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THESISAN ANALYSIS OF

THREE APPROACHES TO THE HELICOPTER PRELIMINARYDESIGN PROBLEM

by

Allen C. Hansen

March 1984

Thesis Advisor: D. M. Layton

Approved for public release; distribution unlimited.

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4. TITLE (old &Aeee010) 19S1 -. _ OF 14EP0ftr a P9CRIO COVERE0SAn Analysis of Three Approaches to the Master's ThesisHelicopter Preliminary Dcsiga Problem __M1arch 1981.

4. P914FORMING ORG. 049004T NUNSER9

""" 1. AUTHON(eJ •S. CONTRACT Oft GOINT NUNOSM,()

Allen C. Hansen

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Naval Postgraduate School,Monterey, California 93943

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SensitivityPreliminary Helicopter Design

, Carpet PlotsHESCOMP

.•. AISTRACT (AIMue 44 Foemse sidleI. D... . .a,, 4 ..Idatg by b60.k .) ....

Three methodologies from which to approach the problem ofpreliminary helicopter design are explored in this paper. Thefirst is a sensitivity analysis of the basic helicopter per-formance equations. The purpose here is to ascertain wherereasonable simplifications can be made that do not seriously

-. 5 degrade the accuracy of the results. The second is a graphicalparametric design method, known as Carpet Plots. In this method

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a graphical solution is developed to meet the design criteriaof the helicopter. In the third, an overview of Boeing Vertol'sHelicopter Sizing and Performance Computer Program is given.The computer routines which enable a person to access HESCOMP onthe Naval Postgraduate School main frame IBM system are alsoprovided.

4i.

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Approved for public release; distribution unlimited.

An Analysis ofThree Approaches to the Helicopter Preliminary

Design Problem

by

Allen C. HansenLieutenant, United States Navy

B.A., University of Pennsylvania, 1976

Submitted in partial fulfillment of therequirements for the degree of

*• MASTER OF SCIENCE IN AERONAUTICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOLMarch 1984

Author: ~(

"Approved by:Thesis Advisor

Chairman, Department of Aeronautics

/ Dean of Science and Engineering

3

ABSTRACT

*• •Three methodologies from which to approach the problem

of preliminary helicopter design are explored in this paper.

The first is a sensitivity analysis of the basic helicopter

performance equations. The purpose here is to ascertain

where reasonable simplifications can be made that do not

seriously degrade the accuracy of the results. The second

is a graphical parametric design method, known as Carpet

Plots. In this method a graphical solution is developed

to meet the design criteria of the helicopter. In the

third, an overview of Boeing Vertol's Helicopter Sizing and

Performance Computer Program is given. The computer

routines which enable a person to access HESCOMP on the

Naval Postgraduate School main frame IBM system are also

provided.,-

4

TABLE OF CONTENTS

I INTRODUCTION . . . . . . . . . . . . . . . . . . 10

i A. GENERAL . . . . . .. . . . . . . . ... 10

B. OBJECTIVE . .. . ... . ... . 11

SII. SENSITIVITY ANALYSES OF BASICHELICOPTER EQUATIONS ......... . . . 13

A. DESCRIPTION OF PROBLEM . . ............ 13

B. SOLIDITY . . . . . . . . . . . . . . . . . . 13

C. DISK LOADING . . . . . . . . . . . . . . . . 14

D. POWER LOADING . . . . . . . . . . . . . . . 14

E. COEFFICIENT OF THRUST AND POWER . . . . .. 14

F. HOVER POWER . . . . . . . . . . . . . . . . 16

G. HELICOPTER SIZING ...... . . . . . . . 18

H. FIGURE OF MERIT . . . . . . . . . . . . . . 19

I. TAIL ROTOR SIZING . . . . . . . . . . . . . 23

J. FORWARD FLIGHT POWER CONSIDERATIONS . . . . 23

K. DENSITY EFFECTS ON TOTAL POWER . . . . . . . 30

III. CARPET PLOT DESIGN STUDY. . . ............ 32

A. DESCRIPTION OF PROBLEM . . . . . . . . . .. 32B ASUPIN ... ............... 33SB . A S S U M P T I O N S . . . . . . . . . . . . . . . . 3

C. METHODOLOGY . ...... . . . . . . . . . . 34D . HOVER EQUATIONS .............. 35

E. WEIGHT EQUATIONS . . . . . . . . . . . . . 39

F. GRAPHICAL ANALYSIS .... ............. ... 45

let I V H s COo .. . . . . . . . . . . . .. . . .A. DESCRIPTION OF PROGRAM . . . . . . . . 54

B. PROGRAM MODIFICATIONS ANDIMPLEMENTATION ...... . S6

C. PROGRAM FLOW . . . . . . . . . . . . . 57

D. PROGRAM INPUT .... ............. ... 59

E. PROGRAM OUTPUT . . . . . . . . . . . 59

V. CONCLUSIONS AND RECOMMENDATIONS . . . . . . 60

APPENDIX A: NOMENCLATURE ...... ..... . 62

APPENDIX B: CARPET PLOT FORMULATION FOR20,000 LB. CLASS HELICOPTER ..... 64

APPENDIX C: CARPET PLOT METHODOLOGY FLOWCHART AND EXAMPLE PROGRAMS . . . . . . 73

APPENDIX D: PROGRAMS TO ACCESS HESCOMP . . . . .. 87

APPENDIX E: HESCOMP INPUT AND OUTPUT EXAMPLES . . 92

LIST OF REFERENCES . . .. ... .. .. . . . . 115

INITIAL DISTRIBUTION LIST ....... ............. 116

.4

6

LIST OF TABLES

2.1 HELICOPTER WEIGHT COMPARISON .. . . . . . . 20

"2.2 TAIL ROTOR SIZING . . . . . . . . . . . . . . . 24

4.1 HELICOPTER CONFIGURATIONS WHICH MAY BESTUDIED USING HESCOMP . . ..................... .ss

4.2 PARTITIONED DATA SET ............. 57

/7N

.9g.

S,,

m7

LIST OF FIGURES

2.1 FM VERSUS BLADE LOADING CT/a . . . . . . . . . 21

2.2 POWER REQUIRED VERSUS FORWARD VELOCITY ..... 25

3.1 WEIGHT EQUATION PLOT: CLR a 0.5 . . . ..... 40

3.2 HELICOPTER CARPET PLOTS: CLR ' 0.S ....... 46

3.3 HELICOPTER CARPET PLOTSFAMILY OF SOLUTIONS . . . . . . . . . . . . . . . 48

." 3.4 HELICOPTER CARPET PLOTS ROTORDIAMETER AND WEIGHT LIMITS ...... . . . . .49

3.5 ASPECT RATIO BOU7NDARY PLOT . . . . . . . . . 51

3.6 HELICOPTER CARPET PLOTSFINAL SOLUTION . . . . . ....... . . . ... . . . 53

4.1 HESCOMP PROGRAM FLOW .............. 58

8

'S..t

ACKNOWLEDGMENT

I would like to acknowledge the invaluable assistanceI of Professor Donald M. Layton in this endeavor. His

encouragement and support greatly contributed to making

this both an interesting and worthwhile experience.

'I

:99

, ON

N/ -

I• INTRODUCTION

A. GENERAL

The helicopter design process, the subject of numerous

articles and studies is an evolving discipline that borders

on being an art. A successful design must balance the

user's needs and desires against practical capabilities.

With the introduction of composite materials and new

technologies, principally in rotor and engine performance,

significant advances have been made in helicopter capabil-

ities. In some instances, the performances of hybrid

helicopter designs rivals that of a similarly sized conven-

tional aircraft. For example, the YVX, a joint Boeing-Bellventure, will have the hover and low speed capabilities

of a helicopter while being able to cruise at 300 knots.

Viable commercial and military helicopter designs are

V only thirty years old. The first major use of helicopters

occurred during the Korean conflict. To put this in

perspective, the first large scale use of conventional type

aircraft was in World War I.

Helicopter design can proceed on a number of different

levels, ranging from comprehensive computer design programs

to preliminary analysis using simplifications of the basic

* performance equations. Each has its merit and place.

Computer-aided design provides a great deal of data.

10

Generally, these programs integrate aircraft configuration

sizing, performance and weight calculations in an iterative

process. An example of a computer design program for heli-

copters is the Helicopter Sizing and Performance Computer

Program [HESCOMP], orginally developed by Boeing-Vertol

. for NASA. This program is currently used as a wide number

of institutions conducting studies in helicopter design.

On the opposite end of the spectrum would be sensitivity

design studies using the performance cquations. Surprisingly

v. accurate simplications of these equations can be made. This

provides the designer with an excellent method for doing

first cut preliminary helicopter sizing at a low cost.

B. OBJECTIVE

This report is an investigation of several of themethods employed in the preliminary design of a helicopter.

Conceptually, the report can be divided into three parts.

In the first section, a sensitivity analysis of the basic

performance equations is performed. The purpose here is to

ascertain where reasonable simplications can be made

that do not seriously degrade the accuracy of the result.

In the second section a graphical method of doing

parametric de&ign studies, known as Carpet Plots, is

developed. This method allows the user to formulate a

graphical solution matrix to meet the design criteria

specified for the helicopter. Carpet Plots are

11

W-1, K 4 dWa %W41WT r r

particularly instructive since they give visual insightinto the interplay of the various design parameters.

In the last section, an overview of HESCOMP is given.

Programs are developed which enable a person to access

HESCOMP on the Naval Postgraduate School Main Frame IBM

C.i system.

* 4

.12

V,

Wwu ' 'U

II. SENSITIVITY ANALYSES OF BASIC HELICOPTER EQUATIONS

A. DESCRIPTION OF PROBLEM

In preliminary helicopter design, there Pre a number of

instances where a quick first cut analysis would be

extremely helpful. This is especially true in determining

the preliminary size of the helicopter required to meet

the specifications.

Historically, there are a number of variables in the

performance equations of helicopters which may be treated'UI

as constants. This may allow for significant simplifica-

tions and aid in the preliminary design process.

in this section, a sensitivity analysis of the per-

formance equations is done. In a sensitivity analysis,

each parameter [or variable] is varied in order to deter-

mine its effect on the equation. Variables which are

shown to have little effect may be treated as constants and

4. the equation simplified accordingly.

B. SOLIDITY"Solidity, a , is the fraction of the disk area that is

composed of blades. It is a function of b , the number

of blades, of a constant cord, c , at a radius, R:

bc (2.1)aa R

13

C. DISK LOADING:

Disk loading is defined as the ratio of the weight to

the total area of the rotor disk.

DL = WEIGHT

(2.2)

mw. W 21a W W (lb/ft 2

'p 7rR

D. POWER LOADING

Power loading is the ratio of weight to input power.

SW

PL - n p7 (lb/hp] (2.3)

In a hover, thrust equals weight; this allows us to

rewrite the power loading for the hover condition as

T T ROTOR THRUSTPL = • = ROTOR HORSEPOWER (lb/hp] (2.4)

in

E,. COEFFICIENT OF THRUST AND POWER

The coefficient of thrust, CT , is a non-dimensional

coefficient which facilitates computations and comparisons:

CT a T T (2.S)

Similarly, a coefficient of power, C , has been

I established as:

14

P P

C -•v 3 (2.6)~' ApV~ T R p(nR)

No significant simplifications can be made to either of

these coefficients. However, it should be observed that

the coefficient of thrust is inversely proportional to the

square of the rotor tip velocity, while the coefficient of

power is inversely proportional to the cube.

Assuming all other factors being equal, increasing the

rotor tip velocity from 600 fps to 700 fps (an increase of

16.7 percent] will have the following result on these

coefficients.

CT AP T

ApVT.67T

Ap(I.167) 2 (2)

S-T

Ap(l.361)

The coefficient of thrust is reduced by 26.9 percent.

Similarly, for the coefficient of power:

15

cm

C P P3

P .(2.6)ApFl1677)

AP (1,589)

The coefficient of power is reduced by 37.1 percent.

F. HOVER POWER

The total power in a hover is made up of two terms,

profile power, Po , and induced power, Pi .

Utilizing black element theory the profile power

required to hover can be expressed as:

Po = a rdo p A(QR) 3 (2.7)

The induced power predicted by momentum theory is:

P i V Vin T

(2.8)

SP~~T 3/2+ o(29

The total power required to hover is:

T .- + p 0 (2.9)

16

1- w...

P T3/ 2"T ... A(R) (2.10

Donald M. Layton in Helicopter Performance, [Ref. 1],

found that for the optimum hover power, the induced power

is equal to twice the profile power. The analysis was

performed in the following manner.

By assuming constant weight, density, solidity, and anaverage profile drag coefficient, as well as a fixed

rotational velocity, equation (2.10) reduces to

C1P +r- C2 R2 (2.11)

where C1 and C2 are constants.

As equation (2.12) shows, profile power increases as

the square of the blade radius while the induced power

decreases with increasing blade radius.

The optimum hover power with respect to rotor radius

can be determined by taking the differential and setting it

equal to zero.

dP a 0 - 1 2 C2 R (2.12A)2

C1 2or =- 2 C2 R (2.12B)

which implies Pi - 2 Po (2.12C)

17

1 7. . . . . .;, r. . . . . .. . . . e e

G. HELICOPTER SIZING

A simplified relationship between the total power

required, gross weight and rotor radius can be developed in

the following manner.

The total power required to hover equation for the main

rotor was developed in the preceding section and is

repeated here for clarity.

PT " i + P0 (2.9)

T K + ar Cdo PIT Vtip 2 (2.0)

In a hover, thrust equals weight. Solving equation

(2.11) for weight one obtains:

W3/2 a [PT - 1a Cdo PT VT 3 R -2 (2.13)

This equation may be further simplified if it is

assumed that the density, average profile drag coefficient

and tip velocity are constants; these are reasonable assump-

tions. Historically, the average profile drag coefficient

of a helicopter has been approximately 0.01. The operating

environment of today's helicopters, especially military,

is below 5,000 feet agl. This allows for the use of the

standard sea level value for density with little error.

Primarily, due to tip mach effects, the upper limit on the

rotor tip velocity is in the range of 700 fps.

18

The resulting equation with these assumptions incor-

porated into a constant, X , is:

W a [47.527 PT R - K bc] 2 / 3 (2.13)

Equation (2.13) can be further reduced when the order

of magnitude of the two terms is considered.

47.527 PT R >> K1 bc

Thus,

W ( [47.527 PT RJ2/ 3 (2.14)

To determine how accurate this simplification is, the

equation is used to approximate the total weight of a

number of helicopters for which the parameters are available.

As Table 2.1 indicates, the weight approximation formula

yields values within six percent of the actual total weight

of these helicopters.

"H. FIGURE OF MERIT

A figure of merit, FM , has been defined for the

helicopter as the ratio of the ideal rotor induced power to

the actual power required-to hover, with non-uniform inducedV.,veoiy

velocity, tip losses and profile drag power.

19

TABLE 2.1

HELICOPTER WEIGHT COMPARISON

HELICOPTER TOTAL GROSS CALCULATED PERCENT OF

WEIGHT GROSS WEIGHT ACTUAL

(1000 ibs) (1000 Ibs) GROSS WEIGHT

AH-64 14.66 14.69 101%

UH-1N 14.20 13.74 97%

H-3H 21.00 20.63 98%

S76 10.00 9.90 99%

UH-6DA 20.25 19.33 95%

H-54B 42.00 42.00 100%

H-53D 42.00 41.00 98%

H-53E 73.SO 69.00 84%

20

a..

In a hover, the figure of merit may be written as:

FMI PL -L

(2q15)

CT 1 .5

p

The figure of merit is customarilty plotted against the

quantity CT/a . According to Zalesch [Ref. 2], CT/c , is

proportional to the average blade angle of attack and can

be used as a measure of rotor efficiency. The curve in

Figure 2.1 is based on data from Reference 2 for a typical

tail rotor helicopter.

Main Rotor Hover Performance

0.00 0.04 o.0o 0.3 ).Slhde Loadng

A Figure 2.1. FM Versus Blade Loading CT/a

21

A

Previous studies have shown that a figure of merit

between 0.70 and 0.80 is considered average.[Ref. 3]

If the induced power is between 70 and 80 percent of the

total power, the figure of merit will be approximately 0.7S.

With the figure of merit limited to values between

0.70 and 0.80, the following simplification can be made,

assuming the hover condition of thrust equaling weight and

standard sea level conditions:

FM - 32(2.16)T

For Navy helicopter design, the rotor radius has been

limited by flight deck spotting constraints to less than

30 feet; the exception to this is the H-3, R - 31 feet and

the H-53, R - 36 to 38 feet [depending on the model].

However, these two helicopters work almost exclusively from

large air dedicated ships such as the LPH, LHA and CV.

If the small deck operating assumption is made,

equation (2.16) can be further simplified to (assuming

R = 28 feet]:

(2.17)

An FM of 0.80 will yield a P to W relationship of:

PT 3/2 (2.18)

,II22

while an N1 of 0.70 yields a relationship

= _ w3/2-P 3 (2. 19)

If equation (2.17) is solved utilizing the approximate

weight relationship developed earlier of

W 3/ 2 - 47.S27 PTR (2.14)

a value for the figure of merit of 0.707 is obtained. Thisis within the historical range of values.

I. TAIL ROTOR SIZING

A historical analysis of typical helicopters [Ref. 3),

shows the following empirical relationship for the tail

rotor radius

RT c 1.3 [1 - 1 1/2 [ft] (2.20)

when comparing the results of this equation with actual

tail rotor radius data, it was found that if a multipli-

cation factor of 1.2 is used vice 1.3 a better approximation

"is obtained. The results are tabulated in Table 2.2.

J. FORWARD FLIGHT POWER CONSIDERATIONS

SThe total power in forward flight consists of induced,

profile and parasite power. If the helicopter is a single

rotor vehicle, the tail rotor power should be taken into

23

p5,'

TABLE 2.2

TAIL ROTOR SIZING

HELICOPTER ACTUAL TAIL ROTOR APPROXIMATION [FT]RADIUS [FT] [2.20] [2.21]

AH-64 4.6 4.98 4.59

UH-1N 4.3 4.90 4.52

SH-3H 5.3 5.95 5.S

S-76 4.0 4.11 3.79

UH-60A 5.5 5.85 5.4

CH-53D 8.0 8.42 7.78

CH-53E 10.0 11.15 10.29

.'241,A'

.4

.4

"I:

account, as well as all mechanical losses (transmission,

etc.] for accurate calculations. However, a reasonable

approximation can be obtained by considering only the main

rotor and increasing this power figure by several percent

to account for these losses.

Figure 2.2 is a plot of the induced, profile, parasite

and total power curves for typical tail rotor helicopter.

MAIN ROTOR POWERSSL CONDITIONS

OUT OF GROUND EF7ECT

6* ao~e 4&.0 "a w.s ins.*e M4 146.6 Ium"

VELOCTY (KNMO)

Figure 2.2. Power Required Versus Forward Velocity

The induced power drops off rapidly with increasing

forward-velocity, whereas the parasite power increases

rapidly."Parasite power is the power required to overcome the

drag forces created by the aircraft's geometry. These drag

forces are due to pressure drag and skin friction.

25

%.V4*4 ~ ~ ( * *~* -4 *~ A t . .. ..

4 ... t.

Parasite drag is extremely sensitive to the helicopter's

loading. It is generally a minimum for forward flight and

increases for sideways flight. Helicopters are generally

streamlined for forward flight and the flat ?late area is

a minimum in this direction. The equation for the parasite

power is:

P V f(2.21)p T f

The parasite power is a function of the cube of the

forward velocity. As such, with the advent of high speed

helicopters a great deal of consideration has been placed

on streamlining the geometric shape in order to reduce this

power requirement.

Blade element theory is commonly used to develop the

profile power equation for forward flight. An excellent

development of this equation is given in Reference 1.

The profile power equation in forward flight is:

Pof p A V [1 + 4.3 (2.22)

Equation (2.23) is a function primarily of the mainrotor geometry. The variable with the most significance

is the rotor tip velocity; increasing the tip velocity from

600 to 700 fps results in a 58.8 percent increase in

profile power [assuming other factors are constant].

26

The induced power is a f'nction of the induced velocity.

In a hover, the total flow through the rotor system is

induced. As the forward velocity increases, the mass flow

* rate through the rotor disc increases due to the forward

translation of the helicopter. This reduces the induced

velocity.

The equation for the induced power requirements at all

forward velocities is:

P T . Vit (2.23)

where

4 2 /V2 '1/2

Vit 2 + Vf/2V2 l .V (2.23a)

At high forward velocities, the induced power required

can be approximated as:

W2Pi WVit 2pAV£ (2.24)

The total power for forward flight is the sum of the

induced, profile and parasite powers.

PT 0P + PO + Pp (2.25)

27

P T.Vit + C p A VT3 [1 + 4.3 P

(2.25a)+ ½ 3 £ £

At high forward velocities, equation (2.23) can be

substituted into equation (2.25), resulting in:

Sw2 +1 AV 3 Vf

T do T [1 + 4.3 d

(2.26)

f V 3

If one makes the following assumptions:

W w const Cdo = const

p = const a = const

VT = const

Equation (2.26) reduce% to

K1 2 2P R + K + P (2.27)PT-2 R +p

The derivative of equation (2.27) with respect to radius is:

dPT 2KI1- + n K2 R (2.28)

R

28

0a

Setting this equal to zero, one obtains:

1*- + 2 K 2 R - 0 (2.28a)R2

R

R * 2K I + 2 K, RI 0 (2.28b)R

K1 R 2 (2.28c)R

P. - P0 (2.28d)

This defines point of minimum total power required for

VMAX range. This corroborates with the results obtained by

Waldo Carmona [Ref. 4].

If the total power required is differentiated with

respect to forward velocity and is set equal to zero, it can

be seen that

Pi = 3 P0 (2.29)

or

•% w2 3pv2

29

a" '

Solving this equation for velocity results in:

Vf = [ ft/sec (2.31)

According to Carmona (Ref. 4], this corresponds to the

best endurance velocity.

K. DENSITY EFFECTS ON TOTAL POWER

The effect of density on the total power required in

forward flight is as follows:

The general operating altitudes of a helicopter are

below 10,000 feet. The corresponding ICAO STANDARD

ATMOSPHERE range for density is

p a 0.0023769 (lb sec2 /ft ] SSL

p = 0.0017553 (lb sec 2 /ft 4] at 10,000 feet

p/pSSL varies from 1 to .7385.

The effect on the components of PT are as follows:

Induced Power:

I/p/pSSL ->l to 1

This translates to a 35 percent increase in the induced

power.

N'

30

ale

Parasite and Profile Power:

Both parasite and profile powers are directly propor-

tional to the density ratio. Therefore, as you go up in

altitude both P0 and P are reduced.

j31

III. CARPET PLOT DESIGN STUDY

A. DESCRIPTION OF PROBLEM

Preliminary helicopter design involves one with a wide

range of choices. For any given payload and performance

specifications, there a number of helicopter designs that

satisfy the requirements. The problem in the preliminary

design process is narrowing these possibilities and

selecting the design which will provide the best helicopter

for the mission.

Obviously, the operating environmental constraints help

to define the basic configuration. These constraints are

usually specified in the Request for Proposal [RFP], in the

case of a military helicopter. For example, typical

constraints placed on the design of a Navy helicopter are

the size of the ship deck and hangar from which it will be

operating, the requirement for a blade fold system, dual

engine configuration and IFR capability.

Even with these design constraints, there is still

a great deal of leeway. In order to insure that the best

helicopter design is selected, an appropriate number of

solutions satisfying the specifications should be inves-

tigated. Since each solution is generally characterizedby a different combination of design parameters, the

32

selection, according to Greenfield [Ref. 5], can best be

made through a parametric study which allows for the

* optimization of many design parameters.

One method of parametric analysis used is Carpet Plots.

This method is based on the simultaneous graphical solution

* of the weight and hover performance equations. To this

solution set is added to the environmental constraints to

the helicopters size. This effectively brackets the area

of acceptable design solutions.

This method assumes that minimum gross weight is the

criterion by which the best [or optimum] design parameters

are selected.

B. ASSUMPTIONS

1. Airfoil used is a derivative of the NACA 0012

with the following mean approximate values from Reference S.

a - slope of airfoil section lift curve, dCt/da,

per rad.

a - 5.73

6 = blade section drag coefficient

6 0 = .009

62 =.3

2. a) The tail rotor radius is assumed to be .16

times the main rotor radius [Ref. 5].

33

b) The distance between the rotors, or tail rotor

moment arm, ZTR is 1.19R [Ref. 5]. These ratios reflect

the values of maximum rotor diameter and overall length

specified as size limitations.

3. B - .97. Historical approximation (Ref. 7].

C. METHODOLOGY

In order to properly develop the weight and performance

equations required for a carpet plot design study, the

payload and performance specifications of the helicopter

are needed. This data is used to tailor the equations for

the design.

The equations will be developed here for a four-place

light helicopter. The equation development procedure is

applicable to other size helicopters; the development for a

medium helicopter, 20,000 lb weight class, is to be found

in Appendix B.

The following specification requirements which are

similar to those in Reference 5 will apply to this design:

1. The rotor diameter should be less than 35.2 feet.

2. The overall length should be less than 41.4 feet.

3. The gross weight of the helicopter should not

exceed 2,450 lbs.

4. The helicopter should be capable of hovering, out

of ground effect at 6,000 feet with an ambient air tem-

perature of 950F.

34

3

S. The useful load at hover shall consist of, as a

minimum, 200 lbs for the pilot, 400 lbs of payload and

sufficient fuel to give the helicopter up to three hours

endurance at sea level conditions.

6. Maximum speed of at least 110 knots using Normal

Rated Power, at sea level.

7. Total Power Required at 6,000 feet and 95°F shall

be not more than 206.

D. HOVER EQUATIONS

1. The main rotor power required to hover out of

ground effect is

Total Main Rotor Power [Hover] - Rotor Profile Power + Rotor

Induced Power

PT = 1.13W I D -S SOBv"•'Tp/p°

(3.1)

+6WVT p/[o 6 + 2 Lo.iI2

At an altitude of 6,000 feet and a temperature of 950

PiPo / .749395 . Therefore, equation (1) can be simplified

to: -

PT6000/95oF = .035479W[DL] 1 / 2 (3.2)

+ .91971 [10]-5(1 + 1.80779 CLR 2 )W VT

CLRo

35

The tail rotor thrust required to counterbalance the

main rotor torque is:

T 550 PTR 550 PTTTR " TR VT "W (.r93.3)

where Z TR h;.s been defined as 1.19R . With RTR defined

as .16R , the tail rotor disk loading can be written,

using equation (3) as:

DL TTR 550 PT 1

TR TT (.16R)(3.4)

550 PT DL

Greenfield [Ref. 5], in his development, assumes that

i the tail rotor tip speed is equal to the main rotor tip

speed and that 6TR '.02 and 8 TR = .90 . With these

assumptions the equation for the tail rotor power required

to hover can be written as:

PT 205.7 DL 11/2 T Hover

TRHover 0(.5)

.012605 PT+• cLRT Hover

36

The equation for the tail rotor mean blade lift coeffi-

cient can be written as

CLRTR (3.6). . 0

if it is assumed that the tail rotor is designed to counter-

balance a sea level main rotor torque equivalent to 90

percent of the installed power.

Substituting equation (3.6) into equation (3.5) one

obtains the following expression for hover tail rotor power:

r 347DL / PH 3/2

TTR6000/950 VT-wj-[ + 5.3134 (3.7)

It is assumed that the gear losses amount to 3 percent

Wand that there is a 1 percent cooling power loss, the total

brake horsepower required to hover becomes:

P PTm + PTTRT 96(.8

Empirical studies have shown that the tail rotor power

required to hover can be approximated by

PTAC * .8 [total horsepower to hover]

This allows one to write the main' rotor power required to

hover as:

PTm = (88)(PTm) (3.9)

37

Following Greenfield's [Ref. 5] development further,

if equations (3.2) and (3.7) are substituted in equation

(3.8), one obtainsSIN

PTH6000/95o - .036757 W /Ml-"

+ .95803 (10)-S [1 + 1.80779 CL2 ] W V (3.10)CLRo LRo T

+ 2473.6 Tm + 5.5348

Utilizing the approximation for tail rotor power,

equation (3.9), equation (3.10) can be solved for W

(gross weight) as a function of variables VT (tip speed),

DL (rotor disk loading), CLRo (rotor mean lift coefficient)

and PT (total power to hover).

H

K 1 - 411.51 DL 31 1 V+ 1/2173/~2 2 1K 3

V DTVT + K4 VDl-

where:

K1 P0(0 (3.11a)

.00025929 2K 0LO (1 + 1.80779 CLRo ) (3.11b)K2 = CLRo 3

38

K3 553480K3 = 5 31c

K4 3695.7 (3.1ld)4 K 5

K .95803 (1 + 1.80779 CL (3.11e)L c Ro LRo

Equation (3.11) has been programmed in Appendix B

and solved for tip speeds from 600 to 700 cps and CLR

of .3 to .7.

* Equation (3.11) is one of the two primary equations used

to obtain the data required for a carpet plot design

analysis. Generally, the variables VT , DL, CLRo and

PT I that are required for solution have specific ranges

of values, depending on the weight class of the helicopter

being designed. The graphical results of equation (3.11)

for tip speeds of 600 to 700 fps and mean lift coefficients

between .3 and .7 are illustrated in Figure 3.1.

Both the Fortran and Disspla programs, as well as a

decision making flow chart are provided in Appendix C

to aid in using this method for a design solution.

E. WEIGHT EQUATIONS

Weight equations need to be developed that realistically

reflect the sizing class of the helicopter being designed.

The evolution is greatly simplified if a specific engine

39

*.. .',.~ -

*11

N% u

0

cj+j

00

Ct)c

(7 4J

'4

5."

(Sf1) 14B.!GM sso1E

40

installation [# and horsepower] is assumed, since the

weight of a number of components depend only on the

installed power; this would include such terms as the engine

controls and accessories. Another category would be those

components whose weights depend on either the gross weight

on two or more of the following in combination: rotor tip

speed (VT) , rotor diameter (R), rotor solidity (a).

The equations developed here are taken from the Hiller

Aircraft Corporation Performance Data Report. (Ref. S] In

this report they assumed a specific engine installation,

the Allison T-63 with a military power rating at sea level

of 250 horsepower.

There is a possible problem of the validity of these

weight relationships when applied to different helicopter

design categories. However, assuming a specific engine

determines a ,umber of the component weights, and thus

minimizes the inaccuracies. Using the weight estimation

relationships developed in the Helicopter Design Manual

[Ref. 2], the engine, control and accessory weight can be

calculated and the weight formulas developed here applied

to give a representative useful load and empty weight

formula for preliminary design analysis. This is done in

Appendix C, for a 20,000 pound class helicopter.

* 41

The following relations are used to reduce the component

weight formulas for the specification helicopter:n2

W/DL - A - rR2 (3.12)

W/PL - MP- 250 (3.13)

(Military rating for Allison T-63 at sea level.) (PLPower Loading.)

P */A 7 VT (3.14)

Using these equations the component weight for the

U.. specified helicopter empty weight may be reduced to the

following:

Engine, Controls and Accessories = 617.5 lbs.

Engine Section 1.07Group .053[W/PL] 19.5 Ibs. (3.15)

Main Trans- Wl.295 .803mission 10.43 .PLVT) 1221 p (3.16)

(PL VT)~

Rotor Drive W1.066pa (3.17)

Shaft 5.56 7... = 266 p*7(LV) (DE). 3 5 ' (.7

SwI1'14 17449 (.8

Tail Rotor 32.22 - 1 VT (3-(PL VT) " VT1.14

42

a -r -- ~ -aIN* I-

The engine, controls and accessories category includes

such items as lubrication and oil cooling system, engines,

:.j communications, engine controls, engine accessories,

instruments starting system, furnishing, flight controls,

electrical system and stabilization. These are considered

fixed weight items determined from specification of the

engine and weight class of the helicopter.

Tail Rotor W'75Gear Box 3.7 5_...... . 59.47 /V (3.19)

(PL VT" (DL)

Tail Rotor W1.355Drive .124 .5 .86P* VShaft (PL VT)57 785 7 2.886 p'5 7 /- (3.20)

Body and. 916Gear - 1.91 W' + .0294 W'Landing

Rotor W1.185 .33Blade 35.15 35.15 - A (3.21)

TTTeetering V(L

Rotor Blade .33Artic- 19.77 , 19.77 - A" a (3.22)ulated VT(DL)* VT

Rotor Hub 1.21Teetering .0088 = .0088 WA' 2 1 (3.23)

DL*Z

Rotor Hub WI.21Artic- .00975 W 00975 WA (3.24)ulated DL

43

IV Fuel System .416 per gallon capacity - .0615 WF (3.25)

where IV fuel weight.

The individual component weights may now be combined

into a single expression for the helicopter empty weight.

.9 W * 617.5 + .0617W * 1221P.863 + 266P'7 + 17449

e F 1.14(3.26)

+ 58.47VIY + 2.886P' 5 7 /v[ + .191W.916 + .0294W' 9 9

-4+ appropriate rotor blade and hub weights.

As stated earlier, the design specifications called for

v a useful load consisting of a pilot (200 lbs), payload

(400 lbs) and the required fuel weight (WF). The fuel

weight is calculated for the Allison T-63 in the following

manner: endurance of three hours at 85 percent of normal

rated powered for the T-63 is 180.2 HP and the specific

fuel consumption at this power is .783 lbs fuel/BHP HR.

Including an allowance for a three-minute warm-up at NRP

and using a 5 percent correction factor on SFC, as

specified in Reference 5, the fuel weight becomes:

4 3WF = 3(180.2)(.822) + 6 (212) (777) (3.27)

An allowance should also be made for oil plus trapped

fuel. This is estimated at 20 lbs.

44

The total useful load is the sum of the useful load

items.

W- 200 + 400 + 452.6 + 20 - 1072.6 lbs (3.28)Vu

A new variable, WBAR , is defined as the sum of the

emply weight plus useful load. It is the of equations

(3.26) and (3.28).

WBAR - 1717.9 + 1221P" 8 6 3 - 266P'7 + 17449 + 58.47VIYVT

W (3.29)+ 2.886P' 5 7 /T + .191W' 916 ' .0294W' 9 9

+ appropriate rotor blade and hub weights.

Equation (3.11) together with equation (3.2,9) form the

basis of a carpet plot design study. These equations are

solved simultaneously for WBAR . This solution is best

illustrated graphically, as in Figure 3.2. The graph in

Figure 3. 2 was generated for a specific value of CLR over

a range of tip speeds-[600 to 700].

F. GRAPHICAL ANALYSIS

Graphs similar to Figure 3.1 are generated for several

value of CLR , and are then cross plotted to form Figure

3.2.

The mean lift coefficient, CLR , values are selected

based on what is considered the historical average range of

45

WW T�1 'W� �W�' '� � .�U � �L r �

S* * g 4 4 NI 4 *I I U aI I I aa 4 * a* a 4 4* * a I U* a a a* a I I* a 4* U I4 a a 4* a I* a a U* a I I �r�J* a a a* a a* 0 4 0I I 4 44 I$4' ____ a a a,

* a a a IIa a a aa a I

3' I U I* a a 4* a a *a a I

* a a a§ * a a a* a U* aa a 4* aas a a I 4 0

a a a -C,) a a a aa * *4a a a 4

__ a a a- a a 0

a aa a e a

a a p a �iJ* a a aa a aa I I

a a a Ua a 6a a a Ia a a a 0

a * a aa a a S: *: :

a a a a *a a a aa a a a

a a a aa a a Ia a a a

a a a a aa a a aa a a a aa a a a aa a a a a*4a a a a 0.)

a I * aa a a aa a a a a

* a a a aa a a a a Na a a a 4a a a a aa a a a aa. a a a

� aa�a�i�iI i�i�!* a a a aa a a a a* a a a aa a a a a

a a a a &

�gg oo�� og*� od*� o�s� ooc� og�(Sal) �L1�!SM $SOJD

46

values. Figure 3.3 is basic plot for a carpet plot design

study. Programs are provided in Appendix D which will

generate the required data sets and plots of Figures 3.2

and 3.3.

The solution field depicted in Figure 3.3 is too large

to be of great analytic value and as such must be reduced.

Three parameters, maximum gross weight, rotor diameter

(both specified in the Design Specification) and the

aspect ratio can be used to narrow the field of solutions.

1. Rotor Diameter Boundary

A net to exceed value for the rotor diameter is

generally giwen in the design specifications. This

limiting valie is based on the operating environment of the

helicopter. With R max specified, there is a linear

relationship between'the disk loading and the gross weight.

W =WDL a --7

Tr R

The resulting bracketing of the solution field by

applying both the maximum gross weight and maximum rotor

diameter limits to the carpet plot are shown in Figure 3.4.

2. Respect Ratio Boundary

It is evident that a further restriction is still

necessary to completely define the region of acceptable

47

dle

400

C, f)JI 01 1

j //

0: 9;

002Z 009 ME 99z 06Z 8(Sfn 14,/ 9 9JE

489

9n I. Ta4

.41

g."4

U'

p1-4

ack

0 t J ~

IS 49 S 1

design solutions. Studies have indicated that a main1.

rotor aspect ratio of 21, is a representative upper limit.

Thus

21 R<mr> . b b po CLR VT2

21 C<mr> Ira ar DL

b p CLR VT2

or DL >

For the case of a two bladed main rotor equation (3.30)

reduces to:

DL > .000012 CLR VT2

The detemination of this boundary graphically is as

follows:

The hover solution plot of Figure 3.2 is replotted 2

relative to the coordinates disk loading and design mean

blade lift coefficient. The limiting curves for

DL - .000012 CLR VT2 are then plotted. The intersection

with the appropriate constant tip speed lines of the hover

solution represent the aspect ratio boundary; Figure 3,5.

1 For a helicopter rotor, the aspect ratio is defined as

Sthe radius divided by the chord.

2 For clarity lines of constant gross weight are omitted.

Sso

I4'00

~t to

lb 008 (2)l

'41

*00

~~Is

'4v4

Soo 0o00 90 *0 to r

un ".4ea o

These intersection points are then cross plotted onto

Figure 3.4. Figure. 3.6 represents a graphical plot of the

solution set satisfying thi performance and structural

design criteria of a small observation helicopter as

specified in this study.

52

_ _ _ _ _ _ lip_ _ _ _ _ _ 0 4

*0 0

v0 4J

aDWD

'4 C4

do$

om~ /og OM '0* 0' 08(sn 1V5e I9JE

S3#

- , ~ ~ ~ ~ ~ ~ ~ ~ '- r m% -j -r~b rT9 r., r i- F, jw v w ~ ~ w ~ 1Il U~~~1 1 W~

IV. HESCOMP

A. DESCRIPTION OF PROGRAM

HESCOMP is a helicopter sizing and performance computer

program developed by the Boeing Vertol Company. The program

was originally formulated to provide for rapid configuration

design studies.

A number of programming options are available to the

user of HESCOMP. When the type and mission profile of the

helicopter are known, HESCOMP may be used to size the

aircraft. Alternately, it may be used for mission profile

calculations when the sizing details [gross weight, payload,

engine size, etc.] are specified. A combination of these

two options is also available; the program may be used to

first size a helicopter for a primary mission and then

calculate the off-design performance for other missions.

Finally, HESCOMP may be used solely for obtaining helicopter

weight.

Sensitivity studies involving both design and per-

formance tradeoffs can easily be done with HESCOMP. Incre-

mental multiplicative and additive factors can be imbedded

in the input data.

The various helicopter configurations that may be

studied using HESCOMP are detailed in Table 4.1.

54

7ý1-.A " *. . -7.A' - .*-.. •* . ,

TABLE 4.1

HELICOPTER CONFIGURATIONSWHICH MAY BE STUDIED USING HESCOMP

".lEcoIpet coluFIGUMTI0oHU WIC. NAV It STUDIO" USING IIEUCOIP.

Additional Lilt/Projulfnion.•-%"-%l atom Componunto Hhiclh

n•"iotet be Added to Propeller Type at Auxilluryf1elcopter • •oure* for Auxiliary Indepanddnt Sngit.es

Type a Auxiliary Independent - -looth Single Tandem !n Propulsion Engines T/5heij ,?rnn T/eot

Pure Helicopter ___,

winged H1ellcopter X

Compound lic Icopter

(1 Coupled Iprim. engines Xdrive auxiliary propulsionsyetum? -

23) Auxiliary independentpropulsion system

(Ju T/Shaft engine x X X X(ib) T/Fan engisa X I Xto) W/eot engine X It X

Auxiliary Propullion eliescopter

III Coupled I prim. egiinee Idrive auxiKiary propulsionsystem-

121 Auxiliary Independentpropulsion system

IaQ T/Shaft engine X X IIb) T/Fan engine XxIol T/Jnla ana-Lne L -

!oaxial Rotor helicopter

M1) Coupled lvrim. eVt19iio 1drive auxiliary propulsioneyetem)

131 Auxiliary Independentpropuel ton system

(a) T/Shalt engine X x X(b) T/ran onghie X(of T/Jet engine x

s5

B. PROGRAM MODIFICATIONS AND IMPLEMENTATION

The computer program received from Boeing Vertol

required some modification and reformating in order to run

properly on the Naval Postgraduate School IBM system.

These alterations did not, however, alter the program output

or usability.

HESCOMP, as received from Boeing Vertol, was 17821

lines long and set-up as a sequential data set to be

assemble on a 'G compiler'. The Batch processing system at

the Naval Postgraduate School accepts only programs set to

run on 'H compiler'. Normally, the differences between

these two compilers are minor and programs that run on one

will run on the other. However, this was not the case with

HESCOMP.

In order to facilitate the program debugging process,

HESCOMP was reformatted as a partitioned data set. What

this effectively did was to break the program down into

"eight members of approximately 2000 lines. The program

breakdown is illustrated in Table 4.2.

Each of these were compiled individually and then error

codes analyzed. The member data set was then modified as

required to properly compile.

Once all the members of the partitioned data set

compiled properly, HESCOMP was again formated as a

sequential data set and run utilizing input data for

56

which there was a known output. This insured that the

modifications made to the original program had not altered

the logic, ie., gave faulty results.

The control language program to access HESCOMB on the

Batch processing system and a sample input and out data

set are shown in Appendix D, These are also available

on the Aero disk for copying and use.

TABLE 4.2

PARTITIONED DATA SET

MEMBER NAME LINE NUMBER SIZE FIRST ROUTINE

S1 1 - 1681 1681 AERO

S2 1682 - 4132 2451 CLIMB

S3 4133 - 6531 2399 XIBIVS4 6532 - 8974 2443 PCWAVL

$5 8975 - 10870 1896 PRINT 1

S6 10871 - 13042 2172 ROT POW

S7 13043 - 15383 2341 CRUS 3

S8 15384 - 17821 2448 TAXI

C. PROGRAM FLOW

The program is conceptually outlined in Figure 4.1,

[Ref. 7]. The program flow is monitored by a general loop,

which controls a series of peripheral programs. Therc are

57

W-6 uospwmiý r INI i ACrp p Pimri4.ý

Itm JIu Wil JSNAW(Lk94?IIP N

a llAIW N&A G11N(M1lot U 6110111111C 01101111 1001SUM S14 d1611 111111Ca 1`1cf"I W ll

11410it AIWINMI P1MA MS L(9PINIIOWC 004,1141ORA 01J

swoul 111 SIINput

* lWON 511 tLL bllM1S

Is t I .f % 10611 4t n

Figur 4.1. 51,S111P Progra F110 ow, 111110,M

UsstsS8

a total of 44 subroutines. Detailed program descriptions

cam be found in Section 4 of the HESCOMP User's Manual.

D. PROGRAM INPUT

Program input can be loosely group into ten categories:

general information, aircraft descriptive information,

mission profile information, rotor tip speed schedule,

incremental rotor performance, auxiliary propulsion input

schedule, engine cycle information, rotor performance

information, propeller performance information, and

supplementary input information.

The actual amount of input data requires varies greatly

with the program options selected. An example of a data

set formatted to run on the IBM system is shown in

Appendix E. A more detailed explantion is available in

Section 5 of the HESCOMP User's Manual.

E. PROGRAM OUTPUT

An example of the program output is included in

Appendix E. The printout consists of general data, input

data, sizing data [program output] and mission performance

data [for the size helicopter]. Detailed descriptions of

these and diagnostic error statements are described in

Section 6 of Reference 6.

I5

V. CONCLUSIONS AND RECOMMENDATIONS

Three approaches to analyzing a preliminary helicopter

design were explored in the course of this paper. It was

found that a number of the performance equations could be

greatly simplified with little degradation in the final

results. A sensitivity analysis brought further insight

into the inter-play of the parameters and how changes in

them tended to effect the helicopter performance equations.

Carpet Plots provided the most interesting method of

analysis. Development of a graphical solution matrix

using this method provides a usual interpretation of what

is occurring when key parameters are varied.

Two cases were explored; a light observation helicopter

ite in the 3,000 pound weight class and a heavier utility

helicopter in the 20,000 pound weight class. The Carpet

Plot method provided reasonable solutions in both cases.

In doing the analysis for the utility helicopter, the

initial weight estimation equation had to be adjusted

upward by approximately 2,000 pounds for the equations to

intersect properly. This is not considered a limitation

to this method of analysis, however, it does point up an

area for further investigation. It may be possible to

develop more accurate weighing factors for this equation

when dealing with higher gross weight helicopters.

60

HESCONIP provides a plethora of information to the user.

However, the price is the amount of inputed data required

for even a simplified analysis. At a preliminary design

* level of analysis, the other methods explored provide a

quicker first-cut look at the potential design.

4'6

561

APPENDIX A: NOMENCLATURE

TERM DEFINITION UNITS

a Slope of Airfoil Section Radians

Lift Curve

A Rotor Disk Area ft2

AR Aspect Ratio Dimensionless

ATR Tail Rotor Disk Area ft 2

b Number of Rotor Baldes Dimensionless

B Tip Loss Factor Dimensionless

C Main Rotor Cord ft

Cdo Profile Drag Coefficient Dimensionlessat Zero LiftCLRo Design Mean Blade Lift Dimensionless

Coefficient at Sea Level

CT Coefficient of Thrust Dimensionless

Cp Coefficient of Power Dimensionless

Blade Section Drag DimensionlessCoefficient

DL Disk Loading lb/ft 2

FM Figure of Merit Dimensionless

HP Horsepower

LTR Tail Rotor Moment Arm ft

P Air Density lb sec 2 /ft4

Advance Ratio Dimensionless

R Rotor Radius ft

62

TERM DEFINITION UNITS

P T Total Power HP

PTM Main Rotor Total Power HP

PTTR Tail Rotor Total Power Hp

P0 Profile Power HP

Pi Induced Power HP

P Parasite Power HP

PL Power Loading LB/HP

R Rotor Radius ft

T Thrust HP

VI Induced Velocity ,ft/sec

VF Forward Velocity ft/sec

V Aircraft Forward Speed ft/sec

VT Rotor Tip Speed ft/sec

W Aircraft Gross Weight lbs

Wc Empty Weight lbs

WF Fuel Weight lbs

W u Useful Load lbs

WBAR Empty Weight PlustUseful Load lbs

a Solidity Dimensionless

63

APPENDIX B: CARPET PLOT FORMULATION FOR 20,000 LB.CLASS HELICOPTER

Bi SPECIFICATIONS:

Maximum Gross Weight: 20,000 pounds

Maximum Rotor Diameter: 30 feet

B2 PRELIMINARY ENGINE SIZING:

B2.1 Utilize equation (2.14) to determine enginehorsepower category.

W - [4.753PTRJ2 / 3

20,000 - [4 7 .5 3 PT 30]2/3

-T - 1983 HP

B2.2 Use the engine selection parameters tables B.lto determine the number and type of power plant[table taken from Reference 3].

B2.2a Type and number selected: 2 type C.

B2.2b Specifications:

Dry Weight Per Engine: 423 pounds

Shaft Horsepower at Standard Sea Level:

Military 1561 HP

Normal 1318 HP

B3 WEIGHT EQUATION FORMULATION

B3.1 To obtain the engine control and accessoryweight use items 7, 9, 10, 11, 12 and 13 ofthe weight estimation relationships developedin Reference 3 for a utility helicopter:#7: 609 lbs; #9: 129 lbs; #10: 76 lbs;#11: 410 lbs; #12: 439 lbs; and #13: 302 lbs.

64

TABLE B.1

ENGINE SELECTION PARAMETERS

The following turboshat power plant data arepresented for one engine.

Engines: A B C D* E F

Dry Weight (ibs) 158 288 423 709 580 750

SHP (ssl) Military 420 708 1561 1800 2500 3400Normal 370 6i9 1318 1530 2200 3000Cruise 278 494 1989 1148 1650 2250

SFC (ssl) Military .650 .573 .460 .595 .615 .543Normal .651 .573 .470 .606 .622 .562Cruise .709 .599 .510 .661 .678 .610

Initial Costs $93K $100K $580K $360K $640K $700K

Operating Costper hour/engine $8 $16 $20 $35 $40 $60

Preventative Maint

per hour/engine $25 $50 $100 $125 $160 $220

MTBMA (hrs) 3.5 3.0 2.0 3.0 4.0 3.5

MDT (hrs) 0.7 0.6 0.5 1.3 2.0 2.6

MTBF (hrs) 185 210 205 285 280 320

MTBR (hrs) 600 750 800 800 1000 750

1~6

,• 65

B3.2 Simplifications

W A a TR2 w - MHP 31,00 ; P -

B3.3 Engine Group

.053(5100)1.07 - 272 lbs

B3.4 Main Transmission

4WI.295 1 W.863 A+.43210.43 wi2 5 = i3 0.43 W

.863- ... W,4' 863V 863

(Lpm Vt) [T] (*.pm)"

= (l0.43)(3100) "863p",863

- 10,748P' 8 6 3

B3.5 Rotor Drive Shaft

5.56 W1.0 = 5.56(3100)'7P.7

(xpm VT) [Lk]

- 1545P'7

B3.6 Tail Rotor

,WI.'14 307,600

32.22 w1.14 307 60(xpm VT)1.14 VT'

66

B3.7 Tail Rotor Gear Box

W.73.7 ...... 75' (3.7)(3100)' S P,"

(9.pm VT)

* 206P' S

B3.8 Tail Rotor Drive Shaft

.124 1.357 7" (.124)(3100)' 5 7 P' 5 7

(Lpm) .7W, 8

- 12.12P' 5 7 VT[-

B3.9 Landing Gear

= .191W' 9 1 6 + .0294W' 9 9

B3.30 Rotor Blades Articulated

197 W1.206 .33

- 19.77 W AVT D

B3.11 Rotor Hub Articulated

.00975 W1 .21 .0097SWA 21

67

*J

0.7

B3..12 Fuel System .0615 IV

Calculation of fuel weight three hours at

cruise SHP

1513 lbs + 10%

1664 lbs

B3.13 Total Equation

WB - 12,987,* + 107948P" 8 6 3 + 1545P. 7

307600 + 206P"5 + 12.12p"57

VT 1. 4 12 1 P ' /T ?

+ .191W 916 + .0294W14 9 9

+19.77 W- Aa 0 S + .00975WA2 1

1VT

70 B4 HOVER EQUATION

Following the formulation in Section of Chapter 3,

the weight equation based on the design mean lift coeffi-

cient and power required is:

F ~~3/4V 1/1 411.51 DL72V

""2 [32 i1+ K3 JT .K 42 VT 3 '1

VT +K 5 KsT

This number was increased from 8987 to 12987 to bringthe curves together. This reflects a 4000 lb useful load.

68

N.

where:

.9583 2;"•K 1 " -c--( +187 CIRo )

-2!K 2 " T6000/gs0 .21

K3 - 0.00025929 (1 + 1.80 7 8CLRo )CLRo

, 1

• B.5 GRAPHICAL, RE.SULTS

• Figure B.1 is an example of equation (3.13) plottedJ'• against equation (B.4) for a specific design mean lift

•: coefficient.

i• Figure B.2 illustrates the family of curves obtained

•-=--•when the design mean lift coefficient is varied from

20.3 to 0.72In Figure B.3 the solution matrix depicted in Figure

S~B.2 is narrowed by the constraints placed on the gross

v,•.','weight, rotor diameter and aspect ratio.

.00

I.A

369569

'I

a a e B U SBe Be U B Ba B U I *

B * * a aB B

�,. �: �:�a fJB

'iDa* * * B * �B B B U 0

9 B U B B* B U BB d B B

* * B B* * C Ba U I S B iiB * B B BB B B, *a a B I

B B B B U* B a U Ua a B Ba a * Ba a B a

a a a C.U a B BB B B BB B B B B* U .B* a I B 0B B U B* B B -

* B £ I* * a

B U * B

�.0 'I U B

0 * * a BB B B Be B B B B

C a B B-- B B B

B B B U U -

0 a B B B B mEwi �-Bp-4B U B * £* U B B

* B UA, B I B 0 �>...

1%' B B B B I *

U U I 0'� U"4B B I B p4B B B

- U I B I: :* B B £ B0. a a a a

* U B B to0 B U B B *U 9 B B -I B a BB I U UB B B U

U I B

4 - U B B B 0B B B Ba B I B B�*

U * B aa . a B i*4

B B a a aB B B

U a aa I B B

a a � � aB B U a a* a a aa a B B

B I a Ba a '

a a B I BB U I a

a U B iN a a j a* p B B* B U B B* U B B B

00961 OOOBL - 00981

C sri 0!�M SSOJDSi. I

I..4 �

70

.� � -�

- ~ * w. ~ W q ~. J W~W9 ~Y ~¶tdW' W'~' ~~~(~ 4 .~ '~ 4

# 0

I,4,J

*0io a0o 0*6 00s 0ssq *4io * P5

71C

r.W*in *. -- � � � � � �' n�i

-�-w *�I, N

I* * 1%� I *: ,.*ii � I

IIg I

a

1/ �0* a a a* a a aII *'� */:

I* 9

;11 ; �* U a

* * a * a'a ' aa * * a* a a I a* : : *

a. * * * a* aaa a *f-4

I I : :a * *0 a a a a. 4%N.0 a a a__ * U a * *

* 44 -%a * a az a

a a * 4 1q1 :* aa aa * aa. �

U *'a a a@1 I a* a

aa S* a* a* a

* a* a* a

a" aaaI

�r4ja

0; S.30

oo9O� oooaz oo�s� ooosL oogrnsqj �PL4 8!OM CSOJ�

� A

72

*1 � -. �: -� �- � - - * � .�,- �

APPENDIX C. CARPET PLOT METHODOLOGY FLOW CHART AND

EXAMPLE PROGRAMS:

This section contains a flow chart to help organize

a carpet analysis and example IBM computer programs to

produce the data sets and disspla graphs.

k- , ,7

S_.4•

01,80a ff* for

OU cI t 3rcp

IToo0oM

slop

74

GRAPUICAL Iz~C ~TFEI~ FlOGBAM

0118H** A! AL VAS E j *4*4*444OTCOE 4**44 f 8*A44I4A

~*4w**44* LIrT COM 1ICENT.

C* li AS CALCOULAEDFCHAPOREDEUTO,1ZAIIZADLES:~lWlGH

C**

C* C I SG il LIT C ! ! C T

C. I **S(50)

C4*

C CT

CCALL rRTCMS "SK L!,E ','T' DIS

1 '~CATA ,A ,CT5'

C

cc 10 10199C CRITI AZ )A

C CIT2DIj AL 1) WN 1 (1) , W21 (1) , W2 (1) 0, WB2 (1)REAPJ2D JA A3

10 CONTI? ,W'IA'I 1 B4t,5I)U5ICC---- CALL DISSILA SCCTINES FOR PLOT-------------------------------------C

CALL TEUPICAL R~fES

CALL PAGE (1. ECALL GIAC! (O.CfCALL PHYSgB (1. U 1.2CALL AREAdD (11CALL IrJAM

CALL sixAIF '3 Atc)*CALL NTAIS

CALL (GUAN! (W) EIGHT I (B) $ DCALL HEIGHT (.,'c I

CALL ACkIN (0~ jLC~T1 (C)ABPET MI)CTS. (CLR=0.5)$S'

C CALL MESSAG ('IR~I0TE CjN B(C)LBPET (P)LCTS: (CLR=O.5)3',

C 1I7TI__

CALL UIZGIT (o20)

CAL CHIM D'~ ~CAL ciil 0 :gCA CoRyl DL.:v,

C RD 4.6,...51

CAL HEGH a~ D :CAL L, ioNIS I~

C CALL C I aS .46 CI~iLE$ 5IPAC CALI L, It (1,f AASZ6S.IPI(),C CALL TLI it CiE(CUV 1

C HAL LI IN D IVE AT' A1,34J4 ,4.8)

C L0NA I~ AT353

! INI

IALIjA It76RSHSlpUC L M G Mviot

AlW

OMAINYC y AtItZ 301 C? I h1I OGA

11iHOWOFSPSLU1811 10*SHI *f*g* **

******* NOSMENCLZD3ZGATUREU~FTI AIL **g*

C: CLI Islas A H1I AT hIF INOM

I I JQH I HACBSIATEZTCH CLASS QUAIO

3ag 2 g5*.W*L*C..oil I111 NHADNo CLLTUt!

C* CLa SGNa I N LEF CZICZNT,C* V , A AT"I 60HIGT! **LI"

mg I a C~gI GH ORC N.

C V42UL E HI ATVTCUSV7 OIS EFUL 7 OAT IW 3IT:6 NXONC: 1j Ii SCM!! 4fVAZjLATL VTiNCS700 I

0- 0 LA I I SP06ODING CIS LCI.* ATVT6C* DV2I6 EUALS TH4 CBI SP ONDENG rIS LCLI ALIN ATV=2

AC* DC7T I OIS Th! CCOISK IC ING FCI CLOAIN T T=5

C' g)6ý2 W~iGM, Al*4DL 5 ~ u 5 IL

Cý6V2 ^AI 1 30102.0 AT 07 V1ý5e6782C EAT&5 DL 45 .E6! AT 4 V c.4 /C* J 9ir I4AL T&1 CCH~.9' 419.§2IN 399.72,2382.A99/U60

C--D 0114 Ah I /- - - -- - - -

LA 646 2124 6§ :'46:8 2 3Sj-x ;8365.10,2352./

14 11/1 P1idil:i72. ''

DA A 1; ý

C--- CALL D13SILA SCDUN!5E FOR PLO% -----------------

V C

2At~ .' 1.2ICAj iINDU 1'0sl

CAIL EIuLTI %CAL,. IN B c K%2SjG

CAL it~ 9 C)is (I OADHTIudll v 100

CA.1 ACI J~CPTZS (C)I1RPIT (P)LOTSS,

CALL RZZGIR (520CAL ORAD (2. ,.1*.3C4,230C..5O..25S0.)

C. 18KCAtL EARA3CA L LIGLIN

CAl C av DL 7w7,50CAL DAS4CALL COD 1 DV 1,6vT, QCALL C BY Dv D'2,6YT.AM5.0

CALL CODY (VI IM5 IVT5,5, 0CALL THKCBY 4. 36)

C CALL U Lall AC maxLNaLINZ T(X A1,300,20)A tk

C CALL L NIS 'I aCYILES INU i3C A1 L H S :f lST$IAC A L YL GN ( CIB OC E1

C L!GZNLE (I A 1,L4,14.I40.8)CA DON IlL

C IKAT SjA!RMINj! 1 ,

END

78

ram

-, I * -

Cs**** rt)A~HLCAL Ei CC;PT~. DESIGN P10AOG SI*aaaac0*0400sI A EC fATC BOUNDABY

C**0ses LOCICIfHCVE AND UI N1L-3JCD S OLUTIONS00***CIII! PLC N 9 HU 1 aRactoss~ooe DY &L HANSIN a .a

c***.**** THIS PSCGSAM IS EZSIXt*L TO GRAPHIC~ALLY DETIRMINE aaaa11Z AS 181j jA T OOLZZ.DAIT REQUIBENNTS OR*aaanoTCH SXIN SING IJZVIOUNLDt ONIRAT IOD ATA ****

Cot

C* VAIIABLZSz aCsCe CLB DESIGN AIAN LITT COEYPICENT

Co VT JPVLCTC. DL SKLCADING

2'C* As ASPECT BATIC. HISTONICALLLY ASSURIED TO BE LESS THAN 21 a

I V AJS EJ CIMPODINGDISK LCACZNG AT VT:6V S~ tII CCRSOUING DISK LOACING VAT ~60C* I UAS 181 CCRA!S; ON I EG IK 5.~C fNG AT VT. ~

C: 0118 3 UALS TB! CCNNESPONCING CISX LCACING AT VT*700c. I U ALS TEE L~lT COZY AT Vla~bOQCC* Z ALS THE LIFT COZY AT V706JC: cc 1 UALS TE1 LIPT COZY AT ýl 6

C~5EUALS TH1 LI.FT COZF AT V1:675Ca C E U ALS TEl LIFT COEY AT V 7 00

814Ji4 CL 4 ~rL (10) C60 (10) ,C625(l0) ,C650(10),C~ (41).hTi)"b IT3 15) , DVT4 (5) ,DVT5 (5)

C---- DEFINE LAIL----A-- ------------------------------------CATA DVT12 .06,2.'41,2.63,2.74 ;2.SO/DATA DlVT3/~.8 :~ : " P 44;. J77;DATA DV TDATA D)VT4,4 05:"84:9 82 & 7/~DATA V5.ODATA CLIJ.* .4,. lA,..7

DATADL/2,~. ,d 1,A.,2 . 4,2.!,2.b,2;12, 2.9DATA C60 .41, .4 5 7:: 65DATA C /4 :4~ ,* ::4, 34D 5J9 * ~ ,. ,fDATA C ý: L',M, :4 *~4 .'9.1,A, 5.CAT A cb7.#if :34:, 41,43 .4 ,.4 ,49 4.1,.3DATA C7QC.1 31 3J. 3 , 7,. 39 .41,.'43,.45,.L7,.49/

CC--- CALL DISSILA SCUTINES FOR PLOT -- - - - - - - -

C CALL TEK618

CAL S17 (3IIALL)CALL HWSCAL (' CSlE

CALL PH!SY

CALL FlBAEC AlL S vISSLCALL BASAL? ('I/flCSD)CALL MIXAL? (S AEC'CALL IMTAXS 901aI

¶ ~~~CALL SZIDCHN .01,0h1CALL HEIGHT

1016)

CALL MES5* IN IOTE (C) ARPET (P) LOTS$'

V 79

CALL oii".Lo.t'n (4--i

Cl T CoV (..Cie)CALL PARA3

CALL CURV (DiC6'g QQ* ~CALL CURV (DLb, IU

CALL C *1,CALL C I V 1

L 21, DLC *1 0

CALL CURVE 'DII CLR,50cAt CURVE DVI .CLB,,CA CURlI i( 0V14CLR, ,uCALL CURVE (DV TiCIB,5,O

* ~CALL T HKCIV(.3)CALL 00NIELSTOPEND

80

~Ippsss***S GRAPHIC AJ.tELLCURTzI DESIGN PEQOGAM s,.ssCos is os*4 Nl!t Y OF SOLUTIONS 5*5*

C ***aCAIN! I PLOT NUPIER 4 ****

cD*Xs*B AL HANSIt *sesC*~*0455* THIS PDCGDAM IS DESIGNID TO ILLUSTRATE THE FAMILY 5555

CF SCIOIICNS FOR HOVIl AHU USEFUL LOADcssss~s~s EQ UIIIIflllSIOF AETEVIERING 10103 SYSTEM **5*

UITH ECICI DIAMETER AID MAX GBOSS BOUNDRIES. 555*C5*s*5** s CUBSEDVATION CLASS HELICCRTER

C*NOMENCLATURE '

C' VARIABLES:4C* CLI ZESIGE MEAN LIFT CGIEICENT i

12 V TIP VELOCITY 5co 14L DISK LCADINGC* N WEIGHT IS CALCULATED ITC! POUER EQUATIONC* WE USEFUL LOAD PLUiS EMIPTb WEIGHTCo P1 ICIER AVAILABLE IN HCDSNPONEB 5

C DLU EQ UALS THE DISK LOADING FCJ CLRw.34C* C14 EQUALS Thl DISK LOADING PCf CLR8.4

C* DLS EQUALS THE DISK LOADING ICE CLRu.5C* CL6 EQUALS THE DISK LOADING 101 CLBu.6C: LEQ UALS THE DISK LOADING 701 CL~tu.7CS WJ 1IQU AL THE %EIGH! FOR CLftu.3,C: 14 EQUALS THE WEIGHT FOR CLRO.4CS is EQUALS THE UEIGHT4 FOR CLB:.5c: 6t EQU ALS THE WEIGEýT FOR CLR.ECS W7 EQUALS THE %EIGHT FOR CLRs.7c* W~ll 7qUALS WEIGHTS AT VTm6 QQ05 1112 I GALS WEIGHTS AT VT=6Ce WV13 EQUALS WEIGHTS AT 'eTu6p05 111T4 EQUALS W EIGHTS AT VT b 5C5 WITS EQ DAIS WZIGHIS AT VTz700C* DVT EQUAf TEE CCREESPONDING DISK LOADING AT VTu 0?C* PV12 EQ JALJ THE CCERESPOHDZHG tISK LOALING AT VT a205 C1T3 EQUALS TEE CCRRESPONDING DISK LOADING AT VT 0C* DYIM S QUAIS THE CCBR!SPQNCING LISK LCADIUG AT VT 611CS iZVTS ZQUALS TEE CCBRISPONDING DISKr LOADIrNG AI VT'* 0C' SL! 30101 DISK kiCUNLAITC* WbG MAX GROSS %EIGHT BOONCARY

(5 ,bl(5' ? )3 h,b I, .b _T .5 i'5b (2)~'"(2)C--- D!IPNE DATa ------- -- ---------------------------------------------

DAA D~e.6j ¶ j.4fi:43 .879213.236.5/DATA DL4/. 9 41' 46g4. .PA A 99.1 ,235I2.9/

DATA OLi.4. 112.8 901-8 *!&DIIA W64 e424 78 , 3

DATA :7 234 ,

DATA 8V i 5:11 .* 852/5DATA DVT~js / ~ .41bl.. i 6

DATA DVTS42.O5,2.47,s.69,2.81 ,2.67/

81

UAJA 1) 14

CATA a~~U. A

CC---- CALL DISSILA SCUTYNZS FOB PLOT -------------------C CALL TZUE 18

* CALL NEDBUF

CALL p IAGI (0.

CALL 0 Act

CALL BARIiCALL PSSWIS L

CALL MIXALF (STAI0r)CALL EIGE? Af'CAL IsAI S AD!G'I0

CAL HEIGET :18CALL HEIHT1.

CALL HACIN LJCOPTES (C)MBET (P)LOTSS'o

CALL HIGH (t.9CALL G A ( . ?1,3.C.230C. 5C.,2550.)

CALL TNICCBV (.0IS)

CA GICALL CURVE DO 3,h35,CALL CURVE DL,4:,',,CALL DSCALL CCUY Bi V L1 w.CALL CO VE D0L7:I,

CALL CURVE D7N,C 1LL CUV jDvl! 1hVT!,5,CALL CURVE DV~zIhVTZ 5,O)CALL CURVE DVI3,hVT3,5,0)CALL CURVE (DV1 ,hVT'4,5.

E UjCRC1V (D~j l VT5,5 :Q)

CALL CONCCTCALL CURVEvir 20CML CURVE (02,RLl,2,0)CAL.L COMME

U ~s7oPI

Jur

82I

CosL~0 OLTCN ******* H lOC******** CAfl PLOT NUMISR 5

BY AL HANS~t?ooso HIS -MQAN1 DEIGI 10. IELUSTkT HE F AMILY

C****** CF SC UIC KS POD NOV I NO ~SIYUL 0OACos***** IQ UIlI~lNS OF A TE12181M0 SOTOR SYSTEMC******N WITH SCTCR CIAMETSR EAX GROSS idlIGHT AND

@0**4*0*o*A h$IJARTXO CIUNDAIL 3.*oo.C*******Cliffi TIO N CLS 11 L ISCETR

Coso 000

Cos VONSNCLITUR! *CsCO VARTABLES2Co *C* CLI CISIG$ BIAS LIFT couFIZCINT *Cs I TIP VIICCZT! 0Co CL CURK LCACINGCo v &EIGHT IS CALCULATED P1CM POWER EQUATION *

C' Ni OSEFOL LOAD PLUS IMPT'Z WEIGHTCO PA f WIiE AVAILABLE lb HCSIk~iEll

C****

Co' EQUI AL$ THE CISK LOADING PCI CLRu.3CO ML 2 UAj THE CISS LOADIb P CLRU..4co 1S 9 UA Thl DISK LOADING FV CLR :5Cs DL6 E UAL3 THE DISK 1OADI&G PCt CLR:.

CO V5 UALS THE hlIGHT FOR CLBS.

Cs W ASTElfGIFPCI:

C VVTS II U11 M CGH AN!

C: CTIJ i A CAISK L4UCAC.11A! ATVaCO OT 3 00K A itCRSP"C) CIS C TEASPEC RAlTIOia GT

Cs OTI S UAS ThlCCCS!SPONZINraE~, CCN A T7

C I %RAX "It0 C "5yD

IIC.4. 4 b ilT .1 (1 4b;G i

JA I& " 006- 01 .07 Si 037 2 ;. 33ZIATA 2,S " 4467k.1 02 a.MI6 j~~a43 . 4DAA A. Al 4k14 9. 644i * .. 40 0SA AO % ;! 6

CA A vY /ýq~ aJ~ 644.6 93234.5

DATA WDvTi1,.2OeN .~.Z6J u 71 90DdJ 72/

83

DATA l0iV DAT~~~~A A 3/1146. ;i~ MO 45.

CALL ZISSILA IC97ZU!S FOR PLO2 --- ---------------

CAL 1150 1 01.4 ~~~~CA4 UA~ (G6

CAL XMAS 1 I Ical5 1%)ODN~.10CAL all a'~CS4)XMTgLS)'10

CAI Puy$ aCAL PlAlA

CALL L 1A 03INrCAL CDV 1 0L M S ,5

CALL C UDVI (0146;CS 14iniH o(Z)SlI

CALL AsCD .OUCALL CI NU~

CALL CORVu 01UG.~8~$tiJ t oa S 8 Ii I ICCA CaaD IY5CA.H5 ( 36CA C.

CA a 1 M

84

C 1113 PROGRAM 1S C131GN TO GENERAll THE EATA FOR THE GRAPHTCrAyL bl.6UilUh wt 'am. arlm' AN" TH usrl LCAD E01IA11UN. mwr.I? rs 5 I

E zAua SU~s A? b A (.AisrT ILO? HELICCPTIR ESSIGN PAPAMtETRIC OPTIMIZATICN

C ASSUMPTIONS:14C 1> INGINISP19CIPIZE

CVIAIZALE OPTICN3

C

CALL PITCHS (OVILI1C11 00002 1,'rzSK $01CRPT100C _ -- -------- ---- ---- ---- ---

C --- --------------Ca ----- a -aaa------------------

CALL F3!TCAS 0!1L!E1 4,'03 ,DTSK ',1CIPT21,C_ >DATA 0,$A

IC-L aa

C PAS 2 i AV ILAl!

c r. '12 013K LODN

- %, C l CUTAT 2~ i VL C17 CZDSEC

K 93/C IS*III +11. 80 7 8*C L 9* 2)K 21 0gC2) /CLSO (11.¶.8078 4CLRt*2)

*4D (.; ODO 0 1C VII*60C,70C.25

CC ARRAY INCR!IN'ZE3s

C ioliGal EQTJATZCbC

W 1402Si(41.1rL*5/ (%T*.1.5)*d1K*?~~.w..K

CALCULASICN 01 WE CAIA

C M

-.- F4? 1: 1641:103) 4/4PO

3 4. D)/O.02379*Z,*V 852

4 w- 4 4 144 ý 4 6* *u~ *4-~- 4 6yu~- 6~ 44A *r~~jw~ 4 444 o ,.0^k*

C HE AS ECI IATIO AC W AP O TE IN CASPIT PLOOTDAC CCIDISPONCINC UBIGHT ?EST BE QBT lNED. ISIS PROGRAE UTILIZES

Cj 111 M.A

CV461111 *OPTIC ~S4AT VI

DATA0

Do 90 .1 5

c NT P 1, :2Pi VA ALZ up

c it ,L DISK LOADINGC VIs TIP VILOCIII ?I/SECCC CONSTANTS BASUr Cb CLI

K1: o.9se3 /CL14t)*('1+1.8O78*CLB(L)**2)

I5J1954/1111H EQUATIC$

I V ~.31 3 ) /Lj IL*.)*5)-K~4 VT +5* 5(bL (L) 590 CONTIN d ~) I

C SUMA? SIATEMIlI

2? MINAT I~. I IWc4//STOPEND

86

APPENDIX D. PROGRAIS TO ACCESS HESCOMP

This section contains the control language programs

needed to access HESCOMP on the IBM main-frame computer.

4,:

87

0*000 too00*0*0 0 4r 4 F01 W fO

0*0 low M

0*0 *000a

... 0*0 A 9~*aN UN N .4 0 SOIWMF C;~~0@ C; 0 0 w %Moo*

00 *S 0* 1%ADo 0N0* N45 00Ao 1

In 0 W0 U

40 14N **.ý . ~ N 0

0*:40 ON 00 U04 99.-fm~r 4 0N '9.9....... 0 0 00 ' N 0NVU90 9ý %4 . S ON

0* ab 0*

*0 *000* 4.10 *0000 0 &

00 sli **0l %4 -A00 * 00. w9 9I~'N* VI& 1 99 0 40wo1. W 0 VN- V9 NO M qVq,@*'"

40 'a 99 00% 000O 9'949Mtf4" 00 P-149 9I Ua 0% 4**1MONMO9 AD 0"J t%, .8;(W4Q* 0 U 0 990$ 0 W:v~f9 W@U4M U#V -a'0U W *'iW109 U D Q 1r99 1

Mv* . - O

o0 al 44 0 "U*ý-a0"w~o f-~

No ~ *04 NO

00 A to*# . 4p

*00 mi* 0 .04. In 1 4 5 -1..9

00~ ~ S 0a'NO 000 0,00@0 .. #..00 1~e. 0 *@ 0N 000 00" O 9 ~"f. 0m

N*994 loin ~^

I.%Otc w;N, I 00ofm"wk 0NOW-4mM"4 40

00 99* 00 88

a ooO 0 --- ----j S.

*ow 0 Agmcq 00o 04NON Wo

eo. 06 0 %UM6@ 0 0 a 604 p 0.

S ~ 0D a 0 a 000 SN *

MOM N0i 0*PN aA fU-o o ko S sNUG aU o900 @.a- -to* :V f ow.A~l- a. 0rm 0010 6916 il AF0 a1 0S* * S Ow Wi owl *0s

C,0. 0 w; OrN = ON-Nrm 0N

'41

*0

OnO0n$0 0UP40 0 Q c

N~I Mm MmS glt n=0N98WW~ KnNOW LMW.~4 N4 soN1 t0" or. took .00

NOG Ul@0q -oO *U¶0 5 lR000000eJ M Q@ 0~ 0 9 0 9 *

N0*0 ,.0,..@.. . ~ 0 9- 0* 0U . .0 S~n~j90~e~89N @

a 0%0d0(40% 0f M. w* ON9 SO :(. 00NN9~ 0 sC% O a 0 0 0 6 .4 . -0.0 4 ON . 0. 0 0 VN. S Cp

bO -09 000- - - * 00 COOI... 6*...00 -1 M. U'. or .*

F-wev@@0 (.0 *j 04 00 4 l.. OMNd In 10 tOO GO U10

ef t . = 4 0 .0 acO S U29 V1=1 W vivi" 60 00 ad.%! .1" 11" UNA~ e10 . U% rO. 0 # d0940 W ~~0 00A.l6%P 'D'" 000 0 U%0 4 LO vf# 000

40 1PlR M4m-&" WCU a%.0 M0Wa11am Woo* W"J0 *4 42F otna t va %.AON~~~. 0 0%N 00#064 N c 0 0 0 O 0 0.010 1s0 to 0I- GM owpl1.0I 400

NO 0 ,. ,C OO0.NOO0000@"w . W . NMONON.W0O Oft FO ON 0 4-* **~~

0 *P -0" G *ol 14 NON" '449 N-M -W- ato warN(. -0* f% a0 df40%NM040 ON-0 90 a* M30

(VNi M U, M .t 1 A60 0AOt-4V 41 60a@10 M .0 ý 904 0 .0*w"o 0M O ENGA ON .1 9- 0 *i C a--fr$0 00a o0i-

4N-C04~E0" N N00 0 N00000"M 0 ERN,&% OwNI 000'0 00(9 *00 W * 6100 V% fi 1eO C eM (NMCwo"

*090

U991

APPENDIX B: HESCOMP INPUT AND OUTPUT EXAMPLES

This section contains samples of the IBM computer

input and output.

92

4~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~a Oro'~ j~ 9i¶ '~W~~ ~~ ~~'Wlq~~r~ j~w

4. f . .4 ,ý

-n 0 3 00 )OCO to-.~J- #000Q 040000

4~fr~rý A40 toolN N ~ 0~0* 4 0 *I 4 f4 t f * 4 0 M! !N # 0 Owr

04

44

44 godhCm 0 00000 .t0j@00~0 00000

AA 4 m @0.oN 0*.J00

00

0 .,0'00.

v 4 0

COS0 -f 4oC

4 .. JA fl2000O O U. 0 0004 4.,3e0*.ZN00

- 0 Li 1-.- - r a Iat4 0

40 -400

a... 044

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LIST OF REFERENCES

1. Layton, Donald M., Helicopter Performance, Naval Post-graduate School, Monterey, California, 1980

2. Zalesch, Steven E., Preliminary Design Methods Appliedto Advanced Rotary Wing'Concepts, university ofMaryland, May 1973.

3. Layton, Donald M., Helicopter Design Manual, NavalPostgraduate School, Monterey, California, July 1983.

4. Carmona, W. F., Computer Programs for Helicopter HighSpeed Flight Analysis, Master's Thesis, Naval Postgrad-uate School, Monterey, California, 1983.

S. Hiller Aircraft Corporation Report 60-92, Proposal forthe Light Observation Helicopter PerformanceDiTaWtaReport, 1960.

6. Class Notes, Helicopter Performance Course, NavalPostgraduate School, Monterey, California, 1963

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INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Technical Information Center 2Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2Naval Postgraduate SchoolMonterey, California 93943

3. Department Chairman, Code 67 1Department of AeronauticsNaval Postgraduate SchoolMonterey, California 93943

4. LT Allen C. Hansen, USN 5Air DepartmentUSS Enterprise (CVN-6S)FPO San Francisco 96601

5. Professor Donald M. Layton SCode 67LnDepartment of AeronauticsNaval Postgraduate SchoolMonterey, California 93943

6. Aviation Safety Programs 2

Code 034 ZgNaval Postgraduate SchoolMonterey, California 93943

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