An analysis of three approaches to the helicopter ...

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Theses and Dissertations Thesis Collection

1984

An analysis of three approaches to the helicopter

preliminary design problem.

Hansen, Allen C.

Monterey, California. Naval Postgraduate School

http://hdl.handle.net/10945/19147

00i_

A 93943

T s y i g fa

i

Monterey, California

THESISTHREE

AN ANALYSIS OFAPPROACHES TO THE HELICOPTER

DESIGN PROBLEMPRELIMINARY

by

Allen C. Hansen

March 1984

Thesis Advisor: I). M. Layton

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An Analysis of Three Approaches to theHelicopter Preliminary Design Problem

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Allen C. Hansen

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SensitivityPreliminary Helicopter DesignCarpet PlotsHESCOMP

20. ABSTRACT (Continue on reroreo eldo It neceeeory mid Identity by block number)

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 per-

formance equations. The purpose here is to ascertain wherereasonable simplifications can be made that do not seriouslydegrade 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.

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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 19 84

DUDLEY KNOX LIBRARYNaval p

MON CALIFORNIA 93943ABSTRACT

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.

TABLE OF CONTENTS

I. INTRODUCTION 10

A. GENERAL 10

B. OBJECTIVE 11

II. 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 52

B. ASSUMPTIONS 3 3

C. METHODOLOGY 54

D. HOVER EQUATIONS 55

E. WEIGHT EQUATIONS 59

F. GRAPHICAL ANALYSIS 45

IV. HESCOMP 54

A. DESCRIPTION OF PROGRAM 54

B. PROGRAM MODIFICATIONS ANDIMPLEMENTATION 56

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 7 3

APPENDIX D: PROGRAMS TO ACCESS HESCOMP 8 7

APPENDIX E: HESCOMP INPUT AND OUTPUT EXAMPLES . . 92

LIST OF REFERENCES 115

INITIAL DISTRIBUTION LIST 116

LIST OF TABLES

2.1 HELICOPTER WEIGHT COMPARISON 20

2.2 TAIL ROTOR SIZING 2 4

4.1 HELICOPTER CONFIGURATIONS WHICH MAY BESTUDIED USING HESCOMP 55

4.2 PARTITIONED DATA SET 57

LIST OF FIGURES

2.1 FM VERSUS BLADE LOADING CT/a 21

2.2 POWER REQUIRED VERSUS FORWARD VELOCITY 2 5

3.1 WEIGHT EQUATION PLOT: C Tn = 0.5 40

3.2 HELICOPTER CARPET PLOTS: C LR=0.5 46

3.3 HELICOPTER CARPET PLOTSFAMILY OF SOLUTIONS 48

3.4 HELICOPTER CARPET PLOTS ROTORDIAMETER AND WEIGHT LIMITS 49

3.5 ASPECT RATIO BOUNDARY PLOT 51

3.6 HELICOPTER CARPET PLOTSFINAL SOLUTION 53

4.1 HESCOMP PROGRAM FLOW 58

ACKNOWLEDGMENT

I would like to acknowledge the invaluable assistance

of Professor Donald M. Layton in this endeavor. His

encouragement and support greatly contributed to making

this both an interesting and worthwhile experience.

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-Bell

venture, 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

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 equations. Surprisingly

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 the

methods 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 design 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

particularly instructive since they give visual insight

into 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

system.

12

II. SENSITIVITY ANALYSES OF BASIC HELICOPTER EQUATIONS

A. DESCRIPTION OF PROBLEM

In preliminary helicopter design, there are 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

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

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:

a = 5| (2.1)TT R

13

C. DISK LOADING:

Disk loading is defined as the ratio of the weight to

the total area of the rotor disk.

m WEIGHTUL ~ AREA

(2.2)

-£ j [lo/ft

]

ttR

D. POWER LOADING

Power loading is the ratio of weight to input power.

PL = p^ [lb/hp] (2.3)in

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

rewrite the power loading for the hover condition as

PT _L- ROTOR THRUST nh/h i r? d1P. ROTOR HORSEPOWER L 1D/n P-l U-^Jin

E. COEFFICIENT OF THRUST AND POWER

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

coefficient which facilitates computations and comparisons

C = —^ = —2-12

(2.5)ApV-jT ttR p(ftR)

Similarly, a coefficient of power, C , has been

established as

:

14

— ;

z (2-6)ApV

T" ttR" p (2R)

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 2

ApV^T

(2.5)Ap(1.167)

Z

T

Ap (1.361)

The coefficient of thrust is reduced by 26.9 percent

Similarly, for the coefficient of power:

15

c . - - ~P . „ 3

ApVT

Ap(1.167)3

(2.6)

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, P , and induced power, P. .

Utilizing black element theory the profiletpower

required to hover can be expressed as

:

The induced power predicted by momentum theory is:

P. = V. Ti in

T 5/2

(2.8)

/-y d 2ZTTpR

The total power required to hover is

PT

-?i

P (2.9)

16

T3/2

1 - 3PT

=^

+ ± ar

CdQ p A(flR)* (2.10)

v

ZnpR2

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 an

average profile drag coefficient, as well as a fixed

rotational velocity, equation (2.10) reduces to

P =T~

+ C2r2 (2 ' 11}

where C-, and C?

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.

m- ° " " |+ 2 C

2R < 2 - 12A)

or — = 2 C2R2 (2.12B)

which implies Pi

= 2 Po

(2.12C)

17

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

- Pi + P (2.9)

5/2PT — • 5

+ 5»r Udo p* vtip

3r2 < 2 - 10 )

/2tt p^

In a hover, thrust equals weight. Solving equation

(2.11) for weight one obtains:

W3/2 = [PT

- -g- a Cdo

pit VT^ R

2] /pA (2.15)

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, K , is:

W = [47.527 PT

R - JH 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 >> K, be

Thus,

W % [47.527 PT

R]2/3

(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 induced

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 lbs) (1000 lbs) 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 19.53 95%•

H-543 42.00 42.00 100%

H-53D 42.00 41.00 98%

H-53E 73.50 69.00 84%

20

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

FM =

rrPL

DL

/p"

(2.15)

CT-

/2C

The figure of merit is customarilty plotted against the

quantity CT/a . According to Zalesch [Ref . 2] , CT/a , 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 0.04 008 0.12

Blade Loading

0.18

Figure 2.1. FM Versus Blade Loading CT/a

21

Previous studies have shown that a figure of merit

between 0.70 and 0.80 is considered average.[Ref . 5]

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

total power, the figure of merit will be approximately 0.75.

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 = IV3/2

67.214 PTR (2.16)

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 = 51 feet and

the H-53, R = 56 to 58 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]

:

P = W5/2

1881.98 FM(2.17)

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

W5/2

T 1505.58 (2.18)

22

while an M of 0.70 yields a relationship

w3/2

P " 1517.39 f-2

'

19 ^

If equation (2.17) is solved utilizing the approximate

weight relationship developed earlier of

W3/2

= 47.527 PTR (2. 14)

a value for the figure of merit of 0.707 is obtained. This

is 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

PT * 1.3 [x^]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 1.5 a better approximation

is obtained. The results are tabulated in Table 2.2.

J. FORWARD FLIGHT POWER CONSIDERATIONS

The 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

HELICOPTER

AH-64

UH--IN

SH-3H

s-:76

UH-6 0A

CH--53D

CH--53E

TABLE 2.2

TAIL ROTOR SIZING

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

4.6 4.98 4.59

4.3 4.90 4.52

5.3 5.95 5.5

4.0 4.11 3.79

5.5 5.85 5.4

8.0 8.42 7.78

10.0 11.15 10.29

24

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 EFFECT

o

o6p-

—-s*/

aLEGEND

INDUCED POWFRo-M

PROFILt- POWtlfi'"Parasite power"""total' twfer

S a-02-UOTQCg-O aX

eneo?"

OO

'••-..^

M

—Ob.

7.0 20 000 80 100.0

VELOCITY (KNOTS)ieo.o I40JI loao

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

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 plate area is

a minimum in this direction. The equation for the parasite

power is:

Pp

= \ P V£3

ff

(2.2 1)

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= i a C

dQp A V

T3

[1 + 4.5 y2

] (2.22)

Equation (2.23) is a function primarily of the main

rotor 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 function 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 . V.*it

(2.2 3)

where

Vit

vf

2/v

2

? 2V£V2V Z

1/2T}+ u .v (2.25a)

At high forward velocities, the induced power required

can be approximated as:

WP. = wv. + =

"vi it 2pAVr

(2.24)

The total power for forward flight is the sum of the

induced, profile and parasite powers.

PT " P

i+ P

o+ ?

p(2.25)

27

PT

= T.Vit

+ ^ a CdQ p A V

T3[1 + 4.3 y

2]

(2.25a)

* \ P ££

vf

3

At high forward velocities, equation (2.23) can be

substituted into equation (2.25), resulting in:

WT 2pAV r 8

u "do

\ P ff

vf

3

1 3Vfi a C, p A V/[1 + 4.3 ±]

T P,R-

I£ one makes the following assumptions

W = const C, = const

(2.26)

p = const

VT = const

a = const

Equation (2.26) reduces to

Kl 2 2

PT = -4 + YT R + PT

R2 p

(2.27)

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

dPT

2K-

dRRt + 2 K

2R (2.28)

28

Setting this equal to zero, one obtains

2K--± + 2 K

?R = (2.28a)

RZ

R2K

1

7 * [- -V + 2 K ? R] = (2.28b)R

-5 Z

Kl 2

-4 = K?

IT (2.28c)R^

Z

P. = P (2.28d)10This defines point of minimum total power required for

VMAX range. This corroborates with the res.ults 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

P. = 5 P (2.29)10or

w 2 3p£Vf_^ = L_ (2 30)

29

Solving this equation for velocity results in

vf

[(

W A1/21 1/2

A 3f 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 = 0.0025769 [lb sec2/ft

4] SSL

p = 0.0017553 [lb sec2/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:

1/p/pSSL => l to7385

This translates to a 35 percent increase in the induced

power

.

30

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 P and P are reduced.o p

31

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 characterized

by 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 5

a = slope of airfoil section lift curve, dC /da,

per rad.

a =5.73

6 = blade section drag coefficient

5Q

= .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, £ TRis 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 95 F.

34

5. 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

1 . 1 3W DL

550B/2pQ ,/p/p o

6WY"T p/p

4400 C LPo

CLRo

Iap/p

Q J

(3.1)

At an altitude of 6,000 feet and a temperature of 95 ,

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

to :

PT6000/95°F

" -035479W[DL]1/2

(3.2)

+ -^1971 [10]" 5

(1 + 1.LLRo

8 779 CT n ")W VTLRo I

35

The tail rotor thrust required to counterbalance the

main rotor torque is

:

550 PTR 550 P

TTR £TR V

T1.19V. (3.3)

where & TRhas been defined as 1.19R . With R„

Rdefined

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

using equation (3) as:

DLTR 550 P

TTR ATD 1.19VT \ 77ZZ2iR T tt ( . 16R)

(3.4)

550 PT DL

1.19(.0256)VT

W

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

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

speed and that o TR= .02 and 3 TR

= .90 . With these

assumptions the equation for the tail rotor power required

to hover can be written as

:

13/2

= 2055.7TRHover

DLW p/p

1/2

.012605 PTHover

C LRTR

THoverVT

(3.5)

36

The equation for the tail rotor mean blade lift coeffi

cient can be written as

TLRTR 562.5(p/p )

(3.6)

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

= 2574.7TR6000/950

DLW

1/2T

II

VT

3/2

+ 5.3134 (5.7)

It is assumed that the gear losses amount to 3 percent

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

brake horsepower required to hover becomes:

T

P + PrTm TTR

96(3.8)

Empirical studies have shown that the tail rotor power

required to hover can be approximated by

AC8 [total horsepower to hover]

This allows one to write the main rotor power required to

hover as :

PTm " C- 88^ PTnP

(3.9)

37

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

if equations (5.2) and (3.7) are substituted in equation

(5.8) , one obtains

PT = .036757 W /DL^6000/95°

(10)" 5[1 + 1.80779 C TD ^

2] W V

T(3.10)

'LRo

+ 2475.6

LRo

'DL

'W

TmVT

3/2

+ 5.534

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), C fR(rotor mean lift coefficient)

and PT (total power to hover)

W =

411.51 DLi/4 V,

1/ 7 "1

TJl1 + K.

T

T/DL

- K

VT

+ K4

/DL(5.11)

where

K, = P(10)

T6000/90w

K5

00025929C LRo

(1 + 1.80779 C LRo^)

(5.11a)

(5.11b)

38

tr o 5 o 4 bK3

= —K— LZ-Hc)

K _ 5695.7K4 k (3. lid)

K5

" 4^ CI * L80779 CLRo

2) (3. lie)

LRo

Equation (3.11) has been programmed in Appendix B

and solved for tip speeds from 600 to 700 cps and CT D

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 V™ , DL , C T n andT LRo

PT , 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 5.1.

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

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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. 5] 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 number 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:

W/DL = A = ttR' (3.12)

W/PL = MHP = 2 50 (3.15)

(Military rating for Allison T-63 at sea level.) (PL =

Power Loading.)

P = /A7V, (5.14)

Using these equations the component weight for the

specified helicopter empty weight may be reduced to the

following

Engine, Controls and Accessories 617.5 lbs

Engine SectionGroup 053 [W/PL]

1.0719.5 lbs. (5.15)

Main Trans-mission 10.43

T(,1.29 5

IV

(PL VT )

86380

1221 p- 0UJ(5.16)

Rotor DriveShaft

Tail Rotor

5.56W1.05

(PL VT

)* (DL)

55

52.22W1.14

(PL VT )

1.7

266 p- 7(5.17)

17449

V,1.14

(5.18)

42

The engine, controls and accessories category includes

such items as lubrication and oil cooling system, engines,

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 S «- = 59.47 /P (3.19)

(PL VT

(DL)""

Tail Rotor w1.355 q7Drive .124 2-— y-^ = 2.886 P /A (3.20)Shaft (PL V

T ) (DL)

"

Body and 916 qqGear = 1.91 W + .0294 WLanding

Rotor ..1.185 .33 ,q ,- --

Blade j>5 . 1 5 t-^-f = o5.15 tt- A a (.3.Z1J

Teetering V-CDL)*103 V

T

Rotor Blade 1.205 .33 9nQ _-

Artie- 19.77 rrrr = 19.77 rr- A a (.3.ZZJ

ulated VT(DL)^ UD V

T

Rotor Hub w l . 21?1

Teetering .0088 ^r = .0088 WA (3.23)DL'

Zi

Rotor Hub w 1 - 2171

Artie- .00975 j±= 00975 WA

*

(3.24)

ulated DL*

43

Fuel System .416 per gallon capacity = .0615 W n (3.25)r

where W_ = fuel weight.

The individual component weights may now be combined

into a single expression for the helicopter empty weight

W = 617.5 + .0617W„ = 1221P'863

+ 266P*7

+F

x "™ 1.14T1

(3.26)

+ 58.47/P + 2.886P,57

/A + .191W 916+ .0294W'"

+ appropriate rotor blade and hub weights.

As stated earlier, the design specifications called for

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

(400 lbs) and the required fuel weight (W_) . The fuelr

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:

Wp

= 3(180.2) (.822) + |g. (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

.

Wu

= 200 + 400 + 452.6 + 20 = 1072.6 lbs (3.28)

A new variable, WgAR , 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'

863= 266P'

7+

17^

4

^ 4+ 58.47/P

VT

(3.29)

57 — 916 99+ 2.886P /A + .191W + .0294W

+ appropriate rotor blade and hub weights.

Equation (3.11) together with equation (3.29) 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 5.2. The graph in

Figure 3.2 was generated for a specific value of C.R

over

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

F. GRAPHICAL ANALYSIS

Graphs similar to Figure 3.1 are generated for several

value of C yR , and are then cross plotted to form Figure

3.2.

The mean lift coefficient, CyR , values are selected

based on what is considered the historical average range of

45

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values. Figure 3.5 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 5.2

and 5.5.

The solution field depicted in Figure 5.5 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 given in the design specifications. This

limiting value is based on the operating environment of the

helicopter. IVith R max specified, there is a linear

relationship between the disk loading and the gross weight.

W WDL = ? =

A D 2t: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 5.4

2 . Respect Ratio Boundary

It is evident that a further restriction is still

necessary to completely define the region of acceptable

47

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design solutions. Studies have indicated that a main

rotor aspect ratio of 21, is a representative upper limit

Thus

21 >R<mr>C<mr>

b_TTCJ

b p oCLR

VT2

QTT DL

or DL >

b p CLR V

126tt

For the case of a two bladed main rotor equation (3.50)

reduces to:

DL > .000012 CLR

VT

"

The detemination of this boundary graphically is as

follows

:

2The hover solution plot of Figure 5.2 is replotted

relative to the coordinates disk loading and design mean

blade lift coefficient. The limiting curves for

DL = .000012 C LR\'

2are then plotted. The intersection

with the appropriate constant tip speed lines of the hover

solution represent the aspect ratio boundary; Figure 5.5.

For a helicopter rotor, the aspect ratio is defined asthe radius divided by the chord.

2For clarity lines of constant gross weight are omitted

50

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a

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4->

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9'0 9'0 V0 ro

51

These intersection points are then cross plotted onto

Figure 3.4. Figure 3.6 represents a graphical plot of the

solution set satisfying the performance and structural

design criteria of a small observation helicopter as

specified in this study.

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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

TABLE 4.1

HELICOPTER CONFIGURATIONSWHICH MAY BE STUDIED USING HESCOMP

HELICOPTER CONFIGURATIONS WHICH HA* BE STUDIED USIHG HESCOMP.

^~"~--^Addltlonal Lif t/Propul.i ion' -~-S.y3tcm Components Which

~^~"-—JJunt be Added toHelicopter

—

^"Pure"Type ^-\Conf.

(Doth Single I Tandem Rotor) ^~"-^_^ Wing

Propellerfor

Auxil laryPropul slon

Auxi llaryIndependentEngines

Type of Auxil loryIndependent Engines 1

T/Shaft T/Fan T/Jet

Pure Helicopter .

winged Helicopter X

Compound Helicopter

(1) Coupled (prim, enginesdrive auxiliary propulsionsy9 tern)

(2) Auxiliary Independentpropulsion system

(u) T/Shaft engine(b) T/Fan engine(e) T/Jet engine

X X

XXX

X XXX

XX

X

Auxiliary Propulsion Helicopter

(1) Coupled (prim, enginesdrive auxiliary propulsionsystem)


(a) T/Shaft engine(b| T/Fan engine(c) T/Jet enalna

X

X X

XX

XX

X

oaxial Rotor Helicopter

(1) Coupled (prim, enginesdrive auxiliary propulsionsystem)


(a) T/Sliaft engine(b) T/Fan engine

(c) T/Jot engine

X

X X

X

X

X

X

X

55

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

SI

S2

S5

S4

S5

S6

S7

S8

1 - 1681 1681 AERO

1682 -• 4132 2451 CLIMB

4153 •• 6551 2399 XIBIV

6532 - 8974 2443 POWAVL

8975 • 10870 1896 PRINT 1

10871 13042 2172 ROT POW

13043 - 15583 2541 CRUS 5

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. There are

57

INUNl AMU PHOflll EH/KUIOR QATA. NLINI SIZING LSI It MIAVllMUl UOHIRIC Of f INI T IONS

SUH'.TSIlN tf ICliT 1RINI) COIFFICIFNTSVI Ml CI L AtRUUTMNIC UIASAUIRISIICSMISSION PHUl lit OAIA

MISSIONPERFORMANCESUBPROGRAM

ACCESSES 9

PERFORMANCESUBROUTINES

INPUT

AEROOTNANICSSUUHOUflNE

SWE 1R1NOSSUOROUIINt

iNGINESUINGSUURDUlINf

Mi IGKISIRtNOSSu«ROUTINE

OOII U'^1. OflAlltO VtHlCll OININMON'j

1 • SUUSTSKMS Mt IGHI aWAADU*1 t ENGINE BAKU PUWI R

1• PARASIIt DRAG BRIArDOUN

NISSION PIRtOHMANU UNI H»TOnT

Figure 4.1. HESCOMP Program Flow

58

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.

59

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

in the 5,000 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

HESCOMP 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.

61

APPENDIX A: NOMENCLATURE

TERM DEFINITION UNITS

a Slope of Airfoil Section RadiansLift Curve

2A Rotor Disk Area ft

AR Aspect Ratio Dimensionless

ATR Tail Rotor Disk Area ft2

b Number of Rotor Baldes Dimensionless

B Tip Loss Factor Dimensionless

C Main Rotor Cord ft

C, Profile Drag Coefficient Dimensionlessat Zero Lift

C, „ Design Mean Blade Lift DimensionlessCoefficient at Sea Level

CT

Coefficient of Thrust Dimensionless

C Coefficient of Power DimensionlessP

5 Blade Section Drag DimensionlessCoefficient

DL Disk Loading lb/ft2

FM Figure of Merit Dimensionless

HP Horsepower

LTR Tail Rotor Moment Arm ft

2 4p Air Density lb sec"/ft

y Advance Ratio Dimensionless

R Rotor Radius ft

62

TERM DEFINITION UNITS

PT

Total Power HP

PTM Main Rotor Total Power HP

PTtd Tail Rotor Total Power Hp

P^ Profile Power HP

P- Induced Power HP

P Parasite Power HPP

PL Power Loading LB/HP

R Rotor Radius ft

T Thrust HP

V, Induced Velocity ft/sec

Vp Forward Velocity ft/sec

V Aircraft Forward Speed ft/sec

VT Rotor Tip Speed ft/sec

W Aircraft Gross Weight lbs

W Empty Weight lbs

W- Fuel Weight lbsF 5

W Useful Load lbsu

WBAD Empty Weight PlustBAK

Useful Load lbs

Solidity Dimensionless

63

APPENDIX B: CARPET PLOT FORMULATION FOR 2 0,0 00 LBCLASS HELICOPTER

Bl SPECIFICATIONS:

Maximum Gross Weight: 20,000 poundsMaximum Rotor Diameter: 30 feet

B2 PRELIMINARY ENGINE SIZING:

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

W = [4.753PTR]

2/o

20,000 = [47.53PT

30]2/3

PT

= 1985 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 5 for a utility helicopter:#7: 609 lbs; #9: 129 lbs; #10: 76 lbs;#11: 410 lbs; #12: 459 lbs; and #15: 502 lbs.

64

TABLE B.l

ENGINE SELECTION PARAMETERS

The following turboshat power plant data arepresented for one engine.

Engines: A B C D* E F

Dry Weight (lbs) 158 288 423 709 580 750

SHP (ssl) Military 420 708 1561 1800 2500 3400Normal 370 659 1318 1530 2200 3000Cruise 278 494 1989 1148 1650 2250

SFC (ssl) Military .650 .573 .460 .595 .615 .545Normal .651 .573 .470 .606 .622 .562Cruise .709 .599 .510 .661 .678 .610

Initial Costs $93K $100K $580K $560K $640K $700K

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

Preventative Maintper hour/eng ine $25 $50 $1

MTBMA (hrs) 3.5 3.0 2.0

MDT (hrs) 0.7 0.6 0.5

MTBF (hrs) 185 210 205

MTBR (hrs) 600 750 800

$50 $100 $125 $160 $220

3.0 4.0 3.5

1.3 2.0 2.6

285 280 320

800 1000 750

65

B3.2 Simplifications

W , D 2

DL £pmW 'A

= MHP = 31,00 ; p = ±-

B5.5 Engine Group

.055(5100)1,07

= 272 lbs

B3.4 Main Transmission

10.43IV1.295

Upm Vt )

163 ~ .432

LA J

= 10.43 W 865A+ - 432

Upmr 863vT

- 863

(10.43) (3100) •86 -5 p- 863

= 10,748P863

B3.5 Rotor Drive Shaft

5.56W1.05

.7w

.35(£pm V

T ) [£]

= 5.56(5100) 'V 7

= 1545P.7

B3.6 Tail Rotor

32.22W1.14

(Jlpm VT )

1.14307,600

VT7TA

VT

66

Tail Rotor Gear Box

.7 5

3. 7 = ~ = (3.7)(3100) Po ^ . o

w(4pm V

T ) [£]

= 206P.5

3.8 Tail Rotor Drive Shaft

124 W1.355

Upm)5 7 .

r. 7 8 5

w

(.124) (3100)- 57

P' 57

/a

A85

12.12P'57

/A

3.9 Landing Gear

916 99= .191W yi ° + .0294W

3.10 Rotor Blades Articulated

19.77,.1.206 .33W a

VT

DL.205

.205 .33= 19.77 ~ A a

vT

B3.ll Rotor Hub Articulated

00975IV

1.2100975WA

.21

DL

67

B5.12 Fuel System 0615 W,

Calculation of fuel weight three hours at

cruise SHP

1513 lbs + 10%

1664 lbs

3.13 Total Equation

WB = 12,987,* + 107948P- 863+ 1545P"

7

307600 in , n .s c 7+J 14

+ 206P ,:>+ 12.12p- b7

/A"vTi - 14

916 99+ .191W + .0294W

W 9 5 3 3 21+ 19.77 ^- A'"

u:5S + .00975WA

VT

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:

K,

W =

1 411 51DL

3/4I1

+ K 7

vT

/ur

1/2

- K

VT

+ K5

/DL

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

68

where

:

9583 ?= -^^ (i + 1.8073 C TD n

1 CLRo LRo

K2

PT6000/950 1J£-1K

l

0.00025929 ,, , ,„„,.„ 2.K

'"LRC~ CI * l-8078CLRb

-)

o

„ 553480.0K4

= —

r

v 5695.7K5

=K1

B. 5 GRAPHICAL RESULTS

Figure B.l is an example of equation (3.13) plotted

against equation (B.4) for a specific design mean lift

coefficient

.

Figure B.2 illustrates the family of curves obtained

when the design mean lift coefficient is varied from

0.3 to 0.7 .

In Figure B.3 the solution matrix depicted in Figure

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

weight, rotor diameter and aspect ratio.

69

ot^

II

5CJ• •

CO4-» COo CO

Q_CD

+-> o>•j^2

CD

CJ DL.

CLOo©

o

II

o

4->

CD

Jh

cs en

O 4->

•H i—

I

i—l -H0) +->

CD

b0

00961 0006L 00581

70

CO*-*

OCL4-» COCD COCL CO

<3(J

>i_ —'CD ~—

*

^-»

Q.OOD

CD

po

ooSh

Ctf '/)

CJ CO

re

Jh i—

I

-M&. XO 4->

<D +J

PQ

0)

boH

00S0S 00003 0096L 00061

sqi ;m6|9m ssojq00S8L

71

05<+-»

oQ.*— €0Q) COQ. CO^^

eg Co >u. —•*

CD• ^M*

— •*

S-~ooCD

+->

o

P.

Oh >,O 4->

pq

<u

DOH

00902 00003 0056L 00061

sqj ;q6i9M ssoj$00981

72

APPENDIX C. CARPET PLOT METHODOLOGY FLOW CHART ANDEXAMPLE 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.

73

oOtalrth«Hcootec

designsoecf-Hcatto

3

slie engine for•etgnt class

•odtfy eqn3.11 a*required

<3«v#loo »efgmeqn: ^roceoureoutlined fn sec

•d* cnot 3

L

graon eqnsto ootain

IntersectionPts

reolotIntersect Otsfor CLr-.3to.7and vt-«oot07oo

aoolyBoundarycondltons

74

C ******** *************44444********<4*****44444*************************

» , ,.,»,». GRAPHICAL fcELICCPTEF DESIGN EFOGRAM **********c ******** CARErT PLCT NUCEER 1 ********«,,,...» EY AL HANSEN ********

C******** ********c ******** TEIS pscGFA* IS DESIGNII TO PBOVIDE A HEIGHT VS. **4***»*........ CISK ICAEING GRAPH Al SEVERAL DIFFERENT ROTOH ********........ TIP VELOCITIES FOR A SPECIFIED DESIGN SEAN ********

C***»**** LIFT COEFf fICEN'T. ********C********** OBSERVATION CLASS **********C***4**************** 444** 4********4****** ******************************C******»*************444444***************************************4»**4*c**** *****C** NOKENCIATURE ***C* **C* VJBIABLES: **C* **C* CLE EESIGN KEAN LIFT COEFIICENT **C* VI TIP VELOCITY **C* DL DISK LCAEINGC* b WEIGHT IS CALCULATED FFC."i POWER EQUATION **C* i'E CESFOL LCAD ILUS EMPTY WEIGHT **C* Pi FCWEE AVAILAELE IN HORSEPOWER **C* *»C**** 4**4*£4*44*********************4****4***44***********************************

311 KJ

*******************4****4***< 4***** **»******************:3EAL CLR,EL f 1 5C ) ,W1 (150) . W2 (1 5C) , W3 (150) . W4 (150) , W5 (150) ,

• E1 (15 0) ,WB2 ( 150) ,WE3 (IbO) , WEM1:>0) , «E5 (150)

INTEGER ICcC DEFINE FILESC

CALL FBTCMS ('FILiDEE ','3 ','DISK •/

, CR?T35'1 'EATA , • A ')

CALL FRTCHS ('JILEEEr ','U ','CISK ','CRPT45'1 TATA • • A

C READ DATA FROM FILE: C2PTX DATA AC

EC 10 1=1,99C CRPT1 DATA A

HEAD (3,"/C) DL (I) ,Vi 1 (I) , WE1 (I) ,W2 (I) ,WE2 (I)C CRPI2 DATA A

BEAD (4,71) W3 (I) ,WE 2 (I) , W4 (I) ,WB4 (I) , W5 (I) , WB5 (I)10 CONTINUECC CALL DISSPLA RCCTINES FOB PLOTC

CALL TEK618CALL MECEUFCALL RESET (3H2IL)CALL HWSCAL ('SCREEN')CALL PAGE (12-C, 9.5)

:l.i,.H,

CALL GBACE (0CALL PHYSCR

(

CALL AEEA2D (10.0,6.CALL FBAKECALL SklESLCALL BASALF ('L/CSTC')CALL MIXAIF ( 'STAND')CALL INTAXSCALL YTICKS (5,CALL XTICKS (5CALL SHDCHR ( - 90 , 1 , . 015 , 1

)

CALL HEIGET (- 1b)CALL XNARE" ('' (D) ISK (L) A DI NG 2 ' , 1 00)

(W) EIGHT | (L3S) )CALL YNAKE ('(G)RCSS (W) EIGHT ( (L3S) ) $ •, 1 00)

CALL HEIGHT (.290)CALL HEAEIN ( ' J H ) ELI COPT E R (C)i>RFET (P)LCTS: (CLR=0.5)S'

C CALL MESSAG ( ' < H)' ELI cCPTE 5 (C)£EF£I (P)LCTS: (CLR=0.5)3'

C 1 100,3.25,7.55)

75

7071

CALL H

CALL TCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALL BMAXLINCALL HCALLCALLCALLCALLCALLCALLCALLCALLSTOPFORMATFOEMATFOEHATEND

EIGET (

HAJ- il.

HKCEVEGLINURVEURVEURVEORVEDEVIASEURVE (DU8VE (DURVE (DURVE (DURVE (DHKCEV (

LREC (4HIE (1,LOEF (1= LIKESTEIGHT (

INESP (IMS ('

INES ('

INES (•INES ('

YLEGN (

EGEND (

ONEEL

. 20)j.- i,2.9,225C. ,5<j. .zoou

(.C18)

(DI ,S1 ,95 ,0[ULf S 2,95,0

B"(D

I,»3,95,0)L,H4,95,0JL,*S,95,0)

L,HI #8L,H

.C3-2,1YG)

E1,95,0)E2,95,0E3,95,0>54,95,0)=5,95,0)0)4.65,1.6 , 1. 35,1)BID)

1$« ,IEAK1

(IEAK1,300,20)

2.0[(

'» ) E I G H(I) NEUC(E FCFI<E) ABAS' (?) CHEIEAK1,4

EDJ {, IPAK ^,2)

LES',IPAK 1,3)

II£J» -IPAK 1,4)E (C) URVES 1 ,16),4.43 ,4.8)

STATES(5 (2X,6(2X,

EST!F 10.F 10. HI

76

c**c**c**c**c**c*»c**c**c**c**c**c**c**c*»c»*c**c**c*c*c*c*c*c*c*c*c*c*c**c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c**

»**********»******4*4*******»***44***************************

******** GHAEHICAI EELICCPTEE DESIGN E50GRAS * ******* FAK1LY OF SOLUTIONS ******* CAEEET PLOT NUBEER 2************************************************

CAEEET PLOT NUBEER 2ES AL HANSEN

FAMILY

C3SE2VATICN CLASS* ******* **4 *** **************** ************ * ****** **********************»4*********»********»***********4******************************

NOMENCIATUEE

» * *

* * ** * ** * *

** *

**** * *

* *** * »

** ** * ***** * *

* * *

* * *

VAHIA3LES:

CLE DESIGN MEAN LIFT COEFEICENTVT TIP VELOCITYDL CISK LOADINGi WEIGHT AS CALCULATED EECM POWEEBE CSEFUL LCAD E LU S EMPTY WEIGHTEA ECi.EE AVAILABLE IN HCBSEPOWEB

EQUATION

CC~-

**DL3EL4DL5CL6CL7V3anV5

17BVT1HVT2WVI3WVT4SVT5EVT1DVI2CVT3DVTU£VI5

4 ******** **BEAL*4 D

*W5(5) ,i6*.VT5(5) ,

*** ************************************************ * * *

********************* * * **

* ************

********

*****EQUAEQUAEQUAEQUAEQUAEQUALEQUALEQU ALEQUALEQUAL" EQUEQUEQUEQUEQUEQUEQUEQUEQUEvU

IS THLS TbLS THLS ItLS THS THES THES THES THES THEALS «

ALS Vi

ALS W

ALS W

ALS W

ALS TALS TALS TALS TALS T*****L3<5)(5) .5;

CVTl (

E DISKE CISKE DISKE CISKE DISKWEIGHTWEIGHTSEIGHTWEIGHTWEIGHT

EIGHTSEIGHTSEIGHTSEIGHTSEIGHTSEE CCERHE CCRSfcE CCEEHE CCREEE CCRE* * 4 4 * * *

ELu (5

LOADING FCELOADING FCFLOADING FCELOADING FCELOADING FCEFOP. CLR=.2FOE CLB=.4FOE CLE =.5

CLS=.6CLB=.7600

CLa= .3CLR= .UCLR= .5CLB= . oCLiv= . 7

FORFOE

at v:

.ELU (5)7 (5) .SV5) ,DVT2

AT VT=o25AT VT=650AT VT=675AT VT=700ESPONDING DISK LCADING AT VT=600ZSPONDING CISK LCACING AT VT=625ESPON'DING DISK LCADING AT VT = 650ESPONDING CISK LCACING AT 7T=675ESPONDING CISK LCACING AT VT=7004********4 4***** **********************,DL5 (5) f

DLC(5) ,DL7f5> ,»J (5) ,*4(5) ,

11(5) ,HVT2{5) ,WV13<5) ,WV1<1 (a) ,

(5) , DVT3 (5) ,DVT4 (5) , DVT5 (5)

********

DEFIt.CATADATACATALATACATADATADATADATALATADATACATADATACATADATADATADATACATADATADATADATA

E DATA —DL3/2.06 ,

2

3/2505- ,2DL4/2.42, 2

Wo/2424. 66DL7/2.60.2S7/2411.92WV^ 1/250 5.W VT2/2478.WVT3/2455.WVT4/2433.WVT5/241 S.DVT1/2.06 ,

DVT2/2.07,DVT3/2. 07 ,

DVT4/2.07,DVT5/2. 05 ,

6 .ZM,244 2

5,24 19

Ut5 2

h 2390467244,2*.23, z J

«2,44,46,«7 ,

«7

.C7,24$.40,•95,.67,.51,.79;.43,.65,.72,.17;2-9519.o99.762.92.63z.652.672.692.69

2.07,5.46,2.47,2419.2.69,2 399.2.81,2383.2 .86,2 372.2 440..24 192,2392,2379,2 36,2.74;2.77,2.79,2.81,2.81

,05I33,47

.69

,a1

'i'i.67

i:3

,13.65

H:. O;.81. a1.8

35 ,2418.25/

399.72,2382.99/

379 .13,2304.65//365.10,2352./

357.35,2342.25/424.67,2411 .92/2402.53.2390.72/3*3 .58,2372.5/,2365. 1.2357. 35/,2352. ,2342.25/

%5/

77

C CALL DISSELA RCCIINES FOB PLOTC

cC70C71

ALLALLALLALLXLLALLALLALLALLALLALLALLALLALLALLALLALLALLALLALLALL

TEK618MEDEOFBESET (3HSSCAL

(

PAGE (12GFAC1 (0PHTSCB (

AEEA2D(

FBARE3WISSL3ASALF

(

dlXALF (

INTAXSYTICKS

(

XTICKS (

SHDCHB (

HEIGET (

XNABE ('

YNAKE I'HEIGHT (

HEAEIN (

HALL)• SCREEN')

:S{e- 5 »

1.0. 1.2)10-0,6.5)

'I/CSTE')• STAl>E' )

50,1, .015, 1

. Ifai

E) I!(Gj BCSS ' (W) EIGHT ('(LBS) ) $' , 1 00)29f

(ElISK (L) OAOINGS', 100)

ALLALLYGRIDALL TALLALLALLALLALLALLALLALLALLALLALLALLALLALLALLALL GALL 3AXLINALL HALLALLALLALLALLALLALLALLTCPCHHATOHflAlOBBATND

EIGfiTB A F (2= 5HKCEVABA3EGLINURVEOBVIOHVEUHVEuhveASfcORVEDBVEDBVEUHVEuavEHKCBVLRECBIE (

LOFF (1=LINESTEIGHT

{

INESP (

INES ('

INES ('

INES ('INES (•

YLEGN (

EGEND (

ON EEL

10)1 JH) ELICCPTEfi (C)fRPET (P)LOTSS',ICC, 1.0, 1)

.20)0,. 1,3. C,230C. ,50. ,2550.)

(.C18)

[D

)D

(

[D(D

(1

B

(

L3,W3,5,0ljj;bu;5;oL5,«5,5,0L6, 1(6, 3,0L7,»7,5,0

V1 1 ,iVT1,5,0)VT2,»VT2,5, 0)VT3,.VT3,5,0)VT4,iVT4,5, 0)VT5.iVT5,5,0).030).2.^.65,1.6, 1.35,1)IYfiRID))

(IEAK 1 ,300, 20). 12)2.0}(h) EIGHTS' ,IEAK1(I(E.

h.IEAK1,4 ,4.4

NEUCEDS 1, IP A K 1,2

HCFILE5' , IPAK 1,3)AEA5ITE3 ' ,IPAK1,4)) CWEB (C) UHVE £' ,16)

3 ,'

(IB V ES4 .8)

STATEMENTS(5 {21,1 10.36 (2X, F 10 rill

78

BY AL HANSEN *»*4***«** ******

B IS DESIGNEE TO GRAPHICALLY DETERMINE ********T SATIO BOUNEARY REQUIREMENTS FOR ********YSTEM USING E5EVIOUSLY GENERATED DATA ********

**********

~ ***** * ************ *444444*****4***4 4***** 4444 4*************************

c********«* GBAtHICil fcELLCCPTEE DESIGN PEOGRAM **********;»«"""» ASPECT RATIC 50UNDARY ***4»***c ******** L0CI Cf HCVER AND USEFUL-LCAD SOLUTIONS ********c ***4**** CAEEET PLCT NDCEER 3 ********c * ,,,*,». 3Y al HANSEN ***4**4*C***<**** ********c **44***4 TBIS PECGEAM«*.»»««. THE ASPECT

,

c . **,.,., A ECTCR SYSTEMC********** ***»,,»»»*c**44****************444*»*********4**4*********************************C**»******4t*********44444*4 ****** **44***********************************C**** *****C** NOMENCLATURE **C* **C* V8BIABLES: **C* **C* CLE DESIGN MEAN LIFT COEFIICENT **C* VT TIP VELOCITY **C* EL DISK LCADINGC* AE ASPECT EATIC. HISTORIC ALLLY ASSUMED TO BE LESS THAN 21 **C* **c**** *****C* DVI1 EQUALS TEE CCRR 5SPC II DI NG DISK LCADING AT VT = 600C* CVT2 EQUALS TfcE CCFB ESPON EING DISK LCADING AT VT=625C* DVI3 EQUALS THE CCRR ESPO N DI NG DISK LCADING AT VT=o50C* EVT4 EQUALS TfcE CCRR ESPO N DI NG DISK LCADING AT VT=675C* DM15 EQUALS TEE CORRESPONDING EISX LCADING AT VT=700C* C600 EQUALS TfcE LIFT COEF AT Vl=o00C* C625 EQUALS TEE LIFT COEF AT VI=o25C* C650 EQUALS TfcE LIFT COEF AT U=o50C* C675 EQUALS TfcE LIFT COEF AT VT=o75C* C700 EQUALS TfcE LIFT COEF AT VI=7G0C**»*****»*»***********************< ************************************

BEAL*U CLE (5) , EL ( 10) ,C600 (1 0) ,C625(1 C) ,Cb5u ( 10) ,

*C675(1 0) .C70J ( 10) ,*DVl1(5),D*I2(5),DVT3l5),DVT4(5) ,DVT5 (5)

CC DEFINE DATA

DATA DVT1/2. 0b,2. U2,2.63, _DATA DVT2/2. C7 ,2.U4,2-65 ,2DATA DVT3/2. 07 ,2.Ut , ^.67,

"

DATA"

DATADATADATADATADATADATADATADATA

CCC CALL DISSELA ECUTINES FOR PLOTC

CALL TEK6 18CALL MEDEUFCALL RESET (3HALL)CALL HWSCAL ( 'SCREEN')CALL PAGE (1^.0, S.5)CALL GEACE (CO)CALL PHYSCR (1.0-1.2)CiLL AEEA2D ( 1 C. ,b. 5)CALL FBAMECALL SWISSLCALL BASALF ('I/CSTE')CALL MIXALF (' STAND' )

CALL INTAXSCALL SHDCER ( . 90 , 1 ,. 15 , 1

]

CALL HEIGHT (. 16)CALL HEIGHT (. lb)CALLXNAME ('(E)ISK (LiOAEINGl • . 1 00]CALL YNAKE ( '

( C [ CEr FICENT OF (1) IFTS ' , 1 00)

CALL HEIGHT (.290)CALL MESSAG (' (H) ELI COPT E R (C)ARPET (P)LGTSS',

79

1 ICO. 2. 25, 7. 55)CALL IlLXUGl (./())L.ui. 'j r d r

l_ . L , . 1 , - . r , . _ , . U 5 ,

I*GRID=5CALL THKCBV (.C 15)CALL PARA3CALL LZGL1NCALL CURVE (DI -C6CC , 10, 0)

(DL,Cc25, 10, 0)DI ,C65C, 10,0!DL,Col5, 10,0DL,C7CC, 10,0

t)

CALL CURVECALL CURVECALL CURVECALL CURVECALL DASECALL CURVECALL CURVECALL CURVECALL CURVE

DVT1 ,C13,5,0)DV12,CLR,5,DVT3,CL3,5,0DVTm,CLR ,5,0)

CALL CURVE (D V 15 . CIR ,5 , )

CALL THKCBV (. C30)CALL DCNEELSTCPENE

80

c*c*c*c*c*c*c*c*c*c** *

c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*c*

VARIABLES:

CLEVTDL

BB

EESIGK MEAN LIFT COEFIICENTTIP VELOCITY

SEIGHT IS CALCULATED EIC^ POKES EQUATIONCSEFUL LOAD ELUS EMPT^ WEIGHTECWER AVAIIAELZ I N* HC RS EFOWE E

CL3 EQUALS THECL4 EQUALS TbEDL5 EQUALS THEDL6 EQUALS TEEEL7 EQUALS THES'3 EQUALS THEK<4 EQUALS THEH5 EQUALS THEB6 EQUALS THEW7 EQUALS THEWVI1 EQUALSWVI2 EQUALSWVI3 EQUALSWVTu EQUALS• VT5 EQUALSCVT1 EQUALSDVI2 EQUALSEVT3 EQUALSDVT4 EQUALS

EQUALS

DISKDISKDISKCISKDISK

LOADINGLOADINGLOADINGLOADINGLOADING

FCFFC5FCFF.CFFCF

CLR=.3CLR=.4CLR=.5CLE=.oCLR=.7

*****

*******

SEIGHT FOE CLR =SEIGHT FOE CLR=.4SEIGHT FOE CLR=.£SEIGHT FOR CLR=-6SEIGHT FOR CLR=.7

HEIGHTS AT V 7=6WEIGHTS AT VT=o25WEIGHTS AT VT=o50WEIGHTS AT VT=o75WEIGHTS AT VT=700TfcS CCEHESPONCING EISK LOADINGTEE CORRESPONDING EISK LCALINGTFZ CORRESPONDING CISK LOADINGTEE CORRESPONDING DISK LOADINGEr CORRESPONDING EISK LCALING

n i.

ATATAT

VT=600VT=o25VT=d50VT=o75VT=730EVT5 .

REE SOIOB DISK ECGNDAEYWBG MAX GFOSS SEIGHT BOUNDARY

C************************** ********* ************************************BEAL*4 DL3 (5) x EL4 i5) ,DL5 (5) , DL6J5) f DL7 (5) , »3(5) . S4 (5) , ED3 (2) ,

*«5 (5) , Wo (5) , B / (5) ,SVT1 (5) ,WV~2 |5] ,WVT3 (5) , KVT4 (5) .WtlG(z) ,

*WVI5 (5) , EVT1 (5) ,DVT2 (5) , D VI 3 ( E) , DVT4 ( 5) ,D VT5 (5 > , L> 1 ( 2) , D2 ( 2 )

CC DEFINE DATA

DATA DL3/2. 06, 2. 07,2.07 ,,2.07, 2. 05/

81

DATA DI/2.52,2.9/IJIU Ntl£/2450. ,2h:u./UA'iA i)Z/ 1.36 ,2.Z^/DATA RD3/2300. ,2450./

C CALL DISSELA HCLTI1.ES FOE PLOTc

1

CALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALL

CALLCALLIIG2CALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLSTOPEND

618EUFETCAL

(

CESCEA2DmeSL

ALFALFAXSCKSCKSCBHGETMEMEGHTDIN

GRTi (

CEVA3LIN'VEVEVEVEVEEVEVrVEVEVECEVDCTVEVEEEL

(3HALL)( 'SCREEN')

1 2 . C , 9.5)

1. 0,1.2)(0-0

• L/CSTC')'STA&D' )

(.90, 1,.015, 1

16)(' (D) ISK (L) OACIMGi ',100)(' (G)SCSS (W) EIGHT | (LBS) ) S' ,100)(.290)(' (H) EIICOPTSB (C)^EPET (E)LOTS3',1CC, 1.0,1)

(.20)2. 0,. 1,3. C,23 C. ,5 C, 2550.)

(-CIS)

<DI3,K3,5,0)(DI«,H4,5,0)pL5,H5,5,0(DLc,«c,3 ,0)( D I 7 ,«/, 5 , 0)

(DVT1 ,kVT 1,5,0)(DVT2,*VI2,5, 0)(DVT3,i'vT3,5,0)(DVT4,SVT«4,5, 0)(DVT5,'.VT5,5, 0)N.C35)

(D1 ,WKG,2,0)(D2 ,3LE,2,0)

82

J;***********************************************************************

^••••..^^ GHAPHICAL fcELICCPTcr uuiui. tfUbtiail **„,*,,..,^C*****»** EAtlLY OF SOLUTIONS *********C******** CAEEET PLOT NUHEEH 5 ********C******** 21 AL HANSEN ********r**»***»* ********..,.,,.. THIS pbcGBAM IS DESIGNEE TO ILLUSTRATE THE FAMILY ********

c ******** c? SOLUTIONS FOE HOVEF AND CSEFUL LOAD ********..,,..,. BEQUIBIHIKSS OF A TEETERING FOTCR SYSTEM ********,,»,,.», HITH pcxc? DIAMETER, FAX GROSS WEIGHT AND ********..,,.»., ASEECT RATIO ECL'NDARIES. ********

C**»»**»* CESEEVATION CLASS HELICCETEE ********C********** **********C******»*************»***** *************** ******************************C ************************** ** ************.******************************c** ** *****C** NOMENCLATURE ***C* **C* VARIA3LES: **C* **C* CLE DESIGN BEAK LIFT COEFIICENT **C* VI TIF VELOCITY **C* DL DISK LOADINGC* U WEIGHT AS CALCULATED FFCM POKER EQUATION **

C* HE DSEFOL LOAD PLUS EMPTi HEIGHT **C* PA ECWER AVAILABLE IN HCRSEtOWEE **C* **c**** *****C* EL3 EQUALS THE DISK LOADING FCF CLR=.3C* DL4 EQUALS THE DISK LOADING FCf CLE=.4C* DL5 EQUALS TEE DISK LOADING FCF CLR=.5C* DL6 EQUALS THE DISK LOADING FCF CLR=.6C* CL7 EQUALS THE DISK LOADING FCF CLR=.7C* H3 EQUALS THE WEIGHT FOE CLR=.3C* K4 EQUALS THE "WEIGHT FOR CLR=.4C* H5 EQUALS THE WEIGHT FOR CLR=.5C* "W6 EQUALS THE WEIGHT FOE CLR=.cC* H7 EQUALS THE WEIGHT FOR CLR=-7C* HVT1 EQUALS HEIGHTS AT VT=600C* WVT2 EQUALS WEIGHTS AT VT=q25C* WVT3 EQUALS WEIGHTS AT VT=650C* WVI4 EQUALS "WEIGHTS AT VT=675C» HVT5 EQUALS WEIGHTS AT VT=700C* DVT1 EQUALS IHE CORRESPONDING DISK LOADING AT VT=600C* DVT2 EQUALS THE CCRR ESPO H DI NG DISK LOADING AT VT=625C* DVT3 EQUALS THE CORRESPONDING DISK LOADING AT V?=o50C* EVT4 EQUALS THE CCRR ES? ON DI NG DISK LOADING AT VT=o75C* DVT5 EQUALS THE CORRESPONDING DISK LOADING AT VT=7G0C* EDE EOTOE DISK ECUNEARYC* WMG MAX GE0S5 WEIGHT BOUNDARYC* AR HEIGHTS FOE THE ASPECT RATIC 30UNDARYC* D3 DISK LOADING CCC E ES? ON DI NG TO THE ASPECT RATIC "WEIGHTS£***«***»***********»****»»*********************************************

REAL*4 DL3(5),DL4(5),DL5(5) ,DLt(5),DL7(5),W3(5).W4(5) ,RDB (2) ,

*i5 (5) . H6 15) , W7 (5) .WVT1 (5) -HVT2 (5) .WVT3 (5) , KVT4 (d) "WKG (2) ,

*HVT5 (5) , EVT1 (5) ,DVT2 (5) , D VT3 < 5) , DVT4 (5) , D VT5 (5) , D 1 ( 2 ) , D2 (2 ) ,

*D3 <5) , AR (5)CC DEFINE DATA

DATA DL3/2.06,2.07,2.07,2.07,2.05/DATA W 3/2 505- ,2476. 2, 24 :>5. 46, 2 43 3. 85 ,24 18.25/DATA DL4/ 2. 42. 2.4^,2. 46, 2. 47, 2. 4 7/DATA W 4/2 467. 17,244 2.95,2 41 9.62,2399.72,2382-9 9/DATA DL5/2. 63, 2. 6 5, 2. 67, 2. o 9, 2.o9/DATA W5/2440. 72,24

1

9.51 ,2399. CC.237 9. 13,2 3o4. 65/DATA DL6/ 2. 74 .2. 7"i .2. 79, 2. 81, 2. 81/DATA H6/24 24. 66, 2402.46,2 33 3. 56. 2 365. 10, 23 52./DATA DL7/ 2. 8 0,2.

6

3,2. 65, 2.8b, 2-87/DATA H 7/2411. 92,2390.72, 2 37 2. EC, 2 357-35, 23 42. 2 5/DATA HVT 1/25 5. ,246 7. 17, 2 44 0. 7 2,2424.67,24 11.92/DAIA HVT 2/2476. 2, 24 4 2- 95. 24 19. 51 .2402.53,2390.72/DATA HVT3/24 55.4o,i4 19. b2,239S.,2383.58,2372.S/DATA HVT 4/ 24 3 3. 8 5, 2 3 99. 7 2 ,2379.13,2365. 1,2357. 35/DATA W'VT 5/ 2416. 25, 2362. 99, 2364. 65, 2352. ,2342.2 5/DATA DVT 1/2. 06, 2. 42, 2. 63, 2. 74,2.6 0/

.,2U50./3/

— CALL DISEELA FCCTINES FJR PL01

1

CALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALL

I

CALLCALLIIGBCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLCALLSTCPINC

TEK618MECEGFRESET (3HALL)HHSCAL ('SCREEN')PAGE (12. C, S.5)-RACE (O.C)

(1.6,1.2)PHXSCRA RZA2DFaACE

(1 C. ,6.5)

S»I££LBASALF ('L/CSTE').MIXALF (•STAhC)INTAXSINTAXSY1ICKSXIICKSSHDCHRHEIGETXNAKEYNAEEHEIGHTHEAI1N

I?)j. 90,1,. 015,1)(. 1b)' (D) I SK (L) OAEING3', 100)

CSS (rf) EIGHT I (LBS) ) $« ,100))

IOPTE5 (C) iErET (?) LO:

| U I H V. .1 (Tl

(.290)(' JH) ELICOPICC, 1.0,1)

HEIGET (.20)GRAF (2. C,. 1,3. C,230C. ,5C.,2550D = 5

'55

GRAFID = 5THKCRVPARA3LEGLINCURVECURVECURVECURVECURVEOASECURVECURVECURVE

(-C13)

(DL3,V.3,5,0)[014,-4,5,0)DL5,«5,5,0)(DLb,'*c,5,0)[DL7,W~,5 ,0)

(D\11,SVT 1,5,0]*» V T 2 , 5 , j

ti rr 1 C i

CURVE (DV12,'«VT2,5,0CURVE (D \ 13, « VI 3,5,0)CURVE (DVl4,'.VT4,5, 0)CURVE (D\15.UVT5,5 , 0)THKCF.V (.030)CHNCCTCURVE ( C 1 , W B G , 2 , 0)CURVE (D2, REE, 2,0)CURVE (D3,£H,5,0)DONEEL

34

C TEIS PROGRAM IS CESIGN TO GENERATE THE LATA FOR THE GRAPHICSL sttUUON or in ariGn-i ANn thf USEFUL LOAD EOUATIOH. Taj" tc n. ucl_ fiflil SXJSf IN A LAbtiT ELOT HELICCETER DESIGN PARAMETRIC OPTIMIZATIONCC ASSUMPTIONS:C 1> ENGINESPECIFIEIC VAHIAELE OPTIONSC

BEAL*4 ClE,PA,tI,K1,K2,K3,K4,i<5,E,S,A,E,;i<10),WB(10)INTEGER VT, D,I,CI

Cc

CALL FRTCKS ('FliEEEF ','02 «,'EISK , ,»CaPT1',> 'EATA ', • A ')

CC

CALL FBTCES ('FILEEEF •,

• 03 ".'DISK , ,'CEPT2 ,#

>'EATA ','A »)

CcC CLB= DESIGN MEAN LIFT COEFFICIENT

DC 90 CL=3.7CLB=CL* (C. 1)

BRITE(2, 10) CLEC EA= POWEB AVAILAELE EP

PA-206C £1= DISK LOADINGC VT= TIF VELOCITY FT/SECCC CONSTANTS BASIC ON CIBC

K1= (0. 9563) /CIS* (1+1. 8078 *CLB**2)K2=PA*10**5/K 1

K3=(G.00C25929)/CLB» (1+ 1.8078*CL3**2)KU=55348C.0/K1K5=3695.7/K1DC 100 D=200,300EL=D* (0.C1)1 =

DO 11C VT = 6CC ,70C,25CC ARRAY INCRECENTER

1=1 + 1

C WEIGHT EQUATIONC

W(I) = (K2*(1-(411.E1*EL**.75)/(\T**1.5)*(1 + K3*VT/DL**„5)**.5)-K4)1/ (VT*K5*EI**.5)

CC CALCULATION OF WE LATAC

A=»(I) /DLB= (A/3. 14) **.

5

P=A**. 5/V1S= (6.* EL)/ (0. 023679 »CLR *VT**2)

CC ASSURING A TEEIESING SYSTEMC

HE (I) =17 17. 9+ 122 1.*?**. 8 63+26€.*P**. 7+1744 9./VT** 1. 141 + 2.886*A**.5*P*».57+. 191 *'»(!) **.916<-.0294*«(I) **. 9 92*35. 15* (W |I)/VT) * JA**.1 85) *S**.33 + . 0Q88*S (I) *A**.21

C W8ITE (5, 2C) VTC WRITE lb, 30) S110 CONTINUE

WRITE (2,3 1) Dl, '» (1), WE (1 ) ,t> (2) ,W E (2)WRITE (3,:1) EI, k (3) , «3(3) ,'i (4) , » E (4) , W (5) ,WB (5)

100 CONTINUE90 CONTINUE

C FCBMAT STATEMENTS10 FOEMAT ( 1' , ' CLB=' , 1F10.4///)31 FORMAT (6 (2X,F 10.3) )

STOPENE

85

C ZE2*i cavavBD .lo Lbit.i xvj uuIAxh iaL tiitii^ <:iun. r H -J TrlL *

C ASPECT BATIC GSAPfc' INTERSECTION ECINT DATA. IN ORDER TO SBAPH *

C I HE ASPECT HATIC ECUNEABY ON THE CAIN CARPET PLOT AC CCBBESFCNCINC WEIGHT BEST BE OBTilNEB. THIS FBOGHA2! UTILIZES *

C THE iiEIGHT ESTIMATION FCHMOLATIOh FBOX THE CARPET PHOGRAM. *

C************»*»»***^»**»**»*»*****»****** »«**#*»*****»<*«»********»*C ****#»**#*****»***#***»»* ****»***^*****#*»**»*****************#****C ASSUMPTIONS: *

C 1> ENGIRESPECIFIEI *

C VABIAELE OPTICNSBEAL*4 VI (5) -CIJ5) ,CIB{5) ,W (5)DATA CLR/. 625,. 57 5,. 5 35, .46 0,. 4 2/DATA VT/6C0. -625- ,6 5 C. ,67 5. , 7CC./DATA DL/ 2. 75, 2. 7 5, 2. 72, 2. 67, 2. 53/

CALL FBTCHS ('EILEBEE ','03 ','DISK ^'CEPTAS 1,

>«DATA • ,'A ')

Cc

DC 90 L=1.5SRITE{3, 1C1CLP (L)HEITE(3,2C VT (I)¥BITE(3,3C) DL jlj

C PA= POKES AVAILABLE HPPA=206

C CL = DISK LOADINGC Vl= TIP VELOCITY ET/SECCC CONSTANTS BASEL CN CIKC

K1= (0- 95e3i/CIB|L)* ( 1+1 . 8078 *C1E (L) **2)K2=PA» 10**D/K 1

K3=(0-00C259 29)/CIR (L) * ( 1 +1- 8 C78*CL2 (L) **2)KU=55348C-0/K1K5=3695.7/K1

C MEIGHI E2UATIOC

V (I) = (K2* |1- (411„51*DL(L) **.75)/ (VT (I) **1.5) *1 (1+K3*7T(L)/CL (L)**.5)**.5j-K4)/(VTL) +K5*(DL(L) **. 5) )

BBITE90 CCNTI!*

BBITE (3,3 1) W (1)~THDr

c FGBMAT10 FCBMAT20 FORMAT30 PCBHAT31 FCa.lAT

STOPEND

STBTEHEKTS('1' •CLR= , ,1F10.U///)2X, f VT = « , 1F1C.4///)2i,«DI=' , 1F1C.4///(2X,F1C3)

86

APPENDIX D. PROGRAMS TO ACCESS HESCOMP

This section contains the control language programs

needed to access HESCOMP on the IBM main- frame computer

87

» * * J33 03-O * * # • r-r-.u-txr*- j- • • '"^ • *-r-ifl ©r^r* •

;z ** • © >oa^r*--3"^)ô ^- r^-LOinr* © ô^\oocm^ (*inO • o •outr-— .^-i-nr-©-i-* * * © O ^"03«-J>^0 X P-* -J rsjr^ (%)*-»-© © COCMipf-'T'OO*-^ C O "^X © t- j f-» "N

O

z *# • tr« iX • • r^.rrr- i • «o • • ©*-"v"o^.ur, or. -O . • • ^ »cs » tîa-r* • * • •-£32 *» © :?>©•-© O • • •*-*-^'M^*^0 • îTlO©©©©'-*-*-'- © ;?>©•-© O • • ,•-*—*--^*-»© • •

3- ,0 3-Crsi • • ^-a-"— 'sj'njo t • • • • © u* (N • . •— rr^- -NfN© •

-^©© ^^^ûôj-oo r*aDcocn^^ 2:0 00 ©oîocoji©-^ -t©o ^^sliojo•00 • t «rN9«flo^ • • ta-o •O'-^j-^'nînô • & o • •••••«•• • •© - • • «N7or • • «3OrNÔOO • • • ,»-^'-<-^0 • t t » • • • • <%!© ^-'N©©© ©©©•-•-— ^M OrNûTlOO • • • »*-*•*-»-

?o 3-\0 • *~rn\0&, • • »rsirsj •O'-^rsi'â-LO^^ • 1 • •cm.'N * * » « * 1 t 1 » . »o J/o • »*—^ ,ox • . •'n

* * «tj •»_._ ^» • t • >o3-(>ivoa>*T*» • *~ » x> 1 unr*» a fNm C7> • • • •*o&<.*4\& cu""11 "'

• o-j • u-ia* ^Tnooa- o?uij, o"Nuiooîô»-(»^DS'w '-'r>o i>*x^-©©~gfNij-iv0©c7^©O'— '•moos ^jjhtomuo* o^; • * «m • • •outers « i**"*nmr» • » »r»o •o*™ ,~r>g'-r>.3, tf"iop*- « • tr-o iti*i«f*i t • •uîncn . #•—ni/tr- • • •<**

*- * 31U O^fN O© Qf-ÔO • • » .^-~-^-aD<NO • • i i • t • iOJOOOÔJfNOOOOOO— «-•- O 0©»-'-'N©0 • i t »*-»-^00• * — — * .- . z• OS # * ">*—* - • * ~ TZ— '-

* xc ***—r>c lo• * e"=3 * * OO «:

* z • # aouo * * u<uju c cjô .0 "în rro t/i o i/tu^© cnui o ô^c^ o ôrNojr^rN uhct* o*oo »«j ûnô lP* ——- • c j- «; ^»r»ooofN %orn -rr*ofNLO © ^âjsorr°J ^ fNaso o rsinvoajoôo<J u^p»ocj©rst ôrn^r** ©cnlOO uj***03cmsc tn • • • #^r*o t*-minr* . . . «x «©^^r>*r->-/m^ •#••1100 ••••••••• • »^r-© • •^"*nnrfc 1 • • •

***s •** umum ©oo^âarsi©© 1 t • .*-^-»»a»»-o •••••!• in-ioo^,^'-uooouo'-^«- ooo^'ô'no'J • • • i«—^•^»

•»«.-»«.*-»***S* '7)r* o©rN©o^'^rsir>*rn'-i -rinun\OsOr--r,,*a>^3A©©^-rMr^-nnnr/un^^©©^-*-rN'*)'^ 3,rrunso^©o*N©o»-»— '>4-Ni'*>'î -finuisO^r-*

• * X* * Dm ** * H~ * *» * O # ** * 35 ;/) * *» + * V* Oz «* * ©M * * 3-

• * -J * * ©* * -^ * \* * *-T£- * * O t

• UZ « * rsi^N

* * zu * ft S* * -HC • * EQ ^* * ME * + II

* * O # vt* «^ * CO

* » Eh * * -e* * 1

* * ^w * * zo ©» * 'j-e * * -c—

X * ** * — j- * * II

^>

» * © * # JC/1* * Q« • * ft -c -^ z

* Z2 * • zEC

88

• *-o«- ooooo.3- • .J*)^ t • . • t

tr* • • o # • «x • r*î

o ij • • 3,oo »<jo ooooouooo . o — t-

o 2 • tiTiro • •«- «n i i « • • fir* tin «a • • •

,00 • 23 *N • sO O • OC O »0-sjÔÔ »CDLJ J">fN tor,oooootnooo © ©rsi*- O O*" * • ©*—

« iouiT) i «»• • ir* i*io^ i i t • i i i i i •••••oiiNffd' •© *o *•••»» * «m tin tin t

Q«— < •3'0©."N ifNO t(N*TM l^^^^Ô*"*"^ *-000»- t«— »f—O •OintNn»—\Cf—»"0^- 3" O • ©«— 'Nr-^C

• a- t "o in in tin in in in• O "N^ jJfNO i • (N "no vO O • QO O « © O

rs»oo irnoojoooo'-oo • tin o • • r*oooooooou m oô ©rN^ o o*- *- o * »i- •-

• • tâ- * t ;s»- t * * * • iOoino »ino<N i • aâ* «• • t t * • • i »o • t • • i to * ' t<"n •© •© • * « i • t .p* tin nn to • • • i

<N*»© 1^3*© I—OffÔf l •rN»0<N^^^»— 3»^«"n «^*"*-^ l*IOf"^'*0 iO»»'-ÔUO^ #*- •*-© tOUl^Jin ^\0*~^0*- f^JÔ «0^ fN 1^ ^©*-©r\jin^-'N'^^ 33* 3> ^^'Nîn'înr^'n'*imin3'u™iin^n.iriu ii^^jiininLnin^^^^^^^^^^rNifNrNirsjrNC^cNrsrf^^rsir^rsr^rsi^rsi^r^ •*!(—»<-nr^

^CD rn^r**-rMfNi "*f,nr,t<zjcj^^©u'* 3*rNinuj<"*i<D i^rTNr*' >*r*»rN3, i^3'CT*r* a>*-cDin^^*"^**~^»—^- •-•«-»-•— ^*—^-^—•»* •—»-^^^^^-^^-*-^.^-^^-^. ^^^^.3 3>UîninOs0r^~^fN^^^^^3OOO^~^r^^^3 3'inUÛ^^0v0 3'u^>0^^©^^^3,flXO^^^3^^s*(Nnj(Nf>atN'NrM">'^',^rH'^"n'^'*i^^«Ovo^-fi ^^^s0ô^sO-o^ô'^ r*> '^' r*^"^3*3'3-3'3'3' 3> inininininininin-^\0^'0^v0'^\c Ovcr*r*-'**r-r*r*r»p^r* cocoasooooooo3ooooooooo^^^^^^^^^^^-^^<N fS''Nioooooooo i3oooooooooooQo,Jooooo30oouoooooooyoo

89

^ f-^dltOf** O0*, ^-CO'N^'''">-*CiJ">*"*ûn<*'1,C o »

. •O'-^J-nûôr- o • O Oo o •*- • • ir, . . • ~o • 5*r*

• • • t 00 J1 ^P*o r— odo uiC'sO so oo Bj^^xôn <£ r» r-*.*Nu->i-*i » .n s in •at irtoo^^no^3BJ-03 oo^D-Nin^-coô— *- r* » o~-~-~ oooo - i/vj"» m»** r*^<^ r-oo .o~"sj<"n-*' ji^p-nO • cro *n • oo • • 'm • • u-t .tn -no . ^ oo • o •

rsio (NO ^rNOOOOOO*-*-^- • — • r*""- o^-'-OO'^^-c^ ^ • «- sO • t tO • **-+* • «-

• ^ • in • • ^ in 3D inin^""*o i/iuj r*KN^ o ^cjouo r* sro^miNr* •— cn j*—ujoj «*f> au \Oin u<^j^NOô^r^Mj lT>iî »£>(_> j(\j*«*u(J? f nu >p**ajtrojcjr- to c* o*~0'*i o<—OO o o or* noorûi i/io;N lO^^'NnJiTOC i • • trsifN • • t • I t • • • 'N o oo •• t • • • «fsj « • i i • CC iO U">«-rN i tO^r*- i

?NO • • • • • t • •—OOO—^"NOOOOOO*-^*- • • • t^«- ^t»-0'NO~s*^-3"* oj r*o »<n • .^ .•--- f • #«-

o j~» .o *-•r* to «- *- • r*-sr*" «o o n^'>*—oô o^n -^^ ~*-»- c tn o •'"1

3(N^)'"XJ5^'-"iO MJ'-OO^.'NuiCXÔO'" tO =0 3- «—O'*' O"ÔO0 CN O • •—lTÔ »rsn— iOO OO -OlTIo §o*"^ '«'•*> .-ru i *or* i » • #r*o itii«iiif ^ • ir io • • ••• «tn*** • • »— a^tfi »r* «ô • (\ io*^^ i^h i iOO •!"*-

rNO »••«•• •X030^D!NOOOOCO'"'"" II r^j »o •*-•" »• 3"i>irsi fNi »0^s0 t i •o*-^' • ifS l«" i • iO i ••• 'N-— j-*n •

— inj* o

i • rsi j oi ^p- fN *- *n«—<j irnno rsitn o jjtNff* a orsjujrsir^ ino"* r-inr-aD o^Nf""**^ • -o tin ir>*rn oô oov£?o o^-w^^fN rw fNsoo o 'Ntn^jcoôoo oo^cjiri i^rsirwm oaooino *-o^ i/ôn ir» iui r**o r**orôo*™p»ood »o*"— rsin^vn\o t • t • *03 •«•#•*•«• toa3^-»r*-ooo i • t • i • # iO irsirô . •^tâoo^*^ • ic*m » »^» • • «c* • • • • •

•"O i • • • • • i •~»r"iOO*-0-~OWOOO<3~«^»^ fn • • t ••» • •^—^^^rgrsiO*-^ SD^-O I • «0*" • « t • trn»p**J»"Ul -Ô^^ t*"0^"^"^

v*9Q j3(NQ3Jo>C!NX| r*'3,osOfNr*tNa)5o^ "*joo JO-fl^"i©w>3^»~'i? f"4j^^»"\o rsjr**-iNr^rsir^<nuôuioi/Ôso*~^^ i^"~o^~^^"'âD*^Ôf^<7*'^corrtaO'r>*LP

•-^•^.^^•^-^^^-^^^•-^-.•-^.••^.^-r-^^-,—m*i*«f*»-*—»- ~-«-*—«— ^-«-0000ooooo^-'oooo0000000000«a©oooooooooooo

90

> m»-mô oo3 • •& «0 I" I ' II•oo «o ••- .«-o oo

in in

m m«- -omooo»ooin • 19 •© »in • •r^ • t»-oo •

•oo «o «^ .—o >oo I %~r-

— —•— »-— »-—— •-———»-^——— CD <Tîn'"^9ini£^cQô~"s*'^\£r^cocr*coc*

91

APPENDIX E: HESCOMP INPUT AND OUTPUT EXAMPLES

This section contains samples of the IBM computer

input and output.

92

I

CJooo aonoo oôoooooooooo ooooooooooooo • o— p-Lp-ur- -r ioouioooooo »oooooooo»-iri•oo ou"r^'-^'*, ^'OOo oor-u"iLT>r*- oo ooooooo r^c, n.oOOO OXX — aT^^lOOO*- TtVJCM'N*— — C OOO^^'flOOO'- «—

u*i .so ocm-tp- • • • • -o • ur^'Nn û^vor- -o •urNuip^'T^ •«!•«-

I t

ooooo oooooo .cooooooooooooo oooooooooocoo * ioa — :?»-o'N'no i «ooc oooooo io • »oooooooou->oOOOOO 3TftinO3ÔO0TCC^J00X0O OOOOOO'XOunO'lOMO 3T*3 O— -O O'N'jn-ÔOOP^'NO'^'DX ,C— OO OOOT-O^'OT*")r-—O~o .o •toNsoT' • • *^ *a & or-iNfNnjuir* ^co ^ soo r*n r» aa ;3"» • i * t

•rN»-.j-i • ^-^-^.^.,-vi •tcgtfi .rsi • »-tN f • i • • •*— »-*-rsi

«e •— fN UJ «c

c III f-t-1 oo z a«: s uj/1 oo >-* TL

as c~ '-O oo 'J *•J 7ZV. * - zr-«O X ^ro , • , UJ in

o =UUUQ.Q. f- -1 O O >. -1

z o^-J-J»J ns

ca: O Q*=» «e arj M z oco -J Z

OH F-t i-H — ^-f- r* JH3 J 3 -J -H —

OO, 3 z a, u a -j < '< CO

a U O z se rr rr > at/>a o -IMHH «*

j 33 Z CJQ 3aj (i. 'JJ7.7.Z • -Z

j ul => 1:000 ««

xu as — — C ^ enz tj F- t/1 71'fl UJ F-i

<: f-i ZIUOJLU z zC -Q :-^£-t -••.Jre •5 'IT---'- O zO u XI '_J<C_> U) t-> Z -fci

hi KUUOU MZ >* 31/1UJ as 3 -J >• *-t

Oi 0.-J 33

a ZO uj •« a

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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 197 3.

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

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

5. Hiller Aircraft Corporation Report 60-92, Proposal forthe Light Observation Helicopter Performance DataReport , 1960.

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

115

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Cameron StationAlexandria, Virginia 22314

2. Library, Code 0142 2

Naval Postgraduate SchooliMonterey, California 93943

3. Department Chairman, Code 67 1

Department of AeronauticsNaval Postgraduate SchooliMonterey, California 93943

4. LT Allen C. Hansen, USN 5

Air DepartmentUSS Enterprise (CVN-65)FPO San Francisco 96601

5. Professor Donald M. Layton 5

Code 67LnDepartment of AeronauticsNaval Postgraduate SchoolMonterey, California 93943

6. Aviation Safety Programs 2

Code 034 ZgNaval Postgraduate SchoolMonterey, California 95943

116

3 KA* 94.31

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GAYLORO S3

Keep this card in the book pocketBook is due on the latest date stamped

0836

ThesisH1996c.l

HansenAn analysis of three

approaches to the heli-opter preliminary de-ign problem.

An analysis of three approaches to the helicopter ...

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