/D) = 0.7080(h/D)3 - 1.4569(h/D) 2 (16)

+ 1.3432(h/D) + 0.5147PT = Pi + Po (17)3.8 DETERMINE THE PARASITE POWER REQUIRED IN FORWARD

FLIGHTEquation 18 shows the relationship between the equivalent

flat plate area loading and the parasite power required inforward flight. There are several methods that can be used

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to determine the equivalent flat plate area in forwardflight. One method is to use HD-8 and the latest estimateof gross weight to find the equivalent flat plate arealoading, then to use Equation 19 to find the equivalent flatplate area in forward flight.Pp = 0.5 * p * V3 * EFPA (18)EFPA U W / Loading (19)3.9 DETERMINE MAIN ROTOR POWER REQUIRED AND THE MACH

NUMBER OF THE ADVANCING BLADE TIP FOR FORWARD FLIGHT.These calculations should be made at both standard sea

level and at specification density altitude using Equations20 through 26. Create tables with the velocity incrementedat least every 20 knots. The cruise velocity should also beincluded. Two programs have been developed either of whichcould also be used to calculate these values: a FORTRANprogram entitled Helicopter Power Computation Package [Ref.7] for use on the IBM-3033, and a program entitled FLITE[Ref. 8] for use with the HP-41CV programmable calculator.Use the format shown in Figure 2 for your report.mu = V / V (20)Po = [1 + 4.3*u 2 ] * Po (21)Vi = V T / [2 * p * 7 * Rl]' (22)Vi4 + 2*V*Vi 3 + (23)

[V 2 + Vz]*Vi 2 - Vi4 = 0Pi = (1/B) * T * Vi (24)

36

' ' , , m n i i i. .................i ...... .... ...


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PT =Pi + Po + Pp (25)M =(V + V) /.y *g * R * T' (26)

MAIN ROTOR POWER PROFILE----------------------------------OWER---------------

AIRSPEED TIP INDUCED PROFILE PARASITE TOTAL(KNOTS) MACH (SHiP) (SHiP) (SHiP) (SHiP)Figure 2: Main Rotor Power Profile Format

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Chapter 4TAIL ROTOR DESIGN

4.1 MAKE PRELIMINARY DETERMINATIONS OF TAIL ROTORGEOMETRY.

Use HD-9 in your determination of radius, rotationalvelocity, drag coefficient, and the number of blades. Thelength of the fuselage from the center-of-gravity to thetail rotor hub should be calculated using Equation 27. Thechord can be determined by Equation 28 and the use of a.value of tail rotor aspect ratio within the historical rangeof 4.5 to 8.0. Use Equation 29 to calculate the tail zotorsolidity.L = R + R + 0.5 ft (27)c = R / AR (28)c = b * c / (7 * R) (29)

4.2 DETERMINE TAIL ROTOR POWER REQUIRED AT HOVER OGE, SSL.The total power of the tail rotor required to hover

out-of-ground effect at standard sea level is the inducedpower, out-of-ground effect with tiploss, added to theprofile power. Use Equations 30 through 36 to determine thetail rotor hover power. The HP-41CV programs entitled TR orHover [Ref. 6] can be used to compute these values.T = PT / ( Q * L ) (30)C = T / [A * * V2 ] (31)

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V':tip-tr> = * R (32)B = 1 -[ V2 * Ccthrust-tr> '/b 1(33)Pi =(i/B) * [T 1* / 2 * g* A~tr> '] (34)Po = 0.125*a*Cdo*P*A~tr>*V3 (35)PT


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TAIL ROTOR POWER PROFILE----------------------------------OWER ----------

AIRSPEED TIP INDUCED PROFILE TOTAL(KNOTS) MACH (SHP) (SHP) (SHIP)

Figure 3: Tail Rotor Power Profile Format

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Chapter 5POWER CALCULATION REFINEMENTS

5.1 DETERMINE TOTAL POWER REQUIRI) FOR HOVER AND FORWARDFLIGHT

These calculations should be made for flight out-of-ground effect at both standard sea level at the specifi-cation density altitude using Equations 47 and 48. Createtables with the velocity incremented at least every 20knots. The cruise velocity should also be included. TheFORTRAN computer program for the IBM-3033 and the HP-41CVprogram mentioned in Step 3.9 can be used to calculate thesevalues. The computation package w:.ll also provide a graphof the induced, profile, parasite, and the total powercurves. The total power curve will be required in Steps 7.4and 7.5. Use the format shown in Figure 4 for your report.PT = PT .i T (47)PT = PT + PT (48)

ROTOR POWER PROFILE---------------POWER---------------AIRSPEED INDUCED PROFILE PARASITE TOTAL(KNOTS) (SHP) (SHP) (SHP) (SHP)

Figure 4: Total Rotor Power Profile Format

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5.2 DETERMINE COMPRESSIBILITY CORRECTION.When an airfoil is operated at a Mach number of 1.0 or

greater, pressure disturbances caused by the airfoil cannotpropagate forward and shock waves will form ahead of theairfoil. The noise level produced by the rotor is greatlyincreased when the shock waves form [Ref. 9]. Weak obliqueshock waves can form at local points on the airfoil evenbefore the free stream reaches Mach 1.0. The free streamMach number at which any local Mach number reaches 1.0 iscalled the critical Mach number. Above this critical Machnumber, drag begins to increase. Therefore, additionalpower is required to overcome the effects of compressibilityon the performance of a helicopter rotor. Use Equations 49through 51 to calculate the compressibility correction, atboth standard sea level and the specification densityaltitude. Note that Equation 50 has been adjusted by 0.06in order to agree with experimental data for a NACA 0012airfoil [Ref. 10]. Assume this equation applies for anyairfoil. The compressibility correction should bedetermined only at the highest Mach number (usually at themaximum velocity). The values of critical Mach number canbe found in HD-IO. Use the lowest value of critical Machnumber (at the highest angle of attack) for your calculations.

P P * A * V 3 * o (49)* [0.012*Md + 0.10*Md 3 ]

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Md M - M - 0.06 (50)M = (V + V) / y * g * R * T1 (51)5.3 DETERMINE THE REQUIRED RSHP AT MAXIMUM VELOCITY.

Add the appropriate compressibility corrections from Step5.2 to the values of total power at maximum velocitydetermined in Step 5.1 (for both standard sea level and thespecification density altitude). After adding the compressi-bility corrections, the higher of the two values should beused as the required rotor shaft horsepower.5.4 DETERMINE THE REQUIRED RSHP FOR HOVER (IGE) AT THE

SPECIFIED CEILING.Use the gross weight tha ; has been used since Step 3.6

and note that the density wi'l be different at thespecification hover ceiling. The specification hoverceiling can be found in HD-1. Use Equations 52 through 59to calculate the main rotor hover power and the equationsprovided in Step 4.2 to calculate the tail rotor hover powerat the specification hover ceiling. Assume a hover heightof 10 feet above ground level. The HP-41CV programsentitled HOVER and TR (Ref. 6] can be used to compute thesevalues. The required RSHP for hover is the aircraft totalhover power.C = T / [A * * V 2 ] (52)B = 1 - [ 2 * C / b ] (53)Pi = (I/B) * [T- / 2 * p * A ] (54)

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Pi = (P/P) * Pi (55)P/P


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Chapter 6ENGINE SELECTION

6.1 SELECT TYPE AND NUMBER OF ENGINES.The number of engines to be used should be determined by

considering the factors of safety, survivability, andreliability. Select the number of engines based on theseconsiderations and briefly explain your decision in yourfinal report. Remember that in Step 5.4 multiple engineinstallation was considered. If you decide to use adifferent number of engines, go back to Step 5.4 andrecompute ESHP.

The criteria for selection of the type of engine to beused are weight, life-cycle costs, availability,reliability, maintainability, and performance.

The weight of the engine should be as small as possible.The life-cycle costs can be computed using the data found

in HD-i and HD-li. The life-cycle costs are the summationof the research and development costs, the initial cost, theyearly operating cost (average value, adjusted forinflation), the yearly maintenance cost (average valueincluding overhauls, adjusted for inflation), thereplacement cost (if the life of the engine is less than thelife of the helicopter) and the salvage value. In order tocompute the life-cycle costs, the expected time of service

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of the helicopter in years, the expected number of flighthours per year of the helicopter, and the expected enginelife (sometimes called mean time between replacements) inhours must be known. If the engine life in hours is lessthan the helicopter life in hours, then the number of enginereplacements must be computed. To find the number of enginereplacements divide the helicopter life in hours by theengine life in hours, round up to the next integer if thereis a remainder, then subtract 1.0 (the initial engine).Equation 61 should be used to compute the life-cycle costs.

The availability is a function of the mean time betweenmaintenance actions and the maintenance down time. Theengine availability can be computed using the relationshipgiven by Equation 62 and tue appropriate values in HD-11.

The reliability of the engine is a function of the meantime between failures (failure rate) and the length of theaverage flight in hours (see HD-i). Equations 63 and 64 canbe used to compute the reliability.

The maintainability is a function of the mean time torepair but is sometimes given as a fraction of themaintenance down time in hours divided by the total flighthours. Either measure can be used for comparison.

The performance of the engine can be measured in manyways, but for this course the measure of performance will bethe shaft horsepower produced by the engine. Insure theengine you select has a military ESHP greater than the

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ESHP you found in Step 5.4. A computer programentitled Helicopter Engine Program [Ref. 11] has beendeveloped that computes the shaft horsepower available atany given altitude and airspeed for various engines;however, this computation is done for a "rubber" engine andshould not be used if real engine data is available.

Once values have been determined for each criteria foreach competing engine, the designer must choose the enginethat best optimizes the six criteria mentioned above. Inorder to select the "best" engine, the six criteria must beweighted according to their importance. For example, highperformance and low weight may be more desirable than lowlife-cycle cost. In order to establish uniform selectioncriteria, the weighting factors for the six criteria aregiven in HD-i1. Your final report should contain acompleted chart using the format of Figure 5 and a briefdiscussion of the decision-making process you used in yourselection of an engine type. Compute the availability,reliability, and maintainability on a per engine basis.LCC = n*[RDC + IC + HL*(YOC+YMC) + n*(RC-SV)] (61)AVAIL = MTBMA / ( MTBMA + MDT ) (62)RELY = e(- * LAF) (63)X = 1 / MTBF (64)

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ENGINE SELECTION CRITERIA----------- ENGINE------------A B C D E F

POWERPLANT WEIGHT:LIFE-CYCLE COST:ENGINE LIFE (HRS):

NUMBER OF REPLACEMENTS:R & D COSTS:INITIAL COST:YEARLY MAINTENANCE COST:YEARLY OPERATING COST:REPLACEMENT COST:SALVAGE VALUE:AVAILABILITY (per engine):

RELIABILITY (per engine):MAINTAINABILITY (per engine):PERFORMANCE (SHP):

Figure 5: Engine Selection Format

6.2 REVISE GROSS WEIGHT AND POWER REQUIRED.Check engine weight (including installation, oil, and

transmission weights) against previous estimates ofpowerplant weight (called propulsion weight in HD-6).Compute a new gross weight using the engine weight. Comparethe new gross weight with the value you have been using fromStep 3.6. If it is not within 10% use the new gross weightand go back to Step 3.3.

6.3 DETERMINE FUEL FLOW RATES AT VARIOUS POWER SETTINGS.The specific fuel consumption can be obtained from the

manufacturer's data on the engine at military, normal, andcruise power settings. The fuel flow rates at the specified

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power settings can then be determined ofl a per engine basisfrom Equation 65.Wf SFC *SHP (65)

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Chapter 7RANGE AND ENDURANCE CALCULATIONS

7.1 DETERMINE THE SLOPE OF THE FUEL FLOW VERSUS SHP LINEAND THE ZERO HORSEPOWER INTERCEPT.

These calculations should be made at standard sea level.The relationship between fuel flow rate and shaft horsepowerfor a turboshaft engine is fairly linear except at lowvalues of shaft horsepower. The average slope of the fuelflow versus SHP line can be found mathematically using thevalues of fuEl flow rate at the military, normal, and cruisepower settings calculated in Step 6.3. The intercept of thefuel flow versus SHP line with the ordinate axis is the zerohorsepower intercept.

FUEL 1FLOW JRATE

ZHI

SHAFT HORSEPOWERFigure 6: Zero Horsepower Intercept

50

- -- ,.---.-. .... . .---


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B = A Wf / A SHP (66)7.2 COMPUTE THE ZERO HORSEPOWER INTERCEPT AT SPECIFICATION

CONDITIONS.At standard sea level, both 0 and 5 are equal to 1.0;

therefore, the value of a can be determined using the zerohorsepower intercept found in Step 7.1. Find e and S at thespecification pressure altitude using Equations 67 and 68,then calculate the zero horsepower intercept using Equation69. The pressure at the specification pressure altitudecan be found using an ICAO standard atmospheric table. Thetemperature at the specification pressure altitude is givenin RD-i.e = T / T (67)S = P / P (68)ZHI = a * 6 * (69)

7.3 DETERMINE THE ZERO HORSEPOWER INCREMENT.The value of the zero horsepower increment is based on

the number of engines, the zero horsepower intercept, andthe fuel flow rate per horsepower. The slope of the fuelflow versus SHP line is the same at all density altitudes.These calculations should be made at the specificationdensity altitude. The zero horsepower increment issometimes called the phantom SHP. Use Equation 70 tocalculate the phantom SHP.P = [n * a * 8 * T' ] / 3 (70)

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7.4 DETERMINE THE MAXIMUM RANGE VELOCITY.Use the total power versus velocity curve at the

specification density altitude. Draw a line through thezero horsepower intercept and tangent to the total powerversus velocity curve found in Step 5.1. Draw a second lineperpendicular to the abscissa which passes through the pointof tangency. The intercept of the second line with theabscissa is the maximum range velocity (see Figure 7).

Slip

V VELOCITYP

Figure 7: Maximum Range Velocity

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7.5 DETERMINE THE MAXIMUM ENDURANCE VELOCITY AND THEREQUIRED FUEL FLOW RATE AT THIS VELOCITY.

Draw a line parallel to the abscissa on the total powerversus velocity curve which is tangent to the lowest valueon the curve. Use the total power versus velocity curve atthe specification density altitude. Draw a second line per-pendicular to the abscissa which passes through the point oftangency. The intercept of the second line with the abscissais the maximum endurance velocity (see Figure 8). Find theRSHP at the maximum endurance velocity from the total powercurve (see Step 5.1) and the phantom SHP from Step 7.3, thenuse Equation 71 to find the required RSHP at the maximumendurance velocity. Use Equation 72, the required RSHP,and the value of found in Step 7.1 to find the re-quired fuel flow rate at the maximum endurance velocity.

SHP

tjV VELOCITYFigure 8: Maximum Endurance Velocity

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RSHP = P + RSHP (71)Wf = RSHP * S (72)

7.6 DETERMINE THE POWER REQUIRED AT SPECIFICATION CRUISEVELOCITY AND THE REQUIRED FUEL FLOW RATE AT THISVELOCITY.

Find the RSHP at cruise velocity from the total powercurve at the specification density altitude (see Step 5.1)and add the phantom SHP found in Step 7.3. This sum (seeEquation 73) is the required RSHP at cruise velocity. Aftercomputing the required RSHP, use Equation 74 to find thefuel flow rate at cruise velocity.RSHP = P + RSHP (73)Wf = RSHP * (74)7.7 DETERMINE THE TOTAL FUEL REQUIREMENTS FOR SPECIFIED

MAXIMUM RANGE.The total fuel requirements are based on the following

assumptions:A) warm-up and take-off requires three minutes of fuel at

normal rated power,B) cruise at specification velocity,C) approach and landing requires three minutes of fuel at

normal rated power, andD) reserve requires fifteen minutes at maximum endurance

velocity.The cruise velocity and the maximum range are specificationsand can be obtained from HD-1. Use Equation 75 to find thefuel weight. Assume the fuel flow rates are constant.

54

i '' . - ....--- -- , - J i , -% w .- -


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FY I 0 05*n*Wf + [(Wf~cruise>*RNG)/V1 (75)+ O.05*n*Wf + O.25*Wf

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Chapter 8MISCELLANEOUS CALCULATIONS

8.1 COMPUTE DESIGN GROSS AND EMPTY WEIGHT.At this point, your power calculations have been made

with an estimated gross weight from Step 3.6 which isdifferent from the design gross weight. The design grossweight includes the actual powerplant weight from Step 6.1and the actual fuel weight from Step 7.7. If the designgross weight is greater than the estimated gross weight,return to Step 3.3. If the design gross weight is lessthan the estimated gross weight, increase the fuel weight orthe internal load capacity so that the design gross weightequals the estimated gross weight. Note that specificationsmay be exceeded if the change is advantageous. If the fuelweight is increased in this manner, the maximum range mustbe recomputed (See Step 7.7).8.2 DETERMINE RETREATING BLADE STALL VELOCITY.

The retreating blade stall velocity can be calculatedusing a technique developed in Reference 10. A program forthe HP-41CV programmable calculator entitled BS [Ref. 12]has been developed utilizing this technique which can beused to calculate the retreating blade stall velocity. Theprogram uses the geometric design parameters of the main

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rotor and the aircraft's forward velocity as input, thenoutputs the maximum angle of attack at the 270 degree point,the amount of collective set, and the amount of cyclic thatis set. The cyclic will be negative for forward flight.The program assumes that the maximum unstalled angle ofattack is 12.5 degrees, that the effective dimensionlessradius is 0.97 and that there is no lateral flapping. Notethat the slope of the lift curve was found in Step 2.12 andthat a value of the twist of the main rotor blade isrequired. (Assume a linear twist of -10 degrees.)

To determine the retreating blade stall velocity atstandard sea level, run the program using various forwardvelocities until the program indicates that the retreatingblade has stalled (use the greatest unstalled velocity) oruntil the specification maximum velocity is reached.

Equations 76 through 92 may also be used to determine theretreating blade stall velocity at standard sea level inlieu of the HP-41CV program. (The assumptions mentionedabove also apply to these equations.) First, determine ifthe blade is stalled by comparing the angle of attack of themain rotor at the 270 degree position with the maximum angleof attack. Second, reduce the forward velocity if themaximum angle of attack (12.5 degrees) is exceeded anditerate to find the greatest unstalled forward velocity.Note that Equations 90 and 91 must be solved simultaneouslyfor the collective and cyclic angles in radians and that

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Equation 92 yields the angle of attack at the 270 degreeposition in degrees.T = 0.4705 + 0.5000 * u2 (76)T = 0.3042 + 0.4850 * u 2 (77)T = 0.2213 + 0.2352 * ui 2 (78)T = 0.2352 * P + 0.1250 * v 2 (79)A = 0.9409 - 0.5000 * u 2 (80)A = [2.0000 * u - 0.5314 * u 3 ] I A (81)A = [2.5867 * u] / A (82)A = [1.9400 * i] / A (83)A - [0.9409 = 1.5000 * v:] / A (84)a = [0.0012 * EFPA * V3 ] / W (85)w = W / [0.0149 * R 2 * V~fwd>] (86)

= (V * a - w) /(Q * R) (87)C = W / [0.0075 * R'> * 2 2 ] (88)Z = (2 * C) /(CL,Os * i) (89)0.0 = a * A + e * A (90)

+ 8 * A + 6 * AZ = a * T + 9 * T (91)

+ 9 * T + 9 * Ta = [(A/ 1+u) - (92)

+ 6 + O] * 57.3

8.3 DETERMINE BEST RATE OF CLIMB.The best rate of climb occurs in forward flight in the

vicinity of the minimum total power on the total main rotor

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power curve. The following procedure should be used inorder to find the best rate of climb:

A) select a velocity near the lowest point on the rotortotal power curve (SSL),B) compute the rotor total power available using Equa-tion 93 (ESHP is the military rated power atSSL multiplied by the number of engines),

C) guess a value of vertical velocity,D) solve for the thrust component of induced velocity

using Equations 94 and 95,E) calculate the induced, profile, parasite, and climb

power using Equations 96 through 100,F) compute main rotor total power using Equation 101,

then add the tail rotor total power calculated usingthe equations in Step 4.3 and compare with the totalrotor power available, and

G) repeat the process until the total rotor power isequal to the total rotor power available or until themain rotor induced power equals zero.

The HP-41CV programs called FLIGHT and TR [Ref. 5] can beused to compute the main rotor power and the tail rotorpower. The final value of vertical velocity is the bestrate of climb.PT = (ESHP-10.0) / (0.10*(n-1)+1.03) (93)Vi - T / [2 * P * *"R2] ' (94)

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Vi4 + 2*V*Vi3 + (95)[V2 + V 21*Vi2 -V14 = 0

Pp = (O.5*p*EFPA*V 3 1 (96)+ (O.5*P*EFPA*V 3 ]

Po - O.125*P*Cdo*r*A.~mr>*V3 (97)*[1 + 4.3*uj 1

EFPA = 2 * EFPA (98)Pc = Tcmr> *V (99)Pi =(1/B) * T *Vi (100)PT = Po +- Pi + Pc + Pp (101)

8.4 COMPUTE MAXIMUM HOVER ALTITUDE (IGE).Calculate the highest altitude at which the helicopter

can hover in ground effect using tte following method:A) assume a hover height of 10 feet above ground level,B) guess an al'titude,

41 C) compute the total power requiired to hover in groundeffect using the equations given in Step 5.1,

D) compare the total power required with the total poweravailable found in Step 8.3 (assume power availableremains constant with increasing altitude) andrepeat the process if they are not equal.

The altitude at which the total power required equals thetotal power available is the maximum hover altitude inground effect.

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8.5 COMPUTE SERVICE CEILING.Service ceiling is defined as the maximum altitude at

which the helicopter exhibits a 100 fpm rate of climbcapability at a given temperature. It is normally definedat the best rate of climb velocity using the normal enginepower rating. The service ceiling may be calculated usingthe following method:

A) guess an altitude,B) compute the total power required for climbing forward

flight at best rate of climb velocity with a verticalvelocity of 100 fpm using the equations in Step 8.2,

C) compute the value of total rotor power available atthe normal engine power rating using Equation 102(assume power available remains constant withincreasing altitude),

D) compare the power available with power required andrepeat the process if they are not equal.

The altitude at which the total power required equals thetotal power available (NRP) is the service ceiling.PT = (ESHP-10.0) / (0.10*(n-1)+1.03) (102)

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Chapter 9FINAL CHECK

9.1 MAKE FINAL CHECK FOR COMPLIANCE WITH SPECIFICATIONS.Check for compliance with specifications as given in HW-1

and insure all work has been redone with your final designparameters.

Prepare your final report and check to insure it containsthe following items:

A) For each step either show your calculations or explainhow you determined the required data. Summarize theresults of Steps 3.2, 3.9, 4.3, 5.1, 2.nd 6.1 using thegiven formats.

B) If a computer or calculator program is used, include aprogram listing unless the program has been referencedin this manual.

C) Be sure to include the brief discussions required inSteps 2.8, 2.11, and 6.1

D) Prepare a final summary using the format found inAppendix A-3.

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Appendix A-1LIST OF HELICOPTER DESIGN COURSE HANDOUTS

HD-1 SpecificationsHD-2 Weight Ratios ChartHD-3 Disk Loading TrendHD-4 Blade Loading LimitsHD-5 Rotor Airfoil DataHD-6 Weight EstimationHD-7 Current Helicopter DataHD-8 Trends In Equivalent Flat Plate LoadingHD-9 Tail Geometry FactorsHD-IO Critical Mach NumberHD-11 Powerplant Selection

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Appendix A-2LIST OF SYMBOLS

a - Speed of soundA - Disk area of main rotorA - Disk area of tail rotorAR - Aspect ratioAVAIL - Availabilityb - Number of main rotor bladesb - Number of tail rotor bladesB - Main rotor tiploss factorB - Tail rotor tiploss factorBL - Blade loadingC~iift> - Coefficient of liftCL,a - Slope of the lift curvec - Main rotor chordC - Main rotor coefficient of thrustC - Tail rotor coefficient of thrustc - Tail rotor chordCdo - Profile drag coefficient of the main rotorCdo - Profile drag coefficient of the tail rotarD - Main rotor diameterDL - Disk loadingEFPA - Equivalent flat plate area in forward flightEFPA - Equivalent flat plate area in vertical flightEL - Engine life in hoursESHP - Engine shaft horsepowerFW - Fuel weightg - Gravitational constantGE - In ground effecth - Height above groundHL - Helicopter life in yearsHRS - Flight hoursIC - Initial costL - Distance from center-of-gravity to tailrotor hub

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LAF - Length of average flight in hoursLoading - Equivalent flat plate area loadingM - Critical Mach number of advancing blade atthe 90 degree pointM - Mach number at rotor tip velocityM - Mach number at maximum tip velocityMd - Drag divergence Mach numberMDT - Maintenance Down TimeMTBF - Mean Time Between FailuresMTBR - Mean Time Between ReplacementsMTBMA - Mean Time Between Maintenance ActionsMTTR - Mean Time to Repairn - Number of enginesn - Number of engine replacementsN - Main rotor RPMNRP - Normal Rated PowerP - Power required to overcome compressibility

effectsP - Phantom SHPPc - Climb power of the main rotorPi - Induced power of the main rotor with tiplossPi - Induced power of the main rotor with tiplossin ground effectPo - Profile power of the main rotorPp - Parasite power of the main rotor in forwardflightPT - Total power of main rotor at a hoverPT - Total power of the tail rotor at a hoverR - Individual gas constantR - Maximum allowable main rotor radiusR - Minimum allowable main rotor radiusR - Design main rotor radiusR - Tail rotor radiusRC - Replacement costRDC - Research and development costRELY - ReliabilityREV - RevolutionRSHP - Rotor shaft horsepowerSFC - Specific fuel consumptionSHP - Shaft horsepowerSV - Salvage valueT - TemperatureT - Thrust due to the main rotorT - Thrust due to the tail rotor

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V - Forward velocityVi - Induced velocity of the main rotorVi - Thrust component of the induced velocity ofthe main rotorV - Maximum forward velocityV - Maximum endurance velocityV - Maximum range velocityV - Maximum tip velocityV - Design tip velocity of the main rotorV - Design tip velocity of the tail rotorw - Downwash angleW - Gross weightWf - Fuel flow rateWf - Fuel flow rate ai; cruise velocityWf - Fuel flow rate a-; maximum endurance velocityWf - Fuel flow rate per engine at CruiseRated PowerWf - Fuel flow rate per engine at MilitaryRated PowerWf - Fuel flow rate per engine at NormalRated PowerYMC - Yearly maintenance costYOC - Yearly operating costa- Angle of attacka - Angle of attack of the retreating mainrotor blade at the 270 degree pointa - Zero usable SHP :fuel flow rate at standardsea level

- Rate of change of fuel flow with horsepower3 - Average rate of change of fuel flow withhorsepower5 - Ratio of pressure at a specific altitude tostandard sea level pressurey - Ratio of specific heatsX -Main rotor inflow rateX - Failure rate

- Advance ratio of the main rotor - Advance ratio of the tail rotor-Main rotor rotational velocity- ail rotor rotationU velocity- Density

5 - Soliditye - Square of the ratio of speed of sound at analtitude to the speed of sound at SSLe - Angular longitudinal cyclic position9 - Angular collective positione - Main rotor blade twist66


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Appendix A-3SAMPLE FINAL SUMMARY FORMAT

PerformanceSpecification Design

Crew:Internal Load [lbs]:Max Hover Altitude (IGE):Service Ceiling:Disk Loading:Velocity [kts] - Cruise:Maximum:

Max Endurance:Max Range:Retreating Blade Stall:

Best Rate of Climb [fpm]:Figure of Merit:Maximum Advance Ratio:Coefficient of Thrust:Coefficient of Lift:Engine - Number / Tvpe:SHP (Military):Maximum Range [nmi]:

GeometrySpecification Design

Weight [lbs] - Max Gross:Empty:Fuel Capacity [ibs] - Internal:Main Rotor - Airfoil Section used:! Chord [ft]:Radius [ft]:

Number of Blades:Drag Coefficient:Rotational Velocity [rad/sec]:Solidity:Aspect Ratio:

Tail Rotor - Airfoil Section used:Chord [ft]:Radius [ft]:Number of Blades:Drag Coefficient:

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Rotational Velocity [rad/sec]:Solidity:Aspect Ratio:

Equivalent Flat Plate Area [ft 2 ] - Forward:Vertical:Distance from CG to Tail Rotor Hub [ft]:

Discussion(a) Comment on deficiencies from specification

requirements, including reasons, if known.(b) If the design is better than specification

requirements, indicate po:ssible advantages, e.g.,increased cargo could be carried by reducing therange to the specificatio: limit.

(I

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LIST OF REFERENCES

1. Layton, Donald M., Helicopter Performance, NavalPostgraduate School, Monterey, CA, 1980.2. Boeing Vertol Company, Helicopter Preliminary DesignReview, p. 100, 1980.3. Pilos, A. S., Selection of Helicopter Rotor Airfoil,Term Paper for AE3304 (Professor Layton), p. 1, NavalPostgraduate School, Monterey, CA, 1982.4. Abbott, Ira A. and Von Duenhoff, Albert E., Theory ofWing Sections, Dover Publications, 1959.5. McDonnell Douglas Corp., USAF Stability and Control

Datcom.6. Fardink, Paul J., Hand-Held Computer Programs forPreliminary Helicopter Design, M.S. Thesis, NavalPostgraduate School, Monterey, CA, 1982.7. Sullivan, Patrick, Helicopter Power Computation Package(FORTRAN), Term Paper for AE4900 (Professor Layton),Naval Postgraduate School, Monterey, CA, 1982.8. Layton, Donald M., FLITE, Program for HP-41CVProgrammable Calculator, Naval Postgraduate School,Monterey, CA, 1980.9. U. S. Army Materiel Command, Engineering DesignHandbook, Helicopter Engineering, Part 1, (AMCP706-201), HQ, U. S. Army Materiel Command, 1974.10. McCormick, Barnes W., Jr., Aerodynamics of V/STOLFlight, Academic Press Inc., 1967.11. O'Neill, Gary S., Helicopter Enginer Program (FORTRAN),Term Paper for AE4900 (Professor Layton), NavalPostgraduate School, Monterey, CA, 1982.12. Layton, Donald M. , BS, Program for HP-41CV ProgrammableCalculator, Naval Postgraduate School, Monterey, CA,

1980. 669


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BIBLIOGRAPHY

Barish, Norman N. and Kaplan, Seymour, Economic Analysis,McGraw-Hill Book Co., 1978.English, John M. (Editor), Cost-Effectiveness, JohnWiley and Sons, Inc., 1968.Haupt, Ulrich, Decision-making and Optimization in Air-craft Design, Naval Postgraduate School, Monterey, CA,1977.Jones, J. Christopher, Design Methods, John Wiley andSons, Inc., 1970.Morrison, Richard B. (Editor), Design Data for Aeronauticsand Astronautics, John Wiley and Sons, Inc., 1962.Newman, Donald G., Engineering Economic Analysis,Engineering Press, 1976.Pitts, G., Techniques in Engineering Design, John Wileyand Sons, Inc., 1973.Saunders, George H., Dynamics of Helicopter Flight,John Wiley and Sons, Inc., 1975.Thuesen, Halger G., Fabrycky, W. J., and Thuesen G. J.,Engineering Economy, 4th ed., Prentice-Hall, In.,1971.Wood, Karl D., Aerospace Vehicle Design. Vol. I(Aircraft Design), 3d ed., Johnson Publishing Co.,1968.

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HD-iAPPENDIX B

HELICOPTER DESIGN COURSE HANDOUTSSPECIFICATIONS

for aSingle Rotor Helicopter

Design Group I II IIICrew 2 3 3Useful Load (lbs) 1,000 3,750 9,000Hover IGE (ft) 11,000 12,000 13,500Service ceiling (ft) 14,500 17,500 21,000V max* (kts) 120 160 180V cruise* (kts) 105 135 150Range max (nmi) 225 250 225Max Rate of Climb (ft/min) 1,750 2,500 1,100Max Gross Weight# (lbs) 11,000 18,000 38,000Max Rotor Diameter# (ft) 54 58 76Max Fuselage Length# (ft) 50 56 68

Average flight hours 120 300 480per year per airframe

Average flight hours 0.7 2.0 4.1per flight

Average airframe service 8 10 12life, years4,000 pressure altitude, OAT 95 deg F

# Not-to-be-exceeded values71


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R

HD- 2

Z32~28

024_00

16

8

0 2 4 6 8 10 12 14 16 I8MANUFACTURERS EMPTY WEIGHT

(1,000 LBS)72


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HD- 4

.10

0

47


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HD-5

.03.~.~1.41.2..

J02 10

...................1 ................

02 2...... 6.. 0

ANGLE OF ATTACK (DEG)

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HD-6

HELICOPTER DESIGN COURSE HANDOUTWeight Estimation

Main Rotor -W - 0.06 * W *R 0- * a

Empty Weight (second cut)-W = W + W + W + W + W +1

Gross Weight (second cut) -W =W + W + W

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liD-7

HELICOPTER DESIGN COURSE HANDOUTHelicopter Parameters

AH-64 UH-1N OR-6A SH-3H S-76Main Rotor

Radius (ft): 24.0 24.0 26.3 31.0 22.0Number of blades: 4 2 4 5 4Height AGL (ft): 12.6 13.0 7.0 14.3 10.0Q (rad/sec): 30.3 30.8 49.2 21.3 30.7Chord (ft): 1.75 1.95 0.57 1.52 1.29Span (ft): 18.8 21.4 11.5 29.3 --Twist (deg): -9 -- -9 -8 -10Cdo: 0.009 0.009 0.009 0.0095 0.009DL: 8.1 5.8 4.68 6.96 6.58

Tail RotorRadius (ft): 4.6 4.3 4.3 5.3 4.0Numoer of blades: 4 2 2 5 49 (rad/sec): 147.0 174.0 315.0 130.0 168.0Chord (ft): 0.83 0.95 0.40 0.61 0.54Span (ft): 3.1 3.3 1.4 4.0 3.3Twist (deg): -8.8 -- -8 0 -8Cdo: 0.009 0.009 0.009 0.0105 0.015

FuselageWidth (ft): 3.96 9.08 4.57 7.08 7.0Length (ft): 49.1 45.9 23.0 31.3 43.4EFPA (sqft): 34.7 25.0 5.0 31.3 11.6EFPA (sqft): 45.8 37.5 10.8 36.0 30.0V: 154 132 116 120 155Range (nmi): 246 238 330 505 404Rate of Climb (fpm): 2490 1810 500 -- 425Hover Ceiling (IGE): 14200 14200 7100 3700 62000Hover Ceiling (OGE): 11000 10000 4200 -- 28000Tail length (ft): 29.7 25.8 15.2 36.6 26.5

WeightAirframe (lbs): 11010 6430 1160 13600 5600Load (lbs) 2020 2450 960 1760 2500Fuel (lbs): 1620 1600 400 5640 1880Total (lbs): 14660 14200 2550 21000 10000

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Helicopter ParametersUH-60A CH-54B CH-53D CH-53E

Main RotorRadius (ft): 26.8 36.0 36.1 38.5Number of blades: 4 6 6 7Height AGL (ft): 11.2 17.6 15.8 16.0Q (rad/seC): 27.2 19.4 19.4 18.7Chord (ft): 1.75 1.97 2.17 2.44Span (ft): 29.3 29.8 28.9 28.6Twist (deg): -18 -8 -6 -13.6Odo: 0.008 0.0095 0.0095 0.009DL: 8.95 10.3 10.3 15.0

Tail RotorRadius (ft): 5.5 8.0 8.0 10.0Number of blades: 4 4 4 402 rad/seC): 125.0 66.0 83.0 73.0Chord (ft): 0.81 1.28 1.28 1.28Span (ft): 4.25 6.45 6.45 8.53Twist (deg): -18 -8 -8 -8Cdo: 0.008 0.0105 0.0095 0.0095

FuselageWidth (ft): 7-75 7.08 8.83 8.83Length (ft): 50.1 70.2 67.2 99.0EFPA (sqft): 25.7

65.0 47.3 120.0EFPA (sqft): 30.8 99.4 90.0 63.6V: 156 110 164 146Range (nmi): 275 200 242 400Rate of Climb (fpmn): 200 189 625 325Hover Ceiling (IGE): 7800 6400 14000 6000Hover Ceiling (OGE): 3900 2400 8000 1400Tail length (ft): 31.5 44.5 44.5 48.0

WeightAirframe (ibs): 10680 19230 23630 24790Load (lbs): 7270 14190 14030 15480Fuel (lbs): 2350 8580 4340 25480Total (lbs): 20250 42000

42000 73500

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HD-8

- 7 40-77

- -- ~-)

.7 -

77_ _-

(2- -e--100 1)SNOI 1-.d ------ CDi~i

* ~- ..- .- - - '~1:~79


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I'D-9

HELICOPTER DESIGN COURSE HANDOUTTail Geometry Factors

The following factors are based on analysis of severaltypical helicopters.

Generalized DataTail radius (ft): R = 1.3 * F W / 1000Tail RPM: Q = 4.5 * Main rotor RPMTail Cdo: Cdo = 0.0138 * Main rotor Cdo

Group: I II IIINumber of blades: 2 3 - 4 4 - 7

80

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HD-10

.70

.60-i0 2 4 6 8ANGLE OF ATTACK (DEG)

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HD-11

HELICOPTER DESIGN COURSE HANDOUTEngine Selection Parameters

The following turboshaft powerplants are available forthe helicopter design. Data are presented on a per enginebasis.Engine: A B C D E FDry Weight (lhs): 136 290 338 709 723 720SHP (SSL) Military: 317 725 1400 1800 2910 4110

Normal: 270 630 1250 1530 2450 3670Cruise: 243 550 1125 1150 2205 3300

SFC (SSL) Military: 0.697 0.620 0.610 0.595 0.490 0.472Normal: 0.706 0.639 0.620 0.616 0.511 0.476Cruise: 0.725 0.658 0.640 0.661 0.525 0.484

Initial Cost: $90K $100K $200K $580K $640K $700KYearly OperatingCost (per hour): $8 $16 $20 $35 $40 $60Yearly MaintenanceCost (per hour): $25 $50 $100 $125 $160 $220

MTBMA (hrs): 3.5 3.0 2.0 3.0 4.0 3.5MDT (hrs): 0.7 0.6 0.5 1.3 2.0 2.6MTBF (hrs): 185 210 205 285 280 320MTBR (hrs): 600 750 800 800 1500 750Replacement Cost: ----------- 1.35 * Initial------------Salvage Cost: ----------- 0.80 * Initial------------Note: These are all existing engines; therefore, the re-search and development costs have been absorbed into theinitial cost.

32

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ .. .........., JL I . . - .. . - ..


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Engine Selection Parameters

Engine Installed Weight:Engine installed weight includes the dry weight of the

engine(s) plus the installation fraction (exhaust system,cooling, controls, starting system and lubrication)multiplied by the dry weight. The installation fraction canbe determined from the following data.

Dry weight Installation Fraction(lbs)

100 - 300 0.29301 - 700 0.27701 - 1100 0.24

> 1100 0.20Transmission and Oil Weight:

W = 0.35 * SHPWeighting Factors:

All parameters factors in the engine selection processare to be weighted equally.

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APPENDIX CEXAMPLE OF CONCEPTUAL HELICOPTER DESIGN

CONTENTSChapter Page1. INTRODUCTION . . ................. . . . . 89

PROCEDURE . . . . . . . . ....... . . . . . 89ASSUMPTIONS ....... .................. . 892. MAIN ROTOR DESIGN ...... ................. 90

MAKE A ROUGH ESTIMATE OF THE MANUFACTURER'S EMPTYWEIGHT ........ ................ 90MAKE A ROUGH ESTIMATE OF GROSS WEIGHT . . . . . 90CALCULATE THE MAXIMUM TIP VELOCITY ........ . 90DETERMINE THE ROTOR RADIUS .. ......... 91DETERMINE A FIRST-CUT ROTATIONAL VELOCITY .... 91MAKE A FIRST-CUT DETERMINATION OF THRUSTCOEFFICIENT .......... ............ 91DETERMINE THE BLADE SOLIDITY"..... . 92DETERMINE THE NUMBER OF MAIN ROTOR BLADES TO'BEUSED .......... .................. 92DETERMINE THE BLADE CHORD.-. . . ...... .. 92DETERMINE THE AVERAGE LIFT COEFFICIENT . . . . . 93CHOOSE AN AIRFOIL SECTION FOR THE MAIN ROTORBLADES ......... ................ . . 93DETERMINE AVERAGE LIFT CURVE SLOPE AND AVERAGEPROFILE DRAG COEFFICIENT ... ............ 93

3. PRELIMINARY POWER CALCULATIONS ... ........... . 94MAKE FIRST ESTIMATE OF THE POWER REQUIRED TOHOVER ................. ........ 94MAKE SECOND GROSS WEIGHT ESTIMATE .. ......... 94ESTABLISH FIGURE OF MERIT AT APPROXIMATELY0.075 ............ .. ...... 95REFINE SECOND GROSS WEIGHT ESTIMATE. 96MAKE THIRD ESTIMATE OF POWER REQUIRED TO HOVER 96REPEAT THE GROSS WEIGHT ESTIMATE AND THE HOVERPOWER REQUIRED ITERATION . ...... 97DETERMINE THE POWER REQUIRED'TO HOVEi IGE, SSL 98DETERMINE THE PARASITE POWER REQUIRED IN FORWARDFLIGHT . . ......... . . . . . . . . . . . . 99

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DETERMINE MAIN ROTOR POWER REQUIRED AND THE MACHNUMBER OF THE ADVANCING BLADE TIP FOR FORWARDFLIGHT ......................... 99

4. TAIL ROTOR DESIGN .......... . . . ........ 101MAKE PRELIMINARY DETERMINATIONS OF TAIL ROTORGEOMETRY ... ......... . . . . ...... .101DETERMINE TAIL ROTOR POWER REQUIRED AT HOVER OGE,SSL ......... .. 101DETERMINE TAIL ROTOR POWER REQUIRED'AND'TIP'MACHEFFECTS FOR FORWARD FLIGHT ..... ............ 102

5. POWER CALCULATION REFINEMENTS ........... . . 104DETERMINE TOTAL POWER REQUIRED FOR HOVER ANDFORWARD FLIGHT ................ . . . . . . 104DETERMINE COMPRESSIBILITY CORRECTION . . . . . . .104DETERMINE THE REQUIRED RSHP AT MAXIMUM VELOCITY .105DETERMINE THE REQUIRED RSHP FOR HOVER (IGE) AT THESPECIFIED CEILING ................... 06DETERMINE THE TOTAL ESHP REQUIRED ......... 107

6. ENGINE SELECTION . . . . ................. 108SELECT TYPE AND NUMBER OF ENGINES .. ........ .108REVISE GROSS WEIGHT AND POWER REQUIRED ........ 108DETERMINE FUEL FLOW RATES AT VARIOUS POWERSETTINGS ......... ..................... 108

7. RANGE AND ENDURANCE CALCULATIONS .... ......... . 110DETERMINE THE SLOPE OF THE FUEL FLOW VERSUS SHPLINE AND THE ZERO HORSEPOWER INTERCEPT ... ...... 110COMPUTE THE ZERO HORSEPOWER INTERCEPT AT THESPECIFIED DENSITY ALTITUDE ... ........ 110DETERMINE THE ZERO HORSEPOWER INCREM.ENT . . . .ilDETERMINE THE MAXIMUM RANGE VELOCITY. ........ .111DETERMINE THE MAXIMUM ENDURANCE VELOCITY AND THEREQUIRED FUEL FLOW RATE AT THIS VELOCITY ...... .111DETERMINE THE POWER REQUIRED AT SPECIFICATIONCRUISE VELOCITY AND THE REQUIRED FUEL FLOW RATEAT THIS VELOCITY ..............._ 113DETERMINE THE TOTAL FUEL REQUIREMENTS FORSPECIFIED MAXIMUM RANGE ..... ............. 113

8. MISCELLANEOUS CALCULATIONS ..... ............. 114COMPUTE DESIGN GROSS AND EMPTY WEIGHT . . . . . . 114DETERMINE RETREATING BLADE STALL VELOCITY . . . . 114DETERMINE BEST RATE OF CLIMB . . . . . . . . . . . 115

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LIST OF TABLES

Table page1. Weight Estimation Table . . . . . . . . . . . . . 952. Main Rotor Power Profile . . . . . . . . . ... 1003. Tail Rotor Power Profile . . . . . . . . .. .. 1034. Total Rotor Power Profile . . . . . . . . . .. . 1065. Engine Selection Criteria . . . . . . . . . . . . 1096. Best Rate of Climb Iterations . .. .. .. . .. 1167. Maximum Hover Altitude (IGE) Iterations . . .. . 1178. Service Ceiling Iterations .. .......... . . 1189. Final Summary .................... . . . .. 119

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4i

LIST OF FIGURES

Figure page1. Maximum Range Velocity . . . . . . . . . . . . . . 1112. Maximum Endurance Velocity...... . . . . . . 112

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Chapter 1INTRODUCTION

1.1 PROCEDUREThis design example is for the conceptual design of a

single main rotor, utility helicopter. The design methodI1 utilizes closed form formulas and symbology obtained from

the design manual [Ref. 1] written for use in AE4306. Italso uses approximations from historical data given in the

various AE4306 handouts (see Appendix B). This example waswritten using the specifications contained in IID-1 forDesign Group I.

1.2 ASSUMPTIONSThere have been several assumptions made in the design

process as per the instructions given in Reference 1. Theseassumptions are mentioned as they occur in the designprocess.

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Chapter 2MAIN ROTOR DESIGN

2.1 MAKE A ROUGH ESTIMATE OF THE MANUFACTURER'S EMPTYWEIGHT.

The specification maximum gross weight from HD-I is11,000 lbs. The graph of historical weight ratios (HD-2)indicates that the manufacturer's empty weight is 60% ofthe gross weight. Therefore, the first estimate ofmanufacturer's empty weight is 6,600 lbs.

2.2 MAKE A ROUGH ESTIMATE OF GROSS WEIGHT.An estimated gross weight which is 80% of the specifi-

cation value of gross weight should be used. The specifica-tion value of gross weight from HD-i is 11,000 lbs.W = 0.8 * 11,000. = 8,800. lbs

2.3 CALCULATE THE MAXIMUM TIP VELOCITY.At a hover, the main rotor tip Mach number should not

exceed 0.65; therefore, M = 0.65. At standardsea level the value of the ratio of specific heats is 1.4,the local gravitational constant is 32.2 ft/sec 2 , the gascons.ant is 53.3 and the temperature is 518.688 degrees R.a= Vy* g*R*T'

1.4 * 32.2 * 53.3 * 518.688 1= 1116.3713 ft/secV = M * a

= 0.65 * 1116.3713 - 725.6413 ft/sec90


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2.4 DETERMINE THE ROTOR RADIUS.Using HD-3 a disk loading value of 6.0 was chosen. The

maximum value of main rotor radius given in HD-1 is 27 ft.R = . W / (DL * ir)

= 8800.0 / (6.0 * 3.1416) 21.6068 ft

2.5 DETERMINE A FIRST-CUT ROTATIONAL VELOCITY.The maximum tip velocity is 725.6413 ft/sec from Step

2.3. The specification maximum forward velocity is 202.6667ft/sec from HD-I. The design rotor radius is 21.6068 ftfrom Step 2.4.Q = V / R

- 725.6413 / 21.6068 = 33.5839 rad/sec2.6 MAKE A FIRST-CUT DETERMINATION OF THRUST COEFFICIENT.

The specification density altitude is 7122.1.3 ft fromjHD-I,t which the density is 0.0019196 slugs/ft. Therotational velocity is 33.5839 rad/sec from Step 2,5.

equals the value of gross weight found in S.ep 2.2.Using the main rotor radius found in Step 2.4, the mainrotor area is 1466.6645 ft2 .V = Q * R

- 33.5839 * 21.6068 = 725.6413 ft/secC - T / [A *p * V2]

= 8800.00/ [1466.6645*0.0019196*(725.6413)2] - 0.0059

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2.7 DETERMINE THE BLADE SOLIDITY.The maximum forward velocity is 202.6667 ft/sec and the

tip velocity is 725.6413 ft/sec from Step 2.6. Using themaximum advance ratio and HD-4, the blade loading is 0.1065.u = V / V

= 202.6667 / 725.6413 = 0.2793a = C / BL

= 0.0059 / 0.1065 = 0.0554

2.8 DETERMINE THE NUMBER OF MAIN ROTOR BLADES TO BE USED.Four rotor blades will be used. (Discuss reasons.)

2.9 DETERMINE THE BLADE CHORD.The solidity is 0,0554 from Step 2.7. The number of

blades (Step 2.8) is 4 and the rotor radius (Step 2.4) is21.6068 ft.c = (a * * R) / b

= (0.0554 * 3.1416 * 21.6068) / 4 = 0.9401 ftAR= R / c = 21.6068 / 0.9401 = 22.9827Since the aspect ratio was not within the limits of 15 to20, the rotational velocity (Step 2.5) was reduced to 31.00rad/sec. Steps 2.6 and 2.7 were recalculated with thefollowing results.l: 31.00 rad/sec V: 669.8108 ft/secC: 0.0070 P: 0.3026BL: 0.1038 U: 0.0674%: 1.1444 ft AR: 18.8803

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2.10 DETERMINE THE AVERAGE LIFT COEFFICIENT.The thrust coefficient is 0.0070 from Step 2.10. The

solidity is 0.0674 from Step 2.10C = ( 6 * C ) / ,

= ( 6 * 0.0070 ) / 0.0674 - 0.62312.11 CHOOSE AN AIRFOIL SECTION FOR THE MAIN ROTOR BLADES.

The selected airfoil section is airfoil "A" from HD-5.(Discuss reasons.)2.12 DETERMINE AVERAGE LIFT CURVE SLOPE AND AVERAGE

PROFILE DRAG COEFFICIENT.From HD-5, the profile drag coefficient for airfoil "A"

is 0.010 and the lift curve slope (CL a ) is 6.4458 perradian.

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Chapter 3PRELIMINARY POWER CALCULATIONS

3.1 MAKE FIRST ESTIMATE OF THE POWER REQUIRED TO HOVER.The HP-41CV program entitled HOVER (Ref. 3] was used to

compute these values. The current value of all designparameters are listed below.DL: 6.00 W: 8800.00 lbsR: 21.61 ft 2: 31.00 rad/secV: 669.81 ft/sec C: 0.0070: 0.3026 BL: 0.1038: 0.0674 b: 4

c: 1.1444 ft AR: 18.88C: 0.6231 Cdo: 0.0100DA: 0.00Pi: 583.91 hpPo: 160.56 hpPT: 744.48 hp3.2 MAKE SECOND GROSS WEIGHT ESTIMATE.

- Using HD-3, the first gross weight estimate used in themain rotor design process was refined. The useful load wascomputed using 200 lbs per crewmember. Table 1 shows theresult of the second gross weight estimate.

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TABLE 1Weight Estimation Table

------------ ITERATION-------------FIRST SECOND THIRD FOURTH

SOLIDITY: - 0.0674 0.0674 0.0745RADIUS: - 21.6068 21.6068 20.7192TOTAL POWER: - 744.4755 734.3833 681.3628ROTOR-LLADES: - 555.89 488.44 444.46

HUB/HINGES: - 323.90 284.59 250.34TOTAL: - 879.79 773.03 694.80

PROPULSION: - 893.37 881.26 817.64FUSELAGE: - 1386.00 1217.82 109S).28FLIGHT CONTROLS: - 396.00 347.96 311.51ELECTRICAL: - 396.00 347.96 311.51FIXED EQUIPMENT: - 1848.00 1623.76 1453.70EMPTY: 6600.00 5799.16 5191.80 4679.43FUEL: - 1500.00 1500.00 1500.00USEFUL LOAD: - 1400.00 1406.00 1400.00GROSS: 8800.00 8699.16 8091.80 7579.43

3.3 ESTABLISH FIGURE OF MERIT AT APPROXIMATELY 0.075.The induced power from Step 3.1 was between 70 to 80% of

the total power from Step 3.1. In order to keep the sameradius, the disk loading was reduced to 5.93 (see Step 2.4).The thrust coefficient (Step 2.6), the solidity (Step 2.7),the chord (Step 2.9), the aspect ratio (Step 2.9), and thelift coefficient (Step 2.10) were adjusted and the hoverpower was recalculated (Step 3.1) using the second grossweight estimate with the following results.

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DL: 5.93 W: 8699.16 lbsR: 21.61 ft s: 31.00 rad/secV: 669.81 ft/sec C: 0.0059u: 0.3026 BL: 0.1038a: 0.0674 b: 4c: 1.1444 ft AR: 18.88C: 0.6231 Cdo: 0.0100DA: 0.00Pi: 573.73 hpPo: 160.66 hpPT: 734.38 hpThe induced power from Step 3.1 was between 70 to 80% of thetotal power from Step 3.1; therefore the Figure of Merit wasapproximated.Figure of Merit = 573.7261 / 734.3833 = 0.7812

3.4 REFINE SECOND GROSS WEIGHT ESTIMATE.See Table 1 for the values of the third iteration.

3.5 MAKE THIRD ESTIMATE OF POWER REQUIRED TO HOVER.Since the third gross weight estimate was much smaller

than the second estimate, the radius (Step 2.4) was changedso that the disk loading would not be too small.R = W / (DL * 7)"

= 8091.8012 / (6 * 3.1416)' = 20.7192 ftSince the radius was changed, a new maximum allowablerotational velocity was calculated (Step 2.5) and the

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low.

current value of rotational velocity did not exceed themaximum allowable value. Then Steps 2.6, 2.7, 2.9, 2.10,and 3.1 were adjusted using the third gross weight estimatewith the following results.DL: 6.00 W: 8091.80 lbsR: 20.7192 ft R: 31.00 rad/secV: 642.30 ft/sec C: 0.0076u: 0.3155 BL: 0.1020a: 0.0745 b: 4c: 1.2123 ft AR: 17.09C: 0.6121 Cdo: 0.0100DA: 0.00Pi: 537.55 hpPo: 143.82 hpPT: 681.36 hpThe induced power was between 70 to 80% of the total powerso the Figure -Z Merit was recalculated.Figure of Merit = 537.5475 / 681.3628 = 0.78893.6 REPEAT THE GROSS WEIGHT ESTIMATE AND THE HOVER POWER

REQUIRED ITERATION.Table 1 shows the result of the fourth gross weight

estimate which is 93.67% of the previous estimate. Sincethe fourth gross weight estimate was close to the previousweight estimate, the disk loading was reduced to 5.62 (seeStep 2.4) rather than calculating a new radius. The thrustcoefficient (Step 2.6), the solidity (Step 2.7), the chord

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(Step 2.9), the aspect ratio (Step 2.9), and the liftcoefficient (Step 2.10) were adjusted and the hover power(Step 3.1) was recomputed using the fourth gross weightestimate with the following results.DL: 5.62 W: 7579.43 lbsR: 20.7192 ft S: 31.00 rad/secV: 642.30 ft/sec C: 0.0071ii: 0.3155 BL: 0.1020c: 0.0696 b: 4c: 1.1327 ft AR: 18.29C: 0.6121 Cdo: 0.0100DA: 0.00Pi: 486.86 hpPo: 134.37 hpPT: 621.24 hpThis hover power estimate is 91.18% of the previous estimate.The induced power from Step 3.1 was between 70 to 80% of thetotal power from Step 3.1; therefore the Figure of Meritwas approximated.Figure of Merit = 486.8628 / 621.2352 = 0.7837

3.7 DETERMINE THE POWER REQUIRED TO HOVER IGE, SSL.An HP-41CV program entitled HOVER [Ref. 3] was used to

compute the hover power in ground effect at standard sealevel. A hover height of 10 feet above ground level wasused.

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Pi: 371.7278 hpPo: 134.3724 hpPT: 506.1002 hp3.8 DETERMINE THE PARASITE POWER REQUIRED IN FORWARD

FLIGHT.Using HD-8 and the latest estimate of gross weight

(7579.43 lbs), the equivalent flat plate area loading is330.0 psf.EFPA = W / Loading

= 7579.43 / 330.0 - 22.9680 ft2The values of parasite power have been listed in Table 2.3.9 DETERMINE MAIN ROTOR POWER REQUIRED AND THE MACH

NUMBER OF THE ADVANCING BLADE TIP FOR FORWARD FLIGHT.A program entitled FLIGHT [Ref. 3.] for use with the

HP-41CV programmable calculator was used to calculate thevalues given in Table 2.

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helicopted deisgn