Computer program user's manual for advanced general aviation propeller study

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COMPUTER PROGRAM USER’S MANUAL

FOR ADVANCED GENERAL

AVIATION PROPELLER STUDY

by Rose Worobel

Prepared by

HAMILTONSTANDARD

, Windsor Locks, Conn.

’ for Advanced Concepts a n d Missions Division

Ofice of AdvancedResearchandTechnology

?I :! ‘ MoflettField, Cui$ 94035

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I S T R A T I O N W A S H I N G T O N , D. C. M A Y 1972

I O N A L A E R O N A U T I C S A N D S P A C E A D M l N

I

d

TECH LIBRARY KAFB, NM

00bL148

1. Report No. 2. Government Accession No. 3. Recipient's C a t a l o g No.

NASA CR-2066 I

5. ReportDate 4. Title and Subtitle May 1972 "Computer Program User's Manual for Advanced General Aviation Propeller S l x d y " 6. PerformingOrganization Code 7. Author(s) 8. Performing Orqanization Report No.

Rose Worobel 10. Work Unit No.

9. Performing Organization Name andAddress Hamilton Standard 11. Contract or Grant No.

Division of United Aircraft Corporation Windsor Locks, Connecticut h L 4 S 2- 6477 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Contractor Report National Aeronautics & Space Administration 14. Sponsoring Agency Code Washington, D.C.

15. Supplementary Notes - ._ 16. Abstract A User's Manual is presented for a computer program for predicting the performance (static, flight, and reverse), noise, weight and cost of propellers for advanced general aviation aircraft of the 1980 time period. Complete listings of this computer program with detailed instructions and samples of input and output are included.

17. Key Words (Suggested by Authorls)) 18. DistributionStatement propellers, propulsion, noise IJNCL4SSIFIJ3-WLIMITED 19. Security Classif. (of this report) 20. Security Classif. (of this page) 22. Price' 21. NO. of Pages Unclassified 3.00 F o r sale by the National Technical Information Service, Springfield, Virginia 22151 CONTENTS SUMMARY 1 INTRODUCTION 3 SYMBOLS 5 TECHNOLOGY IDENTIFICATION Propeller Performance Generalization Static and Forward Flight Reverse Propeller Noise Generalization Propeller Weight Generalization Propeller Cost Generalization Computer Program PARAMETRIC STUDY OPTIONS COMPUTER PROGRAMUSAGEINSTRUCTIONS Program Input Program Output Messages 23 Sample Cases CONCLUDINGREMARKS REFERENCES 26 TABLES

I Advanced GeneralAviationPropellerStudy - Aircraft

Classification

II General Aviation - Generalized Propeller Weight

Equation FIGURES 1 PowerCoefficient Chartfor a 2-Bladed, 150 ActivityFactor, 0.500 Integrated Design C L. Propeller CONTENTS (Contents) FIGURES (Contined) Thrust Coefficient Chart for a 2-Bladed 150 Activity Factor, 0.500 IntegratedDesign C Propeller Li Basic Performance Curve-Variation of Effective Torque Coefficient with Advance Ratio and Blade Angle.

4 Basic Performance Curve-Variation of Effective Thrust Coefficient with Advance Ratio and Blade Cycle 5 Basic Noise Curve.

Category I Parametric Study Category 1 1 Parametric Study 7 35

8 Category IV Parametric Study

Example Reverse Thrust Variation with Landing Speed and Power Setting 10 Sample Input Coding 38

11 Sample Output - SHP Option 40

12 Sample Output - Thrust Option

Sample Output - 50% Stall Option 42

14 Sample Output - Reverse Thrust Option 43

I A Computer Program Flow Chart

2A List of Subroutines

FORTRAN IV Listing

3A 48 APPENDIX

A Flow Charts, SubroutineList, and FORTRAN IV Listingfor

Hamilton Standard Deck H432 45

vi

SUMMARY A major outcome of the studies sponsored by theAdvanced Concept and Mission Division, A. C. M. D.of NASA under Contract No. NAS2-5885 dated 30 January 1970

as reported in CR 114289 and under Contract No. NAS2-6477 dated 6 May 1971 a s

reported in CR 114399 has been the development of a computer program foreval- uating propeller performance (static, flight, reverse), noise, weight, and cost for

general aviation aircraft propellers as a function of the prime geometric and aero-

dynamic variables. Propellers have been divided into five classifications which

distinguish the complexity of general aviation propellers, i. e. , fixed versus variable

pitch, deicing capability, full feathering capability, and reverse thrust capability.

Parameters that may be varied independently include number of blades, blade activity factor, blade integrated design lift coefficient, and blade tipspeed. A User's Manual for the computer program was written under Contract No. NAS2-6477 and is presented herein.

A brief description of the technology development is presented, and a complete listing of the computer program as well as detailed instructions and samples of input and output are included. Examples of parametric studies which can be made with the computer program are shown.

INTRODUCTION

Aviation forecasts for the next ten to fifteen year time period, indicate thecon-

tinued steady growth of gensral aviation. Furthermore, it is apparent that most of

these aircraft, even into the 1980 time period will be propeller driven utilizing primar-

ily reciprocating engines with increased number of turbine engines as their econom- ics improve. The attainment of this forecasted growth is dependent upon the continued improvement in the safety, utility, performance and cost of general aviation aircraft.

In view of this, a study was undertaken under the sponsorship of the Advanced

Concept and Mission Division ofNASA to derive and computerize appropriate propeller performance (static and forward flight), noise, weight and cost criteria to permit sensitivity studies of these factors to be made for advance propeller configurations designed for general aviation aircraft of the 1980 time period. This study is reported in reference 1. A t NASA's request, a contract study was undertaken to provide a

User'sManual which includes a complete listing of this computer program with detail-

ed instructions on its use. Furthermore, the scope of the computer program was ex- tended to incorporate the inclusion of the generalized integrated design lift coefficient (the only prime propeller blade shape variable not included in the original program), the computation of reverse thrust, and the refinement of the weight generalization.

The technology development required to incorporate the above extensions into the computer program for inclusion in the User's Manual is presented in reference 2. The User's Manual is presented in this report.

SYMBOLS AND ABBREVIATIONS 1.0 propeller blade activity factor, AF -0.15 b blade section width, ft

B number of blades

C blade section design lift coefficient LD 1 . 0 C propeller blade integrated design lift coefficient 4 Li 0 . 1 5 SHP ( P o / P ) 1011 power coefficient, cP 2N3D5 SHP ( P o / P ) 1 0 " C torque coefficient for J 5 1.0, 3 5

Q

477 N D

1.514 x 10 T ( P o / P )

thrust coefficient, cT N2D4 D propeller diameter, ft maximum blade section thickness, f t

h

101.4 Vk

J advance ratio, ND free stream Mach number M N propeller speed, rpm P N L perceived noise level, PN'dB SHP ( P o / P ) 10l1 torque coefficient for J’1.0, X -

QC 3 5

4n N D J2

R blade radius at propeller tip, f t

radius at blade element, ft

r

S H P shaft horsepower T propeller thrust, pounds

1.514 x 10 T( Po/, )

thrust coefficient for J = . 1.0, x -

TC

N2D4 J2 freestream velocity, knots vK X fraction of propeller tip radius, r/R propeller blade angle at 3/4 radius 3/4 2 4 P density, lb sec /ft density at sea level standard day, 0.002378 lb sec2/ft4 P O

@/a

Po/P 0 ratio of absolute temperature to absolute temperature at sea level, T/T, ratio of static pressure to static pressure at sea level, p/p0 TECHNOLOGY IDENTIFICATION '

General aviation aircraft covers a very broad spectrum of aircraft implied by

the power plant size range of 100-1500 shaft horsepower. Thus, in order to provide a

meaningful study within the scope intended by the Advanced Concepts and Missions

Division, A. C. M. D. , as an initial step under the study in reference 1 the Contractor

A . C. M. D.

classified into five categories the general aviation aircraft envisioned by For convenience, the categories are repeated here in Table I. Analytical generaliza- tions for predicting the performance (static , forward flight, and reverse) , noise, weight and cost of propellers for general aviation aircraft classified in Table I were established and computerized. With' the aircraft and propeller requirements thus de- fined and the computer program having been established, comprehensive sensitivity studies of the propeller geometric and performance parameters can be conducted.

Such studies were presented in reference 1 for representative aircraft from each general category described in Table I.

The details of the analytical procedures are defined in references 1 and 2. A brief description of each generalization is presented in the following text.

Propeller Performance Generalization A s a means of assessing propeller performance over the entire flight spectrum, performance generalizations were developed for predicting static and forward flight performance. Furthermore, for those aircraft incorporating propellers with the re- verse thrust feature, a method of calculating reverse thrust has been included. These generalizations were made for a family of propellers spanning the prime propeller variables of 2 to 8 in number of blades, 80-200 in blade activity factor, AF, and 0.3 to 0.8 in integrated design lift coefficient, CL..

A brief description of these generalizations is presented in the following test.

Static and forward flight. - A performance generalization was developed for

predicting static and forward flight performance for general aviation propellers. Using the proven propeller performance prediction methods discussed in references 1 and 2 , performance calculations were made for a family of propellers selected on the basis of propeller shapes which prior study had shown to be the most favorable for minimum weight, low noise characteristics and good performance (ref. Afig. 1, 2, 3 and 4 and ref 2, fig. 1). These calculations were used in developing the performance generaliza- tions. The horsepower, thrust, propeller rotational speed, velocity and diameter were included in the non-dimensional form of power coefficient, Cp, thrust coefficient, CT, and advance ratio, J defined as follows.

SHP ( P o / P ) x 10l1 -

-

C 3 5 P 2 N D 1.514x10 T( P , / P ) - - cT

N2 D4

101.4 V

- k

-

J

ND where:

SHP - shaft horsepower

p o/,, - ratio of density at sea-level standard day to density for a

specific operating condition.

D - propeller diameter, ft

N - propeller speed, rpm

T - propeller thrust, pounds

- forwardspeedvelocity,knots

' k Base curves were defined in this non-dimensional form for presenting the per- formance of 2, 4 , 6 and 8 bladed propellers referenced to an activity factor of 150 and 0.5 integrated design lift coefficient. In order to minimize the number of curves and consequently the size and complexity of the computer program, the terms effective power coefficients, C p E and effective thrust coefficient, CTE were -introduced. The effective power and thrust coefficients are defined as follows: - C X P C - ' P ~ ' A F pE Li -

C x TC

- ' T ~ ~ A F TE Li where:

- powercoefficient

'P

- activity factor adjustment to power coefficient (ref. 1, fig. 3A)

'AF

PC - integrateddesign lift coefficientadjustmentfactorto powerco-

Li efficient (ref. 2, fig. 4)

- thrust coefficient

cT - activity factor adjustment factor to thrust coefficient (ref. 1, T~~ fig. 3A)

TC - integrateddesign lift coefficientadjustmentfactortothrust co-

Li efficient (ref. 2, fig. 6 ) Thus, the base curves while referenced to a basic activity factor and integrated design lift coefficient are applicable to the complete range of the prime blade shape parameters including 80-200 activity factor, 0 . 3 to 0.8 integrated design lift' coefficient and 2 to 8 blades. This performance generalization format is shown for 2 bladed propellers referenced to 150 activity factor and 0.5 integrated design lift coefficient on figures 1 and 2 for the effective power coefficient chart and the effective thrust coefficient chart, respectively.

Since it has been projected that general aviation aircraft will be operating at significantly higher speeds by the 1980 time period, a compressibility factor, Ft was derived for use with the base performance plots. The thrust is multiplied by Ft (ref.

2 , fig. 9) to correct for compressibility losses.

The complete generalization together with detailed computational instructions are presented in APPENDIX A of reference 1 and in reference 2.

It is to be noted that the performance predicted by this method is for the isolated propeller since no single body blockage effect could be generalized to cover the wide variety of aircraft included in general aviation.

Reverse. - The analytical method for computing reverse thrust is based on an

existing Hamilton Standard procedurewhich was obtained by generalizing all availa- ble propeller test data. The shaft horsepower, thrust, propeller rotational speed, velocity and diameter are included in the non-dimensional formof torque coefficient, CQ or Q c , thrust coefficient, CT or TC, and advance ratio, J defined as follows: 101.4 VK - -

J

ND 1 0 l 1 SHP ( P , / P )

-

-

C - for J s 1.0

3 5

Q

4 n N D -

-

X- J z 1 . 0

for QC 4 R N3D5 J 2 1 . 5 1 4 x 1 0 T( P , / P )

for J s 1 . 0

1.514 x l o 6 T( Po/P)

.& -

-

x - for J r 1.0

TC

N2D4 J2

where:

SHP - shaft horsepower

po/P - ratio of density at sea level standard day to density for a specific

operating condition

N - propeller speed, rpm

D - propeller diameter, ft

T - propeller thrust, pounds

- forwardspeedvelocity,knots

vK Base curves have been defined in this manner for a 3-b1adedy 100 activity factor, AF, 0.4 integrated design lift coefficient, C L ~ propeller. The term effective torque co-

efficient, CQE or QcE, and effective thrust coefficient, C T ~ o r T C , are used. As

E with the forward flight generalization, these base curves with appropriate adjustments for A F , C L ~ and number of blades can be used in predicting reverse thrust character-

istics for the family of propellers spanning 2 to 8 number of blades, 80-200 A F , and

0.3 to 0.8 C L ~ . The effective torque coefficients and thrust coefficients a r e defined as follows:

C = [ CQ x (3/B?83 x QAF 1 - AC (PCR/100) for J 5 1.0

QE QE2 for J > 1.0 &CE

83 ] - AC (PCR/100) for J I 1 . 0

C TE TE2

= [ TC x (3/BP’ 83 x TAF ] - ATC (PCR/100) for J 1 . 0

E2 where:

C - torquecoefficientfor J 5 1.0

Q

(3/BP83- number of blades, B adjustment

- activity factor adjustment factor to torque (ref. 2, fig. 11)

&AF

AC - integrated design lift coefficient adjustment factor to torque for

Q:E2 J s 1 . 0 (ref. 2, fig. 12)

PCR - percentage of integrateddesignliftcoefficientadjustmentfactor

to be used (ref. 2, fig. 13)

- torque coefficient for J r 1 . 0

QC

- integrated design lift coefficient adjustment factor to torque

*QC

E 2 for J 2 1.0 (ref. 2, fig. 15)

- thrust coefficient for J s 1.0

cT

- activity factor adjustment factor to thrust (ref. 2 , fig. 17)

T~~

- integrated design lift coefficient adjustment factor to thrust

E 2 for J s 1.0 (ref. 2, fig. 18)

- thrust coefficient for J 5 1.0

TC

- integrated design lift coefficient adjustment factor to thrust

ATC ~2 for J > 1.0 (ref. 2, fig. 18) This performance generalization format is shown for 3-bladed propellers refer- enced to 100 activity factor and 0.4 integrated design lift coefficient on figures 3 and 4 for the effective torque coefficients and effective thrust coefficients, respectively. The complete generalization together with detailed instructions for computing the reverse a given throttle setting and the reverse thrust over the landing distance run angle for with the propeller fixed at the reverse angle a r e presented in reference 2 .

Propeller Noise Generalization For assessing propeller noise, the far field perceived noise level (PNL) was selected as the noise rating scale because: 1) It is a good measurement of the relative annoyance of the various aircraft designs considered in general aviation aircraft, 2)

It can be estimated by use of a relatively simple calculation procedure, and 3) It is a

reasonable indication of the subjective reaction to aircraft noise.

An empirical method €or predicting far-field perceived noise levels, P N d B de- veloped a t Hamilton Standard has been includedin the computer program. It presents

a means of calculating noise for a broad range of propeller design and operating para-

meter s.

The required inputs to the propeller noise estimating method are: 1 . Propeller diameter 2. Number of bladesperpropeller 3. Propeller RPM o r tipspeed 4. Shaft horsepower per propeller

5 Ambient temperature

6 . Aircraft forward speed 7. Number of propellers installed 8. Distance from the propeller center of the desired field point at which the noise is to be measured.

The computational procedure consists of a basic noise level (dB) curve (fig. 5)

for a 4-bladed, 10.5 foot diameter propeller defined at 500 feet from the propeller

center. The base curve is a function of shaft horsepower and rotational tipspeed.

There are adjustments for variations in diameter, number of blades, and distance from the propeller center. Then, there is an adjustment to obtain the corresponding per- ceived noise level. The directivity pattern of the noise emanating from the propeller is ignored, and the perceived noise level is computed for the azimuth angle for which the noise is a maximum.

Recent test data on highly loaded low tipspeed propellers have indicated that the

reduction in noise with tipspeed is a function of propeller stall characteristics. It

appears that noise reductions can be achieved with decreasing tip speed at a given

power only to the point where the propeller stall is limited to approximately the inner

50% of the blades. The 50% stall region is defined on the base Cp and CT curves

(fig. 1 and 2). It is recommended that propellers be selected to operate to the left of the indicated 50% stall line. The detailed procedure is explained in APPENDIX B of reference 1.

Since this generalization is for propellers only, it is emphasized that the low noise levels which may be achieved through selected design and operating conditions will not be representative of those from the complete aircraft unless a parallel effort is made to reduce the noise from other sources (particularly from the engine) as these will become predominant and set the perceived noise level of the aircraft.

Propeller Weight Generalization

A weight estimating equation (ref. 2) was derived for preliminary propeller

selection studies. The propeller geometric parameters (diameter, number of blades,

activity factor) and the operational parameters (SHP, RPM, Mach number) incorporat-

ed in this formula are those which experience has shown to have the most predominant

effect on propeller weight and the exponents have been established empirically to best

fit the weight trends of current general aviation propellers and those anticipated for the 1980 time period. The equation is presented on Table II.

The weight equation o f Table I1 provides a useful tool for estimating propeller

weight for any general aviation aircraft installation in this decade within *lo’%

accuracy. However, it must be remembered that parameters other than the basic geometric and performance characteristics used in this equation effect propeller weights. These are variations in propeller environmental temperatures, type of control system and the degree to which individual manufacturers design.for minimum weight.

Propeller Cost Generalization A cost equation (ref. 1) was generalized using end user price lists and weights obtained for representative industry propellersin the five general aviation aircraft categories shown in Table I. The equation is defined as follows: C where:

C - average original equipment manufacturer, 0. E .M. propeller cost

for a number of units/year, $/lb.

- single unit 0. E. M. propeller cost $/lb.

c1

LF

” Z LF1

LF - learning curve factor for a number of units/year

- learning curve factor for a single unit

LFl

B - number of blades

F - single unit cost factor

E - empirical factor

For the computer program, an 89% slope learning curve was assumed. F and E factors were generated to evaluate costs of 1969 and the projected costs of 1980 time periods. The factors for propellers installed on each aircraft category are listed be- low.

196 9 19 80 Category F E Quantity F E Quantity I 3 . 5 1 . 0 19 10 3 . 5 1 . 0 2230 I1 3.7 1.5 2810 3.7 1.5 5470 3 . 2 3 . 5 1030 I11 3 . 2 3 . 5 1990 IV 2 . 6 3 . 5 2 9 5 3 . 5 3 . 5 6 80 V 2 . 0 3 . 5 6 5 3 . 4 3 . 5 36 8 Computer Program The performance generalization for conventional and multi-bladed propellers and the corresponding noise, weight and cost generalizations described in the previous

text have been computerized. The computer program has been coded in FORTRAN Tv

and has been run on the IBM System/370. With this computer program, the afore- mentioned propeller performance characteristics can be readily calculated for a range of selected propeller geometries and desired operating conditions. Examples of para- metric studies made with the computer program are presented in another section of the text.

There are four performance computation options available. First, if an engine is specified, then the operating condition is defined with the horsepower and the cor-

responding propeller thrust is computed. Second, if a propeller thrust requirement

is defined then the thrust is included as input and the horsepower is computed, thus indicating engine size. Third, for operating conditions defined by horsepower or thrust, it is possible to define the tipspeed corresponding to 50% stall. This would be the tipspeed for minimum noise. Fourth, reverse pitch angle and the corresponding

reverse thrusts for a range of landing ground roll velocities operating at the fixed

reverse pitch angle are computed. The corresponding noise ( P N d B ) , weight and cost for the first three options are calculated. The weight and cost are calculated for both the 1969 and 1980 time period where costs are basedon the 89% slope learning curve and the unit costs and quantities selected by Hamilton Standard from available surveys.

There are the options of varying learning curve, unit costs, and quantities.

The required inputs for all options of this computer program a r e the following: Propeller 1 . Diameter range 2 . Number o f blades range (2-8) 3. A F range (80-200)

4. C range (0.3 - 0.8)

Li

Operating conditions (maximum of 10). - For static and forward flight computa-

tion options, the following is required.

1 . Shaft horsepower or thrust 2. Altitude, ft.

3. Velocity, knots

4. Temperature, OF

5. Tipspeed range For the reverse flight computational option, the following is required.

1. Normalrated take-off horsepower, SHP 2. Normal rated take-off speed, rpm 3. Altitude, ft.

4. Touchdown speed, knots

5. Temperature, OF

6. Range of powersettings, % of normal rated shaft horsepower

7. Type of engine,reciprocating or turbine Other

-

1. Number of engines 2 . Distance from the propeller center of the desired field point at which the is to be measured.

noise 3. Airplane classification (Table I) 4. Flight design Mach number 5. Performance computation options 6 . Cost computation options The pertinent input-output instructions are discussed later in the text.

PARAMETRIC STUDY OPTIONS Having developed a computer program incorporating the propeller performance, noise, weight and cost criteria, parametric studies can be undertaken to evaluate the trade-offs among these factors for propeller configurations applicable to general aviation aircraft.

The variety of parametric studies which can be performed with this computer program are illustrated in figures 6 through 9. A study for fixed pitch propellers associated with aircraft Category I is shown as figure 6. Curves of performance (T.O., climb and cruise), noise, weight and cost were plotted versus tipspeed for constant values of diameter for 2 bladed, 100 activity factor, 0 . 5 integrated design lift coefficient propellers for a specific engine application. The SHP was defined and the corresponding thrust was computed. Propeller blade angles as independent variables have been included in the performance curves. Thus, the blade angle providing the best performance compromise for take-off, climb and cruise can be selected as desir- ed by the particular operator. Similar data can be plotted for a range of number of blades, activity factors and integrated design lift coefficients. From an inspection of such curves, the effects of the primary geometric and operating parameters can be

evaluated and a propeller selected as the best compromise for the particular applica-

A similar study is shown for variable pitch propellers applicable to aircraft tion.

Category I1 for a 4 bladed, 150 activity factor, 0.5 integrated design lift coefficient propellers on figure 7. For this example, the thrust requirements were defined and the corresponding SHP's were computed. The minimum tipspeeds shown as end points for each of the curves in figures 6 and 7 represent the tipspeed corresponding to the 50% blade stall lines shown in figures 1 and 2.

An optimum low noise study based on the assumption that the propeller is always operating at the tipspeed corresponding to 50% stall at take-off and consequently

minimum noise can be made as shown on figure 8. The study was made for a repre-

sentative airplane in Category IV showing a variation in diameter and activity factor

for a fixed number of blades and integrated design lift coefficient.

A reverse thrust study is shown on figure 9 for a propeller applicable for Category V. Reverse thrust angles were computed for several throttle settings. Then, reverse thrust, and the corresponding shaft horsepower and propeller rotational speeds were computed for the velocity range corresponding to ground roll. The corresponding runway landing distances can be computed and the reverse angle select- ed corresponding to the required runway distance.

COMPUTER PROGRAMUSAGEINSTRUCTIONS

The flow chart, subroutine list, and FORTRAN IV listings for the computer

program (Hamilton Standard deck H432) are included as APPENDIX A . The detailed description of input and output are presented in the following text.

Program Input The input to the program is defined in the following text.

Cards 1 and 2 include the card number in column 3 and any legal Hollerith punch- ed in columns 4 through 80.

Card 3 contains the following input data in an (13, 3X, 10F6.0) format: 1. Card number 2. Number of engines 3. Airplane classification (Table I) 4. Flight design Mach number Items 5 through 11 include the various cost options. Code all of these items as zero if the cost criteria built into the computer program is to be used. This criteria is de- fined in the section on cost generalization. If any deviations are required, the follow- ing additional information must be coded.

Learning curve variation. - It is based on assuming that a learning curve is a

straight line when plotted on log paper. The learning curve is replaced as follows: 5. Learningcurvefactorforsingleunit 6. Learningcurvefactorfor 1000 units Unit cost factor, C1. - If a revision in unit cost is required, code as follows:

7. C1 - singleunit O.E.M. propellercost,$/lb.for 1970

8. C1 - singleunit O.E.M. propellercost,$/lb.for 1980

Quantities variations. - To investigate the effects of quantity changes on cost, code as follows: 9. Initial quantity to be used 10. Increment to quantity 11. Number of differentquantities Card 4 contains the following input data in an (I3 , 3X, 9F6.0) format where: Card number 1 .

Initial diameter 2.

Increment in diameter if a range of diameters are to be computed

3.

Number of diameters 4.

Initial activity factor (80-200 AF) 5 .

Increment of activity factor if a range of A F is to be computed

6 .

Number of activity factors 7 .

Initial number of blades (2-8 blades) a.

Increment in number of blades, if a range of blades is to be computed 9.

Number of number of blades 10.

Card 5 contains the following input data in a (213, 5F6.0) format.

Card number 1.

Number of operating conditions with a maximum of 10 2.

Initial integrated design lift coefficient (0.3 to 0.8 C ) 3.

Li Increment of integrated design lift coefficient if a range of C i s to be 4.

computed Li Number of C 's 5 .

L i For reverse thrust calculation option if bladeangle P radius is given, 6 .

3/4 code2. If p3/4 radius is tobecomputed,code 1.

For reverse thrust calculation option, code 1. for turbine engines and 2 .

7.

for reciprocating engines.

Subsequent cards are coded as follows with (3X, I3, 10F6.0) format for each operating condition. The number of these cards must be equal to the number specified in 2 on card 5 .

1. Computational option

Code option= 1 - for defining condition with SHP

option = 2 - for defining condition with thrust

option = 3 - for reverse thrust calculation

Shaft horsepower or thrust per propeller depending on option selected in 1 2.

above.

option = 1 - SHP

option = 2 - Thrust

option = 3 - SHP for zero velocity, full throttle setting

3. Altitude in feet For options 1 and 2, forward flight calculations, code 4. Velocity, knots true airspeed

5. Temperature, O F - code 0. forstandard day

nND

6. Initial tipspeed, -

9 fPS 7. Increment of tipspeed 8. Number of tipspeeds 9. Distance of fieldpoint at which noise is to becomputed.Directivityfor peak noise is automatically used. The noise calculation should be made for take-off conditions only; code = 0. when no noise calculation i s to be made.

10. Code = 1 . for computingthetipspeedcorrespondingto 50% stall. The option should be used for take-off conditions only.

11. Code = 1. if cost and weight a r e to be computed. This option must be used with a take-off condition.

For option 3 , reverse thrust calculation, code 4. Landing touch down speed,knots true airspeed 5 . Temperature, O F 6. RPMforzerovelocity, full throttlesetting 7. F i r s t power setting 8. Increment of power setting 9. Number of power settings 10. Reverseangle, p if item 6 on card 5 is coded as 2.

3/4

For subsequent cases, repeat all the input data previously specified. For ter-

mination, include two blank cards and a third card with 99 coded in an I6 format.

Program Output The input prints out initially and then the pertinent data under the following head- ings for options 1 and 2 for forward flight: 1. DUM-FT - propeller diameter, ft.

2. T.S. FPS - tipspeed, fps

3. THRUST o r SHP - dependent on which option is selected

4. PNL - perceived noise in PNdB, value corresponds to the

number of engines specified in the input.

The following cost and weight data prints out when computations a r e requested.

5. QUANTITY - number of units to be included in cost computation

6. WT-LBS - propeller weight, lbs.

7. $COST - propeller cost in dollars

The weight and cost areincluded for both 1970 and 1980 technology.

8. ANGLE - propeller blade angle in degrees at 3/4 radius which is

of particular interest in analyzing fixed pitch propellers.

The following data is included as additional information. For example, from an ex- amination of these parameters, an indicationof the presence and magnitude of com- pressibility losses and the blade loading characteristics may be established.

9. F T - compressibility correction

10. M - free stream Mach number

101.4 VK

11. J - advance ratio =

ND

SHP ( P o / P ) 10"

12. C - power coefficient =

2 N3D5

1.514 x 10 T( p 0 / P )

13. CT - thrust coefficient =

N2D4 For option 3, reverse thrust calculation, the following data prints out.

1. DIA. FT. - propeller diameter, ft.

2. PERCENT THROTTLE - specifies what percent of normal rated power

was used.

REVERSE ANGLE - reverse angle at 3/4 radius

3.

V-KNOTS - landing run velocity

4.

REVERSE THRUST - reverse thrust corresponding to 4 above

5.

SHP - shaft horsepower corresponding to 4 above

6.

7. R P M - propeller speed corresponding to 4 above

The input propeller and operating condition parameters for the parametric studies are varied as follows in the output print outs. For option 1 and 2 , forward flight cal- culations, the calculations a r e made for the input ranges in the following order: 1. Tipspeed 2. Diameter 3 . Number of blades 4. Integrated design lift coefficient 5. Activity factor 6. Operating condition F o r the option where tipspeed for 50% stall is to be defined, the computations a r e made for theinput ranges as follows: 1. Diameter 2. Number of blades 3. Activity factor 4. Integrated design lift coefficient 5. Operating condition For option 3 , reverse thrust calculation, the calculations are made for the input ranges in the following order.

1. Throttle setting 2. Diameter 3 . Number of blades 4. Activity factor 5. Integrated design lift coefficient 6 . Operating condition MESSAGES A series of messages print out which indicate that the limits of the generaliza- tions have been exceeded. These are listed below.

1. ' INPUT ERROR IW = 12, IC = 12' - the input itemspecifying whichoption

is' to be used has been included as other than l . , 2. or 3 . , the only option

values .

2. 'ILLEGAL ACTIVITYFACTOR = F8.1' - theinput A F exceedstheper-

missible 80-200 A F range.

3 . 'ILLEGAL NUMBER OF BLADES = F8.1' - the input number of blades ex-

ceeds the permissible 2-8 blades.

4. 'ILLEGAL INTEGRATED DES. CL = F8.1' - the input C L ~ exceedsthe

permissible range of 0 . 3 to 0.8 C L ~ .

'ADVANCE RATIO TOO HIGH' - check to see that input diameter, RPM, 5.

are correct. The advance ratio limits are 0 to 5.

and velocity

'FAILED STALL ITERATION' - problem encountered in defining tipspeed

6 .

corresponding to 50% stall. If this message is encountered, check input for SHP, RPM, altitude, velocity, and diameter.

******* - print out under PNL indicates that the propeller is operating at

7.

a condition where it is more than 50% stalled.

****** - printout under SHP or THRUST indicates that this condition is off

8.

the limits of the performance curves.

Sample Cases Input coding sample cases for the four performance computation options are shown on figure 10 and the output presented as figures 11 through 14 respectively.

The sample cases are presented in the following order.

1. The condition is definedbySHPandtipspeedvariation.Performanceand cost calculations based on the information included in the computer program is requested.

2. The condition is defined by a thrust requirement andtipspeedvariation.

Only performance calculations a r e requested.

3. The condition is defined by SHP.Tipspeedcorrespondingto 50% stall and cost for a span of quantities will be computed.

4. Reverse thrusts are required for a given propeller geometry for a range

of throttle settings.

Computer Running Time The computer program has been run on an IBM-System/37O. Approximately 1000 operating conditions are computed per minute.

CONCLUDING REMARKS 1 . Generalizations of analyticalmethodsforaccuratelypredictingpropeller performance, noise, weight and cost for general aviation aircraft applica- tion have been made.

3. Thecomputerprogramoffersmanyoptionsforperformingparametric propeller studies for general aviation aircraft.

4. Computer program listings and detailed inputandoutput instructions are presented.

REFERENCES 1. Worobel,R.andMayo,M. : AdvancedGeneralAviationPropellerStudy.

NASA Report CR 114289, April 1971.

2. Worobel, R . andMayo,M. : AdvancedGeneralAviationPropeller Study.

NASA Report CR 114399, Jan . 1972.

TABLE I ADVANCED GENERAL A V I A T I O N P m P U E R STUDY AIKRAFT CLASSIFICATION Gross Weight, Cruise Vel., MPH Engine Power Propeller Type Application lbs. Price Range E x q l e A i r c r a f t Aircraft Class Seats 100-160 100-200 Fixed Pitch Trainer,Private 1000-2500 $8-Z5K CESSNA 150, 172, SQhawk I. Single Eng. 2-h BEECH Musketeer AZ.3-19 Trainer Recip DD 2 Blades Rental, Aerobatic PLPER Super Cub, Fixed Gear Cherokee 120-150 150-300 Constant Speed Adv. Trainer 2000-L000 $20-50K CESSNA Slqwagon 180, 206, 11. Single Eng. b-6 207, 210 Adv. Trainer Recip DD & 2 Blades,Private(Family)

BEECH Bonanza , Musketeer

Retract Gear Geared Some 3 Blades Survey, Business Super IFR Equip. Some %all PIPERComanche C, Turboprops Cherokee Arrow MOONEY M20F 111. Light Twins h-6 150-300 150-300 Constant Speed P r i v a t e (Family) 3500-6000 $LO-lZOK CESSNA Super Skymster, 310Q Retract Gear Recip DD & 2 Blades Survey, Business BEECH Turhbaron, Ir) I F F i Equip. Geared Some 3 Blades 4 Barron 55 Some Small Deicing PIPERTwinComanche C , Turboprops Aztec D M O O N E Y Aerostar I V . Medium Twins 6-U 150-300 250450 Constant Speed Executive 6000-8000 $100-200K CESSNA LOlB, L02BJ LUJ Retract Gear b21 Turboprops, Full Feather Charter BEECH Queen Air Duke IFR Equip.

Recip DD & Deicing Air T a x i

FVERNavajo 300 , Turbo

Geared 3 Blades Navajo j KORTH A M E R T C A N A D C I M G L ” Shrike Commander BRITTEN-NORMAN ISLANDER, Helio Twin S t a l l i o n V. Heavy Twins 1 1 & U p 8000-12,500 $h00-600K DEHAVILLAND Twin Otter 175-hOO 600-1500 Constant Speed Large Executive MOONEX MU-2G Retract Gear Turbines Full Feather Charter, Third NOWH AMERICAN ADCKWUL IFR Equip. Deicing, Tier Air Liners HawkCommander Reverse BEECH King A i r 3 and b Blades H A N D L E Y P A G E Jetstream G e n e r a l i z e d P r o p e l l e r \ V e i g h t Equjltion:

-

Where: B .- No. of Blades A. 1'. . B1:ule Activity I's-tor N = p r o p . S p e e d , Rl'hl (t;Ike-Off) S H P L S h a f tH o r s e p o w c r , HI' (take-off) cW = Y (s) ( B ) (s) (T) -90,000 O.:' = CountcrweightWt.,lbs.

K w , C w , u, v and y vnlues f o r use in the weight equxtion ; r e taken from table below:

'n C l a s s (1) 170 0.9 0.35 0

( 2 ) ( l ) I ( 2 ) 200 0 . 9 0.35 0

220 0.7 0.40 5.0 ( :: ) ( 3 ) I V 190 0.7 0.40 3 . 5 ( 4 ) j ( 4 ) I V 130 0.7 0.20 0 (5) ( 5 ) (1) All fixed-pitch props ( 9 ) hlc C a u l e y n o n - c o u n t e n v c i g h t c d , n o n - l e n t h e r i n g , c o n s t m t s p e e d p r o p s ( 3 ) All H a r t z e l l , :dl HamiltonSt:lnd:trd sn~:tll p r o p s , :lnd fe:lthering hIc C:tule,v ( 4 ) F i b c r g h s s - b l a d c d , c o n s t m t s p e e d , c o u n t e n v e i p h t e d , full f e a t h e r e d (5) 1:iberg'lass-l,l~ded, const;~nt-specd, doul,le-acting (non-countel~\,eighted), full f e a t h e r e d , reverse

Y

(I) w EFFECTIVE POWER COEFFICIENT. c p ~ FIGURE 1. POWER COEFFICIENT CHARTFOR A 2 BLADED, 150 ACTIVITY FACTOR, 0.500 INTEGRATEDDESIGN CL; PROPELLER W -I w z EFFECTIVE THRUST COEFFICIENT, C T ~ F I G U R E 2, THRUST COEFFICIENT CHARTFOR A 2 BLADED, 150 ACTIVITY FACTOR, 0.500 INTEGRATEDDESIGN C L i PROPELLER

3 BLADES/IOO A F / O . ~ cLi

BLADE A N G L E . p 3/4

FIGURE 3. BASIC PERFORMANCE CURVE VARIATION OF EFFECTIVE TORQUE COEFFICIENT WITH ADVANCE RATIO 8r BLADE ANGLE

I

3 BLADES/lOOAF/0.4 C L ~ - 3 0 - 20 - 10 0 10 v

- 20 - 10 0 i o

B L A D E A N G L E , p 3 1 4

FIGURE 4. BASICPERFORMANCECURVE VARIATION OF EFFECTIVE THRUST COEFFICIENT WITH ADVANCE RATIO 8c BLADE ANGLE PROPELLER INPUTHORSEPOWER FIGURE 5. BASICNOISECURVE

2 BLADES - 1 OOAF - 0.5 C

L i MAXIMUM CRUISE

1 12 SHP - 7000 - 1 1 5 KNOTS

tn I

CLIMB 150 QHP - SL - 70.5 KNOTS

I I 100) I I I

20° I 1 5 O I

400 50 D IA=6' 0

T.O. A T 500' SIDELINE

T.O. 150 SHP - S.L. - 52.5 KNOTS

,6' F

tn I I I

0 8' DIA

500 700 900 1100 500 700 900 1100 TIPSPEED FT/SEC TIPSPEED FT/SEC FIGURE 6. CATEGORY I PARAMETRIC STUDY

4 BLADES - 150 A F - 0.5 CLi

M I N I M U M CRUISE

n

370# THRUST - 7500 - 163.2 KNOTS

[r

I- 5 2000

!: 8 '

4 1000

- 6 ' -

d

n

n 4001 I I I

CLlbiB 700 THRUST - S.L. - 95.5 KNOTS

T.O.AT $00' SIDELINE

T.O. 820 THRUST - S..L. - 71.2 KNOTS

urn

~ ja, ~ ' 1

m

60' I I I

3 00 500 700 900 3 00 500 700 900 TIPSPEED FT/SEC TIPSPEED FT/SEC FIGURE 7. CATEGORY I I PARAMETRICSTUDY 4 BLADES - 0 . 6 CLi loo 1 4 , 90 3 000 v)

urn

t - K

In 4 2000

$ E 80

70 1000 " V

T.O. 340 SHP - S.L. - 77.5 KNOTS

4 0 0 '

I J

8 10 12 DIAMETER-FT DIAMETER - FT FIGURE 8. CATEGORY I V PARAMETRIC STUDY CATEGORY V I I LANDING SPEEDS, KNOTS FIGURE 9. EXAMPLEREVERSE T H R U S T VARIATION WITH LANDING SPEED AND POWER SETTING J O B NO: _ _ _ _ _ _ _ . ~ _ _ A C C T N O . : W 0 . N O !

JOB NO.: A C C T . N O : W . O . NO.: !

w W Y A M I I T O Y SThYOA9Q CIYPLITFK DFCK NL1. H 4 3 2 CIYPUTFSPT~FflRY~lYCC,YllISr,kEIGHT,AND C f l S T F 9 R G F H F Q A L 9VlAT IPN PQ(!D€LLFRS 1 4 1 R P L P , l \ r F I N C.¶TEG[lRY I SAMPLE C A S E I 2 S H O Tfil"VT-TIP5UFI:D AN0 3IAYFTF.Q VAKIhTION-COST AN0 WFIGHT 0"EQATlNG CONDTTION SHP = 1 5 1 . vn. O F ENGINFS = 1. W I T FACTUP 1L.C. = 3.22 ALT-FT = 0. 3 r S I G N FLIGHT Y.=O.lHl 1 0 0 0 F4CTflR L.C. = 1.02 V - K T A S = 5 ? . 5 . C L A S S I F I C h T I f l N = 1.

T F M P R = 519. FIELD PQI'VT F T . = 5 n o .

C T C P 7'fl. 1 9 1 n . 3 6 . 2 1 5 . 710. 13.3 0 . 0 7 9 4 0.2 9.3 0,0349 0 . 0 6 9 4 6 . 5 4 3 . 1 0 1 . 22'11). 3 6 . 1.000 9 5 " .

5 . 540. 97. 1 q 1 c . 3 4 . 707. 2 2 3 0 . 34. 2 @ 2 . 16.5 1 .OOO 0 . 0 7 9 4 0.128 0.0487 0 . 0 8 6 3 7 5 1 . ' .

6 . 5 1 4 . 9 2 . 1 7 1 0 . 7 3 . 198. 2 2 3 0 . 33. 193. 20.4 1.000 0.0794 0.372 0 . O 7 0 9 0.1055 4 7 r l . s * c t s t ; 5. 5qn. 1919. 3 1 . 1 8 8 . 2 2 3 0 . 3 1 . 1A4. 25.8 1 .no0 0.0794 0.429 0.1089 0.1283 5 5 7 . 3 7 7 . e t * * * : * h . 1910. 2 5 . 179. 2230. 29. 1 7 3 . 33.8 1.900 0.07q4 0.507 0.1798 0.1440 rp 9 5'1.

9. 524. 97. I 1 9 1 C . 59. 357. 2 2 30. 59. 3 4 8 . 8.8 1. 'lo0 0 . 0 7 9 4 0.293 0.01 9 6 0 . 0 3 7 7 9. q57. s a 3 . 97. 1910. 5 7. 343. 2 2 3 0 . 5 1 . 3 3 5 . 11.5 1 . O O O 0 . 0 7 9 4 0.328 0.0274 0.0524 3 . 7 5 C . 6 1 8 . R E . 1 Q I P . 55. 3 2 9 . 2 2 3 0 . 55. 320. 1 5 . 0 1,000 0 . 0 7 9 4 0.372 0.0713 0.0399 9. ! > 50 . 691. H4. 191 0 . E.?. 312. 2 2 3 0 . 5 2 . 3c5. 19.3 1.009 0.0794 0.429 0.0613 0.0923 8 . 5 5 " . 5 5 9 . 7 0 . 1910. 49. 295. 2 2 3 0 . 49. 7 6 7 . 25.4 I . o o o 0.0794 0.507 0 . 1 0 1 1 0.1200 S H D = 112. NO. f l F E Y G I N E S = 1 .

= 7000. n F S I G N F L I G H T W.=O.187 ALT-FT = 115.0 C L A S S I F I C A T I D N = 1.

V - K T A S TEMP 9 = 494. " O I h l T FT = 0.

F l F L O . . - . .. . -. .

NUMREQ 'lr RLAOC\= 2 . A C T I V I T Y FACTflR=100. INTFGR4TEO D E S I G N CL =.500 0 I b . F T . T.5.FPS THRUST PNL 4NGLF FT Y J CP C T

2 6 7 . 0. 1 6 .'+ 0. 6 4 3 0 . 0 3 2 1 0 . 0 4 2 1

280. 0 . 19.6 0.718 0 . 0 4 4 9 0 . 0 5 5 0 2 7 5 . 0 . 23.7 0.814 0.0652 0 . 0 6 9 5 2 6 5 . 0 . 28.9 0.939 n. 1 0 0 7 n. 0 8 9 2 252. 0. 35.9 1.110 0 . 1 5 5 4 0.1 I 8 4 1 7 9 . 0 . 13.1 0.643 0.0181 0 . 0 1 5 9 2 5 6 . 0. 16.4 n . 7 1 ~ 0 . 0 2 5 2 0 . 0 2 8 3 2 9 2 . 0. 20.1 0. A14 0. (1367 0.041 5 2 a z . 0 .

2 4 . Z 0.939 0 . 0 5 6 4 rl.0534 0. 30.0 260. 1.110 0.0930 0 . a 7 4 1 . . . - . . . . .

. . . . . - . -. .. . .

FIGURE 11. SAMPLE OUTPUT - SHP OPTION - -~ ~ . . . . . . . - .

HAMILTON STANQARD CflMPUTER DECK Nfl. H43Z C O S T FOR COHPUTFS PFoFORYANCE1Y21SE,dEIGHl,AYD GFNFRAL A V I A T I O N PROPELLEKS 1 A17PLANE I N ChTfGPRY 11 SAMPLE CASF 2

Z TH9UST INPUT-TIPSPEEl7 P N l l llIAYETE9 V A R . - COST AND WEIGHT

IPFRATINT, CONDITION " .. .

THRUST = @?O. 40. n F EYSINFS = 1 . IJNIT FACTDR L.C. = 3.22 . .. . . ~... . . " 4 L T - F T 0. .DESIGN FLIGHT Y.=0.762 1000 FACTOR L.C. = 1.02 71.2 CLhSSIFICATIflN 2 .

V-KTAS = *1Y. F I E L D P O I N T F T . = 5 n 0 .

TEMP K = NIJHREQ O F Rl.AnES= 4. A C T I V I T Y FACTflR=150. INTFGRATEO D E S I G N C L =.500

*** 1 9 7 0 TECHNPCOGY *** *** 1 Y A O T E C H N O L n G Y X X X

DIA.FT. T . S . F P S SHP DNL QUANTITY W T - L R S 6C;)ST 'JUAr\lTITY. WT-I.RS $ C O S T ANGLE FT H J CP C T . " 6 . 9 5 0 . 2 7 4 . 9 7 . i'R10. 1 @ 5 . 1 0 3 3 . 5 4 7 0 . 1 0 5 . 925. 1 5 . 2 1 . 0 0 0 0.1077 0.445 0 . 0 8 8 8 0.1309 6. 75n. 78A. 5 4 7 0 . 100. AR4. 270. 93. 2 8 1 0 . 100. 1.030 0 . 1 0 7 7 0.1276 0.1682 18.6 0 . 5 0 4 6. o5C. 2 7 5 . 90. 2 9 1 0 . 9 5 . 9 4 1 . 5 4 7 0 . 95. R43. 1.030 0.1077 0 . 5 8 2 0.1993 0.2239 23.6 5. 5 5 0 . 2 7 3 . 8 6 . 2910. 90. 981. 5 4 7 0 . 9 0 . 7 9 4 . 30.3 1.000 0 . 1 0 7 7 0.687 0.3268 -0.3127

tc. H V . 5 4 7 0 . 1 7 5 . 1 5 4 8 . 11.5 1.000 0.1077 0.445 0 . 0 5 3 5 0.0737

2 9 3 . 9 4 . 2810. 1 7 5 . 1 7 2 9 .

9. 7 5 0 . 2 5 0 . 8 9 . 2 8 1 0 . 1 6 5 . 1 6 3 1 . 5 4 7 0 . 1 6 5 . 1 4 6 0 . 1.000 0.1077 0.504 0. 0690" 0 . 0 9 4 6 .

14.0 8. , h 5 ' ) . 1539. 5 4 7 0 . 1 5 6 . 1 3 7 8 . 17.5 1.000 0.1077 0.582 0.0992 0.1260 2 4 3 . 8 5 . 2 9 1 0 . 1 5 6 .

9. 5 5 0 . 2 4 2 . 91. 2 9 1 0 . 1 4 7 . 1 4 5 1 . 5 4 7 0 . 147. 1 2 9 9 . 22.5 1.noo 0 . 1 0 7 7 0.6R7 0.1634 0.1759 3DFRATINC C O N D I T I O N THRUST = 3 7 0 . N'I. ClF FhlGtNFS = 1.

ALT-FT = 7 5 0 0 . n E s I r x FLIGHT ~ . = 0 . 7 6 2 V - K T A S = 153.2 CLASSIFICATION = 2 .

= 4 0 7 .

TEMP R F I E L D POINT F T = 0.

= 4 .

NLJElYFQ I F 4LADES A C T I V ITY FACTflQ- 1 5 0 , Ik!TE3RATED D F S I G N C L =.500 " DIA.FT. F.S.FPS S t I P PNL ANGLE F T H J CP CT 6 . " 0 A59. 2 2 6 . 0. 2 3 . 5 1 . O O ' l ! ) . 7 5 3 4 1.019 0 . 3 9 1 9 q . 0 7 3 9 6 . 0 0 7 5 0 . 2 1 3 . n. 7 6 . 4 1.010 P.7534 1.155 0.1259 0 .O950 6.nO 6 q P . 7 0 P . 0. 31.5 1.000 0 . 7 5 3 4 1 . 3 3 3 0 . 1 9 9 1 0. I 2 6 4 6.00 5 5 3 . 217. 0. 77.9 1 . n ~ 0 . 2 5 3 4 1.575 0 . 3 1 7 9 0 . 1 7 6 6 3.00 350. 2 6 2 . n. 23.0 1 . o o n 0 . 2 5 3 4 1.019 0. C 5 9 R 0.041 h 9 . m 7 5 9 . ? 3 2 . n. 2 5 . 1 1.0nn 9 . 2 5 3 4 I . 1 5 5 0 . 0 7 7 3 o . n 5 3 4 8 . o ~ h 5 n . 7 1 5 . 0 . 29.1 1.090 0 . 7 5 3 4 1 . 3 3 3 0.1099 0 . 0 7 1 1 9 . 0 1 5 5 , ) . 70 7. 0 . 34.3 I .m)n ~ 7 . 2 ~ 3 4 1.575 0 . 1 7 4 7 0 . 0 9 9 3

FIGURE 12. SAMPLE OUTPUT - THRUST OPTION

HAMILTON SlANDARD COMPUTER DECK NO. H 4 3 2 COMPUTES P E R F O R H A N C E I N O I S E ~ W E I G H T ~ A N O COST FOR GENERAL A V I A T I O N PROPELLERS 1 AIRPLANE I N CATEGORY 1 V SAMPLE C A S E 3 2 SHP INPUT-CALC. TIPSPEED FOR 50PERCENT STALL-COST FOR RANGE QUANT.

OPERATING CONOITION 740. NO. OF ENGINES = 2. U N I T FACTOR L.C. = 3.22 SHP = ALT-FT = 0. DESIGN FLIGHT M.=0.327 1000 FACTOR L.C. = 1.02 77.5 C L I S S I F I C A T I O N = 4.

V-KTAS = TEMP R = 519. FIELO POINT F T . = 500.

NUMBER OF BLAOES= 4. A C T I V I T Y FACTOR-200. INTEGRATED D E S 1 G . N CL =.600

*** 1970 TFCHNOLOGY *** *** 1 9 8 0 TECHNOLOGY ***

0IA.FT. T.S.FPS THRUST S C O S T UT-LBS S C O S T ANGLE FT M J C P PNL QUANTITY WT-LBS QUANTITY C T . - a. 345. B L R . 77. 1. 228. 7770. 46.3 1.000 0.1172 1 . 1 9 4 0 . 9 3 3 3 7106. 1. 1 8 5 . 0.4473 1001.

2 2 8 . 2252. 1001. 1a5. 2 4 6 3 .

2001. 2 2 8 . 2 ~ 0 7 . 2001. 185. 2195.

3001. 22a. 1876. 3001. 185. 2052.

4 0 0 1 . 2 2 8 . 1 7 8 8 . 4 0 0 1 . 1 8 5 . 1956.

NUMBFR OF BLADES= 6. ACTIVITY FACTOR=200. INTEGRATED DESIGN C L =.600

*** 1 9 7 0 TECHNOLOGY * a * *** 1980 TECHNOLOGY ***

DIA.FT. T.S.FPS THRUST PNL QUANTITY WT-LBS S C O S T QUANTITY UT-LBS SCOST ANGLE F T M J CP CT 8. 282. 828. 74. 1. 306. 11926. 1. 245. 12887. 51.2 1.000 0.1171 1.459 1.7021 0 . 6 7 5 9 1001. 306. 3780. 1001. 245. 4084.

2001. 3 0 6 . 3 3 6 8 . 2001. 245. 3640.

3 0 0 1 . 306. 3149. 3001. 3403.

245.

4 0 0 1 . 3 0 6 . 3002. 4001. 245. 3244.

FIGURE 13. SAMPLE OPTION - 50% STALL OPTION

2FClPR7CATIVG F'IGI'JF 6 5 0 .

2109.

547. 2198.

543. 2172.

5 3 a . 2 1 5 1 .

531. 2124.

523. 2092.

5 1 4 . 7 0 5 6 .

5 0 3 . 7 0 1 3 .

501. 2004.

440. 2194.

437. 21R7.

434. 21 7 0 .

4 3 0 . 2 1 4 9 .

425. 2174.

419. 2 0 9 3 .

412. 2 0 5 9 .

404. 2019.

402. 2010.

3 3 0 . 2 2 0 0 .

37R. 21114.

325. 2165.

321. 2141.

3 1 8 . 2117.

311. 2097.

308. 2054.

303. 2019.

302. 2 0 1 0 .

FIGURE 14. SAMPLE OUTPUT - REVERSE THRUST OPTION

.-. - - - APPENDIX A

FLOW CHART, SUBROUTINE LIST AND FORTRAN IV LISTING FOR

HAMILTON STANDARD DECK H432 Hamilton Standard computer deck H432 computers propeller performance (static,

flight, and reverse), noise, weight and cost for a broad spectrum of propeller

geometric configurations over the complete range of potential operating conditions.

The flow chart is presented on figure IA, the list of subroutines on figure 2A, and the FORTRAN IV listing on figure 3A.

(INPUT) INPUT DATA ACTIVITY FACTOR NUMBER OF BLADES TIPSPEED DETERMINE CALCULATES SHP CALCULATES TIPSPEED AT WHICH REVERSE ANGLE FOR GIVEN THRUST BLADE WILL BE AND REVERSE THRUST 50% STALLED YES CALCULATES NOISE CALCULATES

COST I

PRINT

RESULTS -

HAVE A L L ~ No CONDITIONS FOR THIS CASE BEEN COMPUTED

F I G U R E 1A C O M P U T E RP R O G R A M FLOW C H A R T

HAMILTON STANDARD DECK H432 Computer Program for Advanced General Aviation Propeller Studies MAIN INPUT PERFM ZNOISE WAIT C OST REVTHT UNINT BIQUA D Figure 2A LIST OF SUBROUTINES D A T E = 72034 10/08/04 . FORTRAN .CY G L E V E L 2011 H A 1 N ~ 0001 R E A L * 8 B L A N K COnHOH/AFCOR/AFCPE,AFCTE,XFT C O M H O N / A S T R K / C P A S T r C T A S T E R K 0 0 0 3 0004 COMHON/CPECTE/CPEsCTEIBLLLLL 0005. D i M E N S I O N F C ~ l O ~ r A L T P R ~ l l ~ ~ P R E S S R ~ l l ~ ~ R O R O ~ l O ~ ~ Z M S ~ Z ~ 0006 D I M E N S I O N C J I S T ~ l O ) r C O U A N ~ 2 r l l ) r C O S T 7 0 ( 1 0 1 r C O S T 8 O t l O ~ 0007 D I H E N S i O N BHPG(lO)rTHRSTG110)rTIPSDG(ll) 0008 COMMON / Z I N P U T / B H P ~ 1 0 ~ ~ T H R U S T ~ 1 0 ~ r A L T ~ l O ~ r V K T A S ~ l O ~ ~ T ~ l O l * I W I C ( l O ) TNOFIDIDD,NDIAF*DAFINAFIBLADN.D~LADN,D~L~D, N B L * D T S ( l O ) r N D T S I . 10) 2 ~ D I S T ~ X N O E ~ k T C O N ~ Z M W T ~ S T A L I T ~ l O ~ ~ C L F l ~ C L F ~ C K 7 O ~ C ~ 8 O ~ C A M T ~ D A M 3 ~ D C O S T ~ l O ~ ~ C L X ~ ~ D ~ L ~ ~ Z N C L I ~ R T C ~ R O T ~ P C P ~ ~ l O ~ ~ N P C ~ 4DPCPW ( L O ) r R P M C l 1 0 ) r A N D V K ( 10) 0009 DATA ALTPR / 0 ~ r 1 0 0 0 0 ~ ~ 2 0 0 0 0 ~ ~ 3 0 0 0 0 ~ ~ 4 0 0 0 0 ~ ~ 5 0 0 0 0 ~ X 6 0 0 0 0 ~ ~ 7 0 0 0 0 ~ r 8 0 0 0 0 ~ ~ 9 0 0 0 0 ~ ~ 1 0 0 0 0 0 ~ / 00 10 DATA PRESSR / 1 ~ 0 ~ ~ 6 8 7 7 ~ ~ 4 5 9 5 ~ ~ 2 9 7 0 ~ ~ 1 8 5 1 s ~ 1 1 4 5 r . 0 7 X ~ 0 4 4 1 9 ~ ~ 0 2 7 4 1 ~ ~ 0 1 6 9 9 ~ ~ 0 1 0 5 4 / D A T A B L A N K / 6 H / C B R T ( X ) = X * * ( 1 . / 3 . ) 00 13 7 0 1 C O N T I N U E 0014 W R I T E (6.1 I 1 FORMAT ('1',19X'HAMILTON STANDARD COMPUTER DECK NO. H 4 3 2 ' / 1 7 X * C O M P l U T E S P E R F O R M A N C E I N O I S E V W E I G H T * A N D C O S T F O R ' / 2 6 X ' G E N E R A L A V I A T I O N P ZROPELUERS' 1 0016 C A L L I N P U T DO 700 I C = l , N O F N C O S T = D C O S T ~ I C I + . O l 00 1 8 IF ( S T A L L T t IC).LE..SO) G O TO 710 NDTSI. I C ) = l O 0021 D T S ( I C )=O.O 0022 710 C O N T I N U E I W = I W I C ( 1 C ) C I W = 1 H P I N P U T C IW=2 T H R U S T I N P U T C IW=3 REVERSE THRUST I F ( I W . L E . 3 ) GO TO 3 0 024 W Q I T E ( 6 ~ 2 ) I W t I C 0 0 2 5 2 FORMAT * I N P U T ERROR9 I W = ',IZ*' I C = ' * I 2 ) 0026 ~.

0027 GO TO 700 0 0 2 8 3 C O N T I N U E C C O M P U T A T I O N OF D E N S I T Y R A T I O 0029 I F I T ( I C ) ) 1 0 0 ~ 1 0 0 ~ 1 6 0 00 30 100 I F ( A L T I I C ) - 3 6 0 0 0 ~ ) 1 2 0 s l 2 0 ~ 1 4 0 0031 120 T ( 1 6 ) ~ 5 1 8 . 6 8 8 - . 0 0 3 5 6 + A L T ( I C ) GO Tn 180 140 T (I C ) = 3 8 9 . 9 8 8 GO TO 180 160 T ( I ) = T ( I C ) + 4 5 9 . 6 9 0036 1 8 0 TO=5 18.69 T O T = T O / T ( I C ) 00 37 0038 F C I I t ) = S O R T I T O T ) 0 039 C A L LU N I N T( l l * A L T P R v P R E S S R , A L T ( I C ) * P O P I L I M I T ) 0040 R O R O ( I C ) = l . O / I P O P * T O T ) C AF L O O P .AFT=AF-DAF I F (IW.EQ.3) GO T O 7000 0043 WRITE (6,706) 706 FORMAT ~ * O s ~ l 8 X * 0 P E R A T I N GC O N D I T I O N ' / I 0045 I F I N C O S T - 1 ) 2 9 0 r 2 0 0 9 2 9 0 F I G U R E 3A. F O R T R A N IV LISTING FORTRAN I V G L E V E L 2 0 . 1 M A I N O A T S = 7 2 0 3 4 1 0 / 0 8 / 0 4 0 0 4 6 200 I E N T = l 0 0 4 7 C A L L C O S T ( W T C O N ~ B L A D T ~ G L F l ~ C L F I C K 7 0 r C K 7 O ~ C K 8 O ~ C A M T ~ D A M T ~ N A M T ~ C ~ U A N ~ l ~ l ~ ~ W 7 7 0 ~ W T 8 0 ~ C O S T 7 0 ~ C O S T 8 O ~ C C L F l ~ C C L F ~ C C K 7 O ~ C C K 8 O ~ I E N T ~ 0 0 4 8 GO 70 1 2 1 0 * 2 3 0 ) r I W 0049 210 WRITE ( 6 ~ 2 2 0 ) B H P ( I C I m X N O E e C C L F 1 = ' r F 7 . 0 , 9 X ' N O . OF ENGINES =' 1 F 5 . 0 1 9 X ' U N I T F A C T O R 0 0 5 0 2 2 0 F O R M A T ( ' SHP 1 L - C . = ' r F 5 . 2 ) 0051 GO TO 250 0 0 5 2 2 4 0 F O R M A T ( ' THRUST = * r F 7 0 0 9 9 X ' N O . OF E N G I N E S = ' . F ~ . O I ~ X ' U N I T F A C T O R 1L.C. = * r F 5 . 2 ) 0 0 5 3 230 WRITE ( 6 . 2 4 0 ) T H R U S T ( I C l r X N O E t C G L F L 00 5 4 2 5 0 I F ( C K 7 0 . G T . O . . O R . C K 8 O . G T . O . ) GO r 0 2 5 5 W R I T E (6,2521 A L T ( I C ~ ~ Z M W T I C C L F ~ V K T A S ( I C ~ ~ W T C O N I T ( I C ) ~ D I S T ~ I C J 0 0 5 5 2 5 2 F O R M A T ( ' A L T - F T = ' r F 7 . 0 . 9 X . ' D E S I G N F L I G H T M . = ' * F 5 . 3 r 9 X , '1000 FACTO 00 5 6 1 R L.C. = * r F 5 . 2 / ' V-KTAS = ' ~ F ~ . ~ ~ ~ X I ' C L A S S I F I C A T I O N = ' , F 5 - 0 / ' T E 2MP R = ' W F ~ . O , ~ X I ' F I € L D P O I N T F T . = ' . F 5 . 0 ) 0 0 5 7 GO TO 270 0 0 5 8 2 5 5 W R I T E ( 6 ~ 2 6 0 1 A L T ( I C ) v Z M W T ~ C C L F I V K T A S ( I C ) ~ W T C O N I C K 7 0 , T [ I C ) , 1 D I S T ( IC) e CK8O ' A L T - F T = ' P F ~ . Q , ~ X I ' D E S I G N F L I G H T M . = ' . F 5 . 3 r 9 X * ' l 0 0 0 F A C T 0 0 5 9 2 6 0 FORMAT( = ' s F 5 . 2 / ' V - K T A S = ' ~ F 7 . l r 9 X ~ ' C L A S S I F I C A T I O N = ' r F 5 . 0 . 9 X , 1 0 R L.C.

2 ' U h r I T C O S T 1 9 7 0 = ' r F 5 . 1 / * TEMP R = ' . F T . O I ~ X , ' F I E L D P O I N T F T . = 3 ' * F 5 . 0 , 9 X s 1 U N I T C O S T 1 9 8 0 =' t F 5 . 1 ) 0 0 6 0 GO T O 2 7 0 0 0 6 1 2 9 0 GO T O ( 1 0 1 1 2 ) . I W 0062 LO W R I T E (6.111 B H P ( 1 C ) r X N O E 0 0 6 3 11 FORMAT( SHP =I r F 7 . 0 1 2 3 X ' N O . OF E N G I N E S ='1F5.0) OC64 GO T O 1 4 0 0 6 5 1 2 W R I T E ( b e 1 3 1 T H R U S T I I C ) , X N O E

0 0 6 6 1 3 F O R H A T ( ' THRUST ='.F7.0122X'NO. OF E N G I N E S ='.F5.0)

0067 1 4 W R I T E ( 6 ~ 1 5 ) A L T f I C I ~ Z M W T I V K T A S ( I C ) ~ W T C O N ~ T ~ ~ D I S T ( I C ) 15 F O R M A T ( ' A L T - F T = ' r F 7 . 0 v 2 3 X * D E S I G N F L I G H T H . = ' r F 5 . 3 / ' V - K T A S ='t 0 0 6 8 1 F 7 . 1 r 2 3 X 8 C L A S S I F I C A T I O N = ' p F 5 . 0 / ' TEMP R = ' r F 7 . 0 , 2 3 X ' F I E L D P O I N T 2 F T =* r F 5 - 0 ) 0 0 6 9 GO TO 2 7 0 0 0 7 0 2000 W R I T E ( 6 . 2 1 0 0 ) 0 0 7 1 2 1 0 0 FORMAT ( ' ~ ' ~ ~ ~ X I ' R E V E R S E T H R U S T C O M P U T A T I O N ' / / ) 0 0 7 2 I F ( R O T . E O . 1 . 1 GO TO 2 3 0 0 c 0 7 3 W R I T E ( 6 1 2 2 0 0 ) 00 74 2 2 0 0 F O R Y A T ( Z ~ X I ' R E C I P R O C A T I N G E N G I N E * / / ) 0 0 7 5 GO T O 2 4 0 0 0 0 7 6 2 3 0 0 H R I T E ( 6 ~ 2 3 5 0 1 2 3 5 0 F O R M A T ( 2 7 X . ' T U R B I N E E N G I N E ' / / ) 0 0 7 7 0078 2 4 0 0 W R I T E ( 6 r 2 5 0 0 ) B H P ( I C ) r R P M G ( I C ) . A N D V K ( I C ) r A L T ( I C ) . T ( I C ) 0 0 7 9 2 5 0 0 FORMAT ( 2 2 X . ' F U L L T H R O T T L E SHP =' 9 F 6 . 0 / 2 2 X r ' F U L L T H R O T T L E RPM = ;I, I ' ~ F ~ . O / Z Z X I ' T O U C H DOWN V - K N O T S = ' , F 6 . 0 / 2 2 X . ' A L T I T U D E F E F T ~ F ~ . O / Z ~ X I ' T E M P E R A T U R E R A N K I N E = ' r F 6 . 0 / / 1 O C 8 0 2 7 0 DO 1 2 0 0 I A F = l r N A F A F T = A F T + D A F OC82 I F ( A F T . L E . 2 0 0 . . A N D . A F T . G E . E 0 . ) GO TO 1 8 2 0 0 8 3 U R I T E ( 6 . 1 R l ) AFT

0084 1 8 1 F O R M A T ( ' I L L E G A L A C T I V I T Y FACTOR = ' r F 8 . 1 )

0 0 8 5 GO T O 1 2 0 0 O C 8 6 1 8 2 CONT I N U € C I N T E G R A T E D D E S I G N C L L O O P 0 0 8 7 N C L I = Z N C L I + . l 0088 CL I = C L 1 1 - D C L I OC89 DO 1 0 0 1 I C L = l r N C L I FIGURE 3A. FORTRAN I V LISTING (CONTINUED) 1 0 / 0 8 / 0 4 FORTRAN .I.V G L E V E L 2011 . . MA I N D A T E = 72034 C L I = C C I + D C L I I F ( C L I . L E ~ . 8 0 0 0 1 . A N D , C L I . G E . . 2 9 9 9 9 ) GO T O 875 0092 W R I T E (6,870) C L I 0093 870 F O R M A T ( I L L E G A L I N T E G R A T E C D E S I G N C L ='tF5.31 . 0094 GO TO 1 0 0 1 0095 8 7 5 C O N T I N U E C NO. O F B L A D E S LOOP 0096 BLADT=BLADN-DBLAO 00 97 DO 1000 I B = l , N B L 0098 BLADT=BLADT+DRLAD 0099 IF(BLAOT.LE.B..AND.BLADT.GE.2.) GO TO 888 0 100 W R I T E ( 6 . 8 8 7 ) B L A D T 887 F O R M A T ( ' I L L E G A L NO. OF B L A D E S = ' t F R . 1) 0 101 GO T O 1000 0 103 888 C O N T I N U E C P R I N T A P P R O P I A T E H E A D I N G 0104 I F ( I U .LT.3) GO TO 2700 0 1 0 5 W R I T E 16,2650) B L A D T t A F T t C L I 0106 2650 FORMAT ( ' O ' t ' N U M B E R O F B L A O E S = * , F 3 . 0 , * A C T I V I T Y F A C T O R = * t F 4 . 0 , ' 1 I N T E G R . A T E D D E S I G N C L = ' t F 4 . 3 / ) 0 1 0 7 W R I T E (6,2660) 2660 F O R Y A T ( 1 3 X v ' T H R O T T L E R E V E R S E ' p R X . ' R E V E R S E ' / 5 X I ' D I A . F T S E T T I N G A 01 08 l N G L E V-KNOTS THRUST SHP RPM*/) 0 109 GO TO 30 0110 2700 W R I T E (6.20) B L A D T t A F T v C L I 0111 20 FORMATI'O'.' NUMBER OF B L A D E S = ' V F ~ . O ~ ~ ~ X ' A C T I V I T Y F 4 C T O R = ' t F 4 . 0 t X 1 8 X ' I N T E G R A T E D D E S I G N C L = ' r F 4 . 3 ) 0112 IF(NCOST.EQ.1) GO TO 500 GO TO ( 2 1 r 2 4 1 ~ I U . 0113 0114 21 W R I T E (6.22) 2 2 F O R M A T ( ' 0 ' r ' D I A - F T . T.S.FPS T H R U S T P N L A N G L E F T M 1 J C P C T ' / 1 0116 GO TO 30 2 4 W R I T E ( 6 t 2 5 ) 0118 2 5 F O R M A T ( ' 0 ' t ' D I A . F T . T.S.FPS SHP P N L A N G L E F T u L J C P C T ' / 1 0119 GO TO 30 0120 500 G O TO l510t550)rIW 0 1 2 1 510 W R I T E 1 6 , 5 2 0 )

0 1 2 2 5 2 0 FORMAT(.'0',30X**** 1970 TECHNOLOGY *** *** 1 9 8 0 TECHNOLOGY ***I/

1' D I A e F T . T.S.FPS T H R U S T P N L Q U A N T I T Y U T - L B S & C O S T Q U A N T I T Y

2 WT-LBS $COST ANGLE F T N J CP c r * 1 1

GO TO 30 550 W R I T E (6,560) 560 F O R M A T ( ' 0 ' ' 3 0 X ' * * * 1970 TECHNOLOGY *++ *++ 1980 TECHNOLOGY X X X ' / 012s WT-LRS SCOST 1 ' D I A . F T . T.S.FPS SHP P h L Q U A N T I T Y Q U A N T I T Y F T M 2 WT-LBS $COST ANGLE J CP CT' / ) 0 126 30 C O N T I N U E 0 1 2 7 It [NE= I L I N E + 6 C 0 1 ANETEK LOOP D I A=D- DD DO R O O I D = l r N D 0 1 30 01 A = D I A+OD 0 131 I F I I W . E Q . 3 ) GO TO 3 0 0 0 C T I P S P E E D L O O P 0132 I F ( S T A L I T 1 I C ) .LE..50)GO TO 3 1 0 0 1 3 3 D T S ( I C 110.

0134 TRIG=O.

FIGURE.3A. FORTRAN IV LISTING (CONTINUED) OATE = 7 2 0 3 4 1 0 / 0 8 / 0 4 FOHTRAN I V G L E V E L 20.1 M A I N 0 135 N T S= 10 T I PSDC4 1 ) =700.

T I PSPO=700.

0138 GO TO 320 .

0139 310 T l P S P D = T S ( f C ) - D T S ( I C ) 0140 NTS=NDTS I IC 1 0141 320 DO 600 I T S = l * N T S 0 142 T I P S P D = T l P S P D + D T S l I C ) C MACH NUMBER C A L C U L A T I O N A N D A U V A N C E R A T I O J 0 1 4 3 L H S ~ l ~ = . 0 0 1 5 1 2 * V K T A S l I C ~ * F C ~ I C ~ 0 1 4 4 Z M S ( Z I = T I P S P D * f C ( IC)/1120.

0 145 Z M l = Z M S I 1 ) 0146 ZJI=5.309*VKTASllC)/TlPSPD IFlZJI.EQ.0.) Z H L = Z M S ( Z ) 0148 I F I S T A L I T I I C ) . L E . . S O . A N D . Z J I . L E . 5 . 0 ) GO TO 342 0149 I F ( S T A L I T L I C ) . G T . . 5 0 . A N D . Z J I . L € . 3 . 0 ) GO TO 3 4 2 0150 W R I T E ( 6 p 3 4 1 ) Z J I F O E M A T ( ' A D V A N C E R A T I O TOO H I G H = ' 9 F 8 . 4 ) 0 1 5 1 3 4 1 0 1 5 2 GO TO 600 0 153 3 4 2 C O N T l N U E C I T E R A I I O N ON CT OR C P TO GET 50 P F R C E N T S T A L L T I P S P E E D 0 1 5 4 I F I N = O I F ( S T A L I T ( I C J . L E . . 5 0 1 GO TO 399 0 1 5 5 0 1 5 6 I U S V = I W 0 1 5 7 I u = 3 0 1 5 8 C A L L P E R F Y ~ 3 ~ C P ~ Z J I ~ A F T ~ B L A O T ~ C L l ~ C l ~ Z ~ S ~ 7 7 l O ~ 0159 I d = I H S V 0160 I F ( I k . E Q . 2 ) GO T U 7 1 2 0 1 6 1 7 1 1 B H P C l I T S I = 2 . 0 * T I P S D G ~ I T S ) * * 3 * D I A * ~ 2 ~ 6 9 h b . ~ C P / ~ l ~ . E l ~ ~ R ~ R ~ ~ I C ~ l 0 1 6 2 IF(ABSIBHPlIC)-BHPG(lTS)).GE..OO5*BHP(IC~) GO TO 7 0 5 0163 T H H U S T I I C ~ = C T * T I P S P D * * 2 * ~ I A ~ ~ 2 / ~ 1 . 5 1 5 E 0 6 * R O R O ~ I C ~ ~ ~ ~ 6 4 . 7 6 T 4 1 C = l .

0 1 6 5 GO TO 7 2 0 0 166 7 0 5 I F ( I T S . E Q . 1 1 G O T O 7 0 0 0 0 167 T I P S D G ~ I T S + 1 ~ ~ ~ A L O G ~ B H P l I C ~ ~ - A L O G l B H P G l l T S - l ~ ) ) * ( T I P S D G ( l T S ) - 1 T I P S D G l l T S - 1 l ~ / ~ A L O G ~ B H P G ( I T S ~ ~ - A L O G ~ ~ H P G ~ l T S - l ~ ~ ~ + T l P S D G ~ I T S - l ~ 0 1 6 8 G O TO 709 0 169 7000 T I P S D G 1 2 1 = 4 0 0 .

0170 T I P S P O = T I P S D G I I T S + l ) 0171 GO TO 600 0172 712 THRSTG(ITS)=TIPSDG(ITS)**2*DlA**2*364.76*CT/l 1 . 5 1 5 E 0 6 * R D R O ( l C ) ~ 0173 I F l A B S ( T H R U S T ( I C I - T H R S T G ( i T S ~ ~ . ~ E . . O ~ 5 * T H R U S T ~ I C ) ~ GO T O 7 2 2 0174 T I P S P D = T I P S C G ( I T S ) 0175 B H P l I C I = C P * 2 . 0 * T I P S P 0 * * 7 * D I A * * 2 / ( 1 0 . E 1 0 * R O R ~ ~ I C ~ I * 6 9 6 6 .

0 1 76 T R I G = l .

0177 GO TO 720 0178 7 2 2 l F l I T S . E Q . 1 ) GO TO 7000 0179 T I P S D G ~ I T S + L ) = ( A L O G I T H R U S T ( I C ) ) - A L O G ( T H R S T G ( I T S - ~ ~ I ~ * ( T I P S ~ G ( I T S ~ - l T I P S D G ~ I T S - 1 ~ I / ~ A L O G ~ T H R S T G ~ I T S I ~ - A L O G ~ T H R S T G l l ~ S - l J ~ ~ + T I P S D G

2 ( I i s - I 1

o l e o 709 T I P S P D = T I P S O G ( I T S + l )

0 1 0 1 1 F l N T S . N E . I T S ) GO TO 600 0182 W R I T E I 615981 0183 598 FORMAT { / / ' F A I L E D S T A L L I T E R A T I O N ' / / I 0184 GO T O 700 C END OF T I P S P D I T E R A T I O N 50 P E R C E N T S T A L L C C A L C U L A T I O N OF R E Q U I R E D C P OR C T 0185 399 I F l l U - 1 ) 4 0 0 ~ 4 0 0 ~ 4 3 0 FIGURE 3A. FORTRAN I V L-ISTING(CONTINUED) FORTRAN I V G L E V E L 20.1 M A I N OATE = 72034 10/08/04 0186 400 C P = B H P I I C ~ * l O . E 1 0 * R U R O ( I C ~ / ~ 2 . O * T I P S P D * ~ 3 * D I A * * 2 * 6 9 6 6 . ~ 0 1 8 7 C A L L E R F M ( l r C P ~ Z J I , A F T ~ B L A O T ~ C L i ~ C T ~ Z f 4 S ~ L I M I T ~ 0 1 8 8 , 420 T H R U S T ~ I C ~ ~ C T * T I P S P D * * 2 * D l A * * 2 / ~ l ~ 5 l 5 E O 6 * R O R O ~ I C ~ ~ * 3 6 4 ~ 7 6 * X F T 0 1 8 9 I F I C T . E Q . A S T E R K J T H R U S T I I C J = 9 9 9 9 9 9 9 9 9 9 .

0 190 GO Ti) 460 0 191 430 C T ~ T H R U S T ~ I C ~ * 1 ~ 5 l S E O 6 ~ R O R D ~ I C ~ / ~ T I P S P D * * 2 * D ~ A * * 2 * 3 6 4 ~ 7 6 ~ 0 1 9 2 C A L L P E R F M ( ~ ~ C P I Z J I ~ A F T ~ B L A D T ~ C L I ~ C T , Z M S ~ L I M I T ) 0 1 9 3 450 B H P ~ I C ~ = C P * 2 . 0 ~ T I P S P ~ ~ * 3 * ~ I A * ~ 2 / ~ ~ O . E l O * R O R O ~ I C ~ ~ * 6 9 6 6 .

0194 I F I C P . E Q . A S T E R K ) B H P ( I C ) = 9 5 9 9 9 9 9 9 9 .

0 1 9 5 460 I F (CP.NE.ASTERKI G O T O 720 0 196 P N L = 9 9 9 9 9 9 9 9 .

0 1 9 7 0 1 9 8 0 199 C O S T 7 0 ( 1 )=99999.

0200 C O S T 8 0 ( 1 ) = 9 9 9 9 9 .

0 2 0 1 GO T O 7 3 0 0202 7 2 0 PNL=O.@ 0 2 0 3 I S TALL=O 0 2 0 4 I F I D I S T I I C ) . L E . O . ) G O TO 461 0205 C A L L Z N O I S E ( B L A D T ~ D I A , T I P S P D ~ V K T A S ~ I C l ~ ~ H P ~ l C ) ~ O I S T l [ C ~ ~ P N L l F C L I C ) , X N O E I CPA=CP 0 206 CTA=CT 0 2 0 7 0208 SBLLL'BLCLL 0 209 S X F T = X F T 0 2 10 I W S V = I k J 0 2 1 1 I13=3 0212 C A L L P E F F Y ( 3 ~ C P , Z J I ~ A F T ~ B L A D T ~ C L I ~ C T ~ Z M S ~ 7 7 1 0 ~ 0 2 1 3 CPS=CP 0 2 1 4 CP=C P A 0 2 1 5 C T=C T A 0 2 1 6 BLLLL=SE!LLL X F T = S X F T 0 2 1 7 Ik=I wsv 0 2 1 9 I F ( C P . G T . C P S ) P N L = 9 3 9 9 9 9 9 9 .

0 2 2 0 C O N T I N U E 0 2 2 1 k l 7 0 - 9 9 9 9 9 .

W T E 0 = 9 9 9 9 9 .

0 2 2 2 0 223 C O S T 7 0 1 1 ) = 9 9 9 9 9 .

C O S T R O ( 1 ) = 9 9 9 9 9 .

I F N C C l S T - 1 ) 7 3 0 , 7 2 5 1 7 3 0 I F ( N C O S T . E O . 1 ) C A L LW A I T ( k T C O N , Z Y W T , B H P I [ C ) , O I A , A F T r H L A O T , T I P S P D I 0 2 2 6 725 l k f 7 C ~ W T 8 0 1 0 2 2 7 0 2 2 8 C A L L C O S T I W T C O ~ r B L A O T , C L F L ~ C L F 1 C K 7 0 1 C K 7 O ~ C K ~ O ~ C A ~ T ~ ~ A ~ T ~ N A ~ T ~ C ~ U A N ( l ~ l l ~ r ~ l 7 0 r W T 8 O ~ C O S T 7 0 ~ C O S T 8 O ~ C C L F I C C ~ 7 ~ ~ C C K ~ O ~ l E N T ~ 0 2 2 9 G O TO 1 5 7 0 r 5 8 0 1 , I W 0230 5 7 6 W R I T E ( 6 ~ 5 7 5 1 D I A ~ T I P S P D ~ T H R U S T t I C ~ ~ P N L ~ C ~ U A N ~ l ~ l ~ ~ W T 7 O ~ 1 C Q U A N ~ 2 ~ 1 I ~ W T 8 0 ~ C O S T ~ O ~ l ~ ~ B L L L L ~ X f ~ ~ Z ~ l ~ ~ J ~ ~ C P ~ 0 2 3 1 5 7 5 F O P M A T ( 2 F 7 ~ O ~ F 9 ~ 0 ~ F 6 ~ O ~ Z F $ ~ O ~ f 9 ~ O ~ Z ~ ~ ~ O ~ F 9 ~ 1 2 ~ e . 4 ) 0232 GO TU 5 8 5 02 33 580 W R I T E l 6 9 5 7 5 ) D I A v T I P S P D , B H P ( [ C ) r P N L v C Q U A N l 1 1 l ) r W T 7 Q 1 C 3 S T 7 0 ( 11, 1 C Q C A N ~ 2 r l ~ ~ h T 8 O r C O S T B O o r B C L L L ~ ~ X F T ~ Z M l ~ Z J I ~ C P ~ C T 0 2 3 4 5 8 5 I F I N A M T - 1 ) 409401586 0 2 3 5 5 8 6 DO 5 8 8 I = 2 9 r \ l A M T 0 2 3 6 k R I T E ( h , 5 8 7 ) C Q U A N ~ L ~ ~ ~ ~ W T 7 0 ~ C @ S T 7 O ~ I ~ ~ C Q U A N ~ 2 ~ I ~ ~ W 0 2 3 7 FORMAT (29X,2F8.0,F9.0,2F8.0~F9.0) FIGURE 3A. FORTRAN I V LISTING (CONTINUED) FORTRAN I V G L E V E L 2 0 . 1 M A I N D A T E = 7 2 0 3 4 1 0 / 0 8 / 0 4 0 2 3 8 588' C O N 1 I NUE 0 239 GO TO 40 0 2 4 0 730 GO TO ( 3 1 r 3 4 1 r I W 3 1 W R I T E 1 6 , 3 2 ) O t A ~ l I P S P D , T H R U S T I I C ) t P N L , 8 L L L L ~ X F r , Z M l , Z J I r C P ~ C T 0 2 4 1 3 2 F O R ~ A T ( F 7 . 2 r F 7 . O ~ F 9 . O I F 6 . O I F 6 . l r F 8 . 3 1 F 7 . 4 ~ F 8 ~ 3 t 2 F ~ ~ 4 ~ 0 2 4 2 GO TO 40 0 2 4 3 0244 3 4 b l R I T E ( 6 r 3 2 ) D I A ~ T I P S P D r B H P ~ I C l r P N L t e L L L L L ~ X F T ~ Z ~ l ~ ~ J l r C P ~ C T 0 2 4 5 40 I F I T R I G . E O . 1 . ) G O TO 750 0246 I F ( I S T A L L , E C . 2 ) GO TO 800 0 2 4 7 I F I I F I N . E Q . 7 7 1 0 ) GO TO 800 0 2 4 8 6 0 0 CONT I NUE

0249 I F (IW.LT.~) GO ro 7 5 0

C REVERSE THRUST C A L C U L A T I O N 0 2 50 3 0 0 0 I R l = N P C P W I I C 1 P C P W C = P C P W ( I C I 0 2 5 1 0 2 5 2 DO 3 9 0 0I = l r I R T 02 53 IF ( R T C - 1 . ) 3 2 0 0 r 3 1 0 0 ~ 3 2 0 0 0 2 5 4 3 1 0 0 C P ~ B H P I I C ~ * P C P W C * R O R O I I C ) * 1 0 . E 1 0 / ~ 2 ~ O * R ~ ~ C l I C ~ * ~ 3 * D I A * * 5 ~ l O O ~ ~ 0 2 5 5 3 2 0 0 C A L L R E V T H T ~ R T C r R O T , A F T r G L ~ ~ 8 L A D T ~ D I A ~ C P , B E T A ( I C ~ , R U F O I I C ~ ~ 1 BHP( I C 1 r R P M C ( I C ) , P C P W C r A N D V K ( I C ) ) 0 2 5 6 PCPWC=PCPWC+DPCPH I IC 1 02 57 3900 C O N T I N U E 0 2 5 8 7 5 0 C O h T I N U E 0 2 5 9 800 C O N T I N U E 0 2 6 0 1000 GONT I NUE 0 2 6 1 LOO1 C O N T I N U E 0 2 6 2 1 2 0 0 C O N T I N U E 0 2 6 3 700 CONT I NU€ 0 2 6 4 GO TO 701 0 2 6 5 END FIGURE 3A. FORTRAN IV LISTING (CONTINUED) F C l Q T R 4 1 I V G L E V E L 7 0 . 1 I N P U T D A T E = 7 2 0 3 1 , . , .. , 08/48/14 FIGURE 3A. FORTRAN I V LISTING(CONTINUED) ..EDRIRAN-LY. . G . I E Y E L _ . . Z Q r L .. __ .PERFM . . . DATE = .72034 . 1 0 ( 0 8 / 0 4 ..4.Q.01. .._ . . . .. SUBRO-UTINE .PERFH . I I W * C P r Z J I r A F T * B L A D ~ ~ C L I r C T * Z M S * ~ I M I T ) 0002 COMHON/AFCOR/AFCPErAFerEIXFT -.OD01 . ._ . ... . . .... .. . COMHON/CPECTE/CPE sCTEr BLLLL 0004 . ' C O U M O N / A S T R U / C P A S T ~ C T ~ S T ~ A S T E R U .--QQQL. _ _ .-.D"f.WLON ... A F - V A L ( 6 ) . A F C P C . ( 6 1 2 I , A F C T C ( 6 r Z ) * A F C P ( 7 J . A F C i [ ? ) r X L B ( 4 ) r X I N N l 7 ) r Z J J ( 7 ) r C T T ( 7 ) . C P P ( 7 ) r C T i T ( 4 ) rCPPP(C)rCPANG( 1017.4) * . 0007 . . .. . - '0009

. .. . . . . - . -

" 001 .- .

_ .

. Q Q l 3 , . . . " .

00 14 0 0 1 5 0 0 1 7 0 0 1 9 0 0 19 0 0 2 1 0 0 2 2 FORTRAM -1 Y .G..LEYf L ._ 2Q.l. . ._ . PERFH DATE = 7 2 0 3 4 1 0 / 0 8 / 0 4 0025- .

F I G U R E3 A .F O R T R A N IV LISTING(CONTINUED) FORTRAN I V G LEVEL 2 0 . 1 PERFM DATE = 72034 10/08/04 O C 2 9 0 0 3 0 003 1 0 0 3 4 00 36 0 0 3 8 0 0 4 1 FIGURE 3A. FORTRANIVLISTING(CONTINUED) FOXTRAV I V G L F V E L 2 0 . 1 P-ERFH- DATE = 7 2 0 3 5 . - . . .13/ 3 2 i . 2 4 .

3 0 9 7 9 r 0 9 8 1 1 ~ 9 8 4 1 ~ 9 8 7 1 0 9 ~ 0 ~ 0 ~ ~ 3 1 ~ 9 ~ 6 ~ ~ 0 0 0 ~ 1 0 ~ ~ 1 1 0 C 0 ~ 1 0 ..

4 ~ 9 4 4 ~ ~ 9 4 5 ~ ~ 9 5 0 r ~ 9 5 8 ~ ~ 9 6 6 1 ~ 9 7 5 ~ ~ 9 8 4 1 0 9 9 0 1 ~ 9 9 6 ~ 0 ~ 9 9 ~ 1 ~ 5 . 9 0 1 1 . 9 0 5 + . 9 1 2 ~ . 9 2 7 ~ . 9 4 2 1 . ~ 5 4 1 0 9 6 4 1 0 9 7 4 1 ~ ~ ~ 4 T 0 9 9 0 ~ 0 9 0 ~ 1 .9031 .

6 . 8 6 2 ~ . 8 6 6 , . 8 7 5 ~ . R 9 2 1 . 9 0 9 r . 9 2 6 1 . 9 4 2 1 . 9 2 6 ~ . 9 4 2 ~ o ~ 5 7 ~ . 9 7 0 ~ o 9 ~ ~ ~ . 9 8 4 ~ . 9 8 4 ~ 7 . 8 0 6 1 0 8 1 3 1 . 8 2 5 1 0 8 5 1 r . 8 7 7 ~ ~ 9 0 4 + ~ 9 2 4 ? 0 9 3 9 ? o 9 ~ 2 ~ o 9 6 l r ~ 9 7 - 1 ~ ~ 9 ~ ~ / - 0 3 4 2 KK= 1 0 0 4 3 ' AST E R K = 9 9 9 9 9 9 C AN ADJUSTMENT F O R C P A k C CT F C R AF 03 4 4 03 1 2 0 K = l r 2 00 4 5 CALL UNIrVT ' ( ~ ~ A F V A L ~ ~ ) ~ A F C P C . ( ~ ~ K ~ ~ A F T I A F C P I K ~ ~ L I M T T J 00 46 C A L L U N I N TI 6 * A F V A l ( l lr A F C T C ( 1r K )r b F T + A f C T ( K ) q L I M I T 1 , . . . . . . . . .

004 7 1 2 0 CONT I N U F 004R D O 100 K = 3 9 7 00 4 9 A F C P ( K ) = A F C P ( Z ) 0 3 5 0 1 0 0 AFCT ( K ) = A F C T ( 2 1 005 1 I F 1 Z J I 0 G T . . 5 1 GO TO 1 0 5 03 5 2 A F C P E = 2 . * Z J I * I A F C P l 2 ) - A F C P ( l ) ) + A F C P I 1) OD53 A F C T E = 2 . * Z J I * ( A F C T ( 2 I - A F C T ( I I ) + A F C T ( 1) 00 5 4 G O TO 110 0 3 5 5 1 0 5 A F C P F = A F C P ( 2 ) 00 5 6 A F C T E = A F C T [ Z I 0 0 5 7 1 1 0 I F ( Z J I . C T . 1 . 9 ) G O T C 1 4 0 0 3 5 8 1 NRFG= 0 0 5 9 N E N D = 4 00 6 0 G O TO 14R '336 1 140 I F ( Z J I . G T . 1 . 5 ) 60 TO 1 4 2 OOh? NRFG=2 0 0 h 3 NE ND=5 00h4 Gn T O 14R 0065 1 4 2 I F l t J I . G T . 2 . 0 . A N D . I W . L T . 3 ) G O TO 1 4 7 0 3 6 6 N 3 F G = 3 0 3 6 7 NENr)=h COh8 GO TO 14FI 03 6 9 1 4 7 N 3 F G - 4 03 7 0 NFNO=7 C 0 7 1 1 4 8 CUNT I N U € 03 7 2 N 6 L = O 0 3 7 3 D q 1 3 0 I I = l r h

ao 7 4

I Z = T I 0 3 7 5 I F ( A B T ( C L I - C C L I ( II)).LF..OCO91 G O T f l 1 3 5 05 76 1 3 0 C O N T I N U E 0 0 7 7 I F ( C L I aGTm.61 G O T O 1 3 1 03 78 FICL T = l c079 N C L T T = 4 00 80 GO TO 1 1 9 0381 1 3 1 I F ( C L I . G T . . 7 ) G O TO I 3 2 O G 8 2 KC L T =Z 008 3 N Z L T T = 5 0384 GO T O 119 0 3 8 5 1 3 2 FICLT=3 00 8 6 N 3 L J T = 6 9 0 8 7 GO TO 119 009 8 1 3 5 N C L T = I Z 0 0 8 9 N".=1 0 0 9 0 h C L T T = I 2 0091 11 9 C q N T I NtJE 0 0 9 % NB=BLADT+. 1 0 0 9 3 LMcJD=MOC(NB, 2 ) + 1 FIGURE 3A. FORTRAN IV LISTING(CONTINUED) FORTRAN I V G L E V E L 20.1 PERFM D A T E = 72034 10/08/04 0 094 Gfl TO f160r180l rLMOD 0095 160 N B B = l

o a96 L=BLADT/2.+.1

0097 GO TO 200 0098 1 8 0 NBB=4 0 099 L= 1 200 DO 5 0 0 I B B = l r N B B 0 LOO C J I N T E R P O L A T I O N 0 101 DO 300 K=NBEGrNENO 0 102 208 G O T O IZlOr250r21'2)rIW 0 103 212 C A L L U N I N T ( 9 r Z J S T A L , C T S T A L ( I t L I r L J J l K ) * C T T ( K ) , L I M I T ) 0 104 C A L L U N I N T ( 9 r Z J S T A L ~ C P S T A L l l ~ L ) 1 Z J J ( K I 1 C P P ( K I ~ L I M I l ) 0105 C A L L U N I N T ( I N N ( K l r C P A N G I l , K ~ L ) 1 B L D A N G ( 1 1 K ) ~ C P P ( K ) ~ ~ L L ( K ) ~ L I M I T l 0 106 2 1 0 C P E = C P * A F C P ( K ) 0 107 C A L L U N I N T ~ 1 4 r C P E C I l ~ ~ R L O C R ~ 1 ~ L I ~ C P E ~ P ~ L ~ I M I T ~ o 108 C P E l = C P E * P B L * P F C L I ( K 1 0 109 NNCLT=NCLT 01 LO 00 215 K L z N C L T r N C L T T C A L L U N I N T ~ N C L X l N N C L T l ~ C P C C I ~ 1 1 N N C L T I , X P C L T ~ ~ X P C L l ~ l ~ N N C ~ ~ T ~ ~ C P E l 1 l K L I v L I M I T I 01 12 I F L L I M I T . E Q . 1 1 G O T O 591 0113 215 N N C L T = N N C L T + l 0114 I F lNCL.EQ.1) G O TO 220 0115 C A L L U N I N T ( 4 , C C L I ( ~ C L T ) , P X C L I ( N C L T ) , C L I 1 P C L I , P C L I , L I M I T ) 0116 GO T O 221 01 17 220 P C L I = P X C L I ( N C L T I 221 C O K T I N U E C P E = C P E * P C L I C A L L U N I N T f I N N I K ~ r C P A N G ~ l r K , L ~ ~ 8 L D A N ~ ~ l ~ K ) ~ C P E ~ ~ L L l K ~ ~ L 0121 C A L L U N I N T ( I N N ~ K I ~ B L D A N G ( l ~ K ) , C T A N G ( l ~ K ~ L ) , 6 L L ~ K ) ~ C l T ~ K ~ ~ L I 0 122 I F ( L I M I T . E Q . 0 1 G O TO 211 0123 GO T O 591 0 124 211 C O N T I N U E 0125 GO T O 2501 0126 250 NNCLT=NCLT 0127 2200 Dn 260 K L z N C L T v N C L T T 0 128 C T A ( 1 ) = C T 0129 C T A ( 2 ) = 1 * 5 * C T 0 130 DO 2 6 0 0 K J = l t 5 0131 NF TX=K J 0 132 C T E l = C T A ( K J ) * A F C T l K ) 0 1 3 3 C A L L U N T N T 1 1 4 , C T E C ( l ~ ~ B l D C R ( l ~ L ~ ~ C T E ~ T ~ L , I Y [ T ~ 0134 C T E l = C T E l * T B L * T F C L I ( K ) 0 135 C A L L U N I N T ( N C L X ( N N C L T ) r C T C L I ( l ~ N N C L T ) ~ ~ T C L I ( l ~ N N C L l ) ~ C T E l ~ T X C L I 1 I K L I p L I M I T I 0 1 3 6 I F ( L I M I T . E Q . 1 ) G O TO 5 9 1 0137 9998 I F ( Z J J I K ) . E C . O . ) GO TO 40CO C A L L I J N I N T ( l l ~ Z J C L I 1 ) ~ Z M C R L l l r N N C L T l r Z J J ( K ) , ~ ~ C R T ~ L I M I T ~ 0139 9999 DMF\=ZMS(l)-LMCRT G n TO 4 0 5 0 0 140 4000 ZMCRT=ZMCRO(NNCLT) 0 141 D M k Z M S I 2)-LHCRT 4050 X F F T ( K L ) = l . O 0.143 0 144 I F L D M N ) 2300~2300,252 0145 252 C T E 2 = C T E l * T X C L I ( K L ) / T F C L I ( K 1 0 146 C A L LB I O U A D ( Z M M M C , L , O M N , C T F 2 r X F F T ( K L ) , L I M I T ) 0147 2300 C T A l ( K J I = C T - C T A l K J I * X F F T ( K L ) 0 148 I F I C T A 1 l K J ) . E Q . O ~ . A ~ D . K J . E Q . 1 ) GO TO 2700 F I G U R E 3A. F O R T R A N I V LISTING(CONTINUED) FORTRAN I V G LEVEL 20.1 PERFM DATE = 7 2 0 3 4 1 0 / 0 8 / 0 4 I F l K J . L E . 1 ) GO TO 2600 0 1 4 9 0 1 5 0 I F I A B S l C T A 1 l K J ~ 1 ~ ~ C T A l ~ K J ~ ~ / C T ~ L E ~ ~ O O l ~ GO TO 2700 C T A ( K J ~ + l ~ = - C T A l I K J - L ~ * ~ C T A ~ K J ~ - C T A I K J - L ) ~ / ~ C T A l ~ K J ~ - C T A l ~ K J - l ~ ~ + 0 1 5 1 L C T A ( K J - 1 ) .

2 6 0 0 C O N T I N U E 0 1 5 2 WRITE ( 6 , 3 9 1 ) 0 1 5 3 2700 C T ~ [ K ~ ) = C T A ( N F T X ) / X F F T l K L ) 0 1 5 4 260 N N C L T = N N C L T + l 0 1 5 5 0 1 5 6 I F lNCL.EQ.1) GO TO 2 7 0 0 157 C A L L U N I N T ( 4 r C C L I I N C L T ) r T X C L I ( N C L T ~ ~ C L I ~ T C L l ~ L I ~ I T ~ 0 1 5 8 C A L L U N I N T ( 4 , C C L I ( N C L T ) ~ X F F T ( N C L T ) ~ C L I ~ X F T l l K ) ~ L l M I T ~ C A L L U N I N T ~ 4 ~ C C L I l N C L T ~ ~ C T N l N C L T ~ ~ C L I ~ C T T ~ K ~ ~ L I M l T ~ 0 160 GO TO 271 2 7 0 T C L I = T X C L I 1 N C L T ) - XF T L ( K 1 = X F F T ( N C L T ) 0 1 6 2 0 1 6 3 C T T ( K ) = C T N ( N C L T ) 0 1 6 4 271 C T E = C T T l K ) * A F C T ( K 1 * T C L I 0 1 6 5 C A L L U N I N T ~ I N N l K ~ ~ C T A N G l 1 ~ K ~ L ~ ~ B L D A ~ G ~ l ~ K ~ ~ ~ T E ~ B L L l K ~ 0166 C A L L U N I N T ~ ~ N N I K ~ ~ B L D A ~ J G l l r K ~ ~ C P A N G I 1 ~ K ~ L ~ ~ B L L I K ~ r t P P ~ I o

0 167 IF(LIMIT.EO.OI GO ro 2501

0 16fl GO TO 591 0 1 6 9 2 5 0 1 CONT I N U € 0170 300 CONTINUE C A L L U N I N T 1 4 ~ Z J J ( N E E G ) ~ R L L ( N B E C I , Z J I , B L L L L ( C B B ~ ~ L I ~ I T ) 0 171 B L L L L = B L L L ( l B R l 0 1 7 2 GO TO ( 3 1 0 ~ 3 5 0 r 3 1 0 ) v I W 0 1 7 3 3 1 0 C A L L U N I N T ( 4 , Z J J l N ~ E G ) v C T T ( N H E G ) 1 Z J l r C T T T I I B R ) , L I M l T ) 0 1 7 4 0 1 7 5 C T G ( 11=.100 0 1 7 6 C T G l 2 ) = . 2 0 0 0 1 7 7 C A L L U N I N T I 7 ~ Z J J I 1 ) ~ T F C L I ~ l ) ~ Z J I , T F C L l l ~ L I Y I T ) 0178 DO 3 9 0 I L = 1 , 5 0 1 7 9 C T = C T G I I L ) C T E = C T G l I L ) * A F C T E 0 1 8 0 C A L L U N I N T ( 1 4 ~ C T E C ( l ) ~ B T D C R ( l , L ) ~ C T E ~ T ~ L ~ I M I T ) 0 1 8 1 0 1 8 2 C T E l = C T E * T B L * T F C L I I 0 1 8 3 NNCLT=NCLT O l f l 4 00 3 9 6 K L l N C L T t N C L T T 0 1 8 5 C A L L U N I N T ( N C L X ( N N C L T ) , C T C L I ( L ~ ~ N C L T ) ~ X T C L l ( l ~ N N C L T ~ ~ C T E l ~ T X C L I I 1 K L ) p L I M I T ) I f I L Z M 1 T . E Q . L ) GO T O 5 9 1 0 1 8 6 I F ( Z J I . E Q . 0 . ) GO T O 3 0 0 0 0 1 8 7 C A L L U N I N T I L l ~ Z J C L ~ 1 ~ ~ Z M C R L l l ~ N N C L T ~ ~ Z J I ~ Z M C R T ~ L l ~ I T ~ 0 188 O M h = Z M S ( 1 ) - Z M C R T 0 1 8 9 0 1 9 0 GO TO 3 0 5 0 3000 ZMCRT=ZMCRO(NNCLTI 0 191 DMR=ZMS(Z)-ZMCRT 0 1 9 2 3050 X F F T I K L ) = 1 . 0 0 1 9 3 I F I D M N ) 3 9 6 , 3 9 6 , 3 9 9 0 194 3 9 9C T E Z = C T E * T X C L I ( K L ) * T B L 0 1 9 5 C A L L B I Q U A D I Z H H M C ~ l ~ D M N t C T E 2 r X F F T I K L ) . L I M I T ) 0 196 0 1 9 7 3 9 6 N N C L T = N N C L T + l 0 1 9 8 I F lNCL.EO.1) GO TO 395 0 199 C A L L U N I N T ( 4 r C C L I ~ N C L T ) ~ T X C L I ( N C L T ~ ~ C L l ~ T C L I I ~ L I M I T J 0200 C A L L U N I N T I 4 r C C L I ~ N C L T ~ ~ X f F T I N C L T ) r C L I 1 X F T I L [ n I T ) I F ~ X F T . G T , l . I X F T = l . O 0 201 0202 GO T O 3 9 4 3 9 5 T C L I I r T X C L I t N C L T ) 0 2 0 3 0 2 0 4 X F l = X F . F T ( N C L T ) F I G U R E3 A .F O R T R A N I V LISTING(CONTINUED) 3.

. " . -. . . .

. I D R T R A N .IV..G L E V E L 2 0 . 1 . . . . . .. PERFH ..DATE = 7 2 0 3 4 . 1 0 / 0 8 / 0 4 .. .. . 0205 . 394 C T = C T G f I L ) 0206 C T E = C T G I I L ) * A F C T E * T C L I I .. . 0207 C T G l I I L ) = C T E - C l T T l C B B ) 0 2 0 8 I F l ~ B S ~ C T G l ~ L L ~ / C T l T l I ~ B ~ ~ ~ L T ~ , O O L ~ GO TO 3 9 2 -. 3 2 0 9 I E ( I L - L E o 1 ) GO TO 390 0210 CTG( I L + l ) = - C T C l ( I L - l I * ( C T G ( I L ) - C T G ( IL-1) ) / ( C T G l ( I L ) - C ' T G l ( I L - 1 J )+ 1 C T G ( IL-1) 390 C O h ' T I N U E 0 2 1 1 .. . W R I T E (6,391) 0 2 1 2

0 2 1 3 391 FORMAT t ' INTEGRATED DESIGN CL ADJUSTMENT NOT WORKING PROPERLY FO

. .

. . XR CT D E F I N I T I O N ' ) 0214 3 9 2C T T T ( . I B B ) = C T .0215 GO TO ( 3 6 0 9 3 5 0 r 3 4 0 J r I W 0 2 1 6 3 5 0 C A L L U N I N T ( 4 r Z J J ( N B E G l r X F T l ( N B E G ) ~ Z J I r X F T r L I M I T ) 0 2 1 7 IF(XFJ.GT.L.)XFT=l.O 0 2 1 8 340 C A L L U N I N T ~ 4 r Z J J ~ N B E G J r C P P ~ N B E G ) r Z J I r C P P P ~ I B B ~ ~ L I M C T l 0219 C P G I l l = . l 5 0 0 2 2 0 C P G I 2 1 = . 2 0 0 0 2 2 1 ( 4 r Z J J ( N B E G l r P F C L I I N B € G l ~ Z J I r P F C L I I ~ L I ~ I T l C A L L U N I N T 0 2 2 2 DO 290 I L ~ l r 5 . 0 2 2 3 C P = C P G ( I L I 0 2 2 4 CPE=CPG( IL ) * A F C P E 0 2 2 5 C A L LU N I N T( 1 4 m C P E C ( 1) rBLDCR(lrL)rCPErPBL,IMIT) 0 2 2 6 C P E l = C P E + P B L * P F C L I I 0 2 2 7 N N C L T T N C L T 0 2 2 8 DO 2 8 0 K L = N C L T e N C L T T 0 2 2 9 C A L L U N I N T I N C L X ( N N C L T ) r C P C L I ( l r N N C L T l r X P C L I ( l r N N ~ L T ) , C P E l r P X C L I ~ l K L ) * L I . H I T I 0 230. I F . ( L I M I T . E Q . l ! GO TO 591 0 2 3 1 2 8 0N N C L T = N N C L T + l 0 2 3 2 I F ( N C L . E P . 1 ) GO T O 2 8 2 C A L L U N I N T ( 4 , C C L I ( N C L T ) r P X C L I I N C L T ) r C L I r P C L I 1 , L I M I T I 0234 GO TO 2 8 4 0 2 3 5 2 8 2 P C L I I = P X C L I ( N C L T ) 0 2 3 6 2 8 4C P = C P G I I L ) 0 2 3 7 CPE=CPE*PCL I I 0 2 3 8 C P G 1 I I L ) = C P E - C P P P [ IBB) 0 2 3 9 I F 1 A B 4 ~ C P G l I I L l / C P P P o ) . L E ~ ~ O O l ~ GO TO 2 8 7 0 2 4 0 I F C I L . E Q - 1 ) GO TO 290 0 2 4 1 C P G I I L t 1 ~ ~ - C P G l ~ I L - 1 ~ * ( C P C ( I L ~ - C P G ~ I L - l J l / I C ~ G l ~ I L ~ - C P G l ~ I L - i ~ ~ 1 C P G t 1Lf-l) 0 2 4 2 2 9 0 COFtTINUE W R I T E ( 6 9 2 8 5 1 0 2 4 3 0 2 4 4 2 8 5 FORMAT I ' I N T E G R A T E D D E S I G N CL ADJUSTMENT NOT WORKING PROPERLY FOR 1 C PD E F ! I N I T I O N ' 1 0 2 4 5 - 2 8 7 C P P P I I B B I = C P 0 2 4 4 . 360 L=L+1 0 2 4 7 500 C O N T I N U E 0 2 4 8 I F I N B B ' I ) 5 1 0 r 5 9 0 r 5 1 0 0 2 4 9 5 1 0 C A L L U N I N T I 4 r X L B I l ) , B L L L ( l ) r B L A D T r B L L L L r L I M I T ) 0 2 5 0 GO T O I ' 5 2 0 r 5 3 0 r 5 2 0 l r I W 0 2 5 1 5 2 0 C A L L U N I N T (4rXLBll)rCTTT(l)rBLADTrCT,LIMIT) 9252 GO TO 5 9 0 5 3 0 C A L L U N I N T I 4 r X L B l l ) r C P P P I 1 ) r 8 L A D T r C P r L f M I T ) 0 2 5 3 0 2 5 4 5 9 0 C O N T I N U E 0 2 5 5 GO TO 600 0 2 5 6 5 9 1 C T = A S T E R K 0 2 5 7 CP-ASTERK FIGURE 3A. FORTRAN I V LISTING(CONTINUED) D A T E = 7 2 0 3 4 1 0 / 0 8 / 0 4 WRTRAN IY G LEVEL .20.1 PERFM 0 2 58 600 CONTINUE ' RETURN 0 2 5 9 0260 END FIGURE3A.FORTRAN I V LISTING(CONTINUED) F O P T R A U 1 V C , LFVFL 2 3 . 1 Z N O I SF D A T E = 7 2 0 3 1 0 8 / 4 8 / 1 4 0 O n 1 0 0 0 2 O C O r , 0 0 0 8 FIGURE 3A. FORTRAN 1V LISTING (CONTINUED) F o R T R A N I V G L E V E L 20.1 . . . . . 7 N 0 1 S E . . . . . . . . . . . . . .DAT€..=..7-2_03-1-. - 08/48/14 X x3.414.215.41 X on1 1 on12 091 3 00 14 0 0 1 5 2 K K = I R ....

0016 G f l TO 7 5 N B B = 4 0 0 1 7 . . . . . . . . . . . . . . . . . . - On18 K K = 1 001 9 G O T O 7 .

- . . - - - .... " . . . . . . . . . - .. - - - .- . -

0 0 2 9 6 K K = 4 0 0 2 1 N B R = 4 - . . . . . -. . " o n 2 2 7 CONTINUE 8 K=KK*NSR 0073 D O . . . . . . .

- ..

9 1=1,7 0 0 2 4 Dr) 9 CALL UNIb!T ( 1 3 , T M T H ( 1 ) 1 P N L C ( l r I I K ) r T M T , P N L A ( 1 ) ,LIMIT_)- -. __ . .- ...... - .

0 0 2 5 0 3 2 6 9 C A L LU N I N T [ 7 r D I A Y I 1 ) r P N L A ( 1 ) r l 3 I A p P N L B ( K )p L i M I T - 1 PNLD = P N L R I K K ) 0 0 2 7 O P 7 9 I F ( 1 9 . E Q . S ) C 4 L LU N I N T I 4 1 B R L ( l )p P N L B ( 1 )r B L A D T , P N L D . L I M I T - ) 007 9 RMT = T I P S P ? / l 1 2 @ .

0 0 3 n SPL = 1 0 7 . 7 + 6 . 6 Y * A L O G ( B t i P ) - 4 . 3 4 * A L O G ( B L A D T ~ * 2 * D I A * * ~ * D I S T * f 2 j - " X X N f l F ) + 38.1* RYT + PNLD . . . . . . - - .. - . . . . . - . . .. .- . . - .. - . .

o n 3 1 I F ( L l M l T . N F . 0 )S P L = 9 9 9 9 9 9 .

RFTlJRN 0 0 3 7 ...

0 0 3 3 F ND FIGURE 3A. FORTRAN I V LISTING (CONTINUED)

p

FORTRAN I V G L E V E L . . 2 0 . 1 . . " . . . . . W A I T D A T F = 7 2 0 3 1 0 8 / 4 9 / 1 4 S U R ~ O U T I Y E W l l I T ( W T C O ~ , Z Y ~ T , B H P , D T A ~ A F T , ~ L A D T , T I P S P D ~ W T 7 O , W T 8 0 ) 0 3 0 1 IF-[HTCON.LE.O.I RFTURN 0 0 0 2 0003 Z N D = T I P S P D * 6 0 . / 3 . 1 4 1 5 9 0004 Z N = Z N D / D I A 0 0 0 5 Z K 2 = ( D I A / 1 0 . 1 * * 2 0 0 0 6 Z K 3 = ( O L f i O T / 4 . 1 * * . 7 0037 Z K 4 = A F T / 1 0 0 .

0 0 0 8 7 K 5 = 7 N 0 / 2 0 0 0 0 .

0009 Z K h = ( B H P / l O . / D I A * * 3 1 * * . 1 2 00 10 Z K 7 = I Z M W T + 1 . 0 ) * * . 5 o n 1 1 W T F h C = Z K 2 * 7 K 3 + Z K h * Z K 7 C WTCnN DEF I N E S A I RPLANF CATEGnRY e01 2 IWTCnN=WTCOY on1 3 Z t = 3 . 5 * Z & Z * B L A D T * Z K 4 * * 2 * ( l./ZK5)**.3 0 0 14 G l J TC! ( 1 0 , 2 0 , 1 0 , 4 0 r 5 0 ) , I W T C O N 10 H T 7 0 = 1 7 0 . * W T F A C + Z K 4 * * . 9 * Z K 5 * * . 3 5 on15 001 6 k T Y O = W T 7 0

0 0 1 7 GO x 6 0

001 e 2 0 W T 7 0 = 2 0 @ . ~ W T F A C ~ Z Y 4 * * . 9 ~ Z K 5 ~ . + . ~ 5 0019 WTSi?=WT70 nn23 GO TO 6 0 0 3 2 1 3 0 ~ T 7 0 = 2 2 C . * W T F A C * Z K 4 + ~ . 7 * 2 K 5 * ~ . 4 + Z C ~ ( ~ . 0 / 3 . 5 ) WT;3n= WT70 O 0 2 Z 0 0 7 3 G O Tn 6 0 40 V T F h C = W T F A C * Z K 4 * * . 7 + Z K 5 * * . 4 O ~ J 2 4 0 0 2 5 ~ T 7 n = 2 ? @ . + W T F A C + Z C * ( 5 . 0 / 3 . 5 ) OP?6 W T S O = 1 9 @ . * W T F A C + Z C o n 7 7 G O TO 6 0 no2 P 59 W T 7 0 = 2 2 0 . * W T F A C + Z K 4 * * . ? + Z U 5 * * . 4 + Z C * [ 5 . @ / 3 . 5 ) 0 0 2 1 W T S 0 = 1 9 0 . * W T F A C * Z K 4 * * . 7 * Z K 5 * * . 3 0 0 3 0 6 C R FTlJRh!

0 0 3 1 F Nr) FIGURE 3A. FORTRAN I V LISTING (CONTINUED) FC)?TRAIV I V G L E V E L 2 0 . 1 COST D A T E = 7 2 0 3 1 9 8 / 4 5 / 1 4 oon 1 0 0 0 5 O n 0 7 0008 5 9 0 0 9 l c !

no1 c) 0 0 1 1 001 2 2 0 O n 1 4 001 5 I 00 0 0 1 6 40 001 7 001 4 5 0 o n 1 9 60 0 0 2 0 7 0 0 0 7 1 0 0 7 2 90 0 0 2 1 1 1 0 0 0 2 4 1 2 0 0 0 7 5 0 0 2 6 n o 2 7 1 3 0 C 0 2 R 0 0 2 9 1 4 3 0 0 3 0 3 0 3 1 0 0 3 1 0Q3-3 903L 0 0 3 5 ?no 0 0 3 4 1000 0 0 3 7 FIGURE 3A. FORTRAN IV LISTING(CONTINUED) DA.TE _= 08/48/14 0 0 3 5 0 0 0 7 0 0 1 FIGURE 3A. FORTRAN I V LISTING (CONTINUED) FORTRAY I V S LEVEL 7‘3.1 Q E V T H T ? A T E = 7 2 0 3 1 0 8 / 4 9 / 1 4 @ 0 1 2 0 0 1 3 O C 1 4 001 5 O C 1 6 on1 7 0 0 1p 001 c l O n 2 0 0 0 ? 1 0 0 2 7 0 0 2 4 0 0 2 5 cn2h 0 0 7 7 0 0 2 R 0 0 2 9 on 3 0 0 0 3 1 0 0 3 2 3 3 33 0@34 0 0 3 5 0 0 3 6 0 0 3 7 0 0 3 8 0 0 3 9 0 0 4 1 0 0 4 2 0 0 4 3 0 0 4 4 0 0 4 6 0 0 4 7 o n 4 ~ 0 0 4 9 0 0 5 0 on51 0 0 5 2 On53 O Q 5 5 0 0 5 6 0 0 5 7 0 0 5 8 0 0 5 9 0 0 6 2 F I G U R E 3A. FORTRAN IV LISTING(CONTINUED) . ..

F 3 R T p A N 1 V . G L F V E L 20,l - 9 E V T H T D A T E = 7 2 0 3 1 0 8 / 4 9 / 1 4 0 0 6 4 O C 6 5 0 0 6 7 O O b R 0 0 4 9 00 70 0 0 7 3 0 0 7 4 00 75 On77 0 0 7 8 0 0 7 9 0 0 8 0 0 0 8 7 003-4 0 0 3 4 O C 9 5 0 0 8 7 039.9 F I G U R € 3A. F O R T R A N I V L I S T I N G( C O N T I N U E D ) . EOR TRA_N . . . I V.G..L.EVEI ... z o . ~ ... . . . . _ . . . UNLNT . . . -. . ... D A T E .= 7 2 0 3 1 . - , 0 8 / 4 8 / 1 4 " . 09 01 SUBRCIUTINE U N I N T ( N I XAv YA, X I YI L )

c RFWRITTEN SFPTEMRER 1 8 , 1967

C U N I V A R I A T E T A R L E R O U T I N E W I T H S F P E R A T E ARRAYS FOR X AND Y - S 6 6 c .c .

C T H I ' S R O U T I N E I N T F R P O L A T E S OVER A 4 P O I N T I N T E S V A L U S I N G A c . V A R I A T I O V OF 2 N D D E G R F E I N T E R P O L A T I O N TO PRODUCE A C O N T I N U I T Y C O F SLOPE RETWFEN ADJACENT INTERVALS.

00 02 0 0.9 3 0 0 0 4 0 0 0 5 0 0 0 7 00 10 001 1 0 0 1 2 001 3 0 0 14 0 0 1 8 0 0 19 0 0 2 0 0 0 2 1 0 0 7 2 0 0 2 3 0 0 7 4 0 0 2 5 0 0 2 6 00Z9 0 0 3 0 '00 31 0 0 3 2 0 0 3 3 0 0 3 4 0 0 3 5 C036 FIGURE 3A. FORTRAN IV LISTING (CONTINUED) 7 1 FI?RTP.AY IV G L E V E L 20.1 R I O U A D D A T E = 7 2 0 3 1 0 9 / 4 8 / 1 4 S U B R n U T I N F R I Q U A D ( T c I t X I t Y I t Zt K ) F N T T Y 91QllD ( T t I t X I 9 Y I P Z t K ) C T Y T S R O I J T I N E I Y T F R P O L A T F S O V E R A 4 P r 3 I N T I N T F P . V A L U S I Y G A C C V A R I A T I f l Q ( I F 2Nl) O F G K E F I U T E R P O L A T I O M TO P R l D U C F A C O N T I N U I T Y C OF S L O P E RFTki€EN ADJACFNT INTEPVALS.

l ) I b ' F N S I f l % T ( l . ) t X C I 4 ) 9 D ( 4 1 , P ( 5 1 1 Y ( 4 ) , C 1 4 ) C F O I J I V A L € N C E ( X C l 1 ) t D ( 1 1 1 c C T A B L E S F T IJD

C T'TI < Y T A R L F \ I J Y B t R

c T Y I & 1 < # NUMqFR ( I F ?X< VALUES C T % 1 & 2 < # V I J Y R E R OF X Y < VALUFS ZO. FOP U N I V 1 K I A T F T A B L F < T r I & 3 < rl C . VAI-UFS O F %X< I N ASC.EUDING ORDER NX = T ( I + l ) N Y = T ( I + 7 ) J 1 = 1 + 3

J 7 = J 1 + Y X - 1

x = X I C S E A K C H I N X S F Y S F L = O GO T P l O Q 0 Q t T l J Q N H E Q E F2.DY SFARCH r)F X C 100 Y = K X JX = J X 1 C THE ~ O L L O W I h ! ? C O D E P U T S X A N D / O R Y V A L i I E S I N XC BLOCK 1 9 5 DE 1 1 " J = l p ' t = T l J X 1 ) X C t J ) 1 1 ? J X 1 = J X l + l G F T C P F F F . I N Y 5 F N S F C 50 TI? Z r ) 9 r ?

q E T l I / l V H E R F d 1 T t . l C i r F F F . T E S T F O R I J U I V A R E 139 H I V A R T A T F c 7 " ! I I F (RIY) - 3 O O p 2 1 0 , 3 I 7 0 7 10 7 = ? .

J Y = J X + N X QC! 221? J = 1 t 4 I = Z + r l J ) * T ( . J Y ) 2 7 P J Y = J Y + 1 GO T 3 Y Q W

c

? I V j Q I A T E T A ? L F C 390 L = l x = Y I J 1 = J 2 + 1 J7 = J1 + N Y - l SFADCH I N Y SENSF J X l !I SCISSCRIPT C)F 1 S T Y C G 3 T n 1033 K = K + 3 % K Y q n r ) C 1 N T F P D " L A T F 1% X SENSF H A S F Y C . ?F C C L . Yn. O F YS

c S U S S C R I P T -

J Y = J Z + 1 + l J Y - I - ? ) * Q Y + J X l - J 1 DO 5 5 0 V = 1 , 4 J X = J Y Y ( U ) = 0.

Q f i 5 2 0 J = 1 7 4 Y I V I = Y I Y I + C l J ) * T ( J X ) 5 2 0 JX = J)I+YV FIGURE 3A. FORTRAN I V LISTING (CONTINUED) FORTRAN I V G LFVEL 20.1 R IQUAD D A T E = 7 2 0 3 1 5 5 0 J Y = J Y + l 003 8 C C G E T CDEFF. IY Y SFNSE O C 3 9 GO T O 105 0 0 4 0 600 2 = 0.

0 0 4 1 . OD 7 0 0J = l r 4 0 0 4 2 700 r! = Z + C ( J ) * Y I J ) 0 0 4 3 9999 R ETU9N C .

S F A i C HR 9 U T I Y E - I N P U TJ l rJ 2 1 X

C C -OUTPUT P A t R R t K X t J X 1 0 0 4 4 1 0 0 0 K X = 0 @045 DO 1010 J=J1, J 2 0 0 4 6 I F( T ( J ) - X ) 1 0 1 0 ~ 1 0 5 0 ~ 1 0 5 0 0 0 4 7 1010 CONTINUE C 9 F F H I G H E N n X = T ( J 2 1 0 0 4 a 0 0 4 9 Y X = 2 C 1 l S F LAST 4 P n l Y T S A N D CU%VF D 0050 1 0 2 0 J X l = J 2 - 3 005 1 R A = 0 .

0052 G O T O 1690

C TFST F O P - - O F F L O N F Y D , F I R S T I N T E R V A L , O T H E R

0 0 5 3 1 0 5 3 I F ( J - J 1 - 1 1 1 O R 0 7 1 0 9 0 , 1100

0 0 5 4 l O R O I F ( T l J ) - X ) 1 0 A Z ~ l O Y 0 ~ 1 0 8 2 9 0 5 5 10132 K X = 1 0 0 5 6 X = T ( J 1 ) 0 0 5 7 LO90 J X l = J 1 005 8 R A = 1.

0 0 5 9 G O T O 1 4 0 0 c TFST F O R L 4 S T I N T E R V A L Nr?, Y E S , NO

0060 11 00 I F ( J - J 2 ) 1 5 o n , ~ 0 ~ 0 . ~ ~ 0 0

006 1 1500 J X 1 = J - 2

R A = l T ( J ) - X ) / ( T ( J ) - T ( J - 1 ) 1

0 0 4 2

0063 1600 R B = 1. - 4A

c C RFTIJRY R A C K T O M A I N BODY 0064 I F ( L ) 500, 100, 5 0 0 0 0 6 5 0 0 6 1 006A 0 0 7 0 0 0 7 1 0 0 7 2 0 0 7 3 0 0 7 4 0 0 7 6 FIGURE 3A. FORTRAN IV LISTING (CONCLUDED)

NASA-Langley, 1972 - 2 73

"