1 1 I I 1 I I 1 I I I I I I I I I
NASA Contractor Report 178157 -- Volume I1
{NASA-CB-178157) VISCOUS M I N G THEORY ~ a 7 - 1 0 0 4 4 DEVELOPHENT, VOLUHE 2: G B U R W I N G COFIPIJTER PROGRAM USER’S B A N U A L F i n a l Report (Grumman Aerospace Corp.1 117 p CSCL 0 1 A Unclas
G3/02 44359
Viscous Wing Theory Development, Volume II -- “GRUMWING” Computer Program User’s Manual
R.R. Chow and EL. Ogilvie
Grumman Corporate Research Center Bet hpage, NY 11 714-3580
Contract NAS1-16858 October 1986
NASA National Aeronautics and SrJdCC’ Administration
Langley Research Center rlampion. Virginia 23665-5225
REPORT RE-726
VISCOUS WING THEORY DEVELOPMENT
USER'S UANUAL VOLUE I1 - 'GRWING' COWUTER PROGRAM
OCTOBER 1986
prepared by
R.R. Chow and
P.L. O g i l v i e
Grumman Corporate Research Center Bethpage, New York 11714-3580
F i n a l Report - Prepared under Contract No. NAS1-16858
prepared f o r
Langley Research Center Nat ional Aeronautics and Space Admin is t ra t ion
Hampton, V i r g i n i a 23665-5225
Approved by
CONTENTS
Sect i on P a g e
1. INTRODUCTION.. ............................................... 1
2. PROGRAM STRUCTURE DESCRIPTION. . . . . ........................... 5
3. I N P U T DATA F I L E D E S C R I P T I O N . . . . . . . . . . . . . . . . . . . . . . ............ 11
4. PROGRAM RUNNING MODE AND INPUT/OUTPUT PARAMETER DESCRIPTION FOR INTERACTION CALCULATION.. .................... 15
APPEND1 X
A. EXAMPLE OF INPUT DATA. . . . . . . . . . . . . . . . . . . . . . . ................. A-1
6. SAMPLE CASE .................................................. 6-1
i i i
Figure
1
ILLUSTRATIONS
Su brou t i ne Tree. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
V
Page
6
1. INTRODUCTION
The computer program described herein is for the analysis of the steady, viscous transonic flow over wings in free air. The program is applicable for high Reynolds number flow over general wings with moderate swept angle and relatively large aspect ratio. The free-stream Mach number is less than one, and the flow is assumed to be adiabatic. for flows that are turbulent over most of the wing area; no special analysis is offered for the treatment of separated flow. The method, however, does incorporate a procedure to circumvent the difficulty involved when boundary layer separation occurs during an intermediate stage of the computation. The viscous solution is then required to remain attached to the wing surface. principal features of the code include: factorization (AFZ) scheme solution of the inviscid irrotational three- dimensional velocity potential flow equation; integral solutions of the laminar and turbulent three-dimensional boundary layer equations; three- dimensional wake surface curvature and displacement effects; and a local two- dimensional strong interaction solution in the vicinity of the trailing edge. A complete description of the formulation and the numerical method can be found in "VISCOUS WING THEORY DEVELOPMENT VOLUME I - ANALYSIS, METHOD 81 RESULTS," Volume I of this report.
The method was designed primarily
The the finite volume approximate
The inviscid portion of the code consists of a newly-developed, fast and robust, AFZ scheme using Jameson's finite volume formulation and parabolic C - mesh mapping for the computation coordinates. scheme, Jameson's second order treatment is adapted for the supersonic zone calculations. In addition, a Prandtl-Glauert asymptotic formula is used for the far field boundary conditions for improved accuracy and rate of convergence. modified to account for viscous effects using a surface-source formulation of the matching conditions; thus, avoiding the need to carry out repeated coordinate mapping for the shifted-wing surface as would be required using a displacement-thickness approach. self-consistent solution o f the coupled boundary layer and inviscid flow equations, with the viscous matching conditions periodically updated during the course of the inviscid relaxation process. The viscous matching
In conjunction with the AFZ
The local boundary conditions in the inviscid problem are
An iterative scheme is employed to obtain a
1
conditions employed in the theory account for displacement effects on the wing as well as both wake-thickness and wake-curvature effects. curvature in the chordwise direction has been taken into account in the method. A procedure was devised so that results of the strong interaction solution from our two-dimensional viscous airfoil analysis is incorporated for the normal pressure correction to the conventional inviscid-boundary layer iterative method near the trailing edge region.
Only longitudinal
The present method does not provide for special treatment of the strong- interaction phenomenon near shock-wave/boundary-layer interaction zones. Theoretical study in this area for the three-dimensional problem is almost non-existent at the present time. Two-dimensional viscous airfoil studies indicate, however, that ignoring this local strong interaction can yield remarkably accurate results for the pressure distribution near the shock wave. Present three-dimensional results also have yielded a similar conclusion.
The three-dimensional boundary layer development on the wing and in the wake is determined using integral methods. The work of Myring-Smith-Stock is extensively modified to be suitable for the present interaction study. An empirical crossflow boundary layer profile is introduced to explore three- dimensional effects, and the lag-entrainment method of Green is adopted along the direction of external surface streamlines. Of particular importance in our method is the inclusion of the wing thickness when computing the metric coefficients of the boundary layer equations. The resulting partial differential equations derived from the integral method are of hyperbolic type, and the solution is obtained using a surface nonorthogonal curvilinear coordinate system on the wing and in the wake. The initial conditions are prescribed near the leading edge of the wing for starting the laminar boundary layer calculation. Turbulent boundary layer calculations are started either by a pre-set transition location, or by natural transition determined by laminar boundary layer separation. prescribed at the wing root and wing tip. and with relatively large aspect ratio, good results can be obtained without detailed knowledge of the wing tip and wing root conditions. angles, however, the solution can intimately be related to the conditions in these regions. These subtle aspects are not studied in the present work.
Zero gradient boundary conditions are For wings with moderate swept angle
For large sweep
The
2
s o l u t i o n o f the boundary layer and the wake provide the surface source
d i s t r i b u t i o n and the wake matching condi t ion t o the i n v i s c i d f l o w computations.
This repo r t i s intended t o serve as a user 's manual f o r the computer
program GRUMWING. Because o f l i m i t a t i o n s o f computer memory, the code was o r i g i n a l l y composed w i t h a small core memory and employed frequent t r a n s f e r o f t he v e l o c i t y p o t e n t i a l v i a 1/0 devices dur ing the development stage o f t he
program. The code has since been converted t o a large core memory w i t h I/O el iminated. One version i s running on the VPS32 computer a t NASA Langley Research Center and a second version on a CRAY-1M computer a t Grumman.
1 shows the comparison o f respect ive running t imes (CPU's) using var ious modes o f v e c t o r i z a t i o n w i t h the VPS32 computer and the CRAY-1M computer.
t h a t t he s l i g h t decrease i n CPU's (409) from using the small-core vers ion was
the r e s u l t o f some bugs i n the o r i g i n a l program.
was accomplished using the CYBER 200 FORTRAN compiler w i t h the "V" op t i on f o r auto-vector izat ion and the VAST preprocesser on the most heav i l y used
subroutine YSWAFZ. CRAY run was 1.6.
Table
We note
The fastest run on the VPS32
The running-t ime r a t i o f o r t h i s case as compared t o the
3
Scalar Scalar version version" auto-vectorizer
4
Vector version Vector Vector version auto-vectorizer version* auto-vectorizer vast-preprocessor
VPS CPU.s 409 319
VPS system time units 363 265
Cray CPU,s 365 260
- - - - - -
365 152 -
VPS CPU ,s 417 310 445 269
VPS system time units 313 231 335 200
Cray CPU,s 360 256 348 142
228
171
-
1 1 1
2. PROGRAM STRUCTURE DESCRIPTION
I 1
The computer program GRUMWING contains three groups o f subroutines (see
Subroutine Tree Diagram, Fig. 1). The f i r s t group i s s t ructured very s i m i l a r t o Jameson's 3-D i n v i s c i d program FL027/28. It consis ts o f reading i n the
wing geometry and the sect ional ordinates; s e t t i n g up the computational g r i d s
and coordinate mapping; computating the i n v i s c i d so lut ion; c a l c u l a t i n g the pressures and forces; and ou tpu t t i ng the so lut ion. The second group o f
subroutines l i n k s the i n v i s c i d and viscous solut ions, and incorporates the t r a i l i n g edge so lut ion. The t h i r d group o f subroutines computes the 3-D
boundary layer and the viscous wake so lut ion. When the program i s running i n
the i n v i s c i d mode, the second and the t h i r d group o f subroutines are no t used. When the program i s running i n t he i n t e r a c t i o n mode, the frequency o f
boundary layer ca l cu la t i ons i s con t ro l l ed by the number o f cycles o f i n v i s c i d
r e l a x a t i o n per boundary layer ca lcu lat ion. There are two sets o f r e l a x a t i o n
fac to rs :
convergence o f t he i n v i s c i d so lut ion. The second se t cons is ts o f f o u r constants t h a t c o n t r o l the re laxa t i on o f the source d i s t r i b u t i o n s on the wing,
t he source d i s t r i b u t i o n i n the wake, the viscous wake curvature condi t ion, and
the coordinates o f the f l o a t i n g wake i n the global i t e r a t i o n . The computation
can be terminated e i t h e r by a preset number o f boundary layer ca lcu lat ions, o r by a t o t a l number of cumulative i n v i s c i d cycles o f ca lcu lat ions.
The f i r s t set, cons i s t i ng o f three constants, c o n t r o l s the
5
--------------- I
LAYER AND I WAKE SOLUTION
I I I I I IMAIN-J
VISCAL ' I
I I 1 I I I I I I I I I
INPUT, OUTPUT INVISCID SOLUTION
' BOUNDARY
- GEOM
- COORO
- SlNGL
- SURF -L - ESTlM
- MIXFLO YSWAFZ - C O N f R l
INTPL
- REFIN
- SMOO
- VELO
- TOTFOR EUFSET
SYMEL4
LINE
AXIS
PLOTS
PLOT
EUFSET
SYMEL4
- CPLOT
- FORCF
- GRAPH
- RPLOT
LINE
VELO
PLOTS
PLOT
El - DRAW
- THREE0
i I I I I I I I I I I I I I I I I I
---- ------ I
-I I
- SFWAKE
- ECFLUX --------- - VELCOR - G120
- PRECOR J --------- -
1 -----
SOUOEL
EINLES
TEXT
INST
XSTART
META
I METRIC c I
JoHY I I
TRANS
SFEN
YLOIFF
CKK
TOIFF
SSOIFF
XXOIFF
YOlFF
CROSS
FOIFF
ENTRAI
SOIFF
XOIFF
MEM
STEP
OUTP
F1 LAMB SOROER
INTGR
_I I------ -------------- R86-0125-0018
Fig. 1 Subroutine Tree Diagram
6
I iI a U i 1 I I i li I
The subroutines used i n the program are l i s t e d below, along w i t h a b r i e f
desc r ip t i on o f t h e i r usage. c a l l a number o f Calcomp rou t i nes which are members o f a GRUMMAN l i b r a r y . The
user w i l l probably have t o modify these rou t i nes s l i g h t l y t o make them
compatible w i t h d i f f e r e n t graphics i n s t a l l a t i o n s .
The subroutines GRAPH, RPLOT, DRAW AND THREED
GEOM
COORD
SINGL
SURF
SPLIF
INTPL
MIXFLO
Y SWAFZ
CONTRl
ESTIM
REFIN
SMOO
VEL0
CPLOT
FORCE
TOTFOR
GRAPH
RPLOT
DRAW
THREED
SFKAKE
The geometric d e f i n i t i o n o f wing provided by the input data
Sets up the stretched parabol ic and spanwise coordinates
Generates the s ingular l i n e f o r t he square r o o t t ransformat ion
In te rpo la tes the mapped wing surface and the wake surface a t mesh po in ts
The sp l i ne f i t rou t i ne (Jameson)
The i n t e r p o l a t i o n r o u t i n e using Taylor ser ies
Solut ion o f the three-dimensional p o t e n t i a l f l ow equation f o r mixed subsonic and supersonic f l o w
The approximate f a c t o r i z a t i o n f i n i t e volume scheme
Computes the contravar iant f l u x f o r the source d i s t r i b u t i o n
I n i t i a l est imate o f the reduced p o t e n t i a l f unc t i on
Prepares i n i t i a l est imate o f the reduced p o t e n t i a l f unc t i on f o r the halved mesh s i z e
Smooths the reduced p o t e n t i a l f unc t i on
Calculates the i n v i s c i d surface v e l o c i t y
P l o t s Cp a t the computational mesh po in ts from the p r i n t e r
Calculates the sect ion force c o e f f i c i e n t s
Calculates the t o t a l force c o e f f i c i e n t s f o r the wing
Calcomp p l o t s o f the sect ion pressure d i s t r i b u t i o n s
Calcomp p l o t s o f the convergence
Draws the conf igurat ion
Generates the three-dimensional Calcomp p l o t s
Calculates the f l o a t i n g wake c w r d i n a t e s and cmputes the viscous wake curvature cond i t i on
7
BCFLUX Computes the source d i s t r i b u t i o n s from the boundary l a y e r and t h e wake sol u t i o n
VELCOR Computes t h e normal pressure c o r r e c t i o n from t h e t r a i 1 i ng edge sol u t i on
PRECOR Computes the t r a i l i n g edge values of the boundary l a y e r parameters f o r the t r a i l i n g edge c o r r e c t i o n s
6120
V I SCAL
The t r a i l i n g edge s o l u t i o n
The c a l l i n g program f o r the boundary l a y e r and the viscous wake ca l c u l a t i on
SOUDE L
EINLES
Wri tes out the boundary l a y e r separat ion l o c a t i o n
Computes the leading edge l i n e , t h e chord d i s t r i b u t i o n and t h e span coordinates for t h e boundary l a y e r c a l c u l a t i o n
TEXT
I NST
Ind ica tes t h e t o p o r the bottom wing sur face
Ind ica tes t h e number o f boundary l a y e r and wake computation steps
XSTART Determines the s t a r t i n g l o c a t i o n o f boundary l a y e r compuati ons
META Computes t ransformat i on func t ions f o r t h e nonorthogonal c u r v i 1 i near boundary 1 ayer coordinates
METRIC Computes the met r ic c o e f f i c i e n t s f o r t h e nonorthogonal c u r v i 1 i near boundary 1 ayer coordinates
BE I T
VELOVN
Computes t h e d e r i v a t i v e s o f the m e t r i c c o e f f i c i e n t s
I n t e r p o l a t e s the surface v e l o c i t y f o r t h e boundary l a y e r c a l cu l a t i on
ANFAL Computes the i n i t i a l values f o r laminar boundary l a y e r c a l c u l a t i ons
Sets up boundary l a y e r t r a n s i t i o n and computes t h e i n t i a l values f o r t u r b u l e n t boundary l a y e r c a l c u l a t i o n
TRANS
SFEN Computes sk in f r i c t i o n f o r t u r b u l e n t boundary l a y e r c a l CUI a t i on
Computes the l i m i t i n g wal l stream cross- f low boundary l a y e r p r o f i l e
Computes the spanwi se d e r i v a t i v e s l a y e r c a l c u l a t i o n s
JOHNST e p when Johnston i n e ang i s used
f o r the YLDIFF laminar boundary
8
CKK
TDIFF
SSDIFF
XXDIFF
YDIFF
CROSS
FDIFF
ENTRAI
SDIFF
XDIFF
MEM
STEP
OUTP
F I LAMB
SORDER
INTGR
Polynominal velocity profile fits for the laminar boundary 1 ayer
Transformation functions for the laminar boundary layer cal cu 1 at ions
Right-hand-side functions for the laminar boundary layer equations
x-derivatives for the solution of the laminar boundary layer equations
Computes the spanwise derivatives for the turbulent boundary layer calculation
Computes the cross-flow functions of the turbulent boundary 1 ayer
Computes the normalization functions for the reduced integral thicknesses of the turbulent boundary layer
Computes the x-derivative of the entrainment coefficient using lag-entrainment equation
Right-hand-side functions for the turbulent boundary layer equations
x-derivatives for the solution of the turbulent boundary layer equations
Interpolates the displacement thickness and the source at the inviscid computation nodes
Determines the integration step size for the laminar and the turbulent boundary layer calculation
Prints out the boundary layer and the wake solution at a constant chord station
Computes the eigenvalues at each integration step of the boundary layer and the wake calculation
Orders the eigenvalues by their magnitude
Explicit integration routine for the laminar and turbulent boundary layers and the wake computations
9
3. INPUT DATA FILE DESCRIPTION
1 1 1 I i I I 1
I I I
For convenience i n running the program, the input data format i s very
s i m i l a r i n s t ruc tu re t o t h a t o f Jameson's FLO 27/28 code. An add i t iona l name-
l i s t data card i s used t o input the parameters t h a t con t ro l the running o f the
i n t e r a c t i o n mode o f the program. An example o f the input data i s given i n
Appendix A.
I n the fo l lowing, we s h a l l b r i e f l y descr ibe (according t o the order o f the input data format, see Appendix A) the i npu t parameters and t h e i r
suggested values, whenever appl icable. ( t o descr ibe the s p e c i f i c run) fo l lowed by a namel ist card ( f o r i n p u t t i n g the values o f the c o n t r o l l i n g parameters f o r the i n t e r a c t i o n runs) and then by
groups o f data, each s ta r ted w i th a t i t l e card.
The data f i l e begins w i t h a t i t l e card
FNX The number o f mesh c e l l s along the c-coordinate ax is ( i n the chord d i rec t i on )
FNY The number o f mesh c e l l s i n the d i r e c t i o n normal t o the c- coordinate ax is and the span
FNZ The number o f mesh c e l l s i n the span d i r e c t i o n
FMESH The t o t a l number o f sets o f mesh computation f o r the i n v i s c i d f low, f o r i n t e r a c t i o n mode ca lcu la t ion , the boundary layer ca l cu la t i on enters a t the f i n e s t ( l a s t ) mesh computation
FPLOT Controls generation o f p l o t s FPLOT=O. s t a t i o n FPLOT=l. span s t a t i o n FPLOT=Z. s t a t i on FPLOT=3. for a three-dimensional Calcomp p l o t on ly
for a p r i n t p l o t bu t no Calcomp p l o t a t each span
f o r both a p r i n t p l o t and a Calcomp p l o t a t each
for a Calcomp p l o t bu t no p r i n t p l o t a t each span
XSCAL, PSCAL Control the scales o f the Calcomp p l o t s XSCAL40. XSCAL=O. XSCALJIO. sect ion p l o t p ropor t ionate ly t o the l o c a l chord PSCALfO. sec t ion p l o t PSCAL=O. sets the pressure scale t o 0.4 per inch i n each sect ion p l o t . Also,
scales each sect ion p l o t t o XSCAL scales each sect ion p l o t t o 5.0 scales the maximum chord t o XSCAL and each
sets the pressure scale t o PSCAL per inch i n each
FCONT
F I T
cov
FMACH
YAW
ALPHA
C DO
ZSYM
F NS
SWEEP
DIHED
FUS
PSCAL>O. scales the three-dimensional p l o t so t h a t t he span o r semispan i s 5. If PSCAL=O. and XSCALfO. then t h e three-dimensional p l o t i s scaled so t h a t the maximum chord i s 1/2 XSCAL
I n d i c t o r which determines the manner o f s t a r t i n g the program FCONT=O. i nd i ca tes the c a l c u l a t i o n begins a t i t e r a t i o n zero FCONT=l . i nd ica tes the computation i s t o be continued from a previous ca l cu la t i on . v e l o c i t y po ten t i a l and the c i r c u l a t i o n are read from a magnetic tape where they were prev ious ly s tored
I n t h i s case, t he values o f t h e
The maximum number o f i n v i s c i d i t e r a t i o n sweeps which w i l l be computed
The desired accuracy. I f the maximum co r rec t i on i s less than COV, the ca l cu la t i on terminates o r proceeds t o a f i n e r mesh. Otherwise, the number o f cyc les set by FIT i s compl e t ed
The re laxa t i on f a c t o r s fo r i n v i s c i d f low i t e r a t i o n Suggested values f o r ( P l , P Z , P 3 ) are f o r AFZ mode computation, ( P l , P Z , P 3 ) = (1.,0.9,0.6), f o r FL027 mode computation, ( P l , P Z , P 3 ) = (1.6,0.7,1.0)
The f ree-st ream Mach number
The yaw angle o f the wing i n degrees
The angle o f a t tack i n degrees
The estimated f r i c t i o n drag c o e f f i c i e n t o f t he wing - used only when program i s run i n i n v i s c i d mode
Determines whether t o t r e a t a wing on a wa l l o r an i s o l a t e d w i ng ZSYM=l. : ZSYM=O.: by YAW. Used only when program i s run i n inviscid-FL027 mode
t h e wing i s on a wa l l t h e wing i s an i s o l a t e d wing a t a yaw angle given
Ind ica tes t h e number o f sections o f wing coordinates
Sweep o f s i ngul a r 1 i ne fo r the parabol i c coord i nate mapping a t the wing t i p i f ZSYM=l. , or a t t he leading t i p if ZYSM=O
Dihedral of s ingu la r l i n e f o r t he parabo l ic coord inate mapping a t t he wing t i p if ZSYM=l. , o r a t t he leading t i p i f ZYSM=O
Determines whet her the geometry i nc l udes a f use1 age.
i i i I I 1 1 I
I 1
1 2
I 1 C 1 a I 1 1 1
1 I I I 1
PX
PZ
Z
XLE,YLE
CHORD
THICK
ALPHI
YSYM
FNU
FNL
TRL
S LT
XSING, YSING
FUS=O f o r t he present program always
Bunching parameters f o r t he C-mesh nodes near the t r a i l i n g edge region. The suggested V a l ue o f PX i s 0 < PX < 0.5
Bunching parameter f o r the spanwise coordinate nodes near t h e wing t i p region. The suggested value of PZ i s 0 < PZ < 0.5
Span l o c a t i o n of the sect ion
x- and y-coordinates o f the leading edge
The loca l chord value by which the p r o f i l e coordinates are scaled
Modi f i es the section thickness. mu1 ti p l i e d by THICK
The y-coordinates are
The angle through which the sec t ion i s ro ta ted t o in t roduce t w i s t
Ind ica tes the type o f p r o f i l e YSYM= 0. denotes a cambered p r o f i 1 e. Coordinates are suppl ied fo r upper and lower surfaces, each ordered from nose t o c o i l w i t h the leading edge included i n both s u r f aces YSYM=l. denotes a symmetric p r o f i l e . A t a b l e o f coordinates i s read f o r the upper surface only
The number of upper surface coordinates
The number o f lower surface coordinates. For YSYM=l., FNL=FNU even though no lower surface coordinates are given
The included angle a t t he t r a i l i n g edge i n degrees. The p r o f i l e may be open, i n which case it i s t h e d i f f e rence i n angle between the upper and lower surfaces
The slope o f t he mean camber l i n e a t the t r a i l i n g edge
The coordinates of t he s ingu la r po in t i n s i d e t h e nose about which the square roo t t ransformat ion i s appl ied t o generate parabol ic coordinates. This po in t should be located as symmetrical ly as poss ib le between the upper and lower surfaces a t a distance from the nose roughly p ropor t iona l t o the leading edge radius. It can be seen whether the l o c a t j o n has been c o r r e c t l y chosen by inspec t ing t h e coordinates o f the mapped p r o f i l e p r i n ted i n the output. I f the mapped p r o f i l e has a bump a t t he center, t h e s ingu la r po in t should be moved c loser t o the leading edge. I f the mapped p r o f i l e i s not symmetric near t h e center, w i th a step increase i n y, say, as x increases through 0, t h e s ingular po in t should be moved c lose r t o t h e
13
upper surface. chosen relative to the profile coordinates supplied on the cards which follow
The coordinates of the singular point are
The coordinates of the upper or the lower surface. These are read on the data cards following the title card, one pair of coordinates per card in the first two fields of 10, from leading to trailing edge inclusive. The leading edge point is the same for both upper and lower surfaces. The trailing edge point may be different if the profile has an open tail. The lower surface coordinates are read only when ISYM=O.
Y(I), Y(I)
In addition to FPLOT which controls the generation of inviscid solution plots, additional input parameters controlling the boundary layer solution and the interactive solution output are included in the namelist input described in the next section.
14
4. PROGRAM RUNNING MODE AND INPUT/OUTPUT PARAMETER OESCRIPTION FOR INTERACTION CALCULATION
This sect ion describes the parameters included i n the namelist. Values
can be changed through the namel ist card i n the input f i l e .
The f o u r parameters c o n t r o l l i n g the running mode o f the program are
described i n the fo l lowing:
0, code runs w i t h i n v i s c i d mode only LINKBL =
'1, code runs on i n t e r a c t i v e mode
0, code runs w i t h f i x e d wake surface
1, code runs w i t h f l o a t e d wake surface IFLOAT =
0, code runs without t r a i l i n g edge i n t e r a c t i o n
1, code runs w i t h t r a i l i n g edge i n t e r a c t i o n
0, i n v i s c i d surface pressure i s used t o computed the loads
'1, composite surface pressure w i t h t r a i l i n g edge i n t e r a c t i o n i s used t o compute the loads
I V C O R =
JVLOAD =
The f o l l o w i n g i npu t completes the data requi red f o r boundary l aye r and i n t e r a c t i o n ca l cu la t i on :
ITBLMX : Tota l number o f boundary layer ca l cu la t i ons t o be coupled; t he computation stops whenever the value o f ITBLMX o r FIT, the maximum number o f i n v i s c i d i t e r a t i o n s , i s reached
UINF: Normalized free-stream v e l o c i t y i n boundary layer ca l cu la t i on . UINF = 1
RINF: The chord Reynolds number i n m i l l i o n s
XREF: Normalized reference length f o r boundary layer ca l cu la t i on . XREF = 1
AK( 1) ,AK( 2) : Assigned t r a n s i t i o n l oca t i on f o r the upper and lower wing surface as f r a c t i o n o f r o o t chord, respect ive ly . Suggested values for transonic c ru i se wings AK(1) = 0.10, AK(2) = 0.6
TO: Stagnation temperature i n degrees Ke lv in
PO: Stagnation pressure i n standard atmospheric pressure
15
Not used XPROZ:
XDRUCK;
ICROSS=
LAG =
IPRNT:
SLAX :
DGLAX :
VLAX:
DVLAX:
KLINE =
Intervals of location as fraction of chord where boundary layer solution is to be printed out with XDRUCK = 0. Corresponds to no print out
0, Mager cross-flow boundary layer profile is used
when viscous wake is computed) ‘1, Johnston cross-flow boundary layer profile (not used
0, equilibrium turbulent boundary layer model is used
‘1, lag entrainment model is used
Not used
Relaxation factor for iterative floating wake surface with suggested value SLAX = 0.5
Relaxation factor for circulation jump across the wake surface with suggested value DGLAX = 0.5
Relaxation factor for source distribution on the wing with suggested value VLAX = 0.5 Relaxation factor for net source distribution across the wake surface with suggested value DVLAX = 0.5
0, with no tape output from interaction solution
‘1, with tape output from interaction solution used for surface isocline plots. UNIT 7 is for surface pressure, UNIT 9 is for all the integral values from turbulent boundary layer solution
16
I I I
I I I I
LOCKHEED WING A FLOW27 DATA & V W I N G l I T B L M X = 5 . X D R U C K = I . O . G E N D FNX FNY FNZ FMESH FPLOT XSCAL PSCAL FCONT 40 . 4 . 8 . 3 . 0 .0 1 .o 1 .o 0.0 F I T cov P 1 P2 P 3
48 . 0. 1.00 0 . 9 0 . 6 0 48 * 0 . 1 .00 0 . 9 0 . 6 0
640. 0. 1.00 0.9 0 . 6 0 FMACH Y A W ALPHA CDO ,820 0.0 1 .00 0.0 ZSYM FNS SWEEP D I H E D FUS PX PZ F I X 1 .o 6 .000000 27.000000 0.0 0.0 0.0 0.0 0.0 z XLE Y LE CHORD T H I C K A L P H I S E C T I O N
0.0 0.0 0.156495 6.500000 l.oooO00 2.76oooO 1.000000 YSYM FNU FNL
0.0 33.000000 33.000000 T R L SLT X S I N G Y S I N G
1.618387 -0.166050 0.008503 0.000380 X ( 1 ) Y ( 1 ) UPPER SURFACE
0.0 0.0 0 .002410 0 .009520 0 .009610 0 .017580 0 .021530 0 .024310 0 .038060 0.030180 0.059040 0.034960 0 .084270 0.038570 0 .113490 0 .041360 0 ,146450 0.043640 0 .182800 0 045540 0 .222210 0 .047040 0 .264300 0.048070 0 .308660 0.048640 0 .354860 0 .048740 0 ,402450 0.048350 0 .450990 0 .047360 0.500000 0.045740 0.549010 0 .043450 0 .597550 0 .040620 0.645140 0 .037260 0.691340 0.033530 0.735700 0.029580 0 .777790 0 .025540 0.817200 0.021530 0.853550 0.017670 0 .886510 0.014100 0.915730 0 .010870 0 .340960 0 .008060 0 .961940 0 .005740 0 .978470 0.003820 0 .990390 0.002370 0.997590 0 .001240 1.000000 0.000800
0 .0 0.0 0.002110 -0.008000 0 .009610 -0.015780 0 .021530 -0.022050 0 .038060 -0.028220 0.059040 -0.034320 0 084270 -0.040550 0.113490 -0.046640 0.146450 -0.053090 0.182800 -0.058890 0.222210 -0.063910 0.264300 -0.067720 0 .308660 -0.070310 0 .354860 -0.071260 0 .402450 -0.070940 0 .450990 -0.068820 0.500000 -0.065400 0 .549010 -0.060080 0.597550 -0.053490
X ( I 1 Y ( I ) LOWER SURFACE
A-3
0.645140 -0.045480 0.691340 -0.036950 0.735700 -0.028380 0.777790 -0.020340 0.817200 -0.013230 0.853550 -0.007340 0.886510 -0.002830 0.915730 0.000160 0.940960 0.00 1680 0.961940 0.001950 0.9784 70 0.00 14 20 0.990390 0.000480 0.997590 -0.000430 1.000000 -0.000800 2 XLE YLE CHORD T H I C K A L P H I S E C T I O N
3.600000 1.834292 0.089811 5.720000 1.000000 1.799528 2.000000 YSYM F NU FNL 0.0 33.000000 33.000000
TRL SLT X S I N G Y S I N G 1.821813 -0.178989 0.008467 0.000320
X ( 1 ) Y ( I ) UPPER SURFACE 0.0 0.0 0.0024 10 0.00937 1 0.009610 0.017525 0.021530 0.024425 0.038060 0.030441 0.059030 0.035404
0.113490 0.042302 0,146450 0.044816 0.182800 0.046915 0.222210 0.048583 0.264300 0.049759 0.308660 0.050454 0.354860 0.050657 0.402450 0.050351 0.450990 0.049437 0.500000 0.047894 0.539010 0.045681 0.597550 0.042919 0.645140 0.0396 10 0.691340 0.035896 0.735700 0.031895 0.777790 0.027716 0.817200 0.023477 0.853550 0.019323 0.886510 0.015431 0.915730 0.011887 0.940960 0.008798 C.961940 0,006249 0.978470 0.004150 C.990390 0.002592 0.997590 0.001386 1.000000 0.000915
0.0 0.0 0.002410 -0.008090 0.009610 -0.015789 0.021530 -0.021992 0.038060 -0.028008 0.059040 -0.033895 0.084270 -0.039882 0.113490 -0.045908 0.146450 -0.051891 0.182800 -0.057442 0.222210 -0.062247 0.264300 -0.065905 0.308660 -0.068393 0.354860 -0.069320 0.402450 -0.069004 0.450990 -0.066929 0.500000 -0.063509
o.oe4270 0.039255
X ( I ) Y ( 1 ) LOWER SURFACE
A-4
I B 1 1 1 1 1 1 1 R 1 1 1 1 1 1 -I 1 I
0.549010 -0.058185 0.597550 -0.051571 0.645140 -0.043598 0.691340 -0.035145 0.735700 -0.026706 0.777790 -0.018837 0.817200 -0.011937 0.853550 -0.006288 0.886510 -0.002031 0.915730 0.000706 0.940960 0.002002 0.96 1940 0.002097 0.978470 0.001432 0.990390 0.000433 0.997590 -0.000524 1.000000 -0.000915 z XLE Y LE CHORD T H I C K A L P H I S E C T I O N
7.200000 3.668583 0.036192 4.940000 1.OOOOOO 0.839562 3.000000 YSYM F NU FNL 0.0 33.000000 33.000000
TRL SLT X S I N G Y S I N G 2.086462 -0.193383 0.008415 0.000242
X ( I ) Y ( 1 ) UPPER SURFACE 0.0 0.0 0.002410 0.009175 0.009CIO 0.017352 0.021530 0.024575 0.038060 0.030784 0.059040 0.035987 0,084270 0.040155 0.1 13490 0.04354 1 3.146450 0,046364 0.182800 0.048725 0.222210 0.050C13 0.264300 0,051982 0.306660 0.052840 0.3548CO 0.053180 0.302450 0.052984 0.450990 0.052 17 1 0.500003 0.050727 0.549010 0,048616 0.597550 0.045944 0.645140 0,042702 0.69 1340 0.039010 0.735700 0.034940 0.777790 0.030580 0.817200 0,026039 0.853550 0.021497 0.886510 0.017182 0 915730 O.Cl3226 0.94C960 0.009769 0.961940 0.006919 0.978470 0,004584 0.990390 0.002884 0.997590 0.001579 1.000000 0.001067
0.0 0.0 0.002410 -0.008208 0.009610 -0.015801 0.021530 -0.021915 0.038060 -0.027729 0.059040 -0.033335 0.084270 -0.039003 0.113490 -0.044682 0.146450 -0.050313 0.182800 -0.055536 0.222210 -0.060059 0.264300 -0.063516 0.308660 -0.065870 0.354860 -0.066767 0.402450 -0.066456
X ( I ) Y ( I ) LOWER SURFACE
A-5
0.450990 -0.064441 0.500000 -0.061021 0.549010 -0.055691 0.597550 -0.049046 0.645140 -0.041122 0.691340 -0,032771 0.735700 -0.024504 0.777790 -0.016860 0.817200 -0.010236 0.853550 -0.004904 0.886510 -0.000979 0.9 15730 0.001425 0.940960 0.002425 0.961940 0.002291 0.978470 0.001447 0.990390 0.000373 0.997590 -0.000647 1.000000 -0.001067 2 XLE Y LE CHORD T H I C K A L P H I S E C T I O N
10.800000 5.502875 -0.004362 4.160000 1.000000 -0.120168 4.000000 YSYM F NU FNL 0.0 33.000000 33.000000
TRL SLT X S I N G Y S I N G 2.444312 -0,213174 0,008335 0.000133
X ( 1 ) Y ( I ) UPPER SURFACE 0.0 0.0 0.002110 0.008905 0.009610 0,017351 0.021530 0.024782 0.038060 0.031256 0.059040 0.036790 0,084270 0,041394 0.113490 0.045245 0. 146450 0.046492 0. 182800 0.051214 0.222210 0.053404 0.264300 0.055037 0.308660 0.056121 0.354860 0.056649 0.402450 0.056604 0.450990 0.055929 0.500000 0.054624 0.549010 0.052652 0.597550 0.050104 0.645140 0.046954 0.691340 0.043291 0.735700 0,039127 0.777790 0.034517 0.817200 0.029562 0.853550 0,024487 0.8865 10 0.019590 0.9 15730 0 .Oi5066 0.940960 0.011105 0.961940 0.007840 0.978470 0,005181 0.990390 0.003285 0.937590 0.001844 1.000000 0.001276
0.0 0.0 0.002410 -0.008371 0.009610 -0.015817 0.021530 -0.021810 0.038060 -0.027346 0.059040 -0.032565 0.084270 -0.037794 0.113490 -0.042996 0.146450 -0.048144 0.182800 -0.052916 0.222210 -0.057051 0.264300 -0.060231 0.308660 -0.062401
X ( 1 ) Y ( I ) LOWER SURFACE
A-6
I P I I
0.354860 -0.063257 0.402450 -0.062952 0.450990 -0.061020 0.500000 -0.057600 0.549010 -0.052261 0.597550 -0.045574 0.645140 -0.037717 0.691340 -0.029506 0.735700 -0.021476 0.777790 -0.014141 0.817200 -0.007897 0.853550 -0.003001 0.886510 0.000466 0.9 15730 0.0024 14 0.940960 0.003007 0.961940 0.002557 0.978470 0.001469 0.990390 0.000289 0.997590 -0.000816 1.000000 -0.001276 2 XLE YLE CHORD T H I C K A L P H I S E C T I O N
14.400000 7.337166 -0.034852 3.380000 1.000000 -1.079933 5.000000 YSYM F NU FNL 0.0 33.000000 33.000000
TRL SLT X S I N G Y S I N G 2.953534 -0.242100 0.008203 -0.000025
X ( I 1 Y ( I ) UPPER SURFACE 0.0 0.0 0.002410 0.008511 0.009610 0.017205 0.021530 0.025085 0.038060 0.03 1946 0.059040 0.037963 0.083270 0.043204 0.113490 0.047735 0.146450 0.051603 0.182800 0.054851 0.222210 0.057483 0.264300 0.059504 0.308660 0.060917 0.354860 0.061718 0.402450 0.061895 0.450990 0.061422 0.500000 0.060318 0.549010 0.058552 0.597550 0.056183 0.645 140 0.053 168 0.691340 0,049548 0.735700 0.045248 0.777790 0.040212 0.817200 0,034712 0.853550 0.028858 0.886510 0.023109 0.915130 0.017756 0.940960 0.013057 0.961940 0.009186 0.978470 0.006054 0.990390 0.003872 0.997590 0.002231 1 .000000 0.001582
0.0 0.0 0.002410 -0.008609 0.009610 -0.015842 0.021530 -0.021656 0.038060 -0.026786 0.059040 -0.031440 0.084270 -0.036027 0.113490 -0.040532 0.146450 -0.044973 0.182800 -0.049087 0.222210 -0.052655
X ( 1 ) Y ( I ) LOWER SURFACE
A-7
0.264300 -0.055431 0.308660 -0.057332 0.354860 -0.058128 0.402450 -0.057832 0.450990 -0.056020
f 0.549010 -0.047249 0.597550 -0.040499 0.645140 -0.032742 0.691340 -0.024735 0.735700 -0.017051 0.777790 -0.010168 0.817200 -0.004479 0.853550 -0.000220 0.886510 0.002579 0.915730 0.003858 0.940960 0.003858 0.961940 0.002947 0.978470 0.001500 0.990390 0.000166 0.997590 -0.001064 1.000000 -0.001582
c 0.500000 -0.052600
z XLE Y LE CHORD T H I C K A L P H I S E C T I O N 18.000000 9.171458 -0.046276 2.600000 1.000000 -2.040000 6.000000
Y S Y M FNU FNL 0.0 33.000000 33.000000
TRL SLT X S I N G Y S I N G 3.730311 -0.288382 0.007951 -0.000277
X ( I ) Y ( I ) UPPER SURFACE 0.0 0.0 0.002410 0.007880 0.0096 10 0.016970 0.021530 0.025570 0.038060 0.033050 0.059030 0.039830 0.084270 0.046100 0.113490 0.051720 0. 146450 0.056580 0.182800 0.060670 0.222210 0.064010 0.264300 0.066650 0.308660 0.068590 0.354860 0.069830 0.402450 0.070360 0.450990 0.070210 0.500000 0.069430 0.549010 0.067990 0.597550 0.065910 0.645140 0.063110 0.691340 0.059562 0.735700 0.055040 0.777790 0.049480 0.817200 0.042950 0.853550 0.035850 0.886510 0.028740 0.915730 0.022060 0.940960 0.016180 0.961940 0.011340 0.978470 0.007450 0.990390 0.004810 0.997590 0.002850 1 .OOOOOO 0.002070
0.0 0.0 0.0024 10 -0.008990 0.009610 -0.015880 0.021530 -0.021410 0.038060 -0.025890 0.059040 -0.029640 0.084270 -0.033200 0.113490 -0.036590 0.146450 -0.039900
X ( I ) Y ( 1 ) LOWER SURFACE
A-a
0 .182800 -0 .042960 0 .222210 -0 .045620 0 .264300 -0 .047750 0 .308660 -0 .049220 0 .354860 -0 .049920 0 .402450 -0 .049640 0 .450990 -0 .048020 0.50OOOO -0 .044600 0 .549010 -0 .039230 0 . 5 9 7 5 5 0 -0 .032380 0 . 6 4 5 1 4 0 -0 .024780 0 .691340 -0 .017100 0 .735700 -0 .009970 0 .777790 -0 .003810 0 .817200 0 .000990 0 . 8 5 3 5 5 0 0 .004230 0 . 8 8 6 5 1 0 0 .005960 0 .915730 0 .006170 0 .940960 0 .005220 0 . 9 6 I 9 4 0 0 .003570 0 . 9 7 8 4 7 0 0 .001550 0 .990390 -0 .000030 0 . 9 9 7 5 9 0 -0 .001460 1.000000 -0 .002070
A-9
0.9 0.997b 1.WII
ORIGINAL PAGE tG N POoR QUALITY
SECTIOW DLFIYITIOW AT 2 0.00000 lNIo[w I RATIO UPHA
0 : L 0% Fa E.L 2.7-
B-3
1.-
TJ.fSgE
SECTION DEFINITIOY AT 2 - 3.C- CUORD THICKNESS R A T I O MPM 5.7- 1.- 1.79%
YLE 1.MW
XLE I. in3
B -4
PROFILE AT 2 - '4.W f.W
OW!GINAL PAGE OF POOR QUALITY
SECTION DEFIIIITIW AT 2 - 7.-
2a yR& TwIQ(w SS RATIO 2% a T S L I.-
B-5'
PROFILE AT 2 - W . U I I ,
'I.SE %.ME v SInG O.W.1
0.6433 0.8391
1 . M SECTION DEFINITIOI( AT I .I 10.8-
ODRO THICKNESS RATIO ALMA *.lW 1.00H 4.m2 VLE d.W*4
XL E 5.5029
8-6
CIOFILE AT 2 - l8.W
I 1 i
SEtTlOY DLFIYITIOU AT 2 - 18.- O*MD T n I m ss RATIO ALFW 9":FlS -3 .W3 2.C- !.me -1.- YLE
6 -8
I 1
ORIGINAL PAGE )Qi OF POOR QUALITY
-IS€ CELL DISTIIIWIOW IN S Q U I E looT PLANE AND MAPPED SURFACE EOOIDIlUTES AT CUTER LINE UD TIC
I I i I 1 i I I
TI LOCATION 0.5b250
B-9
ORIGINAL PAGE !G OF POOR QUALITY
wo#1L CELL DILTRIMIQ IN LOUUE ROOT C U E V
SPAWISE CELL DISlRIWlI#( A I 0 SIyeUAR LIME
6-10
1
I I I I
47 0 7861b 4 5 40 a r : 9 u e 7 ~ 4 5 u t 3
o~GINAL PAGE I6 OF POOR QUALln
!I
f 40 40 1 1 1 40
d 3 40
40
a 2 40
40 40. 40
i
0.6295OE-07 0.03065 0.529PSE-07 B.030bb
B-11
SECTION OURACTERISTICS MACH NO VW ANG OF A T T U X 1.82OM 1.0eoee l.OMU
a, 1.11829 3 . 6 W 0.45UZ
PLOT OF CP AT COWPVTATIONAL MESH P O I N T S
01 4.18314
SPAN STATION CL
X 3.1152 2.5387 2.1353
f 360) 1.1718 1.- 0.8415 0.6961 1.5639
1 . g t :
1.1131 1.1297 1.0074 1.w 1.M74 1. 0297
@.nu
r.nn
1.8265 2.1353 2.5387 3.1153
V -0.40b8 -0.4216 4 . 4 1 0 1 -1.3825 4 . 3 3 2 0 4 . 2 4 4 9 4.0935 4 . 1 0 5 8 4 . 2 2 8 6 4.3309 4 . 3 7 2 8 4 . 3 b 6 1 4 . 3 2 6 1 4 . 2 b 4 0 4 . 1 9 2 8 4.1246
1 .r ) lb 1.176b 1.2428 1.2870 1.3129 1.uCI 1.3289 0.3193 1.2942 1.2464 1. 1692
-0. 4203
1:m
j# -0.3721 -0.3996 -0.4111 -0.4a98 -0.3964
n4m No 0.8156 0.8130 0.8089 0.8032 0.7949 0.7818 0.7607 0.7104 0. 6972 0.7753 0.8881 0 966 0 : 974g
#.am9 1.7H8 I.CLO1 0.5491 0.6%# 0.9823
3: xw
w1 1 : 2 d
f:ZE 1 . 1 8 4 1.1345 1 . l . M
0.7949 0.8033
0.8130 E.8156
e. 8090
6-12
+. +
+ + +
+
+ +
+
+ L
+ + + + + + +
+ + + +
+
+ + + +
+
+ +
+ +
+ + + + +
X :: M ::1%3 :p
: : ztf
::#I ::m
1.1& 1." 0.841b 0. b9b4
0.3420
0.11
0.#07b
0.0293 r .ns2
0.344
0.841b 1." 1.1720 1.3bll 1.5752 1::s 3: !%
WWO
o.amz7 0.7939 0.7801
: : p b 0.9412' 0.8878
l .w 0 . b m 1.97ba 1.2289 1.32b8 €:E 0.9944
#.?ab8
0.7938
m . a989 :: 3 3 3
SECTIW CHARACTERISTICS YAY AW OF ATTACU
1.- 1.-
10.79999 0.52910 4.M3b3
HAW Y) 0 . 8 2 r n
SPAN STATION CL CD CM 4.21LW
PLOT OF CP AT COHPUTATIONAL YEW POINTS V
4.139) 4.24#b 4.2322
-m.22*8
4.Hl1
4 . 2 8 8 4 4 .2553 4 . 2 b 4 1 4 . 2 4 %
x 7 :
3:%: 4.W38 o.na4 1.1123 0. 1540 0. 1850
4 .2014 4.2216 4 . 2 3 8 1 4 .229# 4 . 2 1 9 2
+
+ +
+
+ +
+ + +
+
8-13
SECTIOT wRIcIEaIsTxcs VAH A r t OF ATTACK
0 .nOn l.0O.U MACH m 0.82mo
U a, U -0.021SO -0.239S3 SPAY STATION 0.51122
I?. 99998
PLOT OF CP AT COMPUTATIONAL MEW POINTS CP
0.88(2 0.0395 0.0154 0.0248 0 . H I I 0.Ob54 0.1080 0.22u 0.2829 1.1865 0.022b 3.101a 3: 1% 0: J21 0 . y .
3:M
4.1123 4.M84 3.w 0.m 4
4.b9)1 -0.7339 -0.6964
0.0211
0.0401 0.0241 0.0149 0.0092 0 . ~ 0
:: i%
B-14
+
+ *
+
CtlOMOMSE CELL DISTRIBUTION I N SOUARE ROOT PLANE A Y ) W E D SURFACE QlQllOIUTEL AT CENTER LINE UO T I P
B-16
" A L CELL Y
1.03131 0.63808 0.45143 0.3M11
0.11546 0.05661 #.Man
t::M
SCAL FACTOR WY R LAN 0.5- ..La
8-17
SPAWILE CELL DISTRIBUlIOW UD S I Y U U I LINE
ITERATIVE sauTiou V U AS OF *ma wAcHw 0 . U w I o . # r w 1.-
YX w YZ
RELAX FtT 1 RELAX FCT 2 RELAX F I X 3 l.rSm 0.- 0 . b M
80 8 1b
MAX CORRECY I J -0.l21CSE-02 80 8
0.9b873E-03 bo 8 0.8H88E-03 80 8
0.18916E-W 68 8 1.31716E-04 69 8 0.50998E-04 (9 8 O.lW62E44 68 8 0.13200E-04 40 8 0.21037E44 69 8 0. 477E-04 b9 8 0.10343E-04 40 8 O.%50E* 40 8
AVG CORRECN
t : %::E% 0.103ll7E-03 0.14368E-03 0.13194E-04 0.31484E-04 0.H234E-04 O.lOlME43 O.lbb47E-04
0.22129EdS 0.41894E-05 0.77773645 0.11077E-05 0.1b719E-05 0.31743E-M 0.59601E-05 O.bb914E-W 0.24330 0.45980 -05 O.bb31 -06
0.1282lE-OJ
0.991 f -06
MAX RESIOAL I -0.32730E43 88 0.119b8E-03 bo 4.27b23E-03 2 0.19710E-03 M 0.1834bE-03 I O 0.18b72E+3 bo 0.17942E-03 80 0.16419E-03 M
0.49333L-4b bo
0.1139BE-B4 79 0 100b5E44 79 0’83771E-M b0 0’80879E-M 80 0*14647E-05 2 O:bbZO2E-.5 M
AVG R E S I D M 0.41222E-M 0.3W25E-05 0.24547E-05 0.19794L-05 0.14953E-05 0.13163E-M 0.12037E-05 0.1W70E45 0.97259E-W 0.91936E-06 0.84359E-06 0.7bbZbE-06 0 71M1 -06 O:b822b~-Y 0.b4 2 E-06 0.58hfE-06 0.529wE-06 0.50729E4S 0.485bIE-06 0.444OSE-Y
::a$EZ 0.38260C-06
0.31494E-06
0.91307E-07 0.75186E47 0 72417E-07 0:68867E-07 0.613~8E47
CIRCULATY SOY1 1.03110 0.0311L 0.03139 0.03158 0.03172 0.03185
0.032bl 0.13277 :::E8
0.03403 0.03444 0.03455 0.034bb 0.034a5 O.US1b 0 0 24 0 : 0 ~ 3 2
O.O%?b 1.a3Sn
#.u(12 #.#%a 1.03621 0.03625 0.03628 0.03b33 0.03635 0.03b36 0.03b38 0.0%41 0.01612 0.03b43 0.0- 0.1- 0.1- 0.u117
IC PTS 39b 401 408 414 i J i 436 444 450 4b1 465 473 47b 4oa 491 491 4% 498 499 499
II I I f f3 503 503 563 502 502 501 501 502 502 501
B-18
X 3.2469 2.8721 2.5791 2.3- 2.1435 1.968b 1.8180 1.6839 1.5628 1.4521 1.35@# 1.2548 1.1C54 1. #a@? l.WO@
0.7049 0.b4ll 1. 1 H 3.4628 1.4398
0 . p
3.1941 1.1bU 1.lM 1.113) @.@E11 1 . w 9 4 0.0418 0.0272 0.0154 0.0017 @.om# 1.1017 #.be69 1.01% 0.0277 @.HZ9
. ::E3
SECTION OURACTfRlST1CS U Y i O F A *o(
1 . a YAM WA #.my
- 4 . 2 8 4 SPAY STATIQY CL W
PLOl OF CP AT COMPUTATIONAL MESH POINTS
#.##ma 1.44118 #.#68U
+ + +
+
+
6-19
1.0454 1.0408
1.1112 1.08b1 1.1368 0.9499
1.7345 0.7542 ::#:it
1 8104 1 h 2 7 ::tis
+
+ + +
' +
+
+
+
+ +
SECTIOY W U C I E R I S T I C f VAN AW of A n -
l.MO.0 Q)
0.03665
PLOT OF CP AT COWUTATIONAL HEW POINTS
WLCH yo 0.UW @.Men
SPAY STATION 1.4$k41 1.80000 -0.&
Y
-0.4771 4.4800 -0.4793 4.4747 4.4661 4.4530 4.4347 4.4103 -0.3783 -0.3370
3%:
-0.1gg Z f U 2 -0.3062 4.3525 4.3829 4.3980 -0.014 -039 41378
-0.2904 3:3ft:
4.1019 -0.0676 -0.0335 0.0000 0.0370 0.0797 0.1243 0.1689 0.2114 8 .2485 1.2791 1.3049 1.3256 1.3395
MACH no 0.8148 6.8146 0.8127 0.8105 0.8080 0.8052 0.8020 0.7982 0.7937 0.7861 HJ i2f;
::& p2J
1.6567 0.7111 0.7199 0.8565 0.9349 0 997
0.7115 0.6791 0.6368 0.5760 0.4913 0.4215 0.4912 0.6M4 0.9173 1.0950 1.2260 1.3051 1.3239 1.2975
+ + + +
+ +
+ * + + +
+ +
+ +
+ + + + +
+ + + +
+
B-20
+ + +
+
0.1W7 I: 1%
0.7084 0.77bb 0.8480 8.9225 l.M.0 ::Est ::si ::m 1.b839 1.8179
1.2443 1.1w 1.1513 1.1m f+f" 1:llV
0.7337
0.7808 0.7881 0.7937 0.7983 0.8020 0.8053 #.HI1
t:T%
a.8in
SECTION OURACTERISTICS MACH no YAW A f f i OF ATTACK 0 .82rn 0.11011 1.0"
3 . b W 0.50519 0. 02103 SPAN STATIOY CL Q) U
4.plU PLOT OF CP AT COHWTATXONAL WESH POINTS
V [email protected] -0.4133 4.419b -0.4224
4.3974 4.105 -0.3579 4.3283 4.2902 4 . 2 W
4.2185 -4.27% 4.3219 3: 3%
4.148 4.11b1 4.0833 -0. 0344 4.0239 0.0103 0.osw 0.09lb 0.1334 0.1734 0.2087 0.212 #.?CY 0.2836 0.2987
MAW NO 0.8146 0.8145 0.8127 0.8105 0.8081 9.8053 8.8021 0.7984 0.7139 0.7883 0.7811 0.7713 0.7573 8.73bS 0.b771 8.b31b 0. b507 0 . 7 H 2 0.7b29 0. 9058 0.9702 1.0124 1.02b2 1.0193 0.9999
e. 8333
!;#I 0.u39 0.8271
0.7332 0.6999 0.b563 0 . 5938 0.3079 e.4405 0.5134 0.7204 0.9452 1.1399 1.2841 1.3792 1.4891 1.4071
: : E3
. *
8-2 1
1. 1-
SECTION CMIUCTERISTICt UG OF rnm
l.w#r MACH WQ V U I e . 6 z m o . w # r
SPAY STATIW 5.nm
Q ) ' o( 0.5:SW 1.01179 4 . m 8
PLOT OF CP AT COMPLITATIOUL MESi4 POIWTS X
3.2459 2.1714 2.5785 2.3401 2.1402 1.9b84 1.1179 1.6139 1.5628 1.4523
1.7760 1.7074 0.6418 0.r"
::43
::E!: 0.0151 0.0069 0.0017 0.0081 1.8017 e.0047
e a 1 7
V -0.3526 4 .3622 4 . 3 b 8 0 4 .3705 4 .3699 4 .3b60
-0.310b 4.2b34 4.24bO 4 . 2 0 2 3 4 . 1 4 3 1
4.07te 4.12% 4.1bbb
4 .3222
3:EB
3: 4%
4. I%# 4 . 1 2 6 7 4 . 0 9 1 4 -0.0718 4 . 0 4 4 1 4 .0127
0 . 0 2 ~ 0
0.1016 1. 1390 0.1725
0.24 7 1.2b14
e. 0627
o.zeio 0.22g6
WACH NO 0.8lb4
0.8125 0.8104 1.8079 0.8052 0 8019 1:79b1 0.7936 e.7171 0.7803 0.7704
e.8143
1.62
O.bZ25 1.8919 1.95p e.w 3
9.7152 0.6718 0.6082
0.44b3
0.9442 1.1422 1.2- 1.3783 1. a 2 6 1.4325
e . 5 1 ~ ~
::E:;
+ + + + +
+ + + + + + + + + + + +
+ +
+ + + + + + + + + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + . * + + + + + + +
+ + + +
B-22
I I
+ + + + +
i 1 1 I i 1 1
1.4141 1.3773
::m 1.8211 #.?S?b 1.73a3 1.7142 #.7b% 1.7811 1.7877 8.79% 8.7981 1 .8128 1. am2 1.uu 1.8104
1.8144 ::ti3
+
+
+
SECTIW owuLnERxsTlcL YAH UIG OF ATTAOI :%A 1.mrr 1.-
CM 1.15516 -0.2114s SPAY STATlW CL
7. 19999 1.145b2 PLOT OF CP AT UWPUTATIONAL HEW POINTS
X Y 3.2458 4.3053 2.8713 4 314 2 784 413194 2:!4#1 4.3218 1.1482 4.3212 1.9b84 4.317b 1.8179 4 . 3 1 U 1. b839 1.5b29 2:m
1 . M 4.M 1.9223 0.847b ::%! n.77bl 4. lW 1.7175 4.1bl1 0.6421 4.1154 1 79b 4 . 2 1 9 9 @:g213 4.2921 n.1642 4.3111 1.4114 4.3199
4.2818 1.19 4.2LII 1 . M 3 4.2359
#.#Ill 4.11W 1.0b13 -0.1343 1.0425 4.1103 0.0277 -0.0853 0.0158 4.Obm 0.0070 4.0322 0.0017 1.0015 1.eae0 0.8374
1.1734 0 . m 7 1.1MZ
::a ::fig
#.HI1 1.21U 1.U14 1.1169
MACtlY) CP 1.8142 1.0124 1.8141 1.8127 0.8123 1 .0 lb5
n.7938 8.7871 t:tfg 1.7796 1.M71 0.7b94 1.lN9 0.7151 1.7338 1. 6711
1.7488 1.11u
1.98b7 4.3518 1.W78 4.3933
1.7284 8.1971 8.6858 0.287b 1.6218 1.4214 1.53#2 #.bo39 0.4531 0.7455
1.9321 4 .2389 1 1% 4.6269 1:274# 4 . 8 9 U 1.%4# -1.B32b 1.4112 -P;l111 1.4249 -1.1222
3% :::x
6-23
+
+
+
+
1.41-
::m 8.97% 1.9288 8.8820 8.8297 0.7571
8.78b9 8.79$9 8.79 7 :::E;
SECTION QURACTERISTICS VAH AYG OF A l l =
0.- 1.-
8 . 99999 1.H145 8.80037
MACH yo o.nm SPAN STATIOY CL CD U
4.22729 PLOT OF CP AT CWPUTATXONAL HEW POINTS
X
2.8713 2.5785 2.1403 1.9b85 1.8181 1.68W 1.5630
3.1458
2.3401
::%: 1.-
0.7817 0.b423 0.5799 8.5287 0.464b 0.4118 0.%22 ::M!
0.0814 0.MM 0.04% 0.0278 0.0159 0.0070 0.0017 0.0000 0.Wlb 0.Wbb 0.0150 8.82bI 8.0417 8.0398 0.0811
Y 4.26bb -0.2728 -0.2778 -0.1800 4.2794 4 . 2 7 b 1 4 . 2 6 9 8 -0.2101 -0.24b7 4 . 2 2 8 8 3:m 4.MM 4.1310 4.0793 4.1334 -a. 1812 -0.2288 -*.2607 4.2804 4.29*3
4.1388 -0.1181 -0.0966 -0.0744 4 . 0 4 8 5 -0.0177
0.0152 0.0403 1.080( 1.1103 0.13b4
Iucn yo 0.8141 0.1139 0.8121 8.8108 0.817b 8.8045 0.1111 1.7971 0.7923 0.78b3 0.778b itjp 0.b 17 8.bZbZ 8. b480 8.6849 1.7427 0.8ldl 0.8757
8.9991
0.9717
::m :: E3 t:;m ::H
2 f:tl
8.8246 0.7978 0.7716 0.7422 0.7009
0.4574 0.5086 0.7087 0.9131 1.0997 1.24b8 1.3373 1.3840 1.48l3
+
+
+
+
+
+
+
+ +
+
+
8-24
1.39bb 1.3791 1.m1
1.9414 1.8697 1.8321 1.75bb 1.7271
1.7781 #.?&e 1.1921 1.7971 1.8111 1 . 8 M 1. as75
3: %#?
it jli .a141
SECTION ~ E R I S T l U VAH Affi Of ATTACK
l.#" CD
PLOT OF CP AT CO(PUIATI0YAL HEW POINTS
HACH yo s.aawe 1.- SPAN STATION o ( '
+.241W # . A b - 1 . ~ 7 1 10.79999
X
2.8715 2. 5786 2.1-3 2.1404 1.9cIC 1.8181
3. zum
::%! 1.1658 1.0811
1. 7178 S. b425 1.5M2 s.5211
1.3bZb ;::E
#.MU 1 . o w 7 0.0428 0.0279 6.0159 1. e070 0.0017 0.0080 1.W16 1.00b5 0.0149 1.02bb 8.M14 1.0595 1.M17
V 4 . 2 2 7 1 -0.2345 4.2391 -1.2411 4.24bb -1.137b
4.1943
4.lM 4.W19 4.Y11 1.1147
-1.lM6
3 : q
2:%f 2: :R:
-e. 14w 4.1232 4.104b -0.015s -0.Oc17 4.0336 -1.m3a 1.02b4 I.05bI 1.0837 8.1M4 1. 13.4 1. 14% 1. 1bb2
HAW NO 1.8139 8.8138 0.8121 m . 8 m m.8m73
::x S.fCb9 1.7521 1.73.b # . L o 3 1 . b W S. b y 1.67 1 1.8mn 0.8679 0.9283 1.9715 1.9916 1.9934 1.9843 1.9b74 8 . 9 9 1.917 1 . u 1.8598 1.8331 1.118b 1.7649 0.7581 0.716b 0,6541 1. 55% 0.u27 1. b835 1.6689 l.Dbb7
e.?=
m . w 7
1.3b74
+ +
+ +
' *
+
+
+
B-25
0.-
0.7%. 0.72H 1.74% 1.7bS7 0.77b9 0.7851
0::x
0.8041 0.8071 ..am 1.8121 0.8139 0.81U
+ +
+
SECTION CHARACTERISTICS VAN UG OF ATTAQ
O.M#OO l.OU.0 luenyo 1.u.w
SPAN STATION 12.59999
PLOT OF CP AT COMPUTATIOYM MESH POIYTS
a4 0.5%41 4.0%b -0.25044
X 3.2U2 2.8717 2.5788 2.1405 2.14W 1.9688 1.8183 1.6841 1.5611
1.2554 1.1659
: : 3:: 1.u
1. 7079 0. b427 0 . 58b4
o.nw
0: tu ::Pi: 0 . 1430 0.0281 O.Clb0 0.0071 O.OQ17 0.oSw
0.0411 0.0591 O.u.2
Y 4 . 1 9 6 8 4. 031 4 . 3 0 8 1 -0.2100
4 . 2 0 1 2 4 . 1 9 3 0 4 . 1 8 1 5 -0.1bb1 4.1460 4 . l Z M 4.ub4 -0.0417
0.0139 0.0287 1.0047
4 . 0 l b 4 4.0835 -0.12% -0. lb93 4.19% -0.21
-0.2348
3:m
- 0 . 2 3
4 . 1 2 5 1 4. IMS -0.8924 4 .0711 4 . 0 4 6 8 -0.0197
0.0075 0.0345 o.eb02 0.0836 0. M4b 0.1234 0 . 1 U l
MACH Yo CP 0.8119 0.0131 0.8139 0.0131 0.8121 0.0170 0.8099 0.0217 0.8073 1.0271 0.8042 0.0340 1.6005 0.0419 0.79b2 0.1513 0.7909 ..Ob26 0.7844 0.07bb
1 .7284 I.bbb4 1.UU O.blb9 1 411 O.b#3 0 : U l f 1.b724 0 11 9 0.7282 0.1921 0.8592 4.0840 0.9202 -0.2117 0.9b39 -0.3049 0.9841 4.3471 0 . 9 W -0. 0 . 9 m -0.
0.9191 1.8932 ..ab74 0.8437 3. 0.8223 +.OM0 0.8019 0.1389 0.7784 1.0896
0.6771 0 .3W1 0.57*8 0.5181 0.4701 0.7154 0.4912 0.6772 0.b618 1.3383 0.8579 -0.0814 1.8261 -0.4319 l.16b2 4 . 7 0 1 2 1 2589 -0 8641 1'3025 -0.9361
0.7416 0 . x . a ~
1:mr 4 : n r c
+
+
+
+
B-26
B I I I I I I I 1 I I 1 I 1 I I 1 I 1
+
+ + +
+ + + + +
+
+
+ -
+
SECTION OURACTERISTICS VIW AMG OF ATTAaC
IucMNo 0.82#m 0.oHea 1 . I w I I 01
4.17451 W
PLOT OF CP AT COWPUTATIONAL MEW POINTS
4 . 0 1 1 1 1 SPAN STATION a.
14.39999 0.59392
x 3.24bb 2. 8720 2.5791 2.3408 2.1- 1.9691 l . 8 l U I . b84b 1.5b33 1.4529 1.2 56 1 . 7 "
!:it: 0.7763
0. 6428
a.4bCn 0.4129 O.Jb34
a.2341
o . m o
5:z:::
5: 3w 8.0022 @.a412 0.0432 0.ezaz 0.01b1 0.0071 0.0017 0.0008 0.W16 0 . W 4 0.0145 #.#ZbO #.OM?
0.0 98 0 .987
V 4 lb8
4 . 1 8 0 4 4. I799 4 . 1 7 7 3 4 . 1 7 2 3 4 lb47 4: 1541 4. 1399 4 . 1 2 1 4 -#.a464 4 . 0 2 b 4 0.026# 8.0398 8.0188
4 . 0 1 8 2 4 . # b 1 3 4 . 1 0 3 8 4 . 1 4 1 1 4 . 1 7 0 1
-0.2059
4.nn -4.1- -4.lb99
4 . 1 3 5 0 4 . 1 2 4 0 -0.1111 -0,0965 4 . 0 7 8 4 -0.0561 4 . 0 3 1 9 -0.0076
0.81bb 0.0403 0.a421 0.0019 0.11bS
3; ::it
4 . n r 4
::E3
3: 3: E#:
4 . z w
o.im
CP 0.0125 0.0123
0.0327 O.w.7 a.msM 8.1772 0.0959
a. a424
3: !E 0.41b4 I.332b 8.2173 #.112#
4 3 3 9 -0:31+3
-4.1bH
4 . w 4 0.1014 0.2390 0.4b55 0.6930 0.b972 0.39bO 4.moM 3::cs! - a . m b 4. 8434 4 . 8 6 1 4
B-27
+ +
+
* .
* +
+ + + + *
+
*
+
O.lb90 O.l7#f
0.19% 0 . 2 m 0.2040
2#24
: : f t43
0.e3b7 - 0 . O l S l -0 . Isa +.OM7
3: fl::
-a:€S?s - 0 6 4 .
SECTION aUR*CIERISTIQ V U ANG OF ATT*Q(
1.- CD
4.01b12
PLOT OF CP AT COWPUTATIWAL MESH POINTS
lwkw r.ann ..om.@ 16.19998 ..sa279
a4 -0.283b3
SPAN STATIo(I a
X 3.2472 2.872b 2.57% 2.3412 2.1412 1 . 9 0 4 1.8189 1. (848 1.5b38 1.4532
0.030 0 . s m e.s219 0 . 4 W 0.4133
e n s a . a m #:04!4
O.Olb2 0.0871 0.0017 O . e w 4 0.0017 # . a 6 4 0.8142 3:s ::m
Y -0.1479 4 . 1 5 4 0 -0.1577 4 . 1 5 9 4 4 . 1 9e
4 . l S l 8 4 . 1 4 4 6 -0.1346
-0,1865
-0.0520 -&e142
..om8 4 . 0 3 7 4
-0.137S 4 .1Sb1 4 . 1 6 7 2 -0.1728
3: !;if
4 . 1 Y 3 -0.1279 4 . 1 1 9 1 4. 1089 4 . 0 9 6 7 -0.0812 -0.06 18 -0.- 4 . 0 1 9 2 0.0023 #.e239
#.OM4 ,.nu
0.0443 0 . ~ 0
MACH NO 1.8154 0.8153 0.8138 #.a121 # . a m 0 8171 #:E037 e.7994 0.7939 0.7869 0.76S7 1.749.
016087 0.6181 0 .7e 9
0.7778
t.2:: e.csy
0.9- 0.9b01 0 9628 0.9492 0.9377 0:mc
::zz 0.8592 0.8489 0.8228 0.75% 0.6434 0.4743 @ .6H2 0.7789 0.931b
0.5071
8-28
+ +
+ +
+
+
+
*
+ +
+
+ . *
SECTION CHARACTERISTICS )(*a4 w) YAM *wi OF ATTACK m . a z m 0.- 1.-
17.99998 m . ~ 3 5 s +.0!2103 o(
-0.238U SPAN STATION CL CD
PLOT OF CP AT CWUTATIONAL MESH POINTS
+
+ f
+
+
+
8-29
IWDIUTIW OF Loc*TIoY OF W I Y i VOlfU SHEET IN tOOMINATE PLANE Y - I.
I
i
i : 1 i
! 1
i
i !
1 3 2
f f f 2 2
3 2
i 2
i 2
i 2
2 2 2 2 2 2 f
2 2 f f f
f f f
3
f f
2
2 2 2 2
2 2 2 2 2
2 2 2 2
2
1 :
II 1 : 1 1
1 1 :: i i
i i
I 1 1 1
i i ii 2
i f f f 2 2
2 2 2 2 1 1 i i i f f
2 2
l 2 2 2 2 2 2 2 f f f
f f
2 2 2 2
2
i 2 2 2 f i f 2
f ; i f
2 2
2 2
2
2
8-3 1
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2 I: If -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 a -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -4 -2 -2 -2 -2 -2 -2 -2 -2
-1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 . -1 -2 -2 - -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
2 -2 -2 -2 -2 -2 -2 I: If -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 - - If I2 -2 -2 -2 - -2 -2 -2
-2 -2 -2 -4 -2 -2 -2 -1 j ;[ -2 -9 If If If If If If If - If 11 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 - -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 - -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 - -2 -2 -2 -2 -2 -2 -2 -1 - -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 - - -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2
- -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-1 - -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 e I I O I I I e I I - 2
-2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 - -2 -2 -2 -2 -2 -2 -2
2 -2 -2 -2 -2 -2 -2
-1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-2 -2 -2 -2 -2 -2 -2 -2 -1 -2 -2 - -2 -2 -2 -2 -2 -2 -2 -2 - - - - -2 -2 - -2 -2 -2 -2 -2
1: If -2 -2 '8 -2 -2 -2 -2 -2 -2 -2
I1 If If I! -8 -2 -2 -2 -2 -2 -2 -2
If -2 -2 -f -2 -2 -2 -2 -2 -2 -2 -2 1: If If If If 3 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-1 -1 - 2 -2 -2 -2 -2 -2 -2 -2 -2 -2
If If -2 3 -2 -2 -2 -2 -2 -2
-1 -f - 2 -2 -2 -2 -2 -2 -2 -2 -2 -2
-: If -2 - -2 -2 -2 -2 -2 -2 -2 -2
3 -1 -2 -2 -2 -f - I: If If If -2 If If rf If If If If -1 -2 -2 -2 3 -2 -2 -2 -2 -2 -2 -2
I; $/;/f/:p2 - If -2 if -2 If If -2 If If -2 If If -2 -2
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SPANbIIfE CELL DISTRIWlION A Y ) SIYQLM LINE
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INTEGRATION SPAN STATION SPAN STATION SPAN STATION SPAN STATION SPAN STATION SPAN STATION SPAN STATION SPAN STATIOW
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BETA n MlNC UE CF TE MLST OELSTX AL
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SPAN V H HI nc UE A 1 DELST OELSTX CF BETA TE
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LAMINAR SEPARATION AT 8.5 PERCENTAGE YINC0I)RD
TRANSITION LAMINAR - TW8NEW
X - 1.M1126
B -36
ORlGlPJAL F L ~ C E S OF POOR QUALITY
LOWER WING SUIFKE BOUNDARY LAYER STARTING NODE LOWER WING IHNODE- 153
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0:9000f+00 0:6364E44 0:1411E43 115592 -02 0 1397143 0 5 5 0 1 f 4 2
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LAMINAR SEPARATION AT 49.8 PERCENTAGE N I " 0 R D
TRANSITIW LUllNAR - NRIULEWT
N H T WWF N H T GAMF N H T GAMF U H T GAMF
N H T W F N H T E G A M F N H T E G A M F N H T E G A M F N H T E G A M F N TE GAM F N M TE GAM F NMTEGAMF N H T E G A M F N H T E G A M F
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0.20366E41 0.20336E41
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0.9136E42 0.8093E-82 0.78PE-02 0.79ME-02 0 7909E-02 0:7834E42
-0.8492E-82 4.8036E-82 4 .7674E42 4 .7344E42 -0.7203E-02 4 .7071E42
B-37
TE DELST DELSTX CF BETA M MINC UE AL
x - 3.005978 SPAN V DELST DELSTX CF BETA TE H HIUC UE AL
1 1 1 II
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X - 3.050b74
SPAN Y TE DELST DELSTX CF BETA M M I NC UE AL
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2
8 10 :: 13 14
if 18 19 ::
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B-38
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X - #.Mi335 TE DELST DELSlX CF BETA H nxwc UE AL SPAN V
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:: 12 !i 0'5433E+I1 0'3734E+01
20 21
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0 5418lf-M 0'93887E-M 0 : 18266E-H 0 36661E-04 0'53351E-05 0'83208E-M 0'16521E-H 0:3%WlE-M
e.mmwo
::m
4.28793E-04 -0 31625E-04 -0:31528E-04 4.29281E-04 -0 24456E-84 4'27635E-04 4'27207E-84 -0:25343€-84
RrrmCTYlCTCLE 0.9409 )(u( -0.5464E-03 I SiDAL 1 )(u 4.2646E-M RESXDAL 2 % L e
6-54
160 160 160 160 160 160 160 160
2 3 0.11503E-86 0.03379 3461 2 3 0.131WE-86 0.03374 3455 2 3 0 11653E-86 0.03364 3444 1 0:11161€-06 0.03341 3420
0 11274E-06 0.03335 3420 f $ I:lM51E-B6 0.03326 3413
0.10362E-06 0.03310 3395
0'11253~-06 0.03346 3431
ORIGINAL PAGE 15 ff POOR QUALITY
SECTION O U l U C T E R I S l I C S
KOT OF a AT COIUTATIQW. MEW POINTS X
2.8725 2.22 I : 4 5 4
2 . n 2 1 1.9C91 1.8915 1.61M 1.7497
1 : 452# 1.4- 1 .35H 1.3021 1.2552 1.2098 1.1657
1.WM 1.Sm 0.9bM 0.9223 0 884 018478 1.8112 1.7757 1.7- 1. ?e49 1. b736
::iic
t : tUf 0.4W5 0.4b28
0.4359 0.4a98 0 . 3 8 4 0.3b02
0.27Ob 0.2s02 0.2307 0.2120 0.1941 0.1771 0.1608 0.1454 0.1308 0 . l lb9 0.1039 0.091b 0.0801 0.0b94 0.0594 0. 0502 0.0418 0.0341 1. 0272 1.0210 1.0154 1.0107 0.M8 0.WU 0.0017 0 . 0 H 4 O . @ O M 1. 0014 1.W17 1.W3b 0 . 6 6 0 1.0lM
1. 1349 0.H29 # . M U #.e611 1.0714 O.Ob2S 0.0944 0.1070 6.12B4 8.1345 0.1494 0. U S 1 1.181b
8.2169 0 . 2357
1. i q m
t:3#
V 4 3 6 4 4:3bJ 3:m m:: 4.3b49
4 . 3 b 7 -#.38bl d.3b44
4.3747 4 . Y 9 8 4 . Y W
If:##
4.3m
3 : p 3. 4: 37 1212 3: 1%
4: l h 5 4 1 b
4.1m 4.2174 4 .2492
3: 3B a:::!! 3::f:: 38f:
4.4147
4 . 4 2 9 3 4 .428b
4.4889 4.3985
4 .3543 4.33b8 6.3179 4 .2977 -0.27b8 -0.2s53 4.233b 4 .2116 -8.1897 d . l b b 2 4 . 1 4 7 1 4.12b4 4 . l O b l -0.Obb3 6 . 0 b 7 1 -0.64b2 4 .0294 4 .1117 #.#e77 1.0258 e. 1449 #.Ob57 # . M I 1 8.1114 1.1351 1 . 1 5 H 1. 182b 1 . 2 W 1. 2294
1.3989 0.3bW 1. 3755 1.381b 0.3bb4 6.3902 8.3931 0.3913 0.39b7
1. 3958 0.39% 1.39Ob 1.3867
Wl% 1.81b8 1.8159 1.8148 0.8137 1.812b 0.8113 1.8099 (1.8091 1. be84 0.8074 1.8eb2 1 . b W 1.8134 1.8018
1. 7937 t : E4 I;% 1.7b8b
0. b85S 1.b19b 1.b210 1.b4b3 1. b849 1.7247 1.7bb4 t:8lW 1.33 e.%= 1.0267 1. n89 1.W83 1. ObbS l.OS4b 1.0358
1.0186 1.WW 1.9b50 0.9b29 0.9431 0.92bO 1.9Wb 1.b852
0.8210 0 . 8080 0.7882 0.7b93 8.7511 0 . 7333 0.71b4 0.7008 0. bbb3 1.b722 1.b583 8.6450
'0.6321 O.blb3 0 . be20
1.53M 1.%9 1. 45b4 1.39bb 1.3478 1.3271 0.35T 1.42 5 1.5211 1.b194 1.7124 1.7909 1.8471 1.8833 1.9181
I : t:51
I: 83:
1.11b9 1.02b7 1.03- 1.0399 1.0451
1.0541 1.1581 1.Ob22 l.Obb4 1.0709 1.0752 1.1792 1. 082b 1.0856
I .
1 . 8 3 1 1.mr 1. W89 0.8113 1. 11%
1.1234 1.1249 1.0272 1.0298 1.132b
1.17
1.1W3 1. 1272 0.2883 1.42% 0.4211 1.- 0.28%
0.1153
4 . U 8 b 4.4512
4 . 4 l b 7 4.3bb4 4.3484 4. 3028 4 . 2 b l b -8.2258 4 .1849 4 139
4. MOO 4 . 0 1 7 2
0.0259 0 . ob85 8.1091 0 .1U3 0.18b4 1.222b 0.2557 0.28bS 1.31b3 1.3455 0.3734 0 . a 2 1. 42M 1.w19 # . H I 1
0 . (518 0.7397 0.8Wb 0.9143 0.9436 0.9011 0.7895 0.b214 1.42b2
4:sttf
t : 8%
::a 4 . 3 9
z:;% -# .2bu *.a5 4.4134
4 .4595 4 .4b99 -0.4792 -0.637b -#.4%b 4. SOW 4.5120 4 .52e4 4 .5291 4.5W8 4.5434 4 .5494
+
+
+
+ +
+ +
+
+
B-55
1.2968 0.3187 0.3415 I: Pf! 1.4944
1.6121 1.6434 0.6756 1.7085 0.7423 0.7767 0.8120 1.8481 1.8849 0.9225 0. 9b09
1.749 1.8186 1.8916 1.9692 2.0521 2.1410 2.2370 2.3411 2.4547 2. 795 2.!179 2.8726 3.0473 3.2472 3.4792
0.3820 0.3763 0.369b 6.3619 0.3532
:: 9:J
:::J:: 3.269
6.1468 0.1161 0.0837 6.0494 6.8132
4 .0244 -0.104 4.1032 4.1486 -0.1847 4.2148
4:2783 :*:it3
4. 3 . w 4:3595 4.3643 4.3684 4.3716 -0.3740 4.3757 -0 3768 4:3771 4.3769 4.3760 4.3745 4.3725 -0.3700 4.3669 4.3633 ::Et
1.0886 1.0916 1.0949 1.1037 1.1892 1.1153 1.1218 1.1284 1.1346 1.1400 1.1446 1.14b4 1.1425 1.1289 1.1012 1.05b5 1. 9862 0.9204 0.8869 0.8633 1.8365 0.8005 1.7354 1.b945 0.7099 1.7324 1.7476
0.7731 1.7784 0.7828 1.7866 1.7399 0.7928
0.7998 0.8017 0.8034 6.8051 0.8066 0.8079 0 . 8088 0.8098 8.8112 0.8127 1.813a 1.8148 1.8158 1.8168 0.8138
1.0989
t::%
I: :3:
4.5551 -1.5609
-0 606 4 : b d
4.bb11 -#Ab46
4 . 9 9 3 -0.4924 4.3500 -0.2140 4.1431 4 e928
0.0419 1 1821 1:2691 0.2364 0.1883
8.1140
1.MH 0.n1r 0 . W 0.0585
z::m
4: 3354
3.: :3z o im 1:MM
I*%? 1:8435 0.0394 0.03Sb 1.0321 1.0289 0.02b0 0.0240 0 . 8220 8.8189 0.0158 0.0133 0.0111 0.0090 0.m9 0.1133
SECTION CHARACTERISTICS YAM Affi OF ATTACU
l.#Bw HACM YO 0.82000 1.eeeee
a4 4.17199
tD 8.04882
CL CO CH ARE BASED 01 VISCOUS PRESSURE
SPAN STATION CL 0.900ob 0.41685
PLOT OF CP AT COHPLITAT10YAL MESH POINTS
X 3.4787 3.2467 3.0468 2.8721 2.7174 2.5791 2.4542 2. 3407
2.0517 1.9689 1.8913 1.8183 1.7495 1.6842 1.6223 1.3632 1.5067 1.4525 1.4a05 1.3504 1.3020 1.2551 1.2097 1.165b 1.1227 1.8809 1.0404 l.00M 0.9666 0.9223 0 884 0:8472 0.8113
0.7410 0.7070 0.6737 0.6413 0.6095 1.5786 0.5485 0.5192 0 . 4917 1.4630
m:
0.7758
Y -0.4833 -0.4760 -0.4694 -0.4634 4.4578 -0.4525 -0.4471 -0.4418 -0.4366 4.4308 -0.4250 4. 4188 4.4123 4.4053 -0.3978 -0.3897 4.3810 4.3715 4.3613 -0.3501 4.3379 4.3245 4.3098 -0.2936 4.27% {ij# -0.1764 -0.1409 -0.1121 4.1092 4.1217 4.1435 -0.1706 -0.2009 -0.2325 -0.2641 -0.2944 4.3224 -0.3478 -0.3686 4 .)a50 4.3984 -0.4077 4.4125
HACM YO 0.8136 0.8167 0.8157 8.8146 0.8136 0.8125 0.8112 0 . 8099 0.8091 0.8083 0.8072 0 . 8060 0.8046 0 . 8032 0.8116 0.7999 0.7960 0.7938 0.7913 0.7885 0 . 7854 0.7819 0.7779 0.7736 6.7690 0.7b51 1.7642 1.7512 1.68b9 0.6217 0.6122 0.6310 0.6611 0.6957 0.7327 0.7718 0.8129 0.8554 0.9018 0.9582 1.0143 1.0552 1.0793 1.6614 1.M7
1.7981
CP 0.0138 0.0072 0.0093 p i 0.0188 0.0216 0.0235
1.0Y2
0.0362 1.039b 6 .e432 0.0472 0.05lb 0.0564
0.0678 1.0745 0.0821 0.-
:::a: 1.0331
e.ni8
ii% 0.1m 0.1479 1.2853 1.4195 0.4411 1.4025 0.3396 0.2666 0.1878 8.1037 0.0153 4.0759 -0.1740 4.2932 4.4000 4.4098
4.5125 23:::
8-56
*
+ + +
?
+ + + + +
+ + + + + + + + + + + + +
+
+
+ +
+
+ + +
+
+ + + + + + +
+ +
+ +
+
+
@.4%1 @.41@@ a.3848
fi.3139 ::m
1.0917 fi.1802 @.ab95 @.M% 1.m3 1.@419 fi.0342 fi.0273 @.a211
@.an8 1. a038 0 . H 1 7 a . m * @.ow@ @.@am fi.Wl7 @.a038 #.@ab9 1.filM fi.fil5b
@ . O W 0.0428 0 051
fi.0824 1.0942 a. lab9 1. 1202 1. 1344
::ti#
::ti#
:.ad
8.21b7 a.2355 t : :sa 0.2967 0.318b 0.3413 a. 364* 0.3892 8.4143 0.44fil 0.4b68 0 . 4943 0.5225 0.5515 0.5814 0.b120 0.6433 0.6755 0.7085
0.8110 0.8480 0.8849 1.9225 0.9b09 1.0000 l .04W 1.0809 1.1227 1.1b51 1.2098 1.2551 1.3@2@ 1.35H 1.- 1.451) 1.5W7 1. 5b32 1. (223 1. b843 1.7495
1 9b&
f : :%
1. g 8 3
: ; 2% # t 2 34.7
2.7174 3. B4bB 3.2467 3.4787
2.a7zi
4 6147 414147
4.
4: :::I 3: 3:: 3%; 4 . 1 1 3 a 4 . 0 9 4 2
4 . M 1 4 . 1 2 2 2 4.M
' 9 4
:::% : : It3
a. 1 4
a. 1875 a . 2 m
a . m 3 0.3141 fi.32b4 0.3372 0.34b4
1.n a.nw a.3732
a. 3754 0 . 3722
0.3b83 0.3b34 1.3516 0.3509 fi.3431 f;j#t
p3ji
0 . 2985 0.2833 0.2b62 0.2474 0.2266 0.2037 0.1788
B.W% a.0250
4 . 0 1 1 0
4 . 1 W 4 4. US9 4 . 1 9 b 3 4.2223 -0 24 1 -0:Zbtl 4 . 2 8 3 2 -0.2994 -0.3141
4. 3518
4 . 3 7 9 4 . 3 8 7 4
3:t::f
3 3 % 4:BY pJ 33iE -0.4314 4 . 4 w 7 -0.4421 -0.kk74 -0.4230 4 . 4 5 9 0 -0.4656 -0.4729
1. MI7 1.142fi
fi.987 fi.9741 1.95b4 1.9354 a . 9 1 u 1.89fib a . u w
I:' fi.7522 1. 7374 1.7131 fi.7088 @.OW 1.68lb fi.bbb9 1. b49#
a.4775 1.4114 1.3594 a.3405 0.3992 a.4974 fi.bl72 fi.7419 @.Ob23 I.%)*
l.l4b* 1.1799 1.2fi77 1.2243 1.22bb
::m
l.lfi42 1.1H1 1.1141 1.1144
1.1052 1.10bb 1.1087 1.1121 1.117fi 1.1227 1. 1288 1.1353 1.141b 1.14b5 1.14% 1.15ar #if
f;;#f
1.0273 0.9bb1 1.920b fi.8912 0.8b71 0.8417 0.8141
0.7231 8.7415 a.7539 @.7b3@ a . 7 7 w a. 77% 1.7803 0.7843 1.7878 fi.7908 0.7935 1.7959 fi.7981 @.la01 a 8a 9 #:8& pJJ @:8M# 0.8097 0.8111 8.8124 0.8135 0.8145 1.815b 8.816b 0.8135
+ +
-0.5871
+.b@OZ [email protected] 4.bZfi3 4 .b318 4. b439 4. b557 4 . b 6 4 8 4 . b 7 0 5 -@.(?I( -0.6611 -0.b259 4.5503 4 . 4 3 4 3
2: 1:;:
3;jg 4. 101a 4 . w 5 @.a122 fi.MZb 0. 1889 1.2431 fi.2M3 1 . lbM 1.1421 1.1227 1.117b 1.0955 @.@E53 O.fi7b7 @.ab93 a. ab28 a . m o @.as18 1.1471 0.wn a . u n #.I354
O.Qb1 0.1243 1.1122 fi.1194 0.01b4 0.0140 0.0117 0 . M 5 0.w74 1.014.
::E!
6-57
+
+
+
+
+
+
+ +
+
SECTION CHARACTERISTICS A N OF ATTACK
1.- W
0.033% U CD CM ARE BASED Ow Vf-S PRESSURE
V U I
SPAY TATION n -IK) 0.82- 0 . m r r
01 -0.1b903 l.8fm 0.428 9
PLOT OF CP AT UlPvTATIOWM MEW POIUS X
322;
til%;
2.8718 2.7172 2.5789 2.4541 I:::$ 1.8912 1.8182 1.7494
1.501 1. 5067 1.4525 1.- 1.3504 1.3020
i:::;:
I;%!! 1.1227 1.0809 1.0400 1.0080 0.9608 0.9223 0.8845 0.8475 0.8113 0.7758 0.7411 0.7071 0.b738 0.b414 0.6097 0. 5788 0.5487 0.5194 0.4909 0.4632
0.4363 0.4102 0.3850 0.3606 0.3369 0.3141 0.2710 0.2506 0.2311 0.2124 0.1945 0.1775 0.1612 0.1457 0.1311 0.1172 0.1041 0.0918 0.0803 0.0696 0.059b 0.0504 0.0420 0.0343 0.0273 0.0211 0.0155 0.0107 0.0068 0.0038 0.0017 0.0004 0 . 0000 0.0004 0.0017 0.0038 0 . W I 0.0107 0.0155 0.0212 0.027b 0.0347 0.0427 0.0514 0.0609 0.0712 0.0813 0.0V41 0.1067 0.1201 0.1492 0.1648 0.1813 0.1986 0.216b 0.2354
0.2921
a. 1342
t:IRt
Y
-0. is45 -0. b744
-0.4499 4.4429 -0.4361 -0.4294 -0.4229 -0.41b2 - 0 . m 4 -0. bo24
3:%
y g -0.37n
-0'34a -0: 3295 3.3:: Z : M 3::s:: -0.2550 4.2352 -0.2129 4.1877 -0.1583 -0.1241 -0.0968 -0. e944 -0.1070 -0.1287 -0.1555 -0.1855 4.21b8 -0.2482 -0.2783 -0.3315 -0.3525 4.3b92 -0.129 -0.3927 -0.3980
-0.3n2
-0.6008 -0.6014 4.3989 -0.3935 -0: 3865 -0.3779 -0.3671
-0.3401 -0.3248 -0.3882 4. 2904 -0.17 19 -0.2529 -0.2336 -0.2141 -0.1946 -0.1754 -0.1565 -0.1380 -0.1197 -6.1019 -0.8846 -4.8676 4.0505 -a 033
0.0000 0.017b 0.I370 0.0579 0.0797 8.1119
0.1b89 0.19Ob 0.2114 0.1485 #.2b44 0.2791
031 0.3329 0.3395 0.3450 0.3495 0.3533 0.3563 0.3587 0.3606 0.3618 8.3624 0.3623 0.3b15 8.3598 8.3574
-e 3542
-O:rl'?
:: i 3 o.nm
::a:: 0: 32z
)urn YO a.8133 0.8164 0.8155 0.8145 0.8125 0.8113 0.8101 0.8091 0.8083 0.8072 0.8060 0.8047 0.8033 0.8018 0.8001 0.7983 0.79b4 0.7942 0.7917 0.7890 0.7859 0.7825 0.7785 8.7741 0.704 0.7b50 0.7629 0.7497 0.b869 0.b222 0.6092 1.6254 0.6527 0. b843 0.7183 0.7544 8.7927 0.8325 0.874b 0.9204 0.9705 1.0222 1.0652 1.0841 1.0798
e.013~
1.0720 1.0648 1.8495 1.0299 1.0153 1.0038 0.9871 0.9654 0.9452 0.9275 0.9089 0.8886 0.8683 0.8487 0.8295 0.8106 0.7925 0.7759 0.7605 8.7455 0.7306 0.7160 0.7019 0.6865 0.b678 0 . b455 0.b2Ob 0.5911 0.5500 0 . 4942 0.4321 1. 3846 0.3799 0.4341 0.5336 9.6546 0.7814 0.9063 1.0223 1.1193 1.180 1.2294 1.2bZS 1.2Hb 1.3228 1.3351 1.3184 1.2910 1.2576 1.2226 1.1909 1.1663 1.1498 1.1402 1.1350 1.1320 1.1297 1.1274 1.1256
i . m r
CP 0.0143 0.0077 8.00% 0.0118 0.0146 0.0162 0.0188 0.0214 0.0234 f$3! 0.0329 0.0359 0.0392 0.0427 0.04bb 0.0509 0.05% 0.MM 0.06b7
0 089
0.1089 0.1184 0.1229 0.1511 0 . 2854 0.4205 0.4472 0.4140 0.3573 0.2908 0.2185 0.1410
4.1170 -0.2141 -0.318b 4.4239 -0.5095 -0.5464 -0.5381
::t:3 o:mrf
4:m
4.5229 -0.5088 -0.478b -0.4394 4.4101 -0.38b8 -0.3527 4.3081 -0.26b1 -0.2289 -0.1897 -0.1468 -0.1035 -0.0blS -0.0204 0.0202 0.0591 0.0949 0.1279 0.1602 0.1923 0.2233 0.2534 0.2861 0.3257 0.3723 0.4238 0.4839
0 7 18 0.8b63 0.7783 0.5974 0.3534 0.0830 -0.1842 4.4243 -0.bl38 -0.806 -0.8702 -0.92b6 -0.%M 4.9Ws -0.9881 -8.96 16 -0.9173 -0.8618 -0.8018 -0.7459 -0.7012 -0.6709 -0.6530 -0.b434 -0.b378 4. (334 -0.6292 -0. b258
::E8 0:8091
*.733#
+
+ +
+ + +
+ + +
+
+ + + +
+ + +
+
+
+ + +
+
+ + +
+
+
+ +
+ +
+
+
+
+
+ +
+ +
+ + +
+ *
I R
5-58
4 . b 2 3 9
4 . b
4.3119 4 .22(1 4. 1775 4.13W 4. e247
@.I311
-e.e?aa e. e942
0.m1 0.w11
0.0291 @ . @2b3 @.e241 e.0220 1.0193 e.e1bb @.e142 @.elm e.m9 0.e14b e.wn
SECTION CHARACTERISTICS
01 4 .1b7b3
W 0.e24be
U CD 01 ARE BASED OY V l S M PRESSURE SPAN STATION CL 2.78000 1.43311
PLOT OF CP AT COMPUTATIONAL HESH POINTS X
3.2463 3 . e u 4 2.0717 2.7171
2.454e 2.3404 2.23b4 2.14M 2.Mlb 1.8911
1. b842 1. b222
1.4525 1 . 4 M 1.35@4 1.3820
3.4712
2.3780
1. )+a?
:: #%
::$E#
I. 1227 1 . W l.WW
e. aa*c
e 74-1
0.8476 0.8113 0.7759
0:70+1 1.b739 0.b41S @.be98 ::p e. 195
0.4911 e.&=
V
4 . 4 4 5 7 4 .43bO 4 . 4 2 @ 9 4 .4215 4.414b 4 .4e79 4 .4@14 4.3950
4 . 4 5 5 0
-3. 3085 pu 3:s: 3:w
::i::3
314% 3: :2: 3:%t
4 . 3 2 b 2 4 . 3 1 b 1 4.3051
4 .2bb 4 . 2 5 4 4 .233
4.1b92
+.e933 4.1148 -0.1414 -0.1710 4 .2820 -0.2331 [email protected] 4. 29e7 4 . 3 1 5 9 4. 3370 4 . 3 5 4 0 4 . 3 b 8 0 4.3781 4.304e
nrcn NO
m.81*4
e.0124 e.0113 o . a m
0.8133 0.81b3 0.8154
e.8134
0.8092 0.8003 0.8072 I.8eb3 e . a w e . a w e.aei9 e . 1 ~ 3 e. 7915 e.796) e.7944 0.7920 e.7892 @.7@b2
e.7743 1.7b94 1.7b48 e . 7 0 4 e.74w
e.?an 0.7717
!ii#i 1. b232 e.6491 0.6791 0.7114 0.7459 0.7823 0. 82e4 0.9827 0.9449 e.9923
1.07@7 1. 0774
e. w o o
1.0400
+
+
+
B-59
1.4365 0.4104 1.3852 1.3608 1.3371 1.3143 1.2923 1.2712 1.2508 1.2313 1.212b 1. 1947 1. 1776 1.1b14 1.1459 1.1312 1.1174 0.1043 0.0920 0.0805 0.0697 0 . 0597 1.0505 0.w21 1.0343 0.0274 1.1211 0.0156 1.0108 1.0068 *.Ha 1.0@17 #.ne4 0.eaM 0 .ne4 1.0117 0.0038 0.mb8 0.0107 0.0155 1.0211 0.0275 0. 0 3 6 0.042b 0.0513 0.0608 0.0711 0.0821 0.0940 1.1066 1 . 1 2 w 0.1341 0.1490 1.1b47 1.1812 0.1984 0.2164 0.2352 0.2548 0.2752
4 .3873 4 .3885 4.386b 4.3820 3.1758 4.3b81 3.3581 3 . M 3 4.331) 4.3189 3.3035 3 . 2 8 0 4 . 2 6 r 4 . 2 5 1 3 .2335 4 .2152 4 .1968 4 .1781 4.1609 4 .1434 4 .1262
4 .1768
4 3 4 4 3 4.1283 4 .1123 0.0046 1.0233 1.uu 1.0644
4.1093
4.0606
:::E ::IF 0.1 18 0.1920 1.2111 0.2282 0.2439 0.2583 0.2717 0.2838 0.2946 0.3040 0.3120 0.3188 0.324b 1.3294 0.33% 1.3371 1.3399 0.3422 0.3439 1. 3450 0.3455 8.3452 0.3442 0.3425
1.1775 1.0750 1.0623 1.1* 1.0319
1.9847 1.9643 a. 9461 0.92b9 1.9062 1.8855 1.8655 1.8459 1.82b6 1.8081 1.7911 0.7754 0.7601 1.1448 1. 7300 1.7155 1.b998 0.6807 1.6580 0.632b 0. be24 0.5605 8.5039 1.4417 1.3951 1.3916 1.w 1.546b 0.6b81 0 . 7958 0.9224 1.1430 1.1437 1.2103 1.2549 1.2950 1.3325 1.3636 1.3847 1.3922 1.3857 1.3b90 1.3447
1 . 2 m 1.2069 1.1808 1.1635 1.1538 1.1667 1.1456 1.1433
La
i:%Y
-0 336 4:3286 -0.5038 3 . 4 6 8 9
4 . 3 4 7 8
4 . 2 b 8 4 2278
3 . 1 4 1 2 3 0976
4 . 1 1 4 1 1.1257 0.0621 0. 1959 0.1289 1.1b18 1.1936 1.2244 0.2579 1. 2984 1.34b3 0.3991 1.4611 1. 5451 1. (537 1 lb53 @:a427
4 . 3 9 8
3: 1848
3:nn
1 .3230 1.0521
4 . 2 1 8 2 4 . 4 6 5 7 4 b 9b 4 . 8 5 7 2 4 . 9 2 3 9 -0.9839 -1.0319 -1.0637 -1.0749 -1.0653 -1.0402 -1.0029 4 . 9 5 3 9 -0.89% 4 . 8 3 2 9 4 . 7 7 4 3 4 . 7 2 7 b 4. b9b2 -0.b783 4 .6b89 4 . 6 1 3 1 4 . 6 5 8 9
4 : 7 f 1 3
0.2964 0.3183 0.3411 0.3646 0.3889 0.4140 0.4399 0.4666 0.4940 0.5223 0.5513 0.5812 0.6118 0.6432 0.6753 0.7083 0.7421 0.7766 0.8119 0 . 8480 0.8848 0.9224 0.9609 1.0000 1.0400 1.0809 1.1228 1.1657 1.2098 1.2552 1.3121 1.3504 1.4005 1.4526 1.5067 1.5632 1.6222 1. C842 1.1494 1.8182 1.1912 1. H87 2.05lb 2.1* 2.2364 2.34@5 2.4540 2. 5788 2.7171 2.8717 3.04b4 3.2663 3.4782
0.3400 0.3367 0.3325
0.3144 0.3061 b.2965 0.2854 0.2726 0.2582 0.2421 0.2243 0.204- 0.1827 0.1591 0.1336 0.1061 0.07b5 0.0451 0.0120
4 .0224 -0.0577 -1.0979
4 .1829 4 .2042 4 .2232 4 .2403 4.2558 4.2699 4.2828 -0.294b 6 .3056 -0.3158 -0.3252 4.3340 -0.3423 4.3512 4.357b
:::::3
3: E95
m:7 4pJ 4.3910 -B.39?5 -0.4041 -0.41 11 -0.4184 -0.4264 -0.4353 -0.4453
1.1417 1.1407 1.1467 1.1423 1.1456 1.1499 1.1544 1.1588 1.1617 1.1b02 1.1510 1.1284 1.0853 1.0248 0.9693 0.93b3 0.9167 0.8971 0.8751 0.8518 0.8274 0.8024 0.7742 0.7311 0.7097 0.7261 0.7439 0. 7559 0.7666 0.7716 0.7771 0.7815 0.7854 1.7887 0.791b 0 . 7942 0.79b5 0.7985 1.8bB4 1.8011 1.8137 1.8a52 1.8065 1.8178 1.8089 0.8099 0.8111 0.8123 0.8133 0.8143 0.8153 0.8162 0.8132
-0.6559 -0.6541 -0.6541 4 . 6 5 7 0 4 . 6 0 1 4 . b 7 1 1 4 . 6 7 9 5 -0.6876 4 . 6 9 2 8 -0.b901 -0. b731 4 . 6 3 1 0 -0.5488 -0.4293 -0.3161 -0.2474 -0.2W3 -0.1648 -0.1180 -0.0681 6 . 0 1 5 9 0.0378 0.098b 0.1910 0.2369 0. 2018 1.1b37 0.1378 0.1188 0.1042 5x5 8. 0674 0.0611 0.0556 1.0506 0 . M 2 1.0421 @ . @ a 4 1.13Y 1.1319 1.1289 1.1211 1.124a 1.0218 1;0192 8.0167 0.0144 0.0123 0.0102 0.0083 0.0146
+ + + + + + + + + + + + + +
+ + + + + + + + + + +
+ + + + + + + + + + + + +
+ + + + + +
+ + + + + + + + +
+ + +
+
+ + + +
+ + +
+ + + +
+
+ + + + + + + + + + + + + + + + +
+ + +
B -60
SECTIW OUlUCTERILTICS
01 4.16749
SPAN TATION a CD bine 3.44b79 a B 01 ARE WED a v i ~ o u s P R E ! ~ ~ ! ' ~
X 3.47ae
2.8716 2.7111 2.5787 2.4539 2.3*
14@4
3:w f:23b3
:: ts#
::::$I f:fg# ::a 1. 2e98 1.1657 1.1227 l .Me9 1.- 1.- 3.9bM 0 . 9223 3.884b e.1476
e.6416 @.be99 @.$?91
~ 3. 490 e.5197 0.4912 0.4635
V
4.u 7 4 .3963
4 414119 42 1
4.3529 4.34bb 4 34 4: 333
4,1516 4.1247
4 .0b78 4.M@4 4.1017
::El
4 . 3 m 338 4 . 3 7 n
4 . 3 7 3 9 4.3756
-0.358 1 4 . 3 4 9 1 -0.3382 -0.3261 4 . 3 1 2 9 4 . 2 9 8 5 4 . 2 8 3 , -0.2668 -0.2501 Z:i%
-0. 3 3
4 . q 4
4 . 1 6 4 4 148 -0:ilbl 4 . 1 - 4.0853 4 . e b 9 9 -8.3 2 4. I239 4 . n 7 c 0.OlU 3.0297 0.05BI 3. 07@7 1.0916 3: :E 3: 3% 3:K# 3.224@ 8.2382
3.283b
0.3047 0.3099 8.3144 0.3182 0.3214 0.3242 0.32b4 0.3281 e. 329) 3.3293 0.3289 e.3271
::::3
w t m I .813l 3.8161 @.I153 3.8143 0.8133 e.8123 3.8;;:
:ih: 1;mJ ::!%I e.796
i;;ii: e.8034 3.8319
3.7944
::Ed e. 77 3.7691 8.7644 3.762@ 0.7485 3. b863
1.6218 3. (468 3.6?6@ 3.7074 0.74.) e.7764 e 81 3.89%
1. 3281 1.0540 1.0675
1.0739 1.0759 1 . M 4 1.0513 1 . 0 U s 1.0313 1.010 8.9962 0.976b 0 . 9584 0.9390 0.9182 0.8975 0.8714 0.8576 0.8380 0.8194 3.8024 0.7866
::ti#:
3:trlf
3 :
iiffii 1.7265 0.71W 8.6916 e. 6687 0.6431 3.6125
e.4491 e.4015 3.3972 0.4516
3.7997 3.9263 1 . w 2 1 . 1 m
3:f%
3:ff::
::#f: 1.4024 1.4140 1.4128 1. bo33 1.3883 1.3682 1.3432 1.3139 1.2814 pgj 1.1741 1.1626 1.1564
C? 3:%2 ::E3
e.nw 3:w e. le%
1.2872 e.4217 @.45M 0.4213
3:24l! e. 17e1
3 . 3
4 . 1
4 . 4 1 9 8 4 . 4 8 7 4 4 . 5 1 4 @
::E!
3:%! 4 . 4 4 2 4 -0.4119 4 . 3 7 1 3 -3.3311 4 . 2 9 3 4 4 . 2 5 3 2 4 .2094 -0.1656 -0.1228 4 . 0 8 % -0.0387 0.0013 0 . 038e ::%E 3: %i 3.937
0.2m 3.2345 0.2753
e.3 72 3.4484
e. 8323 3.8391 0.7482 3.%34 0.3162
3:::y 4 . 8 7 4 . 9 4 2 4
-1.1@45 -1.1049 -1.0910 -1.M90 -1.0369 -1.0007 -0.9544 4 . 9 0 1 6 4. 8458 4 . 7 9 2 7 4.1402 4 . 7 1 % 4 . b 9 4 b 4 . 6 8 3 1
+
+
+ +
+
+
* .
+
+
6-61
0.29b2 0.3182 0.3644 o. 34e9
WJ
::p 8 . 6 6 4 0.4939
: : b ! F 0.64 1 0.6753
0.7765 0.8118 0.8479 0.8848 0.9224 1.00W l.O*W 1.0889 1.1228 1.1b57 1.2898 1.2552 1.3584 l.*m 1.4526 1.5667 1.5b32 1.6222 1.6842 1.7494 1.8182 1.8911 1.9687 2.0516 2.1485 2.2364 2.3404
e.7~2 e.7420
0.96~~8
1. 302e
;;;iff 2.8716 3.261 3.47ae 3 . ~ 3
1. 3259 0.3233 0.3199 1.3157 1.3186 1.3844 1.2978 0. 2883 1.2783 8.2667 1.2535 1.2388 0.2223 0.2839 e. 1837
e . o m 0. e223 4.eic-a
:: ::#: 1.1118 0.0838
4.1445 4.0830 4.1142
4: 1845 4.2025 4.2188
:* 2::
:::El %Ig) 4.2TlZ 4.2992 4.3e75 4.3153 4.3226 4.3296 4.3362 -8.3425 4.3487 a. 3547 4.36bb 4.3666 4.3728 4.3791 4.3859 4.3933 z : 3
1.1535 1.1524
1.1633 1.156 1.1328 1.8926
0.9316
0.8949 0.8734 0.8503 1.8261 0.7731 0.7304 0 . 72- 0 . 7558 0.7b47 0.7715 I 78 6 0:78$4 0 . 7888
0.7965 0.7986 0 . 8 W
8.8038 0.8066
1.8089 0. 8099
e.916
oaeii
0.7091 1.7436
e. 777e
e.7917 e.7942
e.ae22 0 . a m e.8078
e.8111 e.8122 e.8132
e.8111
0.8142 0.8152 0.81be
4.6777 4.b758
4.6828 4.6888 4. 6943 4.088 4 .b958 4.b799 4.6393 -8.W27 4 . 4 5 l b 4.3424 4.2745 4.237b 4.1602 4.1144 4.6651 4.0131
0.1927 0.212b 0.1643
0.1191 0.0924 0.08% 0.6672 O.US4 O . H c 0 0.0383
3:::s:
-8.2119
' e.0447 e.ioio o . m e
1.1382 e . i w 0 . m ~ . o.wio e. e m 0.042e 0. e m 0.e318 e. 0289
0.~192
0.8262 0.0239 0.0217 0.0168 0.8146 0.0125 8.0184 e.- e . o w
SECTION UURACTERISTICS
YAY Affi OF A T 1 A a 1.-
MACH NO 0.82891 0.oown
01 -0.16841
CL CD CL CD CM ARE BASED ON VISCOUS PRESSURE
1.0116) SPAN STATION
4.50000 0.45425
PLOT OF CP AT COMPUTATIONAL MESH POINTS
X 3.4779 3.2460 3.0462 2.8715 2.7169 2.5786 2.4539 2.3403 1.2363 2.0515 1.9687 1.8911 1.8182 1.7493 1.6842 1.6222 1.5631 1.4525 1. 4005 1.3504 1.3020 1.2552 1.2098 l . l b S 7 1.1228 l . M W 1.- l.HO# 0.96I8
0.8476 0.8114 0.7759 8.7413 Q. 7073 0.6741 0.6417 0.6101 0.5792 0.5491 0.5198 0.4914 0.4637
1.1404
i.5e67
e.9223 e.8846
Y
-0.3773 -0.3701 -0.3636 -0.3576 -0.3519 4.3464 -0.3411 -0. 3357 -0.3302 4.3247 4.3189 -4.3128 4.3864 4.2996 -0.2923 -8.2846 -4.2762 -0.2672 -0.2575 -0.2469 4.2228 4.2088 -0.1934 4.1763 4. 1571 4 .1349 -0.1892 4.0793 -8.0562 - 0 8 5 1 4 0676 -0.0886 -0.1143 -0.1431 -0.1732 -C ,2035 -0.2326 -0.2599 4.3061 4.3233 4. 3377 -4.3484 -4.3552
-e.3854
4.2356
-e. 2849
MACH NO 0.8159 0.8151 0.8142 0.8123 0.8112 0.8101 0.8082
e.8132
e.8132
0.8892 e. 8072 8.8669 o . ne47 0 . 8033 0.8018 0 . 8002 0.7984 0.7964 0.7942 0.7917 0.7889 0.7858 0.7822 0.7782 0.773b 8.7686 0.76M 0.7616 0.7481 e. 6855 0.6210 0.6667 0.6284 8.6736 0.7045 0.7374 0.7723 0.8088 0.8476 0.8878 0.92+4 0 . 9625 1 . M 4 1. 8484 l.sS68
e. 6419
' *
+
+ +
B -62
1 I I 1 I I 1
I m
R I I 1 II
::::# t:t% 1.0111 0.m9 0.301 *.ne4 3.mq
min @.a134 0.0239 0.0273 0.0344 0.0423 0.0510 OOb 0 : 0 7 8 ::%I: 0.1#3 0. 1197 0. l 3 q 0.146 #.IC44 0. 1839 0. 1981 0.2lb1 3.2349 3::1:s
4.3470 -3.3339
3: :a# 3:% 4.3344 +.ob% 4. 490
0.3130
0.3144 0.314b 0.3141
::3:33
0.29b1 0.3408 0.3b43 0.388b 0.4137 0.43% 0.4bb3 0 . 4938 0.5220 0.3511 0.C11b 0 . 6430 C.b732 0.7081 0.7419
0.8118 0. 8479 I. 8847 3.9226 3.9bM 1 . W 1.0466
0.3180
e. 588)
0.7764
3 g 1.2098 1.2332 1.3021 1.3304 1.400b 1.43% 1.50b7 1.5C32 1. C222 1. (842 1.7494 1.8181 1.891 j ! ? ! 9 d
2.23b3 2.34W
2.71b9 2.8715 3.04b2 3.2460 3.4779
:: f1R
0.311, 0.3111 0.3084 0.3049 0.-
0.2 12 0.2b17 0.2497 0.23b3 0.2212 0.2062 0.1834 0.1b49
3: ::i: 1.2922
4.n 4.098b If: fLY 3: 1% -3.1983 4 . 2 1 2 2 4 . 2 2 4 9 4.23b4 4 . 2 4 7 0 -3.23C7 -0.2b37
4 . 3 4 1 4 -0.3471 4 . 3 3 3 1 4 . 3 3 9 b -0.36b8 4 . 3 7 4 9
1.0bb8
1.03f7
# . M a ::Mi
0.7017 0.b788
1.14b7
1.3172 1.34b9 1.38W 1.- 1.4lM 1.4202 1.4142 1.4040
::::a
1.28W 1.2321 1.224b 1.1999 1.188)
l . lb8b l . lb22 1.1599 1.1b04 1.1b24 l . lb47 1.M- l . lb42 1.15bb 1.1374 1.1012 1.0495 0.9978 1.9644 0.9473 0.9326 0.9130 0.89%
0.82bl 0.8307 0.7725 0.7298 0.7Mb
0.7554 0.7644 0.7713 0.77b9 3.7813 3.7834 0.7887 0.791b 0.7942 0.79b3 0.798b 0.8304 3.8022 3.8037 0 .8H2
0.8089 0.8399 0.8110 3.8121 0.8131 0.0141 3.8130 0.11158 0.8132
I:tW
3:::'JJ
:::E!
+ +
+ +
+
+
+
4 +
+
+ + + + + + + +
+ + + + + t +
+ + + + + +
+ + + . +
+ +
+ + + + + +
+ + +
+ + + + + + + + +
+ + + +
i I 6-63
SPCTIOII U U R I C T E R l S T ICs
-#.lW19 a,
3.& 3 . n 9 u SPAN STATIOY
g39999 a 01 ARE IALED on vxscous PuEsWilE
X 3.4778 3.2463 3.0461 2.8715 2.7169 2.5786 2.4538 2.3403 2.2W3
1.9686 1.8911 1.8182 1.7493 1.6842
3 : E
:.:g2
&!! 1.- 1.3504 1.3023 1.2552 1.2098 1. 1657 1.1228 1.0809 1.0488 1.0000 8.9608 0.9223 0.8846 0.8476 0.8114 0.7760 0.7413 0.7074 0.6742 0.6418 0.6132 0.5793 0.5493 0.5200 0.4915 0.4639
0.4370 0.4110 0.3858 0.3614 0.3378 0.3150 0.2930 0.2718 0.2515 0.2319 0.2132 0.1953 0.1782 6.1619 0.1464 0.1317 0.1178 0.1047 3.0924 0. 0808 0.0701 0.0600 0.0508 0.0623 0.0345 0.0276 0.0213 0.0157 0.0109 0.0069 0.0039 0.0017 0.0004 0.00fM 3.0064 0.0017 8. 0038 #.Deb7 0.0lbc 0.0153 0.0209 0. 0272 0.3343 @.e422 0.0509 3.0634 0.0707
0.0935 0.1061 0.1195 0.1336 0.1485 0.1642 0.1807 0.1979 0.2160 0.2348 8.2544 0.2747
0.0ai7
Y 4.3496 4.3428 4.3366 4.3310 -0.3259 4.3210 4.3162 4.3115
3::: 4.2804 4 741 4:f674
:: :#H 4.1583 -0.1399 4.1189 4.0943 -0.0658 4.0438 4.0431 -0.0554 4.0760 4.1013 4.12% 4.1591 4.21 6 -0.2446 -0.2693 4.2903 4.3077 4.3222 -0.3332 -0.3404
4. lay
MA04 WQ 3.8132 3.8158 0.8150 3.8141 0.8131 0.8122 1.8111 1.8101
3.8071 3. 8059 3.8046 3.8032 3.8017 3 . 8 M 3.7982 @.79b2 3.7939
:::a
p; 3.7819 I. 7732 0.7682 n.7636 0.7612 3.7479 0.6851 0.6281 0.6058 0.6191 0.6431 0.6714 3.7019 0.7345 0.7693 3.8051 0.8434 3.8832 0.9196 0.9561 0.9975 1.0309 1.0481
3 . m a
4:::f: 4.3476 -0.3451 -0 34 1 -0: 33b -0.32 4 4.3193 4.3091 4.2980 -8.2857 4.2724 -0.2584 -0.2439 -0.2291 -0.2141 -0.1991 -0.1842 4.1695 4.1550 -0.1407 -0.1267 4.1130 -0.0994 4.0856 -0.8718 4.0583 4.0441 4.0292 4.0127 e.ws2 0.0240 0.0432 9.0627 0. 0822 8.1016 @. 1206 8 . 1m 1; f;AJ# #.a13
0.2457 0.2541 0.2614 0.2679 0.2737 0.2788 0.2834 0.2875 1.2941 0.2966 8.2986 @.Me7 8.-
0.2910
8.30~
1.0594 1.0663 1.0615 1.0506 1.0432 1.0364 1.0232
0.9710 0.9525 0.9324 0.9122 0.8924 0.8729 0.8537 0.8353 0.8186 0.8033 0.7883 0.7733 0. 7589 0.7450 0.7298 0.7110 0.6883 0.6627
0.5276 0.4614 0.41m 0.40615 0.4524 0.5495 0.6686 0.7938 0.9179 1.0372 1.1386
1: %:
:::#
!;E Mi: 1.4814 1.4155 1.4181 1.4139 1.4064 1.3961 1.3838 1.3699 1.3549 1.3387 1.3210 1.3013 1.2782 1.2519 1.2212
W @.OM7 3.8091 3.0107 0.0127 0.0148 3.0168 3.0191 3.0214 3.0234
3.0364 3.0331 0.0361 0.0394 3.ww 3 . w 9
0.M14 3.0674 3.3742 0.0819 0.1006 0.1114 3.1214 0.1264 0. 1552 0.2891 0.4242 0. 454s 0.4269 0.3772 0.3180 0.2534 0.1838 3.1097 0 . 0323 4 . m 3 4.1353 4.2124 -0.2887 4.3740 4.4415 -0.4758
;:::a
I: a: 1 .m7
-0.49az -0.5116 4.5023 4.4837 -0.4660 -0.4525 -0.4260 4.3894 -0.3539 6.3197 -0.2812 -0.2393 -0.1968 -0.1549 -0.1134 -0.0722 4.0329 0.0029 0 . 0359 0.0682 0.1005 0.1315 0.1613 0.1938 0.2340 0 . 2822 0.3w3 0.4013 0.4912 0. 6389 0.7309 0.8185 0.8322 0.7468 3.5666 0.3239 0.0564 4.2008 4 .4541 4.b-1 4.7772 4.8631 4.9- 4.9994 -1.Ml3 -1.0884 -1.1087 -1.1124 -1.1065 -1.0955 -1.0806 -1.0624 -1.0416 -1.0187 -0.9937 4.9658 4.9337 4.8964 4.8540 * . m a
+
+
' * +
B -64
i 1 1
I I i I I
::m t : Ettl 0.3-
0.7 0.7418 0.77b4 0 81 7 I. 8847 0.9224 0.9bM 1.000O 1 . M 1.0809 1.1228 l . lbS7 1.2099 1.2553
1.4Wb 1.452b
<0:84+8
::a :: $% :::::i 1.7494 1.8182 1.891
2.23b3 2.3403
2.8713 3.Wb2 3.24bO 3.4778
0.3003 0.2990
::E8 0.2%
0. lob? 1.1bIb e. l4bb e. 123s 0.6984 0.0711 0.0421 0.011b -0.0197 -0.6552 -0.0837 4.1083 4.1294 -0.1477 -#.MU
4.2420 -0.2497 4.25b9 -0.2b3C 4.2b98 -0.27f -0.28 2 -0.28b4 4.2914 -0.29b3
-0.3154 -0.3265 -0.3211 -0.3312 -0.3391
1.2039 1.18% 1.1735 1.1b72 1.1b51 '
1.1b44 1.1b22
1.1090 .ob32
0.9b29 0.9498 0.9344 0.9171 0.8979 8.8762 0.8523 0.820 8.8009 0.7723 0.7295 0.7081 0.7248 0.7421 0.7550 0.7b40 0.7710 0.77Cb 0.7811 0.7852
f : :!;I 1:::::
;;;E! 0.79b4 0.7985 0.8004
t : 0.8088 0.8098 1.8110 0.8111 0.8131 0.8140 0.8149 t:t%
-0.7b89 -0.73b3 4.7143 -0.7018 -0.b9W -0.b978 4 . 0 3 0 -0.b814 -0.C521 3;zg -0.33M 3:8:3t 2: :3;1 -0 .1Cb6 4.1203 -0.0693 1.0411 0.1001 0.1946
+.e149
;;y; 1.1399
0.0834 0.06 7 #.Ob14
0.0463 I. 0423 0.038b 0.0352 0.0320 0.1291 O.OZb4 0.0241 0.0219 0.0194 0.0171 0.0149 6.0129 0.0109
0.07y
::a
::E9
SECTION CHARACTERISTICS
CM -0.172bb
SPAY STATIOY CL W
CL ED CW ARE U S E 0 ON VISCOUS PRESSURE 6.29999 0.4b587 0.00V5
PLOT OF CP AT CWPUTATIOYAL MESH POlWTS
X 3.4778 3.2459 3.04bl 2.8714 2.7168 2 . 9 8 b 2.4538 2.3403 2.213 2.1404 2 0551 1 : 9b8f 1.7494 1.b842 1.b222 1.5b32 1.5067 1.4526 l.40M 1.3505 1.3021 1.2552 1.2098
::E3
I:&!# !:E 1.0488
0 . 884b 0.847b 0.8115 0.7760 0.7414 0.7075 0.67k3 0.6419 8.b103 0.995 0.5494 0. 5202 0.4917 0.4b41
V -0.3143 -8.3087 4.3036 +.me 3:ftX 4.28b7 4.282C 4.278C 4.2744 -0.2700 -0 2b 3 -0 :ZbL
-0.2434 4.23b8 -0.229b 4.2219 -0.2134 4.2041 -0.1939 -0.1827 -0.1713 -0.1%5
3%:
3; # 3:#f +.OM2
4.0439 -0.0640 -0.0888 -0.1164 -0.1454 4.1747 4.2029 -0.22% 4.2548 4.2749 4.2923 4.3070 -0.3182 -4.3257
wcn YO 0.8131 0.81% 0.8149 0.8139 0 . 8 1 1 0.8121
8.8090 0.8081 0. 8070 0.8058 0.8044 0.aom I. 8015 8.7998 0.7980 0.7959 0.7937 0.7912 I. 7884 I. 7852 0.7775 0.7729 0.7b79 0.7b32
#.a47
m.aiie 0.0100
e.7816
t : ::# kf# 0.6414 0.6693 0.6995 0.7319 0.7661 0.8019 1.8199 8.8794 0.9158 0.9515 0.991C 1. 0244 1.0417
CP 0.0144 0.8094 0.0110 0 .01s
0.0193 0.02lb e.023b 0.0257 0.0281
3:t:Q
0.03~ 3::32i: 0.0398 0.0434 0.0474 1.0318 0.05bC 0 . 0b20 I .WW I. 0748 0.MZb 0.0914 0.1014 0.1122 : : :31 0 . 1 y
I: 4 d * 0.289 0 42 4 0.42% 0.3808 0.3224 0.2585 0.1895 0.1160 0.0389 -0.0428 -0.1272 4.2044 4.2792 4.3620 -0.4284 -0.4bm
+ +
+ + + + +
+ +
+ + + + + + + + +
+ + + + +
+ + + + + + + + + +
+ +
+ +
+ + + + + + + + + + + + + + + + + +
+ + + +
+ + +
+
+
B-65
0.4372 0.4112 0.3860 8.3616 0.3380 . 0.3152 0.2932 0.2720 pi: 0.1955 0.1784 8.1621 0.1466 0.1319 8.1180 0.1049 0.0925 0.0810 0.0702 0.8601 0.0424 0. 0346 0.0276 0.0213 0.0157
0.0069 0.0017 0.0004 0.0661) 0.0604 0 0017
0.0067 0.0105 0.0152 0 . 0208 0.0271 0.0342 0.0k2l 0 . 0508 0.0603 0.0705 0.0816 0.0934 0.1060 0.1193 0.1335 0.1484 0.1641 0.1805 0.1978 0.2158 0.2346 0.2542 0.2746
o.mm
o.eim o m s
o : m ~
4.3307 -0.3338 -0.1341 4.3323 4 .3289 4 .3142 4.3177 4 .3095 4 .3003 4 . 2 9 0 8 4.2787 4 . 2 6 6 4 4 .2535 4 .2401 4 .2264 6.2124 4.1984 4 .1845 -0.1709 -0.1573 4 .1439 -0.1388 4.1180 4.1052 4 .0922 4 .0792 4 .0661 -0.0528 2% -m ;.:!E 0 . 0 m 0.0496 0.0684 0.0870
0: 1401 0 1 58 0: 1102 0 1837 0:1963 0.2079 0.2184 0.2279 0.2364 0.2439 0.25D6 0.2566 8.2620 0.2669 0.2713 0.2752 0.2786 8.2816 0.2840 0.2859 0.2871 0.2878
1.0533 1.8608 1.0571 1.0474 I;# 1.0059 0.9894 0.9736 0 9561
0 9168 0:8973 0.8782 0.8592 0.8412 0.8249 0.8099 0.7952 0 . 7805 0.7665 0.7538 0.7383 0.7198 0.6974 0.6719 0.6405 0.5959 0.5349 0.4670 0.4133 8.4021 0.4507 0.5462 8.6648 0.7878 0.9102 1.0273 1.1288 1.1991 1.2500 1.2947 1.3346 1.3681 1.3934 1.4077 1.4110 1.4086
1.3839
0:9367
12% &# 1.3381 1.3253 1.3107 1.2932 1.2728
-0.4860 4.5w 4 . 4 9 3 6 4 414 ".YO2 -0.4 56 4 . 3 9 1 0 4 . 3 5 7 4 4 . 3 2 5 0 4 .2887 4.2482 4.2865 4 . 1 6 5 3 4 . 1 2 4 6 -0.M41 4.0456 4 . 0 1 0. 0533 0.0849 8.1151 0.1440
0.2630 0.3170 0 . 1 2 6 0.4743
4 : 4 6 1 i
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4 . 9 7 2 6 4 . 9 4 9 3 6 . 9 2 1 0 -0.8873
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1.2553 1.3021 1.3505 1.4006 1.4526 1.5068 1.5632 1.6223 1.6842 1.7k94 1.8182 1.8911 1.9687
2.1484 2.1363 2.3403
2.7169 2.8715 3.0461 3.2459 3.4778
0.550n
1.2099
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0.2E78 0.2871 0.2158 0.2838 0.2810 0.2772 0.2725 0.266b 0.2596 0.2512 0.2415 0.2304 0.2178 0.2035 0.1875 0.1698 0.1502 0.1285 0.1047 0.0787 0.0510 0.0217
-0.0083 -0.0423 -0.0696
4 .1131 4 .1305 4 .1468 4 1 98 4 . 1 8 3 4 -0.1936 4 .2028 -1.2113 4 . 2 1 9 1 6 .2262 -0.2328 4 .2389 4 .2446 4.2498 4 .2548 4 . 2 5 9 4 4 .2638 4 .268# 4 . 2 7 2 1 -0.2761 -0.2801 -0.2842 -0.2885 -0.2931 -0.298 1 4 .3037
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1.2501 1.2267
1.1741 1.1639 1.1533 1.1378 1.1124 1.0740 1.0297 0.9953 0.9774 0.9661 0.9527 0.9373 0.9203 0.9010 0.8789 0.8543 0.8281 0.8013 0.7293 0.7078 0.7244 0.7423 0.7545 0.76% 0 . 7786 0.7763 0.7810 0.7849 0 . 7883 0.7913 0.7939 0.7962 0.7983 0.8002 0.8019 0.8035 0.805# 0.8864 0.8076 0.8887 0.8898 0.8120 0.8130 0.8139 0.81k8 0.8156 0.8131
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0.7723
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0.0755 0.0682 0.0618 0.0562 0.0512 0.0467 0.0426 0.6388 0.0354 0.0322 0.8293 o.ozL1 0.0242 0 . 0220 0.0196 0.0172 0.0151 0.0131 0.0112 0.0096 0.0147
6 . 8 m
s.rn*i 0.0840
+ + + + + + + + + +
+
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+ + + +
+ + + + +
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+ + + + + + + +
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8-66
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SECTIW O U l l l l E R l S T I C S
I 1 1 I I I I II i
I I
0 . 4374 0.4114 0.3862 0.Y18 3.3382 0.3154 0.2934 0.2722 0.2519 0.2323 0.21% 0.1957 0.1786 0.1623 0.14b8 0.1320 0.1181 0.1058 0.0927 0.Mll 0.0703 o.eb03 0.0510
0.8214 0.0158 0.00870 0.6039 0.0017 o.w.4 o.ew# @.on4 0.00lb 0.w37 0.0847
0.020 0 . 0270 0.0341
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4.2482 4 .2444 4.2483 4.2359 4.231?
3: WA 4.0892 4 . W W 4.0409 4.0212
4.3033 4.3111
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4.ObM -0.0322 4.0158 0.0194 0.0374 8.8 34 0.n10 0. 1ma 0.1246 0.1398
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1.9203 0.9012 0.8825 0.8bW 0.84b4 0.8305 0.8159
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SECT ION CHARICTERISTlCS Y AH AW OF ATTACK
1.- a, tll
0.68634 4. 17992
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EL u) Cn ARE BASED ON VISCOUS PRESSURE
PLOT OF CP AT COHPUTATIOHAL MESH POINTS
+ + + +
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+ + + + + + +
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+ + + + + + + + + + + + + + +
X 3.4777 3.2459 3.0461 1.8714 2.7169 2.5786 2.4538 2.3403 2.2363 2.1404
1.8912 1.8181 1.7494 1.6842 1.6223 1.5632 1.5068 1. 4527 1.4006 1.3505 1.3621 1.2553 1.2099
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Y -0.2518 -0.2483 -0.2451 4.1422 -0.2394 -0.2339 4.2311 -0.2281 4.2250 4.2216 4.2181 4.2141 4.2098 -0.2000 4.1945 4.1884 4.1817 4.1743 4.1662 4.1573 4.1473 4. 1362 4.1239 4.0942 4.0760 4.0546 4.1296 -#.a111 4.0109 4.0224 -0.0415 -0.0649 -0.09 12 -0.1189 -0.1469 -1.1741 -0.1998 -0.2235 4.2441 -0.2614 4.2761 4.2876 4.29%
4.2367
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CP 0.0149 0.0100 0.0116 0.0136
0.0198 0.0221 0.0242 0.0263 1.0287 0.1314 1. 0343 0.0374 0.-
0.0529 #.e578 1.0633 1.0762 1.M41 0.WY 0. 103a 0.1137
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+ + + + + + + + + + + + + + +
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0.9197
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0.9593
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0.1019 1.1953
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SECTION a u n A c l E R I S T I C S
V 4.2247 4 .2221 4 .219b 4 . 2 1 7 4 4 . 2 1 5 2
4 . 2 0 8 4 4.2059 4 . 2 0 3 2 4 . 2 0 0 3 4 . 1 9 7 1 4 . 1 9 3 6
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)urn NO 0.8130 0.8152 0.8145 0.8136 0.8126 a.1117 0.8107 0.8096 0 8081 0:80?6 0.8065 0.8052 0.8039 0.8024 0.8008 0.7991 0.1972 0.7951 0.7928 0 7903 0: 7875 0.7842 0.7806 0.7764 1.7718 0.76b8 0.1623 0.7bM 0.7475 1. (837 0.6176 0.b018 0.6132 0.b356 0.6625 0.6920 0.7236 0.75?2 0.7915 0.8299 0.8b89 0.90% 0.9411 0.9801 1.0128 1.0304
8.4378 -0.2863 0.4118 -0.2903 0.3866 -0.2920 0.3622 4 . 2 9 1 7 0.3386 -0.2901 0.3158 -0.2873 0.2938 -1.2829 0.2727 4 .2712 0.2523 4.2705 0.2328 4 . 2 6 2 9 0.2160 -0.2544 0.1961 -0.2451 0.1790 -0.2352 0.1626 -0.2249 0. I471 -0.2142 0.1324 -0.2E33 0.1185 -0.1924 0.1053 -0.1815 0.0929 -0.1707 0.0814 -0.1599 0 070 -0.1493 0:060f -0.1388 0.0512 -0.1284 0.0426 6 . 1 1 8 0 0.034d -0.1074 0.0278 -0.09b6 0.0215 -0.085C a.0159 -0.0744 0.0110 4 . 0 6 2 1 0.0070 -0.0485 0.0039 -0 033 0.0004 -0.0011 0.0000 0.0152 a.0004 8.0318 0.0016 0.0403 0.0037 #.064b I.BB1b 8.0806 a.0104 0.0959 0.0150 0.02b8 0.0339 0.1482 0.0417 0.1593 0.0504 0.1696 0.0598 1.1790 0.0701 0.1876 0.0811 0.1955 0.0929 0.2027 0.1056 0.2094 0.1188 0.2156 0.1329 0.2213 0,1478 0.2266 0.1635 0.2315 0.1799 0.2360 0.1972 0 . 2 4 H 0.2152 0.2436 0.2340 0.24b7 0.25W 0.2493 0.2740 0.2514
0.0017 -0:017l
+
+
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0.8015 e.8031 0.8Wb #.8#b@
e.8095 I . 8 1 W e.8117 0.8127 0.81% 0.8144
t:% 1.7978
s::c3
d7997
t:::2:
4.9413 4.9187
+.son 4.4b94 4.39% 4:H 3:x: -4.- 4 . 2 7 b l 4.2423 4.2- 4.1497 4.@914 4.828b #.#35b
p 7 9
t : :23 e . @ y
1bW 0.1435
#.nu #.e7 4 #.WW
#.M% @.e398 0. a3b3 e.e3w #.em 11.8272 0.0248 #.#22b e.e2e2 1.0119 I. 8158 0.8138 e.e12e ::::E
SECTlON CHARACTERISTICS VAH ANG OF ATTACK
1.@@@H HAW NO 0.82we e.emea
9 89999 0.45585 4.00397 4. 18953 ' a , CII
CL d Q1 ARE BASED ON V I S C W S PRESSURE
PLOT OF CP AT C#IWTATlONAL MESH POINTS
X 3.4778 3.24b0 3.0462 2.8715 2.7169 2.5787 2.4539 2.3404 2.2364 2.14M 2." 1.9688 1.8912 1.8183 1.74% 1. b143 1. b224 1. 5b33 1.5W9 1.4527 1.4897 1.35W 1.3@22 1.2554 p v iiq 8 9 b I e. 9223 #.a846 0.8477 0.11116 0.7762 0.741b 0.7078 0.6747 0. (424 0 . b l M 0.5891 0.5591 #.52M e.4924 e.4bu
-0.1974 -0.19% 4 .194e -0.1924 4 .1907 4 .1889 4 . 1 8 7 0 4.1827 4.1U1 4 . 1 7 7 3
4 1bb9
4 .1527 4.14b9 4.1- 4.13% 4.1254 4.11bb 4 . 1 W 7 4 . m 5 4 . M m +.MI7 4 . e 5 2 1 4 . U 2 b 4 . m 7
e.9170
4 . e e 3 7 4 .0214 -0.0433 4 . W 8 1 4 .0942 -0.1207 -0.14b5 4 . 1 7 1 1 4 .1940 4 . 2 l U
4. lase
3: ::a 3; t%
e. e078
;;;E 4.2b55
Iua NO o . m e o . a m 0.1144 m i 3 4 0.8125 1.811b @.8lW
0.8075 I.8eb4 #.8#51 e. 8637 0.8022
0.7989 e. 7971 e. 7949 0.792b 0.79W a.7871 e.7839 #.78#2 #.77b1 e.7714 e.7bb4 I.7b19
:::z a . a m
I .b lb9 0 . b917 #.b11b 0.6335 0.6601 0.6893 0.7207 0.7541 0.7892 1.82b5 e.8653 0.9022 1.9379 1.97b7 1.W97 1.127b
CP 0.0151 @.OlM 0.8121 0.0141 0.Olbl 1.0181 e. 0202 I. 0225 0.0246 #.02b9 @ .0294 ..a321 a. e 3 w e.otl2 #.e417 #.e454 e. e496 0.@541 #.MH 0.N4b 0.0707 e.8777 #.M% ,.nu #.le44 1.1113 e. 12M I;r# e.4314 e.*(*
0.3418 0.2803 S.2133 0.1411 0.0bb3
4 .0139 -0.W71 4.1757 4.2597 4 .3314 4.3988 4 .4349
s: 3%
+
+
+
+
I
I
+
I
+ +
I
+
+ +
+ +
+ +
6-71
0.4380 0.4120 0.3868 0.3624 0.33M 0.3160 0.2940 0.2729 0.2515 0.2330 0.2142 0.1963 0.1792 0.1628 0.1473 8.1326 0.1186 0. 1855 0.0931 p i 0.0513 0.0421 8.0349 0.8219 0.0215 8.0159 0.0110 0.0070 0.0039 0.0017 o . w . 4 0.mm o.w.4 0.0016 0.0031 O . W b 6 0.0103 0.0149 0.0204 0.0267 0. 0337 0.0416 0.0502 0.0597 0.0699 0.0809 0.0927 0.1652 0.1186 0.1327 0.1476 0.1633 0.1797 0.1970 0.2150 0.2338 0.2534 0.2738
0.2950 0.3169 0.3397 8.3632 0.3876 0.5127 0.4386 0.4653 0.4928 0.5211 0.5502 0.5801 0.6108 0.6422 0.6745 0.7075 0.7413 0.7760 0.8114 0.8475 0.8845 0.9607 1.0000 1.0401 1.0810 1.1229 1.1659 1.2100 1.2554 1.3022 1.3506 1.4008 1.4528 1.5069 3.5634 1.6224 1.6844 1.7495 1.8184 1.8913 1.9688 2.0517 2.1- 2.2364 2.3604 2. 4539 2.5787 2.7170 2.8715 3.0462 3.2460 3.4778
0.9222
4.2716 ::::E f : f X
3::#
4.2747 4.2710 4.2660 4.2631 4.2533
4.2283 d.2190 -0.2093 d.1993 d. 1893 d. 1793 d. 1695 -0.1596 -8.1498 4.1481 -8.1305 -8.1209 -1.1111 4.1010 -0.09p7 -0.0801 4.0685 -8.0555 4.0413 -8.0261 4.0105 8.0053 0.0212 1.0369 1.8526 8.8679 8.0827 0.0966
8.1337 0.1445 0.1516 0.164a 8.1726 0.1806 0.1879 0.1948 0.2011 1.2071
0.2225 0.2269 0.2308 0.2343 0.2372 0.2397
:: 1%
::::+‘I
0.2417 0.2432 0.2441 0.2444 0.2441 0.2431 1.2412 0.2385 0.2349 0.2302 0.2244 0.2175 0.1997 0.1886 0.1759 0.1613 0.1446 8.1255 0. 1041 0.0807 0.0299 0.0009 -0.0219 -8.8415 4 . 0 23 -0.0849 4.0960 4.1659 -0.1148 4.1227 -0.1299 -0.1363 -0.1421 4.1473 4.1520 4.1563 4.1601 4.1636 4.1b67 4.1695 4.1720 -0.1743 4.1764 -0.1783 -e. 1800 -0.1817 -0.1833 -0.1850 -0.1867 -0.1885
0.2093
0.0556
-0.0780
1.3034 1.2978 1.2901 1.2784 1.2592 1.2275 1.1784 1.1131 1.0467 1.0046 0.9954 0.9966 0.9907 0.9803 0.9690 0.9557 0.9395 0.9194 0.8945 0.8659 0 . 8354 0.8043 0.7732 0.7292 0.7067 0.7230 0.7406 0.7529 0.1620 0.1691 0.7749 0.7797 0.7637 0.7872 6.7903 0.7930 0 . 7954 0.1976 0. 7993 0.8013 0.8030 I. 8H5
0.8M4 0.8095 0.8106 0.8116 0.8126 0.8135 0.8143 0.8151 0.8131
::tx
4.4564 6.4694 d.4642 -1.4487 -1.4386 d .4299 -1.4110 -1.3841 !.y# -6.2679 4.2Wl -0.1942 4.1582 -e. 1222
-0.0308 0.0243 0.0498 0.0731 0.1334 8.1776 0.2301 0.2979 0.3969 0.6 58 0.1901 0.8314 0.7113 0.6144 0.3936 0.1481
4.6147 4.6684 -0.7565 4.8351 -0.8992 -0.9494 -0.9865 -1.6080 -1.0153 -1.0158 -1.0137 -1.0092 -1.8026 4.9946 -8.9863 4.9784 4.9713 -0.9649 4.9586 4.9520 -0.9451
Z:% -0. 8029
~ ~ 9 9 0
0 . 5 y
3:%3
-0.9375 -0.9285 4.9160 -0.8966 -0.8646 -8.8103 -0.7233 4.6021 -0.4730 -0.3884 4.3696 -0.3726 6.3602 -0.3388 -0.3154 -0.2880 -0.2542 4.2119 -0.1592 -0.0330 0.0337 0.1007 0.1952 0.2432 0.2085 0.1107 0.1444 0. 1246 0. 1095 0.0971 0.0868 0.0181 0.0786 0.0640 0.0581 0.8529 0 . 0483 0 . w 0.0401 0.0366 0.0333 0.0302 0.0274 0.0250 0.0227 0 . 0203 0.0180 0.0160 0.0141 0.0122 0.0149
-0.ew
0.010s
+ + + + + + + + + + + + + + +
+ * + + + + + + + + + + + + + + + +
+ + + + + + + + + + + + + +
+ + + + + + + + + + + + + *
+ + + + + + + *
+ + +
+ + +
+ +
+ + + + +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + *
6-72
bR16!NAL. PAGE OF POOR QUALtm
I I I
SECTION C M I C f E R X S T X C S YAM A f f i OF ATTACK
1.- MACH 110 0 . 8 m r 0.-
m 0 . 4 b 4.+ 4.19492
S P U LTATXOM
CL%%?RE USE0 01 VISCOUS PRES- PLOT OF U AT folvTATIOYIL MEW POINTS
X V 3 4779 4 77b 3:24U 4 : h b
1 . w l b 4 . 0 0 1 0 0.9b07 0.0148 0.9222 0.0147 0.80bb 0.8477 0 .8 l lb 4 . 0 1 3
0.5002 4 997 0. 502 4:11b5 O . h l 0 4.2309 0.49% 4 . 2 4 2 5 0.4658 4 .2509
0.4382 -0.2572 0 4 1 2 -0.2b17 0:38#0 4.2b40 0.362b -0.2b4b 0.3390 4 . 2 b 4 0 0.31b2 4 .2b22 0.2942 4 . 2 5 9 1
0.2332 4 . 2 4 % 0.2144 -0.2368 0.1965 4 . 2 2 9 3 0.1794 -0.2211 0.1blO 4 . 2 1 2 8
&::if 4.2040 4.193:
0.1188 0 1 b ;:t!b8 0:0% 4 . 1 6 7 8 0.881b 4 . 1 5 8 8 0.0708 4 . 1 4 9 8 0.6b07 4 . 1 - 0.0514 -0.1121 0.0420 4 . 1 2 3 2 0:02f9 4 . 1 -
:::::1 4:;:::
e 03 I 4 . 1 1 4 1
0.0039 4 . 0 4 8 2 0.0017 4.0338 0.- 4.0189 0.ooM 4 . 0 0 3 a 0.0004 0.0113 0.0037 0.0413 0 . m 5 0.6%0 0.0103
0.eeib 0.0264
0.0336 0.1197
0.1bb2 0.0925 0.1736 0.1050 0.18W 0.1184 0.1871 0.1325 0.1932 0.1474 0.1989 0.1b31 0.2043 0.1795 0.2093 O.lH8 0 . 2 1 3 0.2148 0.1181 0.23U 0.2219 :::E ::::0:
l u o l w o 0.8134 0.8150 0.8143 0.8133 0.8124 0.8115 0.8105 0.8095 0.8085 0.8074 0.8W2 0.8050 0.80% 0.8021 0.8804
0.79bb 0.7923 0.7897 0.78b8
0.77% 0.7709 0.7659 0.7b15 0.7473 O.b8!29 0.blbO 0. 5994 0. LO97 0.b311 0.b574 0.b8b3 0.717b 0 75 0.8229 0.8blb 0.8988 0.93bb 0.9734 1.wC7 1.0250
:: :tt:
::::a 0.7599
0: 7 8 3
1.0356 1.041b 1.0390 1.0315 1.026b 1.0225 1.0139 1.0817 0.9898 0.9781 0.9643 9.9480 0 . 9309 0.9143 0.8980 0.8817 0.8bb3 0.8528 0.8406 0.828b 0.81bb 0.86% 0.79% 0.7845 0.7694 0.7495 0.7253 0.6934 0 b4 3 I. 4998 0.4316 0.4022 0.4342 0.5178 0.6258 0.7391 0.8497 0.9535 1.048b 1.12H
0: 5778
i;K# ::::If 1.3281 1.3330 1.3340 1.3338 1.3321 1.3291 1.3252 1.3910 1.3171 1.31% 1.1105 1.3074 1.3642 1.3088
CP
0.0143 0.01b3 0.0181 0 0204 0:0227 0.0248 0.8271 0.02% 0 . 0324 0.0354 0.038b # . W l
0.0597 *.#b53 0.0715 0.07M 0.08bg
0. 11b4 1 . 1 2 0 0. 1293 0.15b3 0.29% 0.4312 0.4b71 0.UL1
0.28b 0.22m # . l a 9 0.0737
4 . W 2
4 . 2 4 -#.32bb 4 . 3 9 2 7 -0,4297
::E&
4 . 4 5 0 9 4 . 4 b 2 9 -0.457b 4 . 4 4 2 7 4 . 4 3 2 8 4 . 4 2 4 5 4. 4073 4 .382b 4 . 3 5 8 1 4 . 3 3 4 2 4 . 3 0 5 8 -0.2719 6 . 2 % 1 4 201 4: l6bf 4 . 1 3 2 1 4 . 0 9 9 3 4 . 0 7 0 1 ;;%J :::3:i 0.07b4 0. 1089 0.1517
0.3717 0.5107 0.6613 0.782b 0.8311 0.7781 0. (274 0.4132 1.1739 -#.ab38 4.2833
0.20s 1 . 2 7 1 ~
j g j3Ji 4.Mw 4.8b98
4 . 9 8 4 7 4 . 9 8 6 3 4 . 9 8 5 9 -0.9834 -0.9187 4 . 9 7 2 5 4 . 9 6 5 0 -0.95% 4 . 9 5 4 0 4 . 9 4 9 0 4 . 9 4 4 1 4 . 9 3 8 9 4 . 9 3 3 4
+ +
+
+
. *
+ +
. + +
8-73
1.2948 0.31b7 0. 3395 0.3b3, 0.3874 0.4125 0.4384 0 4b51 0:4927 0.5210
0.blY 0.b421 0. (743 0.7074 1.7412 0.7759 0.8113 0.8475 0.8844 0. 9222 0.9b07 1.06- 3.0401 1.1811 1.1129 l.lb59 1.2lM 1.2554 1 312 1 3507 1.- 1.4528 1.500 1.W34 1. (225 1.b844 1.74% 1.8114 1.8913 1.9b89 2.0517 2.1* I.23b5 2.3405
3: #a
2*%43 ::71# 2.871b 3.04b3 3.2-1 3.4779
1.2305 0.2324 0.2337 8 3 4
0.2343 0: 113
1.2241
0.1974 0.1174 1.1759 1.1b24 8.14b8 0.1289 0.lMb 0.08b1 #.Ob20 1.0314 1.H9b 4.0122 3. 0309 4 . w 7 4.w03 4.0722 4 . U 2 8 4.0922 4.lM 3 . 3 4: 1218 4.lIb2 4.1311 4.1355 4.1394 4.14- 4.1W1 4.1491 3.1515 -0.1537 -0.157 4.15 5 4.1591 4.lb05 3.lb19 4.1b31 4.lb44 4.1b5l 4. 1bb9
1.2971 1.292b 1.280 1.2770
1.19 0 1217
0.9973 1.0014 0.997* 1.986b 0.9754 0.9b24 0.94b0 1.9253 1.8994 0.8b95 0.837b 0.8053 0.77% 0.7293 0.706b 1.7227 0.7432 1.7525 0.7blb 0.7b87 0.7793 0.7834 1.7819 1.79w 0.7921
::;::3 IW
0.7745
pi 1.8012 0 . 8029 0.8044 1. 8059 0.8072 1.8083 0.8094 1.8105 0.8115 0.8115 1.8134 0.8143 0.8154 0.813S
4.9273 4 . 9 2 0 0 4.9099 4.8943 4.8b81 . ::ti8 3::::; 4 3983 4.3818 4.3729 4.35lb
43735
4.1b97 4.lY2 4.1378
0 031b 0.19- 1.2434 1.1715
1: 1 e M
o . m i
0.0979 0.~076 0.0781 0.0712 1.M45 0.058b 0.6534 0 . M b 0. 0443 0 . w 0.03b8 0.0335 0.0384 0.027b 0.0251 0.0228 0.0204 0.0182 0.11bl 1.0142 1.0124 1.1107 0.0150
+ +
+
+
+ + + + + + + + + + +
+
SECTION QURACTERISTICS V u ( ANG OF ATTACK
0.#000# 1.-
-0.00760
MACH NO 0.82000
11.69999 ac
4.2M71 CD CL CD CM ARE BASED ON VISCCUS PRESSURE SPAN STATIOY CL
PLOT OF CP AT CWPUTATIONAL MESH POINTS
X 3.4788 3.2b62 3.0464 2.8717 2.1171 2.5789 2.4541 2.3406 2.236b 2.1407 2.0518 1.9b89 1.8914 1.8185 1.749b 1. b845 1. b225 1.5b34 1.5070 1.4529 1.4088 1.3507 1.3023 1.2555 1.2100 :: pi1 !:-el 1.- 0 . 9C07 0.9222 0.884b 0.8471 0.6116 0.7163 0.7417 0.7079 0.67b8 0. (426 0.b110 0.5803 0.5503 1.5211 0.4927 #.&dl
Y d.lb25 4.1614 -0.1602 4.1590 4.1579 4.lSb6 -0.1553 -0.1538 -0.1521 -0.1502 4.1481 4.1457 4.1430 4.1399 4.13bb -0.1328 4.128b -0.123) -0.1187 -0.1129 3:%3 3:G# 4.0720 4.- 4.8474 -0.0322 4 0142 0.1221 0.0221 0.012b -0.8035 -0.1231 -0.W66 -0.0709 -0.0957 4.1200 4.1433 4.1650 -0.1842 -0.2008 4.2151 4.2265 4.1350
d M 8
MACH NO 0.8129 0.8150 0.8142 0.8133 0.8123 0.8114 0.8104 0.8094 0.8084 0.8014 0. 8W2 1. 8049 1.8035 1.8019 0.8003 1.79b5
0.7920
1.78b4 0.7830 0.7793 1.7750 0. 7713 0.7653 0.7m 0.7593 0 .710 0.b823 0.6149 1.5980 0.b017 0.6285 0.6544 0.6830 0.7140 0.7471 0.7820 0.8190 0.8576 0.8951 0.9312 0.9702 1.0040 1.1229
0.7985 0.7943 0.7893
i I
+
+ +
+ +
+ +
+ + +
+
+ +
B-74
I I
1 1
1.4384
1.
0.1329 1. 11- 0.1058 1.0934 1.@018 0.0709 0.bbM 1.M15
0 . 0281 0.021b 0.01CI
3: $3:
#.Mu 1.- 5 . 3 :
I::%:
t : E3
::wit
1 : m 5 1.m1m2 #.mu 1.1212
1.0413 0.0499 0 .M93
1.1628 1.1792
0.2529 0.2733
4.2414
2: w 3- 1::’ 4: l 4 8 t 4. 14W 4.1326 4 . 1 2 4 4.11b 4 . 1 1 7
4.M If::%
0.@039 1 . l W 7
0.1362 1. 1448
o . n s
5: 11::
1. 1743 0.1087 @.l#bb
1.2024 0.2W9 1.2111 1.2147 0.2179
3: it13
0 . 2945 0.3165 0.3392 0.3628 1.3871 0.4123 0.4382 0.4b49 0.4924 0.5207 0.5498 0.5797 0.6114 0.6419 0. 6742 0 . 7072 0.7411 0.7757 0.8112 0.8474 0.8844 0.9221 1. 9607 1.WW 1.0401 1.0811 1.1229 1.1659 1.2111
1.3507 1.-
1.5635 1. 6225
1.8185 1.8914 l.9bW 2 . n 1 1
f:3B: ::;x ::w
pg 2.4541
2.8717 3.0464 3.2462 3.4780
::fX
0. 2207 0.223# 0.2248 1.12b1
0.2262 0. 2249 6.2227 0.2195 0.2154 0.2103 0.2040 0.1964 0.1875 0.1770 0.1646 0.15W 1. 1330 0.1134 1.0917 1 . W84 1.0444
:::I::
J: 4:13b! 4 121 4 . 0 4 9 8 4.bb13 4 .1714 4.1805 4.0885 4. 1958 4. 1022 4 . 1 0 8 0 4 11 2 4 .1221 4 . 1 2 5 9
4:1A
3: €3 j; $1 4.1414 4 . 1 4 3 8 4 . 1 4 4 5 4 . 1 4 5 9 -0.1 k 7 1 4 . 1 4 8 3 -0.1495 -0.1506 -1.1517
1.1332 1. 1386 1.1350
1.02m 1.0122
E13
a.94 m. 9337 #.91?9 0.9124 1.1869 0.8723 1.8595 1.8481 0.8370
1.7969 1.7829 0.7b39 0.74b2 0.7Ml
1.1262 1.1032 1.1b03 1.2049 1.2413 1.27W 1.2915 1.3#44 1 3- 1:3113
1.3011 1.2988 1.296b 1.2941 1.2914
1.2883 1.2844 1.2791
1.2365 1.2883 1.1461 1.8786 1.0219 1.8610 1.0049 1.0039 8.9941 0.9830 0.9702 1.9536 1.9321 0 . 9 W 1.8735 1.8-
0 7292 1.7224 1.7398 1.7520 0.7b12 0.7b83 0.7741 0.7791 1.7831 1.7867 0.7898 1.792b
1.7993 1.8112
:::%
: : TtS: 1:7#64
::::5: 5: E 3:t t f : 1 .8W3 0.8-4 0 . 8 l M 0.8115 0.8124 0.8133 0.8142 0.8150 0.8130
4 . 4 4 4 1
4. 4.112# 4 . M 4 7 4 . W C u
0.B284 0.0496 0.1798
0 1 17 d 2 U 3 1.3439 #.ab4
# . l y e
3: :x 1.4 1.2038 4 .e274
4 6 4: 7%
3x3 4.9182 4 .9392 4 .9474 4.%M
4. 4.94bb
4 . 9 1 8
4. 9129 4.9#bb 4 .8978 4 .8844 4 .863@ 4.8259 4 .762b 4. b639 4 . 5 3 9 4 . 4 2 3 3 4 .3812 4.3890 -0.3869 -0.3669 4 .3442 -0.3179 4 . 2 8 3 5 4 .2386 4 .1815 4 .1144 4 .0429
0.0297 0 . 0996 0.1951 0.2438 1 .2097 0.1724 0. 1442 0. 1 2 u pf 0.0794 0.0718 0.” 1.85- 1.8537
1 .os9
O W 2
0.0183 0.0163 0.0144 0.0125 0.0107 0.0151
:;::b
+ + + + + + + + + + + + + + + + ’+ + + + + + + + + + + +
+ + + + +
+ + + + + + + + + + +
+ + + + + + + + + + + +
+
+ + + + + + +
+ + + +
+ + + + + + + + + + + + + + + + + + + + + + + + +
8-75
SEtrIaY CHARACTERISTICS Affi OF AlTACU
1.- MACH lm VAN @.8HII a*-
PLOT OF CP AT COWTATIOYAL MEW POIYTS 1
3.6182 3.2463 3.0465 2 81 8 2:7132 2.5lW
2.1- 1.6519 1.9690 1.8915 ::E3 i::tff 1 . p 1. 011 1.4529 1.4809 1.3508 1.3024 1.2555 1.2101
1.0111 1.0481 1.0000 0.9222
8.8116 0.7763 0.7411 0.1a19 a.6149 1.6111 0.5804 0.5505 0.4929 0.4653
:: %
a: Dttf e.96ei
e.6427
e.5213
Y 4.1501 4.14% 4.1482 4.1658 4.1445 4.1418
4.1319 4.1358 4.1335 4.1308 4: 1:::
2:s: 4.ay
4.1016
4 08W -#:e119 4.#62@
4.0231 -e.@&.* 0. a139 0.0284 0. 0287 0.0199 0. 0041 -0.0145 4.0364 4.0591 4.1010 4.12% 4.15w 4. 1693 4.1856 4.19% 4.2195
4 . e 3
4 . ~ 3 5
4.ziie
MACH Iw) a.8129 1.8151 0.8142 0.8133 a.8114 0.8105 0.8095 @.a085 1.8074 a.aOb2 0 . 8049
e.8123
1.8135 a.8m o.awz a.7904 a.1964 0.1942 a.1917 @.law a.1860 a.1826 1.1780
0.7646 @ . l b M 1.7585 a.1463 9.6816 0.5969 e.6057 0.6512 0.6195 l.7428
::m e.6142
e. 6259
e.7102
e.1175 p; 0.9278 1 . 9 6 0 1.0012 1.0209
0.4385 0.4126 0.3814 0.3630 0.3167 0.2941 0.2136 0.2532 0.2336 0.2149 0.1969 0.1798 0.1635 0.1419 0.1331 0.1192 0.1060 0.0936 0.0111 8.0516 0.0430 0.0352
6.3396
m.eai9 o.wie
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0.8591 a.8693 0.0802 0.1045 0.1179 0.1320 0.1468 8.1625 0.1190 0.1962 0.2338
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-0.226e -0.2101 4.2336 -0.234d -8.2358 -0.2362 4.2323 4.2293 4.2255 -3.2211 4.2159 4.2102 4.2039 -0.1913 4.1984 -0.1832 4.1760 4.1681 4.1615 4.1543 -0.1470 -0.1391 4.1325 -0 12 1 4. le95 4.0924
4.0591 4 .04b8
-8.0191 B.W75 3.0111 0. a345 0.@476 o.eba2 0.0722 @.MH a. le46 8.1143 1.1234 0.1320 8.1481 0.1418 0.1551 0.1619 0.1684 3.1746 0.1804 0.1859 0. 1958 0.2aOl
4: 1135 4. lei2 -a. e m 4.eiia
4.8333 + . m e
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1.8310
1.6259 1.8213 1.0171 0.9991 a.9781 0.9666 8.9519 0.9366 0.9218 0.9071 3.8924 0.8787 0.8668 0.8564 0.8462
0.8269 0.8193
0.1812 0.791 0.1249 0.6038 0.5202 0.4036 0.6249 O.IBo( #.La22 a. 7e95 0.8140 0.9121 1.0798 1.1395
1. e357 1. e328
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fg 2673
1.21 9 1.2833 1.2865 1.2894 1.2914 1.2918 1.2910 1.2896 1.2881 1.2868 1.2854 1.2839 1.2822 1.28W
CP 0.Ileb 0.0124 I.0165
1.1226 a 024a @:0271 0 . 0325 a.0389
e. 0154
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e. 4543
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4.4611 -8.6511 4.4452 4.4316 4.4222 4.4149 4.6001 4.3565 -8.3351 -0.3185 4.2801 -8.2169 4.1860
-0.1251 4.1804 4 . 0 5 6 3 -8.0344 -0.0148 0.0015
0.0856 1.1353 a.2044 0.3186 a.4503 I. 6130 a.1611 0.8189 0.7938 1.6599 1.4615 0.2313
4.1966 4 . 3 8 2 1 4.538a 4.6518
4.84a3 4.8149 4.8958 -8.9048 -0.9108 -8.9148 4 . 9 1 8 0 -0.9187 -8.9174 4.9151 4.9105 4.9883 -8.9658 -8.9029 4.8993
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a. lb58 8.1522 a.13b1 8.1173 #.#964 3.0711 a.nw l.0247 #.a844
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8.7828 (1 78b
0.7915
a.7993 #.8#12 8 . 8829 8.8045 8.8659 a.8072 a. 8W4 #.am
8.8133 3 8 4
8.8129 8 : 8 M
4 .8950
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4.b942
4 . 3 9
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SECT I Ow QURACTERI ST I CS
MACH NO YAM A f f i OF ATTACK 0.820am #.ma## l.#WM
SPAN STATION CL W a4 13.49999 8.47116 4.01073 -#.21mb
CL CD 01 ARE BASED Ow VISCOUS PRESSURE
PLOT OF CP AT CWPUfATIOYAL MESH POINTS
X 3.4784
2.8720 2.7174 2.5791 2.4543 2.3408 2.1361 2.1489 1.0528 1.9691 1.891b 1.8186 1.7498 1.684b 1.6227 I . 563b 1.5071 1.4530 1.4010 1,3508 1. 3024 1.2556 1.21a1 1.lbb0
1.w1 l .m, #.)UT a. 9222
0.8116 0.7763 0.ii l .3 0.7080 0.6750 a.6427 8.6113 8. 5885 a.55BL a.5214 0.4931 a.k655
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3: :t:f
Y 4 .1397 -0.1384 4 .1378 4.1357 4. 1344 4 .1330 -0.1316 -0.1388 4. 1282 -0 . l lb3
4 .1192 4 .11b3
4.1055 4 . 1 0 1 1 4.09b2
4 .8788 4 . 8 7 U 4 . 0 6 2 1 4.#52b 4 .#42# 4 .8298 -#.a158 a . m r
#.828J #.a340 1.834b #.#2b4 0.0121
-0.006 1 -8.0269
-8.0721 -0.w4b 4 . 1 1 6 4 4.1367 4. 1558
4 .1847 4 . 1 9 5 8 4.2H3
3: :::: 3: :w1
3: I:R
-0.~492
-0.1701
MACH NO 0.1129 0.8152 1.8143 a.8133 B.8124
8.8097 0.8887 0.837b 8.8064 3.8851 1.8837 a.8821 0 . 8 W 0.7985 0.79b5 0.7942 0.7917 0.7889 3.7858 3.7823 8. 7784 a . 7 7 u a . 7 0 1
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I:::# 3. 7454
I.59b1 8.6839 0.6234 0.6482 0.6761 0.7065
0.7730 8. b#9b 0.8405
0.9635 8.9983 1.8189
0 . m ~
3: os::
CP 1.6154 0.0181 0.8122 a.8143 0.81b4 1.3180 8.0201 8.822# 8.0241 #.02b6 1.8291
#.a462 a.nw 0.0555 @.a6669 #.I736 1.6111 0.MW 3.-
a.wm
a.4716 a.4579 8.4182 0.3667 0.3081
0.1746 0.1018 0.0224
4 .0612 -8.1436 4 .2222 4 . 3 0 4 1 4 37 b
a.2437
4 : 4 1 L
+ + + +
+ + +
+ + + + + + +
+
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+ + + + + + +
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+
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+ + + + + + + +
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B-77
3.4387 3. 4128 3.3876 3.3632 0.3397 3.3169 3.2949 3.2738 3.2534 3.2339
0. 18W 3.1637 3.1481 3.1333 3.1193 0.1061 0.0937 0.0821 0.0712
0.0431
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::2:2
::a+: mf 0.0161
#.a839 3.W17 r.mr *.Mea 3.0004 0.0016 0.0037 0.0065 0.0101 0.0146 3.0199 0.0261 0.0331 0.0409 0.0495 0.0589 0.0690 0 . 0800 0.0917 0.1043 3.1176 0.1317 0.1466 0.1622 0.1787 0.1959 0.2139 0. 2328 0.2524 0.2728
3 : N 4.2181 4 .2203 4.2208 4.22#4 4 .2193 4.2166
-0.2053 4 . 2 W 3 -1.1949 4 .1891 4.1831 -0.1768 4.17b4 -0.16W 4.1576 -0.1512 4 .1446 4 . 1 3 8 1 4.1316 4 12 0
4.1107 4 . 1 0 3 1 -0.0949 4.0858 4.3756
4.0519 4.3392 4 .0263 4 .3134 4.eees 0.0123
0.0498 0.0614 8.0724 0.0829 0.0928 0.1023 0.1113 0.1199 0.1280 0.1357 8.1430
3: :#
4:11{1
4 . ~ 4 2
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5rjg 0.1689 0.1745 1.1199 0 . 1848 0.1894 0.1936 0.1975
0.1840 0.3159 0.3387 0.3b23 0.3866
0.4444 0. 4920 0.5203 0.5494 0.5793 0.6100 0.6415
0.7069 0.7408 0.7755 3.8109 0.8472 0.8842 0.9221 0.9606 1.0000 1.0401 1.0811 1.1230 1.1660 1.2101 1.2556 1.3024 1.3508 1.4010 1.4530 1.5072 1.5636 1.b227 1.b04b 1.7498 1.8187
.a916
2 .10) 2.23b8 2.3408 2.4543 2. 791 2.7174
3.0467 3.2165 3.4784
s: :;#!
0.6731
i:%
2 . ~ 2 0
0 . 2009 0.2039 8.2065 0.2086 0.2102 0.2112 0.2115 0.2113 0.2103 0.2085 0.2059 0.2024 0.1978 0.1921 0.1851 0.1766 0.1662 0.1535 0.1382 0.1203 0.1002 3.0784 0.0560 0.0310 0.0116
4.0050 4 .0191 4.8312 -0.0419 -0.0513 -0.0597 -0.0672 -0.0740 -0.0800 -0.0854 4.0933 4 .0947 -0. 0987 4.1023 -0.1055 4.1084 4.1111 4.1134
4 .1192 -1.1208 -0. 1222 -0.1236 -0.1249 -0.1262 -0.1276 -0.1289
3:M
1.3291 1.0332 1.0304 1:::z 5: :E: pig 9988
3.9682 3.9544 3.9401 3.9262
3. 8753 0.8656 0.8564 0.8472 0.8393 0.8331 0.8263 0.8152 0.7984 0.7760 0.7437 3.6926 0.6194 0.5327 3.4517 0.4453 0 . 4231 3.4908 0.5881 0.6928 3.7942 0.8895 0.9766 1.0555 1.1172 1.1589 1.1915 1.2177 1.2373 1.2496 1.2555 1.2599 1.2646 1.2684 1.2707 1.2715 1.2715 1.2713 1.2709 1.2703 1.2695 1.2683 1.2667
1.2647 1.2621 1.2586 1.2537 1.2462 1.2336 1.2122 1.1769 1.1248 1.0635 1.0183 1.0072 1.0116 1.0074 0.9970 0.9848 0.9682 0.9451 0.9153 0.8805 0.8436 8.8067 0.7726 0.7286 3.7063 3.7220 0.7391 0.7512 0.7604 0.7677 0.7736 0.7786 0.7828 0.71165 0.7897 0.7926 0 79 2
0. 7996 0. bel5 3. 8032 0.8-
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0.8108 0.8117 0.8126 0.8134 0.8143 0.8152 0.8129
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-1.1974 4 .1682
-0.0977 4 . 0 7 8 1 4.0584 4.0414 4 028 -110134
3.0104 3.0444 0.0947 8.1642 0.2732 3.4262
3.8261 0 83 8 0: 67#9 0.4887 0.2728 8. 0554
-1.1488 4.3311 4.4985 4.6#99 4 .6877 -0.7469 -0.7932 4 .8273 -0.8483 4 .8583 -0.8657 4 .8737 +.Ma8 4.8838 4 .8852 4.8853 -0.884 4 .8841 4.8832 4 .8818 4 . 8 7 9 8 4.8772
3: ::I:
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4.8739 4.8695 4 . 8 6 % 4.8553 -0.8425 4 . 8 2 1 0 -0. 7835 4 .7206 4.6242 4 .5061 4 . 4 1 6 0 -0.3938 4 .4025 -0.3942 -0.3730 -0.3481 -0.3138 4 .2659 -0.2034 4. 1295 4.0506
0.0285 0.1019 0.1965 0.2440 0.2105 3.1740 0.1479 0. 1282 3.1126 0.0998 0.0892 8.0800 0.0721 0.w51
0.M4 0.0439 0.0398 3.0361 0.0328 0.0297 3.0273 3.3244 0.0220 0.0199 0.0179 0.0160 0.0142 8.0123 0.0103 0.0152
:: 3::
+ + + + + + + + + + + + + + + + + + + +
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+ + + + +
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+ + + + + + + + + + + + + + + + + + + + + i + + + + .
1 1- i
R O T Of P AT EOWMATIOUL MEW MINTS
m I
1 I
1 I I I i
ORIGINAL PAGE !E OF POOR QUALIW
SECTIOW OUR*CTERISTICS
V 4 . 1 2 1 1 4 1204
4 .1184 4.1174 4.11b4 4 .1113 4 .1140 4 .1125 4.1109 4 .1090 4. lOb9 4.104b 4.1020
4: 1194
;;rd 3:M ;:m 3%
p3 4.03% 4.0212 4.8079
0.0877 0.02b0
0.8100 -#g 4.0829 4.l234 4 . 1 4 1 1
4.1810 4 .1895
4. i o n
3: %I
W I O 0.8131 0.8154 0.8144 0.8134 0.8124 3.811b 3.8109 0.8101
0 .E079 0.8W7 0.b054 #.bo40
0:7988 0.79C7 0.7944
0.7857 0.7821 0.7781 0 . 7 7 1 0.7684 0.7C29
0.8mi
3w 3:::u
0.b883
0.r2m : : t:f: o 8047 O:b42l 0.88lb 0.9282 0 . 9597 0 99 1 1:od2
4 . l U O 4 . 2 O M
4 . 2 W 7 -0.20 9 -0.2013 4.19b2 -0.1945 -0.1903 4.1b5b -0.18W 4.1754 4.1699 4 .1643
4 .1474 4.1416 4 . 1 3 5 1 4.1300 4.1240 4.1178 4.1111 4.1040
4 . 2 y T
3: :z::
4 . M C l 4.0441 4.0319 4.0198 4 . rn7b 0.w15
0: 1- 0 1084 3:llbS 0.1242 0.131b 0.1386 0.1653
b.lC35 0 . l C H 8.1741 0.1789 0.lb33 0.1873
t : :z::
+
+ + +
+
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8-79
8.2937 0.3157 0.3384
38C3 0 41 5 y b 2 0
.:,A4
0.6136 0.7067 0.7406 0.7753 0.8108 0.8471 0.8842 0.9220 0.9b06 1.- 1.0401 1.0811 1.1230 1.1660 1.2102 1.2556
1.453
1. (228 1.6847 1.7499 1.8188 1.8917 1.9b93
2.1410 2.2%) 2.3409
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2.43::
3.0469 3.2467 3.4786
0.1911 0.1943
0.2115 ::I::: ::E ::I19 0.2024 0.2004 0. 1976 0.19s 1.1189 0. 1828
0.1539 0.1395 0. 1225 0.1032 0.0822 0.ww 0.0367 0.0184 0.w27
-0.0105 4.0219
1: 3;
j:z 3:q -0:w 7
4.1728 -0.1773 4.0814 -0.0050 4.0883 -0.0913 -0.6939 4.09b2 -0.0983 4.1002 -0.1018 -0.1033 4.1046 -0.1057 -0.1067 4.1077 4.1007 -0.lWb -0.1104
1.2521 1.2513 1.2494 1.24bb 1.2420
1 1884 ::I:: :&: 1. 025s 1.HS 1. 0088 1 . w 2 0.9995 0 . 9895 0.9744 0.9511 0.9199 0.1831 0.1441
0.7699 0.7209 0.7009 0.7230
0.7514 0.7605 0.7b78 0.7738 0.7788 0.7831 0.7868 0.7901 0.7931 1.7957 0.7980 0 . 8001 0.8019 e.8036 0.8052 0.8065 0.8078 0.8090 0.8101 0.8111 0.8118 0.8127 0.8134 0.8144
1.8053
0.7394
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-0.8535 4 .8513 -0.8480 -0.8432 4 . 8 1 2 3:tiB 3.:" 3rd 4.3863 -0.3970 -0.39m 4.3781 -0.3Slb -0.3265 -0.2784 -0.2130 4 . 1 3 5 1 4.0518 a.0317 0.1077 0.2130 0.2557 0.2085 0.1733 0.1476 0.1280 0.1123 ::a 0 . 0794 0.0713 0.0643 0.0580 0.0524 0.0474 0.0429 0.0388 0.0352 0.0319 0.0290 0.02b3 0.0236 0.0213 0.0193 0.0176 0.0158 0.0141 0.0121 0.0098 0.0146
SECT ION OURACTERISTICS YAM ANG OF ATTACK
1.00000
W -0.01388
CL CD CM AREIASED OY YISCOUS PRESSURE
MAW NO 0 * 82000 0.Wm0
SPAN STATION QI 4 . 2 1 5 M
CL 0.44905 15.29998
PLOT OF CP AT CO)(PUTATIONAL MESH POINTS
X 3.4789 3.2469 3.0471 2.8724 2.7177 2.5795 2.4546 2.3411 2.2371 2.1412 2.0523 1.9694 1.8918 1.8189 1.7501 1.b848 1.6229 1.5638 1.5073 1.4532 1.4011 1.3510 1.3026 1.2557 1.2103 1.1bbl 1.1231 1.0011 1.0401 1.- 0.9607 0.9222 0.8845 0.847b 0.811b 0.7763 0.7418 0.7081 0.6751 0.b429 0.b114 0.5808 0.5509 0.5217 0.4934 8.4658
Y 4.1227 4.1209 4.1191 4 .1174 4.1157 4 .1141
-0.1088
4.1021 4.0995 4.09bb 4.8934 -0.0899 4 . 0 8 6 1 -0.08 19 4.8772 4 .0721 -0.06b4 -0.0600 4.0530 4 .0451 4.1363
2: ::3 :::Et
xq: :!::ti 4n
8.0437 0.0450 #.@a55 0.0263 0.0104
-0.0081 4 .0281 -0.0486 -0.0694 4.0893 -0.1081 4. 1252 4.1403 4. 1534 4 .1641 4. 1724
MAW NO 0.8134 0.1151 0.8145 0.8134 0.8125 0.8118 0.8111 0.8104 0.8094 0.8083 0.8072 0.8060 0.8046 0.8031 0.8014 0.7995 0.7974 0.7951 0.7924 0.7195 8.7862 0.7824
0.7734 #.7b81 0.7624 0.75b8 0.7537 1.7484 0. 6872 0.b149 0.5945 0.6000 0.617b 0.6411 0.bb81 0.6978 0.7295 0.7632 I. 7990 0.8367 0.8748 0.9137 0.9539 0.9904 1. 0149
e . 7 7 8 ~
CP 0.0141 0.0091 0.0119 0.0142 0.0161 0.0177 0.0192 0.0207 0.8228 0.0251 0.0275 8.0302 0.0331 0.0364 0.0400 0.0440 0.8486
0.0593 0.0657 0. 0728 0.1809 0.0900
e . m s
1: Fj 0. 13b0 0. 1427 0.1541 0.2847
0 . 4658 0. 4300 0.3813 0.3249 0.2622 0.1945 0.1223 0.0451
-0.0358 -0.1174 -0.2000 -0.2842 4.3595 4.4092
::t%
B -80
+ +
+ + +
+ + +
+ + +
+ + + + + +
+
+ + + + + + + +
+ + + + + +
+ +
+ + + + +
+ + +
4 + + + + +
+ + +
ORIGINAL PASE 16 OF POOR QUALITY
-#. 1788 4.1834 4.18b9 4. 1890
4.1899 3: 13
4.1b11 4. lf” 4.1 17 3: 1%
-#.11b3 4.1103 4.1039
-#.“
4.0136 4.W24 0.W91 e. 02M 0.0317 a. a425 0.0529 #.Ob27 0.0721 0.0812 0.09W 0.0984
a.1210 0. 1289 0.14 4 0. 1484 0.1w
8: 0 . 1 y
0.1795
0.2933 0.3153 0.1380 0.Wlb 0.uw :.4#
0 : 4 J 0.4914 0.5197 0.5489 0.5788 0.6095 0.b4i0 0. 6734 0. 7M5 0.7404 t : m 0.8470 0.8841 0. 9219 0.9406 1.6000 1.0401 1.0811 1.1231 1.1661
1.30% 1.3510 1.4011 1.4532 1.5073 1.508 1. (229 1.6849
1.89 8 9b44
l:M23
: : ::s:
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2. 8724 3.6411 3.2469 3.4789
1 . 0 2 0 1.0293
0.89b7 0.89W a.8835 1.8770 0.8722 0.8701 0.8b80 0.8blS 0.8483 t : s:u ::E+: :::If: .
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0 . 7 ~
0.74bO
0.9925 l.M& 1.0987 1.1282 1.1510 1.104 1.181b 1.1897
1.207 1.2422 1.2433 1.2444
1.2453 1.24bo
1. 0038 0.9881 1.0031 1.00b3 1.0024
0.9bM 0.926s 0.8872 0.84% 0 . 8048 0.7b88 0.7211
0.7390
0.7b81 0.7742 0.7838 0.787b 0.7910 0.7939 0.79bS 0. 7988 0 . 8 W 0.802T 0 . m 3
8.8082 a.0094 @.81#4 0.8112 0.8120 0.8128 0.8135 0.8145 0.8158 0.8135
0 : :::+
:: ::1: t : RE 0.7794
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+
+
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B-81
SECT IOU W M C T E R I ST ICs Y M A f f i OF ATTACX
LIWY WY) o.nm 0 . m r r
o( 1b 19998 3.487b 3 d 8 3 -0.21551 a d 01 ARE WED ou VISCOUS PRE
PLOT OF CP AT CMPUTATIONAL MEW POINTS X
3. k792 3.2472 3.0473 2.872b 2.7180 2.5797 2.4549 2.3413 2.2373 2.1413 2.0524 1.9b9b
1.7 02 1.b8H ::I;::
&# iiia 4533 1.4012
1.2103 1.lbbl 1.1231 1.0812 1.3402 1.0000 0.9bOb 0.9221 0.8845 0.8476 0. 115 0.#7b3 0.741. 0.7081 0.b751 1. (430 0.b115 0.5809 0.5510 0.5219 0.4935 3.4668
0.4393 0.4133 0.3882 0.3639 0.3413 0.3176 8.2956 0.2745 0.2541 0.2346 0.2158 0.1979 0.1807 0.1b43 0.1487 0.1339 0.1199 0.1067 0.0942 0.082b 0.0716 0.0615 0.0521 0.0434 0.0355 0.0283 0.0219 0.01b2 0.0112 3.0071 3.0039 0.0017 0.- 0.0000 8.0004 3.0017 0.003b 0.Mb4 0.0099 0.1142 0.0195 1.02% 1.0325 p; #.ob82 0.0791 0.0908 8.1032 0.1165 0.1306 0.1455 1. lbll 0.1776 0.1948 1.2128 0.231b I::!::
Y
-0.125b -0 122 -0:119!
2: fltt
-0. in4 -0.1336 -0.1006 4.897k -0.0941 -0.0904
4.06 b
-0.wII 4.0311 4.0212
-0.41 4.04 9
-0.oin ::t% t : 0% 0.0493 0.0438 0.0327 0.0181 3.mo8 -0.0179 -0.1374 -0.07b9 -0.0 59 -0.0939 4.1183 4.1249 4 1375 4: 1479 -0.1561
4.lb24 -0.1672 4.1705 4.1728 4.1742 4.1748 -8.1747 -0.1739 -0.1726 4.1708 4.1685 4.1b58 4.1627 -0.1594 -0.1559 -0.1521 -0.1483 -0.1444 4.1404 4.1363 4.1321 4.1279 -0.123b 4.1191 4.1142 4.1089 -0.1031 4.09b7 -0.0095 -0.0812 -0.0719 *.ob18 -0.M12 -0.0405 -0.0298 4.0192 4.0085 0.0023 0.0132 3.0239 0.0343 1.0443 0.0538 0.3718 0. 1804 3.0888 0.0968 0.1047 0.1122 0.1195 0.1264 0.1331 0.1394 0.1455 0.1513 1. 15bb 0.1b19 0.1bb8 0.1713
0 . n -
l w n y o 0.8140 0.81b2 1.8144 0.8136 3.8129 0.8122 1.8llk 0.81ob 0.8098 0.8091 0.8081 0.8071 0.8044 0.8029 0.8011 0.7991 1.7- 3.7942 1.7913 0.7880 0.7842 3.7798 1.7749 0.7b92 0.7628
3.747b 0.68b3 0.6138 0.5930 0.5974 O.bl40 O.bU7 0. bb30 0.6921 0.7233 0.75b4 &I918 0.8289 0.8b68 0.9050 0 . 943a 0.9805 1.007b
o m s 8
:::Bt
1.0205 1.023b 1.3212 1.016b 1.0118 1.0895 1.0049 0.9988 0.9925 0.98bO 0.9693 0.9594 0.9494 0.9393 0.9291 0.9200 0.9133 0.9083 0.9037 0.8990 0.8964 0.8972 0.8987 0.8957
8.9783
pi 1.7751 3.b92C 0.5928 0.4934 0.4218 0.4078 0.4551 0.53b4 0.6273 0.7175 1.803b 0.8842 1.95b7 1.0185 l.ob25 !;!# 1.1459 1.1564 1.1687 1.1825 1.1953 1.2059 1.214k 1.2213 1.2272 1.2322 1.1365 1.24m 1.2437 1.2471
CP 0.01m 0.0062 3.Ollb 3 0137 0:3153
0.0233 3.1218
0.02
0.0369 3.0407 0.04W
t%#
::a
0.1771 #.#Ob4 0.0970 0.1m2 3.1232 3. 1368 1.1441 1. 155b 0.28bb 3.4377 3.4801 0.4711 3. 4374 0.39eb 0.335b 0.2742 0.2118 3.1367 #.Ob07
-0.3391 4.3944
4.4207 4.42b7
-0.3984
4.3637 4.3504 4.3347 -0.31bO 4.2955 -0.2538 -0.2324 4.2133 4.1990 4.188b 4.1787 -0.1b88 -0.1634 -8.1651 -0.1681 4.1b18 -0.13%
3: Bt3
4.274a
1.7991 3.8220 0.7420 0.5919 0.4099 0.2213 0.0352 -0.1374 -0.2911 -0.41b5
-0.b383 -0.6638 -0.6832 4.7056 -0.7307 4.7537 -0.7725 4.7995 4.8098 4.8185 -0.8258 4.8322 -0.8382 -0.8439
-0.7874
+
+
+ + +
+
+
+ +
+
+
’ * + +
+ + +
+
B -82
ORIGINAL PAGE IS OF POOR QUALITY
8.2929
8 b73 8:7482 8.7749 1.8185 8.8468 8.8848 8.9219 8.9b85 1.-
8.7111
1. b 8 H 1 7582 1.8921 1:r198
3.8474 j:2472
4792
8.1755
3::::t
8.1282 8 1899 8'8897
8.84b2 8.0287 8.8137 a.8889
-8.8183 -8.8281 -8.8291 -8.1378
dw89
4 . 1 1 2 8
-8.8831 -8.Mb5 4 . 8 8 9 b -8.892b -8.8955 -8.8982 4 . 1 8 8 8 -8.ua -8.1111 4 . 1 0 8 8 -8.1116
4:hl -p:p
8.97M i;ji# .81n
l . m 3 8.99b9 1.9714 8.9346 8.8928 8.8464 @.)@bl 8. b93 8.721b 8.7823 8.72% 8.7399 8.7521 @.IC19 8.7b98
8.791 8.7958
8.8841 1.86% 8.8@b9 8.8081 8.8891 0.8899 0.8187 1 . 8 l l b 8.8124 8.8131 8 81 81813 @.OM3 8.8142
SECTION OURACTERISTICS YAW A 6 OF ATTIOL
1.88888 CL tD
8.39482 4 .81998 CL FD CM ARE BASED OY V I S C W S PRESSURE
MACH NO 8.82808 8.80888
cw 4.28984 SPAN STATION
17.09998
PLOT OF CP AT COMPUTATIONAL MEW POINTS
X 3.4795 3.2475 3.047b 2.7182 2.5799 2.455 2.3414 2.2374 2.1415 2.852b 1.9b97 1.1921
a . 8729
1.b231 1. 87b 1.4534 1.4013
1 . p
1.2184
8.8844 8.847b 0.8115 0.7763 0.7418 0.7081 8. 6752 8.6438 8.4116 0.5818 8.5511 8.5228 8.4937 8 . M 2
V
-8.1439 -8.1348 -8.1296
3: :E 4. 1387
4 . 1
-8.LM1 4 . 8 8 3 1 4.8779 -8.8724 -8.8b64 4 . w n -8.8538 -8 84 4 -8:83#1
8 Hb4 818213
8.8378 0.0244 1.8884
4 . 8 6 9 1 4 . 0 2 7 4 4 . 8 4 5 8 -8.8bCM 4.8889
-8.118b -8.1228 4 . 1 3 2 8 -8.1488
-8.mpcc
MACH yo 0.6143 8.0166 8.8155 0.8149 0.8145 8.8148 8.8131
8.8113 8.8lg 8.809 8.8Mb 8.8875 @.awl 8.884b 8. 8829 8.8889 8.798b 8.7%0 1.7938 8.7895 8.7853
:::::+
8.7b81
8.746 1.Ub7 8.b172 1.S9b4 8.5995 0.6142 0. 6352 8.6600 8.6876 0.7173 8.7491 8.7838 0.8187 8. 8553 8.8923 8.9279 8.9b11
a . 7 9
8.9877
. *
+
8-83
0.4394 0.4135
0.21b0
0.1645 :: :tU
0.1069 0.0944 0.0827 0.0718
0.0219 0.01b2 ::x 0 : 00e
0.n- 0.0017 o . m * 0 w
0.0036 0.oeb3 0.0098 0.0141 0.0193 0.0253 0.0322 0.6400 0.0485 0.0578 0.8678 0.0717 0. 0904 0. 1029 0.1161 0.1302 0.1450 0.1b07 0.1771 0.1944 0.2124 0.2312 0. 2508 0.2712
4 .1470 4 .1516
4 . 1 4 6 4 4 . 1 4 3 4 4 . 1 4 0 3 4 . 1 3 7 1 4 . 1 3 3 9 4 . 1 3 3 4 . 1 2 7 4 . 1 2 3 5 4 1 98 -#:lib9 -1.1117 -1.1070 4 .1018 4.0960
4 .0241 4 . 0 1 4 1 4.0039 1.3064 8.0166 8.0166 0.0361 1.0453 0.0541 0.8627 0.0711 0.0793 0.0873 8.0951 8.102b a. 1099 I . l l b 9 8.1236 8 . lm 1.1361
0. 13J8 0.1624
1. w 1 5
1. H49 1.0827
0.99 3 0.9975 0.9948 0.9916 0.9878 0.9830 0.9771
e.9b37 0.95b2 0.9486 0.9419 0.9378 9.9351
0.9328 0.9381 0.944a 0.9472 0 .94@7 e.9230 0.8880
I. 0054
1.T'
o.wn
0.9339 e. 9320
0 . 5251 0.4439
0.b123 0.b983 0.7823 0.8b25 0.9358 0.9981 1.0427 1.0721
1.11% 1.1319 1.1460 1.1625 1.1806 1.1975
I . mss
- 4 . 1 2 1 -4.3900
4 . 3 5 4 1 -4.3442 -0.3322 -4.3188 4.- 3::tft 3: :zz 3::z::
4 . 2 4 6 2 4 . 2 4 2 3 4 . 2 3 8 5 4 . 2 u 1
-0.2701 4 . 2 5 6 b -0.2194 -0.14% 4 0 b1
0' l h 6.61% 0:ma
O.bW9 0.44M 0.2b11 0.0812
-0.0910 -0.2464 4 37 3 4 : 4 6 f l
4 .b068 4 . 6 3 7 5 4 . 6 b 3 9 4 . b 9 4 2 4 . 7 2 7 3
4 .8037 4.82W 4 . 8 3 4 1
3: f:E
If:%:
34% 4:a533 4 . 8 5 1 5 -0.8443
0.2924 0.3144 0.3372 0.3608 0.3852 0.4104 0.4363 0.4631 0.4907 0.5190 0.5482 0.5781 0.6089 0.6404 0.6728 0.7060 0.7399 0.7747 0.8103 0.84b7 0.8838 0.9218 0.9605 0.9999 1.0401 1.0812 1.1232 1.1662 1.2104 1.2559 1.3927 1.3512 1.4013 1.4534 1.507b 1.5641 1 (2 1
1.8192 :;::I: ::tM
::;?Si 2.341
2.7182 2.8729 3.0416 3.2475 3.4795
0.1667 0.1707 0. 1744 0 177b
0.1829 0.1849 0.1864 0.1874 0.1878
0.1850 0.1823 0.1786 0.1733 1.1662 1.1566 0.1442 8. 1289 8.1111 0.0712 8.0493 0.0321 0.0173 0.0044
4 . w 9 4 . 0 1 7 0 4.02b2 -1.0345 4.0421 -0.0491 4 .0555 4 . 6 1 5 4 . 0 6 7 9 -1.0723 -0.0772 4 .M62 4.o9.5 $:098b
-0.1104 4 . 1 1 4 5 -0.1187 -0.1231 -0.1278 4 . 1 3 3 0 -0.1390 -0.1464
0: 1805
:: :t:5
1 . m i s
4.wia
+.nu 4. :E8
1.2381 1.2243 1. 2020 1.1b87 1.1218 1.0616 1.0082 0.9758 0.97b0 0.9946 1.0114 1.0182 1.0175 1.0170 1.0183 1.0159 l.oB42 0.9786 0.9407 0.8973 0.852b
0.7722 0.7255 a. 7079 0.7302 0.7594 0.7687 0.77b2 0.7874 0.7915 e. 7949 0.7979 0.8025
0.8093
0.7470
0.7824
0.8003
:*t": 0:8% 0.8085 0 . 8 1 6 0.8114 1.8119 1.8123 0.8132 0.8141 0.8148 0.8154 0.8160 0.8171 0.8148
o .am
4 . 8 2 9 6 4 . 8 0 4 8 4.7b5b 4. 7057 4 . 6 1 0 5 -0.5064 4 . 3 9 5 7 4.1196 -0.3300 4.3680 4 . 4 0 2 2 -0.4159 4 . 4 1 4 5 -0.4136 4 . 4 1 6 1 4 . 4 1 1 4 4 . 3 8 7 5 4 . 3 3 5 2 -0.2567 4 .1652 4 . 0 7 0 0 0.0231 0.1029 0.2031 1.2408 0. 19II 0.1569 0.1- 0.1104 0.8943 0.0810 0.0701 0.0613 0.0539 0. 0477 0.0423 0.3338 0.0-
0.0247 0.0224 0. 8203
0.0371
n.0274
:::I#/ 0.01b 0.014 0.0128 0.0113 0.0099 0.0085 0.0062 0.0112
+ +
+
+
+
+
+
+
+
+ +
B -84
ORGINAL PAGE 16 OF POOR QUALITY
SECTIOI OUIUCTERISTICS
8.4396 0.4137
::m 1: :::j 0.2163 8.1983
0.1491 0.1343 0.1203
' 8.1071 0.0946 0.0829 0.0711
8.0436 t : I::!
@.eo39 0.0016 0 . m 4 #.mea
::e# 3: n:r t : :tR
I: 3u ::If S:
0.09180
0.1297 0,1446 0. 1602 0.1767 8 . 1939
z: :3t
3: 146, 4.1464 4.14% 4 144 -8 143f 4 .1414 -6.1395 4 .1373
3: :E
3:::a 3: :z 3 : a 3 : x
-0.1111 4 . 1 0 9 2
-#.ob54 4 .0563 4 .0478 4 .8378 4.8287 4 . 0 1 9 4 4.8099 4 .0002
8 0 4 *.IC18
0.01154 0 . 6928 8.1800 0. 1070 0.1136 8.1200 0.1262 0.1320 8.1376 8.1429 0. 1479 0. 1526
8: n# ::E:
w m ::El; 8.8234 1. 8235 0.8136 0.8233 8.8228 0.8222 rn.8217 8.1211 8.8208 8.8281 1.8186 8.8194
::I::: 8.8111 8.8091 0. mob7 8.8030 8.8001 8.7958 0.79IC 8.7847 8.7784 8.7684 8.7282 0.6681 :::E 1: tf l
8.863 0.8894 0.9118 0.9290
8.9393 8.9442 0.9467 8.9484
0 . 9 9 3 0.9567 0. 9555 0.9538 8.9513 0.9483 0.9457 0.9447 0.9451 8 .9456 0.9460 0.9485 8.9548 1.9627 0.9673 0.9641 0.9498 8.9180 0.8615 8.7791 8.6805 8.5862
0 .54n 8.6027 0.6777 8.7578 0.8372
t : Ef
::?a :: :#f u r n 1.1439 1.1513 1.1594 1.1643 1.1650 1.1b13 1.1539 1.1432 1.1293 1.1128 1.0945 1.0753 1.0557
4.2536 4 .2639
4 . 2 9 1 2 4.2980 4 . 2 8 7 5 4 .2839 -0.2787 4 .2724 -0.2678 4 .2649 4 . 2 6 9 4 .2668 4.2676 -0.2729 -0.2868 4 . 3 0 2 5 4 .3119
4.U89 0 . m a 8.2980 8.4930 8.6285
0.-
3:=1 3:%4 4 . 6 5 H 4 . 6 6 W -0.'b730 4 .6836 4.6976 -0.6989 4 .6922 4.6786 4 . 6 5 8 7 4 . 6 3 2 7 4.6815 4.5665 4 529 4:49&
8-85
+ c
+
+ + + + +
+ + + +
+ +
+
+ + + + +
+
+ +
#.292# a.3 ire e.33~ 0: jtr :::$ #.M 7
a.49.3
::g #.7 7 # .7 43
::;:E a.9999 1.#4#1 1 .Ml2 1.1231 1.1663
1.8913 1.9699 2. #518 2.1418 2.2377 2.3418 2 . 4 p 4 : : f 9 2.8732 3.148# 3.2479 3.6?99
ORIGINAL PAGE wL POoR QUALITV
cn ROLL a Y U I -a.BB3%
o( PITCH 4.58732 o .3a919
HING LOMING IS BASED ON VISCOUS PRESSURE
END OF CALCULATION
B -86
~
1. Repott No.
NASA CR-178157
7. Authorb)
R.R. Chow and P.L. O g i l v i e
2 Government Accarion No.
9. Performing Organization N?me and Address Grumnan Corporat ion Bethpage, New York 11714
17 Kev Words ISug tcd by Auth rlsil Computer, Fogram, h e r Manual, Viscous Transonic Flow, Wings, V i s c i d / I n v i s c i d I n t e r a c t i o n
12. Sponsoring Awncv Name and Address
Nat ional Aeronautics and Space Admin is t ra t ion Washington, DC 20546
18 Oisvibution Statement
UNCLASSIFIED - UNLIMITED
Subject Category 02 I
I5 Supplementary Notes
Langley Technical Monitor: Craig S t r e e t t F ina l Report
I9 Security Claui f (of this report] 20 SCcuritr Classif. (of this paw) 21. No of Pages
3. Recipient's Catalog ~ J o
i 22 Rlce
5. Repon Date
Unc 1 a s s i f i ed
October 1986
! Uncl assi f i ed 119
6. Performing Organization &de
8. Performing Organization Report No
RE-726 ~
10. Work Unit No.
11. Contract or Grant No
NAS1-16858 13. Type of Repon and Perloo Covered
Contrd'c t o r Report 14. Swnsoring Agcncy &de
505-60-01-01
16. Abstract
This r e p o r t i s a use r ' s manual which descr ibes the opera t ion o f t he computer program, GRUMWING. dimensional wings us ing a boundary l aye r type v i s c i d - i n v i s c i d i n t e r a c t i o n approach. The i n v i s c i d s o l u t i o n i s obtained by an approximate f a c t o r i z a t i o n (AFZ)method f o r t he f u l l p o t e n t i a l equation. entrainment methods.
The program computes the viscous t ransonic f l o w over three-
The boundary l a y e r s o l u t i o n i s based on i n t e g r a l
I I I I I II