THEORETICAL PREDICTION OF INTERFERENCE LOADING … · INTRODUCTION The computer program described here Is designed to predict aerodynamic interference loadings on aircraft stores

NASA CR-112065-3

THEORETICAL PREDICTION OFINTERFERENCE LOADING

ON AIRCRAFT STORES

PART III - PROGRAMMER'S MANUAL

BY

F. DAN FERNANDES

PREPARED FORNATIONAL AERONAUTICS AND SPACE ADMINISTRATION

LANGLEY RESEARCH CENTERHAMPTON, VIRGINIA 23365

UNDERCONTRACT NUMBER NAS 1-10374

JUNE 1972

GENERAL DYNAMICSElectro Dynamic Division

https://ntrs.nasa.gov/search.jsp?R=19720018373 2018-11-09T02:52:23+00:00Z

NASA CR-112065-3

THEORETICAL PREDICTION OFINTERFERENCE LOADING

ON AIRCRAFT STORES

PART III - PROGRAMMER'S MANUAL

BY

F. DAN FERNANDES

PREPARED FORNATIONAL AERONAUTICS AND SPACE ADMINISTRATION

LANGLEY RESEARCH CENTERHAMPTON, VIRGINIA 23365

UNDERCONTRACT NUMBER NAS1-10374

JUNE 1972

GENERAL DYNAMICSElectro Dynamic Division

P.O. Box 2507, Pomona, California 91766

THEORETICALPREDICTION OF INTERFERENCE LOADING

ON AIRCRAFT STORES; PART III -PROGRAMMER'S MANUAL

SUMMARY

A FORTRAN program is described for predicting interference loading

on aircraft stores. An analysis of the program is presented from a

programmer's point of view, including program organization, subroutine

explanations, and FORTRAN variable definitions. This information

is intended for use in any program modification, extension, or trouble-

shooting efforts. This manual is supplementary to the separately

documented program theory and user information.

ii

CONTENTS

PAGE

SUMMARY ii

LIST OF FIGURES AND TABLES iv

INTRODUCTION 1

REFERENCES 2

PROGRAM ORGANIZATION 3

SUBROUTINE EXPLANATIONS 11

Dual Group 13

Subsonic Group , 26

Supersonic Group 44

VARIABLE DEFINITIONS 67

Dual Group 69

Subsonic Group 72

Supersonic Group 74

APPENDIX A - SHOCK PROGRAM A-l

Program Organization A-l

Subroutine Explanations A-l

IAPPENDIX B - TEST CASES B-li

Program STORLD - subsonic B-l

Program STORLD - supersonic B-2

Program SHOCK B-2

iii

LIST OF FIGURES AND TABLES

FIGURE PAGE

1 Program STORLD Logical Flow 4

2 Program STORLD Communication Network, Subsonic andSupersonic Flow 6

3 Subroutine AIRCFT Communication Network, SubsonicFlow 7

4 Subroutine PARTS Communication Network, SubsonicFlow 8

Subroutine AIRCFT Communication Network, Supersonic

6

7

8

9

10

11

12

13

14

15

16

17

18

A-l

A-2

A-3

Flow

Subroutine PARTS Communication Network, SupersonicFlow

Routine CRSFLW Logical Flow

Routine DISTURB Logical Flow

Routine INFLUN Logical Flow

Routine SLOPE Logical Flow

Routine EQSOL Logical Flow

Routine INTERP Logical Flow

Routine WING Logical Flow (subsonic)

Routine WINGFN Logical Flow (subsonic)

Routine DNWASH Logical Flow

Routine PYLONFN Logical Flow (supersonic)

Routine WING Logical Flow (supersonic)

Routine WINGFN Logical Flow (supersonic)

Program SHOCK Logical Flow

Program SHOCK Communication Network

Routine DETACH Logical Flow

9

10

15

18

20

23

28

31

41

43

53

59

64

66

A-2

A-3

A-10

iv

FIGURE PAGE

B-l Program STORLD - Subsonic, Test Case Input Data B-4

B-2 Program STORLD - Subsonic, Test Case Output Data B-6

B-3 Program STORLD - Supersonic, Test Case Input Data B-12

B-4 Program STORLD - Supersonic, Test Case Output Data B-14

B-5 Program SHOCK - Test Case Input Data B-23

B-6 Program SHOCK - Test Case Output Data B-24

TABLES .

1 Subroutine List for Program STORLD 12

2 Routine DIAFRM 50

3 Common Variable Place of Origin 68

INTRODUCTION

The computer program described here Is designed to predict

aerodynamic interference loadings on aircraft stores. Actually,

three related programs are involved. References 1 and 2 supply the user

information and the technical Information needed by the engineer to

apply these programs. This manual presents the programming details

of the method, intended to allow the programmer to make modifications

to the computer coding. The reader need not be familiar with the

technical and engineering aspects of the program as contained In

References 1 and 2. It is assumed that the reader is familiar with basic

FORTRAN programming techniques. Also, ANSI flowcharting standards

have been used here (Reference 3).

Several possible programming modifications come to mind which

may better adapt the program to the user's particular requirements.

For example, adding a plotting routine would aid in more efficient

output analysis. Also, output (interference coefficients) could be

accumulatively added for stacked runs, and the total outputted at

the end. This would allow efficient separation of the interference

from the different components of the aircraft. Some Intermediate

values may be of special Interest, such as velocity field data or

store load distribution data per unit length; such data may be

printed or punched out for use In other programs. Dimensions may

be decreased to save space or Increased to extend capability.

Unused portions of the program may be removed to save space or time.

Additional error signal print-out may be helpful.

A word of caution on program modifications is required; any

modification, however slight, is not to be taken lightly. A thorough

check-out should be made for each change. This program is very

interdependent. Many variable locations are used more than once to

save space. This increases the possibility of error. The information

contained in this manual should be reviewed thoroughly before any

programming changes are attempted.

This FORTRAN program has been made to run on the Control Data

Corporation 6400 digital computer, using extended FORTRAN, version

2.0. The compiler operates in conjunction with version 1.1 COMPASS

assembly language processor under the control of the SCOPE operating

system, version 3.3. The computer codes are available through COSMIC

(computer software management and information center). Requests should

be directed to "COSMIC, Unlversiry of Georgia, Athens, Georgia, 30601."

REFERENCES

1. Fernandes, F. D., "Theoretical Prediction of Interference Loadingon Aircraft Stores; Part I - Subsonic Flow," NASA CR-112065-1,June 1972.

2. Fernandes, F. D., "Theoretical Prediction of Interference Loadingon Aircraft Stores; Part II - Supersonic Flow," NASA CR-112065-2,June 1972.

3. Chapmln, N., "Flowcharting with the ANSI Standard: A Tutorial,"Computing Surveys, Vol. 2, No. 2, June 1970.

PROGRAM ORGANIZATION

The prediction method consists of two separate main programs,

called STORLD and SHOCK. Program SHOCK is a supplementary program,

used to calculate inputs sometimes required for application of program

STORLD to supersonic flow. The organization of program STORLD will

be presented here; program SHOCK is discussed separately in

APPENDIX A.

There exist two versions of program STORLD (store load), one for

subsonic flow and one for supersonic flow. These two programs are

composed of three groups of subroutines. The first group, referred

to here as the "dual group", is applicable to both subsonic flow and

supersonic flow and is duplicated in the two programs. The second group

is applicable to subsonic flow only, and the third group is applicable

to supersonic flow only. The following discussion is, therefore,

organized by subroutine group rather than by program."

The overall logical flow of program STORLD is presented in

Figure 1. This is a flowchart of the main program itself, which is

very short and serves only to organize the procedure. This procedure

permits run stacking for store location, store geometry, and aircraft

geometry as shown.

The network of communication between program STORLD and its

subroutines is shown in Figure 2 and in the continuation networks

FIGURE 1PROGRAM STORLD LOGICAL FLOW

f START j

IGO = 3

of Figures 3, 4, 5, and 6. Figure 2 shows subroutines AIRCFT

and PARTS with continuation symbols A and B. These two subroutines

serve as an interface between the dual group of subroutines and the

other two groups. Network continuations .A and B are shown in Figures

3 and 4 for the "subsonic" group of subroutines. Network continuations

A and B are shown in Figures 5 and 6 for the "supersonic" group of

subroutines. The purpose of each of the subroutines is presented

in the next section.

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SUBROUTINE EXPLANATIONS

The purpose of each subroutine will now be explained. An attempt

has been made to give enough Information here so that the computer

coding can be examined with some knowledge of what computations are

being performed and how they relate to the total program. Flowcharts

for many subroutines are Included. However, flowcharts are omitted

in cases where they would be trivial, such as for subroutines with

straight-forward flow logic. In these cases, a verbal explanation Is

used. Definitions to key variables are given to help in quick

understanding of the operations In each subroutine. A more extensive

list of variables is given in the next section.

The subroutines for Program STORLD are presented In alphabetical

order in three groups, listed in Table I.

11

TABLE I

Subroutine List1 for Program STORLD

DUAL GROUP (subsonic and supersonic)

1.2.

BODFNCRSFLW

3. DISTURB4. INFLUN5. MATAD6. SLOPE7. STORE8. STRIPFN9. TIMEX10. TITLES

Page13141619212224242525

SUBSONIC GROUP SUPERSONIC GROUP

1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.

AIRCFTCOMPUTEQSOLINTERPMATRIXNOSENOSEFNPARTSPRINTXPYLONFNSTARTSTRIPTHICKVORTEXWINGWINGFN

Page26262729323334353536373738394042

1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.

AIRCFTDIAFRMDIFINDNWASHGENRATLIFTNOSENOSEFNPARTSPRINTXPYLONPYLONFNSTARTSTRIPSWPTHICKWING .WINGFN

Page444551525454555656575758606061626365

12

Dual Group

Subroutine BODFN (body function)

Purpose: to read in nose geometric parameters

Called from: AIRCFT

Calls: SLOPE, NOSEFN

Input: nose data

Output: Computes nose surface slopes through SLOPE; computes nose

source and doublet strengths through NOSEFNj prints all input and

computed data; transforms nose to an equivalent shape to account for

shock effects in supersonic flow.

13

Subroutine CRSFLW (crossflow)

Prupose: To perform operations on the interference velocity field

necessary for computing.store loads.

Called from: INFLUN

Calls: SLOPE

Input: Velocity field, store roll angle.

Output: 1) crossflow angle of attack field in pitch and yaw acting

at store body; 2) crossflow angle of attack field in pitch and yaw acting

on store fins; 3) buoyancy pressure field acting on store body;

4) axial derivitive of body crossflow field; 5) roll velocity field

acting on store fins.

Definitions

K •» index for axial location of field point.UQ, = velocity field due to aircraft angle of attack (U(I=1, 2,3)=

u, v, w),UT = velocity field due to aircraft thickness (U(I=4, 5, 6) =

UT, VT, WT)UA = total velocity field due to aircraftUl, VI, Wl ** velocity field (u, v, w) averaged axially so that

trapezoidal integration of the velocity versus XCcurve gives correct area.

ALZ, ALY = vertical and lateral crossflow angle acting on store body.BZ, BY = vertical and lateral buoyancy parameter acting on store body.WS„ VS = vertical and lateral velocity parameter at store fin root

(skinline)WD, VD = spanwise rate of change of vertical and lateral velocity

parameter from fin root to tip,ARS = roll velocity parameter at fin root,ARD = spanwise rate of change of fin roll velocity parameter from

root to tipALZD, ALYD = axial derivitive of ALZ, ALY.XC = field at axial location In wing coordinates.FTM = maximum fin span from axis to tip, divided by body radius.

14

FIGURE 7ROUTINE CRSFLW LOGICAL FLOW

IN

IUA =

FOR1, NK

K = K

COMPUTEU1, V1, W1FROM UA

COMPUTEALZ, ALYBZ. BYWS VSARSFOR K

WRITEXC, ALY. VS, VD ,BY, ALYD,FOR K = 1, NK

WRITEXC, ALZ, WS, WDBZ, ALZD, ARS, ARDFOR K = 1, NK

ICOMPUTEALZD, ALYDFOR K = 1, NK(CALL SLOPE)

15

Subroutine DISTURB

Purpose: To calculate aircraft interference velocity field acting

at the store over the length of the traverse line.

Called from: STORLD (main program)

Calls: PARTS (through PARTS to WING, PYLON, STRIP, NOSE).

Input: Store traverse line location, computation mode indicators.

Output: Crossflow perturbation velocities, U.

Definitions

UIB

IA

IWFTM

DIAX

XTKNKJ0XX, YY, ZZXP, YP, ZP

interference velocity field (u, v, w, u^, vjif IB = 1, compute velocities at J =1, 4 so thatbuoyancy on store may be computed. IB = 0, computevelocity at J = I1 only (see sketch)if IA = 0, compute velocity at J = I1 and interpolatefrom J = 6, 8 to get J = 1, 4 reducing computing timeby 5/8 (see sketch)number of axial sections at which to write velocitiesmaximum store fin span from axis to tip, divided by bodyradiusstore diameterdistance along traverse line from reference point to fieldpoint (+ = forward)length of traverse lineX indexnumber of axial sections on traverse lineindex of field point location in Y-Z plane (see sketch)store roll anglefield point location in wing coordinatesfield point location in nose coordinates

16

STORE CROSS SECTION SHOWINGFIELD POINT LOCATION AS AFUNCTION OF INDEX J FOR

0 = -45°

YY

6 x

J = 5 x ZZ

SKETCH 1ROUTINE DISTURB

17

FIGURE 8ROUTINE DISTURB LOGICAL FLOW

IN

WRITESTORE

TRAVERSELOCATION

ICOORDINATE

TRANSFORM'SWING - NOSE- STORE

ICHECK

COMPATIBILITYOF

IB. IA. FTM

WRITE/COMPUTATION

MODEIB, IA

FTM. DIA

COMPUTEXX, YY, ZZXP, YP, ZP

EQUATEU (J = 5, 8)

TO U U = 1. 4)

INTERPOLATEU (J = 5, 8)

AND U (J = V)FOR U (J = 1,4)

o- EQUATEU (J = 1, 8)

TOU (J = V)

18

Subroutine INFLUN (influence)

Purpose: to calculate the interference force and moment coefficients

on the store


Calls: CRSFLW

Input: store geometry and aerodynamics, interference crossflow

velocity field

Output: interference force and moment coefficients

Definitions (FORTRAN names noted)

a = angle of attack (ALFW, ALFM)X = distance along traverse line from store CG to reference point

locationC's = force and moment coefficients in pitch and yaw, summed over

store length (CNZ, CNY, CMZ, CMY)NMS = number of store axial sectionsDELX = store section axial length0 = store fin roll angle (ROLL)CR's = C's rotated to 0 orientation (body axis) (CNZR, CNYR,

CMZR, CMYR)XT = traverse length

19

FIGURE 9ROUTINE INFLUN LOGICAL FLOW

IN

ICRSFLW

COMPUTECROSSFLOW

IWRITE

STORE aSTORE 0

X = XSTART

C's

N = 0

N = N + 1

COMPUTEWING - TAIL

DOWNWASH

COMPUTELOAD ATSTORE

SECTION N

INCREMENTC's

X = X JK DELX

20

Subroutine MATAD (matrix addition)

Purpose: add column matrix B to column matrix A

M - W + {•}Called from: PARTS

Calls: (nothing)

Input: A, B

Output: A

Comments: When called from PARTS, B Is the velocity at one field

point produced by one aircraft component (wing, strip, pylon, or nose).

B(I = 1, 6) = u, v, w, UT, VT, WT. B is accumulated in A to get the

total flow velocity. When B is the nose velocity field, (u, w) and

(u , WT) are rotated through the angle ALFNW to transform from nose

coordinates to wing coordinates.

21

Subroutine SLOPE

Purpose: to compute the first derivative of array R versus array X.

Called from: (subsonic program) INTERP; (dual program) BODFN,

CRSFLW.

Calls: (none)

Input: N, X, R:

Output: D, A

Comment: SLOPE curve - fits R versus X with a quadratic, using 3

points at a time, then equates the slope at the middle point to the

analytic derivative of the quadratic at that point. The analytic

derivative at the first and last point of the array is also used.

Coefficients A for only the last 3-point set are returned as output.

If any adjacent values in array X are identical, an error signal

(infinite slope) is printed.

Definitions

N = number of points in arrays X and RX = independent variable arrayR = dependent variable arrayD = first derivitive, dR/dXA = three coefficients in the quadratic equation R = A.XT. +t. A2X + A^H , A , B : writing the above quadratic equation for three

adjacent points and eliminating A-, gives the matrixequation

H ' (A]where FH! « r 2

K = index for grouping arrays R, X, in sets of threeDD = value of the determinant of H

22

FIGURE 10ROUTINE SLOPE LOGICAL FLOW

COMPUTED,A, USING

A STRAIGHTLINE FIT

COMPUTE

(*}

SOLVE,FOR {A}

USINGDETERMINANTS

OUT

0 < K < (N-3)

K = 0

K =; (N-3)

COMPUTE0(1)

COMPUTEDIN)

A3

OUT

23

Subroutine STORE

Purpose: to read in store geometric and aerodynamic properties


Calls: (nothing)

Input: store data

Output: prints all input data; makes input data available to program

through common. Also, computes variables defined below

SETY, SETZ:= store fin roll angle sine and cosine parameters, used

in repeated location of field point for velocity

calculations in DISTURB

XBAR = distance from store section to reference CG divided by reference

diameter

Subroutine STRIPFN (strip function)

Purpose: to read input parameters which define the elementary source

strips used to represent the aircraft thickness envelope (other than

wing and nose thickness). This includes inlets and pylons.

Called from: AIRCFT

Calls: (none)

Input: strip data

Output: Writes all input data

Comment: If Mach number is greater than one, STRIPFN checks for

strip sweep equal to Mach line sweep, and if so, increments the

tangent of the sweep angle by 10%. This is done to avoid error in

subroutine SWP.

24

Subroutine TIMEX

Purpose: to print the expired time used in central processing

(CP time)

Called from: STORLD

Calls: SECOND (a system subroutine)

Input: (none)

Output: print CP time and its increment from the last time called

(in seconds)

Comment: permits easy determination of calculation time taken by

each separate calculation in the program.

Subroutine TITLES

Purpose: to read and write aircraft title, store title, and store

location title


Calls: (none)

Input: mode signals IA, IS, IL

Output: titles are printed

Comments: "lA"is mode signal for aircraft title, "is"for store title,

"lL"for store location title

IA = 2 aircraft title is read and printed

IA = 1 title is printed, not read

IA = 0 title is not read or printed

Similarly for IS and IL

25

Subsonic Group

Subroutine AIRCFT

Purpose: to call the subroutines used to compute the aircraft

representation

Called from: STORLD

Calls: START, COMPUT, WINGFN, PYLONFN, PRINTX, BODFN, STRIPFN

Comment: AIRCFT is an interface subroutine used for calling other

subroutines.

Subroutine COMPUT

Prupose: to perform preliminary computations on the aircraft wing

input data, necessary for representation of the wing by source and

vortex distributions.

Called from: AIRCFT

Calls: (none)

Input: wing input geometry, Mach number

Output: trigonometric functions of the wing section sweep and

dihedral angles; horseshoe vortex locations and control point locations

to represent the wing in compressible flow.

Comment: The Prandtl-Glauert transformation is used to account for

the effects of compressibility.

26

Subroutine EQSOL (equation solver)

Purpose: solves N simultaneous/ linear equations for N unknowns

by the augmented method of matrix inversion

Called from: (subsonic program) WINGFN, PYLONFN, NOSEFN

Calls: (nothing)

Input: H and B of matrix equation

[ H] . {ANS} = f B}

Output: [H] -1, fANS}

Definitions

A : matrix used to augment H ; becomes H by the calculationH : input matrix of coefficients; H "1 is returned in the same

storage location to save spaceIt : row index of H and AP : pivot elementN : number of unknowns ANS («= number of rows and columns in H )

27

FIGURE 11ROUTINE EQSOL LOGICAL FLOW

IN

ISET [A] =

UNIT MATRIX

I = 0

1 = 1 + 1

P = H (I, I)

WRITE•>/ ERROR

SIGNAL

DIVIDE ROWI OF [H]

& [A] BY P

OPERATE ON[H] AND [A]SIMILARLYSUCH THAT

H (I,J) = 0ALL J 4 I

>1 *1

(ANS} = [A] {B}[H] = [A]

11L.

NOW [A] = [H]"1;ORIGINAL HIS REPLACED BYUNIT MATRIX

28

Subroutine INTERP

Purpose: To accurately calculate the lateral velocity induced by a

horseshoe vortex and acting at a field point which is close to the

plane of the vortex.

Called from: WING

Calls: VORTEX, SLOPE

Input: Vortex location and strength; adjacent vortex locations and

strengths, field point location.

Output: Perturbation velocities (u, v, w, UT, VT, w_)

Comment: This subroutine is used to calculate wing-induced velocities

normal to the pylon. The calculation is necessary because of the

close proximity of the pylon to the wing vortices. The input vortex

is divided spanwise into to a number of smaller horseshoe "sub-

vortices," as shown in the sketch. Circulations for these sub-vortices

are taken from a quadratic curve fit through the input vortex and two

adjacent vortices. In this way, the spanwise rate of change of

vorticity is numerically approximated, which permits accurate cal-

culation of spanwise velocity. Since vorticity is not interpolated

chordwise, the vertical and lateral perturbation velocity values do

not have comparable accuracy; however, these are not used in pylon

calculations.

29

i i

~ INPUT VORTEX.— SUB-VORTICES

SKETCH 2ROUTINE INTERP

Definitions

DX, DY, DZX, Y, ZGAM, GAMC

HU, HV, HW

G, GCNDV

coordinate distances between sub-vottex locationsfield point location with origin, at the sub-vortexcirculation strengths of input vortex and two adjacentvorticessub-vortex induced velocities per unit circulationstrengthinterpolated values of GAM and GAMC from curve fitnumber of sub-vortices

30

COMPUTEDX.DY.DZ

INITIAL X,Y,Z

SLOPE

CURVE FITGAM.GAMCVERSUS Y

N = 0

ON = N + 1

X = X - DXY = Y - DYZ = 2 -DZ

VORTEX

COMPUTEHU, HV, HW

FIGURE 12ROUTINE INTERP LOGICAL FLOW

oCOMPUTE

G,GC

INCREMENTVELOCITIES

( OUT )

O31

Subroutine MATRIX

Purpose: to compute the matrix of coefficients which relate the

wing vortex circiulation strengths to the induced velocities at the

wing control points

Called from: WINGFN

Calls: VORTEX

Input: wing control point locations, wing horseshoe vortex geometry

and locations.

Output: coefficient matrix [nj, where

H(I, J) = velocity induced normal to wing at control point I,

by horseshoe vortex J.

Comments: a maximum of 40 horseshoe vortices are used to represent

the left wing. These vortices are mirror-imaged about the Y » 0

plane to represent the right wing. The horseshoe vortex lattice is

distributed chordwise and spanwlse.

Definitions

NU: vortex chordwise indexMU: vortex spanwise indexI : control point chordwise indexJ : control point spanwise indexKC: control point combined indexJC: vortex combined index

32

Subroutine NOSE

Purpose: To compute the perturbation velocities produced by the

nose at a field point.

Called from: PARTS

Calls: (none)

Input: field point location in nose coordinates; locations and

strengths of the nose line singularities.

Output: velocities due to nose thickness and crossflow.

Definitions

UA, VA, WAUC, VC, WCXA, YP, ZP

NSUB 2XBLXUSNASNC

velocities due to nose thicknessvelocities due to nose crossflowfield point location in nose coordinates, with originat nose apex and x-axls the axis of symmetrynumber of nose singularitiesMach function (1 - M2)nose lengthsingularity apex locationssource strengthdoublet strength

33

Subroutine NOSEFN

Purpose: To compute source and doublet strengths used to represent

the aircraft fuselage nose

Called from: BODFN

Calls: EQSOL

Input: nose geometry; Mach number

Output: source and doublet strengths and locations

Comments: A distribution of line sources along the nose axis of

symmetry represents the flow field due to thickness. A similar

distribution of doublets represents the crossflow field. A system

of NBP linear simultaneous equations is used to satisfy the boundary

conditions, and these are solved in EQSOL by matrix inversion to

obtain the singularity strengths.

Definitions

NBPXB, RBDRDXB

XIJ:XBLG, H

SNASNCB

number of body points (input)nose geometry inputslope of RB versus XBapex locations of line source and doubletsaxial termination point of line singularitiesmatrices of coefficients in the matrix equations

line source strengthsline doublet strengthsdistribution of crossflow, taken constant at one degree

34

Subroutine PARTS

Purpose: to sum the velocity field contributed by the various

parts of the aircraft to obtain the total Interference flow field at

each field point.

Called from: DISTURB

Calls: WING, STRIP, NOSE, MATAD

Input: field point location In wing coordinates and nose coordinates

Output: total Interference velocity field at the field point

Comment: PARTS is an interface subprogram used to call other

subprograms.

Subroutine PRINTX

Purpose: To print out the aircraft wing and pylon input parameters

and computed parameters

Called from: AIRCFT

Calls: (none)

35

Subroutine PYLONFN

Purpose: to read pylon location and to compute vortex lattice used

to represent the pylon in the presence of the wing

Called from: AIRCFT

Calls: WING, VORTEX, EOSOL

Input: pylon vortex locations (read in), wing cross flow field at

pylon.

Output: pylon vortex circulation strengths.

Comment: subroutine PYLONFN computes the pylon vortex lattice by

the procedure very similar to that used to compute the wing vortex

lattice in subroutines COMPUT-WINGFN-MATRIX

Procedure: The following steps are performed by the subroutine in

order. FORTRAN variables are indicated.

1. Read the pylon vortex locations

2. Locate the pylon vortex images above the wing, using the wing"

as a plane of symmetry (YI, ZI, SI, etc.).

3. Compute the wing interference crossflow at the pylon face at

control points XP. Compute DW » crossflow due to wing angle

of attack. Compute DT = crossflow due to wing thickness.

4. Compute H = matrix of influence coefficients between pylon

vortex strengths and control point crossflow values} H(I, J) «

crossflow velocity at control point I produced by vortex J of

unit strength.

5. Invert H matrix (call EQSOL).

6. Use H to compute vortex circulation strengths (GAM due to wing

unit angle of attack, GAMC due to wing thickness).

36

Subroutine START

Purpose: to read wing input geometry.

Called from: AIRCFT

Calls: (none)

Input: wing data

Output: Part of the data is printed out

Comment: Array size input parameters are checked to verify that

they do not exceed dimensions.

Subroutine STRIP

Purpose: to compute the perturbation velocities at a field point,

produced by the line source strips used to represent the aircraft

thickness envelope (other than wing and nose thickness).

Called from: PARTS

Calls: (none)

Input: field point location

Output: velocities (UT, VT, WT)

Comments: Source strips representing the inlet ramp are omitted

from the calculation if the field point is behind the inlet lip

(by use of index limit Nl).

37

Subroutine THICK

Purpose: to compute the velocity at a field point, produced by

one spanwlse section of the wing thickness envelope.

Called from: WING

Calls: (none)

Input: field point location; wing spanvise section location

Output: perturbation velocities (UT, VT, WT)

38

Subroutine VORTEX

Purpose: to compute the velocity at one field point, produced by one

horseshoe vortex of unit circulation strength for incompressible flow.

Called from: MATRIX, PYLONFN, WING

Calls: (none)

Input: field point location, horseshoe vortex location and geometry

Output: perturbation velocities (u, v, w) per unit circulation

parameter F/ATT

Comments: The method used is to apply the Blot-Savart law to each

of the three linear segments of the horseshoe vortex. Sweep and

dihedral of the bound vortex is Included. The two trailing vortices

are assumed to be parallel to the wing X-coordinate axis. An error

signal is printed if the field point lies on a vortex filament..

Definitions

XP, Y, Z : field point coordinates referenced to the midpoint ofthe bound vortex as the origin. System is assumedparallel to the wing coordinate system.

S : half-distance between trailing vorticesSAL, CAL : sine and cosine of the sweep angle of the bound vortexSPH, CPH : sine and cosine of the dihedral angle of the bound

vortexHU, HV, HW: perturbation velocities (u, v, w), per unit vortex

circulation parameter r/4""Dl through D8:distances shown in the sketch below

SKETCH 3ROUTINE VORTEX

39

Subroutine WING

Purpose: to compute the perturbation velocities at a field point,

induced by the aircraft wing-pylon combination.

Called from: PARTS, PYLONFN, WINGFN

Calls: THICK, INTERP, VORTEX

Input: field point location

Output: perturbation velocities

Definitions (for flow diagram)

V : perturbation velocities (u, v, w, UT, v™, w_,)J : wing vortex spanwise indexF : factor used to image right wing with left wingNC : index value supplied by the calling subroutine in order to

specify the wing features to be included or omitted in thecalculation (NC =1, 2, or 3)

xiV : increment in perturbation velocities due to each wing elementNTV1: lower limit of index J, as defined by subroutine PYLONFN.

Using NTV1 = NTV + 1.removes the wing from the computationand allows the wing-pylon interference alone to be calculated.

I : wing vortex chordwise indexNRW : number of right wing spanwise sections included for flow field

calculations

40

FIGURE 13ROUTINE WING LOGICAL FLOW (subsonic)

COMPUTE WINGTHICKNESS AV,

V = V + AV

INTERP

COMPUTEAV (I,J)

INTERPOLATED

VORTEX

COMPUTEAV (I, J)

V = V + AV

41

Subroutine WINGFN

Purpose: To compute the circulation strengths of the wing horseshoe

vortex lattice; to compute wing lift and wing spanwise lift

distribution.

Called from: AIRCFT

Calls: WING, MATRIX, EQSOL

Input: Wing geometry, Mach number

Output: vortex circulation, and lift coefficient

Definitions (for flow diagram)

IG, IPGAM

GAMC

H

DWDK

DIDALFDX, XALFOSLCLADCLZEROADS

input control parametersvortex circulation T/ATT per unit angle of attackin degreesvortex circulation T/bit at zero aircraft angleof attackmatrix of coefficients relating vortex circulationstrengths to the crossflow at the control points,by the equations

[H] {GAM} - fowj-[H] {GAMC} .crossflow per unit wing angle of attackcrossflow due to wing camber, thickness, and linearaxial change of angle of attackcrossflow due to wing incidenceinput for linear axial change of angle of attackwing spanwise lift distributionwing lift coefficient per degree angle of attackwing lift coefficient at zero aircraft angle of attackwing area over reference area

42

FIGURE 14ROUTINE WINGFN LOGICAL FLOW (subsonic)

COMPUTEDl, DK, DW

EQSOLREPLACE

[H] BY [H]-1

CALL WINGFOR THICKNESSINTERACTION

COMPUTEGAM,

GAMC

COMPUTESL, CLAD,

CL2ERO, ADS

WRITESL, CLAD,CLZERO,

ADS

43

Supersonic Group

Subroutine AIRCFT

Purpose: To call the routines required to represent the aircraft

wing, pylon, nose, and other thickness surfaces.

Called from: STORLD

Calls: GENRAT, START, WINGFN, DNWASH, PYLONFN, BODFN, STRIPFN

Comment: AIRCFT is an interface routine used for calling other

routines. It makes no computations.

44

Subroutine DIAFRM

Purpose: To compute the source strengths in the Mach boxes on the

diaphragm used to represent the crossflow field of the wing and pylon.

Called from: DNWASH, PYLONFN

Calls: (none)

Input: source values on the planform} Mach box indexing defining

the planform and the size of diaphragm.

Output: source values on the diaphragm; spanwise pressure distri-

bution on the planform.

Definitions

DW

BIINSSJDIILE, ITE:

IMODEIJ.LMLU, MO

C, CUPlanformdiaphgram

UVSLNS

matrix of source values (dovrroash) known on the plan-form, and to be calculated on the diaphragmBETAindex limit for I, defining diaphgram size (see sketch 5)J index at planform tip (sketch 5)J index at diaphragm tip (sketch 5)I Index of planform leading edge and trailing edge,arrays versus Jsignal that defines diaphragm size (see sketch 5)chordwise index of DW (sketch 4)spanwise index of DW (sketch 4)up-index for C (sketch 4)over-index for C (sketch 4)limit indices for L, M for which values of C(L, M) andCU(L) have been computed In Routine GENRAT.aerodynamic influence coefficients (see routine GENRAT)a planar wing (or pylon) surfacesurface behind the Mach line coplanar with (and excluding)the planformaxial perturbation velocity divided by free stream velocitynegative of chordwise sum of UV at each spanwise sectionnumber of Mach boxes on the planform at each spanwisesection.

45

Comments: routine DIAFRM computes the value of the parameter "SUM"

at each box I, J, defined as

SUM(I, J) = V [DWd1, J1) * C(L, M) + DW(I', J) * CU(L)j

MACHFOREGONE

where (I1, J1) are all Mach boxes in the Mach forecone of box (I, J),

and (L, M) are the corresponding index values of the aerodynamic

influence coefficients which relate box (I1, J1) to box (I, J)

(see sketch 1 for indexing convention).

If box (I, J) is on the diaphragm, its value of downwash, DW,

is computed by the equation for zero axial perturbation velocity:

DW (I, J) = SUM

If the box (I, J) is on the planform, its value DW is known at call

time, and therefore the axial perturbation velocity may be computed

by the equation:

uv = SUM - DW (I. J)B

By calculating the value of DW (I, J) using the I, J order explained

in Reference 1, the values of DW (I1, J1) used in the computation

for SUM are always known.

Computation of the parameter SUM is done in 4 parts, corresponding

to the 4 numbered areas marked by dashed lines in sketch 2. The

equations used to compute SUM in each of these 4 areas are:

46

X-L+Ia.

SUM \ \ C(L, M + J . - 1) x DW(I - L + 2 - 2M, M)

M=/

C(L> M)

L-l ft-/

Z. T-l

SIM3 \ > C(L, M) x DW(I - L 4- 1, J - M)/ - , *•• . - •

L'/ M-/

I-lCU(L) x DW(I - L, J)

and SUM = SUMX 4- SUM2 + SUM3 +

The computation of SUM in the first 3 areas is accomplished by

multiple indexing of one double-DO loop in routine DIAFRM. The values

of the index parameters used to accomplish this are listed in Table II.

The area numbers 1-4 are in the order of computation.

47

WING APEX

MACH WAVE

4,1 3,2 2,3 1,4

4-4-4-4-4-4-4-4-

4-+..4-

L INDEXING FOR CU (L)

MACHFOREGONE

BOX (I,J)

SKETCH 4ROUTINE DIAFRM

L,M INDEXINGFOR C (L,MI

48

I 1

I 1

f.

m <1-1

go

H W

co

H§

%K

z*

±L

Lu

-ZS

3ta><°--U

J

,2?35>0

0. OC

(T*£«(N

ÎIÛJ

I

49

TABLE IIROUTINE DIAFRM

INDEX VALUES FOR COMPUTATION OF "SUM"

AreaNumber*

N

Kl

K2

K3

K4

1

0

0

1

1

J-l

2

1

0

1

1

0

3

1

1

0

-1

0

Corresponds to Numbered areas onSketch 5.

50

Subroutine DIFIN

Purpose: To compute the geometric functions GX, GY, GZ, relating

field point location to source box location, and which are required

to calculate the velocities at the field point induced by the source

box. .

Called from: WING, PYLON, THICK

Calls: (none)

Input: Field point location; source box location; S; BETA

Output: GX, GY, GZ, SIG

Comment: Mathematical development of the functions GX, GY, GZ is

contained in Reference 2. Routine DIFIN relates only two corners of

the source box to the field point each time it is called. Thus,

XI, Yl, Zl is the location of the leading edge or the trailing edge

of the source box. The calling routine calls DIFIN once for the

leading edge and once for the trailing edge of the source box, then

uses the increment in GX, GY, GZ to compute the induced velocities.

Definitions

X, Y, Z : field point locationXI, Yl, Zl: source strip locationS : half-width of source stripGX, GY, GZ: geometric functions used in computing u, v, w,

respectivelySIG : signal which, when non-zero, indicates to the calling

routine that the field point is out of the Mach coneinfluence of the source strip

51

Subroutine DNWASH (downwash)

Purpose: To compute the source strength distribution over the wing

leading edge diaphragm and tip diaphragm; to read/write/punch same;

to compute wing lift coefficient

Called from: AIRCFT

Calls: DIAFRM, LIFT

Input: Mach box source strength and locations on the wing

Output: Source strengths on the diaphragm

Definitions (for flowchart)

IG, IP, IW: input control numbers for generate-punch-wrlteDK and DW

DK : diaphragm Mach box source strengths due to wing camber,twist, linear axial change of crossflow

DW : diaphragm source strengths due to unit aircraft angleof attack

aA/C : a*-rcraft angle of attack

52

FIGURE 15ROUTINE DNWASH LOGICAL FLOW

WING LIFTCOEFF. PERUNITQ;A/C

COMPUTEOK ON

DIAPHRAGM

LIFTWING LIFTCOEFF. AT

«A/C

COMPUTEDW ON

DIAPHRAGM

53

Subroutine GENRAT

Purpose: To generate the Zartarlan constants, the Mach box Influence

coefficients used in routine DIAFKM for computing the Mach box source

strengths on the wing and pylon diaphragms.

Called from: AIRCFT

Calls: (none)

Input: Number of rows and columns of coefficients to be generated

(LU and MO read in).

Subroutine LIFT

Purpose: To compute wing lift coefficient.

Called from: DNWASH

Calls: (none)

Input: Spanwise pressure distribution

Output: Spanwise lift distribution and total lift coefficient

Definitions

NSS : number of spanwise wing sectionsSL : axial perturbation velocity summed in chordwise direction

at each spanwise section (negative of)NS : number of Mach boxes on the wing surface at each spanwise

sectionCLAD : lift coefficient referenced to wing surface area (Mach

box approximation)CL : sectional lift coefficient referenced to local chord at

each spanwise section

54

Subroutine NOSE

Purpose: To compute the field point velocity produced by the nose

Called from: PARTS

Calls: (none)

Input: Field point location; strengths and locations of line sources

and doublets representing the nose

Output: Velocities u, v, w, UT, VT, WT

DefinitionsUA, VA, WAUC, VC, WCXP, YP, ZP

N

B :XBL :xuSNA, SNC

velocities due to axial flowvelocities due to crossflowfield point location in nose coordinates, nose apex asorigin and X-axis the axis of symmetrynumber of line singularities

V M 1W J.

dummy variable, for compatibility with subsonic programline singularity apex locationsline source and doublet strength parameters

55

Subroutine NOSEFN

Purpose: To compute the strengths of the line sources and doublets

used to represent flow field about the nose

Called from: BODFN

Calls: (none)

Input: Nose geometry

Output: Source and doublet strengths and locations

Comments: Input points which do not fall inside the Mach cone of

the apex are omitted from the calculation. An error signal results

if the nose points are not in order of ascending axial location.

Subroutine PARTS

Purpose: To call the routines used to compute the velocities

produced by the various aircraft components; to sum these component

effects.

Called from: DISTURB

Calls: WING, PYLON, STRIP, NOSE, MATAD

Input: Field point location in wing coordinates and in nose coordinates.

Outputt Field point perturbation velocities u, v, w due Ee aircraft

angle of attack, and u , VT, w due to aircraft thickness.

56

Subroutine PRINTX

Purpose: To print out wing input parameters and wing computed

parameters.

Called from: AIRCFT

Calls: (none)

Subroutine PYLON

Purpose: To compute the field point velocity produced by the pylon

Called from: PARTS

Calls: DIFIN

Input: Field point location

Output: Velocities (u, v, w, UT, VT, WT)

Comment: The calculation procedure for routine PYLON is the same

as routine WING and will not be repeated here. The only difference

is that routine PYLON removes the field point from the tip diaphragm

if necessary, then interpolates the resulting u, w, i^, WT velocities

toward zero on the diaphragm. This is done to avoid numerical

inaccuracies of the Mach box method.

57

Subroutine PYLONFN

Purpose: To compute the Mach box source values used to represent

the pylon in the presence of wing crossflow.

Called from: AIRCFT

Calls: WING, DIAFRM

Input: Pylon geometry (read In); wing crossflow

Output: Pylon Mach box locations and strengths

Cotmnents: The organization of PYLOWFN and the notation are very

similar to that of the routines WINGFN - DNWASH for computing wing

source values.


DW : matrix of pylon Mach box source strengths proportionalto wing angle of attack («DWP)

DK : matrix of pylon Mach box source strengths proportionalto wing camber, twist, and thickness (=DKP)*

JDIP : number of spanwise divisions of Mach boxes used to representthe pylon and its tip diaphragm

IG, IP : input control variables for generating and punchingthe DW and DK matrices

*The Indexing for matrices DW and DK is that required by routineDIAFRM. The DW, DK values are then transferred to the DWP, DKPmatrices, which have indexing for more efficient use of space.

58

FIGURE 16ROUTINE PYLONFN LOGICAL FLOW (supersonic)

READ/WRITEPYLONINPUT

LOCATEMACHBOXES

PYLONDW, DK

(CALL WING)

>27

JDIP = 27

COMPUTEPYLON

PARAMETERS

IWRITEPYLON

PARAMETERS

59

Subroutine START

Purpose: To read wing geometric inputs

Called from: AIRCFT

Calls: (none)

Input: Wing data

Output: Dimensions are checked; some variables are printed1

Subroutine STRIP

Purpose: To compute the field point velocity produced by the source

strips used to represent the aircraft thickness envelope (other

than wing and nose).

Called from: PARTS

Calls: SWP


Output: Velocities . (u-j., v^, w ,)

Comment: Strips representing the inlet ramp are excluded from the

calculation of the field point inside the Mach cone of the inlet lip

(using index Nl). if the field point lies on the body surface of the

store, STRIP shifts the field point X-coordinate to be on the Mach

cone intersecting the store section midpoint and with apex being on

the nearest tip edge of the strip being computed (by use of control

index ISW). This is done to avoid large erroneous body pressure

loading predictions as discussed in Reference 2 (Part II).

60

Subroutine S¥P (sweep)

Purpose: To compute the flow velocities at a field point induced by

a planar source strip of parallelogram planform.

Called from: STRIP

Calls: (none)

Input: Field point location ; source strip location, geometry, and

strength

Output: Velocities (UT> VT, WT)

Comment: The mathematics of computing the velocity field are taken

from Woodward (Reference 12 of Reference 2 (Part II)). The source

strip is here allowed to be swept, as opposed to subroutine DIFIN,

where only rectangular source strips are considered. The strip

sweep may be either greater or less than the Mach wave sweep.

The case of the strip sweep equal to the Mach wave sweep is not

considered, and is excluded by subroutine STRIPFN. The strip leading

and trailing edges have the same sweep, and the tip edges are parallel

to the X-coordinate direction.

Definitions

F, G : unit values changing sign alternately as each of thefour corners of the strip is considered.

XP, YP, RP, DP: corresponds to the notation used in Reference 12 ofReference 2 (Part II), for the transformed coordinatesV* V1 *. I A »X , Y , r , d .

DX, DY, DZ,R,D: corresponds to the notation used in Reference 12 ofReference 2 (Part II), for the geometric distancesX, Y, r, d.

61

Subroutine THICK

Purpose: To compute the field point velocity produced by the distri-

bution of wing thickness located at one spanwise section.

Called from: WING

Calls: DIFIN

Input: Field point location] Index of wing section used; velocity

functions GX, GY, GZ at the wing leading edge.

Output: Velocities (UT, VT, WT)

Comments; Routine THICK computes velocity due to sources on the wing

using a procedure similar to that used In routine WING for computing

velocity due to sources on the diaphragm of the wing.

Definitions

X, Y, Z : field point locationXI, YSJ : X-Y location of wing section leading edgeJ : wing section spanwise indexXT, YYSS:: geometric parameters which determine If and where the

Mach forecone of the field point intersects the wing sectionTH2, DW2 : incremental velocity parameters used depending on

tests of XT, YYSSUT, VT, WT: field point velocitiesGX2, GY2, GZ2: geometric velocity functions relating field point

to wing section leading edge (computed In DIFIN)

62

Subroutine WING

Purpose: To compute the field point velocity produced by the wing.

Called from: PARTS, PYLONFN

Calls: DIFIN, THICK


Output: Velocities (u, v, w), (UT, VT, WT)

Comment: The wing is represented by a. rectangular grid of Mach

boxes, and routine WING sums the Influence of these to compute

velocity. Mach boxes located ahead of the wing and off the wing tip

form a diaphragm which accounts for the flow field due to angle of attack.

The field point is assumed not to be within the zone of influence

of the wing wake. Wing symmetry about Y = 0 is assumed. See

Reference 2 for a geometric and mathematical explanation.

Definitions (for flow chart)

V : velocities u, v, w, u^, Vj, w^SYS : sign factor for coordinate Y, determining left or right

wingJ : Mach box spanwise IndexK : chordwise index of first non-zero source strengthGX, GY, GZ: geometric factors from corners of Mach box to field

point, proportional to induced velocitiesYSS, XT, DX: parameters which determine if the Mach forcone of

the field point intersects the Mach boxDW2, TH2 : additional velocity components at the field point if the

Mach box lies on the Mach forcone of the field pointNSS : maximum value of J on wingJDI : maximum value of J on tip diaphragm

63-

OFFCONE

IN

V = 0

J = 0

J = J + 1

LEFT WINGSYS = +1

DIFIN

GX, GY, GZAT K

ONCONE

COMPUTEDW2, TH2

FIGURE 17

ROUTINE WING LOGICAL FLOW (supersonic)

V DUE TOSOURCES ONDIAPHRAGM

V DUE TOSOURCES ON

WING

THICK

V DUE TOWING

THICKNESS

RIGHT WINGSYS = -1

64

Subroutine WINGFN

Purpose: To compute the Mach box source representation on the wing.

Called from: AIRCFT

Calls: (none)

Input: Wing geometry

Output: Mach box source strengths on wing; coordinate locations and

indexing for Mach box grid on wing and on diaphragm.

Comment: Note from the list of definitions that wing camber and twist

are included in both matrices DK and DT. This is done to save computing

time when these values are used in routine WING. Thus, DT uses

fewer boxes (not Mach boxes) and accounts for all wing geometric

properties; it is used on the wing. This allows DK to be used only

on the diaphragm.


XS, YS

SMBAPEXILE, ITE

DWDK

DTII

NSS

X-Y locations of Mach box spanwise Sections at leadingedge of wingtangent of leading edge sweep angleBetawing diaphragm Mach forecone apex, X location at Y = 0chordwise index values of Mach boxes on leading edgeand on trailing edge of wing at each spanwise sectionMach box source strengths due to-" angle of attacksource strengths due to camber, twist, and/or linearaxial variation of crossflowsource strengths due to thickness, camber, and twistMach box chordwise index at the first spanwise sectionof the wing tip (see routine DIAFRM)input, number of spanwise sections

65

FIGURE 18ROUTINE WINGFN LOGICAL FLOW (supersonic)

REDEFINEAPEXFOR

SUPERSONICLEADING EDGE

DEFINEILE, ITE

DW, DK, DTFOR WING

II = NSS- 40

DEFINEILE, ITEON TIP

DIAPHRAGM

FOR ASSUMEDINDEXING INROUTINE WING

66

VARIABLE DEFINITIONS

The program makes extensive use of labeled COMMON statements.

The variables contained In these COMMON statements are defined In

this section. These definitions are Intended as an aid to the

understanding of the FORTRAN coding. For this purpose the definitions

are concise. Additional definitions pertinent to each subroutine

are contained In the previous section. A more detailed list of

definitions for the input and output variables is presented in

Reference 1.

As variables are encountered in the coding, it is sometimes

desired to know where they originate. This information for the

variables in the COMMON lists is presented in Table III.

67

TABLE III

COMMON VARIABLE PLACE OF ORIGIN

COMMONNAME

ROUTINE WHEREVARIABLES ORIGINATE

- DUAL SUBSONIC-SUPERSONIC PROGRAM -

BLANKC5CIOCllC12, C13C14.C17C21

DISTURB, CRSFLWSTORLDSTORLDSTOREBODFN, NOSEFNSTRIPFNSTORE, DISTURBSTORE

- SUBSONIC PROGRAM -

ClC2C3C4C7CISC19

STARTCOMPUT, WINGFNSTARTSTART, PYLONFNSTARTSTARTCOMPUT

- SUPERSONIC PROGRAM -

ClC2C4C8C15

START, WINGFNGENRATSTART, WINGFNWINGFN, DNWASH, STARTPYLONFN

68

Dual Group

blank Common - velocity field and' store crossflow parameters

H - used in matrix operationsU (I, J, K) - interference velocity field

I for u, v, w, UT, VT> w-j-J for Y-Z locationK for X location

ALY, ALZ - Y, Z crossflow at bodyBY, BZ - Y, Z buoyancy factorsVS, WS - Y, Z crossflow at fin rootVD, WD - spanwise rate of change of crossflow at finARS - fin roll crossflowARD - spanwise rate of change of ARSALYD, ALZD - X derivative of ALY, ALZXC - X location of crossflow field point

Common C5

RADPIBETABMSUB

- 1/57.3- TT = 3.14159- Mach function- Mach number- BETA

Common CIO - - store traverse parameters

XM, YM, ZM - reference point locationXT - traverse lengthXLFMW - store incidence relative to wing

Common Gil - store geometry

XCGDIANMSXMSDELXXSTARTFTM

store reference CG distance from nosereference diameternumber of store axial sectionsNMSsection lengthCG X-location at start of traversefin tip maximum span v body radius

69

Common CI2 - nose parameters

XBRBDSNASNCXU

control point locationnose radius at XBnose slope at XBsource strengthdoublet strengthline singularity apex

Jommon C13 - nose parameters

NBP - number of body (control) pointsXNOSE, YNOSE,ZNOSE - apex locationALFNW - nose angle relative to wingSNW, CNW - sine and cosine of ALFNWSUP - BETASUB2 - BETA squaredXBL - body length

Common C14 - thickness strip parameters

XST, YST,ZSTSSTNSTNINXLIP, YLIP,ZLIPSPHST,CPHSTTHSTDXSTSALST,CALSTCAST

- X, Y, Z locationsemi-span- number of strips- number of inlet ramp strips

- inlet lip location

- sine and cosine of dihedral angle- slope of thickness surface- chord

- sine and cosine of sweep angle- parameter combining DXST, THST

Common C17 - store location parameters

SETY, SETZ - trig functions of roll angle, defined in STORE, usedin DISTURD-PARTS to locate fins

70

SRA, CRA - sine and cosine of ROLLROLL - store fin roll angle (4- clockwise)NK - number of axial sections in the traverse line

Common C21 - store section properties

CNF - fin force coefficient in constant crossflowCNPF - fin force coefficient in crossflow changing spanwise

linearlyFCP - fin spanwise CP T ref. diameterCNLA - body force coefficient per unit length in constant

crossflowRS - local body radius •£• ref. radiusFT - local fin span -r ref. radiusIDW - index of sections affected by downwash of the wing-tail

typeEP (I, J) - downwash at section I -r crossflow at section JCNLD - section force coefficient per unit axial rate of change

of crossflowXBAR - section moment arm to ref. CG -r ref. diameter

71

Subsonic Group

Common Cl - wing spanwise section parameters and chordwise geometry.All are input but SL.

YVXLECSLz*:PHSVSWPcsDZDX

- section Y- section X leading edge- chotd length- section lift- section Z- dihedral angle- semi-span- sweep factor- chord divisions- mean' line slopes (camber)

Common C2 - wing vortex properties

XVGAMGAMC

- vortex X location- circulation per degree ot- circulation at zero a

Common C3 - wing parameters (input)

ARBWCRALAMDATRATIO

aspect ratiowing spanroot chordquarter chord sweep angletaper ratio

Common C4 - index limits for wing and pylon. All are input but NTV1

For Wing

NTV - number of trailing vorticesNBV - number of bound vorticesNCP - number of control pointsXTV - NTVXBV - NBVNRW - number of right wing trailing vorticesNTV1 - NTV + 1,-or 1

72

For Pylon

NJI - number of wing vortices to be interpolatedJI - J index of wing vortices to be interpolatedNPL - number = 1NVP - NPVNPV - number of pylon (trailing) vorticesNTV2 - NTV + NPV + NPVIWING - input control parameter

Common C7 - wing section input parameters

TTCALFVXCAM

thickness scale factorsection incidence anglecamber scale factor

Common CIS - wing thickness envelope parameters

THUNTCXTC

- thickness envelope slopes- number of thickness sections per chord- NTC

Common Cl9 - wing and pylon vortex and source trig functions

SSA, SCA - sine and cosine of source strip sweep angleSDA, CDA - sine and cosine of source strip dihedral angleSVA, CVA - sine and cosine of wing vortex sweep angle

Blank Common - pylon horseshoe vortex image parameters (multi-useof space)

YIZISIPHISDIGDI

Y locationZ locationsemi-spandihedral anglesine of dihedral anglecosine of dihedral angle

73

Supersonic Group

Common Cl - wing geometry

XSYSZWCS

section leading edge X-locationsection Y-locationwing Z-locationsection chord length

Common C2 - Mach box aerodynamic influence coefficients (AIC's)

CU - influence coefficients from boxes at same axial section,forward of box being influenced.

C - influence coefficients from boxes to either side andforward of box being influenced

LU, MO - limit index of influencing box, L-up and M-Over,from box being influenced

Common C4 - wing parameters

NSSNSCXSSXSCNSS2JDIIIXMAXAPEXSMSBS

number of spanwise sectionsnumber of sections per chordNSSNSCnot usednumber of sections, including tip diaphragmMach box chordwise. limit index at .section NSS + 1Mach box maximum X locationX location of wing apextangent of leading edge sweep anglesection semi-span2 x BETA x S

Common C8 - wing matrix of source strengths

DWDK

Mach box source strengths per degree angle of attackMach box source strengths due to camber, twist, linearaxial crossflow variation

74

DT

CFILE

- source strengths due to bamber, twist, and thickness(not Mach Box)

- chord fractional parts- section leading edge index

Common C15 - pylon parameters

DWP - Mach Box source strengths per degree aircraft angle ofattack

DKP - Mach Box source strength due to wing camber, twist,thickness

ILE - section leading edge indexITE - section trailing edge indexIPS - chordwise index for printing, punching, writing of

DWP, DKPXS - section leading edge X-locationZS - section Z-locationCS - section chord lengthYP - pylon Y-locationZl - pylon upper Z locationAPEXP - apex X locationSP - section semi-spnBSP - 2 x BETA • SPIIP - maximum chordwise index at section NSSP + 1JDIP - maximum section index at diaphragm tipNSSP - number of sections in pylon span (=2)

Blank Common - wing section parameters (multi-use of space)

TTCALPSTHUDZDXXCAMITESLNS

section thickness scale factorsection incidence anglechordwise thickness distributionmean line slopes for cambercamber scale factorsection trailing edge indexproportional to section liftnumber of Mach Boxes per section

75/76

APPENDIX A: SHOCK PROGRAM

Program SHOCK Is separate from program STORLD. Its purpose is

to compute the locations of the aircraft shock waves in supersonic

flow. This information is outputted in the form of the parameter

DSHIFT, defined as the distance of the shock wave ahead of the forward

Mach wave at the store traverse location. Values of DSHIFT are

outputted for the aircraft nose, inlet, and pylons. These values are

used as input to program STORLD in supersonic flow.

Program Organization

Figure A-l presents the overall logical flow of program SHOCK.

This is a flowchart of the main program. Provision for run stacking

of store location, aircraft geometry, and Mach number has been

included.

Figure A-2 is a communication diagram for program SHOCK. This

shows the calling relationships between subroutines. General calling

sequence is from left to right. The purpose of each of these sub-

routines is presented in the next section.

Subroutine Explanations

Following is a list of the routines used with Program SHOCK.

1.2.3.4.5.6.7.

ATTACHCCALCDETACHMACHFNPERCPTSLOPESTART

8. TABLEA (function)

Each routine will now be explained, with the exception of routine SLOPE ,

which is identical to that explained in the main text of this manual.

A-l

FIGURE A-lPROGRAM SHOCK LOGICAL FLOW

C START J

READ/WRITETITLE

MACH NO.

START

READ/WRITENOSE-INLET-PYLON GEOM

IREAD

STORETRAVERSELOCATIONSL = 1, NTL

L = 0

L = L

WRITESTORE

LOCATIONNO. L

ATTACHED

ATTACHED

WRITESHOCKSHIFT

NEXTAIRCRAFT

NEXTSTORE

TRAVERSE

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A-3

Subroutine ATTACH

Purpose: To compute the shock wave distance ahead of the Mach wave

at the store traverse line for the case of the shock attached to the

body.

Called from: SHOCK

Calls: TABLEA, PERCPT

Input: Body apex location; body shape; shock apex angle; Mach number

Output: DSHIFT, distance along traverse line from Mach wave to

shock wave.

Comment: Routine ATTACH uses a step-increment procedure to locate

the shock intersection with the traverse line, starting at point (1)

in the sketch and decreasing X until point (2) is reached.;

Definitions

XO, YO, ZOESODATTHXARC

A, BYMOBETASQBMXKAYD

XMINT

RADMTRADSOKXMSOK

shock apex location, same as body apex locationinput, shock apex angle (half cone)body apex half-cone anglecircular arc length from body apex to shoulder, used toapproximate the body shapegeometric constants defining traverse linetraverse line Y-coordinateM2 - i

Mach number, MK value used as shock scale factor (see APPENDIX A ofReference 2)X-coordinate of intersection of traverse line with Machwavetraverse line radial coordinate at XMINTradial coordinate of shock wave (initially at X = XMINT)X-coordinate of shock wave at radial distance = RADMT

A-4

Y, R

TRAVERSELINE

SKETCH A-lROUTINE ATTACH

A-5

Subroutine CCALC

Purpose: To compute the shock stand-off distance parameter, XPDP,

for detached shocks.

Called from: DETACH

Calls: (none)

Input: Call parameters defined below

Output: XPDP defined below

Comment: The value of XPDP is computed by the equation

XPDP = (.5) (C) cot (DDET)

where C is a function of DELTA such that

At DELTA = DDET, C = 1.0

At DELTA = 90° , C = .7

And the variation of XPDP with DELTA is elliptic. The shape of the

elliptic curve is determined by the conditions that (1) the slope of

the curve is zero at DELTA = 0, and (2) the slope at DELTA = DDET is

the same as the slope of the curve

XPDP = .5 cot (DELTA)

Definitions

DDET body slope at which shock would just detach (6DET OF

DELTATANDXPDPXPDP

Reference 2)body apex half-angle (input)tangent of DDETratio XP/DP (see sketch)distance from shock apex to effective shoulder of bodydiameter of. body at effective shoulder (effective diameter)

A-6

BODY

SKETCH A-2ROUTINE CCALC

A-7

Subroutine DETACH

Purpose: To compute the shock wave distance ahead of the Mach wave

at the store traverse line for the case of the shock detached from

the body.

Called from: SHOCK

Calls: PERCPT, CCALC

Input: Body defined as nose, inlet, or pylon; store traverse line

location; Mach functions.

Output: DSHIFT = distance between Mach wave and shock wave at

traverse line.

Comment: To define the nose shock, an equivalent body is constructed,

using a cone-cylinder (see sketch). The cone passes through point

(P), defined as the point where the body slope angle equals DDET

(compare with sketch of routine CCALC). This is done to better locate

the shock in the far field for shocks that are nearly attached, as

explained in Reference 2.

Definitions

LTYPE : index for type of body to be considered (nose = -1,inlet = 0, pylon = 1)

DELTA : nose semi-vertex angleDDET : maximum DELTA for attached shockXDP, DP : see sketchXPDP : ratio XP/DP defined in CCALCXSN, XMN : X location of intersection of traverse line with

shock wave and Mach wave, respectively, for nose shockDSHIFT : see outputDELTAI : DELTA for inletXP, XO : see sketchXSI, XMI : corresponding values of XSN, XMN for inlet shockXQ : same as XPXSP, XMP : corresponding values of XSN, XMN for pylon shock

A-8

TAND, C, XOTHERM: defined in MACHFNBETASQ : Mach FunctionLP : pylon indexA, B : see routine PERCPT

DDET

SKETCH A-3ROUTINE DETACH

A-9

FIGURE A-3ROUTINE DETACH LOGICAL FLOW

(continued 6ti next page)

CONSTRUCTEQUIVALENTBODY USING

XDP, DP

REDEFINEXDP, DPAT MAX.

DIAMETER

CCALC

FINDXPDP

IDEFINEXP, XO

SEECOMMENTSANDSKETCH

PERCPT

COMPUTEXSN, XMN

4d

d

YWRITEDSHIFT

f WRITEEQUIVALENT

BODYSHAPE1

WRITESHOCK

LOCATION

OUT

A-10

FIGURE A-3 (Continued)ROUTINE DETACH LOGICAL FLOW

INLET PYLON

a

VDEFINEXDP, DP,DELTA!

FOR A CONE

t>

YDEFINE

XDP, DP, XQXO

PERCPT

COMPUTEXSP, XMP

A-ll

Subroutine MACHFN

Purpose: To calculate those parameters required by the program which

are functions of Mach number.

Called from: SHOCK

Calls: TABLEA

Input: Mach number, BM

Output: Parameters defined below

Definitions (for output)

TANDTANETATANESC

DDETXOTHERM

tangent of DDETtangent of ETAtangent of ESempirical parameter used to determine shock stand-offdistance (defined in appendix A, Referenced)maximum body slope angle for attached shocka function of BETA, ES, and ETA, used in the equationfor XO, the detached shock asymptote apex location(see sketch with routine DETACH).

Additional Definitions

BETAMETA, ES

! - lMach numberparameters T) and eg used in the equation for detachedshock asymptote location (see appendix A, Reference 2)

A-12

Subroutine PERCPT

Purpose: To compute the axial coordinate of the intersection of a

detached shock wave surface, or Mach wave surface, with the store

traverse line. This intersection is called the piercing point.

Called from: DETACH

Calls: (none)

Input: Parameters defining equation of surface and line.

Output: XS, piercing point X-coordinate

Comment: The shock wave surface is a hyperboloid and the Mach wave

surface is a cone, both with symmetry about the X axis. Combining

the equation for this surface with the equation of the line gives an

equation for XS of the form

Al (XS)2 + Bl (XS) + Cl - 0

which is solved by the quadratic formula.

Definitions

2Al : parameter 1 - (/3A)BETASQ : M2 - 1 = 0 2

A, B, YM : parameters defining the traverse line as follows

Y = YM (constant)

Z = B 4- A-X

XT, YT, ZT: coordinates of apex of shock (Mach) surfaceATERM : distance from XT to asymptote (=XO in sketch with routine

DETACH), which defines the equation of the shock surfaceas follows

2 2 2 7 7 2X = (ATERM) + j3 Y + p Z

Note ATERM = 0 for the Mach cone

A-13

Subroutine START

Purpose: To read input parameters defining the nose, inlet, and

pylons.

Called from:: SHOCK

Calls: SLOPE

Output: Input variables are written; dimensions are checked for

ryer-run; parameters defined below are computed.

Definitions

RNOSE : maximum nose radiusXARC : X-length of circular arc used to approximate nose for

attached shock calculations (as tangent ogive with semi-vertex angle DELTA)

DRDXB : slope of body, derivative of RB versus XB

Function TABLEA

Purpose: To compute the value of the dependent variable at a

specified value Of the independent variable using a table of given

values.

Called from: MACHFN, ATTACH

Calls: (none)

Input: XIN; X; Y; NPTS

Output: TABLEA

Comment: Linear interpolation is used

Definitions

XIN : specified value of the Independent variableX : independent variable arrayY : dependent variable arrayNPTS ; number of points In each array X, YTABLEA : value of Y at X - XIN

A-14

APPENDIX B - Test Cases

This Appendix presents input data and output listings for test

case runs of programs STORLD - subsonic, STORLD - supersonic, and

program SHOCK. The purpose of these test case runs is to provide a

sample output the reader may use to verify that the programs are

running properly. For this purpose, the test cases have been constructed

to include all major computing modes with as short a run time as

possible. Test case aircraft input geometry is based on the F-4 air-

craft. However, the condition of short run times disallowed an accurate

representation of the aircraft. Store geometry for the test case runs

is taken from Figure 14 of Reference 1, part I.

Program STORLD - Subsonic

Figure B-l lists the test case input data for program STORLD -

subsonic. Refer to Reference 1, Part I fot data format. The subsonic

version of program STORLD occupies less than 50,000 octal storage spaces.

The test case runs require 6.1 seconds of computing time on a CDC 6400

computer. The test cases consist of three stacked runs labeled:

1. Wing with camber, twist, and pylon

2. Fuselage nose

3. Inlet

Figure B-2 lists the output for these data. These runs are

separate to aid in isolating any difficulty in matching the test case

output. Subroutines exclusively affecting the output for each run are:

B-l

run 1: START, COMPUT, WINGFN, PYLONFN, INTERP, VORTEX, WING,THICK, EQSOL

run 2: BODFN, NOSEFN, NOSE, SLOPE

run 3: STRIPFN, STRIP

Program STORLD - Supersonic

Figure B-3 lists the test case input data for program STORLD -

supersonic. Refer to Reference 2 (Part II)for data format. The super-

sonic version of program STORLD occupies less than 55,000 octal storage

spaces. The test case runs require 8 seconds* of computing time on a

CDC 6400 computer. The test cases consist of three stacked runs,

labeled the same as the subsonic test cases and similarly used to

isolate the effectiveness of various portions of the program.

Figure B-4 lists the output for these data. Subroutines exclusively

affecting the output for each run are:

run 1: DIAFRM, DNWASH, GENRAT, LIFT, PYLON, PYLONFN, START,THICK, WING, WINGFN, DIFIN

run 2: BODFN, NOSEFN, NOSE, SLOPE

run 3: STRIPFN, STRIP, SWP

Program SHOCK

Program SHOCK occupies less than 27,000 octal storage spaces.

Figure B-5 lists the test case input data. Refer to Reference 2

Run time is greatly reduced by use of the input values LU = 5, MO = 10,though larger values are required to accurately calculate wing andpylon crossflow.

B-2

(Part II) for input format. Figure B-6 lists the output for these data.

The test case runs require less than one second of computing time on

a CDC 6400 computer.

The test cases consist of two stacked runs. The first run features

the F-4 aircraft nose, inlet, and pylon at Mach 1.2. This run demon-

strates the detached shock capability of the program. The second run

features the nose at Mach 2.0 and serves to check-out the attached

shock capability of the program. Subroutines used exclusively by each

run are:

run 1: DETACH, PERCPT, CCALC

run 2: ATTACH, TABLEA, PERCPT

B-3

FIGURE B-l

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Documents

THEORETICAL PREDICTION OF INTERFERENCE LOADING … · INTRODUCTION The computer program described here Is designed to predict aerodynamic interference loadings on aircraft stores