The COREL and W12SC3 Co Programs for Supersonic Wing Design

The COREL and W12SC3 Co Programs for Supersonic Wing Design

NASA Contractor Report 3676 NASA CR 3676 c.1 The COREL and W12SC3 Co Programs for Supersonic Wing Design and Analysis William CONTRACT DECEMBER ...

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NASA Contractor

Report

3676

NASA CR 3676 c.1

The COREL and W12SC3 Co Programs for Supersonic Wing Design and Analysis

William

CONTRACT DECEMBER

H. Mason

and Bruce

NASl-15357 1983 l

25th Anniversary 1958-1983

S. Rosen

LOAN COPY: RETURN TO AFWL TECHNICAL LIBRARY URTLAND AFB, N.M. 87117

TECH LIBRARY KAFB, NM

NASA

Contractor

Report

3676

The COREL and W12SC3 Computer Programs for Supersonic Wing Design and Analysis

William

H. Mason

Grumman Bet&age,

and Bruce

Aerospace Corporation New York

Prepared for Langley Research Center under Contract NASl-15357

National Aeronautics and Space Administration Sckntifk lnfmrtion 1983

and Technical Branch

S. Rosen

CONTENTS Page SUMMARY................

...............

1

INTRODUCTION .............

...............

1

REVIEW OF THE AERODYNAMIC THEORY ...

...............

3

...............

3

...............

4

...............

5

...........

COREL Program

..........

W12SC3 Program

W12SC3 Program Options

......

TYPICAL APPLICATIONS OF THE PROGRAMS . ...............

12

SOMEAREAS REQUIRING SPECIAL CARE ...

...............

39

COMPUTERPROGRAMDESCRIPTIONS .....

...............

41

...............

42

W12SC3 Program Changes from USSAERO ...............

50

...............

55

...............

55

...............

59

...............

62

...............

63

...............

64

...............

72

...............

79

...............

94

...............

96

...............

96

...............

100

CONCLUSIONS ..............

...............

182

REFERENCES ..............

...............

183

...........

COREL Program

COMPUTERREQUIREMENTS ......... Core Size

.............

Execution

Time

Sample JCL

..........

............

INPUT DESCRIPTION ........... COREL Input Craidon

Instructions

Geometry

W12SC3 Input W12SC3 Output

Definition

Instructions Data

..... .... .....

........

SAMPLECASE .............. Input Output

Data (with

............ Annotations)

.....

iii

THE COREL AND W12SC3 COMPUTERPROGRAMS FOR SUPERSONICWING DESIGN AND ANALYSIS William

H. Mason

Bruce S. Rosen Grumman Aerospace

Corporation

SUMMARY This

report

aerodynamic restricted

contains

design

of

an analysis

assuming

conical

flow

to be irrotational full

a linear

section

for

of

Woodward's

a brief

review

is panel

codes

for

with

The codes

and should

potential

in are

equation

correction

effects.

is assumed

information

about

and any crossflow

the particular theory

fighter

detailed

input

and

on the

elements

of

applications.

used by each method,

examples,

1.3),

shockwaves.

and extends

case of

by

to the solution

to

combines

in

plane

The flowfield

detailed

not

COREL code

than

obtain

the

be valuable

to shock waves less

method which

several

useful

of the wing in the crossflow

crossflow,

of the aerodynamic

illustrated

full

A subsequent

solved

codes

maneuvering.

nonconical

supercritical

computer

case howe'ver,

the section.

equation theory

two

The nonlinear

to account

edge expansion,

the codes is

maneuvering

(Mach numbers normal

potential

W12SC3 is After

over

of

supersonic

of a spanwise

can be made in order

several

for

of applications.

performs

leading

wings

to the supersonic

a wide variety

the

a description

the

use of

instructions,

and

a sample case. INTRODUCTION The "standard" efficient intended

supersonic for

has been given presents

computational wings

supersonic by Miller,

situations

is

methodology based entirely

transport et al,

used for on linear

applications. in Ref.

1.

the aerodynamic theory

A summary of Typically,

in which many of the assumptions

fighter

of linear

design

of

and is primarily that

methodology

aircraft

theory

are no

design

These include

longer

valid.

round

leading

Ref. tools

for

the

which

high

edge

sufficient

to

in Ref.

cambering

codes for

not written

by the authors.

made by the

authors

search is

conical

based on the

so-called

analysis

effects

using

body itself.

authors,

This

is

through

accomplished

around the

pressure

by

leading

gradients

and is

extensive

is

of

achieved

described

Ref.

code,

in more

Ref.

and design

contributions

7.

also

has the

shell

placed

full

design

9).

COREL by Mike

directly. is

a

to perform

a

to the standand optimization;

a conical theory

capability

wing to

panel

similar

calculate

In addition

the W12SC3 code were also

to

capa-

calculations,

around the body rather

use methods

code (Ref. to

geometry

In addition

(including

It

the

The W12SC3 program

program.

supersonic

Grumman Re-

6, as modified

spanwise

fully

"W12SC3" method

8, and has the capability

linear

options

Ref.

to obtain

in that

an interference

the

were

codes were the

In addition,

5.

program,

to 11.

in

nonconical

Ref.

report

In particular,

linear

in Ref.

this to these

4, was written

and the patch

in

modifications

W12SC3 can treat:

correction Ref.

described

at Grumman.

are described

Many of these

analysis

important

programs

Department

capability,

Correction,

"Woodward-I"

Conical

maneuvering

the expansion

and design-optimization

and a local

on-body the

surface

not available

design-analysis

the Carlson

supersonic

adverse

wing

"Woodward II"

of the USSAEROprogram,

bility);

the Super Critical

surface

Grossman,

extension

number of calculations mixed

as

the

"COREL" method,

by Bernard

of this

ard complete

were developed

The concept

co-workers

of the Grumman Research

modification

of

in

layer.

However,

code makes use of the Craidon The details

for

is contained

boundary

the computer

and their flow

Department

Siclari

employing

report

sweeps, .and

3.

The baseline

nonlinear

in this

generating

the

wing

of the problem

such that

without separate

lower

are obtained.

development

by a conical

detail

of wings

coefficients

supercritical

strength

primarily

design

lift

the crossflow

becomes

discussion

SC3 is a wing concept

(SC3).

supersonic

controlling

coefficients,

the two codes described

aerodynamic

Camber concept;\

lift

A more thorough

edges.

In particular,

2.

higher

the

wingthan on

original

to the work by the made by A. Cenko

----

*Note

that

available

2

the

linear

in the baseline

theory code.

code,

W12SC3, retains

all

the

"normal"

options

and J.

A key

Malone.

geometry

program input,

This codes,

report

Ref.

contains

followed

methods

feature

descriptions,

a brief

two methods geometry

review

is

the

use of

the

for both computer

of the aerodynamic

examples

design.

computer

programs,

the

12, to define

by a number of

in aerodynamic

computer

of

programs.

theory

used by both

and some comments on the

Subsequent requirements

sections for

provide

running

Craidon

use of the

a description

the

codes,

of

detailed

the

input

and a sample case. REVIEW OF THE AERODYNAMICTHEORY

The details brief

overview

of

the

methods

are

of the aerodynamic

and emphasize the assumptions

contained

theory

in

the

is presented

references.

However,

here in order

a

to summarize

employed. COREL Program

The important

nonlinear

ops on supersonic

wings

and mixed subsonic/supersonic

at high

code developed

by B. Grossman,

given

section

fied

spanwise section

be adjusted

account

as long

Ref.

4.

for

as the

the

the geometry

obtained

actual

by the

is

using

(nonconical)

potential

flow

Mach number normal

this

the

through

geometry.

COREL about

can

then

The flowfield

which

a

the speci-

approximation

equation,

devel-

the flowfield

passing

to the

that

computed using

The method computes

that

The results

assumed to be represented proximation

coefficients

by assuming

is conical. to

lift

crossflow

is

is

a good ap-

shock waves is

less

than

the

2-D

about 1.3. Under the transonic fluid

stated

problem

dynamics

finite-difference

assumptions,

- and most of

are directly formulation

the the

calculation

recent

applicable.

Therefore,

in which

transforming

the

domain.

In COREL a single

problem Joukowski

in transonic COREL solves

the bow and crossflow

as part of the solution. Other distinguishing nonconservative form of the finite-difference mappings

advances

becomes similar

characteristics equations

from the physical transformation

to

computational the problem

shocks

by a

are captured

are the use of a and the sequence of

domain to the computational is used for

the wing,

so that

3

the

wing

becomes an exact

circular

or elliptic

This

particular

description,

Ref.

solution

a re-mapping of the

initial

second

major

only

sections.

version

of the code includes

The most

on a crude

using

surface

spanwise

4.

obtained

coordinate

significant

grid

to

refinement

is

use of

improvements

location.

than the use of

find

the

(which

can be nearly

direction

and partly

explaination converge

of

in

for

the

relaxation

column

terminology).

singular).

of the method. for

the

Finally,

computer

allows

some cases

to

A

singular

formulas

in the ring

requirement run

to

the program

sweeps to be made partly (see

by

the importance

finite-difference

direction

This

followed

which

for

would

an not

previously.

The spanwise extracted

from

section

section

the

analyzed

Craidon

obtained

at

equations

locations

difference

streamwise increment

program,

slope

of a conical

can then

approximate

between

set,

Ref.

Ref.

7, for

Ref.

the

The surface

patch

the

true

surface

be used to make a correction

the pressures

on the actual

wing analysis.

nonconical

of

program of

code is

shape can be

the

surface

can also section.

to the pressure

patch

be used to

the surface

spanwise

or

geometry

This

the section

slope

the same

input

The Craidon

solution

streamwise with

be specifically 6.

6, so that

and requires

by a Newton iteration.

the

data

program,

of the Craidon arbitrary

in COREL can either

geometry

comes from the Siclari

a modification

obtain

to allow

reduces

expression

rather

has been generalized

is the use of an initial

This

an analytic

of the mapping metric gradients

over the published

the convergence

part

metric

case of uncambered

the bow shock position,

estimate

and improves

the

the

improvement

the computed bow shock

bow shock estimate

for

and the This

slope

coefficient

to

geometry.

W12SC3 Program The panel

method program

the aerodynamics 9). with effort

Although

of the configuration

the most useful

a number of

used for

additional

elements features,

calculating

linear

theory

estimate

is based on the Woodward codes

(Ref.

of

5 and

of both codes have been combined together the

was the Woodward B-00 code obtained

in November 1976.

the

The W12SC3 code consists

baseline

code

for

from the NASA Langley of a combination

the

development

Research

of source

Center

and vortex

panel

singularity

either

distributions.

a constant

constant

or a piecewise

linear

The source

singularities

spanwise.

piecewise-linear

The vortex

streamwise

fashion

for

l

Full

Analysis

l

Full

Design

l

Full

Optimization

l

Mixed Design-Analysis

l

Mixed Design-Optimization.

wing-body

in

and are piecewise-

constant

on body panels

and

on wing panels.

and can be used to perform

The W12SC3 program

are distributed

streamwise are

The W12SC3 code is a Grumman version the SC3 study

singularities

applies

the following

linear

configurations.

of the Woodward II

theory

bitrary

body model (as in Woodward II),

effects

be calculated

aerodynamic

panel

Wing-on-body

code developed

effects

shell

that

the solutions

calculated

or the user may specify

on an interference

I.

functions:

methods to find are

for

on the

that

approximates

ar-

wing-on-body

the actual

body

shape (as in Woodward I). W12SC3 Program Options Reference

5 gives

a detailed

discussion

contained

in W12SC3 and should

be considered

program.

Certain

do

singularity

distributions

the execution

control

no extra

point

numbers). calculated

are

change2

options

are replaced

singularities

locations

These

optimization

improve

W12SC3 options,

in Woodward II

occurs,

fixed are

(see Ref.

on an interference analysis

emphasized, distributions

results

however,

exist,

the

however,

that

for

the

for

the

used in Woodward II. varying

vortex

are used at supersonic

trailing

for

chord

In addition, with

supersonic

the W12SC3 program

(85% for

implementing

cases

the

panels

can reproduce

edges.

used

panels.

When

edges and Mach

design

where wing-on-body

leading

During

subsonic

the

constant-pressure

new

aerodynamic

vortex

10) and for

wings

between

linearly

at 95% panel

methodology

reference

by constant-strength

necessary

shell.

aerodynamics

a primary

used in W12SC3 and those

of several

exclusively this

differences

of

and

effects

are

panels It

Woodward II

should

be

pressure

when desired. 5

The final

output

of

each of

wing camber distribution. slopes,

body shape,

singularity

.This

new design

angle-of-attack

The resulting

are then used to determine

surface

The W12SC3 program

and optimization

camber distribution,

and aircraft

strengths.

numbers.

the

and source

velocities

calculate

Drag polar previous

of

the

results

required

aerodynamic

can be obtained

results

requesting

cycle,

the

influence

by utilizing

previous

the

a

aero panel distributions

coefficients. for

Each new Mach number is compared to the previous

a recalculation

is

wing thickness

singularity

and pressure

to

with

are used to calculate

vortex

can be used

together

options

multiple

value

Mach

to determine

matrices

is

necessary.

camber distribution

Mach number but

changing

if

from

the

a

aircraft

angle-of-attack. The five program

user,

analysis, as well

For each of the and wing-body Full number,

as other

interference

effects

cycle

-

a lifting-pressure

for

wing

panels.

Full

required

wing

program subject

6

lift

coefficient

then

determines

to the given

user

specifies

the input

constraints.

body

geometry,

camber distribution, surface

a.previous

Mach

thickness velocities

design

wing

configuration

and

or optimi-

user

wing

geometry,

Mach

- c (C ) distribution 'LOWER 'UPPER then calculates the wing camber dis-

lifting-pressure

constraint

CL or the the

configuration,

below.

calculation.

- The program

Optimization.

of the

described

configuration

during

The W12SC3 Program

to produce

to the W12SC3

are briefly

are used to determine

coefficient

number, and the type of loading the

specifies

generated

The program

and

available

in the calculations.

The given

attitude

number,

tribution

user

angle-of-attack.

can be used for this

Design.

a body is part

are included

A camber distribution

options

of the code,

if

- The program

and aircraft

pressures.

all

features

options,

and aircraft

Full

and optimization

following

Analysis.

distributions, zation

design,

inputs

desired.

coefficients. configuration

geometry,

The constraint

can be either

CL and center

camber distribution

of pressure, for

Mach

X The CP' minimum wing drag

- The program user specifies

Mixed Design-Analysis.

and a lifting-pressure

Mach number,

For panels

wing panel. specified

camber slopes

(85% for

the camber slopes

the

subsonic

input'slope

were given,

value

for

each

is assumed to be

Mach numbers).

where pressures

geometry,

The program will

and pressures

where

were given.

An additional this

or camber-slope

where cambers are input,

at the 95% box chord

then determine

coefficient

configuration

SC3 option

will

perform

a conical

mixed design-analysis.

For

case: 1. A conical

ray

(outboard

of

dividing

the

ray)

2. At control

dividing

the

dividing

wing

ray)

on the

pressures

may have been calculated

slopes

a conical

supercritical

to

points

panel

(inboard

of the

optimization

are prescribed ACp vs Q.

by COREL (combined

These

COREL/W12SC3 run)

(W12SC3 alone run).

on the subcritical

have

pressures

distribution,

panel,

the code would have used for

that

replaced

these

slopes

camber-slopes

a full

analysis

during

are prescribed cycle

a previous

or camber

design

or

cycle.

4. The code then pressures

panel

panel,

lifting-pressure

by the user

to be those

a supercritical

and a subcritical

according

3. At control

into

is defined.

points

or supplied

planform

determines

camber-slopes

where camber-slopes

where pressures

were given,

and

were given.

Mixed Design-Optimization

(constrained - The program --__~. --.-_--Win&Optimization). user inputs configuration geometry, Mach number, and the wing CL (and X ) conCP straint(s) desired. In addition, the lifting-pressure coefficients on an arbitrary wing

number of wing camber-slopes

straints.

required

The program

wing planform

panels

are specified. to

minimize

wing

user has the option

or on the portion

The program drag

subject

of minimizing

then to

determines the

given

drag on either

of the wing where pressures

the con-

the total

have not been speci-

fied. SC3 option

An additional This

option

ber-slopes

is

similar

at control

to points

the

will

perform

conical on the

a conical

mixed design-optimization.

mixed-design-analysis subcritical

panel

option:

are determined

wing

cam-

so as to

minimize

wing drag subject

producing

the

to

specified

on the supercritical

the

conical

wing

lift

and moment constraints,

lifting-pressure

configurations

flow disturbance 2. In addition

vortex

the

This

conditions

lifting

surface

is

and therefore

algorithm

would be considered

structured

"body"

during

any design

bility

could be quite

or optimization useful

point

linearly

location

automatically

varying

vortex

and number of by the program.

5, pages 43-45).

type panels),

the control

For most options, vortex

panels.

point

Point

if:

The wingby applying

than

effect,

another

paneling

segments.

can be also However,

additional

slopes This

on the

the

segments

are held additional

constant flexi-

Locations

singularities

singularities

(full along

analysis

each wing

selected leading

only) chord

are dependent

and trailing

the control are computed on the

panels

location

at 95% of the box chord.

is fixed

automatically

are specified

selects

flight

edge sweep angles

constant-pressure

the W12SC3 program

This occurs

their

body

for some cases.

The locations If

in

these

calculations.

Mach number and the wing-streamwise-strip (see Ref.

or tail

and thus

parts,

Control For

is,

the

wing.

rather

shell

that

about

approximately

shell

such

entire

model is comprised

on the

shell

wing,

the

an interference

placed shell

the interference

nacelle,

is

is

treated

The interference

surface.

for

models,

those

interference

methods:

or

panel

to

then

on the

account

cross-section

similar

lift

used to model additional solution

to

body shape

constant

due to

body

actual

singularities

body interaction actual

panels

and body source

approximates

boundary

source

one of two distinct

on the body (as in Woodward II),

(as in Woodward I).

the

using

to the wing

that

of planar

points

Effects

may be modeled using

1. Wing and body are paneled

shell

at control

as

panel. Wing-on-Body

Wing-body

distribution

as well

(Woodward I

Woodward I type

I

l

Any option

l

The user inputs

l

Wing control cycle

except

analysis

are used,

vortex

Gauss-Seidel, sive

shells

program

blocked

also

aerodynamic

for

the full

the matrix

the iterative cient

for

a fifth

solution

matrix

technique

polar

new singularity utilizing

is the only

to converge

inverse

distribution

new boundary

the

inversion

aerodynamic

is

obtained

blocked succes-

The W12SC3

based on inversion technique

of

available

The blocked

Jacobi

be used in analysis

a given This

Jacobi,

and

5 and 9, respectively.

for

methods.

is

options.)

in Ref.

determine

case only.

solution

would normally

calculations,

the required

which

to

and blocked

analysis

technique

and optimization

than use of the iterative

of storing

the full

(this

- blocked

overrelaxation,

methods are described

inversion drag

or optimization

techniques

Four methods

- are available

methods fail

for

design

Strength

iterative

strengths.

and mixed design

The matrix However,

Code utilizes successive

influence

inversion

of Singularity

controlled

provides

the

from a preceding

are used.

singularity

overrelaxation

or

or

Woodward II

and source

or

camber-slopes,

camber slopes

Determination The original

is chosen,

wing control-point

point

Interference

l

full

set

of boundary

technique

efficiency

matrix.

conditions.

can be more effi-

is,

in part,

For repeated

by a single

cases when

a result

Mach numbers,

matrix-multiplication

a

step

conditions. Camber Distributions

Camber distributions

can be obtained

by three

methods

within

the

W12SC3

Program. The first

type

two or more airfoil chord,

is a user-supplied chords

as in the standard the

has been calculated, interpolation

and a slope

mean camber-line

and referenced

Craidon-type

to the

input,

Ref.

mean camber-line value

is assigned

distribution,

leading 6.

given

edge Z-height

After

surface

is

to the

leading

along

at each

the wing paneling

curve-fit

using

spline

and trailing

edges of

each panel. 9

~-~

-..-.--.--

-.---.-.

..-.

_-

..-

.

_

..-.---

..-_...-.

-

.._..

-...

.

_....

_,___

-

.

. .

.

.

. ..

.,.,

,,I,,

The second type This

optional

data

of camber distribution input

ated at each panel

control

The third

of

execution

type

of the

camber slopes

full

given

by the program

user.

one per panel,

evalu-

by the

during

location.

camber distribution and mixed

is

design

are given

at each panel

When camber slopes

are obtained

are determined

supplied

of camber slopes,

consists

point

is also

calculated

and optimization

control

program

options.

The resulting

point.

as part

of the

as in Woodward I by integrating

solution,

wing camber-shapes

camber slopes

along

each airfoil

chord. Pressure Velocities shell

control

linear

theory Panels

and pressures wing calculations) are then

pressures For constant

vortex

panel

are used.

chord)

pressuress

chord

panels,

The user may ask for

at all

Correction

is applied

assigned

at 50% panel

stations.

are calculated

The Carlson

points.

Distributions wing,

(a local

point

wing spanwise

These are found by streamwise

vortex

between

pressures

pressure

panels,

control

(pressures

distributions

interpolation

to supersonic

points.

varying

are found by interpolating

and interference

correction

at wing control For linearly

the control

body,

the

points.

at 85% or 95%

at specified

between control

axial

points.

Force and Moment Coefficients Panel axial

pressure

and pitching

force,

in the configuration obtained the

area.

10

Total

lift,

appropriate

direction The panel

on the wing thickness

are used to calculate

moment about a reference

model.

by summing the

freestream

reference

coefficients

slopes,

drag, force

of normal

and moment coefficients the

angles

wing camber slopes,

results

used for

force,

for each aero panel

and moment components

and normalizing inclination

point

values

with these

are then with

respect

to

a user-supplied calculations

and type of panel singularity.

depend

Wing thickness case of also

slopes

the Woodward.

evaluated camber

location.

This

slopes in Ref.

force

evaluated linear

centroid.

the

75% chord

centroids,

panels,

constant

camber slopes

strength

are used rather

improve

as in the

than

drag predictions.

vortex the

are

panels,

centroidal

The rationale

is

9, pages 95-97.

shell, values

at panel

vortex

For

and moment coefficients

the interference configuration

at

For

change was made to

fully

Total

program.

at each panel

however, discussed

are presently

as well

are found

as for

based on the

the

full

Carlson

for

the

body,

configuration.

Correction

the wing,

and

Wing and full-

pressures

are also

calcu-

lated. For

mixed

wing (panels

design-analysis

and mixed

where pressures

are not specified) Paneling

The following l

A total

rules

design-optimization

should

of 1653 panels

forces

551 shell

and additional

are also calculated.

when modeling

may be used to model all

fin,

exposed

Rules

be followed

551wing,

options,

configurations:

surfaces

and canard panels nacelle,

wing,

and canard panels

551 body panels l

A total

of 19 streamwise

strips

is allowed

for

all

wing,

fin,

and canard

direction

is

29 on each

panels l

The maximum number of panels wing,

l

fin,

A total

in

the

streamwise

or canard surface

of 29 panels

in the streamwise

direction

is allowed

for

all

body

segements l

The maximum number of panels

used to model the

body cross-section

is

19

on each body segment a

A total

of 19 streamwise

additional l

nacelle,

wing,

strips

shell

for

all

interference

shell

and

and canard surfaces

The maximum number of panels interference

is allowed in the

and each additional

streamwise nacelle,

direction wing,

is

29 on each

and canard surface

11

If

l

utilizing

iterative

circumferential

fuselage

is

rule,

not

a rigid

used as a solution reasonable For

l

however,

tribution,

the

of

results

leading

a nonuniform will

order

be an integer iteration

if

panels

factor

of SO.

matrix

inversion

techniques

converge

on This is in

a

also

a uniform

wing

paneling

in most cases (see Ref.

,edge thrust

from the

distribution

10)

computed

pressure

dis-

streamwise spacing is necessary with leading edge -2 -3 10 to 10 chord lengths. Spanwise cosine

of improve

constant-strength

accurate

if

problems,

smoother

on the

that

number of

and can be relaxed

method or

For 'calculation

spacing

should

the

number of cycles

produce

boxes

techniques,

strips

design-optimization

should l

solution

results.

vortex

A limited

panels

number of analyses

(Woodward I panels)

indicate

produce

the most

results. TYPICAL APPLICATIONS OF THE PROGRAMS

The two programs used to handle Some examples expected

each contain

most of

the problems

illustrating

to agree with

numerous that

how these experimental

arise

with

and thus

the

for

design

modifying

the

illustrates the

evolves

followed

around

by a strong

spanwise

These results wise section

are taken

is purely

of nonconical

geometry

using general

12

the equivalent (and expensive)

conical.

in

The result

section

results

figure

3.

correction

NCOREL method (Ref.

section.

over

a specified

on the design

design.

for high

14).

analysis

a case in which lift

levels,

and reduce 13.

the cross-

In both cases

was primarily

in COREL, together The experimental

data.

the span-

the more representative

The wing

1,

The predictions

the experimental

from Ref. for

spanwise

is shown in figure crossflow

with

can be

of the code,

previous

section.

supercritical

2, also extracted Typical

are given conical

edge to

13.

in this

a symmetric

shaped to obtain

flow shock wave is shown in figure the geometry

for

shock wave, agree well

has been carefully

can be

wing

submissions

based

point for

leading

from Ref.

they

supersonic

repetitive

sections

starting

the

crossflow

distribution

through

the COREL predictions

expansion

during

data are presented

An example of a typical

results. which

user

the

and together

codes are used and how the results

The COREL code computes the pressure section

options,

with

case

designed the more

data are

from

SPANWISE PRESSURES

67’

i :&

-3

_--- - - -, I’*., f

-/v-.v ---‘----mm-

lnviscid

__--

----

----

_ --

theory

.

.5 11111111111l111l111l~~~l~,~l,,,l~,,l,,,~ 0

.l

3

..I

.I

.S

.6

.7

.8

.9

1.0

ETkrl R63-0961-OOlPP

Figure

1. - Comparison between experiment and COREL spanwise pressure distribution for a symmetric section at M = 1.70 (from ref. 13).

13

SPANWISE

-

lnviscid

theory

.4

.5 0

.1

.2

.3

.4

.5

.6

.7

A

.9 1

ETA,q R634961-002PP

Figure

14

2. - Comparison between experiment and COREL spanwise pressure distribution for a cambered section at M = 1.62 (from ref. 13).

SYM M P

-0.4

PT

a

1.70 11.91

----we--

COREL

---

COREL

48 + NONCONICAL

CORRECTION

-0.3

-0.2

-0.1

=P

0.0

I 0.0

I 0.2

I 0.4

1 0.6

1 0.6

0

rl

0.1

0.1

------------0.l

----____

------___

2.00*10m R./L= Transition f fxed

--------

---

--. -.

--.

A. x = 15.5 a4

Figure

predictions of COREL and COREL + 3. - Typical nonconical correction for the demonstration wing of ref. 15, and including NCOREL predictions, ref. 16.

15

SYM M --------

--

a

PT

COREL

-

COREL + NONCONICAL

CORRECTION

44

4A

-a l-

0

cP

0.CI-

a1

I-

a2

03

R./L= 2.00*10~ Transition Fixed .oA

B. x=19.9 R63-0961-004PP

Figure

16

3. - Continued.

SYM M -0.4

PT

a

0 1.70 11.91 48 -------COREL ---

COREL

+ NONCONICAL

CORRECTION

P2

-0.1

cP a0

I 0.0

I 0.2

I 0.4

I 0.6

I

0.8

v

0.1

0.2

0.S

2.00+10m Re/L= Transition Fixed

0.4

C. x = 24.4 R63-0961-005PP

Figure

3. - Concluded.

17

Ref.

The nonconical

15.

are almost value

correction

as good as the solution

sentative

options

in

problems effect

are

shell,

the

Figure

4 shows the panel

5.

of the complete

of the COREL code in performing Several

II

to the COREL results

report,

Ref.

Figure

a = 5O). problem

of

This with

the

and without

the

basic

that

with

the sample case given for

which

data

can arise,

the

original

are available

the

root

example

case

and the figure

elimination

of

the

18

4. - Singularity

paneling

for

wing-body

Woodward

is shown in figure

wiggles

R63-096i-006PP

Figure

interference

in the original

near the wing

results

Repre-

and the mixed design-optimization.

correction,

distribution

is the case for "wiggles"

analysis

model for the

the

wing design. examples.

Carlson

that

and demonstrates

illustrative

the

5A reproduces

equations

predictions

the W12SC3 code require

A pressure

5.

provide

analysis.

(M = 2.01, shows the with

the

-0.3

, -02

WITHOUT SHEEL

WITH SHELL

WITH SHELL + CARLSON CORRECTION

-0.1

WC C

P

0.4 I

02 I

0

0.6

08 I

1.0 b

0.1 CARLSON

DATA MEMO

CORRECTION

NASA lo-15-56L

‘02

’ b/2

=0.161 A.

M -2.01 a -6’

0.3 R83-0961-007PP

Figure

effect of interference 5. - Wing-body analysis: wing pressures, and comparison with data.

shell

on W12SC3

19

-0.3 I-

NITHOUT

SHELL NOTE:

4.i L,-

NO DATA AVAILABLE THIS MACH NUMBER, SYMBOLS REPRESENT COMPUTED POINTS.

AT

-0.1 WITH

SHELL

WC %

0

I 0.6

I 0.4

, 02

0.1

0.2

d

b/2 B. M=1.72 01 =6’=

0.3 R83-0961-008PP

Figure

20

5. - Concluded.

I 0.6

I 1 .o

use of

the

interference

when the

Carlson

M = 1.72.

This

results

shell,

correction

and the is

Figure

lift.

more severe

case for

7, taken

Figure large

Figure

used.

case shows the dramatic

when the body source

carry-over

improved

singularities

from Ref.

results

more exact

analysis

17, provides

the

data

the

that

required

to

results

interference for

the

correction

are available,

for

for

account

of the Carlson results

occurs

same result

in the wing-body

are not

a typical

in a

Ref.

16.

case with

a

body and canard. An example of the use of the conical

planform

given

design

option

and extent analysis

in

figure

8 is

is used to study

of

the

Figure

11 provides results

in

the

In some cases the results planform

given

in

near the interface

pressure

umetric

near

of

analysis

include

trailing

edge.

leading

not as good as the drag polar

when the

drag

optimization is minimized

leading

edge and camber shape

boundary.

case given

in

good agreement

figure

3 are

except

in the

is supercritical. figure

The

In this

case,

16 was obtained the

by

predicted

vol-

from the wave drag program of Ref.

the poor factors

the agreement

(see figure

this.

the drag predictions.

shown in

agreement which

with

are not

with

the

lift

of

figure

show an irregular

the

pressure

accounted

shock wave drag and the viscous

that

type

require

the cranked

to the

data

obtained

Other

edge. note

drag

despite

the crossflow Also,

the

the W12SC3 code and replacing

the value

are obtained the

the

level

while

that

and pressure-free

show generally

the

the maneuver

case the minimum drag pressure

edge where the crossflow

the drag prediction wave drag with

Notice

15 can be used to evaluate

with

for

the

mixed

This

distribution,

13 and 14 respectively,

These results

leading

to

edge panel.

distributions

Consider

of W12SC3 corresponding

good agreement

These results tions

of Ref.

15.

near the

the very taking

figure

In this

for

case the

the method does not explicitly

are not as smooth.

in figures

predictions

shown in

pressure

between the pressure-fixed

The experiment

leading

camber distribution.

12.

In this

of the minimum drag

and camber distributions

figure

given

distributions,

9.

optimum pressure

even though

surface,

mixed-design-optimization

figure

on the

the target

smooth pressure

the entire

region

pressure

10 shows the predicted of

in

the sensitivity

prescribed

a sample

panel

presented

is used to determine

wing.

for

with

5B provides

improvement

6 shows typical

which

agreement

for

interaction

18.

predicin the at the

and moment results

is

17).

21

DELTA WING -GEOMETRY AIAA 79 - 0345

0.4

0 W12SC3 Cl W12SC3

-BASIC -WITH

SOLUTION CARLSON

CORRECTION

o o -

W12SC3 W12SC3 NCOREL

-BASIC -WITH (REF.

SOLUTION CARLSON 16)

CORRECTION

a.1

CP A

=

71.60

a

=

10”

M

-

1.67

0

,

--0.4

02

0.6

OB

0.1

02.

0.3

0.4

Figure

22

6. - Comparison of W12SC3 with Carlson correction.

exact

B. STN 2 solution

- effect

of

1 1

DELTA WING GEOMETRY FROM AIAA 79-0345

b q

-0.4 -

W126C3 W12SC3 NCOREL

-BASIC -WITH (REF.

SOLUTION CARLSON 161

CORRECTION

-0.3

a.2 3 -0.1

Y 7 4

%

0

----

0.2

-.+

..__ 0.4

5

0.6

0.6

1

n 0.1

-0.4

0.2

T

o q

-

W12SC3 W12SC3 NCOREL

- BASIC SOLUTION -WITH CARLSON (REF. 16)

CORRECTION A

0.3

0.4

C. STN 3

\

Of4

I\

=

71.6”

ff

=

loo

M

=

197

4.6

oi6

1

D. STN 4 R83-0961-OlOf'P

Figure

6. - Cijntinued.

23

DELTA WING GEOMETRY FROM AIAA 79-0345

6

0 0

-0.4 -

-0.3

W12SC3 W12SC3 NCOREL

-BASIC -WITH (REF.

SOLUTION CARLSON 16)

CORRECTION

I

P

6.2

-0.1

M

0.4

=

1.97

E. STN5

1

R83-0961-OllPP

Figure

24

I

6. - Concluded.

,.

/’

SPANWISE PREsuRESY

-%fhfh!

-

!

R83-0961412PP

Figure

I

I

I

I

I

I

I

I

1

1

I

I

I

I

I

I

I

A. PANEL MODEL FOR WING-BODYCANARD ANALYSIS 7. - Comparison of W12SC3 with experimental data of ref.

conceptual 15.

wing-body-canard

25

4

-0.

M

-

1.62

a

-

loo

x

-

132”

TRANSITION

FIXED

REIFT-2~10~

-0.:

-0: CANARD

DATA

OFF

0

ON

0

Wl2SC3

-T-m 0

cP

c

BODY

SIDE

0.1

CANARD TIP

0.2

0.3

0.4

B. CAMBERED WING Figure

26

7. - Continued.

4.4

All =

1.62

a-6” x

-0.3

-

139”

TRANSITION REIFT

FIXED

- 2 X lo6

-0.2

8 -0.1

=P

I

0

0.2

1

I

I

I

0.4

0.6 A

0.6

BODY

I 1.0

CANARD

0.1

I 0.2

CANARD’

DATA

W12SC3

OFF ON

Cl

----

0.3

0.4 i

C. FLAT WING RBJ-0961-014PP Figure

7. - Concluded.

27

PURE TRAPEZOIDAL

PLANFORM

-

2.6

.A

.

-

57O

.X

-

02

=

0.035

.

AR

t/c

PREShlRE PRESCRIBED FOR PANELS OUTBOARD OF DIVIDING RAY

DIVIDING 7,~

qDR

RAY

a l-O

1’0.8744

R63-0961-015PP

Figure

8. - Geometry

and panel

model for

SC3 wing design

example.

28

;i

DIVIDING

RAY

LOCATION,

r),,

026 0El

5404 -- 8744

FLAT WING ANALYSIS

\

- .6163 - .6060 025

.M c

.

- 1.62 CL

- 0.40

0.23 A=,

INVERSE m---m-----

-

(C, -CONSTANT)

022

021

020

---

w-----p-

---v

LINEAR

THEORY 17)~~

MINIMUM

DRAG

El)

ACp *c3 I 0.19

cL

0.36

1.0

1.1

12

1.3

1.4

0.40

0.44

0.48

0.52

0.56

AcP

I SC3

(PRESSURE ou TBOAR,D

SPECIFIED OF DIVIDING

RAY)

R63QiN51Q16PP

Figure

9. - Drag performance using trapezoidal

of SC wing design from linear planform of Figure 8.

theory

1.0

r .M 0

CL

DRAG MINIMIZED SURFACE

ON ENTIRE

-El-

-A--

DRAG MINIMIZED pArEyD OF qDR

ON SURFACE WBCRlTlCAL

- 1.62 -0.4 - 0.46

07)

0.8

0.6

0.0

0.2

0.4

0.6

0.8

1.0

x/c R63-0961-017PP

Figure

30

10. - Minimum drag pressure distributions for the qDR = 0.616 case shown in Figure 8.

0.6

-

.M 0

CL

1.62

-0.4

l r) - 0.46 O-4

0.2

0.2 ‘dz z

0.4

x/c

0.6

0.6

1.0

0.0

-0.2

a.4

-0.6

-a-

DRAG MINIMIZED ENTIRE SURFACE

ON

-4-

DRAG MINIMIZED ON SURFACE INBOARD OF qDR (SUBCRITICAL PANEL)

R83-0961-018PP

Figure

11. - Minimum drag camber distributions the ~DR = 0.616 case shown in FigUre 8.

for

31

CRANKED

LEADING

EDGE COMPARISON STATION

STRAIGHT

LEADING

EDGE

R83-0961-019PP

Figure

0.6

12. - SC3 wing example.

.rvl

= 1.62

0

=0.4

CL

design

model for

cranked

leading

edge

WITH CRANKED LEADING EDGE

0.4 -

STRAIGHT LEADING

AcP

EDGE

0.2 -

COMPARISON

0

Y bR=

STATION,

6.56

I

I

I

I

1

0.2

0.4

0.6

0.6

1.0

x/c R83-0961-02OPP

Figure

32

13. - Effect

of addition

of L.E.

"crankli.

0

M

0

c

-1.62 -0.40

L

PRESSURE

-0.16

-c.w.---

FIXED

-

-c

FREE

0

--

/-

/’

/ /

STRAIGHT LEADING EDGE

dzldx

/

/

-4 /

-0.04

/ /

a 0

/’

0.2

0.4

0.6

0.6

1.0

x/c

0.04

/

COMPARISON

STATION,&

- 0.50

R83-0961-021PP

Figure

14. - Wing slopes for leading edge.

mixed design

with

straight

and cranked

33

.

-

----.m

.T

-0.1

-0.

-0.

-o.,

cP

c

0.1

0.2

0.3

M = 1.62

0.4

ALPHA

A. x = 15.50

TEST

DATA

9.92 7.92

8

13.92 11.93

s

(REF.

15)

R83-0961-022PP

Figure

15. - Pressure predictions from W12SC3 for demonstration wing of ref. 15.

34 h

-0.1

.’

0.2

0.4

h

0.6

c:

IO.6

7 1.0

ALPHA

B. x=19.90

7.92 9.92 11.93 13.92

TEST

DATA

(REF.

15)

8 ;

R83-0961-023PP

Figure

15. - Continued.

35

0.3 1.)

0.4 tr

M=1.62

ALPHA

C.

x

=24.40

R83-0961-02&'P

Figure

36

TEST

DATA

7.92 9.92

8

11.93 13.92

$

15. - Concluded.

(REF.

‘161

w12SC3 RESULTS FOR 19X20 PANELS LOWER DRAG LIMIT W12SC3 OPTIMUM SOLUTIONS 0.6 iA W12SC3

RESULT

UPPER DRAG LIMIT: W12SC3 FLAT WING ANALYSIS

0.4

DEMO

WING PERFORMANCE TEST DATA

0.3 I-DEMO WING PREDICTION WlPSC3 ANALYSIS CL

0.2 ,__ (WING

THICKNESS,

BUT WITH

CD

FOR THICKNESS

DISTRIBUTION AT Cc= 0” REMOVED FROM PiEDICTION REPLACED WITH ESTIMATED CD USING WAVE DRAG 0 FRICTION ESTIMATES)

0.1

0

RUN WITH

AND AND SKIN

I0

R83-0961-025PP

Figure

16. - SC3 demo wing performance: (from ref. 15).

basic

leading

edge, M = 1.62

37

US

W12SC3 ANALYSIS:

19X20 PANELS

0.4

i W12SC3

0.3 C.

(WITH

I.

CARLSON

ANALYSIS

,#

0

CORRECTION)

/

6

6

0

%

0.2

0.1

0 I 2 /

-

4

lb

12.

m

a, DEGREES -.lJR83-0961-026PP

Figure

38

17. - SC3 demo wing: M = 1.62 (from

lift ref.

and moment, basic 15).

leading

edge,

SOMEAREAS REQUIRING SPECIAL CARE To obtain

good results

must understand must, develop fully

the basic

his

studying

look

for

being

skills the

ideas using

computational

and underlying

assumptions

Injthissection

the results

and include

aerodynamics

the code by running

results.

in studying

computed,

using

that

used.

the

user

In addition,

some model problems

we point

to ensure

methods,

he

and care-

out some of the things

the desired

some comments on limitations

solution

is

still

exist

that

in

to fact

in some

areas. In using

COREL, certain

checks

should

be made by looking

at the output

from

each run: 1. Check the

iteration

history

to verify

that

the

SLOR iteration

is

con-

verging. 2. Check that bow shock

JSHMAX and JSHMIN, the in

JSHMAX should

the

computational

be at least

and JSHMIN should Normally,

maximum and minimum locations

grid,

are "reasonable".

two or three

be at least

halfway

JSHMAX and JSHMIN are

mesh points

of the

The value

of

in from the mesh edge,

between the body and the mesh edge.

nearly

equal

after

the

solution

is

remapped. 3. Check that

no points

violate

is zero in the iteration If

COREL does not

"extreme" the

sonic

edge is

leading

which

the

first

step

points

initial

than

guess

that

it

is inside

by the input

about

for

that

normally

the

parameter

1.1,

due to

NPVD

to

it

is

an "extreme"

and is

location

COREL run

EPSHKI.

is

The next be relatively

The initial

A small

is

value

location

case, likely

to plot step

the

leading one for

to be poor. the

input

to

The

geometry

is to check the mapped

smooth,

and the shock must

should

be checked to ensure

shock position (-0.5)

or an

relative

Mach number normal

The singularity edge.

problem

the

are correct.

leading

a geometry

If

the .bow shock

These should

the body.

by making sure that

Mach number can be quantified

a failed

they

body and shock locations. be outside

is

(An "extreme"

in troubleshooting

and verify

always

it

edge Mach number.

much greater

dominance

history.

work,

Mach number.

diagonal

will

can be controlled

move the shock "out"

in

39

the

computational

move

mesh (away from the

the shock "in"

in the grid.

The solution

algorithm

typical

of

design-point the

properly, reliability

is

work

design

work

extremely

so that,

that

convergence

although

for

the

occurs

large

expensive.

In some

convergence

problems.

In defining definition

for

the

for

several

edge and one leading-edge spacing

should

airfoil

not

supersonic

adequate

definition

without

(-1.6)

changes

in

will

geometry

to be performing

excessive

spanwise

cut

section

the spanwise

concern

semi-span)

for

the

this

the

This

points

to the

solution

on the

addition

wing.

actual

is included

sections, for

that

cases

artificial

However,

the

additional

the section.

with

However, their

must intersect

of

which

the

a spanwise edge is cut,

A very

this

inside

A

the point

airfoils.

sections

centerline.

and it

dege.

is consistent

When the trailing the

adequate

nose when based on the

of

section,

consideration. leading

transonic

to the

Because

elimmate

In addition,

accuracy than

at the centerline.

the

affect

the origin

edge.

COREL requires

edges,

the

modern transonic

edge.

layout

between the leading

the

trailing

can be

analysis,

near

of spanwise

trailing

such that

for

be specified

much closer

used.

become prohibitively

require

section

thinner

to

have been developed.

definition

specifying

is

algorithm

could

items

of the leading

can be used to do this.

appended to the

solution

option

should

must be continued

smoothly

direct

be checked

procedure

area is the analysis

supersonic the

solution

must be provided

aft

also

in Mach number or panel

are usually

beginning

section

the

to define

(3) points

requires

intersects

should

for doing this

section

used in sections

be defined

history

COREL, two additional

radius

A second problem

chord.

rules

change abruptly.

definition

because

40

to

value

code appears

iterative

changes

geometry

spanwise

of thumb is that

iteration

converge,

small

geometry Craidon

(0.1%

once the

when the

No precise

the

the

insensitive

numbers of panels

cases,

When using rule

a large

of the computed results.

For cases where W12SC3 does not used,

while

can be accomplished

For W12SC3 calculations, ensure

body),

thin

section

interest

section section the

have

does

not

should

be

centerline

Similarly, areas.

the

W12SC3 code also

The main area

just

slightly

requiring

requires

special

non-coplanar.

For

become erratic

with

"wiggles"

to

problem,

avoid

this

resulting the

ments spanwise,

with

uously

spanwise

varying

segment.

dihedral

dihedral

body source

solution

alone

to

account

in

pressure

distribution

generality

the

canard

section. spanwise code

of

Finally,

the

with

is

not

by using

This

In order straight

of with

seg-

a contineach

is [email protected] the arbitary interference;

when this

eliminate

approach

is

the wiggles

slightly

more

reliably.

contains

a severe

of

canard to ensure

exceeded.

This

panels

to

restriction

twist.

as a nacelle

be taken

nacelle

can

of lo or 2O between

practically

problem

geometry

always

instead

the wing-body

wing.

are

coefficients

as several

a break

will

that

distribution.

can arise

can be input

should

panels

can be overcome

loo

specification

the canard

rows of wing

least

for

on the

is

care

pressure

in several

of wings

influence

be modeled

shell"

the Craidon

input

twist,

the

at

but appears to cure the wiggle

One area in which include

of

the

in which'"wiggles"

the use of an "interference

expensive,

in

attention

the modeling

cases,

(camber)

occurs, the

is

should

breaks

A second situation

care

these

geometry

some special

In

in

the

that

order

in

canard

to

W12SC3 input

a total

restriction

replace

on the

the

of

20

USSAERO

or tail

wing

panels. A problem the

accuracy

surface

that of

the

is given

velocity

spanwise

accurately,

An approximate wise velocity

was discovered

correction

implementing

velocity.

Although

the spanwise

the the

velocity

"Carlson

spanwise

on the

based on uncambered wing results

used in the Carlson

by fundamental

in

correction.

Attempts

changes in the equations

correction" velocity

surface

is

is

off

the

incorrect.

is made to the span-

to correct

the

spanwise

were unsuccessful.

COMPUTERPROGRAMDESCRIPTIONS Both programs system. operating

However, system

any particular report

provides

are designed the

codes

and can,

difficulty. the

overall

to

run on CDC computers

are written

in fact, No

to

be essentially

be converted

general

description

description of

for

with

the NOS operating

independent

use on IBM computers of COREL exists,

the code.

The actual

of

the

without

so that

this

COREL computer

41

code contains

numerous comment cards

code modifications.

One important

in detail

distinction

In C&EL,

between

Z is aligned

direction,

while

in mind while

Y is the spanwise

working

with

is

in other the

with

W12SC3 uses the standard

direction.

the computations

The W12SC3 code description

USSAERO, which has been described

definition.

describing

presented

is

the body axis system

coordinate.

as changes

for from

reports.

two codes

coordinate

and allowing

the

coordinate

system

and X is in the spanwise in which

X is in the body

These distinctions

should

be kept

the codes. COREL Program

The following problems

provides

breakdown

subroutine 1.

calls Start

by groups,

together

Figure with

18 provides description

This

values

a sample case of an elliptic

is

troubleshoot with

19 provides

the

a map of

of each routine.

the NAMELIST, which

execution.

the use of BLOCK DATA for default

to a chart

Figure

a brief

by reading

in the current

provide

information

and the names of the subroutines.

the calculation

to be employed values

sufficient

and make code modifications.

overlay

with

description

done in

defines

the

in the NAMELIST.

the options

main program

and

The default

cone at angle-of-attack,

which

serves

as a check case. 2. in

Establish

Program

generate

the spanwise

GEOM (Overlay,

simple

a spanwise

calculation

requires the

section a table

Three

The (r,9)

However,

the

section;

this

ordinate

of the spanwise

origin

values

choices

from the Craidon of

(r,0)

values and the

are generated

coordinate

is the reason

that,

at the

Some provision

available:

which

describe

location

of

This

the

centerline

spanwise

translating

the singularity

and the

lower

the section

can

section, in polar for

(x,y)

must be located the

done

The numerical

the section

(x = 0),

is

program

from the given

system

must be positive for

COREL.

Geometry Data Set.

internally

(r,8)

section

are

in

read in a specific

the

must be negative.

of

to be analyzed

internally,

number of values,

mapping.

42

1,O).

model geometries

or extract coordinates,

geometry

values.

inside

upper

surface

to ensure

the the

surface ordinate that

the

COREL (2.0) MNSUB -WfWLT ENDPLT INIT CONF INTERP PCS DELTA STRECH RCONF SHOCKR SHOCKI RELAX OUTP EGU IV PMA FORCE GRAF ERPLOT ARCDRV ARCLNG SLOPE SIMP VINTER LIDRAG FAST RFAST SERIES FIT2 INTERX DELTA1 MAST

COREL (1.0) GX AREA MAX DESX ORDMOD PARM GEOCUT GEOMIN START SURF SPFIT PACH PACHX? XPATCH TIPLE TSOLV UWSOLV XCUT VSOLV

R63-0961-027PP

18. - COREL program

Figure origin

is inside

location

of

exception of

the

spanwise

and saved section the

uses at this 3.

controlled

With

the

section for

override

extracted

Additionally, other

singularity

of a possible

sections

generated

the spanwise

from for

is

the

included

mapping

the

Craidon

if

geometry

by Program

in the input internally

section

section

geometry,

corrections.

to be used can be locally point

is

structure.

when the spanwise

nonconical

spanwise

overlay

ordinates

instructions.

generated is input.

additional An option

modified

after

The

with

In the case

information exists it

can be punched

is out

the is

wherein

the

established. and saved

for

desired. established,

MNSUB (Overlay

the 2,0).

solution The first

sequence step

is

begins.

This

to transform

is the

43

spanwise for

section

via

interpolation

transformation

a Joukowski

to

the

does not

transformation

computational

entirely

and spline-fit

grid

eliminate

the

(Note

location. the dependence

that

mesh is

the body and shock are interpolated the

locations

computational

trolled

via

the

predicted

used in the code for

(CONTROL ROUTING TO EXTRACT FROM CRAIDON INPUT)

GEOMIN

the grid SPANWISE

START

(READS

SURF

(CONTROLS

IN CRAIDON

PACHXY *

and spline

the

is then

(COLLECT PATCHES X STATION)

XCUT

(GIVEN VSOLV (FIND

X AND

Y, FIND

(SOLVE LEADING

REQUIRED

EDGE

DATA AND

SET) STORAGE)

FIT COEFFICIENTS POINTS

FOR SPANWISE

AND

SAVE

CALCULATED) MAX

CUT AT SPECIFIED

EQUATIONS

USING

NEWTON’S

ITERATION)

LOCATION)

(SET SPACING)

TSOLV

BOLVES UWSOLV

FOR V (U - 0, W) FROM (SOLVES

PATCH

PATCH

EQUATION)

P

XCUT (SWEEP SPAN)

OUT

a

VSOLV

A. GEOMETRY CALCULATIONS

R83-0961-028l'P

Figure

44

AND

2)

PATCH

19. - COREL subroutine

data

occurs

This work is con-

COEFFICIENTS)

CORNER

and

located

bow shock

GEOMETRY

PATCH

fit.

transformation

indices.

(SPLINE

1 1 (COMPUTE PATCH MIN VALUES)

XPATCH

l

bow shock

is shown in figure

CALCUATION

(COMPUTES

SPFIT 6

TIPLE

of

GEOMETRY

PATCH

single

The body and shock

boundary. grid

the

(CRAIDON’S MAIN PROGRAM; ~3.400 CONTROL ROUTINE FOR READING AND GENERATING PATCH COEFFICIENTS)

PACH

(FIND FINAL VALUES)

shearing

location

The computational

INIT.

the nomenclature

the plane.

in from the edge of the grid

subroutine

GEOCUT

using

and the shock boundary

locations,

mesh so that

mesh points

generated

in the transformed

to the grid

several

with

then

this

of the body coordinate

on its angular location, 9.) An initial guess is made for PB location and it is also mapped with the Joukowski transformation The computational

coordinates

map.

EQUATION)

20 along

in

MNSUB

(MAIN

PROGRAM

STRPLT INIT

FOR NUMERICAL

(ROUTINE (INITIAL

-

TO INITATE

MAPPING,

COW

(SPLINE

PLOTTING)

SPLINE

(CONFORMAL

PCS

SOLUTION)

FIT,

MAPPING

SHOCKI

a’

CONF

at---

PCS

a-

DELTA/lNTERP

(INTERPLATE

DELTA/lNTERP

(INTERPOLATE

STRECH

(ESTIMATE

a

MAPPING

(COMPUTES THE MAPPING AT THE GRID POINTS)

ARCDRV

FOR BODY)

OF SHOCK)

FIT COEFFICIENTS

(INVERSE PLANE) (FIND

ESTABLISHMENT)

OF BOW SHOCK)

(CONFORMAL

RCONF

MESH

OF BODY)

FIT COEFFICIENTS

4.

(SPLINE

AND

FOR SHOCK) BODY

SHOCK

METRIC

OF MAPPING

SECTION

ARCLNG

(COMPUTE

SLOPE

(FIND

DATA

TO GRID

POINTS)

DATA

TO GRID

THE

FREESTREAM

AND

TO SET MESH

POINTS

POINTS) VELOCITIES

IN PHYSICAL

DATA) ARC

SLOPES

LENGTH

OF SECTION)

OF SECTION)

l

t

e. NUMERICAL

SOLUTION CALCULATION

- PAGE 1

R83-0961-029PP

Figure

19. - Continued.

45

MNSUB

(CONTINUED)

RELAX

(SLOR

ITERATION

SHOCKR!

FOR SOLUTION

(REMAP

USING

STRECH ERPLOT OUTP

(GIVEN

FORCE

SOLUTION,

(COMPUTE

VINTER SIMP

(PRINT

EQUIV

PLOT

AND

NON-CONICAL

ARCLNG

(COMPUTE

VINTER

(INTERPOLATE

PMA LIDRAG

GRAF

RESULTS

-MEYER

(COMPUTE

SPAN

LOCATION)

AND

OF INTEREST)

LOWER

TO GET

ARC

INPUT ANGLE

SURFACE

PRESSURES

TO SAME

LOCATION)

LIFT)

CORRECTION

‘e”

HISTORY)

DRAG)

SECTION

(PRANDTL

(PLOT

OF ITERATION

UPPER

SPANLOAD

(MAKE

SHOCK

EQUATION)

(SEE ABOVE)

(INTERPOLATE

(INTEGRATE

COMPUTED

COMPUTE

LIFT

OF POTENTIAL

TO THE PRESURES

DISTRIBUTION)

LENGTH)

GEOMETRY AND

FOR GIVEN

DATA

TO MESH

POINTS)

INVERSE) SPANLOAD

- INDUCED

DRAG

DUE TO TRAILING

VORTICES)

RESULTS)

l

ENDPLT

(ROUTINE

TO STOP PLOTTING)

C. NUMERICAL

SOLUTION CALCULATION

-PAGE 2

R63-0961-030PP

Figure

i-1

i=2

19. - Concluded.

OUTER BOUNDARY p=C(f)),y=l

i=i,

i-i,+1

i= a

/

CoLUMN

, I 1 0

WIND SYMMETRY I‘LANE n 6

1 ?

II



--

x = r/2

I

Rlr UG iMBE:DDE

‘SHOCK t j

~2:

j=l

j

--- ----- --------

----- - ---- ------------

X,i

R63-0961-031PP

Figure

46

plane for COREL calculations, 20. - Computational and program index nomenclature.

4.

With

values

of

the

The initial mation

the values

of the

boundary

a part

The main sweep is possible

no special iterations, that

the

starts

just

outside

the

to

clearly

a constant

line

tional

efficiency

or the

maximum change of

in

convergence history

is

the

number of points the

6.

violating

diagonal

.flowfield

results

compute the pressure

coefficient,

initial

of the

set of

each iteration, This

the

is done to

iteration

in the grid,

sweep

rather

than

first

grid

in the

the

bow shock improve

is

history

both

computa-

and the

bow shock.

or not the solution

less

plot

values

than

of

change

points,

the

and locations

provides

has converged.

the

by print-

the average

supersonic

This

is reached

is traced

location,

number of

located

is

A print

stops.

of

sufficient Virtually

all

job is expended in the SLOR iteration.

F is found and the SLOR iteration

are computed

is used to (nominally),

any two iterations

and its

dominance,

time for the entire

Once the potential

the body (ring).

after

mesh to

The iteration the

of

computed shock shape used to

the iteration

maximum residual,

of the computation

and part

this

100 iterations

between

tolerance,

whether

shock

done so that

potential

the

to evaluate

the

Line

uses a split

Once the maximum number of iterations

maximum and minimum positions

information

Successive

the bow shock.

computational

is then provided.

potential,

After

Thereafter

After

ing out the maximum change of the potential of

the

50 iterations

determined

and the actual

the

and accuracy. the

of

time. This

domain.

grid

is

defined.

is halted

along

convergence

is

save computer

remap the computational

the prescribed

bow shock

maximum -location

the iteration

(nominally),

infor-

Column relaxation

(F) set to zero outside

bow shock

edge,

relaxation.

the bow shock.

ensure

Additional

The program

RELAX.

is made concerning

and the potential

the

points.

is swept around the body (column)

the ring

of the

compute

at the grid

set.

using

For the first

saved,

the outer

are solved

instabilities.

location

to

the bow shock and moves in toward

considered

numerical the

values

are also

in subroutine

of the grid

provision

velocity

used

is also generated.

equations

from outside

STRECH is

conditions

processing

(SLOR) algorithm

the sweep starts avoid

and freestream

The finite-difference so that

sweep,

metric

for output

Over Relaxation

subroutine

established,

mapping

required 5.

grid

in subroutine cross

flow

OUTP.

is terminated,

The calculation

Mach number,

total

is

the

made to

Mach number,

and

47

velocity

components.

surface This

but,

ities

provide

bow shock graphics code.

in

information

planes.

is to call

60 x 60.

out,

nonconical

effects

is then

carried

the graphics

routine

to plot

span

is

carried

computing

point

surface

streamline

The standard

COREL step

spanwise

Pressure

rection,

at the user's

in

and Fast

options

spacing grid

a combined

of

is

grids,

divided

the

units

The

use in the

computational

use in the W12SC3 Transform the

analyzed

pressures

to

The final

usually by two

is nominally

COREL/W12SC3 run

of W12SC3.

for

Used by COREL

I/O and Storage:

USE

UNIT

of

for

and printed.

sequence

and Large Core Arrays

COREL uses the following

Fourier

modification out

for

veloc-

location.

step

two, at

is

5

Input

6

output

7

X, Cp output

8

Spanwise section

punched output

10

Craidon

geometry

data

14

Craidon

patch cut data

for plots

in

each

30 x 30 and

to

size. save

the non-conical AC vs TI (with or without P for use in the conical mixed-design-analysis

option)

I/O Units

output

in

the

of the code, 60 x 60 is the maximum grid

distribution

mixed-design-optimization

both

field.

set of computed

computed and stored next,

on the

in the

where

The next

on a sequence

The grid

version

surface,

only

the results.

out

time.

refinement.

In the standard

7. The final

48

printed

the

grid

at each grid systems.

computed

Optionally,

the

to reduce

successive

are

out

on the

the

are then

and drag

is computed,

The SLOR solution order

computing

"e".

determine for

coordinate

printed

ACp is computed and optionally

The spanload

account

of

locations

Lift

routines.

are

more details

for

line

results

can be output

with

a variety

and sonic

and physical

they

is repeated

are output

results

to

as an option,

information

these

Generally,

the corand

20

Equivalent

32

Data set for W12SC3

99

Graphics

There are six

large

arrays

conical

section

data

which primarily

control

the amount of core required

by

COREL: Common Block

Contents

Array

BLK2

F

The potential

function

H

The non-singular

:

portion

of the metric

of the

mapping BLK3

UI

The freestream

VI

grid

velocity

components

at the

points

WI FFS

FF

An analytically singular

These arrays

are normally

The Craidon

surface

smooth definition in the program and used in information Common Block PATBLK

patch

are stored

program

the

of the metric

Because the

maximum program

size.

splines

of the spline patch

from the flowfield

solution, required

to provide

equations

information

The arrays

these for

is

a

used

generated

large the

arrays geometry

are: Contents

Array PATXY (4,600,2)

Wing panel

corner

600 panels, XPAT

of the

of the mapping.

6) uses bicubic

(Ref.

The coefficients

in core.

separate

part

value

to be 60 x 60.

of the surface.

an overlay

do not control

defined

determined

PATCHX(14,400)

Bicubic for

points;

2 surfaces

surface

patch matrix;

150 patches

i=X,Y,Z;

4 corners,

see Ref.

on 2 surfaces

4 x 4 x 3 (Sic

MBiMT,

7)

49

Common Block

Array

XPAT

Contents

.PATCOR(4,150,2)

Panel corner row of

points

panels;

on local

spanwise

4 corners,

600 panels,

2

surfaces. These arrays eliminate

can be redimensioned

most of the file

searches

if

and drastically

W12SC3 Program: Major

modifications

W12SC3 code. code's solutions

geometric

made to

implement

the

constant-strength modifications options, provide

were

as well

differences

shell of all

between

two will

and flow charts

to

were made to allow

TRPOSE, TRIXY, mentary matrix

Correction.

capability

Direct

tions

the for

ysis,

50

design,

conical

design

the

be discussed.

Inversion

available

use of direct

matrix

allow

more were including

a

in particular,

modifications wing-body

were made to

calculations.

is that

the W12SC3 program

For brevity,

as figures

only

major

W12SC3 program

21, 22, and 23.

Techniques solution

inversion

methods,

techniques.

code addiSubroutines

SOSCAP, RNRW, FUTSOL, QUAS, and INV were added and provide operations

(transpose,

influence

coefficients.

and optimization

multiplication, order"

These matrices solutions

the

and optimization

As a guide,

iterative

OLAY50 was added and is used to form "higher aerodynamic

options,

code modifications

Matrix

Still

SC3 effort

improved

are presented

were made to

For the Finally,

the

and improve

techniques.

from the USSAERO "B" program.

the

As an alternative

revise,

and optimization

implement

of these

different

structure

to

time.

code to nroduce

Others

inversion

capability.

as the Carlson

result

is substantially overlay

needed

an interference

The net

design

panel

correct,

capabilities.

matrix

various

vortex

USSAERO "B"

were made to

by direct

The arrays

Changes From USSAERO --.- -_

and aerodynamic

to be found

are required.

reduce execution

have been made to the

Some modifications

basic

more patches

(e.g.,

and inversion). matrices are

ele-

Overlay

from the matrices

common to all

AWW-AWBABB - 'AsW) -

the analFor

full

of

analysis

cases,

calculated

the

specific

in subroutine

solution

for

a given

set of boundary

conditions

is

DIRECT.

(LWEl,O,O) BLKDAT,TRPOSE,TRIXY~OSCAP,RNRW,FUTSOL,QUAS,INV,OUTW,WINGS

I (LWB.l

I

I

I

.O)

-GEE PANEL SCAMP4 DERIV DERlVl DERlV2 CUBIC2 COMCU

I

I I

(LWB.2.1) .-BODVEL SUBPAN SU PPAN

(LWB,3,0) SD’ VF INVERT PARTIN DIAGIN ITRATE PRESS FORMOM CARLSN SHEXRE MACH PMA INTERP MIXED DRAG DIRECT PCONST INTPOL SHAPE

1 I1

I I

(LWB.l.2) NEWORD

t (LWB.2.3)

I I

VORPAN -I-TRANS

NOTE:

I

PLOTTING

ROUTINES

NOT SHOWN.

(LWB.1.8)

R63-0961-032PP

Figure

21. - W12SC3 program

overlay

structure.

51

MAlti

GEOMI

I I

SOLUTION

YES

* OLAYSO I

1 I

R63-0961-033PP

Figure

52

22. - W12SC3 program:

Overlay

Flowchart.

ISOLATED BODY SOLUTION I

WING SHELL SOLUTION

WING/BODY SOLUTION

I

I

FULL DESIGN OR MIXED DESIGN-ANALYSIS

FULL OPTIMIZATION OR MIXED DESIGN-OPTIMIZATION

FULL ANALYSIS

I I MIXED

I

DIRECT

I

ITRATE

I

I

I

DRAG

I

PCONST

I

I v PRESS I

I

R83-0961-034PP

Figure

23. - W12SC3 programs:

flowchart

for

Overlay

Solve. 53

Design Solutions For full

for

design

set of boundary performed

these

and Optimization

cases make use of the matrices

or mixed design-analysis

cases,

conditions

in

in subroutine

is calculated DRAG for

full

options

influence

require

coefficients

process

of

forming

hence were easily

the

for linearly

extracted

These options

of

vortex

small

nonlinear routine

FORMOMwere

without

the Carlson

to

panel

in

wing) further

subroutine formation Other

order

files,

depending major

vortex being

function

is DRAG

panels.

The

calculated

influence

in

the

coefficients,

and

Options

to subroutines

MIXED and PCONST.

the

calculations. to obtain

calculation

of

this

to

sub-

and moments with

and

Modifications

forces

code changes

shell

were modified

with

accommodate the

the addition

the

all

of is stored

required

in-

are being made.

interference

VELCMP and SOLVE and subroutines

additional

information

or unloads

calculations

(and

and are used for

and aerodynamic

to WINGS loads

wing or shell to

calculate

was simplified

geometric

and one call

Overlays

used to

This procedure

upon whether

Shell

wing routines

WINGS - wing and shell

were required.

54

Existing

calculations.

on out-of-core

This

a given

Correction.

geometry.

shell

for

Correction

wing

NACSHL was added and is

panel

OLAY50.

VORVEL.

Interference Overlay

already

modifications

supersonic

required

solution

MIXED.

CARLSN, SHEXRE, MACH, and PMA handle

correction

in overlay

cases and in subroutines

Design and Optimization

Carlson Subroutines

subroutine

were

from subroutine

required

specific

constant-strength

panels

varying

Conical

formed

cases.

use

such

the

optimization

and PCONST for mixed design-optimization These

Options

shell

capability

PRESS, FORMOM, MIXED,

and DRAG were modified

to properly

influence

calculations,

coefficient

analysis, force

design,

handle

both

wing/body

boundary

or optimization

solutions,

and wing/body/shell specifications,

condition

as well

as velocity,

and

pressure,

and

and moment calculations. In summary,

following

the

W12SC3 program differs

from the USSAERO "B" program

in the

respects: Problem solving

l

Full

analysis,

design,

or optimization

Mixed or conical

design-analysis

Mixed or conical

design-optimization

Solution

l

capability

Method

Iterative Direct 0

Carlson

l

Optional

(full matrix

analysis

only),

or

inversion

Correction

for wing pressures

interference

shell

capability.

COMPUTERREQUIREMENTS Core Size COREL requires of the

core

field.

If

to the

increase

164K8 bytes

is controlled a denser in

of

by the six

storage

storage

for

and the study

crossflow

required

is appropriate

location

for engineering

The W12SC3 code requires The size additional (3,0),

added.

code included

program

in

SOLVE. Overlay

will

these

used in obtaining increase

large

dependence

of the

265K8 bytes

with

larger

The primary

main overlay,

(3,0)

However,

on the

as

mesh

around the

the 60 x 60 grid

24. on the CDC CYBER 175.

in core size

adds an additional

proportion

density

than the original which

the flow-

direct

solution

core storage

increase

The size

Meshes as large

dependence on the grid

work as shown in figure

the

in

arrays.

on the upper surface.

of the code is considerably

the numerous options

the

showed a slight

recompression

on the CDC CYBER 175.

60 x 60 arrays

mesh is desired,

113 x 113 have been used to check density,

core storage

is

USSAEROcode due to occurs

due to the

now 224K

and overlay 8' 28K8 to the core require-

55

GRID a.4

.

.

.

.

SIZE

.29x29

----57x57 113 x 113 -0.3

-0.2

-0.1

cp 0.0

,

4 0.1 0

M

=1.52

0

a

=8’=

OX

60.55 L

0.2

0.3

0.4

0.0

0.2

0.4

A. FLAT WI&

I 0.8

0.8

I 1.0

(REF. 13)

R83-0961435PP

Figure

5fi

24. - Effect

of mesh density

on COlWL solution.

-0.4 I-

.

.

GRID . l

SIZE 29x29 d

m .. . . . .

----57x57 v

113 x 113

. .

-0.2 t-

-0.2

-0.1

cp 0.0

0.1

0.2

.

M

l

O[ =80

‘2

al.82

=055

0.3

0.4

B. CAMBERED WING (REF. 13) R83-0961436Pq

Figure

24. - Continued.

57

-9.4 l.

.

GRID

SIZE

.

l 29X29

.

----57x57 -

-0.: P-

113 x 113

4.1 ,-

-0.: I-

cp 0.0I-

0.1

.

Mml.82

@ a312O .

XsTN

- 19.8

0.2

0.3

0.4

I 0.0

I 02

I 0.4

I 0.08

I 0.8

I 1.0

r)

C. DEMONSTRATION

WING (REF. 15)

R83-0961-037PP

Figure

24. - Concluded.

58

-

!3, ! ,I; BI

b

ment.

The addition

least

of

some overlays

10K8 to 15K8 bytes.

in

SOLVE could

reduce

some additional

In addition,

the

plotting

storage

by at

was added which

adds to the core requirements. Execution The COREL execution The solution correct

is

for

solution

with

It

is

enough for most cases

Figure

case.

Three hundred

iterations. fine

which

to determine

difficult

a particular

and seventy-five

based on the time per grid

is

by an iteration

obtained

answer.

llenough"

time

Time

Typical

exactly

running

times

are

grid

iterations

should

740

300

50

300

90.7

-cL 0.4549

-cD 0.06847

100

117.8

0.4546

0.06852

300

150

143.2

0.4544

0.06852

300

200

164.1

0.4542

0.06852

300

250

192.3

0.4542

0.06852

200

100

103.7

0.4539

0.06814

400

100

131.5

0.4549

0.06858

can vary

Although the

for

different

a 60 x 60 grid solution

iteration

the effective

grid

AIC matrix solution

is

but saved

option

stops

when the

time

is used,

the

after

bow shock

is

of

the

solution

for

initial

reducing

the

bow

first

reached.

depends on the number of panels

is repeated

after

however,

location

50 This

60 x 40 for most cases.

The iterative

requested.

angle-of-attack,

specified,

is actually

The WI2SC3 code execution solution

cases due to changing is

be

set

Iterations

means that

direct

how many iterations

are:

Iterations

iterations

the

to the

(29 x 29; known as 30 x 30)

CYBER

The times

single

slowly

crude grid

Fine Grid

of

only

an example of the change of

Crude Grid

shock.

per iteration.

25 provides

CPU Time,

type

converges

known as 60 x 60)

(57 x 57;

point

is

usually

each angle-of-attack. angle-of-attack

the cost

of additional

used and the faster

for

a

The inverse,of solution

when the

angles-of-attack

59

OENCNSTRATIONWING FOR SCS HING CONCEPT l41.62, ALPHR=12.0 . IV!=33.CXJ XSTtb19.90 co= .1366U CL= .u535 o----w-0.4 1 300 FINE -0.3

CRUDE GRID: 29 X 29 FINE GRID: 57 X 57

GRID ITERATIONS

-02 -0.1 CP 0.0 0.1 02 0.3 0.4 I 0.0

I 02

I 0.4

I 0.6

FINE GRID ITERATIONS

I 0.6

J

1.0

rl

NUMBER OF FINE GRID ITERATIONS

-0.40 NOTES:

1. ONLY AREA INSIDE THE DASHED LINES SHOWED ANY SENSITIVITY TO THE NUMBER OF ITERATIONS, WITHIN RANGE SELECTED. 2. 300 CRUDE GRID ITERATIONS USED EACH CASE.

-Om36

V

25

0 0

50 la0

0

150

0

200

A300 FOR -0.32

ov QV 6

-0.24

ii

cloo

-0.20

-0.16 c

I

I

I

1

4

0.6

0.7

0.8

0.9

1.0

rl

R33-0961.038PP

Figure

60

25. - Effect

of number of iterations

on COREL solution.

results.

Surprisingly,

the calculation

the most

time-consuming

N2.

an isolated

For

divided

steps wing,

of the

influence

in the calculation,

being

modeled with

380 wing

coefficients directly

panels,

is

one of

proportional

the execution

time

to is

as follows:

Case A)

Grumman

NASA LaRC

CYBER 740

CYBER 175 ._~234

1.

Influence

Coefficients

430

2.

Iterative

Analysis

110

60

3.

Direct

480

220

4.

Conical

110

60

190

92

1320

666

Analysis Panel Mixed

Design-Analysis 5.

Conical

Panel Mixed

Design-Optimization Total

CPU seconds:

Grumman CYBER 740

Case B) 1.

Influence

2.

Full

3.

Coefficients

Optimization

660

Direct

Analysis

480

4.

Direct

Analysis

90

5.

Direct

Analysis

90

6.

Direct

Analysis

90

Total For times

430

a wing-body

using

CPU seconds:

calculation,

140 wing panels,

the

1840

following

232 body panels,

case provides and 168 panels

typical for

execution

the interference

shell: Grumman CYBER --___740 Case A)

No Shell Influence

Coefficient

Shell

250

350

Direct

Analysis

200

230

Direct

Analysis

40

70

490

650

Total

CPU seconds:

61

NASA LaRC CYBER 175 136

194

Analysis

22

42

Analysis

22

42

180

278

Influence

Coefficient

Iterative Iterative Total

CPU seconds:

The codes have also differences

in

different

Shell

No Shell

Case B)

been run on a number of different

CPU times

machines.

are

useful

For these

in

comparing

two codes

the

CDC computers,

quoted

results

execution

are given

and the

times

in the

on

folowing

chart: CPU Time, set Code

CDC Computer

COREL

W12SC3

172

1345

1421

174

1077

1087

740

235

308

750

162

219

760

111

150 Sample JCL

The COREL and W12SC3 codes can be run "back on the

information

execution, shown, Langley tion

the

and the

link

binary

forms

copied

62

of

the

in the UPDATE format,

W12SC3 is

being

JCL given

below

the codes is the data codes

which

is

available executed

are used. convenient on all

in

or separately is

from a NASA Langley

set passed on unit

The source for

depending

code is

batch-type

32.

stored

As at

code modifica-

CDC type machines.

a standalone

mode, then

INPUT should

be

to TAPES. The following

trates

between

and is a common utility If

The sample

desired.

to back"

the extremely

sample JCL for simple

the NASA Langley

JCL required

CYBER 175,

for execution.

NOS

System illus-

E:r,I T ,

INPUT DESCRIPTION The input

data

information

required

to

two

run

the

required

is structured

to run the programs

codes

is collected

to allow

together, as follows

or

the user

the maximum flexibility.

is divided

each

into

three

independently,

(and in the order

the

In order

parts. input

information

given):

COREL Alone

Combined COREL/W12SC3

The

W12SC3 Alone

1.

COREL Input

1. COREL Input

1. Craidon

2.

Craidon

2. Craidon

2. W12SC3 Input

3.

W12SC3 Input

During

Geometry

a combined

W12SC3 input. in that

(optionally)

code execution

However,

Geometry

Geometry

the

user

COREL appends conical has to provide

panel

the other

pressure information

data to the contained

section.

The main explained

before

the following A. If

control

for

describing

using the

the input

various in detail.

COREL geometry

options

The NAMELIST for

is

best

COREL includes

control: IRPTS = 1

A spanwise

section

is read from the input

= 0

No spanwise

section

is read in.

63.

IEQV = 1

B. If

The Craidon spanwise

= 0 C. If

geometry section

section data

to the conical

nonconical

geometry geometry

Do not use spanwise

IBQV3 = 0

etry = 1

is

adjustment The Craidon

for

for

the

extracted flow

and the

and used

solution

to

make an

to account

for

the

is not read in. section

analysis,

Use the spanwise

is read from input

extracted

but only

from Craidon

for the nonconical

section

extracted

COREL analysis

as well

correction

from Craidon as for

geom-

geometry

the

nonconical

correction. This

allows

analysis

the

user

or just

first

spaces,

card

employ

the

for the non-conical

In addition, the

to

Craidon

when W12SC3 is executed in the W12SC3 input

are used in

and W12SC3 input

as part

must contain

subroutine

the COREL subroutines

data

sets

for

either

the

entire

correction.

and the AEROIN NAMELIST must contain

keywords

geometry

to Unit

32.

of a combined

COREL/W12SC3 run,

the word AERO in the

the

word END in

spaces

first

four

3-5.

These

START and GEOMIN to copy the Craidon

The W12SC3 data

set

is then

completed

in

OUTP.

The combined (one spanwise

code execution

section

allows

for

only

at one angle-of-attack).

a series

of

cases when executed

required

for each new case.

However,

in a standalone

COREL Input

a single mode.

design

point

analysis

the W12SC3 code can run A new AEROIN NAMELIST is

Instruction&

1. 2 CARD TITLE CASE

for

2. NAMELIST: the

Namelist:*;? Namelist tion

that

*,**See

64

with

INPUT

control

the

of the

name INPUT.

has been found through footnotes,

next

page.

COREL portion The default experience

of values

the

program

reflect

to be generally

is

handled

a "baseline" satisfactory.

via

a

computaOnly

those in.

parameters The Namelist

that

are to be changed from the default

variables,

Variable Combined Code Control

with

default

values,

Default ._---

values

are listed

need to be read

below:

Remarks

Clue

KCCC

0

= O- Complete solution =ICOREL solution only

Flow Conditions EMINF

1.60

Freestream

Mach number

ALP GAMMA

so 1.4

Angle-of-attack Ratio of specific

ETADR

0.0

Dividing ray for split between supercritical conical panel and rest of planform (specified as a fraction of the spanwise section)

TEWSP

0.0

Trailing edge sweep for COREL alone calculation of lift (gives the arrow lift)

heats

Geometry

IRPTS

0

wing

=O, spanwise section is not input explicitly. Section is either generated internally using options described below or

----_ ;k Note that COREL uses a nonstandard coordinate system, so that X is the This is consistent with the coding for COREL. For those spanwise variable. standard airplane variables associated with the actual planform geometry, Thus XSTN, XORIGC, YORIGC, XROOT, and coordinate system nomenclature is used. YWNGRTrefer to the normal aircraft coordinate system (consistent with the Craidon geometry code). Variables used for the spanwise section definition and While appearing confusing, modification refer to the COREL coordinate system. the use of the code with this system is straightforward in practice. +-'- Input data using NAMELIST must satisfy the following rules: 1. The first column on each card must be blank. 2. The first item must be the NAMELIST NAME preceded by a $; i.e, SINPUT followed by a blank. each item being separated 3. Data is input in the form variable = constant, by commas; i.e., IC = 30, AZ = 33.0, . . . 4. The last item must be SEND. 5. The $ above is for CDC; on IBM, the character is &.

65

Variable

Remarks

Default

extracted from Craidon geometry input =l, spanwise section input as X/XLE

,

Y/XLE

pairs NG

199

Number of points defining the internally generated spanwise section (should be odd; NG=199 max)

AZ

33

Included angle of leading edge of conical shape being analyzed (wing or fuselage) AZ = 90°-A LE, in degrees

BZ

1.5

For internally generated spanwise sections, BZ sets the section thickness by specifying the half-angle of the centerline section (in degrees)

LC

0

Camber line clue for sections = 0, No camber = 1, Circular arc = 2, Elliptical arc = 3, Circular cap = 4, Simple flap

CC (dimensioned variable)

0.0

Camber line control geometry generation

LT

1

Thickness envelope generated sections = 0, Circular = 1, Ellipse = 2, Super Ellipse

clue

0.0

Thickness envelope geometry generation

control input

CT (dimensioned variable)

66

internally

generated

(see internal input section) for

internally

(see internal section)

LM

0

Not used

CM (dimensioned variable)

0.0

Not used

IEQV

0

= 0 Do not read Craidon Data Set = 1 Read Craidon Data Set and perform equivalent conical section analysis

Variable IEQV3

Default 0

Remarks = 0 Use spanwise section extracted from Craidon data set for nonconical correction Spanwise section for calculation only. COREL analysis is explicitly read in or internally generated = 1 Use spanwise section extracted from Craidon Data Set for COREL analysis also.

XSTN

1.0

X station at which the section is extracted from the Craidon geometry data and the COREL analysis and equivalent conical section analysis are performed

XORIGC

0.0

X origin of conicity for section from Craidon data set

extracted

YORIGC

0.0

Y origin of conicity for section from Craidon data set

extracted

XROOT

1.0 x lo6

The maximum value of the root prevent the use of Craidon planform) of the origin

chord (to data off

ZROOT

0.0

The elevation calculation

YWNGRT

-1.0

The trailing edge location for the calculation of non-conical correction XSTN is greater than XROOT

the

of the conical

when

IMOD

0

Clue for the addition of a local "cubicll section (actually 6th bump on spanwise order). = 0 No local section modification = 1 Upper surface modification = 2 Lower surface modification surface = 3 Both and lower upper modification

XUl

0.0

Inboard end of section modification on upper surface (as a fraction of spanwise section)

xu2

0.0

Location of maximum thickness position of position of modification on upper surface (as a fraction of spanwise section)

67

Variable

Output

Default

Remarks

XU3

0.0

Outboard end of modification on upper surface (as a fraction of spanwise section)

DTCU

0.0

Magnitude of upper surface percent of semi-span

XL1

0.0

Inboard end of section modification on lower surface (as a fraction of spanwise section)

XL2

0.0

Location of maximum thickness position of modification on lower surface (as fraction of spanwise section)

a

XL3

0.0

Outboard end of modification on lower surface (as a fraction of spanwise section)

DTCL

0.0

Magnitude of lower surface bump in percent of semi-span. A positive value reduces the thickness on the lower surface.

Options IOUT

= 0 = 1

IOUT

= 0 No further abbreviation = 2 Very brief ltterminalfl for online running

IPUNCH

0

Full output everywhere Output on surface only

pressures, (nonconical FlO format IPLOT

1

in flowfield. of output output suitable

= 0 Generated section not punched = 1 Generated section is punched (Unit 8) Data = 3 The solution data is punched. includes Mach, alpha, XSTN, CN, CN-nonconical,

and

spanwise

as x/xLE' correction) on Unit 7)

y,

c

P

section

and

'/'LE' ' , ' P P (All output is in

= 0 Don't plot results routine = 1 Call graphics Langley version). = 2 Plot output is punched, x,

68

bump in

(dummy in

the

in forms

Variable Numerical

Remarks

Default

Solution

IC

30

Initial grid body ring)

in 0 direction

(around

JC

30

Initial column)

in r direction

(away from body

KREF

2

Number of grids

300 150

Maximum number of iterations successive grid

1.0 1.5

Overrelaxation

l.E-6 l.E-6

Convergence grid

criteria

EST

-6.0

Coefficient

of gst,

NSHKR

10

Approximate number of mesh points shock position and grid boundary

KSHKR

8

Number of smoothings location

JDRLX

6

Ring and column relaxation

EPSHKI

1.2

EP in SHOCKI, parameter for initial EPSHKI estimate of bow shock location. is a multiple of the Mach angle

KMAX (dimensioned variable) W(3) DMIN (dimensioned variable)

Available

grid

(presently

factor,

a max of 2) for each

successive

grids

on each successive damping term

of refined

between shock

split

Unused Items

IDESIN, KDESMX, WDES

Intended for use with any design dummy in present code

package,

END OF NAMELIST

69

Sbanwise Section Card No.

Format

Al

Literal

A2

7FlO.O

NOTE:

Field

Format

A3

Literal

A4

7FlO.O

Name

Remarks

TITLE

80 characters describing section definition

1

ZSYM

Section symmetry clue, if ZSYM = 1.0 section is symmetric; read upper surface only. = 0, section is asymmetrical, both upper and lowersurface read in

2

THICK

Section thickness. YU, YL ordinates multiplied by THICK. If = 0, THICK is reset to 1.0, and input section inputs are unchanged

3

FNU

Number of ordinate upper surface

pairs

defining

4

FNL

Number of ordinate lower surface

pairs

defining

5

XKSMTH

Dummy variable, intended to be the number of section smoothings if smoothing is incorporated

6

XSING

X location mapping

of singularity

for

7

YSING

Y location mapping

of singularity

for

Field

1 2

Name

Remarks

TITL

80 character describes surface of sections

xu YU

Upper surface Upper surface

The ordinates are multiplied normalized to physical values.

70

Block

spanwise

should be specified at the The X, Y location of the mapping singularity midpoint of a line drawn between the center of the leading edge radius If XSING=O, the program estimates this position and the leading edge. internally.

Card No.

NOTE:

Input

Repeat card A4 FNU times.

by tan

upper

X coordinate Y coordinate

AZ internally

to

convert

from

Format

Card No.

Field

The section proceeds A5

is

input

A6

at the

leading

edge,

X/XLE = 1, and

X/XLE = 0. TITL

80 characters surface

describing

the lower

XL YL

Lower surface Lower surface

X coordinate Y coordinate

card A6

7FlO.O

NOTE:

starting

to the root,

Literal

If FSYM = 1, skip

Remarks

Name

1

Repeat card A6 FNL times. The leading edge point and the lower surface. Description

of Internal

should

be the same for

Geometry Generation

Parameters

both

the upper surface

Used In Namelist

1. ~CAMBER LC = 0 No Camber = 1 Circular Arc = 2 Elliptic = 3 Circ.

Arc

= CC(2) = CC(3) = 0 = eR CC(2) = CC(3) = 0

CC(l)

= Br (curvature),

angle), CC(3)=0 CC(l) = BR(l.e.

Cap

= 4 Split NOTE:

CC(l) CC(l)

CC(l)

CC(4),

angle),

CC(2) = CE (leading

CC(2) = 0, CC(3) = (x,/C)

= eR, CC(2) = 0, CC(3) = xc/c

CC(S) not operational,

but available.

I

I I-‘\--o =lEI

‘+ 1

-0,

p CIRCULAR ARC

2.

edge

ELIPTIC ‘ARC

R SIMPLE FLAP

CIRCULAR .-CAP

-

THICKNESS

LT = 0 = 1 = 2

Circular Elliptic

Cone Cone

Super Elliptic

CT(l) CT(l)

= CT(2) = 0 = CT(2) = 0

CT(l)

= -4.,

CT(2) = exponent

xB

-2 of 0

CT(3) = exponent

-2 of

I! 0A

71

the. super ellipse

[email protected])

is given

= CT(3) = 1 for

"pure"

Craidon The Craidon

geometry

and W12SC3 alone alone,

section

geometry

the Craidon

is

for

follows

geometry

required

as well

description),

When required

the Craidon

.W12SC3 runs, executed

runs.

super ellipse.

Geometry Definition

definition

when IEQV = 1 (see COREL input

by

for

as for

COREL alone

runs

combined COREL/W12SC3

and and combined

the COREL data

definition

COREL alone

COREL/

When W12SC3 is

inputs.

is the first

section

of two parts:

the

of the input

data. The input scription data

of the initial

which

number,

to the W12SC3 program

specifies

consists

configuration the

singularity

geometry

(Craidon);

paneling

scheme,

and any additional

angle-of-attack,

input

data

numerical

and the

de-

W12SC3 input

program

options,

required

for

Mach

particular

program options. The configuration fore

only

one side

The coordinate Columns l-80

is (the

defined

positive

system notation Variable TITLE1

to be symmetrical y side)

Control

the x-z plane;

of the configuration

is shown in figure Value

about

need be described.

26.

Description This card contains any desired idenifying information. Integers

l-3

JO

0 1

No reference area Reference area to be read

4-6

Jl

0 1 -1

No wing data Cambered wing data to be read Uncambered wing data to be read

72

there-

: I

FUSELAGE

-

ZFUS

CAMBER

LINE

(Z-ORDINATES

OF FUSELAGE

CAMBER

LINE)

R83-0961-039PP

Figure

system 26. - Coordinate CR 3228, 1980).

for

craidon

geometry

(from

NASA

73

Columns

Variable

Value

Description

7-9

52

.O 1

No fuselage data. Data for arbitrarily shaped fuselage to be read. Data for circular fuselage to be read. will be cambered. (With 56 = 0, fuselage be symmetrical With 56 = -1, fuselage will With 36 = 1, with respect to the xy-plane. entire configuration will be symmetrical with respect to the xy-plane.)

-1

53

10-12

0

No Pod data.

1

Pod data to be read.

13-15

54

0 1

No fin (vertical tail) Fin data to be read.

16-18

55

0 1

No canard (horizontal tail) Canard data to be read.

19-21

J6

0

A cambered circular or arbitrary fuselage if 52 is non-zero. Complete configuration is symmetrical with respect to the xy-plane, which implies an uncambered circular fuselage, if there is one. with 52 fuselage Uncambered circular non-zero.

1

-1

data. data

22-24

NWAF

2-20

Number of airfoil sections to describe the wing.

used

25-27

NWAFOR

3-30

Number of ordinates used to define each If the value of wing airfoil section.

expect to read lower NWAFORis input with a negative sign, the program will the airfoil is assumed to be symmetrical. surface ordinates also; otherwise, 28-30

NUFUS

l-4

Number of fuselage

31-33

NRADX(l)

3-20 1

Number of points used to represent half-section of first fuselage segment. If fuselage is circular, the program computes and indicated number of Ythe Z-coordinates.

34-36

NFORX(1)

2-30

Number of stations segment.

------;k W12SC3 will

74

read input

data for pods, but will

segments.

for

first

fuselage

not use them in the panel model.

Columns

Variable

Value

Description

37-39

NRADX(2)

3-20

Same as NRADX(l), but for the second fuselage segment.

40-42

NFORX(2)

2-30

Same as NFORX(l), but for the second fuselage segment.

43-45

NRADX(3)

3-20

Same as NRADX(l), but for the third fuselage segment.

46-48

NFORX(3)

2-30

Same as-NFORX(l), but for the third fuselage segment.

49-51

NRADX(4)

3-20

Same as NRADX(l), but for the fourth fuselage segment.

52-54

NFORX(4)

2-30

Same as NFORX(l), but for the fourth fuselage segment.

55-57

NP

o-9

Number of Pods.+

58-60

NPODOR

4-30

Number of stations at which pod radii are to be specified.;k

61-63

NF

O-6

Number of fins (vertical to be described.

64-66

NFINOR

3-10

Number of ordinates used to describe each fin airfoil section.

67-69

NCAN

O-6

Number of canards (horizontal tails) to be described.

70-72

NCANOR

3-10

Number of ordinates used to define each If the value of canard airfoil section. the program will expect NCANOR is negative, also; to read lower surface ordinates the airfoil is assumed to .be otherwise, symmetrical. Reference

l-7

REFA

tails)

Area

Reference Area Card. l/2 area in W12SC3.

This

is

the planform

-------

;?-W12SC3 will

read input

data for pods, but will

not use them in the panel model.

75

Columns

Variable

Description

Value Wing

l-7

XAF

Cards, each containing up to 10 values of of percent chord, at which ordinates airfoils are to be specified. Total of Each card may be identified NWAFORvalues. in columns 73-80 by XAFJ, where J denotes the last location specified on that card.

WAFORG

NWAF cards, each containing values of: X-coordinate of wing airfoil leading edge, Y-coordinate of wing airfoil leading edge, Z-coordinate of wing airfoil leading edge, Wing airfoil streamwise chord length. Each card may be identified in columns 73-80 by WAFORGJ, where J denotes the airfoil number, starting from the most inboard airfoil.

TZORD

NWAF cards, each containing up to 10 values of DELTAZ (mean 8-14 camber line). A total of NWAFORvalues will be read per airfoil. Each card may be identified in denotes the last location on that card. These values will be input only if Jl = 1.

l-7 8-14 15-21 22-28

l-7

WAFORD Cards, each containing up to 10 values of wing half-thickness, (each specified as percent of the chord) specified for each airfoil. If NWAFOR< 0, the same wing number of values will be read for the lower surface. Body (Fuselage)

l-7 8-14

etc

l-7

XFUS

Cards, each containing up to 10 values of X-coordinates of body axial stations specified for each body segment. Total number of values per segment is specified by NFORX. Each card may be identified in columns 73-80 by XFUSJ, where J denotes the last location on that card.

ZFUS

Cards, each containing up to 10 values of Z-ordinates of fuselage camber line, specified at each body axial station. Total number of values per segment is specified by NFORX. Each card may be identified in columns 73-80 by ZFUSJ, where

8-14

etc

1-7 8-14

etc

76

Columns

Variable

Description

Value

J denotes the last location on that card. Input only if cambered c.ircular fuselage. l-7 8-14 etc

SFUS

Cards, each containing up to 10 values of Y-ordinates of half-cross-section A total of NRADX values are input. points. containing NRADX values of The cards cards are followed by Y-coordinates containing the Z-coordinates of the same points. These sets of cards are repeated for each Input only if fuselage fuselage segment. of arbitrary shape.

1-7 8-14 etc

FUSARD

Cards, each containing up to 10 values values of fuselage cross-sectional areas. Total of NFORX values will be read per Each card may be fuselage segment. identified in columns 73-80 by FUSARDJ, where J denotes last station specified on circular only if card. Input that fuselage. Fin

FINORG X-ordinate on inboard airfoil leading edge, Y-ordinate on inboard airfoil leading edge, Z-ordinate on inboard airfoil leading edge, Chord length of inboard airfoil, X-ordinate on outboard airfoil leading edge, Y-ordinate of outboard airfoil leading edge, Z-ordinate of outboard airfoil leading edge, Chord length of outboard airfoil. in columns This card may be identified 73-80 by FINORGJ, where J denotes the fin number.

l-7 8-14 15-21 22-28 29-35 36-42 43-49 50-56

l-7 8-14 etc

XFIN

1-7

FINORD

Cards, each containing of fin airfoil percent card can be identified XFINJ, where J denotes

up to 10 values chord. Each in columns 73-80 by the fin number.

Cards, each containing up to 10 values of fin airfoil half-thickness, expressed in Since the fin airfoil must percent chord.

77

Columns

Variable

Value

Description be symmetrical, only the ordinates on the positive Y-side of the fin chord plane are required. Each card may be identified in columns 73-80 by FINORDJ, where J denotes the fin number.

NOTE: FINORG, XFIN and FINORD are input

for

each fin.

Canard CANORG l-7

X-ordinate

of inboard

airfoil

leading

edge,

8-14

Y-ordinate

of inboard

airfoil

leading

edge

15-21

Z-ordinate

of inboard

airfoil

leading

edge,

22-28

Chord length

29-35

X-ordinate edge,

of outboard

airfoil

leading

36-42

Y-ordinate edge,

of outboard

airfoil

leading

43-49

Z-ordinate edge,

of outboard

airfoil

leading

50-56

Chord length of outboard. This card may be identified in columns 73-80 by CANORGJ, where J denotes canard number.

of inboard

airfoil.

l-7 8-14 etc

XCAN

Cards, each containing up to 10 values of canard airfoil percent chord. Each card may be identified in columns 73-80 by XCANJ, where J denotes canard number. Total number of values is NCANOR/airfoil.

l-7 8-14 etc

CANORD

Cards, each containing up to 10 values of canard airfoil half-thickness, chord. If canard expressed in percent airfoil is not symmetrical, the lower ordinates are presented on a second CANORD set of cards. The program expect both upper and lower ordinates to be punched as positive values in percent chord.

NOTE: CANORG,XCAN, and CANORDare input

78

for each canard.

-

W12SC3 Input The W12SC3 input runs,

and follows

Title

Card,

(2)

(9)

is required

the Craidon Options

(5) Wing Data Cards, Cards,

data

(6)

Nacelle/Shell

and (11) additional

input

Variable

l-80

TITLE2

'

for

combined COREL/W12SC3 and W12SC3 alone These inputs

Geometry Definition.

Card,

(3)

Control

Body Data Cards, Data Cards,

Integer

Card,

(7)

Data Cards,

Fin

consist

(4) Ref. (8)

of

Lengths

for particular

Paneling

Value

(1)

Card,

Canard Data

(10) Mach Number and Angle-of-Attack

data cards required Singularity

Columns

Instructions

Card,

program options.

Geometry Description

This card contains identifying Columns l-4 information. contain the word AERO for COREL/W12SC3 runs.

should combined

Options l-3

LINBC

Non-planar boundary condition (Subsonic analysis only). Planar boundary condition.

4-6

THICK

Do not calculate wing thickness matrix. Calculate wing thickness matrix if LINBC = 1.

7-8

PRINT

Print option flag. Print the pressures, the forces and the moments. Print option 0 and print the spanwise loads on the wing, fin and canard. Print option 1 and print the velocity source and vortex components, strengths. Print option 2 and print the steps in the iterative solution. Print option 3 and print the axial and normal velocity matrices. If PRINT< 0, the panel geometry will be included in the printout.

3 4

9-12

LCPA

blank

Not used.

13-15

LCPB

blank

Not used.

79

Columns 16-18

Variable ITMETH

032

1 3 4 19-21

ITMAX

0 integer

22-24

CCTEST

Description

Value

Iterative solution method selection flag. Blocked GAUSS-SEIDEL iterative solution procedure. Blocked JACOBI iterative solution procedure. Blocked controlled successive overrelaxation iterative solution procedure. Blocked successive overrelaxation iterative solution procedure. Maximum number of iterations at 50. Maximum number of iterations specified.

real

Convergence 0.001. Convergence

0 real

Divergence Divergence

criterion criterion

0

criterion

set at

criterion

specified.

29-35

DCTEST

36-41

ALFl

Relaxation

factor>1

43-49

ALF2

Relaxation

factor<1

Control l-3

KO

0 1 4-6

Kl 0 1 1 3

7-9

K2 0 1

10-12

80

K3

set

set at 1000. specified.

Integers Reference length flag. No reference length to be read. Reference length to be read. Wing definition flag. (Kl must be >O if wing is to be included in analyses.) No wing data to be read. Wing data follows. Wing has sharp leading edge. Wing data follows. Wing has round leading edge Body (fuselage) definition flag. data to be read. Fuselage data to be read.

No fuselage

Pod definition

flag

(not used).

Columns

Variable

13-15

K4

Value 0 1 3

16-18

K5 0 1

3 19-21

K6

0

1 22-24

KWAF

0,

2-20

Description Fin definition flag. No fin data to be read. Fin data follows. Fin has sharp leading edge. Fin data to be read. Fin has round leading edge. Canard (horizontal tail) definition flag. No canard data to be read. Canard data to follow. Canard has sharp leading edge. Canard data follows. Canard has round leading edge. No nacelle/shell Nacelle/shell

data to be read data to be read.

Number of wing sections used to define the inboard and outboard If KWAF=O, the outboard panel edges. panel edges are defined by NWAF in geometry input. Number of ordinates used to define the leading and trailing edges of the wing panels. If KWAFOR=O, the panel edges are defined by NWAFORin the input geometry.

24-27

KWAFOR

28-30

KFUS

31-33

KRADX(l)

0, 3-20

Number of meridian lines used to define panel edges of first body There are 3 options for segment. If edges. panel the defining the meridian lines are KRADX(l)=O, define by NRADX(l) in geometry input. If KRADX(1) is positive, the meridian lines are calculated at equally spaced If KRADX(l) is negative, the PHIK's. meridian lines are calculated at specified values of PHIK.

34-36

KFORX(1)

0, 2-30

Number of axial stations used to define leading and trailing edges of panels on first body segment. If KFORX(l)=O, the panel edges are defined by NFORX(l) in the geometry input.

0, 3-30

Number of fuselage segments. The program sets KFUS=NFUS.

81

Columns

Variable

37-39

OX

40-42

KFORX(2)

Same as KRADX(l), body segment.

but for

second

, 0,

Same as KFORX(l), body segment.

but for

second

0,

Same as KRADX(l), body segment.

but for third

3-20

0,

3-20 2-30

KRADX(3)

43-45

Description

Value

46-48

KFORX(3)

0, 2-30

Same as KFORX(l), body segment.

but for third

49-51

KRADX(4)

0, 3-20

Same as KRADX(l), body segment.

but for

fourth

52-54

KFORX(4)

0,

Same as KFORX(l), body segment.

but for

fourth

2-30 Additional

Revised

Configuration

Paneling

Description-Control

Intege.rs --..-.

l-3

KF(1)

0, 2-20

Number of fin sections used to define the inboard and outboard fin. If panel edges on the first the root and tip chords KF(l)=O, define the panel edges.

4-6

KFINOR(1)

0, 3-30

Number of ordinates used to the leading and trailing edges of the fin panels on the first fin. the panel edges are If KFINOR(l)=O, defined by NFINOR.

7-9

m(2)

0,

2-20

Same as for KF(l), second fin.

but for

10-12

KFINOR(2)

0, 3-30

Same as for KFINOR(l), second fin.

13-15

m(3)

0, 2-20

Same as for KF(l), fin.

16-18

KFINOR(3)

0, 3-30

Same as for KFINOR(l), third fin.

19-21

f=(4)

0,

2-20

Same as for KF(l), fourth fin.

0, 3-30

Same as for KFINOR(l), fourth fin.

22-24

82

KFINOR(4)

but for

but for third but for

but for but for

Description

Columns

Variable

Value

25-27

m(5)

0, 2-20

Same as for KF(l), fin.

28-30

KFINOR(5)

0, 3-30

Same as for KFINOR(l), fifth fin.

31-33

m(6)

0,

2-20

Same as for KF(l), fin.

but for

fifth

but for

but for sixth

34-36

KFINOR(6)

0, 3-30

Same as for KFINOR(l), sixth fin.

37-39

KCAN(1)

0, 2-20

Number of canard sections used to define edges on the first If KCAN(l)=O, the root and canard. tip chords define the panel edges. If KCAN(1) negative, no vortex sheets body and through the carry concentrated vortices are shed from the inboard edge of the canard or tail surface.

40-42

KCANOR(l)

0,

Number of ordinates used to define the leading and trailing canard. first the edges of KCANOR(l)=O, the panel edges defined by NCANOR.

3-30

but for

43-45

KCAN(2)

0, 2-20

Same as for KCAN(l), second canard.

46-48

KCANOR(2)

0, 3-30

Same as for KCANOR(l), but for second canard.

49-51

KCAN(3)

0, 2-20

Same as for KCAN(l), third canard.

52-54

KCANOR(3)

0, 3-30

Same as for KCANOR(l), but for third canard.

55-57

KCAN(4)

0, 2-20

Same as for KCAN(l), fourth canard.

58-60

KCANOR(4)

0, 3-30

Same as for KCANOR(l), but for fourth canard.

61-63

KCAN(5)

0,

Same as for KCAN(l), fifth canard.

0,

Same as for KCANOR(l), but ior fifth canard.

2-20

64-66

KCANOR(5)

3-30

If are

but for

but for

but for

but for

83

Description

Columns

Variable

Value

67-69

KCAN(6)

0, 2-20

Same as for KCAN(l), sixth canard.

70-72

KCAN(6)

0, 3-30

Same as for KCANOR(l), sixth canard.

REFERENCELENGTHS:

This card can be identified columns 73-80, and contains

but for but for

with REFL in the following:

l-7

REFAR

If REFAR= Half-wing reference area. 0, the value of the reference area is defined as the value of REFA in the geometry input.

8-14

REFB

If REFB = 0, a value Wing semi-span. of 1.0 is used for the reference semi-span.

15-21

REFC

Wing reference chord. If REFC = 0, a value of 1.0 is used for the reference chord.

22-28

REFD

Body reference diameter. If REFD = 0, a value of 1.0 is used for the reference diameter.

29-35

REFL

If REFL = 0, a Body reference length. value of 1.0 is used for the reference length.

36-42

REFX

X-coordinate

of moment center.

43-49

REFZ

Z-coordinate

of moment center.

Wing l-7 8-14 etc

RHO

l-7 8-14 etc

XAFK

84

Cards containing NWAFvalues wing leading edge radius expressed in percent of the Required only if Kl = 3. identified in columns 73-80 where 3 denotes the number radius given on that card. contains NWAFvalues RHO.

of chord. It may be by RHOJ, of the last This card

Cards containing KWAFORvalues of wing panel leading edge locaexpressed in percent chord. tions, This card may be identified in columns 73-80 as XAFKJ, where 3 denotes the

Columns

Variable

Description

Value

last location given Omit if KWAFOR= 0. 1-7 8-4 etc

on that

card.

Card containing KWAFvalues of Y-coordinate of wing panel inboard and outboard edges. This card may be identified in columns 73-80 by YKJ, where J denotes last Y-coordinate on that card.

YK

Body (Fuselage) 1-7 8-14 etc

PHI

Cards containing KRADX(j) values of the body meridian angles expressed in degrees, and may be identified in columns 73-80 by PHIKJ, where J denotes the body segment number. Convention used is that PHIK = 0 at the bottom of the body and PHIK = 180 at the top of the body. Omit, unless KRADX(j) is negative. Repeat same cards for each fuselage segment.

1-7 8-14 etc

XJ

Array containing KFORX(j) values of X-coordinates of body axial stations. This card may be identified in columns 73-80 by XFUSKJ, where J denotes the body segment number. Omit if KFORX(j) = 0. Repeat this card for each fuselage segment. Fin

l-7 8-14 etc

RHO

Array containing NF fin leading This array is reedge RADII. quired only if K4 = 3. This card is identified in columns 73-80 by RHOFIN.

l-7 8-14 etc

XAFK

Array containing KFINOR(j) values of fin panel leading edge locations. This card is required only if K4 = 1. It may be identified in columns 73-80 by KFINKJ, where J denotes the fin number. Repeat this card for each fin.

1-7 8-14 etc

YK

This array contains KF(j) values of the Z-coo'rdinates of the fin panel inboard edges. This card is identified in columns 73-80 as ZFINKJ,

85

Variable

columns

Value

Description where J denotes the fin values start with the values.

number. These most inboard

Canard 1-7 8-14 etc

Cards containing NCAN values of canard leading edge RADII, one value for each canard. This card can be identified in columns 73-80 as RHOCAN. This array is input only if K5 = 3.

RHO

l-7 8-14 etc

XCAN

Card containing KCANOR(j) values of canard panel leading edge Xexpressed in percent coordinates chord. The cards may be identified in columns 73-80 by XCANKJ, where J denotes the canard number. Repeat this card for each canard.

l-7 8-14 etc

YK

Card containing KCAN(j) values 8-14 of Y-coordinates of panel etc inboard in edges. -This card may be identified columns 73-80 by YCANKJ, where J Repeat this denotes canard number. card for each canard. NACELLE/Shell

The nacelle

is

modeled

used to model additional ference

shell

conditions All

is

also

wing,

input

tail,

modeled

so as to properly segments

as a "ring

in

account this

- nacelle

shell

panels

be designed

enter

into

moment calculations.

86

panel

for

nacelle

but

may be

The wing-body

segments.

wing,"

inputs

with

modified

inter-

boundary

interference. will

and additional

boundary

As such,

and canard

section

camber slopes shell

wing."

as a "ring

fixed

cannot

Data Cards

have constant-pressure

panels

wing,

panels,

Shell

or optimized. conditions,

but

tail

and canard

panel

camber slopes

are used for

shell

force

with and

do not and

Panel thickness shell

segments, To input

some non-zero

but these nacelles value.

may be input

are ignored

and/or If

the

set of "AEROIN" namelist

Columns

Variable

for

all

for shell the user

shells,

K6 equals

For K6 non-zero,

omitted. first

slopes

zero,

following

nacelle,

wing,

canard,

or

segments. should

set K6, Card 2.1,

the nacelle/shell cards

tail,

should

data

inputs

be inserted

equal

to

should

be

before

the

and Mach Number cards:

Description

Value Nacelle/Shell

Segment Card

l-3

NNAC

10

Number of nacelle and additional and canard segments to be wing, tail, input.

4-6

NSHL

20

Number of shell input.

The following wing,

tail,

set of cards

and canard segment,

should

be input

followed

by aset

for

segments to be

each nacelle

for each shell

and additional segment:

l-80

TITLE

l-3

NAXI

2-30

Number of chordwise stations defining panel leading and trailing edges. NAXI >O implies uncambered nacelle, wing, tail canard or shell NAXI
4-6

NRAD

2-20

Number of spanwise stations defining panel inboard and outboard edges. NRAD> 0 implies zero thickness nacelle, wing, tail, canard or shell panels. NAXI 0 implies thickness slopes to be input. (Total number of spanwise stations for all nacelle, additional wing, tail and and sheil segments may not canard, exceed 20).

l-7 8-14 etc

xoc

Any identifying

title.

NAXI values of nacelle, wing, tail, canard, or shell panel leading and trailing edge locations, expressed in present chord.

87

Description

Value

Columns

Variable

1-6

X

X-coordinate

of chord leading

edge.

8-14

Y

Y-coordinate

of chord leading

edge.

15-21

z

Z-coordinate

of chord leading

edge.

22-28

C

Chord length. This card is repeated NRAD times, order determining upper input lower surfaces, e.g. :

z

UPPER SURFCE

with and

LOWER SURFACE

Y

X

A INPUT ORDER

ORDER

‘R63096b040PP

l-7 8-14 etc

DZCDX

l-7 8-14 etc

DZTDX

slope values NOTE: Camber and thickness edges along chord through panel centroids.

NRAD-1 sets of cards, one set for each streamwise column of the segment, each containing values of camber slopes (input NAXICO).

NAXI only if

NRAD-1 sets of cards, one set for each streamwise column of the segment, each containing NAXI values of thickness slopes (input only if NRAD
at panel

leading

and trailing

AEROIN Namelist The following the namelist

variables

input

using

standard

Fortran

namelist

format:

name is "AEROIN."

Variable

Default

NOPT(l)

1

If NOPT(l)=l, NOPT(2)

If NOPT(1)=2, NOPT(2)

are

the following

Remarks =1 =2 values

0

the following 0

of NOPT(2) are used: =o =l =2 =3 =4

values

Analysis or design case. Optimization case.

Cambers used from geometry input. Cambers used from previous cycle. Mixed design-analysis case. Full design case. Conical panel mixed designanalysis case.

of NOPT(2) are used: =- 1

Mixed design-optimization with CL constraint only.

z-2

Mixed design-optimization case constraints. with CL and X CP designpanel mixed Conical case with optimization cL constraint only. panel mixed designConical optimization case with CL and Xcp

Z-3

Z-4

=1

constraints. Full optimization,

=2

only Full

optimization,

case

CL constraint CL and Xcp.

constraints. NOPT(3)

0

=o

Iterative variable determine (analysis

=l

Inverse of AIC matrix is used to determine singularity strengths (should be used only if iterative solutions fail to converge or for drag polar calculations).

technique specified by 'ITMETH' is used to singularity strengths case only).

89

Variable

Default

NOPT(4)

0

Remarks

=o

Panels with linearly varying vorProgram autoticity are used. matically assigns C.P. location and trailing edge singularities.

=2

Panels with constant vorticity and C.P.'s at 95% panel chord are No trailing edge singuused. larities are assigned (C.P.'s at 85% chord for subsonic Mach numbers).

=o

For mixed design-optimization drag is minimized on cycles, portion of wing where pressures are not specified.

=1

mixed design-optimization For cycles drag is minimized on total wing surface.

NOPT(6)

=o =l

Normal camber input. Camber slopes are input by user at control points of each panel. cambers replace any (These generated during a cambers previous cycle - use only if NOPT(l) = 1).

NSTNS

Number of wing stations at which the spanwise pressure distribution is desired (maximum of 20).

XSTN(1) XSTN(2) XSTN(3)

X locations at which the spanwise pressure distribution is desired. (NXSTNS values).

NOPT(5)

XLAMDA

57.0

Value of leading edge sweep in (Required for each case) degrees.

XAPEX YAPEX

0 0

Origin for center of conicity for cases where the origin is not zero.

NOTE: XLAMDA is used in the calculation correction "VFIX."

of the spanwise

velocity

XLAMDA, XAPEX, and YAPEX are used to determine the spanwise location of points output for the wing spanwise pressure distribution. These points are at the specified X locations and lie along the chords through wing panel centroids.

90

6! - !i

Mach Number and Angle-of-Attack Remarks

Columns

Variable

l-7

XMACH

The free stream subsonic or supersonic Mach number for which a solution is desired.

8-14

ALPHA

The angle of attack in degrees which a solution is desired.

15-21

CLBAR

Design lift coefficient options only).

22-28

XCP

Center of pressure (x-coordinate) constraint (optimization options only).

Several

of the Options

require

Mixed Design-Analysis

additional (NOPT(l)

for

(optimization

information: = 1, NOPT(2) = 2)

Card No.

Format

Field

Name

Remarks

MA1

15

1

NFIX

Number of panels for which prescribed pressures will input.

be

MA2;:

1015

l-10

IFIX( i=l,NFIX

Panel ID numbers in ascending order for which prescribed pressures are input.

MA3"

7F10.2

l-7

PRESS(i), i=l,NFIX

Prescribed lifting pressure coefficients corresponding to panel ID's on MA2.

MA4;:

7F10.2

l-7

SLOPES(i), i=l,NUM

Wing camber slopes at panel control points for all panels where pressures have not been specified. (NUM = total number wing panels - NFIX).

Full Fll+.

Design l-7

7F10.2 Camber Slope

CSl;';

Input l-7

7F10.2

_---* Repeat card until

(NOPT(l)

all

values

= 1, NOPT(2) = 3)

PRESS(i), i=l,NWING (Full

Analysis SLOPES(i), i=l,NWING

Prescribed coefficients Only)

lifting for

all

pressure wing panels.

(NOPT(6) = 1)

Wing camber slopes control points for

at panel all panels.

are entered.

91

Field

Format

Card No.

Mixed Design-Optimization General

(NOPT(l)

~'2~

NOPT(2) = -1,

-2)

Design 1

15

MD1

Remarks

Name

Number of panels for which prescribed pressures will input.

NFIX

be

MD2;‘:

1015

l-10

IFIX( i=l,NFIX

Panel ID numbers in ascending order for which prescribed pressures are input.

MD3i’:

7F10.2

l-7

PRESS(i), i=l,NFIX

Prescribed coefficients panel ID's

Conical

Panel Mixed Design-Analysis

(NOPT(l),

lifting pressure corresponding to given on MD2.

NOPT(2)=4)

and Conical

Panel Mixed Design-Optimization __... (NOPT(l)

Both of these specification ing

planform

subcritical

panel

For

require

of a conical

this

pressure

options into

planform

(inboard

ACp versus

W12SC3 alone

runs,

the

II.

panel ray) via

user

inputs,

(outboard

via

which

of

dividing

ray)

ETADR, and a conical

c2

5FlO.O

must

supply

the

following

KCCC = 0 (see COREL inputs) COREL execution,

inputs.

these

+c Repeat card until

all

and should

80 characters describing pressure distribution

1

FCCC

Number of n, ACp pairs defining the conical panel pressures

2

XLAMLE

The leading edge sweep angle for; these pressures

values

are entered.

For

parameters

TITLE

_----

and

lifting-

by the user. Literal

include

ETAC and DCPC.

appended to the data set during

Cl

92

additional

-4)

XLAMLE, XORIGC, and YORIGC, a ray divid-

via

of dividing

combined COREL/W12SC3 runs with input

following

a supercritical

distribution,

automatically

the

= 2, NOPT(2) = -3,

conical

are

not be

Format

Card No.

2FlO.O

c3

Name

3

ETADR

The dividing ray (pressures are specified outboard of this ray)

4

XORIGC

X origin of conical this calculation

panel

for

5

YORIGC

Y origin of conical calculation

panel

for this

1

ETAC

n location

2

DCPC

NOTE: Card C3 is repeated with

Remarks

Field

The values

FCCC times.

n = 0 (the centerline)

of AC P ACp at this n value are input

and proceeding

starting

to n = 1 (the

leading

edge). To Start

A New Case - Simply

Angle of Attack To Signal

Card,

repeat

and any required

the

additional

- Execution

End of Execution

AEROIN namelist,

Mach Number and

information.

stops

when the end of the data

set

is

encountered. Paneling

Rules

- The following

rules

should

be

followed

when modeling

configurations: l

A total

of 1653 panels

may be used to model all

551 wing,

fin,

551 shell

and additional

surfaces

and canard panels nacelle,

wing,

and canard panels

551 body panels l

A total

of 19 streamwise

strips

is allowed

for

all

wing,

fin,

and canard

direction

is

29 on each

panels l

The maximum number of panels wing,

l

fin,

A total

in

the

streamwise

or canard surface

of 29 panels

in the streamwise

direction

is allowed

for

all

body

segments l

The maximum number of panels

used to model the

body cross-section

is

19

on each body segment

93

l

A total

of 19 streamwise

additional l

nacelle,

wing,

If

shell

utilizing

iterative

is

rule,

used as a solution reasonable l

For

l

For

method,

of

or if

leading

edge boxes

of

will

the

also

constant

the

shell

and

is

29 on each

and canard surface

number of

be an integer

the iteration

if

panels

factor

of 60.

matrix

inversion

techniques

a uniform

edge thrust 10D2 to

improve

strength

wing

on This is

converge

paneling

in most cases (see ref.

streamwise

order

in

a

from

the

distribution

5)

computed

pressure

dis-

spacing is necessary, with leading -3 10 chord lengths. Spanwise cosine

results.

A limited

number of analyses

vortex

panels

(Woodward I panels)

W12SC3:

Output

Data

produce

indicate the most

results.

The W12SC3 program output l

A complete

a

Program execution

The quantity the

wing,

and can be relaxed

results

a nonuniform

selected,

interference

direction

nacelle,

problems,

tribution,

accurate

streamwise

should

however,

smoother

calculation

that

all

number of cycles

produce

spacing

for

techniques,

strips

design-optimization

should

the

solution

fuselage

a rigid

in

and each additional

circumferential not

is allowed

and canard surfaces

The maximum number of panels interference

l

strips

listing

consists

of two parts:

of the input

data cards

output.

and type

of

execution

number of panels

used,

output

and/or

depends

the

number

upon the of

PRINT option

components

of

the

configuration. The program execution PRINT=

0

output

The program prints

94

are described

the case description,

angle-of-attack,

followed

control

point

pressure

coefficient,

Separate

tables

the planar

options

coordinates normal

are printed

boundary

condition

by

listing

dimensional

force, for

Mach number and

a table

(both

below:

axial

the body, option

force, wing,

the

panel

number,

and nondimensional), and pitching and shell

has been selected,

moment. panels.

the

results

If

for

the wing or shell

by a separate

table

the wing,

pressure

results

tables

giving

the shell,

coefficient

reference

span

pitching

in one table,

the

the

wing

total

or

shell

lower on the

configuration

include

the

chord,

normal

force,

and drag

followed

coefficients

These

tables. lift

for

and the complete

and reference

moment,

are given

giving

Additional

surface. body,

upper surface

coefficients,

follow

reference

area,

axial

and center

the

force,

of pressure

of the component. PRINT = 1

In addition

to the output

prints

additional

out

pitching

moment,

pressure PRINT=

2

giving

velocity printed

for

condition

also

the body,

option

wing and shell In addition program

and the

force,

center

of

surfaces.

the source

velocity

u,

control If

velocity tables

the planar

tables

v,

The normal

Separate

panels. separate

has been selected,

lateral

point.

body panels.

and shell

or the vortex

are

boundary

are given

for

the

upper and lower surfaces.

to the output

prints

strength

number,

panel

for

wing,

axial

for PRINT = 1, the program

the

calculated

force,

on the wing and tail

and the axial w at

normal

coefficients,

the panel

panel,

velocity

is

the

described

listing

of that

for PRINT = 0, the program

and drag

to the output

and vertical

3

lift

out tables

strength

PRINT=

tables

of each column of panels

In addition prints

described

out

arrays

the

described

for PRINT = 2, the program

iteration

number,

at

step

obtained

each

and the of

the

source

iterative

and vortex solution

procedure. PRINT = 4

In addition program which

to the output

prints

out tables

make up the elements

prints

out the matrix

that

row.

this

option

its

influence

described

of the axial

A maximum of nine description

and normal

of the aerodynamic

row number,

is selected,

for PRINT = 3, the program

and gives

matrix

each of which prior

to printing

components The program

matrices.

the number of elements

partitions is

velocity

will

identified the

be printed

in if

by a number and velocity

component

tables.

95

If

a negative

formation panel

value

described

geometry

cards.

This

corner

points,

of PRINT is

above for

description

consists

the

of

the

of tables

control

points,

selected,

positive

values,

configuration

giving

the wing,

inclination

the

angles,

program

prints

together

with

following body, areas,

fin,

the

all the list

tail,

the

in-

complete of

input

and shell

panel

and chords.

SAMPLE CASE The following case

for

provides on both

verification.

case illustrates The wing

the use of the programs alone

mixed

an example of most of the features the

design-optimization

of the two codes.

Input The following

data set is used for

Data the sample case:

a check

calculation This

Grumman CDC CYBER 740 and NASA LaRC CYBER 175, with

s.ults .

96

and provides

case was run identical

re-

0.032869

182236 156434 130526 104528 078459 052336 g26177

0;010039 0.005278 0.000519 -0.004157 -0*008700 -0.013106 -;AWf$9" * d.

ANALYSIS DESIGIY-CRAIDfIN GEOflE:TRY 2.338 7.102 9.242 3.645 .5.235

MBINED

%%t

31.230 78.503

35.261 83,822

0,o

010

0.0

0.2963 0.2990 0.1396 0.5061 0.5473 0.1317 0.6054 0.7521 0.1196 0.6329 ot9050 0.1064 0.6202 019989

0.2977 0.2989 0.1851 0,520O 0.5462 011777 0.6381 017521 0.1634 0.6788 oe9104 0.1470 0.6744 1.0135

8:: ;*;;g 0:2992 0.0972

0.7511 0+0802

0.9810

8:: I:! 0.1328 0.1684

39.483 89,188

:8t9

. 5 43.881 94.5861 iO0’. 000

0,o I:o”

1:8 0.0000

0.2388 0.7757 1.0344

wi 0:9181 0.2889 0.8212 1,0416

0.2279 0.2991 0.2986 0.2793 0.5377

0,2500 Ot2994 0+2986 0.3245 0.5428 0.5433 0.3310 0.7101 0.7500

97

98

i 3 5 0 0 0 01111 171.05 14.697 14.747 0.0 0%91 0.3874 0.3960 0.3967 0.1224 0.1705 0.2189 012650 ii:!066 k:::, 70,oo 0.3967 80.00 OtOOOO 90.00 40.00 0.3967 50*00 0.3967 6OtOO 0.3967 0.~98~ t 0;~98~ * O;~~Is 0.3967 30.00 0.3967 100,00 0.0 1.4697 2.9394 4.4091 sra7aa 7.3485 8,8~8210,28791~.757613.2273 :k&:N XLAflDA=57;0,NOPTI1)-2,NOPT(2)--3,NOPT(4)=2,~OPT(5)=1, ~~~~NS=3rXSTN~1~=15.5~XSTN~2~=19,9~XSTN~3~~24,4rXbPEX~3.907r I.62 12.0 0.4

99

z; 0

SYSTEMDEPENDENTJOBIDENTIFICATION

COREL CONICAL BY B.

(VERSION

2

RELAXATION GROSSMAN,

AERODYNAMIC

1c= 30 GAMHA=1.40

cc(l)= IOUT=

1

JDRLX=

6

IMOD= 0

xL3=

0.000

PRESENTLY

JC= 30 ww1=1.000

KMAXl= 350

BZ= 1.500 ccc21=

I

BY W. MASON

VIRGINIA

POCYTECHNIC

GRUMMAN AEROSPACE

KMAX2= 250 ww3=1.500

NG=199 yxcx;; ooooo

0.000

IDESIN= 0

ETADR==.750

IEQV= 1

xu1= 0.000

DTCL=

XSTN=

THICK= UPPER

-

OF AERONAUTICS

INSTITUTE,BLACKSBURG,VA.

CORPORATION

,BETHPAGEs

N.Y.

(703)

961-6740

(516)

575-6092

0.000

SECTION

1.000000 X

:

1.000000 .999657

3

.996917 .998630

ii i

.994522 .991445 .987688 .983255

:% .951057 : !E% : 8% .923880 .913545 .902585 .a91007 .a78817

AT FNU=

SURFACE

.97ai48 .972370

KMAXJ= EST=-6.00

150

KREF=2

DMINl=

.lOE-05

IiLOT= 1 DtlIN2= .lOE-05

DMINJ=

N.Y.

.lOE-05

FOR SC3 WING CONCEPT , AZ=33.00 XSTN=19.90

SPANWISE ZSYH=O.O

PROFESSOR ADAPTATION

WW2=1.500

WDES=O.OOO

0.000

BETHPAGE

ALP=12.000

DEI,:ONSTRATION WING M=1.62, ALPHA=lP.O AZ=33.000

CORPORATION

SOLUTION

APPLICATIDNS

MINF=1.620

GRUMMAN AEROSPACE

OF SEPT.29,1978)

Y -.021157 -.019435 -.017660 -.015830 -.013943

-.011998 -.009992 -.007927 -.005801 -.003618 -.001380 .000908 .003238 .005602 .007988 010382 :012768 .015130 .017486 .019914

.19.900

XSTNz19.9 61.0

‘0 NS=

4

CT(l)= 0.000 IRPTS= 1 EPSHKI=1.200 xu2=

0.000

IEeV3=

0

FOR COREL FNL=

61.0

Lc= 0 CT(2)= IOUTL=O TESWP=

0.000 0.00

xu3= 0.000 XROOT=**xNRR*%R

LT= 1 CT(3)= 0.000 IPUNCH= KCCC= 0 DCTU= 0.000 ZROOT= 0.00000

LM= CM(l)=

5

0 0.000

NSHKR=lO XORIGC= 3.9070 xLl= 0.000 YWNGRT= -1.00000

YORIGi= xL2=

o.ooi

0 [email protected] 2 z 3

ANALYSIS XKSMTH=

0.0

XSING=

0.000000

YSING=

0.000000

$ g l-t z i WI V

.a66025 .852640 .a38671

.824126 .a09017 .793353 .777146 .760406 .743145 .725374 .707107 .688355 .669131 :~X .608761 .587785 .566406 .544639 .522499 .500000 .477159 .453990 : tfi;:: .382683 : 3335% .309017 .284015 .25aai9 .233445 .207912 .182236 .156434 .130526 .x04528 .078459 : Ef% 0.000000

.022426 .025024 .027712 : K%l .036317 .039358 : :t5zz .048895 : EZ .osaaoo .062061 : Ka:: .071099 .073732 .076104 .07817i .079890 : ixt .082573 : EE .080660 .078690 .076057 : :X%:; : K:ft : %::a .045482 : EZ -031096 .026479 .021799

LOWER SURFACE

I 1 f i

X ':%% .998630 .994522 .996917

76

.991445

a

.9876aa .983255

9

.978148

:P

; zz;H

:i 14

.951057 .942641

Y -.021157 -. 022682 -. 023870 -.024727 -.025266 -.025500 -. 025448 -.025130 -.024568 -.023790 -. 022821 -.021690

-.020426 -.019060

.933580 .923aaO .,913545 .902585 .a91007 .a78817 .a66025 .a52640 .a38671 .a24126 .a09017 .793353 .777146 .760406 .743145 .725374 .707107 .688355 .669131 .649448 .629320 .608761 -587785 .566406 -544639 .522499 .500000 .477159 .453990 .430511 .406737 .382683 .358368 .333807 .309017 .284015 .258819 .233445 .207912 .182236 .156434 .130526 : E25i : K:;f

0'.000000

-.017623 -.016144 -.014655 -.013181 -.011714 -.010180 -.008570 -.006881 -.005106 -.003240 -.001275 .000793 .002968

:KZ :.015338 EE .018012 .020667 .023256 .025744 .028093 .030261 .032207 .033888 .035264 .036295 .036943 : L%z .036250 :x49 .030229 .027015 -023295 : FEZ .010039 .005278 .000519 -.004157 -.008700 -.013106 -.017430 -.021799

PROGRAM 03400

(SPADE)

-

SURFACE

PATCH

DEFINITION

EQUATIONS

FROM THE CRAIDON PROGRAM -SUBROUTINE AIRCRAFT SC3 DEMO

WING

ALONE

FOR

COMBINED ANALYSIS DESIGN-CRAIDON GEOMETRY

010000020300000000 .147 .586 1.317 14.314 17.231 20.391 23.784 53.159 58.011 62.986 68.070 0.000 0.000 0.000 23.840 1.659 .774 -.I66 22.337 3.317 1.547 -.272 20.834 4.975 2.321 -.334 19.332 6.630 3.094 -.362 17.832 8.277 3.868 -.364 16.341 9.905 4.641 -.348 14.871 11.491 5.415 -.323 13.450 13.000 6.188 -.296 12.117 14.410 6.962 -.278.10.917 15.725 7.735 -.286 9.869 16.974 8.509 -.262 8.961 9.282 -.239 la. 188 8.160 10.056 -.2i3 19.388 7.423 10.829 -.218 6.716 11.603 -.216 :;*5;: 6.021 22:965 12.376 -.219 5.331 24.157 13.150 -.229 4.643 25.357 13.924 -.246 3.946 27.500 14.697 -.157 2.306 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 .0085 .0310 .0615 .2665 .2780 .2857 .2908 .2995 ,299s .2995 .2993 .0073 .0281 .0593 0.0000 .3662 .4037 .4365 .4647 .5461 .5480 .5488 .5488 .0063 .0247 0.0000 .3834 .4344 .4827 : L%63 .7250 .7360 .7436 .7484 0.0000 .0055 ,.0214 .0469 .5321 .3684 .4235 -4784 . ..-. .8262 .8516 .a715 .a865 .0409 0.0000 .0047 .olas .3415 .3959 .4516 .5081 .a625 .a993 .9315 .9589 0.0000 .0041 .0160 .0355 .3115 .3633 .4172 .4729 .a559 .8996 .9740 0.0000 .0035 :X .0310 .3826 -4357 .2832 .3317 .a193 .a665 .9101 0.0000 .0031 .0123 : 2: .2580 .3029 .3500 .3992 .7633 .a109 .a565 .9003 0.000

START IN COREL

CONFIGURATION DESCRIPTION 00000000 2.338 3.645 5.235 7.102 9.242 11.649 27.400 31.230 35.261 39.483 43.881 48.445 73.247 78.503 83.822 89.188 94.586100.000

0.0000 0.0000 0.0000 :E .2992 .0972 .4880 .5482 2;;;

0.0000 0.0000 0.0000

.1328 .2963 .2990 .1396. .5061 .5473 .1317 .6054 .7521 .1196 .6329

0.0000 0.0000 0.0000

.1684 .2977 .2989

:E .5462 .1777 .6381 .7521 .1634 .6788

0.0000 0.0000 0.0000

.2006 .2986 .2987 .2323 .5302 .5451 .2269 .6669 .7517 .2109 .7214

:%82 .a974 0706 : 3 : E;: :K .6744 :5645 9810 : ;;i: 1.0135 1%: :0618 .0939 .1308 .1715 .5300 .5877 .6453 1.0053 1.0337 1.0590 1:E 0542 .1162 :4907 .6038 9881 1.0230 1.0552 1.0848 10482 -4502 : ~70~69 : :2: .1382 .6090 .9421 .9816 1.0189 1.0539

0.0000 0.0000 0.0000

.2279 .2991 .2986 .2793 .5377 .5442 .2784

0.0000 0.0000 0.0000

.2500 .2994 .2986 .3245

.5428 :543::

:%J; .2613 .7603

.7101 .7500 .3140 .7953

: ::i:

:Ei

1X 1::::: .2155 .2622 1:z2" 1%:: .1940 .2373 .7156 .7689 1.1119 1.1367 : 2: .2155 .7134 1.0866 1.1170

0.0000 .2423 .7037 0.0000 .2507 .6644 0.0000 .2257 .5942

.0026 .2832 .7505 .0031 .2876 .7093 .0029 .2593 .6361

.1992 .5294' 0.0000 .1734 .4744 0.0000

:E .5678 .0021 .2015 .5090 .oola .1824 .4610 .0016

0.0000

: t::: 0.0000 .1396 .3876 0.0000 .1226 .3449 0.0000 -1052 ,302s 0.0000 : !E; 0.0000 *O?SS

::E :K .3681 .0012 .I243 .3221 .OOlO .1024 .2760 : if::;

:X OGE 1.5517 1.6588

1.9002 0.0000 1.5912 1.9002 0.0000 1.6257 1.9002 0.0000 1.6551 1.9002 0.0000 I.6795 1.9002 0.0000 1.6989 1.9002 0.0000 1.7133 1.9002 0.0000 1.7226 1.9002 0.0000 1.7269 1.9002

1.8141 .2168 1.6873 I.8141 .2432 1.7122 1.8141 .2657 1.7335 1.8141 .2844+ 1.7511 1.8141 .2993 1.7651 1.8141 .3103 1.7755 1.8141 .3174 1.7822 1.8141 .3207 1.7853 1.8141

0105 :3260 .7966

.0235 .3704 .a417

: E73 .7541

: Et .7987 .0253 .3270 .7209 .0220 .2885 .6462

:E .6785

0099 :2590 -6068 .ooas -2294 .5443 .0073 .2089 .4923 .0064 .laas .4419 .0056 .1667 .3916 : K: .3420 .0038 .1192 .2924 .0016 .0551 .1533 .3670 1.7539 1.6990 .4199 1.7727 1.6990 .4'660 1.7891 1.6990 .5054 1.8031 1.6990 .53ai 1.8147 1.6990 -5640 1.8239 1.6990 .5833 1.8307 1.6990 .5958 1.8351 1.6990 .6016 1.8372 1.6990

:Ei .5800 .0163 .2351 .5241 .0144 -2132 .4696 .0124 .1894 .4154 .0105 .1643 .3620 .0085 .1365 .3088 .0036 .0640 .1624 .5412 1.8357 1.5539 .6094 1.8466 1.5539 .6689 1.8561 1.5539 .7197 1.8642 1.5539 .7619 1.8710 1.5539 .7954 1.8763 1.5539 .a202 1.8803 1.5539 .8363 1.8829 1.5539 .a438 1.8841 1.5539

.0413 .4163 .a855 .0487 .4056 .a425 .0443 .3622 .7632 .0386 .3193 .6857 : !E .6161 : EL .5563 .0253 .2375 .4977

0636 4635 9277 0750 4472 8855 0677 3983 8051 0590 3514 7253 0506 3139 6523 0442 2871 .5887 :Ei

:::3: 9274 :0950 .4351 .8463 .0830 .3847 .7645 : iit: .6886

.1613 .1235 2015 .6086 6566 .5601 1 1.0438 1: 0786 ': %i .l758 2132 .5760 .5327 6199 1.0069 1: 0444 .i578 1916 : E3 .5125 .5529 .4731 .9262 .a868 .9644 2% .a034

:Z'9 .8416

: :69:; .a790

; gqg

.1193 .4074 .7605

: tti; .7958

:K8 .6863 .0942 .3354 .6117 .0822 .2997 .5368

.1304 .4001 .7185 .1163 .3612 .6401 .ioia .3221 .5612

.0832 .3420 .6538 .0738 .3101 .5831

.5260

: it242 .621: EZ : .5545

: i::: .4394 .olas

2::: .4636 .0287

:Ei .4879 .0408

:E .5124 .0547

: :X4:

.4024 .2051

.4227 .2252

-2449 .4431

: K: .3253 0064 0734 1715 7088 9029 :: 3781 7856 9081 :: 3781 8527 9126 :: 3781 9099 9165 :: 3781 9574 9198 :: 3781 9951 9223 :: 3781 0231 t: 9242 3781 :: 0412 9255 :: 3781 0496 :: 9260 1. 3781

: i% .3419 .OlOO

.0332 : EZ

: 82 .3749 .0195

1x 1.9867

1.1685 1.9998 .6649 1.2393 1.9998 .6649 1.3012 1.9998 .6649 1.3540 1.9998 .6649 1.3978 1.9998 .6649 1.4325 1.9998 .6649 1.4583 1.9998 .6649 1.4751 1.9998 .6649 1.4828 1.9998 .6649

:E .a696 1.9538 1.1712 .9490 1.9555 1.1712 1.0184 1.9571 1.1712 1.0776 1.9584 1.1712 1.1268 1.9596 1.1712 1.1658 1.9604 1.1712 1.1947 1.9611 1.1712 1.2135 1.9615 1.1712 1.2222 1.9617 1.1712

x

1:Ef 1.9870 .9333 1.1674 1.9872 -9333 1.2249 1.9874 1:EZ 1.9876 1:E 1.9878 .9333 1.3385 1.9879 1%:: 1.9879 1:39E 1.9880 .9333

::Z

:E% :K .4634 .4837 .0574 .0714 .2262 .2434 .3914 -4078 .0253 .03ia 1154 .1267 2082 .2173 3057 .4337 9912 .9587 3668 .0400 3674 .4845 9912 .9587 3668 .0400 4212 .5290 9912 .9587 3668 .0400 4672 .5669 :: 9912 : .9587 3668 .0400 5054 .5984 :: 9912 : -9587 3668 .0400 1: 5357 .6234 1. 9912 .9587 3668 .0400 5581 .6419 :: 9912 .9587 3668 .0400 5727 .6539 :: 9912 3668 : 09% 5795 .6595 :: 9912 .9587 3668 .0400

1.4834 1.9998 .6649 1.4834 1.9998 .664i 1.4834 1.9998 .6649 1.4834 1.9998 .6649 l-4834 1.9998 .6649 1.4834

0.0000

1.7273 1.9002 0.0000 1.7273 1.9002 0.0000 XfT1 o:oooo 1.7273 :-E I:7273 1.9002 0.0000

1.6599 1.9587 .0400 1.6599 1.9587 .0400 1.6599 I.9587 .0400 1.6599 1.9587 .0400 1.6599 1.9587 .0400 1.6599 1.9587 1.9912 .3668 .0400 1.5800 1.9912 : '69~~79 .3668 :0400 1.5800 1.6599 1.9912 .3668 ':E 1.5800 1.6599 1.9912 1.9587 .3668 .0400 1.5800 1.6599 1.9912 1.9587 .3668 .0400 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

i.9998

.6649 1.4834 1.9998 .6649 1.4834 1.9998 .6649 1.4834 1.9998 -6649 1.4834 i.9998 .6649 0.0000 0.0000 0.0000

:'79% o:oooo 1.7273 1.9002 0.0000 1.7273 1.9002 0.0000 1.7273

af**

1.5800 1.9912 .3668 1.5800 1.9912 .3668 1.5800 1.9912 .3668 1.5800 1.9912 .3668 1.5800 1.9912 .3668 1.5800

‘LETED *)o(

SPLI

)IIY

WING NSURF= NUMBER OF :ATCNES= 551 NUMBER OF PATCHES= 551 IWI~ CORNER POINTS OF PATCHES

NN(* Y36I

HAVE BEEN COMPUTED

33 LEADING EDGE PANEL DETECTED AT NXLE= 1 It** 39 PATCHES FOR XCUT ON SURFACE 2 **N 39 PATCHES FOR XCUT ON SURFACE XTIP= 19.90000 YTIP= 10.38742 ZTIP=

ON SURFACE

-.21985

AND STORED

1

AS COMMON PATBLK

It**

SPANWISE

SECTION

GEOMETRY ZAVG=

19.90000

FROM CRAIDON .OOOc

YHARL .ooooo .03457 .06904

2 -.01416 -.00843 -.00248

: :::3:

X45

: :%t .23652 .26838 .29948 .32973 .35904 .38734 .41454 .44056 .46534 .48879 .51086 .53149 .55060 .56816 .58410 .59839 .61098 .62184 .63094 .63825 .64375 .64743 .64927 .64950 .64927 .64743 .64375 .63825 .63094 .62184 .61098 .59839 .58410 .56816 .55060 .53149 .51086 .48879 .46534 .44056 .41454 .38734 .35904 .32973 .2994a

: %E .02290 .02409 .02389 .02263 : ::;a44 :%Z : E:! .00109 -.00162 -.00407 -.00629 -.00829 -.01024 -.a1220 -.01395 -.01536 -.01628 -.01657 -.01607 -.01466 -.01375 -.01271 -.01023 -.00767 -.00498 -.00213 .00086 .00396

GEOMETRY

PACKAGE

DALP= -.OO DEGREES CENTERLINE AVERAGE VALUE DNY -.16186 -.16555 -.17481 -.18137 -.17513 -.15178 -.I1303 -.06366 -.01386 .02505 : OOE .10948 .12688 .13583 .13927 .13653 .13255

DNZ : 99885515 : ;Et .98371 .98750 -99242 .99631 : %:i : 99;::: .98919 .98675 .98542 : 2285 .98642 .98743

: :Zt .12393

: 8Ei

: :2::; .15778

: 99XS~~ .98099 :.;:j179: .99286 .99997

:X .01344 .01687 .02052 .02441

:X .09579 -.00729 -.30488 -.79785 -.82437 .81048 -60934 .46671 .38733 .32688 .28694 .25664 .22681 .19953 .19152 .18882 .18464 . la386

: K%Z .03717

: :;:;09 .16811

: 8E;: .97224 .97469 .97566 .97701 97762 197885 .98016 .98245

:X

: :z

: EZS

: %fJi .05319

: Xt .03574

: E5 .99919

: S:E .18948 .25748 .68689 -83104 .88739 : 82Z

IF ZAVG IS NOT ZERO, THE SECTION IS TRANSLATED TO KEEP THE SPANWISE SECTION AT THE COORDINATE SYSTEM ORIGIN, AND THE ANGLE OF ATTACK IS CHANGED BY DALP TO ACCOUNT FOR THE TRANSLATION. DNX -.04639 -.04517 -.04317 -.04112 -.04051 -.04241 -.04817 -.05764 -.06807 -.07722 -.08549 -.09251 -.09752 -.10116 -.10245 -.10233 -.09991 -.09703 -.09399 -.09336 -.09220 -.09398 -.10502 -.11301 -.11315 -.10168 -.07106 -.00311 ::1'::: .53339 -.52614 -.39609 1:;;;;; -.20947 -.18217 I: ;g;; -.I2224 -.11532 -.11156 -.10657 -.10225 -.09615 -. oa937 -.08076 -.07ioa -.05952 -.04715 -.03320 -.01851

XSTN 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000

YD .ooooo .55284 :%:: 2:19572 2.73296 3.26245 3.78269 ,4.29221 4.78956 5.27334 5.74217 6.19472 6.62971 7.04591 7.44214 7.81727 8.17024 8.50005 8.80577 9.08653 9.34153 9.57005 9.77145 9.94514 10.09065 10.20755 10.29552 10.35430 10.38374 10.38742 10.38374 10.35430 10.29552 10.20755 10.09065 9.94514 9.77145 9.57005 9.34153 9.08653 a.80577 a.50005 a.17024 7 .a1727 7.44214 7.04591 6.62971 6.19472 5.74217 5.27334 4.7a956

ZD -.;2643 -.I3489 -.03968 .05985 : :% .32003 .36631 .38530 .38215 .36185 .32729 .28207 .22954 .17394 .11837 : KG -.02584 1:;;;;; -.13252 -.16378 -.19505 -.22313 -.24568 1:;;;;; -.257oa -.23450 -.21985 -.2032a -.16362 -.12271 -.07960 -.03403 .01371 .06332 .11414 .16421 :K .32a2i .39035 .45623 .52469 .59452 :.fZ .7a167 . a2423 .a5073

zt 55:

.23652 .26838 .17088 .20399

.05366 .05263 .04527 .04978 .03952 .03309

810

.13729 .10331 .06904 .03457 .ooooo

I

YHARL

-02658

.02028 .01416 2

YHARL IS TAKEN TO BE A 61 POINT COSINE SPACING CHOSEN TO CONCENTRATE POINTS AT THE L.E. OF THE SPANWlSE SECTION,

-.00716 -.06077 -.ii32a -.15463 -.18027 1: :g; -.17590 -.I7357 DNY

.99997 .998oa .99323 .98735 .98279 .98115 .98202 .98338 .98373 DNi!

-:W .02561 .03514 .04040 .04296 .04405 .04494 .04630 DNX

19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 19.90000 XSTN

4.29221 3.78269 3.26245 2.73296 2.19572 KEf 1552a4 .ooooo YD

.a5117 .a4164 :E8

.63203 .52927 .42514 .32435 .22643 ZD

INTERNALLY

GENERATED

SINGULARITY

LOCATION

X(IN)=

.64918

Y(IN)=

-.01473

ERG=

.64825 -64732

YcYSING=

-.01426 -.01379

XSING=

.99822

YSING=

NORMALIZED

FOR MAPPING IN=

WITH

THE

60

-.02196

.016988

XAREAF

BY XLE

yo=

.64825

x0=

GENERATED FROM PARM: X(IN), Y(IN): THE POINT ON THE SECTION SMALLEST RADIUS OF CURVATURE. XC, YC: THE ORIGIN OF THE L.E. RADIUS

Yl=

-.014260

CROSS SECTIONAL OF THE SPANWISE

.014260

AREA SECTION

/ ‘SING

HAPPED

BODY

(B)

AND SHOCK BODY

(Cl

-

LOCATIONS

WITH

1ST

(PR)

AND 2ND

LOCATION

I

X

B

BPR

BSEC

2

-.15708EtOl -.14586EtOl -.13464EtOl -.12342EtOl -.11220EtOl -.10098EtOl

.33265EtOO .32632EtOO

0. -.59303E-01 -.58877E-01 -.43504E-01 -.19378E-01 15004E-02 :16013~-01 .23252E-01 .23597E-01 .21913E-01 .26358E-01 .42010E-01 .61776E-01 .63611E-01 .51667E-01

-.10047EtOl

: 2 x

::

-.89760EtOO -.78540EtOO -.67320EtOO -.56100EtOO -.44880EtOO -.33660EtOO -.22440EtOO

::

-.71054E-14

1: ::

.31934EtOO .31311EtOO .30958EtOO .30876EtOO .30992EtOO

.31236EtOO .31513EtOO .31765EtOO

-.11220EtOO

:x if

.11220EtOO .22440EtOO .33660EtOO .44880EtOO

23

$45 %S tt 30

I

.67320EtOO .78540EtOO

.a9760Etoo .10098EtOl .11220EtOl .12342EtOl .13464EtOl .14586EtOl . 15708EtOl

.35268EtOO

.35410EtOO .35629EtOO .35882EtOO .36083EtOO

.36125EtOO .35931EtOO .35417EtOO .34648EtOO .33a53Etoo

.80847E-01 .19015EtOO .16219EtOO -.1294aEtoo

-.83429E-01 -.29035EtOO -.27893E-01 -.38926E-01 .51188E-01 .60647E-01 .27643E-01 -.41415E-01

.33162EtOO

VELOCITIES

.17133EtOl .17662EtOl .18172EtOl .18647EtOl .19073EtOl 19445EtOl :19755EtOl .19994EtOl .20148EtOl .20209EtOl

-.25377EtOO -.20345EtOO -.19685E-01

.a2267E-01 .10977EtOl

BPR

AND FREESTREAM

.16601E+ol

-.12589EtOO -.18801EtOO

-.67568E-02 -.31540E-01 -.57190E-01 -.69707E-01 -.66197E-01 0.

X METRIC

.26552E-01 -.20397E-01 -.96187E-02

.20238E-01 .10053E-01

BSEC

-----B
.21409EtOO .21596EtOO .15620EtOO .10249EtOO

12845E-01 :90962E-02 .97841E-02 .16058E-01 .21011E-01

DERIVATIVES

.13554EtOl .13557EtOl .13552EtOl .13542EtOl .13529EtOl .13519EtOl .13520EtOl .13538EtOl .13581EtOl .13656EtOl .13771EtOl .13933EtOl 14147EtOl :14417EtOl 14751EtOl :15143EtOl .15592EtOl .16082EtOl

-.52367E-01 .59949E-01

.3069aE-01

.35191EtOO

.56100EtOO

;:

.32005EtOO .32357E+oo .32948EtOO .33743EtOO .34375EtOO .34902EtOO .35064EtOO

(SEC)

‘SING

ASSUMED BOW SHOCK LOCATION C

-----

C

CPR

0. -.71327E-03 -.69877E-02 -.10481E-01 -.10162E-01 -.40285E-02 .84379E-02 .27389E-01 .52861E-01

.84aa5E-01 .12317EtOO .16713EtOO .21600EtOO .26927EtOO .32324EtOO .37466EtOO

.41834EtOO .44975EtOO .46834EtOO .47294EtOO .46342EtOO .43878EtOO

.40146itOO .35583EtOO .30382Etoo .24442EtOO

.17532EtOO .96017E-01

0.

CSEC .57343E-01 -.70057E-01

-.4178aE-01 -.20488E-01

.26188E-01 .83138E-01 .13908E+OO

XSING, YSING IS THE MIDPOINT OF THE LINE CONNECTING THE CENTER OF THE CIRCLE AND THE TANGENT POINT OF THE CIRCLE TO THE SPANWISE SECTION.

.19a72Etoo .25533EtOO

.31550EtOO .36691EtOO .416aOE+OO .4541aEtoo .49551EtOO .46655EtOO .44988EtOO .32a74Etoo

.23122EtOO .10017EtOO -.la230E-01 -.15147EtOO - .28763E+OO -.37775E+OO -.43554EtOO

-.49163EtOO

-.56707EtOO -.66475EtOO

-.74aaoEtoo -.96274EtOO

CPR

CSEC

y AT

GRID

POINTS

NOTE:

THE KBJKOWSKI MAPPING LEADS TO A NEAR CIRCLE, B IS NOT A CONSTANT IN THE MAPPED SPACE.

SO THAT

MAPPED

PLANE

RHO .33265EtOO .32632EtOO

.31934E+OO .31311E+OO

.30958EtOO .30a76EtOO .30992EtOO .31236EtOO

.31513E+OO .31765E+OO

.32005EtOO .32357EtOO .3294aEtoo .33743EtOO .34375EtOO .34902EtOO .35064EtOO

.35191E+OO

.3526aEtOO .35410EtOO .35629EtOO .35882EtOO .36083EtOO

.36125E+OO

.3593IEtOO

.35417E+OO .3464aEtOO .33153Etoo

.33162E*OO

PHYSICAL THE

-.1570aE+ol -.14586E+Ol -.13464E+Ol -.12342E+Ol -.11220E+Ol -.10098E+Ol -.89760EtOO -.78540EtOO -.67320EtOO -.5610OEtOO -.4488OEtOO

-.33660&00 -.22440EtOO

-.11220E+OO

-.71054E-14

PSI .14155E-01 .67881E-01

.13508E+OO

.20070EtOO .26277EtOO .32034EtOO .37295EtOO

.42019E+OO .46172E+OO .49717E+OO .52622EtOO .54862EtOO .56433EtOO .57352EtOO .57604EtOO

.11220E+OO

.57183E+OO

.22440EtOO .33660EtOO .44880EtOO

.56056EtOO .54267EtOO

.56100E+OO .67320EtOO .78540EtOO .a9760EtOO

.51831E+OO .48790EtOO .451a2Etoo

.10098E+Ol

.41045E+OO .36411E+OO .31305E+OO

.11220Et01

.25755EtOO

.12342E+Ol .13464E+Ol .145a6E+Ol .15708E+Ol

.19780E+OO .i3455E+oi .69789E-01 .14155E-01

MAPPING METRIC .-

PLANE OMEG

UI

N

-.1570aE+ol

.18209E+Ol 18428E+Ol :18407E+Ol 18059E+Ol :17269E+Ol .16068E+Ol .14559E+Ol .12840E+Ol llOllE+Ol :91293E+OO .72156E+OO

-.39586E-01 .71027E-01 97679E-01 :89595~-01 .68000E-01 .44056E-01 .22401E-01 .58178E-02 -.56375E-02 -.13566E-01 -.19970E-01 -.24708E-01 -.25427E-01 '.20627E-01 -.11807E-01 -.16665E-02 .99505E-02 .22866E-01 .39078E-01 .60445E-01 .88278E-01

.52693EtOi .33308EtOO .15624EtOO .99749E-01 .24009EtOO .39910EtOO .55922EtOO

-.19996E+OO -.26184E+OO -.31854E+OO -.36915E+OO -.41308E+OO -.45034EtOO

-.48114E+OO -.50529EtOO -.52023EtOO

-.51507E+OO -.41163E+OO

.71587E+OO .86535EtOO

.12263E+OO 16203E+OO

:2045OEtOO .24506EtOO .28569EtOO .37816EtOO

.10045E+Ol .11315E+Ol .12469E+Ol .13524E+Ol .14501Et01

.15431E+Ol .16297E+Oi .16995E+Ol .17444E+Ol

Y---- w x w .1570aE+ol

CROSS-SECTION

PLAN

VIEW

VI

.12312E-14 -.67280E-01 -.13445EtOO

.38659EtOO .56409EtOO .55990EtOO .54027EtOO

.5147aE+oo .41461E+OO .44955EtOO

.4091aE+oo .36323EtOO

.31174E+OO .25520EtOO

.19437E+OO .13056E+OO .65345E-01 .11382E-13 FREESiREAM

-.22174E+OO -.21022E+OO -.19659EtOO

-.18304E+OO -.17342E+OO -.16a37E+OO -.16700E+OO -.16856E+OO -.17135E+OO -.17418E+OO -.17797E+OO -.19083EtOO -.23699EtOO -.40022EtOO -.42600EtOO

-.a6176E-01 .22197E-01 .615a9E-01

.9509aE-01 .10970E+OO .11763E+OO .12232E+OO .12646E+OO .13211E+OO .14041E+OO .15259E+OO .16763E+OO .11203E+oo .19405E+OO VELiiClTlES

WI .97511E+OO .97534EtOO

.97122E+OO .96256EtOO .94940EtOO .93283EtOO .91424EtOO .a9496EtOO .87626EtOO

.85917E+OO

.a4440Etoo .a3244Etoo .82373EtOO

.81a77E+OO .a1796E+OO .a2121E+oo .a2a27E+oo

.a3169Etoo .85203EtOO .a6782EtOO .aa548Etoo .90422EtOO .9230aEtoo .94094EtOO .95664EtOO .96a99EtOO

.97717E+OO .9a112Etoo .9a099Etoo

NOTE THAT THE PROGRAM FROM THE ORIGIN, 24. SURFACE

I : 3 2 7 8 9

ARC LENGTH

CS)

X/Z

Y/Z

-. 00000 .06793 .13556 .20247 .26791 .33100

-.01416 -.00269 .00964 .01984 .02407 .02254 .01723

.39088

::

::

.62773 .60303 .57017 .53029 .48442 .43347 .37824 .31946 .25792 .19443 .12988 .06496 .ooooo

E 20 t: 23 24 25 26 27

20 29

I

: ES:: .02073 .02932 .03837 .04662

0.00000 .06889 .13764 .20533 .27093 .33406 .39418 .45045 -50184 .54728 .58575 .61634 .63835 .65166 .65653 .66581 .68300 .70869 .74231 .78292 .82959 .88133 .93718

: EE5

;: Hi%;;

.03815 .02581 .01416

1:18691 1.25299 1.31900

.04862

X/Z

THETA

PSI

9.19264 9.95043 9.45096 5.60673 1.10677 -2.73573 -6.13507 -7.67253 -7.72597 -7.34760 -7.69958 -8.61171 -5.02490 28.32868 64.90918 144.55220 160.42027 165.88655 168.45740 169.23119 169.65527 170.72479

.31414 .03245 -.46571 -1.08595 -1.11797 -1.02233 -.71223 -.I5398 -06862 -.01984 -.30916 .73202 8.90770 77.08674 136.75686 39.59667 6.38028

-.ooooo

l: E73 .23402 .23377

:X: .81660 .74597 .66751 .58246 .49194 .39717 .29940 .20001 .10004

173.18175 177.31196 181.55226 186.30045 189.95137 190.4608a 189.86743

S

Y/Z

SLOR

1.31900

SOLUTION

XMAX=

BEGINS

ITERATION

.64938

DELMX

I

J

(Y/Z)/XMAX

.10461 .20876 .31179 .41257 .50972 .60192 .6(1786 .76623 .83561

.89438 .94102 .9744a .99439

1.00000 .99096 .96665

1.1158a

.46051 -.01128 -.26637

.ooooo

PSI

SURFACE SLOPE

DISTANCE

(X/Z)/XMAX

DYBP/DZP

-.02iao -.00414 .01485 .03055 .03706 .03471 .02654 .01541 .00446 -.00471 -.01213 -.oia79

-.22360 -.22405 -.22236

1: g;:; -.02063 -.01170 -.00161 .00924 .02ooa .03193 .04514 .05908 .07179 .08041 -08237 .074aa .05875 .03974 .02iao

-.57398 -1.60970 .24109 .01279 -.05182 -.07996 -.08785 -.09170 -.ioo2a -.11760 -.14222 -.16294 -.ia22a -.194oa -.19562 -.i952a

:;:;o';; -.i71oa A.15019 -.I3926 -.13904 -.14253

-.138ao 1:;;;:;

(Y/Z)/XMAX

DYBP/DZP

CURVATURE

SMAX/XMAX=

2.03115

ON MESH 1 NO. OF POINTS

ITER

(X/Z)/XMAX

: 595% 1.21130 1.24687

THETA

ARC LENGTH FROM BOTTOM OF SECTION SMAX=

AT A UNIT

(PSI)

AND CURVATURE S

.00289 -.00306 -.00788 -.01221 -.01564 -.01642 -.01340 -.00760 -.00105

.64930 .64351

:65 17

(THETA)

.OlOOl

.44668 .49758 .54263 .58080 .61108 .63281 .64574

12

SLOPE

OPERATES

VIOLATING

DELAVG

RESMX

I

J

.300aE-03 .2484E-03 .2226E-03 .206aE-03 .1931E-03 .1839E-03

-.llllE*02 -.5506E*Ol .3227E+Ol .2579E+Ol .2126E+Ol .1021E+ol .1591E+Ol -.1417E+Ol -.12.97E+Ol

4

2

3: 30 30 30 30

f 2

x

I

DIAGONAL

DOMINANCE

RESAVG

KSUP

< NPVD

y J MAX SHOCK JSHMAX ISHMAX JSHMIN

MIN SHOCK ISHMIN

EDGE OF COMPl ITATIONAL .1103E-01 .6625E-02 .5177E-02 .4283E-02 .3622E-02 .3155E-02 .2792E-02 .2504E-02 .2269E-02

.1761E-03 .1694E-03 .1633E-03

f 2

.16a5E+OO 1172EtOO :9971E-01

.a992E-01

.8291E-01 .7740E-01

525

2aJ

0 Q

i

55:

sx 28

: 0

i

i

;x

i 0

1 0

: 0

Fl

i

8

52a

.7208E-01

E 532

.6902E-01 .6563E-01

z34

:x 28

GRID

--------l.

*2073E-02 3o :

.1908E-02 .1765E-02 .1641E-02 .1532E-02 .1435E-02 .1349E-02 .1271E-02 .12OlE-02 .1137E-02 .1079E-02 .1025E-02 .9750E-03 .9219E-03

30 30 30 30 30 30 30 30 30 30 30 30 30

.a457E-03 .aoaoE-03 .7725E-03 .7391E-03 .7075E-03 .6776E-03

ii 30 30 30 30 30

.6225E-03 .5971E-03 .5731E-03 .5504E-03 .5288E-03

ii 30 30 30 30

.i3859E-03 .---..-

.6493E-03-_-._--

3; 36 37

3a 42 tt 45 46 47

.5011E-03 -.4729E-03 . - .- --.4a96E-03

30

30 2 2

I 2 z

.1020&03

x 2 ii 2

:EE-it .9424E-04 .9170E-04

i

.0439E-04 .8215E-04 .a004E-04 .7794E-04 .7587E-04 .7380E-04 .7182E-04

x H I 2 f

2

2

I I

2 2

2

-.4570E-03 -.4417E-03 -.4271E-03 -.4131E-03 -.3997E-03 -.3a68E-03 -.3745E-03

i

i

s

% 2

-.3512E-03 -.3405E-03 -.3304E-03 -.3210E-03 -.3125E-03 -.3050E-03 -.2984E-03

ii 2

-.2926E-03

2

-.2a74E-03 -.2a26E-03

2 2

-.2734E-03 -.26a9E-03 -.2643E-03 -.2597E-03 -.2550E-03 -.2503E-03 -.2456E-03 -.2361E-03 -.2313E-03 -.2266E-03

-.3626E-03 .-_--- __

-.7779E-03 ._. .- _-

-.2409E-03 ._._.- _-

IF I-

30

.1577E-03 .1525E-03 .1476E-03 .1430E-03 .1381E-03 1338E-03 :1301E-03 .1265E-03 .1230E-03 .1198E-03 .1166E-03 .1136E-03 .1103E-03 .1074E-03

I2 ii 2

2

t

2

.1046E-03

.a919E-04 .8672E-04

.69X9E-04 .6796E-04 .6609E-04 .6436E-04 .6260E-04 .6012E-04 .5910E-04 .5740E-04

.5577E-04

-.119aE+ol -.1112E+Ol -.1036E+Ol

-.4011E+OO -.3857E+OO

-.3713E+OO -.3578E+OO -.3450E+OO -.3328E+OO -.3213E+OO

-.3104E+OO

-.3000E+OO -.2902E+OO -.2810E+OO -.2722E+OO -.2637E+OO -.2556E+OO -.2478E+OO -.2402E+OO -.2330E+OO -.2259E+OO

2

2

2 2

2

.1115E-03

i 2

ii 2

.1052E-03 .1024E-03

:

f

t 2

: 2

: tEE-1: .9412E-04 .9142E-04 .8167E-04

i

i

.1405E-04

z

s

.7965E-04

2

% 2 ii t

2

.114aE-03

.1082E-03

.8639E-04 .a176E-04

2

-.4174E+OO

-.2152E+OO -.2128E+OO

f i

2

-.9680E+OO -.9064E+OO -.8503E+OO -.7992E+OO -.7525E+OO -.7098E+OO -.6707E+OO -.6349E+OO -.6021E+OO -.5718E+OO -.5440E+OO -.5186E+OO -.4953E+OO -.4737E+OO -.4536E+OO -.4349E+OO

.5447E-04 .5303E-04 .5187E-04 .1270E-03 .1256E-03 .1234E-03 1210E-03 :1179E-03

2

t I

-.2068E+OO

-.2011E+OO -.1960E+OO -.1913E+OO -.1872E+OO

t f sI dz 4

5 f

-.1835E+OO

f 4

t 2 2

-.1770E+OO

::

t

-.1801E+OO

-.1740E+OO -.i711E+oo

4

-.16a2E+OO

:

-.1653E+OO -.1624E+OO -.1596E+OO -.1567E+OO -.153aE+oo -.1509E+OO -.148Oi+OO -.1450E+OO -.1421E+OO

I a

E 2

4 2I : 2

4 f 4

2

.4681E-01 .4599E-01 .4514E-01 .4427E-01 .4328E-01 .4234E-01 .4134E-01 .4029E-01 .3933E-01 .3a3aE-01 .3742E-01 .3660E-01 .3567E-01 .3470E-01 .3378E-01 .3293E-01 .3209E-01 .3124E-01 .3043E-01

534 534 534 535 534 535 536 535 535 534 535 534 535 534 531 530 529 528 528 528 528 528 529 529 531 528 530 527 527 527 527 525 525 525 526 525 524 521 521 521 521 229 229 228

221 227 227 227 226 226 227 227 227 228 22a 226 226 225 224 224

-.221aE-03 -.2172E-03 -.2125E-03 -.2079E-03 -.2034E-03 -.1990E-03 -.1946E-03 -.1904E-03 -.1862E-03

-.la22E-03 -.17a2E-03

li0 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 iia 119 120 121 122 123 124 125 126 127 128 129

-.1744E-03 -.1706E-03 -.1669E-03 -.1632E-03 -.1596E-03 -.1561E-03 -.1527E-03 -.1493E-03 -.1460E-03 -.1427E-03 -.1395E-03 -.1364E-03 -.1333E-03 -.1303E-03 -.1273E-03 -.1244E-03 -.1216E-03 -.1188E-03 -.1161E-03 -.1135E-03 -.1109E-03

-.1014E-03

-.1059E-03 -.1035E-03 -.1012E-03 -.9893E-04 -.9673E-04 -.9458E-04 -.9249E-04 -.9044E-04 -.8844E-04 -.8649E-04 -.8457E-04 -.8269E-04 -.8084E-04 -.7904E-04 -.7726E-04 -.7552E-04 -.7381E-04 -.7213E-04 -.7048E-04 -.6886E-04 -.6727E-04 -.6571E-04 -.6418E-04 -.6268E-04 -.6121E-04 -.5977E-04 -.5835E-04

.7757E-04 .7550E-04 .7392E-04 .7207E-04 .7035E-04 .6890E-04 .6732E-04 .6579E-04 .6423E-04 .6265E-04 .6105E-04 .5964E-04 .5818E-04 .5671E-04 .5522E-04 .5373E-04 .5223E-04 .5076E-04 .4930E-04 .4803E-04 .4675E-04 .4547E-04 .4416E-04 .4291E-04 .4169E-04 .4041E-04 .3923E-04 .3799E-04 .3687E-04 .3578E-04 .3505E-04 .3415E-04 .3326E-04 .3237E-04 .3189E-04 .3117E-04 .3043E-04 .2968E-04 .2893E-04 .2819E-04 .2752E-04 ..2683E-04 .2616E-04 .2550E-04 .2486E-04 .2438E-04 .2382E-04 .2327E-04 .2274E-04 .2222E-04 .2171E-04 .2122E-04 .2076E-04 .2032E-04 1990E-04 :1949E-04 .1910E-04 1872E-04 1 i835E-04 .1799E-04

-.1392E+OO -.1364E+OO -.1335E+OO -.1307E+OO

-.12aoE+oo -.1252E+OO -.1226E*OO -.1200E*OO -.1175E+OO -.1150E*OO -.1125E*OO -.1102E*OO -.1078E+OV -.1055E+OO -.1032E+OO -.lOlOE+OO -.9a82E-01 -.9667E-01 -.9455E-01 -.9247E-01 -.9043E-01 -.8843E-01 -.8646E-01 -.8453E-01 -.8264E-01 -.8079E-01 -.7898E-01 -.7721E-01 -.7548E-01 -.7378E-01 -.7211E-01 -.7049E-01 -.6890E-01 -.6735E-01 -.6584E-01 -.6438E-01 -.6296E-01 -.6157E-01 -.6021E-01 -.5888E-01 -.5758E-01 -.5631E-01 -.5507E-01 -.5385E-01 -.5265E-01 -.5147E-01 -.5032E-01 -.4918E-01 -.4807E-01 -.4698E-01 -.4590E-01 -.4485E-01 -.4381E-01 -.4280E-01 -.4180E-01 -.4082E-01 -.3986E-01 -.3893E-01 -.3800E-01 -.3710E-01

.2964E-01

.2aa6E-01 .2a22E-01 .2753E-01 .26alE-01 .2617E-01 .2562E-01 .2501E-01 .2442E-01

.2303E-01 .2325E-01 .2279E-01 .2225E-01 .2172E-01 .2119E-01 .2066E-01 .2013E-01 .1961E-01 .1910E-01 .1875E-01 .1828E-01 .1782E-01 .1739E-01 .1696E-01 .1655E-01 ::;::~I:: : :~;~~I;: .1452E-01 .1431E-01 .1395E-01 .1360E-01 .1328E-01 1315E-01 :1279E-01 .1245E-01 .1214E-01 .1182E-01 1152E-01 :1123E-01 1093E-01 :1064~-01 ::::E-~: .9947E-02 9679E-02 :9423E-02 .9186E-02 .8969E-02 .8763E-02 .8567E-02 .8382E-02 .8226E-02 .8085E-02 .7950E-02 .7828E-02 .7712E-02 .7603E-02 .7498E-02

224 224 224 224 224 224 223 223 223 223 223 222 222 222 222 222 222 222 222 221 221 222 223 223 223 222 222 221 221 221 220 220 220 220 218 218 218

218 218 210 217 217 217 217 217 216 216 216 216 216 216 216 216 216 216 216 216 216 216 216

i0

i0 ::

ii

::: 14

130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

148 149

150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167

16a 169 170 171 172 173 174 175 176 177 178 179 la0 la1 182 183 Ii34 185

116 187 181 la9

-.5696E-04 -.5561E-04 -.5428E-04 -.5297E-04 -.5170E-04 -.5045E-04 -.4923E-04 -.QaOQE-OB -.4688E-04 -.4574E-04 -.8066E-04 -.6072E-04 -.46alE-04 -.4146E-04 -.4046E-04 -.3949E-04 -.3854E-04 -.3762E-04 -.3673E-04 -.3587E-04 -.3503E-04 -.3422E-04 -.3343E-04 -.3267E-04 -.3193E-04 -.3121E-04 -.3051E-04 -.2982E-04 -.2916E-04 -.2851E-04 -.2788E-04 -.2726E-04 -.7661E-04 -.4362E-04 -.2780E-04 -.2494E-04 -.2440E-04 -.2386E-04 -.2334E-04 -.2284E-04 -.2234E-04 -.2186E-04 -.5914E-04 -.4771E-04 -.3894E-04 -.3214E-04 -.26a4E-04 -.2267E-04 .9228E-04 -.1978E-04 .9393E-04 .3271E-04 -.1721E-04 -.1681E-04 -.1641E-04 -.1603E-04 -.1567E-04 -.1532E-04 -.1500E-04 -.1469E-04

.1764E-04 .1730E-04 .1696E-04 .1663E-04 .1631E-04 .1600E-04 .1569E-04 .1539E-04 .1510E-04 .148lE-04 .1490E-04 .1471E-04 .1451E-04 .1428E-04 .1405E-04 .1382E-04 .1358E-04 .1334E-04 .1311E-04 .1288E-04 .1265E-04 .1243E-04 .1221E-04 .1199E-04 .1178E-04 1157E-04 :1137E-04 1117E-04 :1097E-04 .1078E-04 .1059E-04 .1040E-04 1079E-04 :1063~-04 .1045E-04 .1026E-04 .1007E-04 .9889E-05 9710E-05 :9536E-05 9366E-05 :9201E-05 .9290E-05 9195E-05 :9079E-05 .8951E-05 .8817E-05 .8680E-05 .8712E-05 .8618E-05 .8468E-05 .8051E-05 .7852E-05 .7715E-05 .7604E-05 .7497E-05 .7390E-05 .7282E-05 .7174E-05 .7066E-05

-.3622E-01 -.3536E-01 -.3451E-01 -.3368E-01

-.3287E-01 -.3208E-01 -.3155E-01 -.3193E-01

-.3248E-01 -.3293E-01 -.5556E-01 -.4387E-01 -.3583E-01 -.3514E-01 -.3545E-01 -.3563E-01 -.3570E-01 -.3566E-01 -.3552E-01 -.3532E-01 -.3505E-01 -.3475E-01 -.3441E-01 -.3406E-01 -.3370E-01 -.3334E-01

-.3299E-01

-.3264.E-01 -.3230E-01

-.3197E-01

-.3164E-01 -.3132E-01 -.3158E-01 -.3213E-01 -.3254E-01 -.3275E-01 -.3276E-01 -.3259E-01 -.3227E-01 .3235E-01 .3264E-01 .3292E-01 -.3832E-01 .3349E-01 .3377E-01 .3406E-01 .3433E-01 .346lE-01 .3488E-01 .3514E-01 .3540E-01 .3565E-01 .3590E-01 .3614E-01 .3637E-01 .3660E-01 .3682E-01 .3703E-01 .3724E-01 .3744E-01

.7393E-02 .7289E-02 .7185E-02 .7082E-02 .6980E-02 .6879E-02 .6778E-02 .66aOE-02 .6584E-02 .6489E-02 .6569E-02 .6448E-02 .6332E-02 .6222E-02 .6118E-02 .6020E-02 .5928E-02 .5845E-02 .5762E-02 .5680E-02 .5598E-02 .5517E-02 .5437E-02 .5357E-02 .5279E-02 .5202E-02 .51.26E-02 .5052E-02 .4979E-02 .4907E-02 .4838E-02 4769E-02 :4806~-02 .4716E-02 .4636E-02 .4567E-02 .4504E-02 .4442E-02 .4380E-02 .4319E-02 .4259E-02 .4200E-02 .4227E-02 .4150E-02 .4077E-02 .4007E-02 .3944E-02 .3887E-02 .3809E-02 .3823E-02 .3715E-02 .3679E-02 .3644E-02 .3606E-02 .3569E-02 .3531E-02 .3492E-02 .3453E-02 .3414E-02 .3376E-02

216 216 216 216 216 216 216 216 216 216 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 215 214 214 214 214 214 214 214 214 214 214 213 213 213 213 213 213 213 212 212 212 212 212 212 212 212 212 212 212

0

16

30

10

14

0

16

30

10

14

16 !I 00

if 16

iS : 0

i 0

16 :8 16

:t

16

30 2 30

:i 10

30

10

3: :i

:z 15 15

:z

15 15

190 191 :8f 194 :;: 197 ii8 200

-.1439E-04 -.141lE-04 -.1383E-04 -.1357E-04 -.1332E-04 -.1307E-04 -.12a3E-O4 -.1260E-04 -.1237E-04 -.1215E-04 -.1193E-04

REMAP USING

MAPPING

.695aE-05 .6851E-05 .6744E-05

2

.3763E-01 .3782E-01 .3800E-01 .3818E-01 .3835E-01 .3853E-01 .3869E-01 .3886E-01 .3902E-01 .3918E-01 .3933E-01

.6639E-05 .6535 -05 .6432 E -05 .6329E-05 .6228E-05 .6129E-05 .6030E-05 .5933E-05

INITIAL

METRIC

COMPUTED

SHOCK

AND FREESTREAM

LOCATION

VELOCITIES

9 9 9 9 9 9 9 9 9 9 9

11 11 11 11 11 11 11 11 11 11 11

.

AT

GRID

RHO 2 : 2 ll 9

:: 12 :43 :z ii

.33265EtOS .32632EtOO .31934EtOO

.31311EtOO .30958EtOO .30876EtOO .30992EtOO

.31236EtOO .31513EtOO .31765EtOO .32005EtOO .32357EtOO .32948EtOO .33743EtOO .34375EtOO .34902EtOO .35064EtOO

.35191EtOO .3526aEtOO

ff 22 23 24 25 26 27 28 29 30

35410EtOO

:35629EtOO .35882EtOO 36083EtOO :36125EtOO

.3593lEtOO .35417EtOO .34648EtOO .33853EtOO .33162E+OO

THE

-.1570aE+ol -.145a6EtOl -.13464bOl -.12342EtOl -.11220Etol -.10098EtOl -.i9760EtOO -.78540EtOO -.67320EtOO

-.56100EtOO -.44880EtOO -.33660EtOO -.22440EtOO

-.11220EtOO -.71054E-14

11220EtOO

:22440EtOO .33660EtOO .44880EtOO

.56lOOEtOO .67320EtOO .78540EtOO .89760EtOO

.10098EtOl 11220EtOl :12342EtOl .13464EtOl .14586EtOl .15708EtOl

PSI .14155E-01 .678alE-01 .13508EtOO .20070EtOO .26277EtOO .32034EtOO .37295EtOO

.42019EtOO .46172EtOO .49717EtOO .52622EtOO .54862EtOO .56433EtOO .57352EtOO .57604EtOO

.57183EtOO .56056EtOO .54267EtOO

.51831EtOO .48790EtOO

.45182EtOO .41045EtOO .36411EtOO .31305EtOO .25755EtOO

.19780EtOO .13455EtOO

.69789E-01 .14155E-01

REMAP USING COMPUTATIONAL SHOCK SHAPE: JSHMAX AND JSHMIN SHOULD EVEN UP AND MOVE OUT

POINTS I=2

I

.3337E-02 .3299E-02 .3261E-02 .3223E-02 .3185E-02 .3148E-02 .3111E-02 .3075E-02 .3039E-02 .3003E-02 .2969E-02

I=16

I=30

BODY OMEG

-.1570aEtol -.395a6E-01 .71027E-01 .97679E-01

.a9595E-01 .6aOOOE-01 .44056E-01 .22401E-01 .58178E-02 -.56375E-02 -ii3566E-01 -.19970E-01 -.24708E-01 -.25427E-01 -.20627E-01 -.11807E-01 -.16665E-02 99505E-02

:22866E-01 .39078E-01 .60445E-01 .88278E-01

.12263EtOO

.16203i+OO .20450EtOO .24506EtOO .28569EtOO .37816EtOO

.15708EtOl

H

.la209Etol .1842aEtOl .i8407EtOi .18059EtOl .17269EtOl .16068EtOl .i4559Etol 12840EtOl :11011Et01 .91293EtOO .72i56EtOO .52693EtOO .33308EtOO

15624EtOO

:99749E-01 .24009EtOO

.39910EtOO .55922EtOO

.71587EtOO .86535EtOO

10045EtOl :11315EtOl .12469EtOl .13524EtOl 14501EtOl :15431EtOl .16297Etbl .16995EtOl .17444EtOl

UI .12312E-14 -.67280E-01

-.13445EtOO -.19996EtOO -.26laQEtOO -.31854EtOO -.36915EtOO -.4130aEtoo -.45034EtOO

-.48114EtOO

-.50529EtOO -.52023EtOO

-.51507EtOO -.41163EtOO .38659EtOO .56409EtOO .55990EtOO .54027EtOO

.51478EtOO .48461EtOO .44955EtOO .40918EtOO .36323EtOO

.31174EtOO .25520EtOO

.19437EtOO 13056EtOO :65345E-01 .11382E-13

VI -.22174EtOO -.21022EtOO -.19659EtOO -.18304EtOO -.17342EtUO -.16837EtOO -.16700EtOO -.16a56EtOO ti.17135Et00 -.17418EtOO -.17797EtOO -.19083EtOO -.23699EtOO -.40022EtOO -.4269OEtOO -.86176E-01 .22197E-01 .68589E-01 .95098E-01

.10970EtOO .11763EtOO .12232Etoo 12646EtOO :13211EtOO .1404lEtOO .15259EtOO .16763EtOO .la203Etoo .19405EtOO

WI .97511E+OO .97534EtOO .97122EtOO .96256EtOO .94940EtOO .932a3Etoo .91424EtOO .a9496EtOO .a7626EtOO

.a5917Etoo .a4440Etoo .a3244Etoo .a2373Etoo .81877EtOO .81796EtOO

.82121EtOO .82827EtOO .a3869EtOO .85203EtOO .86782EtOO .88548EtOO .90422EtOO .92308EtOO

94094EtOO

:95664EtOO .96899EtOO

.97717EtOO .98112EtOO .98099EtOO

SURFACE

I

ARC LENG ITH (5 1 SLOPE x/z

Y/Z

-.ooooo

-.01416 -.00269 .00964 .01984 .02407

.06793 .13556 .20247 .26791 .33100 .3908a .44668 .49758 .54263

!

8 9

.5ao80 .61108 .63281

:!i 12

.64574

.64938 .64351 .62773 .60303 .57017 .53029 .48442 .43347 .37824 .31946 .25792 .19443 .12988 .06496 .ooooo x/z

SMAX=

1.31900

(THETA)

: K1:

.OlOOl .00289 -.00306 -.00788 -.01221 -.01564 -.01642 -.01340 -.00760 -.00105 .00600 .01304 .02073 .02932 .03837 .04662 .05222 -05349 .04862 .03815 .02581 .01416

AND CURVATURE

S 0.00000 .06889 .13764 .20533 .27093 .33406 .39418 .45045

.5ola4

.54728 .58575 .61634 .63835 .65166 .65653 .66581 .68300 .70869 .74231 .78292 .82959

.88133 .93718 .99624 1.05782

1.12151

1.18691 1.25299

1.31900

Y/Z

XMAX=

(PSI) THETA 9.19264 9.95043 9.45096 5.60673 1.10677 -2.73573 -6.13507 -7.67253 -7.72597 -7.34760 -7.69958

-a.61171

-5.02490 28.32868 64.90918 144.55220 160.42027 165.88655 168.45740 169.23119 169.65527

170.72479 173.18175 177.31196 i81.55226 186.30045 189.95137

190.46088 189.86743

PSI

SMAX/XMAX=

(Y/Z)/XMAX

.31414 .03245 -.46571 -1.08595 -1.11797 -1.02233 -.71223 -.15398 .06862 -.01984 -.30916 .73202 8.90770 77.08674

-.ooooo

-.02iao

136.75686

.10461 .20876 .31179 .41257 -50972 .60192 .68786 .76623 .83561 .89438 .94102 .97448 .99439

1.00000

39.59667 6.38028 1.95459 -62664 .23402 .23377 .52468 .93847 1.21130 1.24687 1.11588 .46051 -.01128 -.26637

.99096 .96665 .92862 .87801 .81660 .74597 .66751 .58246 .49194 .39717 .29940 .20001 .10004 .ooooo

-.00414 .01485 .03055 .03706 .03471 .02654 .01541 .00446 -.00471 -.01213 -.01879 -.02408 -.02529 -.02063 -.01170 -.00161 .00924 .02008 .03193 .04514 .059oa .07179 . oao4i .08237 .07481 .05875 .03974 .02180

PSI

(X/Z)/XMAX

THETA

.6493a

(X/Z)/XMAX

2.0311'5

(Y/Z)/XMAX

DYBP/DZP -.22360 -.22405 -.22236 -.20948 -.19055 -.17108 -.15019 -.13926 -.13904 -.14253 -.13880 -.12910 -.16944 -.57398 -1.60970 .24109 .01279 -.05182 -.07996 -.01785 -.09170 -.10028 -.11760 -.14222 -.16294 -.1822a -.i94oa -.19562 -. i952a DYBP/DZP

NEW SHOCK

I

LOCATION

C(I)

CPR(1)

.9512aaE+oo

0. -.190599E-01 -.409115E-01 -.664552E-01 -.939573E-01

.950266EtOO

.947011EtOO .941086EtOO .932099EtOO .920002EtOO

-.119642EtOO -.13a976EtOO -.147887EtOO -.143427EtOO -.123665EtOO -.a72152E-01

.905251EtOO .aaaai6Etoo

.a72065EtOO

.a56631EtOO .a44315Etoo .837060EtOO .a36a58EtOO .845509Etoo .a64277EtOO .a93605EtOO .933045EtW

-.332324E-01 .376545E-01 .1221aaEtoo

.214329EtOO .306454EtOO .391133EtOO

9a1375Etoo :1036a5EtOl .109745EtOl .116114EtOl 1225aaEtol :12a961EtOl .135011EtOl .140499EtOl .145169EtOl .14a759Etol .151031EtOl .151809EtOl

I

C(I)

ITER

DELMX

I

J

DELAVG

RESMX

I

-.9215E-03 -.a137E-03

17 17

2

-.6480E-03 -.5028E-03 -.3735E-03 -.3555E-03 -.3101E-03 -.2402E-03 -.1957E-03 -.1778E-03 -.1614E-03 -.1491E-03 -.1371E-03 -.1346E-03 -.130lE-03 -.1245E-03 -.1182E-03

16 16 16 17 17 17 18 18

;

.4208E-04 .2161E-04

-.2965EtOl -.1499EtOl -.1552EtOl -.1098EtOl -.7551EtOO -.6931EtOO -.5516EtOO -.4147EtOO

16 16 16 16 17 17 17 17

-.3259EtOO -.2908EtOO

18 18

18 19 19 19 19 19

1

201 202 203 204 205 206 207

208 209 210 211 212 213 214 215 216 217

CSEC(1)

CPRCI)

la

I z 2 i

I ; 2.

.la74E-04

.1683E-04 .1539E-04 .1493E-04 .lQOlE-04 .1302E-04 .1222E-04 1166E-04 :1125E-04 1091E-04 :1064~-04 .1044E-04 .1029E-04 .1014E-04 lOOlE-04

-.2581EtOO

-.2285EtOO -.2020E+00 -.1787EtOO -.1693EtOO

-.1527Etoo -.1441EtOO

la la

ia 18 19

19 19

J

RESAVG

KSUP

.9079E-01 .2697E-01 .2026E-01 .1694E-01

292 148 148 149 148 147 147 147 147 147 147 147 147 146 146 146. 146

.1508E-01 .1441E-01 .1371E-01 .1300E-01 .1229E-01 .ll(lOE-01 .1150E-01 .1127E-01 : :;g::;: .108.0E-01 .1070E-01 .1060E-01

JSHMAX

ISHMAX

JSNMIN

ISHMIN

x:

x xi :i 2

20

9

21

2

20

9

2

20 20

9 9

21

5: 21

21

;:

21

f z

f

2

zi

:i

20

8

8

9

218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239

-._

240

241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264

265

266 267 268 269 270 271 272 273 274 275 276 277

-.1118E-03 -.1054E-03 -.1042E-03 -.1022E-03 -.9961E-04 -.9662E-04 -.9335E-04 -.8993E-04 -.8645E-04 -.8297&04 -.8052E-04 -.7934E-04 -.7788E-04 -.7621E-04 -.7438E-04 -.7244E-04 -.70435-04 -.6838E-04 -.6610E-04 -.6405E-04 -.6198E-04 -.5992E-04 -.5790E-04 -.5594E-04 -.5443E-04 -.5342E-04 -.5234E-04 -.5121E-04 -.5004E-04 -.4885E-04 -.4763E-04 -.4640E-04 -.4517E-04 -.4395E-04 -.4274E-04 -.4155E-04 -.4038E-04 -.3923E-04 -.3811E-04 -.3703E-04 -.3597E-04 -.3494E-04 -.3394E-04 -.3298E-04 -.3204E-04 -.3114E-04 -.3027E-04 -.2942E-04 -.2860E-04 -.2782E-04 -.2706E-04 -.2632E-04 -.2561E-04 -.2493E-04 -.2427E-04 -.2363E-04 -.2301E-04 -.2242E-04 -.2185E-04 -.2129E-04

5:

f

f f

z

.9997E-05 .9932E-05 .9906E-05 .9893E-05 .9864E-05 .9858E-05 .9848E-05 .9836E-05 .9821E-05 .9808E-05 .9795E-05 .9776E-05 .9751E-05 .9722E-05 .9689E-05 .9652E-05 .9612E-05 .9569E-05 .9503E-05 .9452E-05 .9400E-05 .9346E-05 .9292E-05 .9237E-05 .9182E-05 .9127E-05 .9071E-05 .9015E-05 .8958E-05 .8902E-05 .8844E-05 .8787E-05 .8729E-05 .8670E-05 .8611E-05 .8552E-05 .8493E-05 .8433E-05 .8373E-05 .8312E-05 .8252E-05 .8191E-05 .8130E-05 .8068E-05 .8007E-05 .7945E-05 .7883E-05 .7821E-05 .7759E-05 .7697E-05 .7635E-05 .7572E-05 .7510E-05 .7448E-05 .7385E-05 .7323E-05 .7261E-05 .7199E-05 .7136E-05 .7074E-05

-.1353E+OO

19

-.1008E+OO -.9670E-01 -.9264E-01 -.8863E-0' -.8473E-0 -.8096E-0 -.7733E-0 -.7387E-0 -.7057E-0 -.6744E-0 -.6447E-0 -.6166E-0 -.5911E-0 -.5719E-0 -.5529E-0 -.5342E-0 -.5158E-0 -.4977E-0 -.4799E-0 -.4627E-0 -.4459E-0 -.4296E-0 -.4139E-0 -.3994E-0 -.3859E-0 -.3730E-0 -.3606E-0 -.3487E-0 -.3373E-0 -.3265E-0 -.3160E-0 -.3061E-0 -.2966E-0 -.2875E-0 -.2788E-0 -.2704E-0 .2658E-0 .2657E-0 .2656E-0 .2656E-0 .2655E-0 .2654E-0 .2654E-0 .2653E-0 .2653E-0 .2652E-0 .2652E-0 .2652E-0 .2652E-0 .2652E-0 .2652E-0 .2653E-0 .2653E-0 .2654E-0

20 20 20

-.1266E+OO -.1182E+OO -.1117E+OO -.1084E+OO -.1047E+OO

19 19 20 20 20

.1053E-01 .1043E-01 .1035E-01 .1028E-01 .1020E-01 .1012E-01 .1004E-01 .9959E-02 .9874E-02 .9796E-02 9714E-02 :9630~-02 9544E-02 :9456~-02 .9370E-02 ..9284E-02 9197E-02 :9109E-02 .9017E-02 .8923E-02 .8831E-02 .8739E-02 .8647E-02 .8558E-02 .8470E-02 .8384E-02 .8299E-02 .8217E-02 .8137E-02 .8057E-02 .7978E-02 .7900E-02 .7823E-02 .7748E-02 .7675E-02 .7603E-02 .7532E-02 .7462E-02 .7393E-02 .7325E-02 .7257E-02 .7190E-02 .7124E-02 .7058E-02 .6994E-02 .6930E-02 .6866E-02 .6804E-02 .6742E-02 .6681E-02 .6620E-02 .6561E-02 .6501E-02 .6443E-02 .6385E-02 .6327E-02 .6271E-02 .6214E-02 .6159E-02 .6104E-02

145 145 145 145 144 144 144 144 144 144 144 144 144 144 144 144 144 144 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 ::3 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143 143

I d

278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 ~~~ 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337

-.2076E-04 -.2024E-04 -.1974E;04 -.1926E-04 -.1879E-04 -.1834E-04 -.1791E-04 -.4068E-04 -.3077E-04 -.2605E-04

-.1382E-04 -.1290E-04 -.12'JSE-04

-.liidE-04

22 22 22 22 22 22 22 10 10 10

20 20 20

20

I 2 z 2 2 20 20 I

.7012E-05 .6950E-05 .6889E-05 .6827E-05 .6766E-05 .6705E-05 .6644E-05 .6732E-05 .6712E-05 .6688E-05 .6661E-05 .6633E-05 .6602E-05 .6570E-05 .6535E-05 .6497E-05 .6456E-05 .6411E-05 .6364E-05 .6313E-05 .6260E-05 .6197E-05 .6139E-05 .6081E-05 .6022E-05 .5962E-05 .5901E-05 .5841E-05 .5781E-05 .5722E-05 .5663E-05 .5604E-05 .5546E-05 .5489E-05 .5433E-05 .5378E-05 .5323E-05 .5269E-05 .5215E-05 .5163E-05 .5111E-05 .5060E-05 .5009E-05 .4960E-05 .4910E-05 .4862E-05 .4814E-05 .4839E-05 .4824E-05 .4805E-05 .4783E-05 .4758E-05 .4732E-05 .4703E-05 .4673E-05 .4642E-05 .4610E-05 .4577E-05 .4543E-05 .4508E-05

.2655E-01 .2656E-01 .2658E-01 .2659E-01 .2661E-01 .2663E-01 .2665E-01 .2667E-01 .2669E-01 .2671E-01 .2674E-01 .2677E-01 .2680E-01 .2683E-01 .2686E-01 .2689E-01 .2693E-01 .2696E-01 .2700E-01 .2704E-01 .2707E-01 .2711E-01 .2715E-01 .2719E-01 .2724E-01 .2728E-01 .2732E-01 .2736E-01 .2741E-01 .2745E-01 .2750E-01 .2754E-01 .2759E-01 .2763E-01 .2768E-01 .2772E-01 .2777E-01 .2782E-01 .2786E-01 .2791E-01 .2796E-01 .2800E-01 .2805E-01 .2809E-01 .2814E-01 .2819E-01 .2823E-01 -.2924E-01 -.2611E-01 -.2342E-01 .2125E-01 .2138E-01 .2158E-01 .2184E-01 .2212E-01 .2244E-01 .2277E-01 .2311E-01 .2345E-01 .2379E-01

19 19 19 19

.6049E-02 .5995E-02 .5942E-02 .5889E-02 .5837E-02 .5785E-02 .5734E-02 .5733E-02 .5695E-02 .5661E-02 .5636E-02 .5609E-02 .5581E-02 .5553E-02 .5523E-02 .5492E-02 .5460E-02 .5427E-02 .5392E-02 .5356E-02 .5318E-02 .5279E-02 .5243E-02 .5206E-02 .5168E-02 .5130E-02 .5091E-02 .5052E-02 .5012E-02 .4973E-02 .4933E-02 .4894E-02 .4854E-02 .4815E-02 .4776E-02 .4738E-02 .4699E-02 .4661E-02 .4623E-02 .4585E-02 .4548E-02 .4512E-02 .4475E-02 .4440E-02 .4404E-02 .4369E-02 .4334E-02 .4338E-02 .4297E-02 .4259E-02 .4223E-02 .4189E-02 .4155E-02 .4123E-02 .4091E-02 .4059E-02 .4028E-02 .3997E-02 .3966E-02 .3936E-02

143 143 143 143 143 :f: 143 142 142 142 :t; 142 142 142 142 ;:I 142 142 141 2: 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 141 140 140 140 140 140 140 140 140 140 140 140 140 140

338 339 340 341 342 343 344 345 346 347 348 349 350 ITER

-.1054E-04 -.9877E-05 -.9261E-05 -.8689E-05 -.8158E-05 -.7664E-05 -.7204E-05 -.6775E-05 -.6531E-05 -.4410E-04 -.2961E-04 -.2378E-04 -.2196E-04

20 20 20 20 20 20 20 20 1:

20 20 20 20 20 20 20 20 2;

11 11 11

20 20 20

.4472E-05 .4436E-05 .4400E-05 .4363E-05 .4326E-05 .4288E-05 .4251E-05 .4213E-05 .4175E-05 .4303E-05 .4294E-05 .4285E-05 .4279E-05

DELMX

I

J

DELAVG

.2414E-01 .2447E-01

19

19

.3906E-02 .3877E-02

140

fl

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.2480E-01 .2512E-01 .2543E-01 .2573E-01 .2602E-Oi .2630E-01 .2657E-01

19 19 19 19 19 19

19 19 19 19 19 19

.3847E-02 .3818E-02 .3789E-02 .3761E-02 .3732E-02 .3704E-02 .3676E-02

140 140 140 140 140 140

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.2683E-01 .2707E-01 .2731E-01 .2754E-01

19 19 19

19 19 19

.3691E-02 .3674E-02 .3665E-02 .3661E-02

139 139 139

I:

22

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RESAVG

RESMX

KSUP

zi 20

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201 /JSHMAX

NOTE:

IS~IMAX

JSHMIN

IMPROVED SHOCK LOCATION, NEARLY ON A CONSTANT GRID LINE 21 OUT OF 28 MAX IS A REASONABLE INSET

ISHMIN

CONVERGENCE

INITIAL

HISTORY ERROR(r)

Ii

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: : I

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t t t t t t t t t t

:

: ** :** :::

t t t t t

I

:

:

t t t t t t t

: : : : : : : f :

:

3:: 327 328 329

E 335 336 337 338 339 340 341 342 343 344 345 346 347 348

t * I t * t * : : t * t * : : t * t : : * --------t----------r---*--------------t i I * I

: I

:

:

:

I

:

:

: I

: I

i

:

: -------------------:-------------------: :

:

BASIC RESULT5

RHO

.33265E+OO .32632EtOO .31934EtOO

.31311Et00 .30958EtOO .30876EtOO .30992EtOO .31236EtOO .31513EtOO

.31765EtOO

.32005EtOO .32357EtOO .32948EtOO .33743EtOO .34375EtCrO .34902EtOO .35064EtOO

.35191EtOO

.35268EtOO .35410EtOO .35629EtOO .35882EtOO .36083EtOO

.36125EtOO .35931EtOO .35417EtOO .34648EtOO .33853EtOO

.33162EtOO

-

SURFACE RESULTS

IF IOUT = 0, THIS DATA BLOCK IS REPEATED FOR ALL J’s

THE

F

-.15708EtOl -.14586EtOl -.13464EtOl -.12342EtOl -.11220EtOl -.10098EtOl

-.82695E-01 -.83982E-01 -.83455E-01

-.89760EtOO -.78540EtOO -.67320EtOO

-.56100EtOO -.44880EtOO -.33660EtOO -.22440EtOO

-.11220EtOO -.71054E-14

.11220EtOO .22440EtOO .33660EtOO .44880EtOO

.56100EtOO

.67320EtOO .78540EtOO .89760EtOO .10098EtOl

.11220EtOl 12342EtOl :13464EtOl .14586EtOl .15708EtOl

-.80685E-01 -.75412E-01 -.68494E-01 -.ao971c-01 -.53599E-01 -.46806E-01 -.40604E-01 -.34891E-01 -.29827E-01 -.25880E-01 -.23278E-01 -.21977E-01 -.19427E-01 -.15074E-01 -.88519E-02 -.88775E-03 .82522E-02 .18224E-01 .28723E-01 .38059E-01

.47844E-Oi .57294E-01 .65826E-01 .72814E-01 .77712E-01 .80619E-01

POTENTIAL (W VELOCITY)

U .12312E-14 -.33598E-01 -.70793E-01

-.10904EtOO -.14878EtOO -.18965EtOO -.23005EtOO -.26675EtOO -.29461EtOO -.30858EtOO -.30988EtOO -.30435EtOO -.28361EtOO

-.15175EtOO .80487EtOO

91651EtOO

:89625EtOO

.86271EtOO .81869EtOO .76596EtOO .70893EtOO

.63178EtOO .55593EtOO .48456EtOO .39363EtOO .28874EtOO .18322EtOO .86883E-01 .11382E-13

V

MC

-.26645E-14 .60972E-02 13043E-01 :15143E-01 93095E-02 -:92128E-03 -.11883E-01 -.19852E-01 -.22054E-01 -.2128lE-01 -.25511E-01 -.39494E-01 -.53132E-01 -.28515E-01

.45197E-14 .52571E-01

.i2109EtOO

.80639E-01 .32839E-01 .22303E-01 .22715E-01 .34739E-01 .41812E-01 .35638E-01 .16723E-01 -.90640E-02 -.34557E-01 -.46632E-01 -.36871E-01 -.16998E-01 .26645E-14

CROSS FLOW VELOCITIES

.11076EtOO .16924EtOO .22898EtOO

.29110EtOO .35343EtOO

.41024EtOO .45265EtOO .47286EtOO

.47381EtOO .46620EtOO .43646EtOO .23025EtOO

.14348EtOl 17290EtOl :16714EtOl .15906EtOl .14903EtOl .13772EtOl .12616EtOl .11068EtOl .96177EtOO .83296EtOO .67352E+OO .49456EtOO .31432EtOO

.14853EtOO .19602E-13

CROSS FLOW MACH NUMBER

M

.13741EtOl .13733lzt01 .13705EtOl .13663EtOl .13619EtOl .13583EtOl 13560EtOl :13540EtOl .13491Etol .13377EtOl .13214Etoi .13053EtOl .12833EtOl .12084E+Ol .20068EtOl .22934EtOl .22562EtOl .22067EtOl .21494EtOl .2091lEtOl .20419EtOl 19717EtOl :19203EtOl .18926EtOl .18548EtOl .18183EtOl .17936EtOl .17827EtOl .17802EtOl TOTAL MACH NO.

CP .23227EtOO .23320EtOO .23625EtOO .24079EtOO .24565EtOO

.24961EtOO .25212EtOO .25435EtOO .25983EtOO .27253EtOO

.29105EtOO

.30968EtOO .33553EtOO .42782EtOO -.24295EtOO

-.35175EtOO -.34022EtOO -.32377EtOO -.30308EtOO -.28008EtOO -.25897EtOO -.22604EtOO

-.19961EtOO -.18455EtOO -.16300EtOO -.14099EtOO

-.12545EtOO -.11842EtOO -.11678EtOO PRESSURE COEFFICIENT

SURFACE RESULTS X/XMAX -.oooo .1046

.2088 .3118 .4126 .5097 .6019 .6879 .7662 .8356 .8944 .9410 .9745 .9944

l: Ki .9666 .9286 .8780 .8166 .7460 .6675 .5825 .4919 .3972 .2994 .2000 .lOOO .oooo

XIXMAX

Y/XMAX

-.0218 -.0041 .0149 .0306 .0371 .0347 .0265 .0154 .0045 -.0047 -.0121 -.0188 -.0241 -.0253 -.0206 -.0117 -.0016 .0092 .0201 .0319 .0451 .0591 .0718 .0804 .0824 .0749 .0587 .0397 .0218 YIXMAX

PSI .81 3.89 7.74 11.50 15.06 18.35 21.37 24.07 26.45 28.49 30.15 ::*3: 32:86 33.00 32.76 32.12 31.09 29.70 27.95 25.89 23.52 20.86 17.94 14.76 11.33 7.71 4.00 .81 PSI

OMEG

-90.00 -2.27 4.07 5.60 5.13 3.90 2.52 1.28 .33 -.32 -.78 -1.14 -1.42 -1.46 -1.18 -.68 -.lO .57 1.31 2.24 3.46 5.06 7.03 9.28 11.72 14.04 16.37 21.67 90.00

OMEG

CP

.2323 .2332 .2363 .2408 .2456 .2496 . .2521 .2543 .2598 .2725 .2910 .3097 .3355 .4278 -.2429 -.3517 -.3402 -.3238 -.3031 -.2801 -.2590 -.2260 -.1996 -.1846 -.1630 -.1410 -.1254 -.1184 -.1168

V W

a

U IS “OUT”

CP

MC

U

.oooo

.8924 .8914 .8878 .8819 .8740 .8643 .8533 -8414 .8295 .8186 .8095 .8026 .7979 .7955 .796.0 .8018 .8132 .8298 .8511 .8761 .9037 .9329 .9611

.0526 ::2: .2290 .2911 .3534 .4102 .4527 .4729 .4738 .4662 .4365 .2302 1.4348 1.7290 1.6714 1.5906 1.4903 1.3772 1.2616 1.1068 .9618 .8330 .6735 .4946 .3143 .1485 .oooo MC

\

1:E 1.0348 1.0500 1.0588 1.0616

U

V -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo .oooo -.oooo -.oooo -.oooo -.oooo -. 0000 -.oooo -.oooo .oooo .oooo 0.0000

-.oooo -.oooo -.oooo -.oooo -.oooo -.oooo

-.oooo -.oooo -.oooo -.oooo .oooo

V

W .oooo

-.0341 -.0720 -.llOl -.1491 -.1896 -.2304 -.2675 -.2954 -.3093 -.3109 -.3069 -.2885 -.1544 .8139 .9201 .8969 .8630 .8190 .7667 .7102 .6328 .5562 .4846 .3951 .2925 .1869 .0885 .oooo

WA

BETA .oo

-2.19 ' -4.64 -7.12 ! -9.68 , ~12.38 -15.11

-17.64 -19.60 -20.70 -21.01 -20.93 I -19.88 -10.98 45.64 48.93 47.80 46.12 43.90 41.19 38.16 34.15 30.06 26.11 21.29 15.78 10.09 4.78 .oo

VS 0.00

-77,78 -84.62 -89.99 -94.03 -96.63 -9i3.66 -98.96 -98.06 -97.02 -96.92 -97.47 -93.61 -60.21 -23.91 55.23 70.52 75.32 77.15 76.99 76.19 75.67 76.16 78.03 79.84 82.26 83.58 78.79 4514.54

BETA

VS

ws 0.00

.06 .14 .61 -.13 -.94 -.80 -.87 -.95 -.99 -1.22 -1.81 -3.80 -17.46 36.39 -.31 -2.12 -2.00 -1.66 -1.55 -1.43 -1.26 -1.13 -1.29 -.34 .34 .02 .05 2.78 ws

SURFACE VELOCITIES

UC

vc

WC

-.0126 -.0083 -.0035 .0054 .0182 .0313 .0422 .0479 ::ii .0469 .1214 .0425 .1410 .0421 .1611 .0463 .1858 .0326 .3040 -.0407 .3023 .7886 -.1930 .5311 -.2733 -3307 -.2818 .2450 -.2717 .1991 -.2522 .1830 -.2327 .I729 -.2009 .1530 -.1762 .1231 -.1603 .0865 -.1296 .0467 -.0878 .0169 -.0473 .0078 -.0182 .0112 .oooo .0150 \ UC vc .oooo

.0269 .0489 .0677 .0821 .0918 .0975

CARTESIAN

VELOCITY

.8923 .8916 .8893 .8861 -8826 .8796 .8774 .8757 .8726 .8655 .8546 .8428 .8272 .7501 .7634 :-E 1:1375

1.1321 1.1217 1.1122

1.0987 1.0895 1.0860 1.0795 1.0716 1.0654 1.0623 1.0615

WC{

DELTA

0.00 -77.72 -84.48 -89.38 I;;-:; -99:46 -99.83 -99.01 -98.02 -98.14 -99.28 -97.41 -77.67 12.49 54.92 68.39 73.31 75.48 75.44 74.76 74.41 75.03 76.74 79.50 82.60 83.60 78.84 0.00

DELTA

COMPONENTS

f ANGLE BETWEEN THE RAY AND THE VELOCITY VECTOR

; n

THE RAY L

I

/

THE ANGLE BETWEEN THE SURFACE NORMAL AND THE SPHERICAL COORDINATE

(J co

IMCMIN=

6

MCMIN=

.22898

CROSSFLOWSONIC LINE NUMBEROF POINTS

16

J

XXI

YYI

:

.65189 .64915

-.00885 -.01485

:

.65618 .65490

.01529 .00012

ii

.65577 .65733

.06236 .03459

i 9 ::

.62887 .64940 .52791 .46812 .49204

.10139 .16375 .26602 .24882 .22112

::

.43875 .45133

.15371 .18855

:z 16

.42725 .41334 .39316

: iii% .04447

X, Y LOCATION

OF CROSS

FLOW

SONIC

LINE

CONICAL

FORCE

X(I)

CD

CL

::-z;;; -1:3464 -1.2342 -1.1220 -1:;;;; -.7854 -.6732 -.5610 -.4488 -.3366 -.2244 -.1122 -.oooo .1122 .2244 .3366 .4488 .5610 .6732 .7854 .8976 1.0098 1.1220 1.2342 :%z I:5708

.0990 .0921 .0846 .0770 .0676 .0544 .0388 .0230 .0028 .0274 .0484 .0647 .0761 .0826 .0861 .0823 .0779 .0759 .0696 .0614 .0550 .0519 .0510

.0664

.1989

cLL=

.2520

.0215

CDL=

.0449

6.789

L/D

ETADR=

.750

LOCATIONS YYB

XXB

OMEG

-.0142

-.oooo

-90.0000 -83.5714 .0241 -77.1429 .0230 -70.7143 SO206 -64.2857 -0177 -57.8571 .0149 -51.4286 .0130 -45.0000 .Oll9 -38.5714 .Olll -32.1429 .0094 -25.7143 .0069 -19.2857 .0056 -12.8571 .0079 -6.4286 -.0044 -.oooo -.0044 6.4286 .OOOl 12.8571 .0037. 19.2857 .0063 25.7143 .0074 32.1429 .0080 38.5714 .0083 45.0000 .0091 51.4286 .0106 57.8571 .0114 64.2857 .0114 70.7143 .0108 77.1429 .0103 83.5714 .OlOl 90.0000

CD =

10

SHOCK

-.0027 .0096 .0198 .0241 .0225 .0172

: it::

:E .1071 .1077 .1070 .1042

.4508

INITL=

BODY AND

DISTRIBUTIONS.

UPPER

=

IFINL= CL(ETADR)=

: Ka9

.2025 .2679 .3310 ::::79 .4976 .5426 .5808 .6111 .6328 .6457 .6494 .6435 .6277 .6030 .5702 .5303 .4844 .4335 .3782 .3195 .2579 .1944 .1299 .0650

: iE8 -.0031 -.0079 -.0122 -.0156 -.0164 -.0134 -.0076 -.OOlO .0060 .0130 .0207 .0293 : 2% .0522 .0535 :E! .0258 .0142

\ .oooo BODY

9.248

L/D

LOWER

q

RB

xxs

.0142

-. 0000

.0680 .I359 .2034 .2690 .3318 .3913 .4468 .4976 .5426 .5809 .6112 .6330 .6460 .6495 .6436 .6277 .6031 .5703 .5307 .4853 .4352 .3811 .3237 .2634 .2004 .1354 .0699 .0142/

LOCATION

RS

.0983 -1950 -2888 .3785 .4628 .5404 .6100 .6706 .7217 .7655 .8029 .8343 .8602 .8811 .8969

:.9079 E83 .8916 .8615 .8152 .7512

.6686 .5665, .4455 .3076 .1572 \ .oooo

SHOCK

5.6118

23 .1518

CD(ETADR)=

* 0142

-.6011 -.5960 -.5815 -.5584 -.5275 -.4894 -.4451 -.3955 -.3419 -.2860 -.2309 -.I770 -.1231 -.0678 -.0088 .0561 .1289 .2117 .3051 .4072 .5166 .6306 .7460 .8590 .9644 1.0559 1.1268 1.1718 1.1870

LIFT AND DRAG OUTBOARD OF qDR BOW SHOCK

LOCATION

\ .6011

.6040 .6133 .6287 .6492 .6736 .7001 .7270 .7527 .7763 .7995 .8222

RS/RB

42.4627 8.8843 4.5125 3.0902 2.4135 y;p 1:6272

:% 1:0587

xz 1:3765 1.3451 1.3322 1.3358 1.3566 1.3964 1.4591 1.5514 1.6794 1.8470 2.0699 2.3683 2.7781

1.0885 1.1185 1.1460 1.1681 1.1823 1.18701

x: 5:7182 8.6289 16.9132 83.8522

:E .8811 .8987 .9159 .9356 .9578 .9802

DELTA

CP ,

I ;

FLAT

ETASPN .oooo .I000

PLATE

LINEAR CPU

-.1168 -.1184 -.1254 -.1410 -.1630 -.1846

t

.2994 .2000

2

.4919 .3972

ii

.6675 .5825

1:

.8166 .7460

::

.8780 .9286 .9666 .9910 1.0000

-.2801 -.3031 -.3238 -.3402 -.3517 -.2429

ETASPN

CPU

I

1: ;g; -.2590

DCP

,

AND SPANLOAD

CPL

.2323 .2332 .2360 .2402 .2449 .2489 .2516 .2538 .2584 .2691 .2859 .3047 .3295 .4119 -..2429 CPL

DELTACP .3491

.3516 .3614 .3812 .4079 .4334 .4512 .4799 .5174 .5491 .5890 .6285 .6697 .7637 0.0000 DELTACP

DISTRIBUTION DCPLIN

.2870 .2885 .2929 .3008 .3127 .3297 .3531 .3855 .4310 .4973 .5997 -7736 1.1207

CCL/CA

.6981 .6974 .6888 -6357 .4411 .3689 .2948 .2216 .1527 .0913 .0419

kZ

o:Ki

DCPLIN

CCL/CA LINEAR THEORY FOR AN UNCAMBERED WING

SPANWISE

LOADING

rl =

+2

IN AIRPLANE

SPANLOAD

COORDINATES

DISTRIBUTION

MODIFICATION

OF PRESSURES

MCOH 1.37414 1.37329 1.37048 1.36632 1.36189 1.35829 1.35602 1.35400 1.34907 1.33773 1..32143 1.30530 1.28333 1.20837 2.00681 2.29337 2.25621 2.20669 2.14940 2.09114 2.04189 1.97170 1.92026 :-x 1:81830 1.79359 1.78268 1.78018 MCOH -r

MCON ICAL

NUCON

TO ACCOUNT

FOR NON-CONICAL

YIN

DNY

.14392 .14349 .14209 -14003 -13783 -13605

-.ooooo 1.08644 2.16809 3.23809 4.28474 5.29376

-.16186 -.17451 -.17544 -.11481 -.01460 .05990

:::3;i: .13150

: Xd .13495

.53075 .50370 .48045 .44675 .42163 .40799 .38924 .37094

6.25135 7.14383 7.95781 8.67827 9.28871 9.77304 10.12055 10.32735 10.38560 10.29171 10.03923 9.64427 9.11869 8.48092 7.74731 6.93251 6.04916 5.10904 4.12484 3.10950

: E49': .35170

2;07721 1.03896 .ooooo

: :::;i .11023 .09978 .06572 .46369 .59544 :;;W;

jiucq

f-V

YIN

: :I::: : :5;;19 -.19116 -.64629 .45743 .31048 : :z : :;;i: : :;3;; .06009 -.02568 -.12586 -.18218 -.18254 -.17354

DNY

GEOMETRY

DNX -.04639 -.04324 -.04054 -.04791 -.06791 -.08579 -.09799 -.10242 -.09876 -.09363 -.09361 -.11301 -.09383 .11723 .41797 -.29644 -.19826 1:::;;; -.10621 -.09473 -.07792 -.05530 -.02794 .00168 .02851 -04100 .04417 .04632

CPP .23227 .23320 .23625 .24079 .24565 .24961 .25212 .25435 .25983 .27253 .29105 .30968 .33553 .42782 -.24295 1:;:;;;. -.32377 -.30308 -.28008 -.25897 -.22604 -.19961 -.18455 -.16300 -.14099 -.12545 -.11842 -.11678

DNX

CPNC .10977 : ::35: .13457 .14637 .15793 .17227 .18587 ::K .22611 .24230 .26949 .36428 -.26400 -.35857 -.33684 -.32488 -.30839 -.29066 -.27857 -.25689 -.23910 -.23080 -.21680 -.20178 I: :g; -.19007

CPP -

CONICAL i P

“PCONlCAL

CPNC

DELMCH .12070 .11581 ::Zi : ii::: .07519 .06395 .05852 .05714 : KZ .05711 .05105 .04648 .02305 -.01047 .00323 .01423 .02616 .04560 .06553 .07841 .08882 .09843 .10603 .11172 .11735 .12243

DELNUD 3.50765 3.36312 3.19441 2.97194 2.74604 2.50866 2.15979 1.83194 1.67135 1.62366 1.64744 1.66812 1.57467 1.31238 1.27056 .57682 -.26693 .08350 .37426 .69949 1.23386 1.80409 2.18525 2.48971 2.78168 3.01924 3.19675 3.36338 3.50885

DELMCH

DELNUD

AM

Au

CPNON-CONICAL

DELTA

I

CP FROM NON CONICAL CORRECTION ETASPN

CPU

CPL

.oooo

:

.lOOO .2994 .2000

-.I901 -.I887 -.2018 -.1916

::Et .1226

2

.4919 .3972

-.2308 -.2168

: :E

i

.6675 .5825

-.2569 -.2391

: :E

9

.7460

-.2786

: ::569

:i

.8166 .8780

-.3084 -.2907

.2216 .2064

:5 E

.9286 1.0000 : XE

-.3249 -.3368 -.2640 -.3586

.2380 .2631 -.2640 .3479

I

ETASPN

CPU

:

NON-CONICAL CM=

.4110

FORCE

RESULTS

CPL

DELTACP

.2998 :Z .3350 : 2t .4083 .4395 .4724 :Z .5629 .6000 .7065 0.0000 DELTACP

PURE CONICAL

FORCE COEFFICIENT

CM (FROM

DELTA

SPAN E=

.8694

CL=

.45084

CD=

.06640

CM=

.45480

A =

.6608

CP 1

CM (FROM

.4599

q

SPANLOAD)

ALPF12.0000

REPEAT JOB IDENTIFICATION FINISH 1ST GRID AND REPEAT

-----.64825

HAPPED

BODY (9)

T i 4 8 9 :: if :z 16 ::

E

I SAME OUTPUT ON 2ND GRID

x0=

I

.4590

=.

CA= -.02878

EMINF= 1.6200

JOBN-

RESULTS

yo=

AND SHOCK (C)

X

B

-.15708E*Ol -.15147E+Ol -.14586E*Ol -.14025E+Ol -.13464E+Ol -.12903E+Ol -.12342E+Ol -.11781E*Ol -.11220E+Ol -.10659E+Ol -.10098E+Ol

.33265EtOO .32955EtOO .32632EtOO .32287EtOO

-.95370EtOO -.89760EtOO -.84150EtOO -.78540EtOO -.72930EtOO -.67320EtOO

:8

-.61710E+OO -.56100E+OO

I: 23 24

-.50490EtOO -.44880EtOO -.39270EtOO -.33660EtOO

Yl=

-.014260

LOCATIONS

.31934E+OO .31599E*OO .31311E+OO .31093E+OO .30958EtOO .30889EtOO .30876EtOO .30913EtOO .30992EtOO

.31102E+OO .31236E+OO .31376E+OO .31513E+OO .31643E+OO .31765E+OO .31884E+OO .32005EtOO

.32151E+OO .32357EtOO

- WITH

BPR

NM= 58

.014260

1ST

(PR)

AND 2ND

BSEC

0.

-.19717E+Ol

-.56365E-01 -.59465E-01 -.62241E-01 -.61334E-01 -.55514E-01 -.45098E-01 -.31493E-01 -.18180E-01 -.72624E-02 .21'319E-02 .10263E-01 .16857E-01 .21762E-01 .24390E-01 .24741E-01 .23797E-01 .22453E-01 .21481E-01 .21374E-01 .23798E-01 .31342E-01 .42078E-01

-.37777E-01 -.72759E-01 -.26173E-01 .58503E-01 .14897EtOO .22236EtOO .26266EtOO

.21198E+OO .17722E+OO .15770EtOO

.13219E+OO .10288E+OO .71987E-01 .21677E-01 -.91345E-02 -.24526E-01 -.23401E-01 -.11247E-01 .74199E-02 .79021E-01 .18993EtOO

.19280E+OO

DERIVATIVES

(SEC)

C .95129E+OO .95104E+OO

.95027EtOO .94895EtOO

.9470lE+OO .94441E+OO .94109E+OO .93698EtOO

.93210E+OO .92641E+OO .92000EtOO

.91290E+OO .90525EtOO

.89716E+OO .88882EtOO .88038EtOO .87207EtOO .86407EtOO .85663EtOO .84996EtOO

.8443lE+OO .83993EtOO .83706EtOO

CPR

0. - -.91102E-02 -.18711E-01 -.290lOE-Oi -.40450E-01 -.52813E-01 -.66210E-01 -.80097E-01 -.94184E-01

-.10782E+OO -.12044E+OO -.13147E+OO -.14028E+OO -.14648E+OO -.14956E+OO -.14929E*OO -.14534E+OO

-.13756EtOO -.12575EtOO

-.10977E+OO -.89407E-01 -.64664E-01 -.35345E-01

CSEC

-.15491E*OO -.16987E*[email protected] -.17240E+OO -.19476E*OO -.21310E+OO -.22766E+OO -.24995EtOO

-.24512E+OO -.25711E+OO -.22892EtOO -.22094EtOO

-.17231E+OO -.14182E+OO -.79428E-01 -.30183E-01 .39753E-01

.10109E+OO .17613E*OO .24499EtOO .32487EtOO .40098EtOO

.48113E*OO .56408E*OO

.32623EtOO .32948EtOO .33327EtOO .33743EtOO .34073EtOO .34375EtOO

-.28050EtOO -.22440EtOO

-.16830E+OO -.11220E+OO -.56100E-01 -.71054E-14 .56100E-01

.11220E+OO 16830EtOO :22440EtOO .28050EtOO .33660EtOO .39270EtOO .44880EtOO .50490EtOO

.34751E+OO .34902EtOO .34990EtOO .35064EtOO

.35132E+OO .3519lE+OO

.56100E+OO .61710E+OO

.35233EtOO .35268EtOO .35328EtOO

.354lOE+OO .35512E+OO

.67320EtOO .72930EtOO .78540EtOO

.35629EtOO .35754EtOO .35882EtOO .35996EtOO .36083EtOO .36129EtOO .36125EtOO

.84150E+OO .89760EtOO 95370EtOO

:10098E+Ol 10659E+Ol :11220E+Ol .1178lE+Ol .12342E+Ol .12903E+Ol ..13464E+Ol 14025EtOl :14586E+Ol 15147EtOl :15708E+Ol

.36061E+OO .35931E+OO .35718E+OO .35417E+OO .35051E+OO

,34648EtOO .34240EtOO .33853EtOO .33500EtOO

X MAPPING

I f z 4 8

1: :: 13. 14

J

.33162E+OO

RHO

VELOCITIES

THE

.31093EtOO .30958EtOO .30889EtOO .30876EtOO

-.15708E+Ol -.15147E+Ol -.14586E+Ol -.14025E+Ol -.13464E+Ol -.12903E+Ol -.12342E+Ol -.1178lE+Ol -.11220E+Ol -.10659E+Ol -.10098E+Ol

.30992EtOO

-.95370EtOO' -.89760EtOO

31934EtOO

:31599EtOO

.313llE+OO

.30913E+OO

-.12643E+OO -.16197E+OO -.19052E+OO -.20903EtOO -.26367EtOO -.27869EtOO -.20983EtOO

-.11543E+OO -.15098E-01 .66889E-01

.10493E+OO .52309E-01

.21431E+Ol

BPR

AND FREESTREAM

.33265EtOO .32955EtOO .32632EtOO .32287EtOO

.11828E+OO

-.27387EtOO -.88442E-01 .23239EtOO -.71006EtOO -.20322EtOO -.44919E-01 -.18737E-01 -.29180E-01 -.52749E-01 -.21028E-01 .76567E-01 .72647E-01 .61908E-01 .46124E-01 .28508E-01 .74325E-02 -.42193E-01 -.88707E-01

0.

B

METRIC

.18508EtOO .17270E+OO

.52677E-01 .62713E-01 .70875E-01 .66511E-01 .56348E-01 .60385E-01 .46987E-01 .21370E-01 .14410E-01 .12624E-01 .11280E-01 .89819E-02 .69124E-02 .84703E-02 12656E-01 :i6430E-01 19460E-01 :21554E-01 .22562E-01 .21587E-01 .17915E-01 11880E-01 :37906E-02 -.60967E-02 -.17304E-01 -.30563E-01 -.45777E-01 -.59479E-01 -.68603E-01 -.72264E-01 -.70812E-01 -.65992E-01 -.61581E-01

.8455lE+OO

.75342EtOO

.81975E+OO .82122E+OO

12124EtOO :16727E+OO .21433E+OO .26139E+OO

.85360EtOO .86428EtOO .87765EtOO .89360EtOO

.85667EtOO

.82107E+OO .81858E+OO

.30738EtOO

91214EtOO

.35152E+OO

:93304EtOO

95621EtOO :98137E+OO 10083EtOl :10368E+Ol .10666E+Ol 10975EtOl :11290E+Ol .1161lE+Ol .li935E+Ol 12259EtOl :1258OE+Ol .12896E+Ol 13204EtOl :1350lE+Ol .13784E+Ol .14050E+Ol .14295E+Ol .14517E+Ol .147llE+Ol 14876E+Ol :15007E+Ol .15103E+Ol 1516lEtOl :1518lE+Ol

.63179E+OO .71401E+OO

-.1801lE-02 .35949E-01 .77110E-01

.75472EtOO

.39279EtOO .43075EtOO .46466EtOO .49439EtOO .51954EtOO

.7167OE+OO

.56765EtOO .57462EtOO .57702EtOO .57486EtOO

.16424E+OO

.63670EtOO .57224EtOO .48759EtOO .40894EtOO .32647EtOO .24456EtOO

.54017E+OO .55618E+OO

.56794EtOQ .__. .- __ .55614E+OO .5392lE+OO .51694E+OO .48913E+OO .45556EtOO

.41621E+OO .37089EtOO .32000EtOO .26354EtOO .20247EtOO 13727EtOO :69407~-01 0.

C

BSEC

AT GRID

.83596EtOO .83686EtOO .84000EtOO

.84273E-01 .13112E-02 -.78216E-01

-.16849E+OO -.25230EtOO

-.35120E+OO -.44299EtOO

-.54814E+OO -.64898EtOO

-.75371E+OO -.86183E+OO -.95251E+OO -.10605E+Ol -.11167E+Ol -.12077E+Ol -.12116E+Ol -.12629E+Ol

CPR

CSEC

POINTS

PSI 14155E-01 :350i8~-01 .67881E-01

10152EtOO :13508E+OO .16823EtOO .20070EtOO .23227EtOO .26'277EtOO .29215EtOO .32034E-+OO .34729EtOO .37296E+OO

OMEG

-.15708E+Ol -.24543EtOO -.39586E-01 .34050E-01 .71027E-01 .90173E-01 .97679E-01 96692E-01 :89595~-01 .79487E-01 .68000E-01 .5597lE-01 .44056E-01

H

.18209E+Ol .18349E+il 18428EtOl :18450E+Ol 18407EtOl :18282E+Ol 18059E+Ol :17722E+Ol .17269E+Ol .16713E+Ol 16068EtOl :15346E+01 :14559E+Ol

UI 12312E-14 -:33579E-01 -.67280E-01

-.10096E+OO -.13445E+OO -.16753EtOO

-.19996E+OO -.23148E+OO -.26184E+OO -.29090EtOO

-.31854E+OO -.34465EtOO

-.36915E+OO

VI -.22174E+OO -.21616E+OO -.21022E+OO -.20363EtOO

-.19659E+OO -.18955E+OO -.18304E+OO -.17755E+OO -.17342E+OO -.17041E+OO -.16837E+OO -.16726E+OO -.16700E+OO

WI .97511E+OO .97578EtOO .97534EtOO .97383EtOO .97122EtOO .96747EtOO .96256EtOO .95650EtOO .94940EtOO

.94146E+OO 93283EtOO :92371EtOO

.91424E+Otl

.31102EtOO .31236EtOO .31376EtOO .31513EtOO .31643EtOO .31765EtOO .31884EtOO .32005EtOO

.32151EtOO .32357EtOO .32623EtOO

.32948&00

.33327EtOO .33743EtOO .34073EtOO .34375EtOO

.3475lEtOO .34902EtOO .34990EtOO .35064EtOO .35132EtOO

.3519lEtOO

-.84150EtOO -.78540EtOO -.72930EtOO -.67320EtOO

-.61710EtOO -.56lOOEtOO

-.50490EtOO -.44880EtOO -.39270EtOO -.33660EtOO -.28050EtOO -.22440EtOO

-.16830EtOO -.11220EtOO

-.56lOOE-01 -.71054E-14 .56lOOE-01

.11220EtOO .16830EtOO

.22440EtOO .28050EtOO .3366OEtOO .39270EtOO .44880EtOO .50490EtOO

.56lOOEtOO .61710EtOO .67320EtOO .72930EtOO .78540EtOO

.84150EtOO

.34648EtOO .34240EtOO .33853EtOO .33500Et00

.33162EtOO

.42019EtOO .44169EtOO .46172EtOO .48023EtOO .49717EtOO

.51252EtOO

.52622E+OO .53826EtOO .54862EtOO .55730EtOO .56433EtOO .56974EtOO .57352EtOO .57562EtOO .57604EtOO .57489EtOO

.57183EtOO .56704EtOi .56056EtOO .55243EtOO .54267EtOO .53128EtOO

.5183lEtOO .50383EtOO .48790EtOO .47055EtOO

.45182EtOO .43177EtOO .41045EtOO .38788EtOO

.3641lEtOO

.89760EtOO 95370EtOO

.33915E+OO

.12342EtOl

.28584EtOO .25755EtOO .22820EtOO .19780EtOO

:10098EtOl .10659EtOl .11220EtOl .11781EtOl .35051E+00

.39726EtOO

.12903EtOl .13464EtOl .14025EtOl .14586EtOl .15147EtOl .15708EtOl

.31305EtOO

.1665lEtOO .13455EtOO 10219EtOO :69789E-01 .38093E-01 .14155E-01

.32750E-01 .2240lE-01 .13402E-01 .58178E-02 -.45849E-03 -.56375E-02 -.99438E-02 -.13566E-01 -.16825E-01 -.19970E-01 -.2270lE-01 -.24708E-01 -.257llE-01 -.25427E-01 -.23593E-01 -.20627E-01 -.16438E-01 -.11807E-01

-.69089602 -.16665E-02 .39601E-02 .99505E-02 .16217E-01 .22866E-01 .30418E-01 .39078E-01 .49032E-01 .60445E-01 .73479E-01 .88278E-01 10472EtOO

.13719EtOl .12840EtOl .11934EtOl llO11EtOl :10075EtOl 91293EtOO :81758EtOO .72156EtO3 .62469EtOO .52693EtOO .42928EtOO 33308EtOO :24045EtOO .15624EtOO 94154E-01 :99749E-01 .16534EtOO .24009EtOO

.31887EtOO 399lOEtOO

:47944EtOO .55922EtOO

.26416EtOO .28569EtOO .31698EtOO

.37816EtOO .55085EtOO

.15708EtOl

-.43252EtOO -.45034EtOO -.46654EtOO

-.48114EtOO

-.49408EtOO -.50529EtOO

-.51434EtOO -.52023EtOO

-.52157EtOO -.51507EtOO -.49087EtOO

-.41163EtOO -.13029EtOO .38659EtOO .53533EtOO .56409EtOO .56585EtOO .55990EtOO .55095EtOO .54027EtOO

.52817EtOO .51478EtOO .50028EtOO

.4846lEtOO .46772EtOO .44955EtOO .43004EtOO .40918EtOO

:12263EtOO .14182EtOO .16203EtOO .18300EtOO .20450EtOO .22548EtOO .24506EtOO

-.39196EtOO -.41308EtOO

.15877EtOl .16297EtOl 16674EtOl :16995EtOl 17250EtOl :17444EtOl

-.16748EtOO -.16856EtOO -.1699lEtOO -.17135EtOO -.17276EtOO

-.17418EtOO -.17580EtOO -.17797EtOO -.18202EtOO -.19083EtOO -.20730EtOO -.23699EtOO -.29223EtOO -.40022EtOO -.56048EtOO -.42600EtOO -.20632EtOO -.86176E-01 -.18745E-01 .22197E-01 .49252E-01 .68589E-01 .83470E-01 .95098E-01

.10354EtOO .10970EtOO .11424EtOO, .11763EtOO .12023EtOO .12232EtOO .12430EtOO .12646EtOO .1290lEtOO .132llEtOO .13589EtOO .1404lEtOO .14595EtOO .15259EtOO .15997EtOO .16763EtOO .175llEtOO .18203EtOO .18823EtOO

.19405EtOO

.9046lEtOO .89496EtOO

SURFACE

ARC LENGTH X/Z -.ooooo

.03398 .06793 .10181

: ::59:65

.20247 .23543 .26791 .29981 .33100 .36140 .39088 .41934 :X .49758 .52090 .54263 .56264 .58080 .59698 .61108 .62304 .63281 .64038 .64574 : tX .64779 .64351 .63678 .62773 .61645 .60303 .58756 .57017 :%$J .50804 .48442 .45953 .43347 .40635 .37824 .34924

(S)

SLOPE

(THETA)

AND CURVATURE

Y/Z -.01416 -.00851

-.00269 : k%a4: : FE: : !Z .02388 .02254 .02025 :W ; pi;

-.00024 -.00306 -.00559 -.00788 -.01005 -.01221 -.01415 -.01564 -.01647 -.01642 -.01531 -.01340 -.01065 -.00760 -.00440 -.00105 .00244 : 8Kif : oO:a370; .02073 : Ef .03383 .03837 .04271 .04662 .04986

S 0.00000

.03445

: ESS : ::K+ .20533 .23843 .27094 .30284 .33406 .36455 .39418 .42286 .45045 .47683 :K .54728 .56745 .58576 -60209 .61635 .62846 -63835 .64597 -65135 .65464 .65670 .65995 .66524 .67271 .68236 .69417 .70805 .72392 .74166 .76116 .78228 .80492 .82894 .85424 .88069 : K:: : ;69:::

: 23% .25792 .22636 -19443

: EE .05349 .05192 -04862

1.02611 1.05717 1.08877 1.12087

: :62;::

:x

: : :E:


9.27993 9.57893

PSI

161.15812 163.93357 166.12317 167.85510

168.77447 169.07257 169.24399 169.39714 169.60480 169.92175 170.51090 171.50808 172.88719 174.62837 176.73171 179.26369 181.40207 184.06729 187.00510 189.16568

190.41072

(Y/Z)/XMAX

-.ooooo : :i:E:

10.01198

10.33667 9.94767 8.59966 6.32239 3.33591 .90658 -1.03859 :;-gg;; -a:39887 -7.37860 -7.88701 -7.95343 -7.77588 -7.51854 -7.30492 -7.19540 -7.40480 -8.18029 -8.98144 -8.92193 -7.19999 -2.30565 8.01381 51.46930 90.10833 129.25381 149.03810 156.95057

(X/Z)/XMAX

-: iEa9859

-.38189 -.87694 -1.33307 -1.41768 -1.15692 -1.13566 -1.09565 -.89996 -.69636 -.43487 -.13290

: 10;2:: : ::z -.05963 -.44954 -.91588 -.52492 .59714 4.81384 17.08161 69.38116

278.73204 264.31107 104.66419 29.50386 10.76401 5.31823 3.29739 2.24793 1.24980 .53431 : :;59:82 : :z .28856 .49388 .73557 1: 19:i83: 1.32169 1.30579 1.31191 1.53015 1.32168 .84763 .36172

.05233 .10461 .I5678 -20876 .26047 .31179 .36255 .41257 .46168 .50972 .55653 .60192 -64576 .68786 .72808 .76623 .80214 .83561 :X8282 -91931 .94102

.999oi 1.Lloooo : K% .98059

:E698Z

-92862 .90479 .87801 .84855 .81660

-.00414 .00534 .01485 : L%E .03517 .03706 .03678 .03471 .03118 : K% .01541 : Xf -.00037 -.00471 -.00862 -.01213 -.01547 -.01879 -.02178 -.02529 -.02357 -.02063 -.01640 -.01170 -.00677 -.00161 .00376 :"001Z : ix .03193

: :Ef; .70763

: Et:49 .05209

:X .58246 .53781 .49194 .44500 .39717 .34858 .29940 .24983 .20001

: II%; :%3X .08041 .08236 .08237 .07996 .07488 .06757 .05875

DYBP/DZP

-.22360 -.2236$ -.22412 -.22454 -.22357 -.21973 1:;;;;; -.18961 -.18012 -.16810 :::;;j; -.14140 -.13755 -.13705 -.13860 -.14093 1:;;;;; -.14184 -.13367 -.12506 I:::;;$ 1:;;;;; -1.03944 343.34222 .57267 .16904 .05711 .00372 -.02946 -.05446 -.07347 -.08324 -.08629 -.08797 1: ;g;; -.09394 -.09862 -.10606 :::g; -.13898 :::z;;; -.17361 -.18471 -.19174 -.I9515

:Kit

54

.03247 .ooooo

z:

57 I

ITER

ITERATION

DELHX

I

*5191E-03 5z

-.3030E-03 .1176E-03 -.8528E-04 -.7080E-04 -.6851E-04 -.6931E-04 -.5709E-04 -.7074E-04 -.5741E-04 -.3977E-04 -.3987E-04 -.3910E-04 -.3778E-04 -.3614E-04 -.3611E-04 -.3596E-04 -.3542E-04 -.3462E-04 -.3365E-04 -.3257E-04 -.3253E-04 -.3227E-04 -.3185E-04 -.3129E-04 -.3064E-04 -.2993E-04 -.2917E-04 -.2873E-04 -.2850E-04 -.2819E-04 -.27BOE-04 -.2736E-04 -.2686E-04 -.2634E-04 -.2579E-04 -.2523E-04 -.2495E-04 -.2473E-04 -.2447E-04 -.2417E-04

t; U

E 190

.01416

1.31836

190

S

XMAX=

1.31836

SLOR SOLUTION

1.21930 1.25235 1.28537

Y/Z

x/z

SHAX-

:.01995 kX

57 32 33 21 21 21 22 22 35 35 35 35 35 36 36 36 36 36 36 37 37 37 37 37 37 37 38 38 38 38 38 38 38 38 38 39 39 39 39

BEGINS

76273 47562 16898 05525

.01733 -.15674 -.09873 -.00923

.15005 -10004 .05001 .ooooo

HETA

PSI

(X/Z)/XMAX

SMAX/XMAX=

.64938

.04922 E358 : .02180 (Y/Z)/XMAX

1: :;;g ::I';;;; DYBPIDZP

2.03016

ON MESH 2 DELAVG .1753E-04 .8217E-05 .5031E-05 .3834E-05 .3190E-05 .2953E-05 .2735E-05 .2632E-05 .2567E-05 .2468E-05 .2353E-05 .2279E-05 .2247E-05 .2220E-05 .2184E-05 .2150E-05 .2119E-05 .2094E-05 .2073E-05 .2060E-05 .2052E-05 .2043E-05 .2033E-05 .2023E-05 .ZOlOE-05 .1995E-05 .1978E-05 .1961E-05 .1944E-05 .1926E-05 .1912E-05 .1898E-05 .1883E-05 .1870E-05 .1860E-05 .1850E-05 .1840E-05 .1831E-05 .1822E-05 .1815E-05 .1805E-05

RESMX

I

RESAVG .7925E-01 .3422E-01 .2020E-01 .1471E-01 .1194E-01 .1061E-01 .9609E-02 .8986E-02 .8525E-02 .8088E-02 .7682E-02 .7384E-02 .7180E-02 .7016E-02 .6863E-02 .6721E-02 .6596E-02 .6491E-02 .6403E-02 .6336E-02 .6285E-02 .6240E-02 .6193E-02 .6150E-02 .6110E-02 .6066E-02 .6020E-02 .5972E-02 .5926E-02 .5876E-02 .5833E-02 .5794E-02 .5754E-02 .5717E-02 .5684E-02 .5651E-02 .5618E-02 .5584E-02 .5551E-02 .5521E-02 .5487E-02

KSUP 1172 1173 1175 1174 ::33 1173 1171 1171 1172 1172 1171 1171 1171 1171 1170 1170 1170 ::it 1169 ::z :::; ::t:: ::tt 1168 1168 1168 1167 1166 1166 1166 1166 1166 1166 1166 1166

JSNHIN

ISHMIN

-.2384E-04 -.2348E-04 -.2310E-04 -.2270E-04 -.2229E-04 -.2187E-04 -.2159E-04 -.2140E-04 -.2119E-04 .2146E-04 -.2052E-04 -.2020E-04 -.1987E-04 .2846E-04 .2243E-04 -.1888E-04 -.1855E-04 -.1822E-04 -.lSOOE-04 -.1783E-04 -.1764E-04 -.1743E-04 -.1722E-04 -.1699E-04 -.1675i-04 -.1651E-04 -.1626E-04 -.1600E-04 -.1574E-04 -.1548E-04 -.1522E-04 -.1495E-04 -.1469E-04 -.1454E-04 -.1438E-04 -.1421E-04 -.1404E-04 -.1386E-04 -.1368E-04 -.1349E-04 -.1331E-04 -.1312E-04 -.1292E-04 -.1273E-04 -.1254E-04 -.1234E-04 -.1215E-04 -.1195E-04 -.1176E-04 -.1157E-04 -.1138E-04 -.1119E-04 -.llOOE-04 -.lOSlE-04 -.1063E-04 -.1046E-04 -.1033E-04 -.lOZOE-04 -.1007E-04 -.9937E-05

.1794E-05 .1784E-05 .1774E-05

.1763E-05

.1754E-05 .1745E-05 1737E-05 :1730E-05 .1724E-05 .2566E-05 .2359E-05 .2255E-05 .2190E-05 .2257E-05 .2169E-05 .ZllOE-05 .2067E-05 .2035E-05 .ZOllE-05 .1991E-05 .1976E-05 : :8E-~~ .1943E-05 .1935E-05 .1929E-05 .1924E-05 .1919E-05 .i914E-05 1910E-05 :i906~-05 .1902E-05 .1899E-05 .1895E-05 .1891E-05

t: 42 44: 43

t3

: :xz-i55 .1879E-05 1875E-05 :187i~-05 .1866E-05 1862E-05 :i857~-05 .1853E-05 .1848E-05 .1843E-05 .1838E-05 .1832E-05 .1827E-05 .1821E-05 .1816E-05 lSlOE-05 1 i804E-05 .1798E-05 .1792E-05 .1786E-05 .1780E-05 1774E-05 :i767E-05 .1761E-05

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

;Koo: 7775E-01 7662E-01 7543E-01

%Ei 7161E-01 7028E-01 9210E-01 8717E-01 8296E-01 7937E-01 1025E+OO 8772E-01 7539E-01 6979E-01 6828E-01 6703E-01 6600E-01 6516E-01 6447E-01 6392E-01 6348E-01 6314E-01 628,7E-01 6267E-01 6252E-01 6241E-01 6234E-01 6230E:01 6229E-01 6229E-01 6231E-01 6235E-01 6239E-01 6244E-01 6250E-01 6257E-01 6263E-01 6270E-Oi 6277E-01 6285E-01 6292E-01 6299E-01 6306E-01 6314E-01 6321E-01 6328E-01 6334E-01 6341E-01 6347E-01 6354E-01 636OE-01 6366E-01 6372E-01 6i77E-Oi 6383E-01 6388E-01 6393E-01

.5454E-02 .5421E-02 .5387E-02 .5352E-02 .5317E-02 .5281E-02 .5247E-02 .5214E-02 .5182E-02 .7341E-02 .7069E-02 .6930E-02 .6836E-02 .6834E-02 .6703E-02 .6616E-02 .6550E-02 .6494E-02 .6444E-02 .6399E-02 .6357E-02 .6317E-02 .6278E-02 .6241E-02 .6205E-02 .6170E-02 .6134E-02 .6100E-02 .6065E-02 .6031E-02 .5998E-02 .5964E-02 .5931E-02 .5897E-02 .5864E-02 .5830E-02 .5797E-02 .5764E-02 .5731E-02 .5697E-02 .5665E-02 .5632E-02 .5600E-02 .5567E-02 .5535E-02 .5504E-02 .5472E-02 .5441E-02 .5409E-02 .5379E-02 .5348E-02 .5318E-02 .5288E-02 .5258E-02 .5228E-02 .5199E-02 .5170E-02 .514OE-02 .5112E-02 .5083E-02

1166 1166 1166 1166 1166 1167 1167 1167 1168 370 370 371 371 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 373 i;: 374 374 374 374 374 374

: ii

26 26

38

5s

38 38

26

3: 58

!I

Hf 26 26

HEi 38

26 26

3x 3x

It Xf

38

26

102 ::i :ii

107 108 ::09 111 112 ::;I ::z 117 ::: :si 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161

w’ W

-.9iOSE-05 -.9671E-05 -.9537E-05 -.9403E-05 -.9269E-05 -.9135E-05 -.9002E-05 -.8869E-05 -.8737E-05 -.8606E-05 -.8475E-05 -.8346E-05 -.8217E-05 -.8090E-05 -.7964E-05 -.7839E-05 -.7716E-05 -.7594E-05 -.7474E-05 -.7355E-05 -.7237E-05 -.712lE-05 -.7007E-05 -.6894E-05 -.6783E-05 -.6674E-05 -.6566E-05 -.6460E-05 -.6355E-05 -.6252E-05 -.6149E-05 -.6048E-05 -.5949E-05 -.5852E-05 -.5756E-05 -.5663E-05 -.5570E-05 -.5480E-05 -.539lE-05 -.5304E-05 -.5219E-05 -.5135E-05 -.5052E-05 -.4971E-05 -.4892E-05 -.4814E-05 -.4738E-05 -.4663E-05 -.4589E-05 -.4517E-05 -.4446E-05 -.4376E-05 -.4308E-05 -.424lE-05 -.4176E-05 -.41llE-05 -.4048E-05 -.3986E-05 -.3925E-05 -.3865E-05

.1754E-05 .1747E-05 .1741E-05 .1734E-05 .1727E-'05 .1720E-05 .1713E-05 .1706E-05 .1699E-05 .1692E-05 .1684E-05 : K-E : :x-E .1648E-05 .1641E-05 .1633E-05 .1626E-05 .1618E-05 .1611E-05 .1603E-05 .1596E-05 .1588E-05 .158lE-05 .1573E-05 .1566E-05 .1558E-05 .1550E-05 .1543E-05 .1534E-05 .1527E-05 .1519E-05 .15IlE-05 .1504E-05 .1496E-05 .1488E-05 1481E-05 :1473E-05 .1466E-05 .1458E-05 .1450E-05 .1443E-05 .1435E-05 : :t22E .1412E-05 .1404E-05 .1397E-05 .1389E-05 .1382E-05 .1374E-05 .1366E-05 .1359E-05 .1351E-05 .1344E-05 .1336E-05 .1329E-05 .132lE-05 .1314E-05

.6398E-01 .6402E-01 .6407E-01 .641lE-01 .6415E-01 .6419E-01 .6423E-01 .6427E-01 .643lE-01 .6434E-01 .6438E-01 .644lE-01 .6444E-01 .6448E-01 .645lE-01 .6453E-01 .6456E-01 .6459E-01 .6462E-01 .6464E-01 .6467E-01 .6470E-01 .6472E-01 .6474E-01 .6477E-01 .6479E-01 .648lE-01 .6484E-01 .6486&Oi .6488E-01 .6490E-01 .6492E-01 .6495E-01 .6497E-01 .6499E-01 .650lE-01 .6503E-01 .6505E-01 .6507E-01 .6509E-01 .6511E-01 .6514E-01 .6516E-01 .6518E-01 .6520E-01 .6522E-01 .6524E-01 .6526i-Oi .6528E-01 .6530E-01 .6533E-01 .6535E-01 .6537E-01 .6539E-01 .654lE-01

.6543E-Oi .6546E-01 .6548E-01 .6550E-01 .6552E-01

35

33

.5055E-02 .5027E-02 .4999E-02 .4971E-02 .4943E-02 .4916E-02 .4888E-02 .4861E-02 .4835E-02 .4808E-02 .478lE-02 .4755E-02 .4729E-02 .4703E-02 .4677E-02 .4652E-02 .4626E-02 .460lE-02 .4576E-02 .455lE-02 .4526E-02 .4502E-02 .4478E-02 .4454E-02 .4430E-02 .4406E-02 .4382E-02 .4359E-02 .4336E-02 .4313E-02 .4289E-02 .4266E-02 .4243E-02 .4221E-02 .4199E-02 .4176E-02 .4154E-02 .4132E-02 .4lllE-02 .4089E-02 .4067E-02 .4046E-02 .4024E-02 .4003E-02 .3982E-02 .3961E-02 .3940E-02 .3919E-02 .3899E-02 .3878E-02 .3858E-02 .3837E-02 .3817E-02 .3797E-02 .3777E-02 .3757E-02 .3737E-02 .3718E-02 .3698E-02 .3679E-02

374

0

40

2

38

26

26 26 2266

374 374 374 374 374 374 374 374 374 374 374 374 374 374 374 374

i i i i i 00 00 00

:z 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 2: 210 211 212 213 214 215 216 217 218 219 220 221

-.3806E-05 -.3749E-05 -.3692E-05 -.3637E-05 -.3582E-05 -.3529E-05 -.3476E-05 -.3425E-05 -.3375E-05 -.3325E-05 -.3276E-05 -.3229E-05 -.3182E-05 -.3136E-05 -.309lE-05 -.3046E-05 -.3003E-05 -.2960E-05 -.2918E-05 -.2877E-05 -.2837E-05 -.2797E-05 -.2758E-05 -.2720E-05 -.2682E-05 -.2645E-05 -.2609E-05 -.2573E-05 -.2538E-05 -.2504E-05 -.2470E-05 -.2437E-05 -.2404E-05 -.2372E-05 -.234lE-05 -.2310E-05 -.2279E-05 -.2250E-05 -.2220E-05 -.2191E-05 -.2163E-05 -.2135E-05 -.2108E-05 -.208lE-05 -.2054E-05 -.2028E-05 -.2003E-05 -.1977E-05 -.1953E-05 -.1928E-05 -.1904E-05

-.iiiiE-05

-.1857E-05 -.1835E-05 -.lSlZE-05 -.1790E-05 -.1768E-05 -.1747E-05 -.1726E-05 -.1705E-05

43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 43 $3 43 43 43 43 43 43 43 43 43 45 43 43 43 43 43 43 43 43

.1306E-05 .1299E-05 .1291E-05 .1284E-05 .1277E-05 .1269E-05 .1262E-05 .1254E-05 .1247E-05 .1240E-05 .1233E-05

.6555E-01 .6557E-01 .6559E-01 .6562E-01 .6564E-01 .6566E-01 .6569E-01 .6571E-01 .6573E-01 .6576E-01 .6578E-01

33 33 33 33 33 33 33 33 33 33 33

37 37 37 37 37 37 37 37 37 37 37

: :f:E-E .lZllE-05 .1204E-05 .1197E-05 .1189E-05 1182E-05 :1175E-05 .1168E-05 .1161E-05 .1154E-05 .1147E-05 .1140E-05 .1133E-05 .1126E-05 .llZOE-05 .1113E-05 .1106E-05 .1099E-05 .1093E-05 1086E-05 :1079E-05 .1073E-05 .1066E-05 .1059E-05 .1053E-05 .1046E-05 .1040E-05 .1034E-05 .1027E-05 .lOZlE-05 .1014E-05 .lOOSE-05 .lOOZE-05 .9958E-06 .9896E-06 .9834E-06 .9773E-06 .9713E-06 .9653E-06 .9593E-06 .9533E-06 .9474E-06 .9415E-06 .9357E-06 .9299E-06

.6583E-01 .6585E-01 .6588E-01 .6590E-01 .6593E-01 .6595E-01 .6598E-01 .6600E-01 .6603E-01 .6605E-01 .6608E-01 .6610E-01 .6613E-01 .6615E-01 .6618E-01 .6620E-01 .6623E-01 .6625E-01 .6628E-01 .6630E-01 .6633E-01 .6635E-01 .6638E-01 .6640E-01 .6643E-01 .6645E-01 .6648E-01

33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33

37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37

: 8:xf .9127E-06

.658OE-Oi

33

37

.3659E-02 .3640E-02 .3621E-02 .3602E-02 .3583E-02 .3564E-02 .3545E-02 .3527E-02 .3508E-02 .3490E-02 .347lE-02 .3453E-02 .3435E-02 .3417E-02 .3399E-02 .3382E-02 .3364E-02 .3346E-02 .3329E-02 .3312E-02 .3294E-02 .3277E-02 .3260E-02 .3243E-02 .3226E-02 .3210E-02 .3193E-02

.3176E-02 .3160E-02 .3144E-02 .3127E-02 .31llE-02 .3095E-02 .3079E-02 .3063E-02 .3048E-02 .3032E-02 .3016E-02 .3001E-02 .2986E-02 .2970E-02 .2955E-02 .2940E-02 .2925E-02 .29lOE-02 .2895E-02 .2880E-02 .2866E-02 .2851E-02 .2837E-02 .2822E-02 .2808E-02 .2794E-02 .2780E-02 .2766E-02 .2752E-02 .2738E-02 .2724E-02 .27lOE-02 .2697E-02

374 374 33;:: 374 374 374 374 374 374 374 3;: 374 374 374 374 374 374 374 374 374 374 374 :77: 374 374

I! 38

38

38 58 38 i% 38

3a

26 26

2

26 26

$2 26

;;: 374 33;:: :3: 374 374 374 374 374 374 374 374 3:: 374 374 374 :3:: 374 374 374 374 374 374 374 374 374 374

3a

26

3: 3x

22: X8

38 38

26 26

222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 ITER

.9070E-06 9014E-06 :8958E-06 .8902E-06 .8847E-06 .8792E-06 .8738E-06 .8684E-06 .8630E-06 .8576E-06 .8523E-06

.847lE-06 .8418E-06

-.1292E-05 -.1286E-05 -.1280E-05 -.1274E-05

8 x 8

.8366E-06 .8315E-06 .8264E-06 .8213E-06 .8162E-06 .8112E-06 .8062E-06 .8012E-06 .7963E-06 .7914E-06 .7866E-06 .7817E-06 .7770E-06 .7722E-06 .7675E-06 .7628E-06

DELMX

I

DELAVG

-.i304E-05 -.1298E-05

i!

.6703E-0 .6705E-0 .6708E-0 .67lOE-0 .6713E-0 .6715E-0 .6717E-0 .6720E-0 .6722E-0 .6724E-0 .6727E-0 .6729E-0 .673lE-0 .6734E-0 .6736E-0 .6738E-0 .6740E-0 .6743E-0 .6745E-0 : g'gg; .6752E-0 .6754E-0 .6756E-0 .6759E-0 : ;;;;:I; .6765E-01 .6767E-01 RESMX

:

1 : : : : : : : : 1 : : : 1

33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33 33

37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37 37

.2683E-02 .2670E-02 .2656E-02 .2643E-02 .2630E-02 .2617E-02 .2604E-02 259lE-02 :2578~-02 .2565E-02 .2552E-02 .2540E-02 .2527E-02 .2515E-02 .2502E-02 .2490E-02 .2478E-02 .2465E-02 .2453E-02 .244lE-02 .2429E-02 .2417E-02 .2406E-02 .2394E-02 .2382E-02 .237lE-02 .2359E-02 .2348E-02 .2336E-02

I

J

RESAVG

KSUP

NPVD

JSHMAX

ISHMAX

JSHMIN ISHMIN

CONVERGENCE

INITIAL

HISTORY ERROR(r)

IS

.5191E-03

INITIAL

RESIDUAL(+)

.1648E+Ol

IS

*

#I *

* * * r

t

: I

+

I I : : : I :

:

:

: I

:

:

: I

: I I

I

:

:

:

: I

: I

:

: I

: I

:

: I

: I

:

:

:

: :

:

* N

:

:

:

:

: I

: I

:

:

: I

: :

: I

+I +1 +I +I +I +I + I + I + I + I + I + I

:

: I

: I

:

: I

: I

: I

+ :

2: 52

+

+

: : :

+ +

t +

+ + t

+ i

I :

: I I : I : I : : :

89 99: 85 8f 9976 8: K. 102 103 104 105 :84 108 K 111 112

+ t t + + t t t + + + + t t + t t t t + + + + + t + + + t + t t t + t + t t t + + t

113 114 r:: 117 118 ::i 121

*I 34 I * I n I #I * I I I w I *

I u

I : :

+ tt t + t+

:

t +

i

I I

i I I : i : :

158

::09 161 162

if:

165 166

+ t t + + + t t t t l

+

+ + + tt t+ + tt tt t+ t

* x * * * 36

::i

175 176 177 178 179 180 181 182

* 3t *

* *

::t 185 :x; 188 :89;: 191 :z 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222

* x I * *

* *

I

:

I

: I : I : : : I : : : : :

t

I

t t t t

: :

+ t

I I

: : I : I : : I : :

I:43 ;:a 227 228’ 229

: : 1t :I

tz 232

+

I

II

l +

i I

:

:. :

233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250

I

i : : ------.-:

I

3t

I I

* *

i

*

I

i * : ::: : - ::-----------------I----------------+--

l

I

I

1 : : ,’ :I-------------------I-------------------I :

I

: II

BASIC

I

J

RESULTS

RHO .33265E+OO .32955E+OO .32632E+OO

THE

-.15708E+Ol -.15147E+Ol

-.14586E+Ol -.14025E+Ol

-.13464E+Ol -.12903E+Ol

-.12342E+Ol -.1178lE+Ol -.llZZOE+Ol

-.10659E+Ol -.10098E+Ol -.95370E+OO -.89760E+OO -.84150E+OO -.78540E+Oi -.72930E+OO -.6732OE+OO

-.617lOE+OO -.56100E+OO -.50490E+OO -.44880E+OO -.39270E+OO -.53660E+OO -.28050E+OO -.22440E+OO -.16830E+OO

.33743E+iO .34073E+OO .34375E+OO

.3475lE+OO

-.llZZOE+OO -.56lOOE-01 -.71054E-14 .56lOOE-01

F -.83326E-01 -.84226E-01 -.84626E-01 -.84604E-01 -.84104E-01 -.83027E-01 -.8130lE-01 -.78920E-01 -.75969E-01 -.72629E-01 -.69033E-01 -.65287E-01 -.61496E-01 -.5775lE-01 -.54124E-01 -.50663E-01 -.47368E-01 -.4422lE-01 -.41203E-01 -.38304E-01 -.35523E-01 -.32872E-01 -.30420E-01 -.28260E-01 -.26434E-01 -.2495lE-01 -.23796E-01 -.2298lE-01 -.22490E-01 -.21824E-01

U .12312E-14 -.15316E-01 -.33470E-01 -.51959E-01 -.70185E-01 -.88265E-01

-.10664E+OO -.12595E+OO -.14627E+OO -.16706E+OO

-.18780E+OO -.20838E+OO -.22870E+OO -.24848E+OO -.26709E+OO -.28334E+OO

-.29612E+OO -.30493E+OO -.30966E+OO

-.31026E+OO -.30715E+OO

-.30277E+OO -.29893E+OO -.29373E+OO

-.28124E+OO -.24830E+OO

-.15148E+OO .13615E+OO .59397E+OO .78460E+OO .87056E+OO .88246E+OO .87762EtOO

.87158E+OO

.86529E+OO .85253E+OO .83077E+OO .80~50i+OO .77724E+OO .74969E+OO

.72161E+OO .68880E+oo .62895E+OO

.58115E+OO .55930E+OO .52792E+OO .49006E+OO .44748E+OO .4005ZE+OO .34814E+OO

.29177E+OO

.23530E+OO .34648E+OO .34240E+OO .33853E+oo .33500E+OO

.33162E+OO

.13464E+Oi

.14025E+Ol .14586E+Ol .15147E+Ol

.15708E+Ol

.72940E-01 .75630E-01 .77767E-01 .79406E-01 .80668E-01

.18155E+OO .13156E+OO .8512lE-01 .4136lE-01 .11382E-13

V -.88818E-14 .26164E-02 .60958E-02 .lOOlZE-01 .13476E-01 .15503E-01 15357E-01 :12755E-01 .85884E-02 .39272E-02 -.12965E-02 -.69176E-02 -.12438E-01 -.17384E-01 -.20853E-01 -.22340E-01 -.22359E-01 -.21634E-01 -.20938E-01 -.20796E-01 -.22836E-01 -.295lOE-01 -.38866E-01 -.47416E-01 -.53512E-01 -.52778E-01 -.29818E-01 .2257lE-01

.10439E+OO .106llE+OO

.53309E-01 .36345E-01 .31600E-01 .27986E-01 .22086E-01 .16727E-01 .19954E-01 .28822E-01 .36065E-01 .41084E-01 .43656E-01 .43467E-01 .37839E-01 .28924E-01 .18416E-01 .55389E-02 -.82709E-02 -.21473E-01 -.34070E-01 -.44620E-01 -.49003E-01 -.46058E-01 -.37870E-01 -.272llE-01 -.16596E-01 -.76065E-02 .26645E-14

MC

13803E-13 :23918~-01 .52362E-01 .81423E-01 .10993E+OO

.13779E+OO .16558i+OO .19447E+OO .22498E+OO .25648E+OO .28816E+OO .31984E+OO

.35128E+OO .38200E+OO

M .13728E+Ol .13726E+Ol

CP .23372E+OO .23394E+OO .23469E+OO .23599E+OO .23784E+OO .24019E+OO .24287E+OO .24553E+OO .24790E+OO .24996E+OO .25175E+OO

.25314E+OO .254lOE+OO .25465E+OO .25522E+OO .25667E+OO .25986E+OO .26527E+OO

SURFACE X/XMAX -.oooo : !Z63 : :% .2605 .3118 .3625 :f% .5097 .5565

RESULTS Y/XMAX

I: ;::; -.0041 :Ei : Eif .0352 .0371 :Kf .0312 .0265

PSI .81 2.01 3.89 5.82 7.74 9.64 11.50' :;-it 16:74 18.35 19.90 21.37

:f% :fXZ .7662 .8021 .8356 .8664 .a944

: K:Z .0098 .0045 1:;;;;

: Kf

1:;:;; -.0155 -.0188

: E45

::;;g

: ;Ei

1:;;;; -.0236

l: 8% .9910

1:;:;: -.0117

:E .9493 .9286 .9048 .8780 .8486 .8166

1:;;;; .0038 0092 :0147 .0201

: :$f: .7076 .6675 .6257 .5825 .5378 .4919 .4450 .3972

:K .0521

:.2498 E .2000 .1501

.lOOO

.0500 .oooo X/XMAX

: Kt

: Zi .0718 .0768 .0804 : Et .0800 0749 :0676 .0587 .0492 .0397 .0307 .0218 Y/XMAX

5:-E 25:31 26.45 27.51 %a9 30:15 30.84 31.43 31.93 %-E 32:86 32.98 33.00 :zt 32:49 32.12 31.65 31.09 30.44 29.70 28.87 27.95 26.96 25.89 24.74 23.52 22.22 20.86 19.43 :x 14:76 13.07 11.33 9.54 7.71 5.86 4.00 2.18 .81

PSI

CP

OMEG I;:*!; -2127 1.95 4.07 5.17 5.60 5.54 5.13 4.55 3.90 3.21 2.52 1.88 1.28 .77 .33 -.03 -.32 -.57 -.78 -.96 I:-;: -1:42 1: -;;: -1:35 -1.18 -.94 -.68 -.40

-.lO

.23 .57 1::: 1.74 2.24 2.81 3.46 4.21 5.06 6.00 7.03 8.13 9.28 :~~:x 12:92 14.04 15.13 :;4 21:6-r 31.56 90.00 OMEG

.2337 .2339 .2347 .2360 :fZ :22Z .2479 .2500 .2517 .2531 :% .2552 .2567 .2599 .2653 .2730 -2830 .2949 .3063 .3156 .3247 .3386 .3670 -.4291 .4366 -:%5 -.3067

NC .oooo .0239 .0524 .0814 .1099 .1378 : :69:65 .2250 .2565 .2882 .3198 .3513 .3820 .4108 .4357 .4550 .4679 .4744 .4745 .4690 .4624 .4575 .4508 .4328 .3820 :22z .9761 kx 1:6253 1.6168 1.6063

1:;;:; -.3228 -.3246 -.3219 -.3126 -.3006 -.2891 -.2788 -.2694 -.2573 -.2232 -.2004 -.2015 -.1963 -.1878 -.i778 -.1668 -.1548 -.1427 -.1325 -.1252 -.1207 -.1182 -.1172 -.1169

x69: 1:5209 1.4628 1.4045 1.3477 1.2912 1.2251 1.1006 1.0065 .9684

:%f

.8892 .8871 .8844 .a813 _----

-8776 .a734 .a680 .8638 .8584 .8527 .8469 .8408 .8348 .8289 .8232 .8180 .8132 .8089 .8052 .8020 .7994 .7973 .7958 .7950 .7949 .7972 .7955 .8006 .8054 .8116 .8192 .8281 .8383 .8496 .8618 .8749 .8886 .9029 .9176 : E2

.9605 .9746 .9883 1.0014 1.0137 1.0249 1.0349 :E .4042 1.0433 1.0501 :23::69 1.0553 .1455 1.0589 1.0610 : 007000TJ 1.0617 NC U

.9117 .8435 .7679 .6861

CP

.8918

W

V

U -.oooo -.oooo -.oooo

-.oooo -.oooo -.oooo -.oooo ~.... -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo .oooo -: k%i -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo -.oooo .oooo V

.oooo -.0155 -.0340 -.0529 -.0715 -.0896 -.1077 -.1266 -.1465 -.1671 -.1878 -.2085 -.2290 -.2491 -.2679 -.2842 -.2970 -.3057 -.3104 -.3110 -.3080 -.3042 -.3014 -.2975 -.2863 -.2539 -.1544 :E .7917 .8722 .8832 .8782 .8720 -8656 .8527 .8310 .8050 .7781 .7508 .7229 .6902 .6301 .5819 .5596 .5279 .4901 .4480 .4020 .3510 .2959 .2398 : :3:: : :51:: .oooo W

VS

ws

.fJ0***w**** -66.36 -1.00 -77.72 -2.19 -81.61 -3.41 -84.12 -4.61 -86.57 -5.79 -89.27 -6.97 -92.20 -8.21 -94.23 -9.52 -95.59 ::g; -97.15 -98.23 -13:65 -98.92 -15.03 -99.26 -16.39 -17.67 -99.17 -98.72 -18.80 -98.11 -19.71 -97.49 -20.37 -96.98 -20.78 -20.93 -96.63 -96.63 -20 .a5 -97.22 -20.70 -97.84 -20.60 -20.42 I;;$; -19.75 -90:83 -17.69 -10.99 -80.53 -37.18 9.85 37.17 1.29 44.80 40.20 47.45 59.71 67.35 47.64 47.26 71.25 46.79 73.71 46.27 75.55 45.49 76.93 44.37 77.46 43.05 77.33 41.65 77.00 40.20 76.59 38.68 76.14 36.95 75.71 34.05 75.45 31.59 75.51 30.23 75.86 28.45 76.50 26.38 77.45 24.10 78.78 21.63 79.68 18.90 81.15 82.96 15.95 12.94 84.03 10.02 84.04 7.26 82.60 4.68 78.81

159.30 .Ol .04 .05

BETA

2.27 68.61 00 3930.91 'BETA VS

3 .18 .29 -.15 -.63 -.54 -.59 -.69 -.79 -.86 -.91 -.94 -.95 -.96 -.98 -1.06 -1.26 -1.46 -1.61 -1.79 -1.74 2.36 -6.50 9.78 -.22 -3.27 -3.15 -2.83 -2.52 -2.22 -1.95 -1.77 -1.69 -1.62 -1.55 -1.47 -1.37 -1.26 -1.13 -1.00 -.88 -.82 -.95 -.34 .07 -.Ol -.03 -.03 -.02 -.oo 2 ws

UC :Ki

.0269 : Et .0602 :Kf : :X49: :K : Ki .lOll :KX .1122 ii;;; :E .1746 :X .3035 .5149 .3483 .0166 1::;;: -.2596 -.2739 -.2849 -.2889 -.2832 -.2728 -.2624 -.2529 -.2442 -.2326 -.1982 -.1763 -.1794 -.1750 -.1656 -.I527 -.1363 -.1153 -.0908 -.0666 -.0457 -.0290 -.0165 -.0069 .oooo UC

vc

WC

-.0126 -.0102

.8917

-.0083 -.0065

28::

1:;::; .0051

:X% :Iti:t .a799

:K .0426

:XE .8764 ,875s

:X .0331 .005a -.0394 .0877 .5848 .6065 .4842 .3860

:XE .8727 :E .8598 .8528 .8456 :X .8255

rgg-; -9715

:%i

I;;.: -43:6

:% .9457 1.0666 :'K p;:

:Z :E .1989 .1915 .1863 .1817 : Zf .1548 : :f;f .1074 .0878 .0678 %$ .0079 .0068 .0087 .0116 :K vc

0.0 -66.3 -77.6 -81.5

:X

%E .025i

: ::69;: .0490 .0473 .044a .0422 .0399 .0392 ..0422

DEL1

11.0

39.9 56.4 64.2 Es: 7313

1:1400 1.1369 1.1312 1.1257 :-11:6079 1:1115 :-GE p;;

74.1 74.3 74.8 75.6

1:0871 1.0842 1.0809 1.0768

E-t3 7913

:-z:: 1:0654 1.0634 :*K 1:0616 WC

t:.: 84:O XE 7818 68.6

DE

IHCHIN= CROSSFLOW

HCMIN=

6 SONIC

NUMBER OF POINTS

LINE

30

XXI

YYI

.64935 .65019 .65110 .65196 -65264 .65324 .65350 .65375 .65331 .65255 .65113 .64824 .64345 .63496 .61702 .53378

-.01326 -.01048 -.00685 -.00229 .00352 .01039 .01877 .02825 .03982 .05297 .06821 .08659 .10865 .13674 .17751 .26092 .26641 .25800 .24325

: t;;:t .46802 .45952 -45338 .44902 .44473 .44062 .43652 .43214 .42707 .42094 .41347 .40161

: Ef .I8998 .17145 .15302 .13470 : :;:,5: .08040 .06204 .04338

.10993

CONICAL FORCE DISTkBUTIONS, X(I) -1.5708 -1.5147 -1.4586 -1.4025 -1.3464 -1.2903 -1.2342 -1.1781 -1.1220 -1.0659 -1.0098 -.9537 -.8976 -.8415 -.7854 -.7293 -.6732 -.6171 -.5610 -.5049 -.4488 -.3927 -.3366 -.2805 -.2244 -.1683 -.1122 -.0561 -.oooo :X .1683 .2244 -2805 .3366 .3927 .4488 .5049 .5610 .6171 .6732 .7293 .7854 .8415 .8976 .9537 1.0098 1.0659 1.1220 1.1781 1.2342 1.2903 1.3464 1.4025

CL

CD

.1063 .1065

..0242 .0242 .0243 .0244 .0244 .0241

::Ki .1078 .1083 .1087 -1086 .1080 -1068 .1050 .1027 .0998 .0963 .0924 : :::a5 .0809 .0771 .0731 : Et5 .0554 .p474 : KS : KG3 -.oooo : EJ .0358 .0458 : 00% .b73o .0786 .0824 .0853 : :X79: .0897 : :;:; -0786 : 00:;: : %i : KBi : i;:i .0530

BODY AND SHOCK LOCATIONS OMEG

XXB

-90.0000 -86.7857 -83.5714 -80.3571 r77.1429 -73.9286 -70.7143 : ES: -67.5000 .0207 -64.2857 -61.0714 : Z5 -57.8571 -54.6429 : Ef -51.4286 .0138 -48.2143 -45.0000 :KS -41.7857 .0119 -38.5714 .0116 -35.3571 .0112 -32.1429 .0107 -28.9286 .0098 -25.7143 .0085 -22.5000 .0070 -19.2857 .0060 -16.0714 .0056 -12.8571 .0060 -9.6429 .0079 -6.4286 .0083 -3.2143 .OOOl -.oooo -.0039 3.2143 -.0034 6.4286 -.0016 9.6429 12.8571 :KA 16.0714 19.2857 : E; 22.5000 .0067 25.7143 .0072 28.9286 32.1429 : !loDE 35.3571 .0083 38.5714 41.7857 :Kl 45.0000 48.2143 : iit: 51.4286 54.6429 :oOE 57.8571 61.0714 :K 64.285.7 67.5000 :Ki 70.7143 .0112 73.9286 -0108 77.1429 .0105 80.3571

-.oooo .0340 .0679 :E! ::fS: .2354 .2679 .2998 .3310 .3614 .3909 .4193 .4467 .4728 .4976 .5209 .5426 .5626 .5808 .5970 .6111 .6230 .6328 .6404 .6457 .6487 .6494 .6478 .6435 ,636s .6277 .6164 .6030 .5876 .5702 .5510 -5303 .5080 .4844 .4595 .4335 .4063 .3782 .3492 .3195 .2890 .2579 .2264 : :694: .1299 -0974

YYB

RB

xxs

-.0142 -.0085 -.0027 .0035 SO096 .0153

.0142 .0350 .0680 .1019 .1359 .1698 .2034 .2365 .2690 .3008 -3318 .3620 .3913 .4196 .4468 .4728 .4976 .5209 .5426 .5627 .5809 .5971 .6112 .6232 .6330 .6406 .6460

-.oooo .0494 .0986 .1474 .1956 .2431 .2898 .3354 .3799 .4229 .4643 .5038 .5411 .5764 .6100 .6422 .6724 .7006 .7267 .7507 .7727 .7926 .8104 .8257 .8392 .8523 .8646 .8757 .8857 .8945

:21X .0241 .0239 : KE .0172 .0137 .OlOO : Ki -.0002 -.0031 -.0056 -.0079 -.OlOO -.0122 -.0141 -.0156 -.0165 -.0164 -.0153 -.0134 -.0106 -.0076 -.0044 -.OOlO : %i .0095 .0130 .0168 .0207 : ES .0338 .0384 .0427 .0466 : E2929 : Ei; .0519 : i48369

:z .6479 .6436 .6368 .6277 .6165 .6031 .5876 .5703 .5513 .5307 .5087 .4853 .4608 .4352 .4086 .3811 .3528 .3237 .2939 .2634 .2322 .2004 : EZ '.1026

: Ei .9155 .9192 :X49 : GE .8966 .8826 .8650 .8434 .8176 .7874 .7527 .7133 .6693 .6205 .5671 .5090 .4463 .3793 .3084 .2343

YYS -.6050 -.6035 -.5997 -.5934 -.5850 -.5745 -.5620 -.5475 -.5311 -.5128 -.4926 -.4705 -.4464 -.4210 -.3955 -.3699 -.3438 -.3172 -.2903 -.2631 1:;;;; -.1807 -.1527 -.1247 -.0968 -.0684 -.0392 -.0088 : Ei63: : !Z:: .1723 .2156 .2611 .3089 .3588 .4108 .4645 .5197 .5761 .6332 .6906 .7479 .8046 .8602 : ii2 1.0140 1.0584 1.0976 1.1306 1.1571

RS .6050 .6056 .6077 .6115 .6169 .6238 .6323 .6421 .6530 .6647 .6770 .6893 .7015 .7138 .7270 .7411 .7552 .7690 .7825 .7955 .8079. .8195 .8303 .a397 .8484 .8578 .8673 .a766 .8857 .8947 : 8K .9249 : ;::i : ;i;: .9755 : Z: 1.0091 1.0213 1.0341 1.0473 1.0611 1.0753 1.0899 1.1048 1.1198 1.1345 1.1487 1.1613 1.1719 1.1805

RS/RB :?183z 8:9389 6.0027 4.5388 3.6731 3.1079 2.7144 2.4274 2.2101 2.0405 1.9044 1.7929 1.7012 1.6272 :-%3 1:4764 1.4420 1.4138 :-3% 1:3584 :-3% 1:3391 1.3427 1.3509 1.3637 1.3810 1.4040 1.4349 1.4734 1.5172 1.5676 1.6256 1.6925 1.7695 1.8583 1.9608 2.0793 2.2166 $.. 3;:: 2:7843 3.0480 3.3670 3.7592 4.2511 4.8851 5.7316 6.9098 8.6572 11.5116

56

:GE

.0519

.0103

ix74

.0650

.0258

z:

1:570e

.0513 .0511

.OlOl

90:oooo

.oooo .0325

.0142 .0199

CL =

-4535

CD

q

.0684

au=

.2001

c11=

..2535

CDU=

.0223

CDL=

.0461

L/D=

6.629

L/D

18

INITL= ETADR= DELTA

CP ,

I

ETASPN .oooo

LINEAR CPU

: f:;: .4919

-.1771 -.u7a -.1963 -.2015 -.2004 -.2232 -.2573 -.2694 -.27a8 -.2a9i -:3006 -.3126 -.3219

:EZ .a486 .8780 .9048 .9286 .9493 .9666 : Kf .9976 1.0000 I

PLATE

::::f; -.iia2 -.1207

:%i .7460

ETASPN

.1495

CL(EiADR)=

.0500 .lOOO .1501 .2000 .2498 .2994 .3486

: Z! .6257

L/D

LOWER

q

5.4964

IFINL= 42

.750 FLAT

8.972

UPPER =

I: :gf -.1427 1::;;;

DCP , CPL

a2337 .2339 .2346 .2358 .2375 .2397 .2422 .2448 .2472 .2493 .2511

F;;%;;

:Eff .2544 .2549 .2559 .2582 .2623 .2686 ;2772 .2sao .2996 .3103 .3197

1:;;;; -.2203 .0035

: :3:: .4033 .4342 .0035

CPU

CPL

CD(ETADR)=

AND SPANLOAD DELTACP

.0156

DISTRIBUTION DCPLIN

CCL/CA

.2aa7 .2891

.7012

.3506 .3511 .3529 .3565 .3628 .3722 .3a49 .3996 .4140 .4270 .4319 .4419 .4552 .4548 .47a1 .5133 .5276 .5411 .5577 .577a .6005 .6216 .6349 .6425 .6534 .6748 .7099 .6545 0.0000

:%; 2:1521 4.1294 0.0000

.6975 .6926 .6856 .6757 .6570 .6351 .6094 .5802 .5484 .5145 .4795 .4440 .4092 .3743 .u3372 .2990 .2615 .2248 .1891 .1548 .1223 .0924 .0660 .0435 .0250 .0106 .0016 0.0000

DELTACP

DCPLIN

cc L/CA

.2902 .2920 .2947 .2982 .3026 .3080 .3146 .3224 .3316 .3425 .3552 .3701 .3a7a .4086 .4335 .4636 .5002 .5457 .6032 .6780 .7782 .9183

.0699 .0381 .0142

.1577 .0793 .oooo

:-:z: 1:1919

1.1868 1.1907 1.1919

16.9786 31.2413 84.1924

OF PRESSURES

MODIFICATION

MCON 1.37281 1.37261 1.37192 1.37073 1.36903

1'.36687 1.36443 1.36200 1.35984 1.35797 1.35636 1.35509 1.35423 1.35373 1.35322

1.35191 1.34904 1.34420 1.33734 1.32846 1.31807 1.30823 1.30024 1.29246 1.28074 1.25716 1.20739 1.20150 1.61565 1.96022 2.15899

NUCON

.14325 .14315 .14281 .14221 .14137 -14030 .13909 .I3789 : EXS : E879 .13405 .13380 : EE .13149 .12911 : :I::: : ::t::

.10781 .10410 : K%

2,19970 2.20154 2.20389 2.20912 2.20132 2.17504 2.14290 2.11348 2.08811 2.06586 2.03820 1.96594 1.92165 1.92377 1.91404 1.89847 1.88047 1.86139 1.84099 1.82107 1.80472 1.79323 1.78619 1.78243 1.78075 1.78031

: KE .26744 .44117 .53515 .55370 .55453 .55560 .55796 .55443 .54249 -52775 .51413 .50227 .49181 .47869 .44395 .42232 .42336 .41858 .41090 .40199 .39251 .38232 .37233 .36410 .35831 .35474 .35284 .35199 -35177

MCON

NUCON

TO ACCOUNT

YIN -.ooooo .54348 1.08644 1.62821 2.16809 2.70514 3.23809 3.76527 4.28474 4.79480 5.29376 5.77985 6.25135 6.70657 7.14383 7.56151 7.95781 8.33075 8.67827 8.99827 9.28871 9.54755 9.77304 9.96424 10.12055 10.24166 10.32735 10.37540 10.38560 10.36018 10.29171 10.18400 10.03923 9.85887 9.64427 9.39683 9.11869 8.81273 8.48092 8.12516 7.74731 7.34919 6.93251 6.49869 6.04916 5.58543 5.10904 4.62161 4.12484 3.62021 3.10950 2.59463 2.07721 1.55841 1.03896 .51936 .ooooo YIN

FOR NON-CONICAL

DNY -.16186 -.16549 -.17451 -.18108 -.17544 -.15299 -.11481 -.06531

-.01459 : EE .08935 : ::A53 -13668 .13840 .13495 .12987 : :;:5: .12568 .14293 .15779 : :2::: -05575 -.16695 -.62860 -.38400 .65084 .46471 .37587 .31313 .27212 .23800 .20630 .19257

GEOMETRY

DNZ

.98572 .98518 .98370 : Et: : Kl : E:; .99668 : ;264: : Et: .98531 : EE -98691 .98753 : 8Ei : %%49 .98141 .98679 .99562 : ES .20780 .59830 .83246 .89387 : E: .95975 : ;::::

: :Xi

: ;:56043

: :K .17487

:X

: ::i:: : KE : ES1 -.02459 -.07698 -.12507 -.16114 -.18203 -.18762 -.18268

-.17577 -.17358 DNY

: EE .98659 .99056 : ;z .99945

DNX -.04639 -.04519 -.04324 -.04121 -.04054 -.04231 -.04791 -.05732 -.06791 -.07731 -.08579 -.09293 -.09799 -.10140 -.10242 -.10156 -.09876 -.09555 -.09363 -.09257 -.09361 -.10393 -.11301 -.11164

-SO9384 -.04467 .10139 .40433 .24799 -.42292 -.30126 -.24233 -.20007 -.17173 -.14801 -.12673 -.11624 -.11167 -.10634 -.10150 -.09491 -.08738 -.07816 -.06763 ::gg;': -.02825 -.01355

: iZ%

:X9

: ;E

: iEE .04095 .04315

: ;x:5; -98218 : ;274: DNZ

: K% .04629 DNX

CPP

.23372 .23394 .23469 .23599 .23784 .24019 .24287 .24553 .24790 .24996 .25175 .25314 .25410 .25465 .25522 .25667 .25986 .26527 .27297 .28303 .29490 .30626 .31558 .32471 .33861 .36703 .42908 .43659 -:EE -.30667 -.32134 -.32198 -.32280 -.32460 -.32190 -.31256 -.30061 -.28914 -.27883 -.26944 -.25732 -.22318 -.20035 -.20148 -.19628 -.18780 -.17776 -.16683 -.15479 -.14270 -.13252 -.12522 -.12069 -.11825 -.11716 -.11687 CPP

CPNC

DELMCH

DELNUD

.11099 .11326 .11649

.12074

.12032 .12468 .13043

: :::2 .11303 .11020 .10641

: EE .14833

: ES .09519

: :z

: oO:::t .08153 .07524 .06877 .06397 .06074

3.50765 3.44287 3.36312 3.27910 3.19441 3.08112 2.97195 2.87275 2.74601 2.63771 2.50864 2.34336 2.15976 1.97138 1.83192 1.73756 1.67134 1.63335 1.62366 1.62233 1.64745 1.65845 1.66811 1.65641 1.57467 1.45973 1.32289 1.25731 1.14905 .73396 -.58705 -.44300 -.27636 -.10080 .07594 .22053 .36877 .51567 .69247 -94246 1.22598 1.52788 1.79863 2.01482 2.18191 2.33554 2.48655 2.64197 2.77972 2.89850 3.01757 3.11440 3.19509 3.28324 3.36194 3.43355 3.50743

:X : ::E .19137 .19668 .20302 .21045 .21972 .22963 .23957 .24767 .25642 .27229 .30283 .36493 .37473 -.02735 -.23334 -.29825 -.31531 -.31824 -.32144 -.32561 -.32485 -.31764 -.30797 -.29934 -.29306 -.28835 -.28154 -.25416 -.23684 -.24074 -.23867 -.23366 -.22742 -.22016 -.21168 -.20325 -.19615 -.19132 -.18908 -.18849 -.18894 -.19012 CPNC

: OOE : K:: .05851 .05920 : E% : ZE .05150 : KE -: Et63 -.01703 -.01064 -.00389 :K :X : KY : KG : KE : K57363 : E3 -09852 .10228 .10604 10908 :111aa :::;ii : E3X DELMCH

DELNUD

DELTA

CP.FROM

NON CONICAL

CORRECTION

CPU

ETASPN

CPL

.lllO .1132

-.1901

.oooo

.0500 .lOOO .1501 .2000 .2498

: 5492 .3972 .4450 .4919 .5378 .5825 .6257 .6675 .7P76 .7460 .7823 .8166 .8486 .8780 .9048 .9286 .9493 .9666 .9806 .9910 .9976 1.0000

DELTACP .3011 .3021

-.1889 -.1885 -.1891 -.1913 -.1961 -.2032 -.2117 -.2202 -.2274 -.2337 -.2387 -.2407 -.2368 -.2542 -.2815 -.2884 -.2931 -.2993 -.3080 -.3176 -.3248 -.3256 -.3214 -.3182 -.3153 -.2983 1:;;;;

:EJ .1709 .1779 .1840 .1890 .1939 .1995 -2062 .2143 .2238 .2338 .2430 .2516 .2640 .2883 .3391 .3716 -.0274

: 3iZ: .3794 .3913 .4027 .4117 .4148 .4382 .4705 .4822 .4926 .5056 .5223 .5415 .5586 .5687 .5730 .5823 .6036 .6374 .6050 0.0000

CPU

CPL

DELTACP

ETASPN

:::"9; .1239 .1292 .1349 : :t:: .1520

.3047 .3089 : 3:5543 .3332

NON-CONICAL FORCE RESULTS .4102

CN=

PURE CONICAL FORCE COEFFICIENT

CN (FROH DELTA CP 1 = SPAN E=

CL=

.45353

CD=

.06841

CN=

.45784

A=

.6612

.4595

RESULTS

CN (FROH SPANLOAD) =,

.a774

EHINF= 1.6200

CA; -.02737

ALP=12.0000

JOBN COREL ANALYSIS FINISHED

.4595

GRUMMAN W12/SC3

SEPT

PROGRAH

LIST

OF INPUT

1980

CARDS

GRUMMAN PROGRAM

0O000OOO0111111111122222222223333333333444444444455555555556666666666?7777777778 1234567890123456789012345678901234567890123456789012345678901234567890123456789O SC3 0

DEMO 1 0

53:159 1:%4

WING ALONE FOR COMBINED ANALYSIS 0 0 0 02030 0 147 o 586 1 317 2 338 3.645

58:011 17'231

20'391 62:986

-0.0000 1.6587 0.0 0.7735-~'~656~~%~~ 3.3171 1.5471-0:272320:8338 4.9747 2.3206-0.334119.3317 6.6296 3.0941-0.361617.8324 8.2770 3.8676-0.363716.3413 9.9051 4.6412-0.348414.8714 11.4905 5.4147-0.323313.4495 13.0004 6.1882-0.295512.1174 14.4103 6.9617-0.278110.9170 15.7249 7.7353-0.2864 16.9739 8.5088-0.2616 18.1883 9.2823-0.2386 19.387910.0558-0.2230 20.581910.8294-0.2179 21.773911.6029-0.2164 22.965312.3764-0.2192 24.156613.1499-0.2286 25.357313.9235-0.2459 27.500014.6970-0.1566 "3

68:070 23'784

73:247 27'400

78:503 31 230

DESIGN-CRAIDON 5.235 83:822 35 261

7.102 89.188 39.483

GEOMETRY 9.242 11.649 43.881 48.445 94.586100.000

9.8687 8.9614 8.1602 7.4225 6.7156 6.0212 5.3313 4.6430 3.9456 2.3063

0.0000

0.0

:::

::i

El

ki

::i

1::

21

:-: 0'2780 0'0085 0:2995

2: 0'2857 0'0310 0:2995

if!615 0'2908 0:2993

i'i962 0'2942 0:2992

it!328 0'2963 0:2990

i-f684 0'2977 0:2989

00~~006 0'2986 0:2987

is:279 0'2991 0:2986

k::! 0'2994 0:2986

'::662 1.5461 0.0 0.3834 ;.;250

00'4037 0073 0:5480 0.0063 0.4344 0.0055 0.7360

00'4365 0281 0:5488 0.0247 0.4827 0.0214 0.7436

00'4647 0593 0:5488 0.0533 0..5276 0.0469 0.7484

0 0972 0'4880 0:5482 0.0898 0.5685 0.0802 0.7511

00'5061 1396 0:5473 0.1317 0.6054 0.1196 0.7521

00'5200 1851 0:5462 0.1777 0.6381 0.1634 0.7521

0 5302 0.2323 0:5451 0.2269 0.6669 0.2109 0.7517

0.2793 0 5377 0:5442 0.2784 0.6909 0.2613 0.7509

0.3245 0 5428 0:5433 0.3310 0.7101 0.3140 0.7500

0:3684 ;.;262

0.4235 0.8516 0.0047

0.4784 0.8715 0.0185

0.5321 0.8865 0.0409

0.5838 0.8974 0.0706

0.6329 0.9050 0.1064

0.6788 0.9104 0.1470

0.7214 0.9142 0.1913

0.7603 0.2388 0.9167

0.7953 0.2889 0.9181

.O ::665 .2995

0:3415

0.3959

0.4516

0.5081

0.5645

0.6202

0.6744

0.7265

0.7757

0.8212

;.;a25 0:3115

0.8993 0.0041 0.3633

0.9315 0.0160 0.4172

0.9589 0.0355 0.4729

0.9810 0.0618 0.5300

0.9989 0.0939 0.5877

0.1308 1.0135 0.6453

1.0251 0.1715 0.7019

1.0344 0.2155 0.7564

1.0416 0.2622 0.8080

;.:559 0:2832 0.8193

0.8996 0.0035 0.3317 0.8665

0.9390 0.0140 0.3826 0.9101

0.9740 0.0310 0.4357 0.9505

1.0053 0.0542 0.4907 0.9881

1.0337 0.0829 0.5470 1.0230

1.0590 0.1162 0.6038 1.0552

0.1535 1.0807 0.6603 1.0848

1.0992 0.1940 0.7156 1.1119

0.2373 1.1149 0.7689 1.1367

W12SC3 STARTS

0 0031 :-i580 0'3029 0:7633 a:8109 -----I::423 i-iii& 0:2832

0.0123 0 0275 0 0482 0 0739 0.1041 0.1382 0.1755 0.2155 0'3500 0'3992 0'4502 0'5026 0 5557 0 6090 0 6618 0 7134 0:8565 0:9003 0:9421 0:9816 1:0189 1:0539 1:0866 A:1170 0902 00:5601 1235 0.6086 0.1613 B.2015 6.6566 0636 00:5116 0:3260 0 0105 i0:3704 0235 00:4163 0413 00:4635

0.1057 iI; 0.7505 0.0031 0.7966 0.0123 0.0276 0.8417 0.8855 0.0487 0.0750 0.9277 0.9683 0.2507 0.2876 0.3257 0.3650 0.4056 0.4472 0.4897 0.9274 0.0950 0.0443 0.0677 0.8855 iI; ft.0029 0.7093 0.0114 0.7987 ____-- 0.8425 -.-...~... ___ ______ 0.7541 ___--. 0.0253 0.2257 0.2593 0.2926 0.3270 0.3622 6.3983 0.4351 0.5942 0.6361 0.6785 0.7209 0.7632 0.8051 0.8463

0.1396 1.0070 0.5327 0.1253 0.9679 0.4731 0.8868

1.0438 0.1758 0.5760 0.1578 1.0069 0.5125 0.9262

1.0786 0.2132 0.6199 0.1916 1.0444 0.5529 0.9644

0 4192 00.1384 4549 0.1685 0 4917 3847 0.1096 0386 00'3514 0590 00.0830 i-i992 00'2295 0025 00'2590 0099 00'2885 0220 00'3193 0:5294 0:5678 0:6068 0:6462 0:685-r 0:7253 0:7645 0:8034 0:8416 0:8790 !:!734

0.3753 0.1193 0.4074 0.1458 0.4405 0.3441 0.0942 0330 0.0506 0.3139 0.0712 00:2015 0021 00:2294 0085 00:2568 0188 00:2848

;.:744 iii561

0.5090 0.0073 0.0018 0.5443 0.5800 0.0163 0.6161 0.0287 0.6523 0.0442 0.1824 6.208s 0.2351 0.2608 0.2871 0.0253 0.5563 0.0390 ;I;302 0.4610 0.0016 0.0064 0.0144 ___ ______ 0.4923 ___-_. 0.5241 -.--.. ..._.~ 0.5887 ~~~~ 0.1396 0.1638 0.1885 0.2132 0.2375 0.2613 0.3876 0.4145 0.4419 0.4696 0.4977 0.5260

0.6886 0.0624 0.3142 0.6213 0.0552 ~~ 0.2854 0.5545

0.7247 0.0832 0.3420 0.6538 0.0738 0.3101 0.5831

0.7605 0.1060 0.3707 0.6863 0.0942 0.3354 0.6117

0.7958 0.1304 0.4001 0.1163 0.7185 0.3612 0.6401

0 0124 0'1894 0:4154 0 0105 0'1643 0:3620 0.0085 0.1365

00'2120 0219 0:4394 0 0185 0'1847 0:3821 0.0151 0.1543

0 0338 0'2344 0:4636 0 0287 0'2051 0:4024 0.0233 0.1723

00.0480 2561 0:4879 0.0408 0 2252 0:4227 0.0332 0.1905

0.0642 0 2777 0:5124 0.0547 0 2449 0:4431 0.0446 0.2085

00.0822 2997 0:5368 0.0702 0 2639 0:4634 0.0574 0.2262

0 3221 0.1018 0:5612 0.0871 0 2831 0:4837 0.0714 0.2434

;:;597 0.2760 0.0004 0.0016 0.0036 ___ _._... 0.2924 ..-- 0.3088 ..~. 0.0389 0.0467 0.0551 0.0640 0.1555 0.1444 0.1533 0.1624 0 1866 0 3670 0 5412 :-:517 1'6588 1'7539 1'8357 1:9002 1:8141 1:6990 1:5539 ii0 0.2168 0.4199 0.6094 1.5912 1.6873 1.7727 1.8466 1.9002 1.8141 1.6990 1.5539

0.3253 0.0064 ~~~ 0.0734 0.1715 0 7088 1'9029 1:3781 0.7856 1.9081 1.3781

0.3419 0.0100 6.0833 0.1806 0.8696 1 9538 1:1712 0.9490 1.9555 1.1712

0.3584 0.0144 0.0936 0.1898 1.0230 1 9867 0:9333 1.1001 1.9870 0.9333

0.3749 0.0195 0.1043 0.1990 1.1685 1 9998 0:6649 1.2393 1.9998 0.6649

0.3914 0.0253 0.1154 0.2082 1.3057 1 9912 0:3668 1.3674 1.9912 0.3668

0.4078 0.0318 0.1267 0.2173 1.4337 1 9587 0:0400 1.4845 1.9587 0.0400

1.9998 1.9912 1.3012 1.4212 1.4672 1.3540 0.6649 ~~ 0.3668 1.9998 1.9912 0.6649 0.3668

1.5290 1.9587 1.5669 0.0400 1.9587 0.0400

i-:226 00'1444 0014 0:3449 0:3681 0 0012 i-f052 0'1243 a:3025 013221 0.0010 0.0 iI.i1864 0.1024

0'1667 0 0056 0:3916 0 0047 0'1441 a:3420 0.0038 0.1192

1.1674 0184 1.9872 01:7122 2432 01:7891 4660 01:8561 6689 01:9126 8527 11:9571 1.2249 0.9099 1.0776 ;:a9002 0.2657 1.8141 0.5054 0.7197 - 0.9333 - -~ ___ _.-_-. 1.6990 _.-_-. 1.5539 _.___. 1.3781 _..-.. 1.1712 1.6551 1.7335 1.8031 1.8642 1.9165 1.9584 1.9874 1.9002 1.8141 1.6990 1.5539 1.3781 1.1712 0.9333

!::257

9876 11.3978 9998 11.5054 9912 1.5984 1 9587 i-:795 01'7511 2844 01'8147 5381 01'8710 7619 01'9198 9574 11'9596 1268 11.2726 1:9002 1:8141 1:6990 1:5539 1:3781 1:1712 0:9333 0:6649 0:3668 0:0400 9878 1.4325 1 9998 11.5357 9912 1.6234 1 9587 f-:989 01'7651 2993 01'8239 5640 01'8763 7954 01'9223 9951 11'9604 1658 11.3104 1:9002 1:8141 I:6990 1:5539 1:3781 1:1712 0:9333 0:6649 0:3668 0:0400 1.9879 1.4583 1.9998 01:7755 3103 01:8307 5833 01:8803 8202 11:9242 0231 11:9611 1947 1.3385 1.3568 0.9333 1.4751 1.3781 1.2135 1.1712 LiOO2 1.8141 0.3174 0.5958 0.8363 - ~~~~ 0.6649 ___ __--. 1.6990 _.-_-- 1.5539 __--.- 1.0412 -...--.--.1.7226 1.7822 1.8351 1.8829 1.9255 1.9615 1.9879 1.9998 1.9002 1.8141 1.6990 1.5539 1.3781 1.1712 0.9333 0.6649

::;133

1.9912 1.5581 0.3668 1.5727 1.9912 0.3668

1.9587 1.6419 0.0400 1.6539 1.9587 0.0400

0.0 1.7269 1.9002

0.3207 1.7853 1.8141

0.6016 1.8372 1.6990

0.8438 1.8841 1.5539

1.0496 1.9260 1.3781

1.2222 1.9617 1.1712

:-$73 I:9002

01'7855 3210 1:8141

01'8373 6020

01'8841 8443

11'9261 0503

1 9617 1.3658 1.2229 1 9880 1.4834 1 9998 1.5800 1 9912 1.6599 1 9587

1.8141

1.6990

1.5539

1.3781

1.1712

,,0 ..o 1.7273 1.9002

1:6990 0.6020 1.8373

0.3210 1.7855

1:5539 0.8443 1.8841

1:3781 1.0503 1.9261

1.3652 1.9880 0.9333

1:1712 1.2229 1.9617

0:9333 1.3658 1.9880 0.9333

1.4828 1.9998 0.6649

0:6649 1.4834 1.9998 0.6649

l..5795 1.9912 0.3668

1.6595 1.9587 0.0400

0:3668 1.5800 1.9912

0:0400 1.6599 1.9587

0.3668

0.0400

1 9261 1.2229 1.0503 1 9617 1.3658 1 9880 1.4834 1 9998 1.5800 1 9912 1.6599 1 9587

:'!273

01'7855 3210

0:9333

0:6649

0:3668

0:0400

k!273

01:7855 3210 01:8373 6020 01:8841 8443 11:9261 0503 11:9617 2229 1.3658 1.9880

1.9998 1.4834

1.9912 1.5800

1.9587 1.6599

;.;002

1:7273 1.9002

1.8141 0.3210 1.7855 1.8141

0.6649 1.4834 1.9998 0.6649

1.5800 0.3668 1.9912 0.3668

0.0400 1.6599 1.9587 0.0400

f-i273

01'7855 3210 01'8373 6020 01'8841 8443 11'9261 0503 11'9617 2229 1.3658 1 9880 1.4834 1 9998 1.5800 1 9912 1.6599 1 9587 1:8141

1:6990

1:5539

1:3781

::;273

1:7855 0 3210

01:8373 6020

01:8841 8443

11:9261 0503 11:9617 2229 11:9880 3658 11:9998 4834 1.5800 1.9912

1.9587 1.6599

i.09002

0.3210 1.8141

1.6990 0.6020 1.8373 1.6990

1.5539 0.8443 1.8841 1.5539

1.3781 1.0503 1.9261 1.3781

0.0400 1.6599 1.9587 0.0400

I:9002

1:9002

01'8373 6020

1:8141

1:6990

0.6020 1.6990 1.8373 1.6990

01'8841 8443

1:5539

0.8443 1.5539 1.8841 1.5539

1:3781

1.0503 1.3781 1.9261 1.3781

1:1712

1.2229 1.1712 1.9617 1.1712

0.9333 1.3658 1.9880 0.9333

1:1712

0:9333

1.1712 1.2229 1.9617 1.1712

0.9333 1.3658 1.9880 0.9333

0:6649

0.6649 1.4834 1.9998 0.6649

0:3668

0:0400

0.3668 1.5800 1.9912 0.3668

1:7273 1.9002

1.7855 I.8141

:+273

3210 01'8373 01'7855 6020 01'8841 8443 11'9261 0503 1'9617 1 2229 11'9880 3658 11'9998 4834 1.5800 1 9912 1.6599 1 9587

1:9002

i-i273

1:8141 01'7855 3210

1:6990 01'8373 6020

1:5539 01'8841 8443

1:3781 1:1712 0:9333 0:6649 0:3668 0:0400 1 0503 11'9617 1'9261 2229 11'9880 3658 1'9998 1 4834 11'9912 5800 11'9587 6599

1:9002 0.0 0.0000

1:8141 0.0000 0.0000

1:6990 0.0000 0.0000

1:5539 0.0000 0.0000

1:3781 0.0000 0.0000

1

3

171.05 0.1224 0.3967

0

0

0

14.697 0.1705 0.3967

0

I:1712 0.0000 0.0000

0:9333 0.0000 0.0000 0.0000

0.00 10.00 20.00 100.00 0.0 1.4697 2.9394

t :'iOSS 0:3967

ki:: 0:3967

O"ii91 0:3967

4.4091

5.8788

7.3485

8.818210.287911.757613.2273

30.00

40.00

50.00

60.00

0 3874 0:3967

70.00

N~~TNS=3,XSTN~1~=15.5,XSTN~2~=19.9,XSTN~3~=24.4,X~~E~=3~~07,

0 Qrk-0.0000 .4000 0.0000 M-1.62, ALPHA=12.0 , AZ=33.00 .750000 29.000000 56.999999 .oooooo -301115 2A .050007 Xll,"OR .100039 -304694 7)DR -150055 .308909 --. .200009 .315267 .249fl'9 I--I .325394 .29! ?405 .338177 .34i $580 .352118 ““_I

0:0400 0.0000 a.0000 o.o-

0.0 0.2650 0.3967

l&697 -.--_ IIN XLAMDA=57.O.NOPT(1)=2.NOPT(2)=-3.NOPT(4)=2.NOPT~5~=1. SAERO-.. ..-....-.. _. .._.._ .-. -_... ..-. ._ _.

.

0:3668 0.0000 0.0000 0.0000

lST4LETTERSMUSTBEAERO

ollll

14.747 0.2189 0.3967

0:6649 0.0000 0.0000 0.0000

CRAIDONDATASE

0 3960 0:3967

W12SC3DATASET

0 3967 0:OOOO

80.00

90.00

/

ENDMUSTBE

INCOL.3-5

XSTN=19.90

3.907000 \7

0.000000

I”

ORIGINOF DIVIDING RAY

_II OUTPUTFROM CORELRUN, q AND AC,.

AC, ISFROMNONCONICALCORR

;ECTlON

.T

.397169 .445002 .491935 : ZE .625741 .667512 .707633

:if853; :30’E59 :%SSf :ffZi .4822ii :fEE .522309

.904794 : EXf .966649 .9805aa i990960 .997553 1.000000

: Zdfi .568655 : E; .603604 %ZZ 0.000000

00000000011111111112222222222333333333344444444445555555555666666666677777777778 12345678901234567890123456789012345678901234567890123456789012345678901234567890

WING PANEL CORNER POINT COORDINATES 1 AND 3 INDICATE WING PANEL LEADING-EDGE X

0.00000

Y

1

2.38401 4.76802 7.15203 9.53604 11.92005 14.30406 16.68807 19.07208 21.45609 3.15117 5.24959 7.34801 9.44643 11.54485 13.64326 15.74168 17.84010 19.93852 22.03693 6.29862 8.11185 9.92507 11.73830 13.55152 15.36475 17.17798 18.99120 20.80443 22.61765 9.41663 10.94787 12.47911 14.01035 15.54159 17.07283 18.60407 20.13531 21.66655 23.19780 12.39644 13.66146 14.92649 16.19151 17.45654 18.72156 19.98658 21.25161 22.51663 23.78166 15.06760 16.10689 17.14617

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

Z

1'

1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 7.34850 7.34850 7.34850

1

X

Y

2 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

-.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -a35299 -.35299 -.35299 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.28225 -.28225 -.28225

POINTS, 2 AND 4 INDICATE TRAILING-EDGE POINTS

18.99120 20.80443 22.61765 24.43088 10.94787 12.47911 14.01035 15.54159 17.07283 18.60407 20.13531 21.66655 23.19780 24.72904 13.66146 14.92649 16.19151 17.45654 18.72156 19.98658 21.25161 22.51663 23.78166 25.04668 16.10689 17.14617 18.18546

Z

2

1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 7.34850 7.34850 7.34850

2

X

3

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

-.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.352$9 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.28225 -.28225 -.28225

20.80443 22.61765 9.41663 10.94787 i2.479il 14.01035 15.54159 17.07283 18.60407 20.13531 21.66655 23.19780 12.39644 13.66146 14.92649 16.19151 17.45654 18.72156 19.98658 21.25161 22.51663 23.78166 15.06760 16.10689 17.14617 18.18546 19.22474 20.26403 21.30331 22.34260 23.38188 24.42117 17.45966 18.32375 19.18784

Y

3

1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 i.46970 1.46970 1.46970 1.46970 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 8.81820 8.81820 8.81820

Z

-.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 I:;;;;; -.25240 -.25240 -.25240

3

X

4

5.24959 7.34801 9.44643 11.54485 13.64326 15.74168 17.84010 19.93852 22.03693 24.13535 8.11185 9.92507 11.73830 13.55152 15.36475 17.17798 18.99120 20.80443 22.61765 24.43088 10.94787 12.47911 14.01035 15.54159 17.07283 18.60407 20.13531 21.66655 23.19780 24.:..'14 13.6~~46 14.92649 16.19151 17.45654 18.72156 19.98658 21.25161 22.51663 23.78166 25.04668 16.10689 17.14617 18.18546 19.22474 20.26403 21.30331 22.34260 23.38188 24.42117 25.46045 18.32375 19.18784 20.05194

Y

4

1.46970 :::f;Z 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 1.46970 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 2.93940 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 4.40910 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 5.87880 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 8.81820 8.81820 8.81820

Z

4

I:;f;8; -.26162 -.26162 -..26162 -.26162 -.26162 -.26162 -.26162 -.26162 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35610 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.35299 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.30662 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.25240 -.25240 -.25240

18.18546 19.22474 20.26403

18.32375 19.18784

24.37240

7.34850 7.34850 8.81820 8.81820 8.81820 t-X:Xfi 8:81820 8.81820 8.81820 8.81820 8.81820 :~%;~ lo:28790 10.28790 10.28790

24.07238 24.79342 X% 22:01218 22.60050 23.18882

26.71876 27.30708 24.27673

11.75760 11.75760 11.75760 11.75760 13.22730

KIZ 13:22730 13.22730 EEZ 13.22730 27102067 13.22730 27.47799 13.22730 27.93531 13.22730 28.39263 13.22730 ~45-:E~ 25:64870

-.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 1:;;;;; -.25240 1:;;;;; -.25240 -.25240 -.25240 -.25240 -.25240 -.22147 -.22147 -.22147 -.22147 ::g:;; 1:;;:;: -.22147 -.22147 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 1:;:;;; -.21696 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033

7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 7.34850 8.81820 E8~E 19:18784 8.81820 8.81820 20.05194 8.81820 8.81820 %EE 8.81820 22:64421 8.81820 s:* %43i 8.81820 8.81820 25:23649 8.81820 Z: :aOS:! 10.28790 21.18821 10.28790 21.90925 10.28790 22.63030 10.28790 10.28790 10.28790 5x3: ;: : ;;%I;; 10.28790 10.28790 26:23550 10.28790 26.95654 10.28790 22.60050 11.75760 23.18882 11.75760 23.77715 11.75760 24.36547 11.75760 24.95379 11.75760 25.54211 11.75760 26.13043 11.75760 26.71876 11.75760 27.30708 11.75760 27.89540 24.73405 ::-3zl 13122730 13.22730 I55%3: 26:10602 13.22730 26.56334 13.22730 27402067 13.22730 27.47799 13.22730 27.93531 13.22730 19.22474

93:X

:E:;i

-.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.28225 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033

20.05194 20.91603 21.78012 55%~ 24:37240 f59%~S 20:46717 21.18821 21.90925 22.63030 23.35134 24.07238 24.79342 25.51446 26.23550 22.01218 22.60050 23.18882 23.77715 24.36547 24.95379 25.54211 26.13043 26.71876 27.30708 24.27673 24.73405 25.19138 25.64870 26.10602 26.56334 27.02067 27.47799 27.93531 K% 27:73063 27.96126 28.19189 28.42252 28.65315 28.88378 29.11441 29.34504 29.57567

8.81820 8.81820 8.81820 8.81820 8.81820 8.81820 8.81820 10.28790 10.28790 10.28790 10.28790 10.28790 10.28790 10.28790 10.28790 10.28790 :~*:E 11:75760 11.75760 11.75760 11.75760 il.75760 11.75760 11.75760 11.75760 ::-11% 13:22730 13.22730 13.22730 13.22730 13.22730 13.22730 13.22730 13.22730 13.22730 14.69700 14.69700 14.69700 14.69700 14.69700 14.69700 14.69700 14.69700 14.69700 14.69700

-.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.25240 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.22147 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.21696 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.15660 -.15660 -.15660 -.15660 -.15660 -.15660 -.I5660 -.15660 -.15660 -.15660

a.81820

22.64421 23.50830 24.37240 25.23649 I8-tz 21:18821 f:-E: 23:35134 24.07238 24.79342 25.51446 26.23550 26.95654 22.60050 23.18882 23.77715 24.36547 __._-24.95379 25.54211 26.13043 26.71876 27.30708 27.89540 24.73405 25.19138 25.64870 26.10602 26.56334 27.02067 IEZ ;; :;;;"9; 27:73063 27.96126 28.19189 28.42252 28.65315 28.88378 29.11441 29.34504 29.57567 29.80630

X%i

a:81820 t%XIi 8:81820

10.28790 10.28790

11.75760 11.75760 11.75760 11.75760 11.75760 11.75760 :3%: 13:22730 13.22730 13.22730 :E53! 13:22730 :~%:El 14:69700 14.69700 14.69700 14.69700 ::%ii 14169700 XE~ 14:69700

1:;;;;; 1:;;;;; 1:;;;;; 1:;;:;; -.22147 I:;;:;; -.22147 -.22147 1:;;:;; -.22147 -.22147 -.21696 -.21696 -.21696 -.21696 -.21696 -.il696 1:;:;;; -.21696 -.21696 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 -.23033 1:;;;;; -.15660 -.15660 -.15660 1:;;;;;

WING PANEL EDGE POINTS ON CHORD PASSING THROUGH CENTROID,

X

CP

1.54212 3.78637 6.03062 8.27486 10.51911 12.76336 15.00760 17.25185 19.49610 21.74034 23.98459 4s%% a:60523 :1-zl 14:48309 :8'44::2 20:36095 22.32024 24.27952 7.81381 9.49000

Y

CP

24.57577

::%:: 13:66397 15.06632

16.46868 17.87103 19.27339

20.67575 22.07810 23.48046

CP

SLOPE TKTDACAMBER -.17617

:;:;I:

1: :g;;

:K -71924

:::;g; -.I2803

:EXt .71924 -71924

1::;;;;

::;;f;;

1::;;;;

I: g:;

:;:tt:

1::;;;;

1: :;t:; -.a6419 -.06419 -.06419

2.18669

::;g; 1:;;;;:

2.18669 2.18669 2.18669 2.18669 5-E%

3:65360 E% 3:65360

19.54718 21.22338 22.89957

Z

3%: 3:65360 3.65360 3.fEl 5:12063 5.12063 5.12063 5.12063

1:;;;;: -.30771 -.30771 -.30771 -.30771 -.30771 -.35459 -.35459 -.35459 I: ;;g; -.35459 -.35459 1: ;;g; 1:;;;;; 1:;;;;; -.33054 -.33054 1:;;;;; -.33054 -.33054

:3-K 14:84425 16.00009 17.15593

xt3 6:58965 6.58965 6.58965 6.58965

:;':tZX; 20:62345 21.77929 22.93513 24.09097

f %fZ 6:58965 6.58965 6.58965 6.58965

1:;;:;; -.33054 1:;;;;; 1:;;;;; -.29483 -.29483 -.29483 -.29483 ::;g;;

AND INCLINATION

I::;f:; 1: :;;:;

I: :g;:; -.06419 -.06419 -.06419 -.06419 -.06419 -.06419 .00212 .00212 .00212 .00212 .00212 : %:I : OR .00212 .00212 .03154 : Kt .03154 .03154 .03154 .03154 .03154 .03154 .03154 .03154 .01658 .01658 .01658 .01658 .01658 .01658 .01658 .01658 .01658 .01658

.24757 .04066 .00836 .00204 .00060

.OOOll

.00003 -.00007 -.00007 -.00012 .00004 .22607 -11128 -06991 .04366 -02720 .oi483 .00694 .00234 -.00007 -.00070 -.00089 .20064 .I2746 .I0248 .083oi .06598 .05oia .03549

: ::3t: .00908 .00526 .18141 .13367 .I1637 .10546 .09215 .07651 .06129 .04951 .04101 .03315 .02683 .16756 .14700 : :z ::%Z .08084 .07283 .06498 .05773

ANGLES

THICKNESS SLOPE .22476 .05069 .02517 .01160

-.00001

-.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .24992 .04370 .02078 .OlB40

-.00001

-.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .26777 .03874 .01769 .00954 -.00002 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293 -27824 -03582 .oi587 .00903 -.00002 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .28155 .03489 .01532 .00888 -.00003 -.01151 -.02260 -.03327 -.04356 -.05342

THETA DEG -10.09362 -10.09362 -10.09362 -iO.O9362 -10.09362 -10.09362 -10.09362 -10.09362 -10.09362 -10.09362 -10.09362 -3.67804 -3.67804 -3.67804 -3.67804

-3.67804 -3.67804 I;-f;;it :12123 .12123 : EE -12123 .12123 .12123 : :I:33 :KX3 :-xx i:ao714 ;.a;'l;. 1:80714

1.80714 1.80714 1.80714

11%:: : 8% : K; -94997 -94997 .94997 .94997 .94997 .94997

25.24681 16.22693 17.18131 18.13569 19.09006 20.04444 20.99881 21.95319 22.90757 23.86194 24.81632 25.77069 18.56850 19.36322 HXXsgd ;p;;; 23:33681 AXE 25:72097 I8-E879 21:49780 fEX 23:46857 24.12549 24.78242 25.43934 26.09626 26.75319 27.41011 23.09717 23.62273 24.14829 24.67384 25.19940 25.72496 26.25052 26.77607 IXif 28:35275 25.71135 It%:;: ;p;;;; 27 149348 27.84990 28.20633 28.56275 28.91918 29.27560

6.58965 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 :!-88;8I 12:46176 12.46176 12.46176 12.46176 12.46176 12.46176 12.46176 12.46176 12.46176 12.46176 12.46176 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143

-.29483 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.21929 -.21929 -.21929 -.21929 -.21929 -.21929 -.21929 -.21929 -.21929 -.21929 -.il929 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751 -.19751

.01658 .02031 .02031 .02031 .02031 .02031 .02031 .02031 .02031 .02031 .02031 .02031 .02104 .02104 .02104 .02104 .02104 .02104 .02104 .02104 .02104 .02104 .02104 .00307 .00307 .00307 .00307 .00307 .00307 .00307 .00307 .00307 .00307 .00307 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 -.00910 .05013 .05013 .05013 .05013 .05013 .05013 .05013 -05013 .05013 .05013 .05013

.05104 .21703 .15970 .11822 .10738 .10063 .09681 .09308 .08834 .08323 .07774. .07234 .20328 .15367 .11183 .I0228 .09938 .09781 .09602 .09377 .09116 .08825 .08473 : :X .12246 .10188 .09720 .09473 .09327 .09219 .09095 .08952 .08773 .17826 .15366 .13000 .10887 .09458 .09069 .08841 .08665 .08534 .08463 .08399 .17521 .14852 .13272 .11784 .10374 .08835 .08389 .08100 .07904 .07786 .07665

-.06293 : :S%t .01531 .00886 -.00003 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .28166 .03486 .01531 .00886 -,00003 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .28166 .03486 .01531 .00886 -.00003 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293 .28166 .03486 .01531 .00886 -.00003 -.01151 -SO2260 -.03327 -.04356 -.05342 -.06293 .28166 .03486 .01531 .00886 -.00003 -.01151 -.02260 -.03327 -.04356 -.05342 -.06293

.94997 :':z: p; 1:16353 1.16353 1.16353 1.16353 1.16353 1.16353 1.16353 1.20562 1.20562 1.20562 :-fE 1:20562 1.20562 1.20562 1.20562 1.20562 1.20562 .17582 .17582 .17582 .17582 .17582 .17582 .17582 .17582 .17582 .17582 .17582 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 -.52125 2.87197 2.87197 2.87197 2.87197 2.87197 2.87197 2.87197 X-X3 2187197 2.87197

WING PANEL AREAS AND CHORDS AREA

3.34569 3.34569 3.34569 3.34569 3.34569 3.34569 3.34569 3.34569 3.34569 3.34569 2.88040 2.88040 2.88040 2.88040 2.88040 2.88040 2.88040 2.88040 2.88040 2.88040 2.45769 2.45769 2.45769 2.45769 2.45769 2.45769 2.45769 2.45769 2.45769 2.45769 2.05586 2.05586 2.05586 2.05586 2.05586 2.05586 2.05586 2.05586 2.05586 2.05586 1.69355 1.69355 1.69355 1.69355 1.69355 1.69355 1.69355 1.69355 1.69355 1.69355 1.39899 1.39899 1.39899 1.39899 1.39899 1.39899 1.39899

CHORD

2.24425 2.24425 2.24425 2.24425 2.24425 2.24425 2.24425 2.24425 2.24425 2.24425 1.95929 1.95929 1.95929 1.95929 1.95929 1.95929 1.95929 1.95929 1.95929 1.95929 1.67620 1.67620 1.67620 1.67620 1.67620 1.67620 1.67620 1.67620 1.67620 1.67620 1.40236 1.40236 1.40236 1.40236 1.40236 1.40236 1.40236 1.40236 1.40236 1.40236 1.15584 1.15584 1.15584 1.15584 1.15584 1.15584 1.15584 1.15584 :-:z4 :95438 .95438 .95438 .95438 .95438 .95438 .95438

:%x8::

.95438

1:39899 1.16509 1.16509 1.16509 1.16509 1.16509 1.16509 1.16509 1.16509 1.16509 1.16509 .9621.9 -96219

.96219 .96219 .96219 .96219 .96219 .96219 .96219 -96219 .76842 .76842 .76842 -76142 .76842 .76842 .76842 .76842 .76842 .76842 .50618 .50618 .50618 .50618 .50618 .50618 .50618 .50618 .50618 .50618

.95438 .95438 ..79472 .79472 .79472 .79472 .79472 .79472 .79472 .79472 .79472 .79472 .65692 .65692 .65692 .65692 .65692 .65692 .65692 .65692 -65692 .65692 .52556 .52556 .52556 .52556 : Xf ~52556 .52556 .52556 .52556 .35643 .35643 .35643 .35643 ::Z: : E9i .35643 .35643

ECHO OF W12 CONTROL BLOCK NAMELIST

SAEROIN

-3,

0, 2, 1, 0, 0, 0, 0, 0.

NOPT

= 2.

NXSTNS

= 3,

XSTN

= .155Et02. 0.0,

0.0,

XAPEX

= .3907E+Ol,

YAPEX

= 0.0,

XLAMDA

= .57E+02,

.199E+02,

.244Et02,

0.0,

0.0,

0.0,

0.0,

0.0,

SEND

1

IPART=

NWING=

100

NCPT=

10

NROWCN),N=lr

10

10

NCOLC:),N=l,

10

NSEG=

10

10

10

10

10

10

10

10

1

1

1

1

1

1

1

1

10

1

110

PARTITION = 5 TIHE = 214.94400 INFLUENCE OF WING ON WING

END OF AIC CALCULATIONS, TIME = 249.42000 NIODY=

0

1

NBBLOK=

IPART= NWING=

1 100

NROW(N),N=l,

10

NCPT=

10

10

NCOLCN)rN=l, 1 1

10

NWBLOK=

10

IPART=

2

NWING=

0

NWBLOK=

110

10

NSEG=

10

10

10

10

10

10

10

10

1

1

1

1

1

1

1

1

NCPT= 1

VELCMP, TIME = 249.77200

0

NSEG=

0

0.0,

0.0,

0.0,

0.0,

0.0,

0.0.

0.0,

0.0.

0.0,

0.0,

1st DEPARTURE WING/BODY

FROM

USSAERO

SOLUTION CONICAL CAHBER PANEL DESIGN

M-1.62,

INPUT

ALPHA=l2.0

XLAMLE 57.00000

FCCCC 29.00000 ETA “:%Z .10004

.15006 .20001 .24983 .29941 .34858 :X -49194 .53781 : EE .66751 .70763 .74597

: l%i .84855 .a7801 .90479 .92862 .94928 .96665 .98059 .99096 .99755 1.00000

, AZ=33.00

XSTN=l9.90

XORIGC

ETADR .75000

3.90700

YORIGC 0.00000

DCP .30112 .30210 : Z6919 .31527

.32539 .33818 .35212 .36654 .37938 .39126 .40267 .41166 .41476 .43818 .47052 .48221 .49259 .50557 .52231 .54146 .55863 .56866 .57304 .58228 .60360 .63736 .60497 0.00000

IF q<

PANEL :

;.A;;

3

10.40690 8:16265

2

12.65115 14.89539 17.13964 19.38389 21.62813 23.87238

i 9 10

.71;24 .71924 .71924 .71924 .71924 .71924 .71924 .71924 .71924 .71924

ETA

1.00000 .55063 .26025 .17039 .12666 .10079 .08370 -07156 .06250 .05547

PRESSURE .ooooo

?‘jDR, PRESSURE

THE PANEL. VALUE

OF

IS NOT SPECIFIED

IF r)> ?‘jDR,THE

AC, IS PRESCRIBED.

ON

INTERPOLATED

6.54797 8.50726 i6.34441 18.30370 20.26299 22.22227 24.18156

x: 934 25

f76 28 29 30

9.40619 11.08239 12.75859 14.43478 16.11098 17.78717 19.46337 21.13957 22.81576 24.49196

Xf8 2:18669

2.18669 2.18669 2.18669 2.18669 2.18669 I: X

x553::

3:65360 3.65360 3.65360

3'f~% 3165360 3.65360 3.65360

1.00000 .73196 .51333 .39527 .32136 .27073 .23389 .20587 .18385 .16608

.ooooo

1.00000 .78408 .63560 .53440 .46100 .40533 .36166 .32648 .29754 .27331

.ooooo .49324

12.19149 13.59385 14.99620 16.39856 17.80092 19.20327 20.60563 22.00799 25.41034 24.81270

5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.i2063 5.12063

:E’oi .71106

.57438 .50458

14.78646 15.94230

6.58965 6.58965 6.58965

.93269 .84312 .76924 -70727 ii.5454 .60912 .56960 .53490 .50418 .47680

:X .48885

:K .82010

.57074 .53970 .50741 .48948

:i-x 19:40982 20.56566 21.72150 22.87734 24.03318 25.18902 17.13359 18.08797 19.04234 19.99672 20.95110 21.90547 22.85985 23.81422 24.76860 25.72298

f:E 6.58965 6.58965 6.58965 6.58965 6.58965 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080

.63123 .i6?52 .51549 .47220 .43562 .40429 .37717

.77146 .72826 .68965 .65492 .62352 .59500 .56897

19.32349 20.11821 20.91292 21.70764 22.50236 23.29708 24.09180 24.88651 25.68123 26.47595 21.46495 22.12187 22.77880 23.43572 24.09265 24.74957 25.40649 26.06342 26.72034 27.37726

PANEL

10.99792

:z;f

lo:99792 10.99792 10.99792 10.99792 :K8% lo:99792

23.59645 24.12201 24.64757 25.17312 25.69868 26.22424 26.74980 27.27535 27.80091 28.32647

:5::t:F5 12.46176

26.04995 26.40638 26.76280 27.11923 27.47565 27.83208 28.18851 28.54493 28.90136 29.25778

13.88143

X

x:366 12:46176 12.46176

:xti

13:88143 :33-xx:si 13:88143 ::-xx::~ 13:88143 Y

.95199 .90532 .86302 .82449 .78925 .75690 .72710 .69956 .67403 .65029

.57448

.96454 .92975 .89739 .86720 .83898 .81254 .78771 .76435 .74234 .72157

.58116 .56890 .55388 -53443 .ii729 .50403 .49462 .48746

.97461 .94927 .92521 .90235 .88059 .a5985 .84007 .82117 .80311 .78583

.59445 .57304 .56722 .55706 .54311 .52965 -51786 .50797 .50046 .49391

.96534 .95005 .93524 .92087 .90695 .89344 .88032 .a6759 .85522 .84319

.58158 .57345 -57006 .56540 .55954 .55135 .54294 .53468 -52664 .51950

rl

:.48533 XII

ACP

WING

DESIGNED

CAMBER

MIXED

FOR

SLOPES

AT PANEL

CONTROL

SPANWISE STATION CHORDWISE

WING

POINTS

1

: i

-. .05663 18038 -. -.40399 34828

i

-.32930 -.37131

ii

-.25976 -.29035

1:

-.20364 -.23002

.12507 -.02475 -.10448 -.13539 -.12809 -.12915 -. 13045 -.13324 -. 14508 -.15657

- OPTIMAZATION

RESULTS

(95% of Panel)

2

STATION

DESIGN

3 .15772 I%:; -.08731 -.10306 -.11329 -. 12286 -.13408 -.14717

4 :::;gp -.17095 -.20048 -.21317 -.21797 -.20705 -.19405 -.17799 -.16484

5

6

7

8

9

10

1:;;;:; -.10640 -.13231 -. 14348 -.14510 -.14616 -.14649

.01929 -.01487 -.03068 -. 03081 -.07114 -.09661 -.12079 -. 13398 -.13863 -.13729

.02787 -.00797 -.02682 -.03669 -. 04247 -.04806 -.07920 -.09664 -.10984 -.11813

.03718 .00255 -.01796 -. 03088 -.04209 -.05122 -.05427 -.05935 -.08247 -.09474

.04737 .01614 -.00384 -.01920 -.03234 -.04565 -.05637 -. 06476 -. 07282 -.07723

.15638 _09926 : 06457 ,03998 .02014 .00368 -.01025

I:;$;

CHORD LENGTHS(C)

22.44247 TANGENT

OF THE

LOCAL

19.59287

INCIDENCE

.25604 CAMBER

SLOPE

SPANWISE

STATION

CHORDWISE

CAMBER

STATION

(slopes 1

16.76196

14.02357

11.55840

9.54376

7.94718

6.56924

5.25557

3.56426

.06519

.17812

.09569

.07555

.05379

.03933

.03087

-.02677

9

10 .12961 .07249 .03780 .01321 -.00663 -. 02309 -.03703 -.04877 -. 06280 -, 07478

10

ANGLE

.09621

have a removed, 3 2

.31267 .07565 -.09224 -.14795 -.11527 -.07326 -. 03431 -.00372 .02602 .05240

.22128 -: i% -. 03918 -. 03188 -. 03294 -. 03424 -.03702 -. 04887 -.06036

1 .03127 .03883 .02961 .01481 .00329

.22290 : %2

so that the camber line 5 4 EE :.00717

KZ :.06048

starts 6 .09484 : 1%

and ends at 0.0) 7 8 .08167 .02698 .04583

.07651 .04187

-.01398

-. 02236

.02752

K

.01710

-. -.03787 02212 -. 04810 -. 05767 -. 06889 -.08199

-.03506 -. 03985 -. 02893 -.01594 .00012 .01328

-.01071 -. 03661 -.04779 -.04940 -.05047 -. 05080

-.02106 : -.04524 -.05843 -.06308 -.06174

: XZ -. 02541 -.04284 -.05605 -.06434

: %Z -. 00277 -.01189 -.01495 -.02003 -. 04315 -.05541

: Kf:: .02703 .01167 -.00147 -.01478 -. 02550 -.03389 -.04195 -. 04636

2

3

4

5

6

7

8

9

.02213 .02927 02845 : 02453 .02134

.02229

.00655

.00948

.00817

.00765 .01184 .01397

SHAPE

STATION

SPANWISE

CHORDWISESTATION :

; p;; .02945 Note:

.01296 -95% : :E :$$f of panel .01523 :.01064 KS .02183 :.02458 Xi .02004 .02451 .01555 .01545 .01716 .01275 .01640 .02531 .00713 .02351 .02495 .01829 :X2 .01625 .02465 95% is taken to be equal to the T.E. location on the last panel

6

::i;;g -.00784 -.00524 -.ooooo

x 109 WING

CAMBER SLOPES

SPANWISE

STATION

CHORDWISE

1

STATION

:iX5

.02566

.01092 .00604 -.ooooo

: KG .00820 -.ooooo

.00315 .00025 -.00134 -.00133 -.ooooo

AT 75 PERCENT

PANEL

1

2

3

.10404 -.13298 -.31470 -.39285 -.37785 -.33770 -.29814 -.26588 -.23596 -.20892

.15504 .00522 -.08854 -.12921 -.12955 -.12894 -.13019 -.I3268 -.14271 -.15427

.18748 .03865 -.02345 -.06964 -.08568 -.09991

NOTE:

.01985 .01507 .01013 .00508 -.ooooo

: Et: : Et -.ooooo

.01886 .01632 .01204 .00643 -.ooooo

.01335 .01186 .00986 .00554 -.ooooo

.01477 .01222 .00883 .00464 -.ooooo

.02234 .01863 .01376 .00748 .ooooo

CHORD

-.11124

-.I2094 -.13184 -.14455

4 -.11079 :::;;:I; -.19457 -.21063 -.21701 -.20923 -.19665 -.18121

-.I6747

5

6

7

8

10

.00226 -.02498 -.03426 -.06158 -.09875 -.12713 -.14125 -.I4477 -.14595 -.14643

.02613 -.00804 -.02752 -.03079 -.06307 -.09151 -.11595 1: :g;t -.13756

.03504 -.00080 -.02305 -.03472 -.04131 -.04694 -.07297 -.09315 -.10720 -.11648

.04411 .00947 -.01386 -.02830 -.03985 -.04939 -.05366 -.05834 -.07785 -.09228

: t:ii': .04490 .02411 -00697 -.00746 -.01965 -.03322 -.04561

ONCE THE CAMBER SLOPES ARE DEFINED, THE PROGRAM BEGINS A STANDARD ANALYSIS. IF a + 0, THEN a IS ADDED TO THE SLOPES FOR ANALYSIS.

.16781

VFlX:

WING

UPPER

POINT

SURFACE CONTROL POINTS, CONTROL POINTS

X

:

3.67416 5.91841

3 5 6 7 8 9 10 11

lS5692 12:65115 14.89539 17.13964 19.38389 21.62813 23.87238 6.54797

E llf%~; 14 12:42584

15 16 17 18 19 20

:: 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

14.38512 16 .34441 18 .30370 20 .26299 22 .22227 24 .I8156 1.40619 1: .08239 12 .75859 14.43478 16.11098 17.78717 19.46337 21.13957 22.81576 24.49196 12.19149 13.59385 14.99620 16.39856 17.80092 19.20327 20.60563 22.00799 23.41034 24.81270 14.78646 15.94230 17.09814 18.25398 19.40982 20.56566 21.72150 22.87734 24.03318 25.18902 17.13359 18.08797 19.04234 19.99672 20.95110

Y .71924 .71924 .71924 .?I924 .71924 .71924 .7192'4 .71924 .71924 .71924 2.18669 2.18669 2.18669 2.18669 2.18669 2.18669 2.18669 2.18669 2.18669 2.18669 3.65360 3.65360 E7:: 3:65360 3.65360 3.65360 3.65360 3.65360 3.65360 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 8.06080 8.06080 8.06080 8.06080 8.06080

MACH=1.620 SOLUTION

L

-.12803 1::;;;; -.12803 -.12803 -.12803 -.12803 -.I2803 -.12803 -.I2803 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.26778 -.26778 -.26778 -.26778 -.26778

G .ooooo

-25386 .34ai2 .29355 .17152

ALPHA= U

-.00416 .11214

.16490 : i49t;i :X

: EG .07252 .ooooo .22952 .28722 .26708 .18776

: kX -07804

: :4z .I1887

: EE .09339 .09693 .I0305 .03628

X2 .14711 : E5

: ::Zl .ooooo .24662 .28962 .29320 .21040 -17731

: :5353:1 .15580 .12409 .11539

: :22; .13656

:EE .10980

: :X .25229 .2aa76 .28274 .21354

:X

: ::%i : :::3: .25973 -24443 .27922 .25971 -23153 .20048 : KS: .14536 .28537 .26985 .25370 .24474 -27854

: Et445 .15540 : ::8z .10899 .10396 :X .20663 .15003 .13968 .I5734 .15720 XS :X .12629 .22470 .16278 : Xi .17134

AT CONTROL

:;,

POINTS

CP

V

-.01955 -.26585 -.35451 -.31837 -.2342a -.19717 -.18380 -.18267 -.17593 -.17617 -.05431 -.24562 -.28720 -.26867 -.22016 -.20106 -.19250 -.19097 -.19245 -.19055 -.08629 -.27300 -.29683 -.29454 -.24989 -.23199 -.22112 -.21603 -.21480 -.21282 -.39215 -.30223 -.31814 -.30848 -.27407 -.25684 -.24235 -.23706 -.23226 -.23024 -.37698 -.28770 -.26595 -.28339 -.28130 -.26959 -.25611 -.24513 -.24113 -.23762 -.36678 -.27573 -.25212 -.23900 -.26842

CORRECTION IS BASED ON FLAT THEORY AND IS 0 FOR DESIGN

0.00000 SlOPES

: 21:

:x

VFIX-

0.000

FOR CARLSON PLATE LINEAR (a = 0).

_-_-_

-.27769 -.35298 -.34697 -.32275 -.29698 -.27711 -.25864 -.2419a : iX -.07456 -.I1718 -.12535 -.13870 -.15132 -.16462 -.18637 -.20764 .20671 -: EE -.07934 -.09879 I: :g;: -.16636 -.18746 -.21008 -.07737 -.I1428 -.17120 -.20988 -.23287 -.24823 -.24755 -.24493 -.23854 -.23482 -:EE -.03076 -.07274 -.12202 -.I5884 -.18049 -.19224 -.20311 -.21292 05909 -:00418 -.02652 -.03517 -.08744

-.18038 -.34828 -.40399 -.37131 -.32930 -.29035 -.25976 -.23002 -.20364

-: zi: -.10448 -.13539 -.12809 -.12915 -.13045 -.13324 -.I4508 -.15657 .15772 00888 -:03153 -.07917 -.08731 -.10306 -.11329 -.12286 -.13408 -.14717 -.11266 -.12201 -.17095 -.20048 -.21317 -.21797 -.20705 -.19405 -.17799 -.16484 -.003ia -.03042 -.03522 -.06817 -.10640 -.13231 -.I4348 -.14510 -.14616 -.14649 .01929 -.01487 -.03068 -.03081 -.07114

CPSTR

POINT

ooK~RLSO/2~~3RECT!ON)

.02645 .01228 .00057 -.01093 -.02204 -.03274 -.04305 -.05292 -.06246 : E: .01092 -:K -.02204 -.03274 -.04305 -.05292 -.06246 .05019 .01874 .00995 -: k%;: -.02204 -.03274 -.04305 -.05292 -.06246 .04794 : K53 .00043 -.01093 -.02204 -.03274 -.04305 -.05292 -.06246 04722 :01630 .00920 00042 -:01094 -.02204 -.03274 -.04305 -.05292 -.06246 .04720 : K88 .00042 -.01094

-.22428 -.32980 -.28982 -.19301 -.14555 -.13946 -.I4182 -.14733 -.15607 -.03909 -.23031 -.29423 -.27316 -.22171 -.19368 -.lai90 -.18678 -.19387 -.20611 -.07256 -.26613 -.31171 -.31160 -.24818 -.23077 -.21205 -.21168 -.21960 -.22342 -.3aa90 -.28291 -.31849 -.31081 -.25858 -.23910 -.21798 -.20791 -.20830 -.21566 -.41326 -.30006 -.27936 -.31469 -.31439 -.29400 -.28025 -.26095 -.25348 -.25257 -.44940 -.32556 -.29432 -.28678 -.34269

-.22681 -.263al -.16779 -.06088 -.03207 -.04857 -.06728 -.08512 -.10402 -.00103 -.24815 1:;;;;; -.21978 -.18958 -.17476 -.17514 -.17534 -.17844 -.02647 -.28125 -.31867 -.31540 -.25704 -.23532 1:;;;;; -.20951 -.20600 -.39101 -.29824 -.31944 -.30462 -.25037 -.22480 -.20329 -.19461 -.19562 -.20229 -.39762 -.30869 -.28829. -.31490 -.31010 -.28829 -.27081 -.25109 -.24187 -.23773 -.41016 -.32098 -.29413 -.28519 -.32701

56

21.90547 %%%I 24:76860

2 t:65

:c 3fZ 20111821

t;

68

2 71

72 73 2 76 77

8.06080 8.06080 8.06080 8.06080 a.06080 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 12.46176 :xz ;p;;; p;;;

88 a9 90 99: ;t 95 96 97

.. 27.83208 28.iaa51 28.54493 Z% 28.90136 100 29.25778

12:46176 :E:f 13188143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143

-.26778 -.26778 -.26778 -.26778 -.26778 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.21929 -.21929 -.21929 -.21929 -.21929 -.2i929 -.21929 -.21929 -.21929 -.21929 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.I9751 -.19751 -.I9751 -.19751 -.19751 -.I9751 -.19751 1::;;;: -.19751

.27076 .25216 .21905 .19114 .16992 .28724 .27943 -26586 .25485 .24760 .24267 .27582 .26415 .24085 .21174 .29058 .28445 .27694 .26722 .25865 .25202 .24731 .24373 .26874 .25832 .29723 .28652 .28361 .27853 .27156 .26483 .25893 .25398 .25023 .24695 .29079 .28673 .28503 .28270 .27977 .27568 .27147 .26734 .26332 .25975

.17260 .I6824 .15862 14893 :14201 .24097 ::;t:: .15469 : :2:: .18296 : :;8369: .16879 -25237 : ::3:5 .I6536 : :E% .I7737 :X .19878 .26526 .18992 .I7285 .17305 .iai32 .I9055 .19468 :K .2oi48 .23525 : :893:; .I8867 .I8899 .19400 .19593 .19957 .20859 .21108

-.26857 -.26335 -.24885 -.23894 -.23334 -.37345 -.27885 -.25606 -.24527 -.24786 -.25089 -.26752 -.26880 -.25771 -.24639 -.38431 -.28797 -.26758 -.26452 -.26131 -.26363 -.26610 -.26660 -.28184 -.27645 -.39917 -.29623 -.27776 -.28220 -.27262 -.27392 -.27443 -.27558 -.27304 -.27840 -.4798i -.40657 -.40038 -.40732 -.41259 -.42344 -.43044 -.43392 -.42733 -.42863

-.12413 -.I5890 -.18212 -.19644 -.20453 .06725 -: tx -.04143 -.05861 -.07537 -.11760 -.14537 -.I6823 -.I8582 .08269 -:x -.03191 -.05441 -.07473 -.08857 -.10322 -.I3626 -.15805 .09779 03490 :00770 -.01644 -.04122 -.06563 -.oa708 -.I0582 -.I2326 -.13717 .I8111 .09633 -.00946 -.03720 -.06184 -.08374 -.10700 -.13211

-.09661 -.I2079 -.13398 -.13863 -.13729 .02787 -.00797 -.02682 -.03669 -.04247 -.04806 -.07920 -.09664 -.I0984 -.iiai3 .037ia 00255 -:01796 -.03088 -.04209 -.05122 -.05427 -.05935 -.08247 -.09474 04737 :01614 -.00384 -.01920 -.03234 -.04565 -.05637 -.06476 -.07282 -.07723 .I5638

-.02204 -.03274 -.04305 -.05292 -.06246 .04720 .01628 .00918 .00042 -.01094 -.02204 -.03274 -.04305 -.05i92 -.06246 04720 :01628 .00918 .00042 -.01094 -.02204 -.03274 -.04305 -.05292 -.06246 .04720 .01628 .00918 -:%zz -.02204 -.03274 -.04305 -.05292 -.06246 .04720 .01628

: I2495276 .009la .0399a .00042 .02014 -.01094 -.02204 -: Es: -.03274 -.02200 -.04305 -.03602 -.05292 -.04800 -.06246

-.34520 -.33649 -.31725 -.29787 -.28402 -.48194 -.34914 -.31201 -.30939 -.32015 -.32803 -.36592 -.36737 -.35781 -.33758 -.50473 -.36593 -.33007 -.33072 -.33944 -.34814 -.35475 -.35766 -.39327 -.39756 -.53052 -.37984 ::;g; 1:;;:;; -.38935 -.39514 -.39351 -.40297 -.47050 -.38666 -.37421 -.37734 -.37797 -.38801 -.39187 -.39914 -.41719 -.42216

-.32566 -.31465 -.29424 -.27534 -.26215 -.42551 -.33601 -.30679 -.30174 -.30880 -.31383 -.33858 -.33708 -.32536 -.30662 -.43719 -.34815 -.32138 -.32061 -.32433 -.32925 -.33304 -.33369 -.35548 -.35406 -.45014 -.35793 -.33374 -.33506 -.34150 -.35141 -.35494 -.35710 -.35387 -.35917 -.43678 -.38746 -.38358 -.38981 1:;;;;; -.40567 y.40970 -.41485 -.41689

56

f: 843 65

IN”

SC3 DEMO WING ALONE FOR COMBINED ANALYSIS AERO SECTION - DEMO WING - BASIC L.E.

DESIGN-CRAIDON

GEOMETRY

SPANWISE PRESSURE DISTRIBUTION ON THE WING UPPER

JSTN= 1 JQ

X(JST)= Y .71924 2.18669 3.65360 5.12063 6.58965

: t 5

SURFACE

CARLSON 15.50000

ETA .09554 .29045 .48530 .68016 .87528

BASIC CP -.14391 -.20576 -.27129 -.31573 -.34338

CORRECTION CPSTR -.03651 -.20259 -.27831 -.31412 -.34272

INTERPOLATION OF RESULTS FROM CONTROL POINTS TO SPECIFIED X STATION TO PROVIDE SPANWISE PRESSURE DISTRIBUTIONS

JSTN= 2 JQ

JSTN=

3

JQ : t i 7

X(JST)=

19.90000

Y

ETA

.71924

.06925

23'K 5:12063 6.58965 8.06080 9.53094

.21054 .35178 .49303 .63448 .77612 .91767

X(JST)= Y 3.65360 5.12063 6.58965 8.06080 9.53094 10.99792 12.46176

CP I: :g; -.21195 -.22861 -.30574 -.28755 -.38560

CPSTR -.07138 -.17507 -.21273 -.21411 -.30085 -.28610 -.36058

24.40000 ETA .27454 .38477 .49515 .60570 .71616 .82640 .93639

CP -.22321 -.21349 -.25319 -.30535 ::;g;; -.36178

CPSTR -.20619 -.20033 -.24056 -.28264 -.33800 -.32663 -.34513

SC3 DEMO WING ALONE FOR COMBINED ANALYSIS AERO SECTION - DEMO WING - BASIC L.E. INTEGRATION

OF THE PRESSURE

ON THE WING

UPPER SURFACE

MACH=

1.6200 Y

.71924 .71924 .71924 .71924 .71924 .71924 .71924 .71924 .71924 .71924 2.18669 2.18669 2.18669 X% 2:18669 2.18669 2.18669 2.18669 2.18669 3.65360 3.65360 3.65360 3.65360 3.65360 3.65360 3.65360 3.65360 3.65360 3.65360 5.12063 5.12063 5.12063 zf:f: p: $ pm; $;;M; 6:58965 t-z 6:58965

ALPHA= Z

-.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.30771 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.29483 -.29483 -.29483 -.29483 -.29483

DESIGN-CRAIDON

GEOMETRY

DISTRIBUTION INTERPOLATION OF PRESSURES TO PANEL MIDPOINT

0.0000 x/c

.05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 :z::i .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000

2Y/B .04894 .04894 .04894 .04894 .04694 .04894 .04894 .04894 .04894 .04894 .14878 : EX .14878 -14878 .14878 .14878 .14878 .14878 .14878 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .34841 .34841 .34841 .34841 .34841 .34841 .34841 .34841 .34841 ':X .44837 .44837 .44837 .44837

z/c 0.00000 0.00000 0.00000 Xoo~~ o:ooooo .ooooo 0.00000 0.00000 0.00000 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -.ooooo 0.00000 0.00000 0.00000 0.00000 .ooooo 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

CP -:Ei

-.32980 -.28982 -.19301 -.14555 -.13946 -.14182 -.14733 -.15607 -.03909 -.23031 -.29423 1: f;:;; -.19368 -.I8190 -.18678 -.19387 -.20611 -.07256 -.26613 -.31171 -.31160 -.24818

-.23077 -.21205 -.21168 -.21960 -.22342 -.38890 -.28291 -.31849 -.31081 -.25858 -.23910 -.21798 -.20791 -.20830 -.21566 -.41326 -.30006 -.27936 -.31469 -.31439

CPSTR

POINT

-:E%X! -.26381

-.16779 -.06088 -.03207 -.04857 -.06728 -.08512 -.10402 -.00103 -.24815 -.29884 -.27295 -.21978 -.18958 -.I7476 -.17514 -.17534 -.17844 -.02647 -.28125 -.31867 -.31540 -.25704 -.23532 ::;g; -.20951 -.20600 -.39101 -.29824 -.31944 -.30462 -.25037 -.22480 -.20329 -.19461 -.19562 -.20229 -.39762 -.30869 -.28829 -.31490 -.3lOlO

46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 - 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

20.04553 21.20137 22.35721 23.51305 24.66889 16.70412 17.65850 18.61287 19.56725 20.52163 21.47600 22.43038 23.38475 24.33913 25.29351 18.96586 19.76058 20.55530 21.35002 22.14474 22.93945 23.73417 24.52889 25.32361 26.11833 21.16934 21.82626 22.48318 23.14011 23.79703 24.45395 25.11088 25.76780 26.42473 27.08165 23.35995 23.88551 24.41107 24.93662 25.46218 25.98774 26.51330 27.03885 27.56441 28.08997 25.88956 26.24598 26.60241 26.95884 27.31526 27.67169 28.02811 28.38454 28.74097 29.09739

6.58965 6.58965 6.58965 6.58965 6.58965 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 9.53094 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 10.99792 12.46176 12.46176 12.46176 12.46176 12.46176 12.46lZ6 :Ef:;f 12:46176 12.46176 :?xx:93 13:88143 E%E 13:88143 13.88143 E-tt:z 13:88143

-.29483 1:;;;;; -.29483 -.29483 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.26778 -.23740 .-.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.21929 -.21929 -.21929 -.21929 ::;:g -.21929 -.21929 -.21929 ::g:;;;

.55000 .65000 .75000 .85000 .95000 .05000 .I5000 .25000 .35000 .45000 .55000 .65000 .75000 .a5000

I:;;;;; -.22337 1: g;g; -.22337 -.22337 1:;;;;; -.19751 -.I9751 -.19751 -.19751 -.19751 -.19751 1::;;;; -.19751 -.19751

:E% .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .I5000

: CM .I5000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 255::: .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000

:Ei .45000 22% .75000 .85000 .95000

:.44837 :1::;

.44837 .44837 .54847 .54847

: 5544%; : E% .54847 : E:; : 2:;: .64850 .64850 : t::;; .64850 -64850 .64850 .64850 .64850 -.74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .84791 :X$39': :::77;: .84791 .84791 ::45'9: .84791 .94451 .94451 .94451 .94451 : 2;; : Et;: .94451

0.00000 0.ooooo 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.ooooo 0.00000 0.00000 0.00000 0.00000 1::;:;: .ooooo -.ooooo -. 00000 -.ooooo 0.00000 1::;;:: 0.00000 EE o:ooooo 0.00000 0.00000 5*9x o:ooooo 0.00000 :-%ooi o:ooooo 0.00000 XK o:ooooo 0.00000 0.00000 0.00000 0.00000 .ooooo .ooooo .ooooo .ooooo .ooooo 0.00000 .ooooo .ooooo .ooooo

-.29400 -.28025 -.26095 -.25348 -.25257 -.44940 -.32556 -.29432 ::;g;; -.34520 -.33649 -.31725 -.29787 -.28402 -.48194 -.34914 -.31201 -.30939 -.32015 -.32803 -.36592 -.36737 -.35781 -.33758 -.50473 -.36593 -.33007 -.33072 1: 3;;;:: -.35475 -.35766 -.39327 -.39756 -.53052 -.37984 -.34570 -.34610 ::;g;; 1: 3;;:: -.39351 -.40297 I: 3;;;; -.37421 -.37734 -.37797 -.38801 -.39187 -.39914 -.41719 -.42216

-.28829 -.27081 -.25109 -.24187 -.23773 -.41016 -.32098 -.29413 -.28519 -.32701 -.32566 -.31465 -.29424 -.27534 1:;;;;: -.33601 -.30679 -.30174 -.30880 -.31383 -.33858 -.33708 -.32536 -.30662 -.43719 -.34815 f : ;I;;; -.32433 -.32925 -.33304 -.33369 I: 3;;;; -.45014 ::;;g I: g:;; -.35141 -.35494 -.35710 1:;;;;; -.43678 1: g;;; -.38981 1:;;;;; -.40567 -.40970 -.41485 -.41689

WING

LOWER SURFACE

POINT

X

:

3.67416 5.91841

: 5 6 7 8 9 10

I:%;: 12:65115 14.89539 17.13964 19.38389 21.62813 2yn33

:: 13 14 15 16 17 18 19 20

a:50726 10.46655 12.42584 14.38512 16.34441 18.30370 20.26299 22.22227 24.18156

I: 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55

lEE8 12175859 14.43478 16.11098 17.78717 19.46337 21.13957 22.81576 24.49196 12.19149 13.59385 14.99620 16.39856 17.80092 19.20327 20.60563 22.00799 23.41034 24.81270 14.78646 15.94230 17.09814 18.25398 19.40982 20.56566 21.72150 22.87734 24.03318 25.18902 17.13359 18.08797 19.04234 19.99672 20.95110

CONTROL Y .71924 .71924 .71924 .71924 .71924 :K

.?I924 .71924 .71924 2.18669 2.18669 2.18669 2.18669 Xfi 2:18669 2.18669 t-E:; 3:65360 3.65360 3.65360 3.65360

3.65360 xt3 5:12063 5.12063

6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 6.58965 8.06080 8.06080 ixx 8:06080

POINTS,

MACH=1.620

Z

-.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.12803 -.I2803 -.30771 -.30771 -.30771 -.30771 -.30771 1:;;;;: -.30771 -.30771 -.30771 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 -.35459 1:;;:;; -.33054 -.33054 I: 3;;;; -.33054 ::;g; -.33054 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.29483 -.26778 -.26778 -.26778 -.26778 -.26778

G .ooooo

.25386 .34812 .29355 .17152 .10642 .08541 .07951 .07356 .07252 .ooooo .22952 .28722 .26708 .18776 .14724 : ::z .I1940 .11804 .ooooo .24662 .28962 .29320 .21040 .17731 .15177 .13940 .13656 .13300 .28719 .25229 .28876 .28274 : :::5t .14936 .13090 .11764 .11538 .28476 .25973 .24443 .27922 .25971 .23253 .20048 .17271 .15775 .14536 .28537 .26985 .25370 : E:

ALPHA= U -.00416 -.14172 -.I8322 -.I4864

-.07502 -.03365 -.01568 -.00860 .OOOll : KE -.11437 -.14010 -.I3050 -.07691 -.05040 -.03594 -.02548 -.02246 -.01499 .03628 -.11356 -.I3376 I: :;;;: -.06192 -.04574 -.03356 -.02676 -.02129 -.09274 -.11084 -.12951 -.12733 -.08425 -.06079 -.04037 -.02694 -.01348 -.00755 -.07813 -.10970 -.10475 -.I2187 -.10252 -.08453 -.06036 -.04224 1:;;;;; -.06067 -.I0707 -.I0654 -.10135 -.10720

VFIX=

0.000 V

-.04037 .20465 .28134 .23901 .I6547 .13249 .12968 : E69792 .13945 -.06124 .19673 .25731 .24590 .18803 .16129 .15141 .14800 .14810 .15069 -.08608 .20297 :X .I9410 .17350 : :;3:3 .15447 : :i;:: .21616 .26044 .26061 .20423 .I8355 .I6826 : Eo9 .I5593 : :X .18702 .21647 .19473 .17651 : ES .14672 .14452 .09941 : :::t: .I6810 .17710

0.00000 W

.0&951 -.24107 -.41583 -.45336 -.39592 -.33665 -.28628 -.24531 -.20679 -.17128 .07253 -. 05868 -.13144 -.15128 -.12968 -.11781 -.10781 -.10014 -.10219 -.10440 -%Z -.04094 -.07907 -.07598 -.08066 -.08022 -.07947 -.08083 -.08438 -.I5486 -.13168 -.17171 -.19279 -.19590 -.19023 -.16909 -.14629 -.12040 -.09765 -.04805 -.04355 -.04165 -.06529 -.09225 -.10735 -.10808 -.09954 -.09082 -.08165 -.02586 -.02779 -.03637 I: :g;;

DZCDX

.05663 -.18038 -.34828 -.40399 -.37131 -.32930 -.29035 -.25976 -.23002 -.20364 .12507 -.02475 -.10448 -.13539 -.12809 -.12915 -.13045 -.13324 -.14508 -.15657 .15772 .00888 -.03153 -.07917 -.08731 -.10306 -.11329 -.12286 1::;;;; 1:::;;; -.17095 ::;g';; -.21797 1::;;;; -.17799 -.I6484 -.00318 -.03042 -.03522 -.06817 I::;;;: -.14348 -.14510 -.14616 -: Ki -.01487 -.03068 -.03081 -.07114

DZTDX : E:;

.01228 .00057 -.01093 -.02204 ,-.03274 -.04305 -.05292 -.06246 .05401 .02192 : i%;: 1:::;;; 1: g;; -.05292 -.06246 .05019 .01874 .00995 .00046 -.01093 -.02204 -.03274 -.04305 -.05292 -.06246 .04794 .01687 .00938 .00043 -.01093 -.02204 -.03274 -.04305 -.05292 -.06246 .04722 .01630 .00920 .00042 -.01094 -.02204 -.03274 -.04305 -.05292 -.06246 .04720 .01628 .00918 .00042 -.01094

CP

.00833 .28344 -36645 .29728 .15003 .06729 .03136 .01721 -.00021 -.01104 -.03909 .22873 -28021 .26101 .15381 .10080 .07187 .05096 .04493 .02998 -.07256 .22712 .26752 .27481 .17262 : E4i .06712 .05351 : K: .22167 : Z49E : KZ79 .08074 .05388 .02697 -01510 : ::693: : ES :::i:; .I2072 .08447 .06202 .03815 .I2135 .21414 : 8%: .21440

CPSTR

.00661 .29529 .42450 : 24:; Xi! .04113 .00585 -.01651 -.03706 : :570;t :::5;3 .08782 .05932 .03741 : KS -.06578 .18001 :Ef .14089 .I0189 .07429 : %E .02710 .I9160 .20528 .23965 .24738 .18864 .I4309 .09422 .05903 .02320 : %Z .I8382 .17425 : E6379 .15597 : :EZ .05188 .02615 .I1320 .18611 .18599 .17377 .I8685

POINT

21.90547

8.06080

E-t:21 24:76860 25.72298 19.32349 20.11821 20.91292 21.70764 22.50236 23.29708 24.09180 24.88651 25.68123 26.47595 21.46495 22.12187 22.77880 23.43572 24.09265 24.74957 25.40649 26.06342 26.72034 27.37726 23.59645 24.12201 24.64757 25.17312 25.69868 26.22424 26.74980 27.27535 27.80091 28.32647 26.04995

:-x 8:06080 8.06080 9.53094 9.53094 9.53094 9.53094

Xf %fi 27:11923 27.47565 27.83208 28.18851 28.54493. 28.90136 29.25778

;-zi;t 9:53094 9.53094 9.53094 9.53094 '1~'9999;;; lo:99792 10.99792 10.99792 ::-99;77;: lo:99792 10.99792

12.46176 12.46176 12.46176 12.46176 13.88143 13.88143 13.88143 13.88143 13.88143 13.88143 13.8814i 13.88143 13.88143 13.88143

1:;;;;: -.26778 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.23740 -.21929 -.21929 -.21929 I:;:;;; -.21929 -.21929 -.21929 -.21929 -.21929 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 -.19751 -.I9751 -.19751 -.19751 -.19751 -.I9751 -.19751 -.19751 -.I9751 -.I9751

:.21905 Z:: .19114 : ::79;: .27943 .26586 : I:;:: .24267 .27582 .26415 -24085 .21174 .29058 : 249: .26722 .25865 .25202 .24731 .24373 -26874 .25832 .29723 .28652 .28361 .27853 .27156 .26483 .25893 .25398 : EE :X :SX% .27977 .27568 .27i47 .26734 .26332 .25975

-.09816 -.08391 -.06043 -.04220 -.02792 -.04627 -.10486 -.10985 -.10016 -.08753 -.07865 -.09285 -.08046 -.06195 -.04296 -.03821 -.10148 -.I1191 -.I0185 -.08892 -.07795 -.06994 -.06490 -.07211 -.05954 -.03196 -.09660 -.I1076 -.10548 -.09023 -.07428 -.06426 -.05641 -.05347 -.04547 -.05554 -.09340 -.09793 -.09403 -.09078 -.08167 -.07554 -.06777 -.05473 -.04867

.16846 .15628 : :%:I .12827 .07522 : K2 .15767 : :I;% .I5249 : :3::s9 .I2431 .06401 .15126 .I6138 .I5203 .I4505 : i;a5:3 : :%a7 .12730 .05791 .14587 .I6050 .14976 : KY :K .I3068 .12308 .I6107 .22294 .22523 .21339 : ::263;: .17122 .16212 : :fK

-.07116 -.08489 I: ;g; -.07224 -.01774 -.02094 -.03259 -.03378 -.02845 -.02310 -.04326 -.05064 -.05413 -.05307 -.01034 -.01350 -.02682 -.03146 -.03130 -.02941 -.02189 -.01592 -.02915 -.03189 -.00078 -.00169 -.01464 -.02120 .-.02321 -.02533 -.02534 -.02342 -.02108 -.01589 :X .06804 .05191 .04329 .03745 .03390 .03237 .02864 .02244

-.09661 I: ;g;; -.I3863 -.13729 .02787 -.00797 -.02682 -.03669 -.04247 -.04806 -.07920 -.09664 -.10984 -.I1813 .03718 .00255 -.01796 -.03088 -.04209 -.05122 -.05427 -.05935 -.08247 -.09474 .04737 .01614 -.00384 -.01920 -.03234 -.04565 -.05637 -.06476 -.07282 -.07723 .15638 .09926 .06457 .03998 .02014 .00368 -.01025 -.02200 -.03602 -.04800

-.02204 -.03274 -.04305 1: ;;;f; .04720 :%X .00042 -.01094 -.02204 -.03274 1:;;;;; -.06246 .04720 : XX .00042 -.01094 -.02204 -.03274 -.04305 -.05292 -.06246 .04720 .01628 .00918 .00042 ::$;g; -.03274 -.04305 -.05292 -.06246 .04720 .01628 .00918 .00042 ::$g -.03274 -.04305 -.05292 -.06246

.19631 .16783 : fK .05583 .09255 .20972 .21970 .20031 .I7506 : ::33!i .16092 .12389 .08591 -07643 .20296 .i55si

:.I4421 EXI .11908 .06393

: :X:2! .21096 ::E .I2851 : :'oftf .09094 .I1109 .18679 .19585 : Ei .I6334 : :53:: .I0945 .09734

.17580 : KZt .07635 : :E

60

: :E: : 11;::: : ::58; :X : :;;t: .17885 .19688 .18085 -15738 : ::5:45 .11428 .I2821 :X : :X : 11%: .I2787 :X .08960 .07542 : Xi .13983 : Kli: .12564 .11900 : KG .07055

x:

83

SC3 DEMO WING ALONE FOR COMBINED ANALYSIS AERO SECTION - DEMO WING - BASIC L.E. SPANWISE

PRESSURE

ON THE WING

JSTN=

1

JQ

DISTRIBUTION

LOWER SURFACE

X(JST)= Y .71924 2.18669 3.65360 5.12063 6.58965

JSTN=

2

X(JST)= Y

JQ

.71924 2.18669 3.65360 5.12063 6.58965 8.06080 9.53094 JSTN=

3

JQ : : 7 7

DESIGN-CRAIDON

X(JST)= Y 3.65360 5.12063 6.58965 8..06080 9.53094

ii: ta9:;:

15.50000 ETA

CP

.09554 .29045 .48530

.05761 .I2365 .20987 .25746 .19524

.68016

.87528

CPSTR .I2285 .10761 .I6396 .24243 .16700

19.90000 ETA

CP

.06925 .21054 .35178 .49303 .63448 .77612 .91767

.01320 .05483 .085i4 .10129 .18978 .20375 .17755

CPSTR .03301 : it: : :i::: .17501 .15789

24.40000 ETA

CP

.27454 .38477 .49515 -60570 .71616 .82640 .93639

.04319 .01859 .05445 .09849 .17610 .I6758 .20818

CPSTR .02768 .00992 .04371 .09019 .15734 .14843

.18285

GEOMETRY

zco

SC3 DEMO WING ALONE FOR COMBINED ANALYSIS AERO SECTION - DEMO WING - BASIC L.E.

DESIGN-CRAIDON GEOMETRY

INTEGRATION OF THE PRESSURE DISTRIBUTION ON THE

MACH= POINT

X

:

2.66425 4.90849

: 5 6 7 8 9 10 11

7.15274 9.39699 11.64123 13.88548 16.12973 18.37397 20.61822 22.86247 5.66629

:: 7.62558 9.58487 14 11.54416 15 13.50344 16 15.46273 17 17.42202 18 19.38131 19 '21.34059 20 23.29988 :: 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

1~*X 12:00430 13.68049 15.35669 17.03289 18.70908 20.38528 22.06147 23.73767 11.56043 12.96279 14.36514 i5.76750 17.16986 18.57221 19.97457 21.37693 22.77928 24.18164 14.26633 15.42217 16.57801 17.73385 18.88969

WING

LOWER SURFACE

1.6200

ALPHA=

Y :K

.71924 .71924 .71924 .71924 :EXf .71924 .71924 ZiE 2:18669 P:Xff; 2:18669 2.18669 Xfi 2:18669 3.65360 3.65360 3.65360 3.65360 3.65360 ~-fzl 3:65360 3.65360 3.65360 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 5.12063 ZEN 6 158965 6.58965 6.58965 6.58965

2 -.li803 -.I2803 -.I2803 -.12803 -.12803

-.12803 -.I2803 -.I2803 -.I2803 -.I2803 1:;;;;: -.30771 I: g;:: -.30771 -.30771 1:;;;;: -.30771 ::;;g; ::;g:; I: 3;;;; -.35459 I; gg; -.35459 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.33054 -.29483 -.29483

-.29483 -.29483 -.29483

0.0000 x/c

.05000 :% .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 95000 :05000 15000 :25000 .35000 .45000

2Y/B .04894 .04894 .04894 .04894 .04894 .04894 .04894 .04894 .04894 .04894 .14878 .14878 .14878 .I4878 .I4878 : :tt:: .14878 : :fX:: .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .24859 .34841 .34841 .3484i .34841 .34841 .3484i .3484i .34841 .3484i .3484i .44837 .44837 .44837 .44837 .44837

z/c 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0%~~ 0.00000 0.00000 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 -.ooooo 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -.ooooo 0.00000 0.00000 0.00000 0.00000 0:X 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0 .ooooo 0.00000

CP

CPSTR

.00833 .28344 .36645 .29728 .I5003

.00661 .29529 .42450 .41696 .25517 -14053 .07490 .04113 .00585 -.01651 -.03706

: KS9 .01721 -.00021 -.01104 -.03909 .22873 .28021 .26101 .15381 : KXS .05096 : Ef -.07256 .22712 .26752 .27481 .17262 : E559 : i653:: : !E; .22167 .25903 -25467 -16849 : %52 : 005632 : GE: .21940 .20949 .24374 .20504

: :::t: .21708 .13374 : E794X : EE .01583 -.06578 .18001 :X :X8 .07429 : W! .02710 .19160 .20528 .23965 .24738 : :fK

.09422 : EE .00439 : :2::: : :EJ .17937

POINT

6.58965 6.58965 6.58965 6.58965 6.58965 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 8.06080 9.53094 9.53094 9.53094 9.53094 9.53994 9.53094

10.99792 10.99792 10.99792 10.99792 10.99792

12.46176 12.46176 12.46176 12.46176 12.46176 13.88143 :3*x:::: 13:88143 13.88143

I:;;dX; -.29483 -.29483 -.29483 -.26778 -.26778 1:;;;;; -.26778 -.26778 -.26778 -.26778 -.26778 -.26776 1:;;;;; -.23740 -.23740 -.23740 -.23740 -.23740 ::f;:;: -.23740 -.21929 1:;:;;; -.21929 -.21929 -.21929 -.21929 1:;:;;; -.21929 1:;;;;; -.22337 -.22337 -.22337 -.22337 -.22337 -.22337 ::;2";;; -.19751 -.I9751 -;19751 1:;;;;: -.19751 -.I9751 -.19751 -.19751 -.19751

:K .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .I5000 :5%! .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 .85000 .95000 .05000 .15000 .25000 .35000 .45000 .55000 .65000 .75000 :K

.44837 .44837 .44837 .44837 .44837 .54847 .54847 .54847 .54847 .54847 .54847 -54847 .54847 .54847 .54847 .64850 .64850 .64850 .64850 .64850 .64850 .64850 .64850 .64850 .64850 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .74831 .84791 .84791 .84791 .84791 -84791 .a4791 .84791 .84791 .84791 .a4791 .94451 .94451 : EZ .94451 .94451 .94451 .94451 .94451 .94451

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -.ooooo -.ooooo .ooooo -.ooooo -.ooooo -.ooooo 0.00000 I:$;;; 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 .ooooo .ooooo .ooooo .ooooo .ooooo 0.00000 .ooooo .ooooo .ooooo

.16907 -12072 .08447 .06202 .03815 .12135 .21414 .21308 : EZi .19631 .16783 .I2086 .08441 .05583 .09255 .20972 .21970 .20031 .17506 .I5730 .18571 .16092 .12389 : KG .20296 .22382 .20371 .I7785 .I5589 : :Z: .I4421 .I1908 .06393 .19320 .22153 .21096 .18047 .14856 .12851 .11283 .I0695 .09094 .11109 .18679 .19585 .18805 .18156 .16334 .15108 .I3555 .I0945 .09734

.15597 .11213 .07564 .05188 .02615 .11320 .I8611 .la599 .17377 .18685 .17580 .15528 .11219 .07635 .04663 .08799 .18435 .19426 .17637 .I5446 .I3891 .16497 .14529 .11066 : Ei9 .17885 .19688 .I8085 .I5738 .I3825 .12364 .11428 .i282i .10376 .06086 .17065 : :z: .15674 .I2787 .10974 .09551 .08960 .07542 .09591 .13637 .I3983 .13703 .13563 .12564 .11900 .I0708 .08051 .07055

TOTAL COEFFICIENTS __---------------ON THE WING INPUT

REFERENCE

AREA

REFA=

171.0.500

REFB=

14.6970

REFX=

16.7010

REFZ=

0.0000

MACH= ALPHA= ;;: CM=

CDCL=

.21579

BASED ON THE CARLSON CORRECTION

CDCL=

REFERENCE PLANFORM WITH

.40000 .04401 -. 03583 .40000 .04401 .08958

&f xcp=

14.7470

1.62000 0.00000

g xcp=

MACH= ALPHA= CN= g=

NOTE:

REFC=

PCLL

1.62000 0.00000 .36941 .04109 -.03109 .36941 .04109 .08415 -23623

AREA=

172.34067

(TOTAL-AREA)-

INTERNALLY

AREA=

118.97679

(EXPOSED-AREA)-

MEANS PANELS WHERE PRESSURES ARE NOT SPECIFIED

CNF=

.26123

(EXPOSED-LIFT)

CDF=

.04407

(EXPOSED-DRAG)

.21611

(EXPOSED DRAG-TOTAL LIFT)

CDFCl=

BASED ON THE CARLSON CORRECTJON CNF=

.24125

(EXPOSED-LIFT)

CDF=

.04056

(EkPOSED-DRAG)

CDFCL =

.23322

(EXPOSED DRAG-TOTAL LIFT)

COMPUTED

PLANFORM

AREA

AREA AREA,

WOODWARD

IS l/2 TOTAL CONSISTENT I PRACTICE.

SECTION COEFFICIENTS _------------------ON THE WING Y

ETA

.71924 2.1a669

3.65360 5.12063 6.58965 a.06OaO 9.53094

x:7962 13:aa143

lBASlC SPANWISE DISTRIBUTIONS

C/CAVE

;04894 .14a7a .24059 .34a4i .44a37 .54a47

CrCL/CAVE

CwCD/CAVE

.562aa

.17495 .05967 .03656 .0827a 03565

1.92031

1.6a346

.53732 .51090

:*x :99312 .a2002

.64850 .74831 .a4791

.48463

.44259 .39ala .34998 .29790

: E:: .45157 .30625

.94451

.24laa .16309

: 02467 .a1498

.ooa74 .00499

-.00585

USING STANDARD PRESSURES)

CN

CA

CL

.29191 .3i9la .35473

.09073 .03545 .02538

!91Q' :;19ii .35473

.44565 .48558 .51254 : KS

.03590

.40221

.53255

.06870

.402?’

.03ooa

28

.02193 .0154a .01106 -.01911

CD

,

i4565 ;5;n .512& .5277' .! .!

.“<_.”

CM

non77

.03545 .02538 “L1-l”

.03598 .03OOL .02193 "llc‘1

.----j

: :K;

.02043 .00172 -.064oa -. i307a -.19a53 -.26314 -.3246a -.3aal6

XCP

K

-.39974 -.19002 -.05760 -.00427 .14379 .26932 : 34:;:; .60614 .72aa7

SECTION COEFFICIENTS _____------__------ON THE WING BASED ON THE CARLSON CORRECTION ETA

Y

C/CAVE

CwCL/CAVE CICD/CAVE

:

-71924

. i4a7a .04a94

:-:a25:6’

.4a4i7 .50736

: :z3

3

?5:12063 ff%

.34a4i .24a59

1.20494 1:44023

.oai23 .03559

s5

6.5B965 a.06oao

.44a37 .54a47 .64a50

.46222 .47797

:X .6a2a4

; 9

10

1t-K 12:46176

i3.aai43

CPSTAG- = SOLVE, TltlE

l.a3906

.74a3i

.56444 .45157 .30625

.a4791 .94451 CPCRIT

= 261.32300

SOLVE, TIHE = 261.32300

q

.71476

.41643 .36967 .322ia

: EX;

.01394

.27294 .2ia43 .15311 CPVAC

. ooa26 .00474

-.00515 q

-.54434

CN

CA

.26311 .2a761 .32094 .39668 .41932 .45oao .47182 .4a355 .4a372 .49996

.oai9i : Ei .06741 .03351 : :5:4: .01463 .01049 -.016a2

CH : ::::63 : SE

-.05992 -.12102 1: ;g;; -.292a7 -.36491

XCP -.44a97 -.i9iai

-.05126 -.0092a .14291 .26a47 : 3% .60546 .729aa

K

CONCLUSIONS The two computer icist

with

a very powerful

In particular,

the

in more detail with

and provides

W12SC3 code offers used

for

potential

many linear the

characteristics. Grumman Aerospace Bethpage, October

182

Corporation

New York

11714

14, 1983

the

impact

provide

to do supersonic leading

section

eliminates

the

SC3 wing

aerodynam-

wing design.

mapping which, leading

and analysis design

the

edge can be analyzed

of the supercritical

wing design of

report

of the

spanwise

treatment theory

this

capability

equation,

the explicit

investigating

in

in the vicinity

COREL due to

full for

described

and flexible

flowfield

using

the complete

ity

programs

on total

together

edge singularcrossflow.

options

The

and can be

configuration

REFERENCES 1.

Miller,

D.S.,

Carlson,

Method of Constrained of the SCAR Conf., 2.

Mason,

W.H.,

Supersonic July, 3.

H.W.,

Optimization

Mason,

and Miller,

Wings

W.H.,

Grossman,

6.

and DaForno,

Flows,"

"Controlled

Cruise

Theory

Wing Design,"

Supercritical

Validation,"

Proc.

Crossflow

on

AIAA Paper

No. 80-1421,

Supersonic

Performance

Vol.

I and II,

for

AIAA Paper No. 79-1527,

Procedure

for

the

Computation

July

of

1979.

Supersonic

17, No. 8, Aug. 1979, pp. 828-837.

"An Improved

Configurations

"Opportunities

Aerodynamics,"

AIAA J.,

Body-Tail

Craidon,

G.,

"A Numerical

B.,

F.A.,

craft

D.S.,

- An Experimental

Woodward, Parts

Supersonic

"A Linearized

1980.

Conical 5.

for

W.D.,

NASA CP-001, November 1976.

Gains Through Non-Linear 4.

and Middleton,

Method for

in

Subsonic

the

Aerodynamic

and Supersonic

Analysis

Flow,"

of Wing-

NASA CR-2228,

1973.

C.B.,

"A Computer

Configuration

Program

for

Fitting

Smooth Surfaces

and Other Three-Dimensional

Geometries,"

to

an Air-

NASA TM X-3206,

1975. 7.

Siclari,

M.J.,

and Marconi

Based on Inviscid Solutions

with

F.,

Nonlinear

Explicit

"Analysis

Eulerian

Shock Fitting,

and Design Equations,"

of

Supersonic

Part

I,

AFWAL TR-80-3110,

Aircraft

Rotational October

Euler 1980,

pp.

53-56. 8.

Woodward,

F.A.,

"USSAERO Computer

Program Development,

Versions

B and C,"

NASA CR-3227, 1980. 9.

Woodward,

F.A.,

Supersonic Field,"

Part

Tinoco,

Wing-Body

E.N.,

and Larsen,

Combinations,

I - Theory and Application,

Including

J.W.,

"Analysis

Flow Properties

NASA CR-73106,

and Design in the

of Near

1967.

183

10.

Cenko,

A.,

"Advances

of Aircraft, 11.

Vol.

in

"A Modification

Carlson,

H.W.,

Pressure

Loadings

13.

Craidon,

C.B.,

on Lifting

Configuration

Plots,"

Miller,

Landrum,

Force

Data

for

Recompression 14.

Siclari,

15.

16.

17.

Nonlinear with

"Experimental

Grumman Aerodynamics

the author

upon request.)

Grossman,

B.,

over Delta

Wings",

and Siclari,

Methods,"

Journal

a Digital

"Experimental

of Flat

Computer

J.C.,

NASA TP-1759, "Analysis

Eulerian

Pressure

M.J.,

393-81-1,

for

Airplane

"Pressure

Wing Having

and Design

and

a Shockless

of Supersonic

Part

II,

AFWAL TR-80-3110,

Distributions 393-82-02,

January

Distributions

July

Nonlinear October

Poten1980.

for

Charac-

Supersonic

Maneu-

1982.

(Available

from

Supersonic

Potential

Flow

1980. and Aerodynamic

Wing-Body

October

Aircraft

and Aerodynamic

a Wing Concept

and Cambered Conceptual Report

Program

1981.

"The Nonlinear

Pressure

of

Mach Numbers and

and Mason, W.H.,

Equations",

Wing for Report

Supersonic

Prediction

1970.

Townsend,

B.,

for

1979.

AIAA Paper No. 80-0269,

Grumman Aerodynamics

1981.

Charac-

and Wing-Body-Canard", (Available

from

the

upon request.)

Harris, TM X-947,

i84

at High

Shock Capturing,

vering",

author

Design

Theory

Wing and a Warped Conical

of a Demonstration

teristics

18.

E.J.,

teristics

Mason, W.H.,

of

and Grossman,

Flow Solutions

Mason, W.H.,

Surfaces

NASA TMX-2074,

at Mach 1.62",

M.J.,

Linearized

NASA TP-1406,

a Flat

Based on Inviscid tial

to

"Description

D.S.,

Configuration

17, No. 2, Feb. 1980, pp. 119-126.

Large Angles of Attack," 12.

Supersonic

R.V., 1964.

Jr.,

"An Analysis

and Correlation

of Aircraft

Wave Drag",

NASA

2. ~ovmment

1. Repcd No.

Accahm

3. Recipient% crubg

No..

No.

NASA CR-3676

5. Report Datr

4. Title nd Subtitle

December

THE COREL.AND W12SC3 COMPUTER PROGRAMS FOR SUPERSONIC WING DESIGN AND ANALYSIS

1983

6. Performing Orgsnizrtion codr 8. Performing Orpniution

7. Author(r)

William

H. Mason and Bruce

._ 9. Performing Oqniution

Report No.

S. Rosen 10. Work Unit No.

Name and Address

Grumman Aerospace Corporation Bethpage, New York 11714

11. Contrra

or Grant No.

NASl-15351 13. Type of Repon and Period Coverbd

Contractor

12. Sponsoring Agmcy Nwne nd Address

National Aeronautics Washington, D.C.

& Space Administration 20564

Repor-t

14. Sponsoring Agency code

15. Supplementary Notes

Langley Technical Final Report

Monitor:

David

S. Miller

16. Abstract

This report contains a description of two computer codes useful inthe including the supersonic maneuver case.. supersonic aerodynamic design of wings, The non-linear full potential equation COREL code performs an analysis of a spanwise section of the wingin the crossflow plane by assuming conical flow over the section. A s,ubsequent approximate correction to the solution can be made in order to account for nonconical effects. In COREL, the flow-field is assumed to be irrotional (Mach numbers normal to shock waves less than about 1.3) and the full potential equation is solved to obtain detailed results for the leading edge expansion, supercritical crossflow, and any crossflow shockwaves. W12SC3 is a linear theory panel method which combines and extends elements of several of Woodward's codes, with emphasis on fighter applications. After a brief review of the aerodynamic theory used by each method, the use of the codes is illustrated with several examples, detailed inpu, instructions and a sample case.

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

18. Distribution

Statement

Unclassified-Unlimited

Aerodynamics Supersonic Flow Conical Flow Supercritical Crossflow

Subject IS. Qcurity

Classif. (of this rrportl

Unclassified It-305

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(of this plpl)

21. No. of Pw

Unclassified

Category 22. Rice

190

f0f sat8 by the National TKhnical InformationService, Springfield, Virginia 22161 aU.S.GOVERNMENTPRINT~GOFFICE:l984

-739-0101

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