aerodynamic design and analysis system for … · (geometry module), draw a picture of the...

N A S A C O N T R A C T O R

R E P O R T

CS|CS|u-»CNIi

N A S A C R - 2 5 2 2

AERODYNAMIC DESIGN AND ANALYSIS SYSTEM

FOR SUPERSONIC AIRCRAFT

Part 3 - Computer Program Description

W. D. Middleton, J. L. Lundry, and R. G. Coleman

Prepared by

BOEING COMMERCIAL AIRPLANE COMPANY

Seattle, Wash. 98124

for Langley Research Center

NATIONAL A E R O N A U T I C S AND SPACE ADMINISTRATION • WASHINGTON, D. C. • MARCH 1975

https://ntrs.nasa.gov/search.jsp?R=19750010114 2020-04-04T03:53:39+00:00Z

1. Report No.

NASA CR-25222. Government Accession No. 3. Recipient's Catalog No.

4. Title and SubtitleAerodynamic Design and Analysis System forSupersonic Aircraft.Part 3—Computer Program Description

5. Report Date

March 19756. Performing Organization Code

7. Author(s)

W. D. Middleton, J. L. Lundry, and R. G. Coleman

8. Performing Organization Report No.

D6-41769

10. Work Unit No.9. Performing Organization Name and Address

Boeing Commercial Airplane CompanyP.O. Box 3707Seattle, Washington 98124

11. Contract or Grant No.

HASl-12052

12. Sponsoring Agency Name and Address

National Aeronautics and Space AdministrationWashington, D.C. 20546

13, Type of Report and Period CoveredContractor ReportJan. 1973— Nov. 1974

14. Sponsoring Agency Code

15, Supplementary Notes

Three of three final reports

16. Abstract

An integrated system of computer programs has been developed forthe design and analysis of supersonic configurations. The systemuses linearized theory methods for the calculation of surfacepressures and supersonic area rule concepts in combination withlinearized theory for calculation of aerodynamic force coeffi-cients. Interactive graphics are optional at the user's request.

The description of the design and analysis system is broken intothree parts:

Part 1—General Description and Theoretical DevelopmentPart 2—User's ManualPart 3—Computer Program Description

This part contains schematics of the program structure anddescribes the individual overlays and subroutines.

17. Key Words (Suggested by Author(s))

Wing designConfiguration analysisWave dragPressure distribution

18. Distribution Statement

Unclassified—Unlimited

New Subject Category 02

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

96

22. Price*

$4.75

'For sale by the National Technical Information Service, Springfield, Virginia 22151

CONTENTS

1.0 SUMMARY

2.0 DISCUSSION ............... ........... 32.1 Executive Module ..................... 62.2 Geometry Module ..................... 82.3 Skin Friction Module ................... 202.4 Near-Field Wave Drag Module ............... 252.5 Wing Design and Optimization Module ........... 452.6 Lift Analysis Module ................. . . 62

3.0 REFERENCES .......................... 85

APPENDIX A — Interactive Graphics Subroutines ...... ...... 87

ill

Page Intentionally Left Blank

A E R O D Y N A M I C D E S I G N A N D A A L Y S I S ' S Y S T E MFOB SUPEHSONIC A I R C R A F T

PAST 3 - COMPUTER P R O G R A M D E S C R I P T I O N

W. D. Middleton, J. L. Lundry, and R. G. ColemanBoeing Commercial Airplane Company

1.0 S U M M A R Y

An integrated system of computer programs has been developed forthe design and analysis of supersonic configurations.

The system consists of an executive driver and seven basiccomputer programs including a plot module, which are used to build.up the theoretical force coefficients of a selected configuration.

Documentation of the system has been broken into three parts:

Part 1 - General Description & Theoretical DevelopmentPart 2 - User's ManualPart 3 - Computer Program Description

This part, the computer program description, contains schematicsof the program structure and written descriptions of theindividual overlays and subroutines.

Interactive graphics for use with the system are optional,employing the NASA-LRC CRT display and associated software.

The computer program is written in FORTRAN IV for a SCOPE 3.0 orKRONOS 2.0 operating system and library file. It is designed forthe CDC 6600 series of computers and executes in OVERLAY mode.The system requires approximately 1100008 (octal) central memorywords and uses seven peripheral disc files in addition to theinput and output files.

2.0 DISCUSSION

A schematic of the design and analysis system overlay structure isshown in figure 2.0-1. The system is a single overlaid program,with the executive driver as the main overlay and the basicprograms as primary overlays. The basic programs manipulate input(geometry module), draw a picture of the configuration (plotmodule), or perform design or analysis calculations.

The format of the computer program documentation is to presentschematics or block diagrams of the major program structure,together with subroutine descriptions, for each module developedunder the design and analysis system contract. The plot and far-field wave drag modules are not included in this procedure, sincethey are described in other NASA documentation (references 1 and2).

The description of the overlay structure follows the convention oflabeling overlays with octal numbers, but calling them with theirdecimal eguivalents.

A typical test case and associated program output is given in theUser's Manual (part 2).

File Usage

File usage in the system is assigned as follows:

1 basic geometry storage2 interface file3 restart data5 card input6 output9, 10, 11, 12 storage files for far-field wave

drag module9, 11, 12 storage files for plot module

Program Structure

A block diagram of the design and analysis system is shown infigure 2.0-2. The largest element of the system with the NASA-LRCgraphics software attached occurs with the geometry display moduleloaded, and is approximately 110000Q (octal). A "stripped"version of the system (graphics software excluded) would have itslargest core requirement with the lift analysis module loaded, andwould be approximately 700008-

iThese core sizes are for an absolute version of the program,without the operating system loader.

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2.1 EXECUTIVE MODULE

The executive level (0,0 overlay) is used to read executivecontrol cards and request execution of the basic programs (primaryoverlays) as instructed. The executive cards are described in theuser's manual (part 2) and summarized under subroutine CHECKIN.

PURPOSE:

METHOD:

INPUT:

SUBROUTINESCALLED:

Program SUPERD

To read program executive cardsoverlays.

and call primary

SUPERD is the program name assigned to theexecutive level (SDA, 0, 0). It reads executivecards, calls subroutine CHECKIN to find thecorresponding overlay number, calls the geometrymodule to read or sort input, then calls theappropriate primary overlay for problem execution.

CRT is a special executive card used only to turnon (or . off) the graphics routines as described inthe user's manual.

Executive cards (see user's manual)

CHECKIN

PURPOSE:

METHOD:

Program CHECKIN

To identify primary overlay number corresponding toexecutive card.

The overlay number for the different primaryoverlays is given by variable IPRG, in commonblock/SAVI/. CHECKIN sets the value of IPRG byfinding the executive card word corresponding toIPRG. The correspondence is:

EXECUTIVE_CARD

PL0TFFHDSKFRGEJ2TMNFWDANL2WDS2FSUPWGUP

IPRG

2345678910

USE:

INPUT:

SUBROUTINESCALLED:

CALL CHECKIN

Executive control card word (ISKIP)

None

P U R P O S E :

M E T H O D :

USE:

INPUT:

SUBROUTINESCALLED:

Function TBLU1Integer Function L0PKUP

To perform linear or second order interpola-tion from one-dimensional array.

TBLU1 and the associated integer function L00KUPare general purpose interpolation routines, foreither linear or second order interpolation. Theprogram call is:

whereXXX

Y

MD

N

2

TBLU1 (X, XX, Y, MD, N)

independent variablearray containing independentvariablearray containing dependentvariablecode defining interpolation type1 = linear2 = second ordernumber of variables in arrayXX or Ydependent variable (answer)

Array XX must be monotonically increasing.

Z =TBLU1 (X, XX, Y, MD, N)

As described above

TBLU1 calls associated subroutine LJ2T0KUP

1 7

2.2 GEOMETRY MODULE

The geometry module is primary overlay 5. It contains subprogramsto read, store, or display the configuration geometry, and to setup the input for the other basic programs. A schematic of thegeometry module is shown in Figure 2.2-1.

PURPOSE;

METHOD:

Program PDPACK

To route geometry handling requests from theexecutive to geometry routines, based on executivecontrol cards.

Program PDPACK is the primary level of the geometrymodule. It is entered from the executive to store,add, or change input data; to update wing cambersurface or fuselage basic geometry; or to enter theinterface routines to set up input data for theother modules. A schematic of PDPACK is shown infigure 2.2-2.

The executive control cards corresponding tovariables in PDPACK are as follows:

EXECUTIVECARD

GE0M NEWGE0HPL0TFFHDSKFRNFWDANL2HDE2FSUPWGUP

PDPACKVARIABLE

IFIRST=0IFIRST=1IPRG=2IPRG=3IPRG=4IPRG=6IPRG=7IPRG=8IPRG=9IPRG=10

PRINCIPALPROGRAMS OR

SUBROUTINES CALLED

EDITSINPUTS,INPUTS,INPUTS,INPUTS,INPUTS,INPUTS,INPUTS,INPUTS,INPUTS,

EDITSGE0MPLTGE0M80GE0M158GE0M916GE0M201GE0M253FUSUPDNEWCAM

Configuration geometry is read from cards inprogram EDITS and stored on tape 1 'when thegeometry module is not in core. Program INPUTSretrieves the geometry from tape 1 when thegeometry module is called. Subroutines HRGE0M andPRINTG write the configuration geometry on tape 1for storage or print the geometry onto the outputtape, respectively.

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USE:

INPUT:

SUBROUTINESCALLED:

The interface programs write data onto tape 2,which becomes the input tape for the individualbasic modules.

CALL OVERLAY (SDA, 5, 0, 0)

Executive card variables listed above.

See schematic on page 10 .

PURPOSE;

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine HRGEJ2TM

To write geometry data onto tape 1 for storage, oronto tape 2 for plot program or far-field wave dragprogram.

Subroutine WRGE0M uses the input format of theNASA-LRC plot program and is used to write thebasic geometry data onto tape 1 when the geometrymodule leaves core, or to write the geometry dataonto the interface tape (2) as a part of the plotor far-field wave drag program interfaces.

CALL HRG20M

Configuration geometry (see user's manual)

None

PURPOSE:

METHOD:

Subroutine

To calculate the 2 distance between the nacellecenterline and the local wing camber surface.

The basic configuration geometry input (read inEDITS) allows the nacelles to be input with eitherof two 2 dimensions: in the 8 system of theconfiguration coordinates, or with 2 measured tothe local wing camberline. Subroutine 2P#D isused, regardless of which 2 definition is input, tocalculate the other definition and store it in thebasic geometry.

If the nacelle origin is forward or aft of the wingplanform, the 2 distance is measured from the wingleading edge or trailing edge (whichever is closer)at the same Y station.

11

USE:

INPOTS:

SUBROUTINESCALLED:

As a special case, 2P0D is also used to compute thedistance between the fuselage centerline and thewing camber line at the side of the fuselage (inprogram GE0TM916) .

CALL 2P0D(NN)

NNP0D0RGXAF,HAF0RG,WAF0RD,T2RD

None

Nacelle origin indexNacelle origin data

Wing definition (planform,thickness, camberline)

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine PRINTG

To write configuration geometry(tape 6) .

onto output tape

After configuration geometry is read or changed,subroutine PRINTG is used to write the currentgeometry definition. In the case where thefuselage or wing camber surface is updated(executive cards FSUP or WGUP), only the fuselageor camber surface is output. This is controlled byvariable ISKIP1 (=98 for fuselage only, =99 forcamber surface only).

CALL PRINTG

Geometry definition (see user's manual)ISKIP1

SUBROUTINESCALLED: .None

PURPOSE:

METHOD:

Subroutine NEHCAM

To interpolate a wing camber surface for basicgeometry definition (TZ RD) from wing design oranalysis definition (W20BD).

The camber surface definition generated or used bythe wing design or analysis modules, called W20RD,may be different from the basic geometry definition(T20RD). This can happen either because thedefinition is being created by the design program,

12

USE:

INPUT

or because the analysis program input option for W20RD was used. NEWCAM linearly interpolates for T2PRO from W20RD, and is called by program PDPACK ifexecutive card WGUP is read. NEWCAM is alsoautomatically called by the analysis programinterface if the W20RD option is used.

CALL NEHCAM (FACTOR)

FACTOR

SUBROUTINESCALLED:

N0PCT,P,JBYMAX,Y,H20RD,IF2C

XAF,WAF0RG,T20RD

INTERP

Multiplier used to scale cambersurface ordinates, if desired.

Camber surface definition WZJ3RDcontained in common block /CAMBER/

Camber surface definition (T20RD)of basic geometry contained incommon block /WING/

PURPOSE:

METHOD:

USE:

Subroutine INTERPr\

To interpolate two-dimensional array.

INTERP is used to linearly interpolate W80RDdefinition (used in conjunction with subroutineNEWCAM).

CALL INTERP (A, 0, N, X, Y, M)

INPUT A

9

NX

M

Y

First array location for abscissavaluesFirst array location for ordinatevaluesNumber of values in A and $ arraysArray of abscissa for ordinateoutputsNumber of values in X and Y arraysoutputArray of calculated ordinates.

SUBROUTINESCALLED: None

13

Program GE0MPLT

PURPOSE

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

To write input tape for PLOT module.

GE0WPLT is the interface program between theexecutive and the PLOT module, entered when theexecutive card PL0T is read. The interface readsthe plot title card and configuration codes, thenuses WRGE0M to write the corresponding basicgeometry data onto tape 2 (the program input tape).GE0MPLT then reads the plot view cards and writesthem onto tape 2.CALL OVERLAY (SDA, 5, 2, 0)

See user's manual for input description

WRGE0M

PURPOSE

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Program GE0M80

To write input tape for far-field wave drag module.

GE0M80 is the interface program between theexecutive and the far-field wave drag program,entered when the executive card FFWD is read. Theinterface reads a title card and the configurationcodes, then uses WRGE0TM to write the correspondingbasic geometry data onto tape 2. GE0M80 then readsthe case and restraint cards (if used) and writesthem onto tape 2.

CALL 0VERLAY (SDA, 5, 3, 0)


HRGE0M

PURPOSE:

METHOD:

Program GE0H158

To write input tape for skin friction module.

GE0M158 is the interface program between theexecutive and the skin friction drag module,entered when the executive card SKFR is read. Itreads title information, flight conditions, andconfiguration data, and structures those inputstogether with basic geometry to write the inputtape (tape 2) for the skin friction module.

14

USE:

INPUT:

SUBROUTINESCALLED:



None

PURPOSE;

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Program GEJ2TM916

To write input tape for near-field wave dragmodule.

GEJZFM916 is the interface program between theexecutive and the near-field wave drag module,entered when the executive card NFWD is read. Itreads title information, Mach number, etc., andstructures those inputs together with basicgeometry to write the input tape (tape 2) for thenear-field wave drag module.

The near-field program considers the configurationto be uncambered; the wing and fuselage havethickness but have a flat mean-line. Wing heightin the side of the fuselage is preserved, however,being the distance from the fuselage centerline tothe wing at the side of the fuselage. In GEJ2TM916,the wing height dimensions are computed by aspecial use of 2P0TD, in which the fuselagecenterline is treated as a nacelle origin in aseries of calculations.

The nacelle 2 dimension used in the near-fieldprogram is the distance from the local wingcamberline.


See user's manual for input description.

2P0TD, NEWAREA

PURPOSE:

METHOD:

Subroutine NEWAREA

To check for and remove "steps" in input fuselagearea definition corresponding to inlet or exitstream tubes.

The basic geometry fuselage definition allows forinput of the fuselage in four segments. If the

15

first cross-section of segment 2 is input at thesame X station as the last cross-section of segment1, and the cross-sectional areas of the two inputsare different, then the far-field wave drag programextends a streamtube to account for the area"step", so that no area discontinuity occurs in thewave drag calculations. This can occur, also,between other segments. The near-field wave dragfuselage calculations cannot accommodate an areastep at a fuselage station other than the first orlast. If one occurs, subroutine NEHAREA removesthe step by collapsing the fuselage to a solid bodyhaving the same area growth.

USE:

INPUT;

SUBBOUTINESCALLED:

NEHABEA also reduces the fuselage area definitionto 50 values in X, 2 and area if more than 50 totalvalues were input in all fuselage segments, sincethe near-field program allows only 50 points.

CALL NEHAREA (X, 2, A, L)

2

L/B0TDY/

None

Output array of fuselage X valuesfor analysis program.Output array of fuselage camberline2 values.Output array of fuselage cross-sectional areas.Number of values in X, 2, or. A arraysCommon block containing fuselagebasic geometry definition.

PURPOSE:

METHOD:

Program GE0M201

To write input tape for lift analysis module.

GE0M201 is the interface program between theexecutive and the lift analysis module, enteredwhen the executive card ANL2 is read. It readstitle information, Mach number, etc., andstructures those inputs together with basicgeometry to write the input tape (tape 2) for thelift analysis module.

The lift analysis interface allows the wing cambersurface to be read as the W20BD definition, orpassed in through common block /CAMBER/, in

16

USE:

INPUT:SUBROUTINESCALLED:

addition to the basic geometry definition. If W20RD is used, the basic geometry is automaticallyupdated by means of subroutines NEKCAM and HRGE0M.

In addition, since the lift analysis program logicdoes not permit step discontinuities in fuselagearea between the most forward and aft X stations,subroutine NEWAREA is used to prepare the fuselagecross-sectional area definition. (NEHAREA isdescribed in connection with GE0M916).

The nacelle origin £ dimension is the verticaldistance to the local wing camber line.

CALL OVERLAY (SDA, 5, 7, Q)


NEWAREA, NEHCAM, WBGE0M

PURPOSE:

METHOD:

Program GE0M253

'To write input tape for wing design module.

GE0TM253 is the interface between the executive andthe wing design module, entered when the executivecard WDE2 is read. It reads title information.Bach number, loadings data, etc., and structuresthose inputs together with basic geometry to writethe input tape (tape 2) for the wing design module.

The wing design program may employ pressure fieldsgenerated by the near-field wave drag module oranalysis module. The existence of these pressurefields is tested in the corresponding commonblocks. This involves the codes BJ2TDCPX, B0TDUPX,and CPNACX. The actual use of these pressurefields is controlled by input of the correspondingloading numbers.

The nacelle 8 origin is the verticalthe local wing camber surface.

dimension to

USE:

INPUT:

The restart data deck is substantial. Logic forthis part of the interface is copied from the wingdesign program input.



17


PURPOSE:

METHOD:

USE:INPUT:

SUBROUTINESCALLED:

Program FUSUPD

To update the fuselage definition in the basicgeometry to the optimum area distribution generatedby the far-field wave drag program.

The far-field wave drag program contains a fuselageoptimization feature, which area-rules the fuselagesubject to input constraints. FUSUPD uses theoptimized definition to update the basic fuselagegeometry, and is accessed by means of the executivecard FSUP.

FSUP first reads the value of 0PHOH, which controlsthe optimization interpolation. (0PH0TW ' - -,interpolate at original fuselage X stations; 0PH0W=+ , interpolate at 50 equally spaced X stations).It then changes the basic geometry definition tothe optimum body area distribution, contained incommon block/j2PBOD/. The original fuselage 8definition is preserved. Fuselage perimeters areproportioned to the new area distribution.

CALL OVERLAY (SDA, 5, 9, 0)OPHprw Interpolation codeX0P Opt imum fuselage definition. XJ?PA0P array, A#P = area array, J0P =J0P number of X0P or A0P values.

TBLU1

= X

PURPOSE:

METHOD:

USE:

INPUT:

Program INPTS

To read basic geometry data from tape into core.

Program INPTS is used to reread the configurationbasic geometry back into core when the geometrymodule is accessed. INPTS uses the same format asprogram WRGE#M, which was used to store the basicgeometry on tape 1.

CALL J3VERLAY (SDA, 5, 10, 0)

Tape 1

18


Program EDITS

PURPOSE: To read configuration geometry from cards.

METHOD: Program EDITS is used to read the configurationgeometry from cards, and is accessed by either theGEJJM NEW or GE0M executive cards. (GE0M NEW zeroesall the configuration J1, J2f etc., codes, so thatEDITS reads all new data; GE0TM preserves allexisting codes, so that new geometry read replacesor adds to existing geometry read by INPTS).

The input format of program EDITS is basically thatif the NASA-LRC plot program, with a few additionalinput variables added as noted in the user'smanual.

USE: CALL OVERLAY (SDA, 5, 11, 0)INPUT: See user's manual for input descriptionSUBROUTINESCALLED: BP0D

19

2.3 SKIN FRICTION MODULE

The skin friction module is primary overlay U. Its principalsubprograms calculate the wetted areas of the configuration, andthen 'the skin friction drag for a series of input flightconditions. A schematic of the skin friction module is shown infigure 2.3-1.

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Program TEA-158A

To read configuration data, flight conditions, andcalculate wetted areas and lengths to be used inskin friction drag calculations.

Program first reads all input data, which consistsof configuration geometry and either .Mach number-altitude or Mach number-Reynolds number flightconditions.

For each configuration component, the correspondingwetted areas and reference lengths are computed.In the case of the wing or canard (s) of f in (s) , theparts are broken into strips to permit moreaccuracy in determining an average skin frictioncoefficient. (The wing is broken intoapproximately 50 strips, canard or fin into 10strips.)

The wetted areas and references lengths are passedto subroutine DRAG for the skin frictioncoefficient calculations. \

CALL OVERLAY (SDA, 4, 0)

Input is read from interface tape (tape 2) , set upby skin friction interface in geometry module.

DBAG

PURPOSE:

METHOD:

Subroutine DRAG

To calculate configuration skin frictioncoefficients and print answers for all input flightconditions.

Given the set of configuration wetted areas andinput flight conditions, the skin frictioncoefficients for each component are computed andsummed to obtain the total skin friction drag. If

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USE:

INPUT:

PRINCIPALVARIABLES:

the graphics routines are activated, the frictiondrag coefficients are also printed on the CRT.

CALL DRAG

Input is passed in common blocks from program TEA-158A

Same as program TEA-158A, plus:SCAM Scale factor to convert configura-

tion reference lengths to feet foruse in subroutine FICT

SREF Wing reference areaSBETT Total configuration wetted areaCDFT Total skin friction drag coefficient

AM, Mach number - altitude flightAL, condition input AM = Bach number,DELT, AL = altitude (feet) , DELT =SCAM0D temperature deviation from standard

(«F) , SCAMJ2TD = input scale factor.

AM, Mach number - Reynolds numberRNPFL, condition input. RNPFL = ReynoldsSCAM0D, number per foot/1,000,000. T0TEM =T0TEM total temperature (ORankine)

SWETRB Fuselage wetted areaFUSL Fuselage reference lengthSWETB Fuselage wetted area corrected for

overlap areas of wing, fin(s), andcanard(s)

AREAJ Planform area of a wing stripHINGL Length of wing stripLCOUNT Total number of wing stripsSWETW (nominally 50) total wing wetted

area

TSHTNA Hetted area of nacelle(s) at firstTP0DL input origin, corresponding length,SWETNA total wetted area for all nacellesNPJ?D Number of nacelle origins

SWTFN Planform area of a fin strip (10CHDFN total strips), corresponding stripNFIN length, number of fins

TSWTC Planform area of canard stripTCCAN corresponding strip lengthNCAN Number of canards

22

OUTPUT:

SUBROUTINESCALLED:

SWETXP Wetted area of an arbitrary con-RLXP figuration part, correspondingNXTPT reference length, number of

arbitrary parts.

Output consists of flight conditions, wettedarea and skin friction coefficient buildups,total skin friction drag coefficient and con-figuration wetted area.

FICT, DISP158

PURPOSE;

METHOD:

USE:

INPUT:

PRINCIPALVARIABLES;

OUTPUT:

SUBROUTINESCALLED:

Subroutine FICT

To calculate the turbulent skin frictiondrag coefficient for a given reference length,Mach number, Reynolds number, and totaltemperature.

The skin friction coefficient is calculatedfrom the T1 method described in the aerody-namic theory document (part 1).

CALL FICT {AMX, ALX, EEL, C)

AMXALXEEL

TISCAM

SI

C

Mach numberAltitude, feetReference length

Total temperature, degrees RankineScale factor to convert inputreference length to feetFree stream Reynolds number

Skin friction coefficient

ATM062, SKIN

PURPOSE:

METHOD:

USE:

Subroutine ATM062

To provide standard atmospheric data

Program uses 1962 standard altitude definition(reference 3).

CALL ATM062 (2, TEMP, SIGMA, AX)

23

INPUT:

OUTPUT:

SUBROUTINES

Z Geometric altitude, feet

TEMP Temperature, degrees centigradeSIGMA Density ratioAX Speed of sound, knots

CALLED: None

PURPOSE:

METHOD:

USE:

INPUT:

OUTPUT:

SUBROUTINESCALLED:

ERRORRETURN:

Subroutine SKIN

To iterate for skin friction coefficient.

Program is used to solve the Karman-Schoenherrequation

242using T^f = 1°910 <CF *

value for CF. Solution is iterative, andis satisfied when successive iterations agreewithin .0001 per cent. A maximum of 50iterations is allowed.

CALL SKIN (REY, CF)

REY Reynolds number

CF Skin friction coefficient

None

Program uses 50th iteration for CF ifconvergence dees not occur, and prints errormessage.

24

2 . U NEAR-FIELD W A V E D R A G M O D U L E

The near-field wave drag module is primary overlay 6. it containsprincipal subprograms to calculate the near-field pressure dataand drag coefficients and to display the calculated results. Aschematic of the principal program structure is given in f igures2.4-1 and 2.4-2.

PURPOSE:

METHOD:

USE:

INPUT:

Program TEA-356

Near-field wave drag primary overlay

Program TEA-356 is the primary level of thenear-field wave drag program. It calls theinput overlay (1), and contains the Mach numberloop which calls the main program (overlay 2)and the graphics display (overlay 3) .


Executive card NFWD

SUBROUTINESCALLE.D: Overlays 6,1 to 6,3

PURPOSE;

METHOD:

Program P916

To perform thickness pressure calculations in near-field wave drag module.

Program P916 is the main program of the near-fieldwave drag module. It solves for the thicknesspressure distribution on the surface of anarbitrary wing-fuselage-nacelle configuration, andintegrates the pressures over the surface to obtainwave drag.

The equations used in the thickness pressuresolution are given in the theory document (part 1).A consistent nomenclature is used, as possible,between the theory equations and the Fortranvariable names.

The major subprogram of P916 is NACPF, whichcalculates the nacelle thickness pressures and allnacelle interference terms except for the nacelle-on-wing and wing-on-nacelle terms.

The principal program logic is as follows:

1) Convert planform geometry into wing

25

• Readinput

LOAD6(6,2)

1 PSIG

—TjDZCALC

TEA-356(6,0)

1

DISP916(6,3) CRT display

P916(6,1)

Wing thickness pressuresand drag coefficient summary

Nacelle terms(See figure 2.4-2)

TRNSFM Setup grid system

INTSEC I Wing-fuselage intersection

BODY | Fuselage F(y) and thickness pressure

Fuselage pressure field

Grid system slopes

~—I GETNCP I Nacelle pressure field signature

[ GRAB

WONAC

ADDUM

Wing or fuselage pressurefield interpolation

Wing-on-nacelle term

Fuselage drag

Nacelle drag summary

FIGURE 2.4-1.-NEAR-FIELD WA VE DRAG MODULE SCHEMA TIC

26

NACPF

1

YSETUP

NSETUP

1

PSIG

GLANCE

MERGE

CUTOFF

COMBINE

BODY

PSIG

PINGRT

BSETUP

PSIG

BPINT

PSIG

PINfiRT

PI ITAPP

Y stations for nacelle pressure field

Separate nacelles, above and below wing

—[BODY Nacelle wave drag, F(y)

Calculatenacellepressurefieldacting onwing

Fuselage-on-nacelleterm

Nacelle-on-fuselageterm

Nacelle-on-nacelleterm

RETURN

FIGURE 2.4-2. -NA CELLE TERMS SCHEMA TIC

27

grid system (subroutine TRNSFM)2) Locate wing-fuselage intersection

(INTSEC)3) Calculate nacelle data (NACPF)4) Calculate fuselage pressure field acting on

wing. This is done for each selected semi-span station (TYB2) in loop D0 130. Theresultant fuselage pressure field is stored inPBWG, which is printed in loop D0 150.

5) Calculate wing thickness pressure field. Thisis done for the selected semi-span stations inloop D0 830. The semi-span element row isNSTAR and the associated x elements are LSTAH.For each NSTAR and LSTAR, the upstream regionof integration contains elements located at Nand LVAR. The local wing slopes are DiDX,contained in array TBC. The loop D0 450performs the influence function times slopecalculation described in the theory document.The velocity potential (PHI) is thencalculated, and differenced to get pressurecoefficient (CP) .After all pressure coefficients are calculatedat a given semi-span station, they aresmoothed in loop 710, resulting in CPAVG.Calculation of the drag terms (pressure timeswing slope) employs these variables names:

DBwG fuselage pressure actingon wing

DAVG wing thickness pressureDNAC nacelle pressure acting on

wing.

6) Interpolate wing thickness pressures foroutput. This is done at the selected semi-span stations in loop DJ? 770. The wingthickness pressures are then output in loop D0840. At the same time, the common blockcontaining the wing thickness pressures,/PLIM/, is completed to make it self-sufficient for use in other modules, where:

FYB2 per cent semi-span array,MYFR values

TNMPC per cent chord array, NMPCvalues .

VAR(X,Y) thickness pressure array

The wing thickness pressure plus fuselagepressure field is then summed and output inloop D(2T 860.

28

7) Integrate drag terms spanwise to get totalwing drag. This is done in loop D0 900.

8) Calculate wing thickness pressure on nacellevolume term (subroutine H0NAC)

9) Calculate fuselage pressure drag plus wingthickness pressure on fuselage drag terms.This is done in subroutine BDRAG and resultsin drag terms DBD and DW0B, respectively.

10) Convert drag terms to coefficient form, outputwing section drag coefficients, nacelle dragcoefficients, and final drag summary. This isdone starting at loop D0 920, using thefollowing nomenclature:

YB2 semi-span fractionCHORD local wing chordCAS wing section drag coefficientBEF section drag of fuselage on

wingCNACS section drag of nacelle on

wingCINT sum of CAS, BEF, CNACSDFR fraction of total wing drag

occuring at YB2CDAVG wing thickness drag coefficieentCDB fuselage thickness drag coef-

ficientCDBOW interference drag coefficient

x of fuselage on wingCDHOB interference drag coefficient

of nacelle on wingCDTOT total drag coefficient

The nacelle drag coefficient summary isprinted in subroutine ADDUM.

USE: CALL J2TVERLAY (SDA, 6, 1, 6HRECALL)

INPUT: HK Mach number index variable (fromoverlay 6, 0). Configuration datafrom overlay 6, 1.

SUBROUTINESCALLED: See schematic, figure 2.U-1.

Subroutine ADDUM

PURPOSE: To sum nacelle drag terms, convert them tocoefficient form (based on wing reference area) andwrite them onto the output file.

29

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine NACPF generates all nacelle thicknessdrag terms except for the wing on nacelle andnacelle on wing terms. These are saved in commonblock /NDRAG/ and printed by ADDUM when the mainprogram (P916) writes the final drag summary. Thedrag coefficient nomenclature is as follows:

TNISOL isolated nacelle wave drag coef-ficient

TFB0N interference drag coefficient offuselage on nacelles

TFN03 interference drag coefficient ofnacelle on fuselage

TFNON interference drag of othernacelles on nacelle

TFIMAG "image" drag coefficient ofnacelle on itself

TF0IMG "image" drag coefficient ofother nacelles

TDW0N interference drag coefficientof wing on nacelles

CALL ADDUM (SUMM)

SUMM Sum of nacelle drag coefficients

None

PURPOSE

METHOD:

USE:

INPUT:

Subroutine BDRAG

To integrate fuselage thickness pressures overfuselage to get wave drag, and calculate wing-on-fuselage interference drag term.

The fuselage is broken into TNCUT lengthwisestrips, and 5 radial segments (per half section)per strip. The fuselage thickness pressures andwing pressures acting on the carry-over regioncovered by the fuselage are integrated over thefuselage segments. Wing pressures are transferredaft along Mach lines to obtain the point ofapplication on the fuselage.

CALL BDRAG (TNCUT)

(SetTNCUT Number of fuselage strips.at 50 in main program) .

TNMPC, Wing pressure field extended alongfuselage centerline. TPHE = pres-

TPWE, sure coefficient array, TNMPC = X

30

SUBROUTINESCALLED:

NHPC array, NMPC = number of pressure coef-ficient values

/PLIH/ Common block containing wingthickness pressures

TXCPBY, Fuselage thickness pressure arrayTCPBY, TXCPBY = X, TCPBY = pressure

coefficient,NCPB NCPB values

GRAB, TBL01

PURPOSE:

METHOD:

Subroutine B0DY

To calculate the Whitham F(y) function for anarbitrary body of revolution, then compute surfacepressure distribution, wave drag, and wetted area.

Subroutine B0DY first computes the Whitham F(y)function, according to the Stieltjes integralformulation. The equations used are summarized inthe theoretical document (part 1). The F(y)function is computed at TNCUT+1 X-stations (whereTNCUT is an input in the main program, usually 50) .To remove minor irregularities in the final F (y)function, extra points are inserted between each ofthe X-stations, F(y) is computed there also, and afive point smoothing formula applied.

The F (y) function is also computed at X-stationsdownstream of the last body station, to define the"tail" on the F (y) function which is needed in thearea-balancing technique for pressure coefficient.The loop for the F(y) equations begins at statement60, which results in the unsmoothed F(y) arraystored in TFY, with corresponding, y values in BT0,JFY total values. After smoothing and extendingthe F(y) function aft of the body, the final F (y)function is stored in TFTAU, with corresponding yvalues in TTAU, JST0 total values.

The body surface pressure calculations loop startsat D0 330, using the equations given in the theorydocument (part 1). The body is again broken intoTNCUT+1 segments, and the resulting thicknesspressures stored in TCPBY, with corresponding Xvalues in TXCPBY. The wetted area calculation andthe integration of the thickness pressures to getwave drag is performed in loop DJ7 310.

31

DSE:

INPUT:

Subroutine B0DY will handle bodies having openfront or aft ends, but assumes smooth geometry in-between.

CALL B0DY (TXB, TRB, TNXB, TNCUT, TTAU,TFTAO, JST0T, HAVE, SNHET)

SUBROUTINESCALLED:

TXBTRB,TNXBTNCUT

TTAUTFTAU,JST0WAVESNHET

TBLU1

Body definition. TXB = x array,TRB = radii array, TNXB values inX or radius.Number of body segments in F(y)and thickness pressure calculationsF(y) function. TTAU = y,TFTAU = F(y), JST0 values in y orF (Y) -/C dA = wave drag/q

Betted area of body, assumingcircular cross-sections

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine BPINT

To integrate the nacelle(s) pressure signature overfuselage surface to obtain interference drag.

The composite nacelle pressure signature (containedin XVAL, CPVAL, JNEXT values) is applied to thefuselage area distribution obtained in subroutineBSETUP. The process is repeated for each nacelleorigin. The integral of Cp* area is called BF0RCE.

CALL SUBROUTINE (ZNAC, BFJ2TRCE, JNEXT)

2NAC

BF0RCEJNEXT

TBLU1

Nacelle vertical deminsion, rela-tive to wingResulting pressure forceNumber of values in nacelle pres-sure signature

PURPOSE:

Subroutine BSETUP

To calculate fuselage area growth for use inintegrating nacelle-on-fuselage interference dragterm.

32

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

The fuselage is broken into 3 pieces: forebody,mid-body region (wing part) , and aft body. Themid-body region covers the X interval of the wing-fuselage intersection.

Each fuselage piece is broken into 50 segments,the area growth associated with each segment storedin an array (for use later in subroutine BPINT) .The arrays are:

FBX, FBDABMXBttDAUBMDALABX, ABDA

CALL BSETUP

forebody X and areamid-body Xarea growth, above wingarea growth below wingaft-body X and area

Fuselage geometry contained in /FUSLG/wing-fuselage intersection contained in/WBINT/

TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine COMBINE

To combine two nacelle pressure - fields, fornacelles located above and below the wing, into asingle composite pressure field.

If nacelles are located both above and below thewing, subroutine NACPF generates two nacellepressure fields: TCPDN (nacelles below) and TCPN(nacelles above). COMBINE sums these two nacellepressure fields, to use in computing the thicknesspressure interference drag. The resulting pressurefield is stored in TXPN (per cent chord array) andTCPN (pressure coefficient array), with NYP semi-span per cents contained in TYP

CALL COMBINE

Nacelle pressure fields described above

TBLU1

33

Subroutine CUTOFF

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

To delete portions of a nacelle pressure field.

In constructing nacelle pressure signatures at anarbitrary distance from the generating body,subroutine NACPF calls CUT0FF to delete parts ofthe signature intercepted (or not reflected) byintermediate configuration components. Thepressure signature is contained in BT0 AND CT0T (xand pressure coefficients, respectively) .

CALL CUT0FF (X , X,)]J. ^ !

X1'X2

TBLU1

Bounding values of X, between which thepressure coefficients are set to zero.

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine DBCALC

To calculate wing slopes for all grid elementsrepresenting wing planform.

The wing thickness definition is contained incommon block /THICK/, consisting of the array T20RD(thickness profile), TPCT . (per cent chord array,NJ2TPCT values) . The Y stations corresponding to TB0RD are the planform input stations, in array YLED,DBCALC first interpolates the TB#HD array linearlyat the midpoint of eavch semi-span element, storeingthe results in ABC. The A«C array is theninterpolated chordwise to obtain the dz/dx slopefor each element, storing the slopes in T2C. Thechordwise interpolation may be either linear orguadratic depending upon an input code. (The T«Cstorage scheme is described under subroutineTRNSFB.)

Inboard of the wing side-of-body Y value (inputANYB0D, if ANYBfJD = +) , the wing slopes are set tozero.

CALL DSCALC

Wing planform, thickness, ANYB0D(described above).

TBLU1

34

Subroutine GETNCP

PURPOSE:

METHOD:

OSE:

INPUT:

To interpolate a nacelle pressure signature atgiven wing semi-span station, for usecalculating nacelle-on-wing interference drag.

ain

The nacelle pressure field, TCPN, is a two-dimensional array (for per cent chord and span).The wing program, P916, performs wing thicknesspressure calculations at selected span stations.It is convenient to have a one-dimensional array,versus X only at that span station, for use ininterpolating nacelle pressures for the nacelle-on-wing interference drag.

GETNCP interpolates TCPN to obtain the requiredpressure signature, which is stored in TXNCH (percent chord) and TCPNCW (pressure coefficient).

CALL GETNCP (YB2)

YB2 Semi-span fraction/NPF/ nacelle pressure field definition

common block.


PURPOSE:

METHOD:

USE:

INPUT:

Subroutine GLANCE

To perform cutoff of nacelle pressure signatureaccording to glance feature of nacelle pressurefield.

If the "glance" option of calculating the nacellepressure field is used, this subroutine calculateswhat part of a pressure signature' from a selectednacelle acting at a given spanwise station shouldbe deleted. The approximation is made that thepressure signature propagates along Mach lines forthis calculation.

If deletion of part of the signaturesubroutine CUTOFF is called.

CALL GLANCE (Y, YNAC, BETA)

is required,

YYNAC

BETA

Y station on wingY station of nacelle generatingpressure signatureMach number parameter, -\fM2-1

35

SUBROUTINESCALLED: CUT0FF

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine GRAB

To interpolate pressure coefficient at agiven planform location from the wing thick-ness pressure table or fuselage-on-winginterference pressure table.

Linear interpolation for pressure coefficientfrom a two-dimensional array.

CALL GRAB (X, Y, XCP, JTELL)

SUBROUTINESUSED:

XYXCPJTELL

VARPBHG

None

X coordinate on wing planformY coordinate on wing planformInterpolated pressure coefficientVariable to select interpolationarray1 = wing thickness pressure2.= fuselage-on-wing pressureWing thickness pressure arrayFuselage-on-wing pressure array

PURPOSE:

METHOD:

Subroutine INTPLT

To generate a detailed definition of the tiltedF (y) function for a selected right-running leg.

Subroutine PSIG identifies all right-running legsof the tilted F(y) function. INTPLT is used toenrich the definition for use in laterinterpolations. The selected leg may either be a"base" leg, or a leg that possibly contains anarea-balancing solution. The maximum number ofpoints used to enrich the leg definition is 300.The enriched definitions end up in the followingarrays:

Tilted F(y)F{y)Integrated areaunder tilted F(y)

Base leg

BT0BFTAU

BAREA

Other leg

CTfSCFTAU

CAREA

36

USE:

INPUT:

SUBROUTINESCALLED:

CALL INTPLT (SUH, TPRE, FPRE, NL, NR, NSET,TFTAU)

SUM Area under tilted F(y) functioncorresponding to left end of leg

TPRE,FPRE Value of tilted Y, (F(y) at leftend of leg

NL, NR Storage index of tilted F(y) array(arrays TT0 = tilted y, TFTAU = F(y)

NSET Index for leg definition1 = base leg2 = succeeding leg

TFTAU F(y) array

None

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine INTSEC

To locate the wing-fuselage intersection and•compute corresponding exposed wing wetted area.

The wing-fuselage intersection code is controlledby input ANYBJ2TD. If positive, ANYB0D defines theinboard end of the wing for purposes of thethickness definition, whether a fuselage is presentor not. If ANYB0D is negative, the intersection ofthe wing and fuselage is calculated by solving forthe point at which each constant per cent chordmeanline of the wing crosses through the fuselagesurface (assuming the fuselage to be circular).

The wing-fuselage intersection is stored inblock /WBINT/.iX X location of intersectionWY,W8,HT Corresponding Y,S, and thickness

values

CALL INTSEC (HSH)

WSW Exposed wing wetted area

TBLU1

common

PURPOSE:

Subroutine MERGE

To create a single composite pressurefrom multiple superimposed signatures.

signature

37

METHOD:

USE:

INPUT:

The nacelle pressure field in NACPF at a given Ystation is built up from contributions from allnacelles. The pressure signature from a singlenacelle is contained in arrays BT0 and CT0 (x andpressure coefficient), NW values of each. Thecomposite signature becomes XVAL and CPVAL, withJNEXT values of each.

All values of the new pressure signature areretained, and are merged with any previous valuesin XVAL and CPVAL, except that the merged pressuresignature is cat off aft of an input X value (XTE).In addition, the location of the bow shock of allpressure signatures in CPVAL is saved (in TSX,NWHAT values).

CALL MERGE (JNEXT, NHHAT, XTE)

JNEXT Number of values in compositeCPVAL array

NWHAT Number of combined pressuresignatures

XTE Aft-most X value of interest

SUBROUTINESCALLED: TBLU1

Subroutine NACPF

PURPOSE:

METHOD:

To calculate pressureassociated drag terms.

field of nacelles and

NACPF is a major subprogram of P916, which is usedto calculate the nacelle thickness pressures, andall nacelle interference terms except the wing-on-nacelle and nacelle-on-wing terms. A schematic ofthe program is shown in Figure 2.4-2. Thecalculation sequence is as follows:

1. Construct the pressure field of the nacellesacting on the wing. To do this, a series ofwing semi-span stations is set up (in ISETUP).The program then calculates the compositepressure signature from all nacelles acting atthose Y stations, for nacelles first below thewing, then for nacelles above the wing (ifany). Either glance or wrap nacelle pressurefield option may be used.

38

The nacelle pressure field is shrunk to 20 Xand pressure coefficient values at each ystation, stored in common block NPF:

TXPN x array, per cent chordTCPN pressure coefficient arrayTYP y semi-span stations (per cent),

NYP values

2. Calculate composite pressure signatures andinterference drag terms between nacelles orbetween nacelles and fuselage. The compositepressure signatures are applied to the areagrowth of the affected component to get thedrag force.

3. "Image" effects of the nacelles arecalculated. If the nacelle is located next tothe wing, the pressure signature from itselfreflects off the wing and back onto thegenerating , nacelle. Similarly, the reflectedsignature from other nacelles may cause aninterference drag. Drag interference due toreflected pressure signatures are calculatedseparately from the direct effects under (2).

USE: CALL NACPF

INPUT: Configuration geometry, passed to NACPF incommon blocks.'

SUBROUTINESCALLED: See schematic, figure 2.4-2.

Subroutine NSETUP

PURPOSE: To separate nacelles into those above or belowwing, write nacelle geometry, and calculate nacellewave drag, wetted area, and F(y) function.

METHOD: NSETUP is used for general bookkeeping involvingthe nacelles, and is called by NACPF. It scans thenacelle origins and separates them into those belowand above the wing. It prints the nacelle input,and then zeroes the tables used to sum the nacelleinterference drag terms. It then calls subroutineB0DY to calculate the nacelle F(y) function, wavedrag, and wetted areas.

39

USE:

INPUT:

SUBROUTINESCALLED:

If all nacelles have the same goemetry, NSETUPcalculates the nacelle F (y) only once, and shiftsit appropriately for other nacelle origins.

CALL NSETUP

Nacelle data in common blocks

BJ7DY

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine J7RDER

To arrange an arbitrary set of numbers into amonotonically increasing array.

The nacelle bow shock locations contained in TSX(NHHAT values) are in random order. Forinterpolation by TBLUI, they. must be inmonotonically increasing order, and cannot bedouble-valued. 0RDER is used to rework TSX asreguired.

CALL PRDER (TSX, NWHAT)

TSXNWHAT

None

Array of bow shock X locationsNumber of values in TSX array

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINES

40

Subroutine PINGRT

To integrate pressure field over surface ofnacelle.

Given a pressure signature defined by theXVAL, CPVAL arrays, PINGRT is used to inte-grate the signature as a buoyancy field overa nacelle area distribution.

CALL PINGRT (J, F0RCE, JNEXT)

J Index value of nacelle originF0RCE Resultant pressure drag term,

PJNEXT Number of values in XVAL or CPVAL

array

CALLED: TBL01

Subroutine PSIG

PURPOSE: To calculate the near-field pressure signature fora body of revolution at a given distance from thebody.

METHOD: Given an F(y) function, Mach number, and radialdistance from the body, PSIG is used to calculatethe resultant pressure signature. The method isdescribed in the aerodynamic theory document (part1).

The basic steps in the calculation sequence are asfollows:

1. The tilted F(y) function is constructed fromthe input F (y) function, and the running sumof area under the tilted F(y) functioncomputed. (The input function is defined byarrays TTAU, TFTAU and the tilted function byTT0, TFTAO, with the area corresponding to TT0in TAEEA) .

2. The bow shock position is identified by theleft-most value of TT0r for which TABEA = 0.(Interpolation of the TAREA array is used foraccuracy.)

3. The tilted F(y) function remaining after thebow shock is located is searched to identifyall right-running legs.

4. All right-running legs are compared for commonTAREA values, which would identify possibleshock wave locations. (Again, interpolationis used to enrich the TAREA definition, usingsubroutine INTPLT.)

5. Valid shock wave solutions are identified,based on the left-most criteria described inthe theory document.

6. The resulting tilted and area-balanced F(y)function is converted to pressure coefficientby means of the multiplier CJ7NST and stored inarrays BT0 and CT0 (x and pressurecoefficient) . The BT0 and CTfS arrays are cutoff if x becomes greater than input value YED.

41

OSE:

INPUT

SUBROUTINESCALLED:

CALL PSIG {TTAU, TFTAU, JST0, R, YED)

TTADTFTAUJST0RYED

F (y) definition, Y = TTAU array,F(y) = TFTAU array, JST0 values

Radial distance from body centerlineLargest x-value of interest forpressure signature

INTPLT, TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine TRNSFM

To convert input planform geometry to programsystem.

grid

The wing planform is represented in the near-fieldwave drag program as a set of recilinear elements,described in the theory document (part 1). Giventhe number of semi-span rows (TN N) used to definethe right-hand wing, TRNSFM interpolates theplanform definition at the mid-point of each semi-span row for the leading edge and trailing edge xvalue. These x values are converted to programscale (by means of RATI0 = Ywing-tip * BETA/TN0N)and stored in arrays TXLE and TXTE, with XLE0 andXTE0 defining the wing centerline grid points.

Storage of wing pressure coefficients and surfaceslopes uses a space-conserving technique: Theleading edge of a spanwise element row is storedimmediately after the trailing edge of the adjacentinboard row. The index array for the row storageis J2, which totals the number of elements storedup to the leading edge of a selected row. Theallowable total number of elements representing theright hand wing is 2750; if this total is exceededfor a given value of TN0N, the program reduces TN0Nuntil the 2750 limit is not exceeded.

CALL TRNSFM

Input geometry in common blocks

TBLU1

42

Subroutine W0NAC

PURPOSE:

METHOD:

USE:

INPUT

SUBROUTINESCALLED:

To calculate buoyancy effectpressures acting on nacelle.

of wing thickness

The wing-on-nacelle interference drag term,consisting of wing thickness pressures acting onthe nacelle area distribution, is computed inH0NAC. Wing thickness pressures are transferredaft along Mach lines to a series of nacelle firstruns. The resulting interference drag terms, •'cp

dA'are -stored in array, TDH0N, with storage indexcorresponding to the nacelle origin number.

CALL W0NAC

Ming thickness pressure definition (VAR) ,configu-ration geometry passed in through common blocks.

TBLUI

Subroutine YSETUP

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

To set up semi-span Y values fornacelle pressure field.

calculation of

A set of Y stations on the right hand wing areidentified in YSETUP for use in defining thenacelle pressure field. This set of Y stationsconsists of the semi-span Y values used in the wingthickness pressure calculations (contained in TYB2)plus extra stations immediately inboard andoutboard of each nacelle centerline.

The set of Y values is arranged in monotonicallyincreasing order by calling subroutine 0RDER. Theresulting array is TYP, with NYP values.

CALL YSETUP

Configuration gemmetry passed in through commonblocks

0RDER

43

Program L0AD6

PURPOSE: To read input geometry for near-field wave dragmodule.

METHOD: L0AD6 reads the input set up by the near-fieldprogram interface in the geometry module.

USE: CALL OVERLAY (SDA, 6, 2, 0)

INPUT: See input instructions in user's manual.

SUBROUTINESCALLED: TBLUI

44

2.5 WING DESIGN AND OPTIMIZATION MODULE

The wing design and optimization module is primary overlay 8.contains secondary overlays to calculate:

• The flat wing solution for the input planformand Mach number

• The wing shape and force characteristics for agiven loading

• The optimum combination of loadings for leastdrag, subject to imposed constraints.

A schematic of the wing design and optimization module isshown in figure 2.5-1.

It

PDRPOSE:

METHOD:

USE:

INPUT:

SUBROUTINES/OVERLAYSCALLED:

Program TEA-253

To call the three secondary overlays of thewing camber design program and to call theinteractive graphics displays (if used).

Standard FORTRAN statements

Call OVERLAY (SDA, 10, 0)

Input is in secondary OVERLAY (SDA, 10, 1)

JLTIME, OVERLAY (SDA, 10, 1),OVERLAY (SDA, 10, 2),OVERLAY (SDA, 10, 3)

PURPOSE;

METHOD:

USE:

INPUT:

Function CPARB

To define lifting pressure coefficient in thearbitrarily defined planform region for com-ponent loading 11.

At a given span station, linear interpolationis used to establish the chordwise coordinateof the arbitrary region's leading edge. Then,Cp is proportional to distance aft of thislocation.

CP = CPARB (XF, YF, CHORD)

XFYF

the chordwise and spanwise locationon the wing planform in fractionsof local chord and semispan atwhich pressure coefficient is to beprovided.

45

oro«- inJ-CN •

>§-IDC

> DCOa.

DC LU C < Q —< Q ± Z I- l-Q. Q- Q. D- Q 1O O O O O - j

-5 10-°§<8S*^ *-\ /*- rrf

-; o DC ip= - u> Q DCO W5 Q.

JOQ.

DC0

O D C

cotoclaEo0 w

e ?

• O

* O ^^- CD 3E i- o

:.111 ..,• DC < LU DC

Uj-J^QO

^§

ro J2: njQ u. o

d.O

i<*CD?5UjQCO

l_f^

LO

§CO

46

CHORD local wing chord at span station YF.

PRINCIPALVARIABLES:

In addition, a definition of the arbitraryregion is passed through COMMON/BLOCK^/.

CPARB the lifting pressure coefficientin the arbitrarily defined region.

XARB chordwise and spanwise coordinatesYARB of points defining the arbitrary

region.

PDRPOSE:

METHOD:

USE:

INPUT

Subroutine CPDEF

To define lifting pressure coefficient as afunction of chordwise and spanwise planformlocation for each of the seventeen componentloadings; further, to also define this pres-sure coefficient for an optimum combinationof loadings.

Lifting pressure coefficients for loadings1-11 are defined by analytical expressionsand for loadings 12-17 by linear interpola-tion in tables as a function of chordwise andspanwise planform location.

CALL CPDEF (DX, BETAY, CHORD, KOPT, IFLAG)

DX is distance aft of leading edge inprogram units.

BETAY is the product of the Mach numberfactor (.VM2-1) and spanwise distancefrom the centerline in program units.

CHORD is wing chord in program units atspan station BETAY. »

KOPT is the index for the loading numbertable LOADNO. '

IFLAG is a parameter which offers theoption of deleting the contributionto lifting Cp of the three configu-

• ration-dependent loadings. Thisoption is used during camber surfacecalculations which use lifting pres-sures, but not during calculation ofwing surface pressures.

Input is also provided through the use ofcommon blocks.

47

PRINCIPALVARIABLES: AI

CPBODL

CPBUPH

CPDEF

FLOAD

LOADNO

NLOADSXBODUPYBODDP

XCPBODYCPBOD

a table of loading factors computedby program OPTIMUM in OVERLAY(SDA, 10, 3), one for each of thecomponent loadings, that defines theoptimum combination of loadings,a table of lifting pressure coef-ficient acting on the wing andcreated by nonsymmetric bodyvolume distribution,a table of lifting pressure coef-ficients acting on the wing andcreated by the body upwash flowfield.lifting pressure coefficient(lower surface c - upper surface

V*a table of scaling factors set inprogram P151 which produces com-ponent loading lift coefficientsof order 1.0.a table of component loadingnumbers with index KOPT that areinput data in program P151.the number of component loadingsthe chordwise and spanwise tablescorresponding to the body upwashloading table CPBUPW, in units ofpercent of local chord and percentof local span, respectively,the chordwise and spanwise tablescorresponding to the body buoyancyloading CPBODL, in units of percentof local chord and percent oflocal span, respectively.

SUBROUTINESCALLED: CPARB, CPINIR, CPNACI

PURPOSE;

METHOD:

USE:

48

Function CPINTR

This program interpolates linearly in chordwise and spanwise directions for pressuredistributions not defined in COMMON blocks.

Chordwise linear interpolation is used firstfor two span stations bracketing the spanstation of interest; then, linear spanwiseinterpolation is used.

CP = CPINTR (XF, YF, X, Y, CP, NX, NY,

NXMAX, NYMAX)

INPUT:

PRINCIPALVARIABLES:

XFYF

XY

CP

the chordwise and spanwise coordi-nates of the point on the plan-form for which pressure coefficientis to be found, in fractions oflocal chord and of semispan, re-spectively.tables of chordwise and spanwiselocations at which pressure coef-ficient CP is defined. NX and NYvalues, respectively, are definedand NXBAX and NYMAX, respectively,are the maximum values of NX and NY.a two-dimensional array of pressurecoefficients.

CPINTR interpolated value of pressurecoefficient.

PURPOSE:

METHOD:

USE:

INPUT:

Function CPNACI

To interpolate linearly both chordwise andspanwise for lift pressures due to nacellesthat are defined in COMMON. The chordwiselocations at which nacelle pressures aredefined vary from span station to spanstation.

The span stations bracketing the" desiredspan station are located first. Linear in-terpolation chordwise is completed at thesetwo span stations for the desired chordwiselocation, and finally, spanwise interpolationis carried out at the desired chordwiselocation.

CP = CPNACI (XF, YF)

XFYF

chordwise and spanwise locationson the wing planform in fractionsof local chord and semispan, re-spectively.

In addition, the nacelle pressure field CPand the spanwise and chordwise locations atwhich it is defined, Y and X, are defined byCOMMON NPF.

PRINCIPAL

49

VARIABLES: CP a two-dimensional table of nacellepressure field defined in theanalysis program.

CPWACI interpolated value of the nacellepressure coefficient.

X a two-dimensional table of chord-wise locations corresponding on aone-to-one basis with the CP table.

Y a one-dimensional table of semispanstations corresponding to the span-wise variations of both X and CP.

PURPOSE:

METHOD:

USE:

INPUT:

Function CPTDEF

To interpolate linearly both chordwise andspanwise for pressure coefficient due to wingthickness and defined in COMMON.

Linear interpolation is carried out chordwiseat the two span stations bracketing the de-sired span station, and is followed bylinear spanwise interpolation.

CPT = CPTDEF (XF, YF)

XFYF

chordwise and spanwise stations onthe wing planform in fractions oflocal chord and semispan, respect-ively.

In addition, the wing thickness pressuresare defined in a two-dimensional array CPTin COMMON block PLIM; the chordwise locationsX and spanwise locations Y corresponding tothe elements in CPT are also defined inCOMMON.

PRINCIPALVARIABLES: All defined above.

PURPOSE:

METHOD:

Subroutine JLTIME

To print .out time since job began executionand to print out the time increment sincethe immediately preceding call to thissubroutine.

Interrogate the system timing subroutineSECOND.

50

USE:

INPUT:

OUTPUT:

CALL JLTIME

None

Time .increment and time mentioned above,both in decimal seconds.

SUBROUTINECALLED: SECOND

PURPOSE:

HETHOD:

Program P151

To read input for the wing design and optimizationmodule; to calculate the flat wing loading; and toset normalizing factors for component loadings 1-10so that their lift coefficients will beapproximately 1.0.

The initial part of P151 reads the input data (setup by the wing design interface in the geometrymodule) and writes it out according to the printcode selected in the input. The wing grid systemis also established (in subroutine TRNSFM). Then(if the RESTART feature is not being used), theflat wing solution for the planform is calculated.

The method of the flat wing solution is essentiallythe same as described for the lift analysis module(using the equations given in the theory document,part 1), except that only the wing is present (nofuselage, nacelles, etc). The wing is scanned fromfront to back and centerline to right hand wingtip, computing the pressure coefficients (CP) forall field point elements (LSTAH, NSTAB). The 9-point smoothing equation is applied after allpressure coefficients are calculated.

The lifting pressure distribution is calculatedover the surface of the wing to obtain liftcoefficient (SCL9) , drag coefficient (SCD9) ,dCi/dCL (DCMCL) and drag-due-to-lift factor (KF) ,based on input reference geometry.

USE:

For the given planform, normalizing factors (arrayFL0AD) are then calculated which will produce alift coefficient of approximately unity when usedwith each of the analytically defined basicloadings (1-10) in program P91615.


51

INPUT:

SUBROUTINESCALLED:

See User's Manual

TRANSFM, M A X M I N , REGRID, JLTIHE

PURPOSE:

METHOD:

USE:

INPUT:

OUTPUT:

Subroutine MAXMIN

To identify and print both the maximum andthe minimum elements in a two-dimensionalarray.

Standard FORTRAN library subroutines.

CALL MAXHIN (A, NX, NY, NXMAX, NYNAX)

A a two-dimensional array with maxi-mum dimensions NXMAX and NYMAXcontaining (NX) (NY) values to besearched for maximum and minimum.

THEMAX The maximum element of ATHEMIN The minimum element of A.

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine REGRID

To define grid system data when the RESTARToption is used.

When the RESTART option is used, all basicloading data is input from cards (or tape)and grid system calculations normally made,(which will be needed) are bypassed.REGRID sets up the appropriate arrays, whichinclude the wing chord at each of the span-wise calculation stations, and the per centchord and per cent wing length associatedwith each grid element along those spanwisestations.

CALL REGRID

COMMON block BLOCK1 is used to input adefinition of the wing planform and theassociated parameters required to definethe Hach box grid system.

52

Subroutine TRNSFM

PURPOSE:

METHOD:

USE:

INPUT:

To convert input data to program units andwing grid system.

set up

The wing is represented in the program by a set ofrectilinear elements, with the number of semi-spanelement rows given by input TN0N. TRNSFMinterpolates the planform at the centerline of eachelement row to define the leading edge and trailingedge values, converts them to program scale (usingRATIP = Ywing tip*BETA/TN0N), and stores them inarrays TXLE and TXTE. Special values XLE0 and XTE0define the wing centerline leading edge andtrailing edge.

If the parabolic apex option is selected in theinput (YSN00TX).), the wing leading edge out toYSNP0T is altered to a parabolic shape.

CALL TRNSFM

A definition of the wing planform in physical unitsis passed to TRNSFH by COMMON block. BLOCK1 andblock SNOOT.

SUBROUTINESCALLED: TBLU1

PURPOSE:

METHOD:

OVERLAY (SDA, 10, 2)Program P91615

To calculate the aerodynamic characteristics of aspecified lift loading and the camber surfacerequired to support it. Both component loadingsand combinations of component loadings are handled.If requested, all data for the RESTART option arepunched in this program.

Program P91615 solves for the camber surfacerequired to support a specified loading and theassociated force coefficients, using the equationsgiven in the thepry document (part 1). The programis actually used in two ways:

1) To calculate the force coefficients andinterference drag characteristics of a set ofbasic loadings.

2) To calculate the camber surface for an optimumcombination of loadings.

53

The program code used to define the usage of P91615is K0PTI. If K0PTI is greater than the number ofbasic loadings used, then option (2) above isemployed.

Option,!!).:

In the calculation of the camber surface and force coefficients,a series of semi-span stations are selected in the program input(TJBYS). The program then picks a loading, calculates therequired surface slopes for all elements at each TJBYS station,and integrates the slope distribution to obtain the camberline.In these calculations, each element along TJBYS is identified bythe nomenclature LSTAB (X) and NSTAR (3 ), as described in thetheory document. y

After the camberlines and sectional force coefficients of allspanwise stations have been computed, the characteristics areintegrated spanwise to obtain lift coefficient (CL), dragcoefficient (CD) , and pitching moment coefficient (CMAPEX). Theseare converted to input reference geometry basis and become CLR andCDR, lift and drag coefficients. The pitching moment coefficientis adjusted to the value at zero lift, and becomes CM0R. Drag-due-to-lift factor is labeled KE = CDE/(CLR)2. The interferencedrag coefficients are stored in array GDI.

After all calculations are completed for a given loading, theforce coefficients are stored in array TDRAG, and the processrepeated until all loadings have been used.

The force coefficients and interference drag coefficients of allloadings are then converted to the component and interferenceforms used in the matrix solution described in the theorydocument, and stored in common blocks to be passed to programOPTIMUM.

Finally, the RESTART data is written onto tape 3, and also punchedinto cards, if requested. These data consist of all component andinterference drag terms, the configuration-dependent loadings (ifused), and grid system data calculated by P91615.

Option (2) :

If option 2 was selected, involving .the calculation of the wingshape for an optimum combination of loadings, the calculationsequence is the same as if a basic loading was being used.However, the interference characteristics are not required. Theresulting camber surface is stored in common block/CAMBER/ in thefollowing form:

TPCT percent chord array, N0PCT values.

54

PYB2TZ0RD (X,y)IFZC

semi-span array, JBYMAXI values,camber surface 2/C values, in per cent.1, to denote 3/C in per cent.

The camber surface will also be punched into cards,in the program input.

if requested

USE:

INPUT:

SUBROUTINESCALLED:


All input is handled by COMMON blocks, whichpass the required data from P151.

CDHONN, CPDEF, CPINTR, CPNACI, CPTDEF,HEADER, JLTIME, SH00TH3, TBLU1

PURPOSE;

METHOD:

USE:

INPUT:

PRINCIPALVARIABLES:

Function CDWONN

To calculate the axial force acting onnacelles due to the wing-lift flow-field.

The wing lower surface lifting pressures areprojected downward in a vertical plane andaft along Mach lines to the nacelle locationswhere their product with nacelle incrementalfrontal area is numerically integrated toproduce a nacelle axial force.

CDN = CDWONN (K0PT)

K0PT component loading index.

In addition, wing planform information ispassed to CDWONN by COMMON block BLOCK 1and nacelle geometry is passed by blockBLOCK11.

CPTERM wing lower surface pressure coef-ficient due to wing lift only.

XLEN longitudinal coordinates of theXTEN wing leading and trailing edges atCRDN the nacelle span station, and the

corresponding wing chord.RNAC two-dimensional arrays definingXNAC nacelle radius as a function of

nacelle longitudinal station.The first parameter is the nacellenumber index.

XYZ a two-dimensional array specifyingthe coordinates of each of the

55

SOBBODTINECAL1ED:

PORPOSE:

METHOD:

OSE:

INPUT:

OOTPDT:

CPDEP

nacelles' forward-most point. Thefirst parameter is the nacellenumber index, and the second para-meter defines the coordinate beingreferenced - i.e., first value is X,second is Y, and third iz Z.

Subroutine HEADER

To write out loading number and caseidentification.

Standard FORTRAN statements.

CALL HEADER(K0PT)

K0PT component loading index.

In addition, the loading number index,loading name, and case identification arepassed via COSHON statements.

Titling information for each componentloading prior to its aerodynamic and camberanalysis.

PORPOSE;

METHOD:

Subroutine SMOOTHS

To apply 3-point smoothing to a selectedrange of elements within a one-dimensionalarray.

Each element to be smoothed is replacedaccording to the following algorithum:

where i-1 and yi+l are the immediateneighbors of yi before smoothing. If ^is the first element in the array to besmoothed, then

1,

and if is the last,

+ 2Yi)

56

DSE:

INPDT:

CALL S M O O T H 3 ( A , IFIRST, ILAST, N, N A R R A Y )

A the one-dimensional array of datato be smoothed.

IFIRST first and last elements in A to beILAST smoothed. All elements between

will be smoothed.N the number of times the smoothing

algorithum is to be applied,NARRAY the maximum number of elements in A.

PURPOSE:

METHOD:

OVERLAY (SDA, 10, 3.)Program OPTIMUM

To define various optimum combinations of liftloadings in terms of their load strength factorsA. .

Lagrange's method of undermined multipliers (asdescribed in Part I: Theory), as a function of theaerodynamic characteristics of each of thecomponent loadings and their mutual interferences.In program OPTIMUM, the DO loop on statement 610(index ILOOP) is used twice only if a constraint onpitching moment coefficient is used. For ILOOP =1, program OPTIMUM produces a solution for minimumdrag with only a lift constraint; 21 solutions ofthe drag-due-to-lift factor (KE) and zero liftpitching moment coefficient (CMO) defining thedesign "bracket" plot; and if requested, a solutionfor minimum drag with lift coefficient and wingupper surface pressure constraints. If the lattersolution is satisfied by the first solution, thelatter is set egual to'the first. For ILOOP = 2,program OPTIMUM adds a constraint on pitchingmoment coefficient at zero lift to both thesolution with lift coefficient constraint and thesolution with lift and pressure constraints.

Within the ILOOP loop, the left-hand-side solutionmatrix AMAT and the right-hand-side solution matrixBMAT are calculated first, corresponding to figure4.4-4 of the theory document (part I). The left-hand-side matrix is stored in ATEMP formultiplication with the solution as a test of itsaccuracy; this multiplication should produce theright-hand-side.

Subroutine MATINV is called to solve for the loadstrength factors A^^ and the Lagrange multipliers,corresponding to the lef t-haoid-side column matrix

57

in figure 3.4-3 of the theory document. Thesolution load strength factors \ are stored in twoarrays - the AI array so that the current solutionis defined in the wing lifting pressure subroutineCPDEF, and in the TAI array, so that the solutionwill be defined for program P91615 after programOPTIMUM has been exited. The array TAI hascapacity for four sets of load strength factors(under IDUH), corresponding to the four types ofavailable solutions as follows:

Pitching WingIDOM Lift Moment Pressure

Constraint Constraint Constraint(s)

1• yes no no

2 yes yes no

3 yes no yes

4 yes yes yes

Lift coefficient CLSOL, drag coefficient CDSOL, andpitching moment coefficient CMOS are computed inprogram units from the load strength factors andthe aerodynamic coefficients of the componentloadings. These parameters are then converted tothe input reference geometry basis, CLR, CDR, andCMOB, respectively. Values of KE and CMO fromprevious solutions (if any) for IDDM = 4 areshifted one location toward the rear of the"bucket" plot arrays CKE and CM8ERO, and thecurrent solution data are stored in these arrays.

The wing upper surface pressure coefficient CPUS iscalculated and compared with the user-defined uppersurface limiting pressure CPLIM everywhere on theplanform, and the minimum value of the differenceCPMIN = (CPUS-CPLIM) is identified, along with itsplanform location. This completes the solutioncorresponding to IDUM = 1 above.

Then, if ILOOP = 1 and if no pressure constraintshave been applied, values of KE and CMO aregenerated by the DO loop on 560 for the "bucket"plot. This solution parallels the one justdescribed, except that a constraint on designpitching moment coefficient at zero lift CMOD is

58

DSE:

INPUT:

PRINCIPALVARIABLES:

added and is varied through 21 values. The rangeof values of CHOD depends on design liftcoefficient CLD2IN, and is centered on the pitchingmoment coefficient corresponding to the solutionfor IDUM = 1, if available, or on zero. Values ofCHOD are truncated for plotting convenience.

After the bucket plot data are generated andstored, program OPTIMUM tests to see if pressureconstraints on the wing upper surface have beenreguested and whether they are necessary, ifreguested. If both tests are positive, then a loopto statement 10 is used to apply a constraint onwing lifting pressure at the planform location ofCPMIN. This loop is within the loop on 560 (index= ILOOP). The wing lifting pressure coefficientCPLMAX is calculated which will provide a wingupper surface pressure coefficient CPUS egual tothe limit pressure coefficient CPLIM, and theconstraint on lifting pressure is set to 95% ofCPLMAX to provide a small margin so thatimmediately adjacent planform locations do notexceed the limit by a trivial amount. This innerloop to statement 10 (not a DO loop) has indexNCPCON, the number of pressure coefficientconstraints, and halts when either:

(1) The wing upper surface pressure satisfies theuser-defined limiting pressures, or

(2) the number of solution constraints of alltypes is egual to the number of componentloadings.

In the latter case, a note is printed and the \for the last cycle of the loop on NCPCON areretained in TAI.

For ILOOP =2, a pitching moment constraint isadded to the solution, and both lift coefficientand pressure limiting constraints function as theydid for ILOOP =1. The bucket plot calculationsare omitted.


A.ll input is by means of COMMON blocks.

AIAMATBMATCDIJ

load strength factor \left-hand-side solution matrixright-hand-side solution matrixinterference drag coefficient

59

OUTPUT;

CDSOL solution drag coefficientCDWON interference drag coefficient of

wing lift acting on nacelles,CLDEIN design lift coefficientCLI the ith component lift coefficientCPBODL lifting pressure coefficient due

to unsymmetric body volumedistribution

CPBODU body pressure coefficient actingon the wing upper surface

CPBUPW lifting pressure coefficient dueto the body upwash loading

CPLIMIT wing upper surface limit pressurecoefficient (on input table)

CPNAC wing lifting pressures due tonacelles

NCMAX maximum number of solution con-straints

NCPCON number of pressure coefficientconstraints

NLCON number of direct solution loadingconstraints due to use of configu-ration-dependent loadings

OPTION integer array controlling extentof four types of solutions

TAI up to four sets of load strengthfactors A£» corresponding to thefour types of solutions.

TBETAY stored parameters which define aTDXM solution lifting pressure con-CHORDT straint, namely, spanwise locationCPLMX chordwise location, local chord,

and allowable lifting pressurecoefficient, respectively.

USEBOY a logical flag indicating use ofbody buoyancy loading if true

USEBUP a logical flag indicating use ofbody upwash loading if true

USECKC a logical flag indicating use ofpitching moment constraint if true

USECPL a logical flag indicating use ofwing upper surface pressurelimiting if true

USEOPT a logical flag indicating use ofwing thickness pressures if true

USENAC a logical flag indicating use ofnacelle buoyancy loading if true

Essential output is the set of up to four solutiondefinitions in terms of the loading strengthfactors AJ/ These are passed by COMMON blocks backto the camber surface calculation overlay, OVERLAY

60

SUBROUTINESCALLED:

(SDA, 10, 2). In addition, varying amounts ofinformation about the solutions are printed,depending on the choice of the print controlparameter. These are described in more detail forthe example case in the User's Manual, part 2.

CPDEF, CPINTE, CPNACI, CPTDEF, MATINV

PURPOSE:

METHOD:

USE:

Subroutine MATINV

To solve a set of linear, simultaneous equations.This is a NASA-LRC library subroutine.

See LRC library.

CALL MATINV (A, N, B, M, DETERM,' IPIVOT,INDEX, NMAX, ISCALE)

61

2.6 LIFT ANALYSIS MODULE

The lift analysis program is primacy overlay 7. The program isdivided into separate elements to read input, transform input intoprogram units, and perform the lifting pressure calculations asshown schematically in figure 2.6-1.

The graphics displays are called in program FINISH.

PURPOSE:

METHOD:

Program TEA201

Primary level of lift analysis module

TEA201 sets up the calculation seguence for thedrag-due-to-lift analysis program. The calculationloops are:

Dp 50 JDp

DP UO MLIMT

DP 30 JCALP

Mach number loop, repeated foreach Mach number.

Pressure limiting loop. LIMITangles of attack, if limitingreguested.

Canard angle of attack loop.Repeated for each canardalpha, if canard is present.

OSE:

INPUT:

SUBROUTINESCALLED:

CALL OVERLAY (SDA, 7, o, 0)

See user's manual.

RCALC

PURPOSE

METHOD:

USE:

INPUT:

62

Subroutine DUBINT

To perform double interpolation in array

Given a two-dimensional array, DUBINT performsdouble linear interpolation for an answer at aspecified location in array.

CALL DDBINT (11, Y1, TX, TY, NX, NY, TBL, MX, MY,ANS)

X1Y 1

X locationY location

EC

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CO «

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c3 ~4= 3

'C Q.

pi i-Z W ^-»

O ST8

HiCC enO =5

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Oi

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I

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NUj<t=>CO

63

SUBROUTINESCALLED:

TXTYTBLMX, MYANS

None

X array, NX valuesY Array, NY valuesTable being interpolatedSize of TBL in TBL DIMENSION statementInterpolated answer at Xl, Y1

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine GETR

To calculate influence factor for specified gridelement.

Given an element located in the forecone from aselected field point element, GETR provides thecorresponding influence factor. (The influencefactor equation is discussed in the theorydocument, part 1).

CALL GETR (LSTAB, LVAR, NDIF, R)

LSTAR Field point elementLVAR Specified grid elementNDIF INSTAR - N|R Influence factor


PURPOSE:

METHOD:

USE:

INPUT:

Subroutine GGRID

To define leading edge and trailing edge data forgrid system for specified semi-span element row.

Given a wing semi-span station, GGRID defines theleading edge and trailing X values, thecorresponding grid elements, and the associatedelement fractions. GGRID is used for wing, canardor horizontal tail.

CALL GGPID (JBY, XLE, XTE, LLE, LIE, ALE, ATE,NK)

JBY Semi-span element rowXLE, XTE Leading and trailing edge X-locations

of planform at JBY.LLE, LTE Grid elements corresponding to XLE,

XTE.

64

ALE, ATE Fractions of elements defining plan-form at LLE, LTE.

NK Code to identify configuration component1 = Canard2 = Hing3 = Horizontal tail

SUBROUTINESCALLED:

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

None

Subroutine RCALC

To calculate a standard set of influence factors

The influence factors used in the lift analysisprogram are a function only of the relativeposition of the field point element and theinfluencing element. RCALC is used to precalculatea standard set of influence factors for use in theprogram to reduce computer time associated withrepeated calculations. The factors are stored inarray TRSAVE.

CALL RCALC

None

None

PURPOSE:

METHOD:

Program FUSLGE

To calculate upvash field of fuselage and tocalculate isolated fuselage force coefficients.

Fuselage is used to calculate the wing-fuselageintersection (subroutine INTSEC) , then to calculatethe isolated fuselage lift distribution and forcecoefficients using slender body theory, and then tocalculate the fuselage upwash field acting in theplane of the wing, canard, or horizontal tail.

The eguations used in the fuselage liftdistribution and upwash field calculations aregiven in the theory document (part 1). Thefuselage forces in the presence of the wingdownwash field are later repeated in subroutineFUSCF under overlay (7,5). The upwash field ofcanard, wing, or horizontal tail is defined by an

65

array of upwasb value at specified chord and semi-span percentages:

% ChordSemi-spanfractionUpwash angleUpwash angleper deg. angleof attack

CANAED

TXUPHTYCCW

TUPCCTDPCF

WING

TXPWTYUPW

TUPWCTUPHF

TAIL

TXUPWTYHTW

TUPHCTUPHF

USE:

INPUT:

SUBROUTINESCALLED:

The upwash angle calculations are performedin subroutine UPWASH.


Geometry definition contained in common blocks.MLIMT = loop index variable from (7,0) overlay.

I NTS EC, UPWASH

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine INTSEC

To locate wing-fuselage intersection

If input SYMM is less than zero, then the analysisprogram is to solve for the wing-fuselageintersection in order to define the exposed and"carry-over" wing pieces. INTSEC selects eachpercent chord line of the wing camber surfacedefinition and locates the intersection betweenwing and fuselage. The fuselage area distributionis considered to be made up of circular cross-sections in the intersection calculations. Theresultant intersection is stored in commonblock/WBINT/, with X, Y, and % values in arrays WX,WY, and W8.

CALL INTSEC.

Configuration geometry contained in commonblocks.

TBLU1

66

Subroutine U P H A S H

PDHPOSE:

HETHOD:

USE:

INPDT:

SUBROUTINESCALLED:

To calculate fuselage upwash

UPBASH calculates fuselage upwash angle in theplane of the canard, wing, or horizontal tail,using the slender body equations discussed in thetheory document (part 1). Upwash angles arecomputed for a series of percent chord values atselected semi-span stations.

CALL UPHASH (Y , DELX, I, L)

Configuration geometry contained in common blocks,plus:

Y semi-span y stationI span storage index for upwash arrayL variable defining component

1= canard2= wing3= tail

TBLU1

PURPOSE:

METHOD:

Program WING

To calculate lifting pressure distribution on wingor canard.

A schematic of WING is shown in figure 2.6-2.

The equations used in calculation of the wing orcanard lifting pressures are given in the theorydocument (part 1). The program scans thewing/canard grid system from front to back (Dp 470)and from the centerline to right hand wing tip (D0450), locating field point elements on the wing orcanard. When a field point element. (LSTAR, NSTAB)is located, the program (D# 200) computes theupstream influence of elements located in the Machforecone from LSTAH, NSTAB. The local pressurecoefficient (CP) is then computed, with thefuselage upwash added to the local surface slope toobtain the effective element angle of attack. Ifthe field point element is located inside the side-6f-fuselage station, the element angle of attack isset to zero. (Either of the two pressurecoefficient smoothing options may be used in thesecalculations, controlled by input variable SM0G0.)

67

1Calculation oflifting pressuresat LSTAR, NSTAR

1

WING7,2

, I ,P91611

, I ,GETNCP

IGGRID

, I ,GETR

ICKLIM

I ,SMOOTH

ICPTAB

, I ,CANPRES

I ,HUPWSH

I ,WONAC

Slopes for grid system

Nacelle pressure signature

Planform definition'(grid system)

Influence factors

Limiting pressure check

Pressure coefficient smoothing

Lifting pressure tabulation

Canard pressure integration

Downwash on horizontal tail

Wing-on-nacelle term

FIGURE 2.6-2.-PROGRAM WING SCHEMA TIC

68

USE:

INPUT:

SUBROUTINESCALLED:

After CP is calculated, pressure limiting isapplied if input LIMIT is greater than zero, usingsubroutine CKLIM.

After all pressure coefficients are calculated,they are smoothed {DP 630) and integrated over theconfiguration surface to get lift, drag, andpitching moment. At the same time, the localnacelle pressure coefficients (CPNAC) andasymmetric fuselage volume pressure coefficients(CPASYM) are superimposed. Pressure coeffficientsare applied to the wing slopes in the exposed wingarea portion, and to the fuselage slopes interiorto the side-of-fuselage station.

Corresponding calculations and summations arecarried on simultaneously for the flat wing at 1degree angle of attack. The interference drag termof flat wing pressure coefficients on the camberedwing slopes is also computed. Separate summationscarry the nacelle drag, lift, and pitching momentand the configuration streamwise and spanwise liftdistributions.

The wing pressure coefficient arrays (TWCP andTWCPF) are then interpolated over the wing planformfor the output pressure summary (subroutine CPTAB).The canard lift, whose direct lift summation hasbeen kept separate from the wing, is totaled insubroutine CANPBES.

The downwash due to the wing/canard combinationacting in the plane of the horizontal tail is thencomputed in subroutine HOPMSH. The effect of thewing lifting pressures acting on the nacelle areadistribution is computed in subroutine W0NAC.

Program HING is called by two loops in the 7,0level: the canard angle of attack loop and thepressure limiting angle of attack loop. Bothresult in changes to the wing/canard angle ofattack distribution that cannot be handled bysuperposition,

CALL 0VEHLAI (SDA, 7, 2, 0)

Configuration data in common blocks.

See schematic, figure 2,6-2,

69

PURPOSE:

METHOD:

OSE:

INPUT:

SUBROUTINESCALLED:

Subroutine CANPRES

To sum pressure distributions over canard for lift,drag, and pitching moment.

The canard pressure distributions are calculated inprogram WING, and stored in arrays TCCP (at inputcanard alpha) and TCCPF (per degree alpha).CANPRES integrates these to get lift, drag, andpitching moment. Drag is computed by applying thelifting pressure to the exposed canard slopes orthe fuselage slopes, as appropriate.

CALL CANPRES

Configuration data in common blocks.

GGRID, TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine CKLIM

Checks to see if calculated pressure coefficientsviolate limiting pressure coefficient.

The sum of the wing upper surface lifting pressurecoefficient (-.5* calculated lifting pressurecoefficient) plus the wing thickness pressure plusthe fuselage pressure acting on the wing uppersurface is checked against the limiting pressurecoefficient. If the summed value, CPCHK, is morenegative than the limit, the computed value isreset.

CALL CKLIM (YFR, XPC, CP, CPLIMT, PTEST, CPT)

Pressure coefficient arrays in common blocks, plus:

SUBROUTINESCALLED:

YFRXPCCPCPLIMT

PTEST

CPT

DUBINT

semi-span wing stationpercent chordcalculated lifting pressure coefficientlimiting upper surface pressurecoefficientindicator variable showing limitingapplicationthickness pressure coefficient

70

Subroutine CPTAB

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

To interpolate wing pressure arrays for output

The wing lifting pressure distributions for thegrid system are computed in HING. CPTAB is used tointerpolate the grid pressure distributions foreach semi-span row at selected per cent chordvalues. The interpolated pressure coefficients arestored in arrays VAR (basic angle of attack) andVAR1 (flat plate solution per degree alpha).

Call CPTAB

Configuration data and pressure coefficients incommon blocks.

GGRID, TBLU1

PURPOSE:

HETHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine GETNCP

To interpolate a nacelle pressure signature at agiven wing semi-span station, for use incalculating nacelle-on-wing interference drag.

Same as described for subroutine GETNCP for thenear-field wave drag program.

CALL GETNCP (YB2)

YB2 wing semi-span fraction •

None

PURPOSE:

METHOD

USE:

INPUT:

Subroutine GETUP

To perform double interpolation for fuselage upwashangle

GETUP double-interpolates linearly for fuselageupwash angle in arrays TUPWC (upwash at basicfuselage incidence) and TUPWF (upwash per degreefuselage alpha).

CALL GETUP (XPC, YF8, UPC, UPF)

XPCYFR

per cent chordsemi-span fraction

71

UPC,OFF upwash angles, radians


PURPOSE:

HETHOD:

Subroutine HUPWSH

To compute wing/canard downwash

HUPHSH is used to compute the local downwash actingalong the fuselage centerline and in the plane ofthe horizontal tail. The fuselage asymoetriclifting pressure distribution (if any) is includedin the wing lifting pressure definition.

The computed downwash is stored in arrays THWSHC(basic angle of attack) and THHSHF (per degree) forthe' horizontal tail; the arrays for the fuselageare BX (length fraction), BCC (downwash angle forbasic angle of attack) and BCF (per degree).

USE:

INPUT:

CALL HUPHSH

Configuration geometry andin common blocks

pressure distributions

SUBROUTINESCALLED: GGRID, GETR, DUBINT, TBLU1

PURPOSE;

METHOD:

Subroutine P91611

To calculate local wing slopes for grid system

Subroutine P91611 interpolates the wing cambersurface definition for the streamwise slopes of thewing grid system. Interpolation is linear spanwisealong constant per cent chord lines, followed byguadratic chordwise. The resultant slopes arestored in array TD8DX-.

If wing twist tables or trailing edge flaps areinput, the slopes are incremented by theappropriate slopes. Also, the grid element arraycontaining the wing-fuselage intersection (INTN) isidentified together with the correspondingfractional element (TNFR) .

If the configuration angle of attack is not zero,as may be the case with limiting pressurecalculations, all slopes are incremented by alpha.

72

OSE:

INPUT:

SUBROUTINESCALLED:

If input WHUP =1.0, the camber surface slopes areall zeroed, (This feature is used to generate thewing loading due to fuselage upwash only).

CALL P91611

Configuration geometry contained in common blocks

GGRID, TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

AREA9

SUBROUTINESCALLED:

Subroutine

To smooth wing pressure coefficients andarea

sum wing

SH0J?TH is called by program WING after all wingpressure coefficients have been calculated, toremove irregularities in the calculated values.Either a 9 point or 3 point smoothing equation isapplied, depending upon the wing pressurecalculation technique used (discussed in the theory"document, part 1). The wing area is alsocalculated, by summing the areas of the individualelements.

CALL SM0J2TTH (AREA9, SM0G0)

Configuration data contained in common blocks/SM0TTH/, /INDEX/, and pressure data in /PC)2fEF) .

(wing area of right hand wing)

Smoothing technique code

0.= 9 term smoothing1.= 3 term smoothing

None

PURPOSE:

METHOD:

Subroutine H0NAC

To calculate drag of wing lifting pressures actingon nacelle area distribution

W0NAC is used to compute the thjrust or drag forcedue to the wing lifting pressures acting on the

73

USE:

INPUT:

SUBROUTINESCALLED:

nacelle cross-sectional distribution. For thiscalculation, the lifting pressure is broken intoupper and lower surface halves and the proper halfused depending upon whether the nacelles are aboveor below the wing. The pressures are transferredaft along Mach lines from the wing to elementalfrustrums describing the nacelle shape.

The drag increments for both the wing pressuredistribution at basic incidence and per degreealpha are computed.

CALL W0NAC

Configuration geometry and wing pressure fieldcontained in common blocks.

GGRID, TBLU1

PURPOSE

METHOD:

INPUT:

SUBROUTINESCALLED:

Program PUT0UT

To print input data

PUT0UT is used to write the input and pertinentprogram data onto the output file.


Configuration geometry in common blocks

None

PURPOSE:

METHOD:

Program NACPF

To calculate pressure fields acting on the wing dueto nacelles and asymmetric fuselage volume.

This overlay calculates the pressure fields due tonacelles and asymmetric fuselage volume acting onthe wing. A schematic of the overlay is given infigure 2.6-3.

The program initially calculates the asymmetricfuselage pressure distribution by callingsubroutines SEGRT and SPLIT, using the fuselagerepresentation described in the theory document.

74

• Fuselagebuoyancyfield

• Nacellepressurefield

NACPF7.4

SEGRT

MERGE

ICUTOFF

ICOMBINE

Return

Fuselage area representations

Fuselage bouyancy pressures

F(y) function

Pressure signatures

Y stations for nacelle pressure field

Nacelle setup

BODY | F(y) for nacelles

Pressure signatures

Glance option

, Composite pressurefield

FIGURE 2.6-3.-PROGRAM NACPF SCHEMA TIC

75

DSE:

INPUT:

The nacelle pressure field is next calculated. Aseries of semi-span Y stations are selected, andthe composite pressure signature due to allnacelles is computed; first for all nacelles belowthe wing, then for all nacelles above the wing. Ifthere are nacelles both above and below the wing,a single nacelle lifting pressure definition iscalculated in subroutine COMBINE.

The basic program format is the same as the NACPFsubroutine described in the near-field wave dragprogram, except that the nacelle and fuselageinterference terms are not computed in the analysisprogram version. In addition, there is an optionalfeature in the analysis program version to permitcalculation of the nacelle pressure field at a Machnumber other than free stream (to account for localMach number effects, using input TMLJ/C) . Theresulting pressure field is afterwards referencedto free stream dynamic pressure.

The following subroutines associated with NACPF arethe same as those previously described in the near-field wave drag program: COMBINE, CUTJ2FFF, GLANCE,INTPLT, MERGE, NSETUP, 0TRDER, PSIG.


Configuration geometry, Mach number containedin -common blocks.

SUBROUTINESCALLED: See schematic, figure 2.6-3

PURPOSE:

HETBOD:

Subroutine BJ2TDY

To calculate Whitham F (y)revolution

function for body of

Subroutine B0DY is the same as the previouslydescribed B0DY subroutine in the near-field wavedrag module, with two additional provisions:

1) It will compute the F(y) function using the"smooth body" form of the F(y) eguation discussedin reference 4, in addition to the - Stieltjesintegral equation. This provision is controlled byinput FYLB , in the calling statement. (FYLB lessthan zero uses smooth body equation).

76

USE:

INPUT:

2) Linear interpolation may be used (instead ofquadratic) in fairing the body radius distribution.This provision is selected if FYL3 is less thanzero or greater than 9.0.

CALL B0DY (TXB, TRB, TNXB, TNCUT, TTAU, TFTAU,JSTO, FYLB, SHET)

TXB,TRB,

Input body X stations and radiusvalues, TNXB of each.

TNCUT

TTAU,TFTAU,JST0

FYLB

Number of body intervals in F(y)function

Y and F(y) function calculated forbody, JST0 values of each

Calculation method code (see above)

SUBROUTINESUSED: TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Subroutine SEGET

To set up area representations forabove wing fuselage areas

below-wing and

The logic of the below-wing and above-wing fuselagearea representations is described in the theorydocument (Part 1). Subroutine SEGRT computes thesearea distributions using the wing-body intersectiondefinition found in INTSEC, The fuselage isconsidered circular in the calculation of the twoarea distributions, resulting in:

TRABV above-wing radius distributionTRBLJ2FW below-wing radius distribution

Alternatively, SEGRT may use input valuesof fuselage areas (if SYHM = 2.0)

CALL SEGRT

Configuration geometry and wing-fuselageintersection definition contained in common blocks

None

77

Subroutine SPLIT

PURPOSE:

METHOD;

USE:

INPUT;

To calculate asymmetric fuselage volume pressurefield

Subroutine SPLIT is used to calculate the fuselagepressure field acting on the wing, according toinput SYMM. If SYMH=0., the configuration isconsidered to be mid-wing, and the input fuselagedefinition is used to calculate a symmetric (non-lifting) fuselage thickness pressure field. IfSYMM> 1.0, the above-wing and below-wing fuselagearea representations obtained in SEGRT are used tocalculate the respective pressure fields acting onthe wing.

Pressure signatures due to the fuselage arecalculated at the same X and Y stations used forthe fuselage upwash field. The resultant fuselagevolume pressure field is stored in commonblock/CPBASM/:

RXUPWRYUPWPAB0VEPBEL0W

per cent chord arraysemi-span percentagespressure coefficients above wingpressure coefficients below wing

CALL SPLIT


SYMM calculation code

SUBROUTINESCALLED: B0DY, PSIG, TBLU1

PURPOSE:

METHOD:

USE:

78

Subroutine YSETUP

To set updefinition

Y array for nacelle pressure field

YSETUP sets up a series of Y stations located ateach 5 per cent semi-span, plus extra stationslocated immediately inboard and outboard of eachnacelle centerline. Subroutine 0RDER is used tostore the array (TYP) in monotonically increasingfashion.

CALL YSETUP

INPUT:

SUBROUTINESC&LLED:


PRDER

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Program FINISH

To compute fuselage forces in presence of wingdownwash field, add in contribution of horizontaltail, and write out complete configuration forcecoefficient summaries.

The wing/canard lifting pressure distribution andforce coefficients are computed in program WING.Summary data from WING are passed to FINISH bycommon blocks, where the fuselage contribution inthe wing/canard downwash field is calculated(subroutine FUSCF), and the direct effects of thecanard are added in. All coefficients are based oninput reference geometry.

A calculation loop (D0 140) then calculates thecontribution of the horizontal tail at variousinput incidences (in subroutine HTPART), and addsit to the wing-fuselage-canard data.

A summary of the configuration force coefficients,nacelle-on and nacelle-off, is then computed andprinted. This includes lift (XCL) , drag (ST#T andSCDN) and pitching moment (CMA and CMB)coefficients. Corresponding coefficients for theflat wing configuration are printed for reference.

The streamwise lift distribution is then summed andprinted (subroutine STRMH8). If wing liftingpressure coefficients atcoefficients were requested,

specifiedthese are

liftthen

calculated and printed. Finally, thespanwise lift distribution is printed.

CALL (OVERLAY (SDA, 7, 5, 0}

Configuration data in common blocks

FUSCF, SUMIS, HTPART, STRMWa

wing-canard

Subroutine HTPART

PURPOSE: To calculate the horizontal tail liftingdistribution and force coefficients

pressure

METHOD:

USE:

INPUT:

Subroutine HTPART is used to compute liftingpressure distributions on the tail in the presenceof wing-canard downwash. The equations used arethe same as those employed for the wing; the tailis broken into exposed and fuselage-carry-overportions, and fuselage upwash and wing downwashadded to tail alpha for the purposes of computinglift coefficients.

The lifting pressure distributions are summed overthe tail planform to get tail force coefficients,which are then added to the force coefficients ofthe rest of the configuration. These are passedback to FINISH in common blocks,

CALL HTPABT (NH, REPAR)

NH Tail incidence loop indexREFAR Reference area in program units

SUBROUTINESCALLED: GGRID, GETR, DUBINT, TBLU1

PURPOSE:

METHOD:

USE:

Subroutine STBM»£

To sum and print streamwise lift distribution

In STRMWB, the streamwise lift distributions due towing/canard, nacelles, fuselage, and horizontaltail are summed together and printed. Thepresentation is in fraction of total liftcoefficient, so that the final number printed forthe complete configuration is 1.0.

CALL STPMWa (REFAR, SCLN9)

INPUT: REFAR Reference area in program unitsSCLN9 Total lift coefficient

SUBROUTINESCALLED: TBLD1

80

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

To summarizecoefficients

Subroutine SUMI2

and print configuration force

The configuration force coefficients, including theinterference drag terms, are summarized for programFINISH in subroutine SUMIB.

CALL SUMT3(N)

Index variable to identify printoutseries

1= WING2= WING + FUSELAGE3= WING + FUSELAGE * CANARD

None

PURPOSE:

METHOD:

Subroutine FUSCF

To calculate force coefficientspresence of wing downwash field

of fuselage in

FUSCF repeats the slender body fuselage liftcalculations of program FUSLGE, adding the wingdownwash field computed in HUPWSH to the basicfuselage angle of attack. The fuselage is brokeninto segments and the equations given in the theorydocument (Part 1) are used to calculate thefuselage lift. Fuselage drag is computed byapplying the fuselage lift distribution to thelocal mean-line slopes.

Lift for the fuselage at basic incidence and thecorresponding incremental (flat) fuselage at onedegree angle of attack, plus interference dragterms, are all calculated. The results are storedin common blocks /B0DS0L/ and /BFND/:

TBDLCTBDLFCLCND, CLFND

CDCND, CDFNDCMCND, CMFND

basic incidence streamwise liftflat body streamwise lift (1° alpha)lift coefficients of basiq andflat solutionsdrag coefficientspitching moment coefficients

Data for the isolated fuselage.solution (nowing downwash) are also printed for reference.

81

OSE:

INPUT:

SUBROUTINESCALLED:

CALL FUSCF

Configuration geometry contained in commonblocks. Isolated fuselage force datain /B0DSPL/.

TBLU1

PURPOSE:

METHOD:

USE:

INPUT:

SUBROUTINESCALLED:

Program L0AD9

To read input data for lift analysis module

Program L0AD9 reads input data (interface tapewritten by analysis subprogram of geometry module).


See user's manual

None

Program TRNSFM9

PURPOSE To convert input data to program units and set upgrid system

METHOD: The wing, canard, and horizontal tail planforms arerepresented in the analysis program as a set ofrectilinear elements, as described in the theorydocument (Part 1). Given the number of semi-spanelement rows (FN0N) used to define the right-handwing, TRNSFH interpolates the wing planformdefinition at the mid point of each semi-span rowfor leading edge and trailing edge X-value. TheseX values are converted to program scale (by meansof RATIpr= y wing tip * BETA/FNJ2TN) and stored inarrays TXLE and TXTE, with XLEJ7 and XTE0 definingthe wing centerline grid points.

Storage of wing pressure coefficients and surfaceslopes uses a space-conserving technique: Theleading edge of a spanwise row is storedimmediately after the trailing edge of the adjacentinboard row. The index array for the row storageis J2H, which gives the number of elements stored

82

ahead of the leading edge of a selected row. Thesame storage arrangement is used for canard andhorizontal tail, based on indices JSC and J8H.

The factor RATI0 is also used to scale the canardand horizontal tail arrays, as follows:

Canard Tail

Leading edge array TCXLE THXLETrailing edge array TCXTE THXTECenterline leading edge CXLE0 HXTEJ?Centerline trailing edge CXTEP HXTE0

The maximum size of the pressure coefficient arraysfor the right hand wing is 2500 for the wing, 200for the canard, and 500 for the horizontal tail.Also, the maximum X dimension of the configuration,to the most aft point on the wing, is 205 (programunits) . If any of these dimensions are exceeded,TBNSFM rescales the program units by reducing FN0N.

TRNSFH is also used to identify the grid elementsassociated with trailing edge flaps. Since theflap edges will usually not coincide with elementedges, an approximate element array is used torepresent the flaps and the input flap deflectionangles are altered such that the product of flaparea times deflection is the same for the input andthe approximate program definition. The input flaparea is computed in subroutine PHLAP.

USE: CALL OVERLAY (SDA, 7, 9, 0)

INPUT: Configuration geometry read in program L0AD9

SUBROUTINESCALLED: PHLAP, GGRID, TBLU1

83

3.0 REFERENCES

1. Harris, Roy V., Jr.: An Analysis and Correlation of AircraftWave Drag. NASA TM X947, 1964.

2. Craidon, Charlotte: Description of a Digital Computer Programfor Airplane Configuration Plots. NASA TB X-207U, 1970.

3. Anon: United States Standard Atmosphere, 1962. NASA, USAF,0. S. Weather Bureau. D. S. Printing Office, Washington D.C., 1962.

U. Whitham, G. B.: The Flow Pattern of a supersonicProjectile, Coamunications on Pure and Applied Mathematics,Vol. V, No. 3, August 1952, pp. 301-348.

85

APPENDIX A

INTERACTIVE GRAPHICS SUBROUTINES

The graphics subroutines in the design and analysis program aredescribed in this appendix, excepting the LRC standard CRTsoftware routines.

Three general purpose subroutines are described first, followed bythe subroutines associated with the individual modules:

PURPOSE:

METHOD:

USE:

INPUT:

0UTPUT:

SUBROUTINESCALLED:

PURPOSE:

METHOD:

USE:

Subroutine CSCALE

Computes a plot origin and scale factor given anarray of values.If the values in the input array are not egual, LRCsubroutine ASCALE is called to compute an originand scale factor. If the values in the input arrayare egual, the origin is set to that value -.5, andthe scale factor is set to 2.0/length over whichthe data is plotted.CALL CSCALE (ARRAY, S,N,K,DV)

ARRAY = Array of data to be scaled.S = Length over which data will be plotted.N = Number of values in ARRAY.K = Interleave factor. (1=all points).

DY = Number of divisions per inch of paper.

ARRAY (N*K+1) = Plot originARRAY (N*K+1+K) = Plot scale factor

ASCALE

Subroutine SHOWEntry SHOW I

To display an array of floating point valueson the CDC250.LRC subroutines N0TATE and NUMBER are calledto display a variable name, equal sign and anumber of values on the same line. When thedisplay line is complete, the vertical coord-inate of the line is decremented by a presetvalue. Alternate entry point SHOW I is usedfor integer values.

CALL SHOW (A,N,BCD,NC)CALL SHOWI (L,N,BCD,NC)

87

INPUT:

OUTPUT:

SUBROUTINESCALLED:

EXAMPLE:

A Floating point variable or arrayL Integer variable or arrayN Number of values to displayBCD Hollerith label preceding the

first valueNC Number of characters in BCDCOHMON/PBLOK/YOfiGV O R G

Y D E LVDELC HCSTHETAN D

Y coordinate of display lineX coordinate of first value to dis-play. If values to be displayedare negative, the negative signwill be positioned at VORG-CS,VORG+VDEL-CS and VORG+VDEL+VDEL-CSVertical distance between linesHorizontal distance between valuesCharacter heightSpacing between characters (6/7*CH)Angle of display for label and valuesN u m b e r of decimal places to display

COMMON/PBLOK/XJ?RG = Coordinate of first character in BCD

N O T A T E , N U M B E R

R( 1R ( 4

) = 1,25= 6.73

•3.799.50

5.86-3.17

PURPOSE;

METHOD:

USE:

INPUT:

Subroutine SHOWS

To display a label and three floating pointvariables on the CDC 250.LRC subroutines NOTATE and NUMBER are calledto display a Hollerith label and three valueson the same display line. When the line hasbeen displayed, the vertical coordinate ofthe line is decremented by a preset value.

CALL SHOH3 (VI, V2, V3, BCD)

V1 = First variable to displayV2 = Second variable to displayV3 = Third variable to displayBCD = Hollerith label (10 character maximum)

COMMON/PBLOK/

XORG = X coordinate of label

88

YORG = Y coordinate of display lineVORG = X coordinate of V1VDEL = X distance between variables

If negative, the variables aredisplayed at VORG-CS, VORG+VDEL-CSand VORG+VDEL+VDEL-CS

YDEL = Y distance between display lines.CH = Character heightCS = Spacing between characters (6/7*CH)

THETA = Angle of display for label and variablesND = Number of.decimal places to display. ^

SUBROUTINESCALLED:

EXAMPLE:

NOTATE, NUMBER

NAC1 -57.254NAC2 69.874

9.00016.785

5.790-9.103

GEOMETRY M O D U L E

Configuration geometry is displayed and/or edited by programDISGE^M, a secondary overlay in the geometry module.

PURPOSE;METHOD:

USE:

Program DISGEpfM

To display and/or edit configuration geometryA description of the display capabilitypresented in Appendix A of the user's manual.CALL OVERLAY (SDA, 5, 5, 0)

is

PURPOSE:

METHOD:

Subroutine ALTER

To alter the wing camber surface shape to match anew trailing edge definition.The camber definition at each input airfoil isrotated about the airfoil leading edge point untilthe trailing edge point coincides with the newtrailing edge definition. The new camber surfacedefinition is stored in temporary array B20RD

USE: CALL ALTER (2TE)

89

INPUT: ,ZTE = Array of new trailing edge values.COMMON/TEMP/

LECODELECODE

+, 8TE array consists of camber values-, 8TE array consists of camber values

+ the a value of the leading edge

COHMON/HING/TB0RD = Original camber definition

OUTPOT; COMMON/TEMP/B2J2TRD = Altered camber definition

PURPOSE:

METHOD:

USE:

INPUT:

OUTPUT:

Subroutine PLTSIB

To compute the configuration minimum and maximum Xand Y coordinates, and the fuselage minimum andmaximum 2 coordinates, A plot scale factor is alsooutput.

Each configuration component is analyzed as to itscoordinate values. The minimum and maximum valuesare stored in common. If the range of data in theX direction is greater than that in Y, SCALE iscomputed as:

XMAX-XMIN10.0

If the range of data in the Y direction isthan that in X, SCALE is computed as:

YMAX-YMIN7.0

CALL PLTSI8 (SCALE)

All configuration geometry in COMMON,

factor

greater

SCALE = Plot scaleCOHMON/0VL1/XMINXMAXYWINYMAX2MINBMAX

MinimumMaximumMinimumMaximumMinimumMaximum

value of configurationvalue of configurationvalue of configurationvalue of configurationvalue of fuselagevalue of fuselage

90

FAR-FIELD W A V E DRAG MODULE

The graphics subroutine (DIS080) in the far-field wave drag moduleis located in program PUT, overlay (3,6).

Subroutine PUT

PURPOSE: To display area plots and drag summary

METHOD: The CRT is used to display far-field wave dragmodule results as described in the user's manual,Appendix A.

USE CALL DIS080 (S, B, BJ7, C, RC, N)

INPUT: S Array of X valuesB Array of fuselage areasBJ? A r r a y of opt imum fuselage areasC Array of overall configuration areasRC A r r a y of restrained areasN Number of values in input arrays

NEAR-FIELD W A V E D R A G MODULE

The graphics program (DISP916) is called f rom the primary level ofthe near-field wave drag overlay.

Program DISP916+

PURPOSE: To display near-field wave drag module results

METHOD: DISP916 displays summary results described inthe user's manual, Appendix A

USE: CALL OVERLAY (SDA, 6, 3. 0)

IHPUT: Summary data in common blocks

SKIN FRICTION DRAG MODULE

The graphics subroutine (DISP158) in the skin friction module iscalled from subroutine DRAG.

91

POBPOSE:

HETHOD:

USE:

INPUT:

Subroutine DISP158

To display skin friction module results

DISP158 displays summary results described in theuser's manual, Appendix A.

CALL DISP158

Summary data in common blocks

HING DESIGN HODDLE

Display and editing in the wing design module is performed bythree graphics programs called from the primary overlay.

PURPOSE:

METHOD:

USE:

INPUT:

Program BUCKETP

To display drag-due-to-lift bucket plot

BUCKETP is used to display the K versus Cmo plotplus design point solutions described in AppendixA of the user's manual.

CALL J2TVERLAY (SDA, 10, U, 0)

Data in common block/BUCKET/

PURPOSE:

HETHOD:

USE:

-Program SDBUCK-

To permit editing of design point variables

EDBUCK allows user to edit wing design programvariables Cmo, CLD2IN, RESTART, and CJ2fNSTR(1)through CJ?NSTR(U). In addition it allows the userto execute next design case or calculating editeddesign point, as described in Appendix A of theuser's manual.


PURPOSE:

HETHOD:

92

Program ST0TP0P

To permit termination of wing design programcasesST0TP0P allows user to exit from a series of wingdesign cases, as described in Appendix A of the

USE:

user's manual.


LIFT ANALYSIS MODULE

The graphics displays in the analysis module consist of twoovsrlays called from the primary overlay, plus two subroutinescalled from program FINISH.

PURPOSE:

HETBOD:

DSE:

INPUT:

Program DISTHST

To display wing twist and permit editing of twistand several execution codes.DISTWST displays and permits editing of wing twistarray, plus canard angles of attack, SYMM, WHOP,and ANYBOD. The display presentation is describedin Appendix A of the user's manual.


Input variables in common blocks

PURPOSE;

METHOD:

USE:

INPUT:

Program DISUPHS

To display fuselage upwash and wingcoefficient data

pressure

DISUPHS provides display options for calculatedfuselage upwash or wing pressure coefficient data,as described in Appendix A of the user's manual.


Data in common blocks/UPWSH/and/CPBUPW1/.

PURPOSE:

METHOD:

USE:

Subroutine DISTAB

To display analysis module force coefficientsummary and permit editing of horizontal tail angleof attack.

DISTAB provides display of analysis program resultsas described in Appendix A of the user's manual.

CALL DISTAB (NH, HTALP)

93

INPUT: NB Horizontal tail angle of attackloop index

HTALP edited tail alpha

PURPOSE:

METHOD:

USE:

INPUT:

Subroutine EXL0T0P

To display and permit editing of variableswithin DO loops.

EXLJ3J7P displays current values of Mach number,configuration alpha, and canard alpha. Itthen permits editing of the next value tochange within the cycle, as described inAppendix A of the user's manual,

CALL EXL00TP

Configuration data in common blocks

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aerodynamic design and analysis system for … · (geometry module), draw a picture of the...

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