Appendix 1
Appendix 1
Sample Output From "HYGRID"
_ith .b_. fite was user input ftn66 =*** clusterings .=****=.
x = .000000 number of points for The intervat x = 1.000000 to is 75 on the to_er surface min spacing on ends are .0075000 .0010000 x = 1.000000 number of points for the interval x = .000000 to is 75 on the upper surface min spacing on ends are .0010000 .0075000 distance to outer boundary = 6.0 nwake = 31 jmax = 211 jtai[1 = 31 jtai[2 = 181 kmax,normaL _atl spacing 50 1.000000000000000E-05
Appendix 2
Appendix 2
Computational Grids
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Appendix 3
Appendix 3
Listing Of "ROTATE" Code
PROGRAM ROTATE D]HENSION XU(IOO),YU(IO0), XL(IO0), YL(IO0) DIHENSION Xl(lOO),Yl(lOO),X2(100),Y2(100) C ............................ " ...................... ° ......................... C C ]FLAG = 1 NACA-O015 Airfoi[ C C ............................................................................. C ]FLAG = I C ............................ " ................................................ C C FLAG FOR OUTPUT GEONETRY FORNAT C C ]OUT = 1 ====> OUTPUT FORNAT FOR HYGR]D PROGRAN C C ]OUT : 2 ==::> OUTPUT FORMAT FOR FO]LN PROGRAM C C ]OUT = ] =:=:> OUTPUT FORNAT FOR NAC PLOTTING C C ................... * ........ _ ................................................ C 5JR]TE (6,*) e SELECT FLAG FOR OUTPUT FILE FORMAT:; tJR[TE 46,*) e " FORINAT FOR HYGRID PROGRAN "-> ENTER 1' WRITE (6,*) _ - FORI(AT FOR FOILN PROGRN( *-> ENTER 2 t IdR]TE (6,*) ' - FORMAT FOR MAC PROGRAM -*> ENTER 3 e READ (5,*) IOUT NU = 51 NL = 51 XL]N = 0.75 XP]V = 0._ P[ = 4.0 * ATAN(I.0) C .............................................................................. C C NOTE: NEGATIVE DELTAS INPLY FLAP DOWN C C POSITIVE DELTAS IMPLY FLAP UP C C ................................................... * ........ " ................. G VR]TE 46,*) ' ENTER THE ROTATION ANGLE IN DEGREES ' _,/RZTE (6,*) f - FLAP UP DEFLECT]QNS ARE POSITIVE' t/RITE (6.*) ' " FLAP DOWN DEFLECTIONS ARE NEGATIVE t READ (5,*) DELTA DELTR = DELTA * P]/180.0 C .............................................................................. C C READ THE A[RFOIL COORDINATES C C .............................................................................. C IF (]FLAG.EQ.1) THEN OPEN (50 F]LE='nacaO015. in', STATUS=' OLD' ) END IF c OPEN (6,FILE="foi I..out S , STATUS='UNICNOMN" ) C OPEN (7,FILE=#foi l .rot I ,STATUS='UNKNOMN' ) 00 10 [ = 1 , NU READ (5,*) XU(]),YU(]) X1(]) : XU(]) YI(]) = YU(]) 10 CONTINUE READ (5,1000) DO 20 ] = 1 , NL READ (S,*) XL(I),YL(i) X2([) : XL(I) Y2(I) = YL(Z) 20 CONTI NUE C ................................. ° ............................................ C C CONPUTE X,Y LOCATIONS OF FLAP PIVOT POINT (HINGE POINT) C C .............................................................................. C CALL TAINT (XU,YU,XP]V, YPU,MU, 1,NER,NON) CALL TAINT (XL,YL,XP]V, YPL,NL, 1,NER,NON) YPZV - 0.5 * (YPU + YPL) gR]TE (6,881) XPIV,YP]V 88"1 FORMAT (2X, ' XP|V:' ,lB.5, lOX, 'YPIV=', F8.5,/) C .............................................................................. C CAHNED ROTATE THE AIRFOIL - UPPER SURFACE POINTS C C ........................................................ _ ..................... C 00 60 ] : 1 , NU IF (XU([).GE.XL]N) THEN DX : XU(I) - XPIV DY = YU(]) - YP]V RAD = SQRT(DX*I)X + DYwDY) IF (DX.EQ.O.) GO TO 57 BETA = ATAN;>(DY,DX) GO T058 57 BETA = PI/2.0 IF (DY.LT.O.) BETA = -BETA 58 CONTINUE XI(]) = XPIV + PAD * COS(BETA ÷ DELTR) YI(I) : YPIV ÷ leAD * SIN(BETA ÷ DELTR) BETAD = BETA * 180.0/P] _,q_iTE (6,300) I,DX.DY,BETAD,XU([),YU(]),XI(I),YI(]),RA[ c I I # , , I I I c300 FORNAT(2X, ]= ,]2,3X, DX= ,FS.4,3X, DY= ,F8.4,3X, BETAD= ,F8.3, lz • I I , • I • I C 3X, XU: ,FB.5,3X. YU= ,FB.S,3x, Xl: ,F8.S,3X, YI: , c • F8.5,]x, ' rad=,, fB.Z,) END IF 6O CONT I HUE C .............................................................................. C CAHHED ROTATE THE AIRFOIL - LOWER SURFACE POINTS C C .............................................................................. C WRITE (T/',IO00) DO 65 I = I , NL IF (XL(1).GE.XLIH) THEN DX = XL(I) - XPIV DY = YL(]) - YPIV RAD = SQRT(DX*DX + OY*DY) IF (DX.EQ.O.) GO TO 53 BEIA = ATAH2(DY,DX) GO TO 54 53 BETA = PI/2.0 IF (DY.LT.O.) BETA = -BETA 54 X2(I) = XPIV + RAD * COS(BETA + DELTR) Y2(i) = YPIV + RAD * SIN(BETA + DELTR) BETAD = BETA * 180.0/P1 c WRITE (6,301) [oDX,DY,BETAD,XL(I),YL(I),X2(I),Y2(1)oRAD c301 FORMAT(ZX,'I=',I2,3X,'DX=',FB.6,3X,'OY=',FB.4,3X,'BETAD=', F8.3, c * 3X,'XL=',FB.$,3X,'YL=',FB.S,3x,_X2=',FB.S,3X,'Y2 =t , c * F8.5,3x,'rad=',f8.4) END IF 65 CONTINUE C .............................................................................. C C HYGRID AND ARC2D GEOMETRY FORRAT C C ............................................................................... C IF (IOUT.EQ.I) THEN DO 1 I = NL , 1 , "1 URITE (66,101) X2(I)/x2(nl),Y2(I)/x2(n() 1 CONTINUE DO2I=E,NU tJRITE (66,101) Xl(I)/xl(nu),Yl(II/xl(nu) 2 CONTINUE END IF C .............................................................................. C C NULT AND FOILN GECNETRY FORHAT C C .............................................................................. C IF ([OUT.EQ.2) THEN DO 222 ] = 1 , NU URITE (66,101) XI(])/XI(NU),YI(I)/XI(NU) 222 CONTINUE _iTE (66.1000) DO 111 I = 1 , NL WRITE (66,101) X2(I)/X2(NL),Y2(I)/X2(NL) 111 CONTINUE END IF C .............................................................................. C C HAC PLOTTING: XU,YU, XL,YL C C .............................................................................. C IF (IOUT.EQ.3) THEN DO 223 ! = 1 , NU S/RITE (66,102) XI(1)/Xl(NU),YI(I)/XI(NU), • XZCI)IX2CNL),YZCI)/X2(NL) 223 CONTINUE END IF STOP 7"/'7 I00 FORHAT (8(5X,FIO.8)) 105 FORMAT (2x, i3,_x,8(Sx,flO.8)) 101 FORMAT (2(SX,FIO.8)} 102 FORMAT (4(5X,F10.8)) lOOO FORMAT (Ix) STOP END SUBROUTINE TAINT (XTAB,FTAB,X,FX.N.K,NER,HON) REAL XTAB(201).FTAB(2OI).T(IO).C(IO) C NASA - AMES ROUTINE FOR POLYNORIAL INTERPOLATION C OF A TABULATED FUNCTION IF(N-K| I , I , 2 I HER = 2 RETURN 2 IF(K-9) 3,3,1 3 IF(NON) 4,4,5 5 IF(NON-2) 6,7,4 4J=O NH1 = N - 1 DO 8 l = 1 , _1 IF(XTAB(1) - XTAB(I+I)) 9,11,10 11 NER = 3 RETURN 9J=J-1 GOLD8 10 J = J+l 8 CONTINUE NON = 1 IF(J) 12 , 6, 6 12NON =2 7 DO 13 I = 1 , N IF(X - XTAB(II) 14,14,13 14J=!
GO TO 18 13 CO_T; NUE GO TO 15 6 DO 16 ] = 1 , N ] F(X-XTAB(l)) 16,17,17 17J=% GO TO 18 16 CONTINUE 15J=N 18 J = J - (K÷I) / 2 IF(J) 19, 19o20 19J=I 20M=J+I( IF(M - N) 21,21,22 22J=J-1 GO TO 20 21 KP1 = K + 1 DO 23 L = 1o lOP1 C(L] = X - XTAB(J) T(L) = FTAB(J) 23 J = J+l DO24J = 1,K ! = J+l 25 T(I) = (C(J)*T(I)-C(I)*T(J))/(C(J)-C([)) ] = l+1 IF(i'KP1) 25,25,24 24 CONTINUE FX : T(I(P1) NER = I RETURN END
Appendix 4
Appendix 4
Sample "ARC2D" Input, Output
NACA-0015 Airfoil
(Minf = 0.30, 5 = +15 degs., c_ = 5 degs., Re = 3 million)
$]NPUTS FSIdACH= .3, ALPHA-- 5.0, RE= 3000000, METH=3, ,)I4AX= 211, _= 50, JTAILI= 31, JTA]L2= 181, TRANSLO= 0.0, TRANSUP= 0.0, RESTART=FALSEq D]S4X= 0.(>4, D]S4Y= 0.64, DZS2X= 0., DIS2Y= 0., ]PR]NT=IO, [READ= Z, STORE= TRUE, ]SPEC=I, BCA]RF= TRUE, C]RCLIL= FALSE, PERI(]O]C= FALSE, V]SCOUS= TRUE, TURBULNT= TRUE, VISX[: TRUE, NP= 100000, NPCP=IO0000, JACDT=I, ISAVE=IO000 $ SF]NFO XLIN=0.T5, XHINGE=O.75, [FLAG=l, FANG=15. $ ]SEOUAL IF ISEOUAL GT la DT%SEQ : ]]=I,]SEIa.IAL JMX], 104Xi, ]ENDS, DT ISEQ, DTMiNS 211, 50, 350, 1.0, 0.0 211, 50, 500, 3.0, 0.0 211, 50, 750, 5.0, O.O . _ tce_vr ttr t_r /_¢rttt t_t/rt : . tt _ _t _t t _t /r tt : ......... o ....... o°o°oo.o ........ o°°o,.°°.°° ..... °o°°o°o..°, ................. °..°° ....... °.°.o°°°° ............ ...°.°._°° ARC2D : An implicit finite difference code for airfoils For further details see self documentation or contact Thomas H. PutLiam, MS 202A-1, NASA Ames Research Center Moffett FieLd, Ca. t 94035, Phone : 415 - 604 - 6417 NOTE : NOTE : Th=s code should not be distributed NOTE : NOTE : without the permission of T. Pu|Lia_.
NOTE NOTE DO NOT distribute this code NOTE : NOTE : outside the United States !!!!
Modified by Jeff Currier for the HDHC I FLOW FIELD CONDITIONS I ......................................................
J FSMACH = .3 ALPHA = 5.0 [
• I
VISCOUS PARAMETERS [
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REYNOLDS NUMBER = 3000000.
TINF -- _60.0 TRANSLO = .0 TRANSUP = .O EXPLICIT VISCOUS TERMS iN XI USED EXPLICIT VISCOUS TERMS IN ETA USED BALDU|N-LOMAX TUBULENCE HODEL iS BEING USED UNMOOIFiED MODEL IVlS = 2 PENTA DIAG IN Xl AND ETA : IMP. VIS. EIG. VAL.
......................................................
ALGORITHM PARAMETERS ......................................................
I TIME ACCURACY :: I
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THETADT = 1.0 PHIDT = .0 EULER IMPLICIT JST ORDER ACCURATE VARIABLE TIME STEP PAR JACDT = 1 DTRATE = 1.0 <<<<<< VARIABLE DT = I./(I+SQRT(J)) >>>>>>>>> I I SLON START TIME :: STRTIT = 12.0
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*_ X-Y order of implicit integration** I | ......................................................
) METHOD CHOICE I ......................................................
EXPLICIT AND INPLICIT 4-Z DISSIPATION :: I DISSIPATION COEFICIENTS ::
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DISZX = .0 DIS4X = .6399999 DISZY = .0 01S4Y = .6399999 FORN SPECTX AND SPECTY INDEPENDENTLY SPECTX = (ABS(UU) + CCX)/XYJ SPECTY = (ABS(W) + CCY)/XYJ GRID SPECIFICATIONS J i UNFORNATrED GRID FILE iS BEING READ FROH UNIT 8 I THIS IS A I_/PERIODIC GRID
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JNAX = 211 KNAX = 50 JTAIL1 = 31 JTAIL2 = 181
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BOUNDARY CONDITION TYPE J | BOUNDARY CONDITIONS FOR AIRFOIL USED J
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......................................................
I/O SPECIFICATIONS I
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DATA SET VILL STORED ON UNIT 4 UPON CONPLETION J I OUTPUT FREQUENCY PARAMETERS: PRINTED Q DATA :: NP = 100000 PRINTED CONVERGENCE DATA :: IPRINT 10 STORED CP VRS TINE :: NPCP = 100000 STORED CO_/TOURS VRS TIHE :: NPCOWT 100000 STORED SOLUTION/RESTART :: ISAVE = 10000 NIN/NAX/INC FOR COWTOURS :: CONNIN = .0 CORNAX = 2.0 CONINC = 5.00000E-02
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YOU ARE RUNNING ON A CRAY ] ......................................................
RE scaled by freestream, reset to : .1DOE+08 Enter ISEQUAL the rxJmber of grid/time step sequences Enter JNAXCi), KNAX(J), NumStep(i), DT(i), DTNIN(i) ................... o ............................................
GRID ANO TIME STEP SEQUENCING .......................... _ .....................................
GRID 1 JNAX = 211 _ = 50 JSKIP = 1 STEPS = 350 DT = 1.0 DTNIN = .0 GRID 2 JHAX = 211 K)IAX = 50 JSKIP = 1 STEPS = 500 DT = 3.0 DTNIM = .0 GRID 3 JP_AX = 211 IOIAX = 50 JSKIP = 1 STEPS = 750 DT = S.O DTNIN = .0 J HESH REFINEIqENT NUlqSER 1
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I GRID SIZES 211 50 J DT = 1.0 WITH DTMIN = .0 J FOR 350 TIME STEPS J CPU TIME AFTER GRID REFINEMENT = .0 I i .....................................................
.....................................................
i .... .................
max CFL = 279.9838 at j,k = 2 2 ( J dt used = 3.10827E-03 .....................................................
0 N RESIDUAL S-S PTS CL CD CN CLF CDF CMF MAX RESID AT J K 10 .229E-04 0 1.76264 1.13269 -.73734 .98176 .43489 -.12865 .148E-03 166 26 20 .347E-04 0 1.70595 .98601 -.69343 .87144 .37739 -.11232 .258E-03 163 30 .384E-04 0 1.47370 .68391 -.51740 .53465 .23144 -.05081 .219E-03 197 41 40 .459E-04 0 1.23031 .33778 -.29988 .16540 .06017 .01160 .324E-03 207 47 50 .486E-04 0 1.01264 .02601 -.10358 -.11796 -.07044 .03902 .287E-03 201 44 60 .553E-04 0 .74244 -.19880 .07302 -.25660 -.11457 .03675 .393E-03 207 48 70 .597E-04 0 .43639 -.27904 .17522 -.17821 -.06611 .01470 .399E-03 209 48 80 .543E-04 0 .19870 -.19776 .13682 .04009 .01203 -.00936 .339E-03 209 48 90 .553E-04 0 .06955 -.03704 -.00733 .21177 .06467 -.01_ .377E-03 93 100 .538E-04 0 .11855 .10460 -.16154 .23926 .08691 -.01906 .495E-03 209 48 _÷÷÷÷÷_-k÷÷_÷÷'l_÷4"+÷4-_÷÷÷÷÷+_4-+÷÷÷÷+÷_k÷4_t-÷÷÷÷÷÷÷÷÷÷÷÷÷ I J CONVERGENCE RATE AT N = 100 IS 1.001 I
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÷÷÷+÷÷÷÷÷÷÷÷÷÷÷_÷÷÷'1_÷÷4_÷÷÷÷÷-1-1-÷÷4-1-4-1-÷÷÷÷÷_-4_÷÷÷÷4-÷÷÷ max CFL = 280.3146 at j,k = 210 2 ] J dt used = 3.10827E-03 .....................................................
0 N RESIDUAL S-S PTS CL CD CM CLF CDF CMF MAX RESID AT J K 110 .380E-04 0 .41135 .20251 -.25563 .18136 .08717 -.01505 .400E-03 209 48 120 .281E-04 0 .89979 .27965 -.30231 .17003 .08154 -.01517 .237E-03 210 49 130 .302E-04 0 1.39394 .32819 -.32340 .23982 .08629 -.02129 .189E-03 210 45 140 .344E-04 0 1.71870 .31679 -.29875 .29379 .09040 -.02706 .301E-03 3 48 150 .303E-04 0 1.81069 .23788 -.24435 .27044 .07332 -.02676 .344E-03 3 48 160 .224E-04 0 1.63097 .12022 -.19798 .21003 .04249 -.01658 .294E-03 2 49 170 .199E-04 0 1.22593 -.00039 -.15833 .15043 .02043 -.00985 .182E-03 2 49 180 .228E-04 0 .78570 -.09511 -.10647 .09398 .01572 -.00581 .154E-03 9 {*6 190 .221E-04 0 .51053 -.12648 -.04980 .04951 .02220 -.00187 .240E-03 3 48 200 .172E-04 0 .47923 -.06481 -.01876 .03728 .03418 .00106 .198E-03 3 49 ÷÷÷'_÷÷4_÷'l_÷÷÷÷÷÷-l-lk÷÷÷÷4-_÷÷÷4-qk4-_÷÷÷4_,k÷+÷÷-_÷÷÷ CONVERGENCE I RATE AT N = 200 IS .9886639 I
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÷÷÷+÷'IH-÷÷'I'4"÷÷÷,I_,._÷+÷+÷_÷÷+÷÷÷,IHh÷,I_÷÷÷÷÷÷+÷÷÷÷-1_.÷4_÷÷÷÷ J max CFL = 279.3561 at j,k = 210 2 J I dt used= 3.10827E-03 J ......................................................
0 N RESIDUAL S-S PTS CL CO CM CLF COF CHF MAX RESID AT J K 210 .137E-04 0 .64895 .07782 ".04097 .07135 .05247 -.00106 .133E-03 2 49 220 .142E-04 0 .92822 .23505 -.12035 .14710 .07611 -.01002 .894E-04 2 44 230 .153E-04 0 1.23453 .32400 -.22976 .24020 .09747 -.02228 .852E-04 7 48 240 .143E-04 0 1.50194 .30462 -.31938 .31177 .10619 -.03100 .107E-03 3 48 250 .129E-04 0 1.68201 .19821 -.34087 .32158 .09437 -.03094 .981E-04 2 49 260 .135E-04 0 1.74490 .06364 -.28_04 .25835 .06382 -.02211 .923E-04 2 49 270 .129E-04 0 1.67174 -.03477 -.18743 .15803 .02935 -.00984 .115E-03 209 48 280 .110E-04 0 1.46042 -.05961 -.10238 .08082 .01088 -.00133 .893E-04 209 49 290 .127E-04 0 1.15436 -.02143 -.05452 .06113 .01691 -.00050 .700E-04 210 45 300 .156E-04 0 .86110 .03704 -.04233 .08379 .03685 -.00503 .994E-04 209 48 ÷÷÷÷÷÷÷'lk÷÷÷÷÷÷÷÷÷'_k÷÷4-_÷÷÷÷÷÷÷÷-_÷_,l-1-÷÷÷÷÷4-t--k,#_l-÷÷+÷÷ !
CONVERGENCE RATE AT N = 300 IS .9_?04_ I
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÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷_÷'1"4"÷÷÷'1_÷÷÷÷_'-4_÷÷÷÷4-÷÷4_÷,l-_4_1-÷÷
I I
I max CFL = 279.0767 at j,k = 210 2 dt used = 3.10827E-03 I ......................................................
0 N RESIDUAL S-S PTS CL CD CH CLF CDF CI4F MAX RESID AT J 310 .151E-04 O .70968 •080]4 -.05681 •11280 .05339 -.00916 .143E-03 3 4E 320 .119E-04 0 .77098 .10103 -.09141 •13143 .05958 -.00988 .153E-03 3 4E 330 .109E-04 0 1.01605 .11048 -.14016 .14921 .06121 -.00968 .110E-03 2 4_ 340 •137E-04 0 1.34109 •11904 .19501 .18016 .06576 -.0126& .735E-04 10 4E 350 .150E-04 0 1.62612 .12540 -.24346 •22352 .07_89 -.01901 .131E-03 3 4E MESH REFINEMENT NUMBER 2 ......................................................
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GRID SIZES 211 50
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DT = 3.0 _ITH DTMZN = .0 FOR 500 TIME STEPS 1 .......... o ...........................................
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CPU TIME AFTER GRID REFINEMENT = .0
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............................... o..oo.... ..............
i .... .................
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max CFL = 837.6842 at j,k = 2 2 dt used = 9•32482E-03
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0 N RESIDUAL S-S PTS CL CO CM CLF CDF CHF MAX RESID AT J K . 793E-05 0 1.6._527 .06071 -.20156 .21187 .06176 -.01804 .864E'04 2 45 370 • 738E-05 0 1 . 01927 - . 00920 - .03838 .05267 .02138 .00102 .912E-04 3 48 380 ,490E-05 0 1 . 13478 .07325 -.13139 • 15858 • 05863 -.01272 .502E-04 2 45 390 ,430E- 05 0 1 . 60078 . 10016 - . 22(_>9 .223?3 .0T319 -.01911 .388E-04 2 46 400 .327E-05 0 1.44755 .03643 -•13163 • 13787 .04505 -.00893 .365E-04 2 44 ......................................................
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max CFL = 858•2871 at j,k = 2 2 I dt used = 9.32482E-03
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0 N RESIDUAL S-S PT5 CL CO CM CLF CDF CMF MAX RESID A1 J K 410 .315E-05 0 1.12265 .01811 -.08405 .10838 .03877 -.00620 .3T2E-04 210 49 420 .286E-05 0 1.30862 .05872 -.15208 • 16490 .05787 -.01283 .276E-04 209 2 430 .222E-05 0 1.51113 .07806 -.17953 • 18469 .08209 -.01465 .213E-04 210 49 440 .235E-05 0 1.34439 .03270 -.11908 .13031 .04274 -.00820 .174E-04 208 46 450 .140E-05 0 1.23659 .02313 -.10748 • 12623 • 04396 -.00826 .171E-04 210 45 +÷.k.l-.Pt.4,+ 4-t- ÷I-_1- _ _ +-IP ÷ +-t-++_P4-PIk4_ 4--44.+.F4-+ 4.t- + ++÷ ++-IP÷+-t-t. 4-4-,k +4-+ COMVIERGENCE RATE AT N = 450 IS .9915241 J
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÷_-4"÷'t._._÷+,l-÷4-1_÷÷4-4,-l.4_+_-4.4-F4_ +4-+._k,lk÷_rO-_ +-4.4-÷ +-(. ÷-IP,I-k,p4-÷ 4-1. + 460 .163E-05 0 1 . 36053 .05886 -.15237 .16508 .05762 -.01270 .149E-04 209 47 470 .109E-05 0 1.41974 •05665 -.14732 • 15497 .05179 -.01112 .108E-04 207 46 480 .115E-05 0 1.32696 .02909 -•11768 • 13230 .04372 -.00872 .108E-04 209 47 490 .850E-06 0 1.29291 •03245 -.12278 • 13878 .04775 -.00962 .834E-05 207 46 500 .785E-06 0 1.35616 .05148 -•13912 .15087 • 05192 -.01089 .745E-05 210 49 ......................................................
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I max CFL = 837.7537 at j,k = 210 2 I dt used = 9.32482E-03
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........................... o ..........................
0 N RESIDUAL S-S PTS CL CO CM CLF CDF CMF MAX RESID AT J K 510 .662E-06 0 1.37179 •04466 -.13354 .14531 .0_32 -.01015 .666E-05 209 48 520 .576E-06 0 1.32500 .03045 -.12134 • 13558 .04503 -.00910 .534E-05 210 49 530 .479E-06 0 1.31268 .03721 -.12450 .13888 .04T37 -.00954 .478E-05 208 46 540 .407E-06 0 1.34381 .04538 -.13151 .14417 .04878 -.01006 .48&E-05 210 45 550 .349E-06 0 1•35005 •03887 -.12829 • 14096 .04667 -.00962 .359E-05 209 48 'PP÷÷÷÷÷1_'÷÷++÷÷÷÷_k-t-'4"÷'P4.+_4-÷+_l'÷+4,_"t-++÷÷÷÷÷_÷÷4"+-k+÷÷4-k+÷ CONVERGENCE RATE AT N = 550 IS •9862235 I ÷÷÷÷÷÷÷d'+÷÷_÷÷÷÷÷÷_÷÷_l-t'÷_,F_÷÷÷_'t'+÷_4-t'÷÷÷_'t_-4-4"÷+_l-t'÷÷÷÷÷ 560 .326E-06 0 1.32399 .03368 -.12252 .13633 .04539 -.00912 .244E-05 210 49 570 .227_-06 0 1.31888 .03847 -.12402 .13780 • 04644 -.00928 .204E-05 208 46 580 .255E-06 0 1.33845 .04130 -.12814 .14113 .04711 -.00963 .207E-05 210 45 590 .162E-06 O 1.34036 .03764 -.12659 • 13956 .04615 -.00942 .183E-05 2 45 600 . 192E-06 0 1.32493 .03610 - . 12319 .13679 .04552 -.00911 .150E-05 210 49 ......................................................
I
max CFL = 837.8007 at j,k = 210 2 dt used= 9.32482E-03 .....................................................
0 N RESIDUAL S-S PTS CL CD CM CLF CDF CMF MAX RESID AT J K 610 .121E-06 0 1.32560 .03874 -.12484 • 13843 .04623 -.00930 .111E-05 2 45 620 .152E-06 0 1.33841 .03966 -.12745 .14041 .04658 -.00950 .127E-05 3 48 630 .872E-07 O 1.33725 .03777 -.12579 .13873 .04586 -.00927 .122E-05 2 45 640 .101E-06 0 1.32859 .03706 -.12388 .13719 • 04548 -.00909 .968E-06 210 49 650 .830E-07 0 1.33176 .03831 -.12533 .13844 .04590 -.00922 .870E-06 6 2 ÷÷aP÷+÷÷÷÷+_÷'k÷+'i_k_4--ik÷÷÷÷÷4--H-÷÷÷÷4-H-_+÷÷÷÷÷4_÷_l_÷÷÷÷÷÷
I
CONVERGENCE RATE J AT N = 650 IS .9857484
I
÷÷÷÷÷4"1"4_÷÷÷÷÷÷÷+_÷÷÷_÷+_÷÷÷4-+÷÷4-4-4-1k÷4-i-1-÷_÷4-1-÷÷÷÷÷_+÷ 660 .792E-07 0 1.33890 .03861 -.12641 .13911 .04594 -. 00926 .700E-06 210 44 670 .531E-07 0 1.35660 .03741 -.12497 .13773 .04540 -. 00907 .489E-06 210 38 680 .469E-07 0 1.33278 .03702 -.12425 •13719 .04526 -. 00900 .615E-06 2 46 690 .522E-07 0 1.33619 .03777 -.12534 .1_ .04553 -. 00908 .578E-06 2 45 700 .406E-07 0 1.33969 .03781 -.12563 .13816 .04545 -. 00906 .645E-06 210 38 ......................................................
I
max CFL = 837.7634 at j,k = 2 2 dt used = 9.32482E-03
I
......................................................
0 N RESIDUAL S-S PTS CL CD CM CLF CDF CMF MAX RESID AT J K 710 .351E-07 0 1.33801 .03703 -.12478 .13739 .04514 -.00895 .439E-06 210 38 720 .309E-07 0 1.33700 .03693 -.12471 .13736 .04514 -.00893 .461E-06 210 38 730 .371E-07 0 1.33959 .03742 -.12536 .13787 .04529 -.00897 .476E-06 193 740 .261E-07 0 1.34135 .03732 -.12542 .13784 .04521 -.00894 .359E-06 193 750 .226E-07 0 1.34073 .03688 -,12508 • 13756 .04508 -.00889 .342E-06 210 38 ÷÷÷÷÷÷÷÷4_÷÷÷÷÷÷+'1"÷÷-1-_÷_-1-4-1H-4_÷÷÷÷_÷+÷÷÷÷÷÷_÷÷÷÷÷÷÷4_÷
I
l CONVERGENCE RATE AT N = 750 IS .987065
I
_l'÷÷÷÷÷÷÷÷+'l'÷_k÷÷÷÷÷÷4"l'÷÷÷÷'l-l-÷_÷÷÷÷_k4k÷4-ik÷÷4--k+ 760 .247E-07 0 1.34099 .03696 -.12524 • 13772 .04515 - • 00890 .374E-06 210 39 770 .264E-07 0 1.34291 .03723 -.12565 .13806 .04523 -. 00892 .335E-06 210 39 780 .207E-07 0 1.34414 .03710 -.1257"2 .13811 .04520 -. 00891 .307E-06 210 39 790 .184E-07 O 1.34428 .03690 -.12566 .13809 .04518 -. 00890 .298E-06 210 39 800 .209E-07 0 1.34503 .03701 -.12586 .13829 .04525 - .00891 .278E-06 210 38 ......................................................
I
max CFL = 837.7596 at j,k = 210 2 dt used = 9.32482E-03 .....................................................
N RESIDUAL S-S PTS CL CD 04 CLF CDF CMF MAX RESID AT J K 810 .223E-07 0 1.34655 .03713 -.12615 .13855 • 04532 -.00893 .253E-06 210 39 820 .192E-07 0 1.34762 .03703 -.12626 .13867 .04533 -.00893 .226E-06 210 39 830 .181E-07 0 1.34815 .03696 -.12633 .13876 .04536 -.00893 .222E-06 206 2 840 .196E-07 0 1.34908 .03703 -.12654 • 13899 • 04543 -.00895 .211E-06 5 2 850 .20OE-O7 0 1.35041 .03709 -.12679 .13924 .04550 -.00897 .182E-06 207 2 ÷÷÷÷÷÷+÷÷÷+÷÷÷÷÷_lk÷÷+4"4-'l-÷÷4-_÷÷4-+÷4-4-÷4-k++÷÷÷-1--1_4-4-+-_k÷÷÷ i CONVERGENCE J RATE AT N = 850 IS .9987747 I
I
..................... o ................................
I
max CFL = 1396.252 at j,k = 2 2 dt used = 1.55414E-02
I
O N RESIDUAL S-S PTS CL CD CM CLF CDF CNF MAX RES]D AT J •13941 .04554 860 .229E-07 0 1 •35175 •03698 - . 12693 -.00898 .253E-06 192 32 870 • 249E-07 0 1 •35328 •03702 - •12723 .13975 .04564 - .00901 .296E-06 193 3z 880 •313E-07 0 1.35488 •03700 -.12748 • 14002 .04575 - .00903 .691E-06 191 2_ 890 .272E- 07 0 1 . 35620 .03700 - . 12770 .14028 • 0/.582 - . 00905 .399E-06 194 3z 900 .246E-07 0 1.35770 •03701 -•12796 .14057 .04591 -. 00908 .359E- 06 194 3_ ......................................................
I
max CFL = 1396.231 at j,k = 210 2 dt used = 1.55414E-02
I
......................................................
0 N RESIDUAL S-S PTS CL CD CM CLF CDF CHF NAX RESID AT J tc 910 .221E-07 0 1.35900 .03700 -.12817 .14082 .046430 -.00910 .323E-06 192 33 920 .208E- 07 0 1 . 36031 .03700 -. 12839 .14107 .04608 -.00912 .28QE-06 194 34 930 . 197E-07 0 1.36151 .03697 -. 12856 .14128 .04614 -.00914 .251E-06 194 34 940 . 186E-07 O 1.36262 .03695 -. 1287"3 .14148 .04621 -.00916 .227E-06 5 2 950 •169E-07 0 1.363_ .03694 -. 12892 .14170 • 04628 -.00918 .198E-06 192 33 • e-l-÷÷÷e +-.l-÷+÷ .I--II-4--I.+,I,-I-k.(-IH,-#-#.4-I-.Q--H-÷-I,,,P,H,÷-(,-I-e_ _÷_+ _+ + CONVERGENCE RATE AT N = 950 IS ._62365 I
I
÷+ +4-÷÷+_k a_ _P+ ÷÷4-P4P4-1P÷ 4-q-) _¢ ._._ ¢ .1 ._ .1 : _ _ l-÷÷ ++÷÷q-P4Pq-4_P _÷÷4-4P 960 .161E-07 0 1.30477 .03693 -.12909 .14191 • 04635 -.00920 .199E-06 192 33 970 .159E-07 0 1.36576 .03692 - .12925 .14210 .04041 -.00921 .204E-06 192 33 980 . 153E-07 0 1 . 36666 .03690 - • 12938 .14225 • 04046 -.00923 .201E-06 192 33 990 . 147E-07 0 1.36751 .03688 -.12951 .14241 .04652 -.00924 .186E-06 7 2 1000 .136_- 07 0 1.36834 •03687 -. 12964 .04657 .14257 -.00926 .184E-06 4 2 dt used = 1•55414E-02 I max CFL = 1396.197 at j,k = 2 2 [
I
................................ . .....................
0 N RESIDUAL S-S PTS CL CD CN CLF CDF CMF MAX RESID AT J K 1010 . 129E-07 0 1.36913 .03_87 - • 12977 .142TE • 04662 -.00927 .168E-06 3 2 1020 .122E-07 0 1.36987 •03686 - • 12989 .14286 .04667 -.00928 .160E-06 192 33 1030 .119E-07 0 1.37057 .03685 -. 12999 .14298 • 04671 -.00929 .154E-06 192 33 1040 . 113E-07 0 1.37122 .03683 - . 13009 .14310 .04675 -.00930 .145E-06 11 2 1050 .111E-07 0 1.37185 .03682 -.13018 .14322 .04679 -.00931 .148E-06 2 49 ÷ +÷++÷÷+ 4-t-÷ ÷q-q-÷ 4.k÷ 4-4-++q-p4-÷q-4p+ ÷÷÷4-_kq-t-pl-+-p+ 4-q_+÷4-t-(-+4- ÷4-_ I CONVERGENCE RATE AT N = 150 ]S .9957904 J
I
_P _-÷.k _P4-4- ÷4-t-e ÷q-÷ -1. <-IP÷ ÷÷÷ ÷ 41-k+4-(-_÷4-4- _-4k-I-'_ _H-.'# ÷-t-_-k-IHPq-4-t-÷4-_-+ 4-4-1- 1060 . 104E-07 0 1 •37244 .03682 - . 13028 .14333 .04683 -.00932 .129E-06 3 2 1070 .961E-08 0 1•37302 .03681 -•13037 .14344 .04687 -.00933 .162E-06 2 49 1080 .959E- 08 0 1 . 37357 .03681 -. 13046 .14355 .04690 -.00934 .122E-00 208 49 1090 .935E- 08 0 1 •37409 .03680 - • 13054 .14365 .04693 -.00935 .124E-06 208 49 1100 .949E-08 0 1.37458 .03679 -•13061 .14373 .04696 -.00936 .213E'06 2 49 ......................................................
I
max CFL = 1396.177 at j,k = 2 2 dt used = 1.55414E-02
I
......................................................
0 N RESIDUAL S-S PTS CL (:I) CM CLF CDF CMF MAX RESID AT J K 1110 •911E-08 0 1 •37504 •03678 - . 13068 .14381 .046_ -.00936 .141E-06 210 49 1120 .863E-08 0 1.37547 .03677 -.13075 .14389 .04702 49 -.00937 .148E-06 3 1130 •784E-08 0 1.37589 .03677 -.13081 •14396 .04704 -.00938 .925E-07 192 33 1140 .763E- 08 0 1 . 37627 .03676 - • 13086 .047_ 49 .14403 -.00938 .133E-06 T 1150 .312E-07 0 1.37690 .03688 -.13111 .14436 .04_2 -.00945 .832E-06 184 23 +÷÷4.÷÷÷ 4,t-.k +_-+ ÷-Pt-1"4-.t-'_÷÷.I-t-t-t_.H-Pt.÷4p4k÷4-k +÷_P÷ ÷4-÷+-'p÷_l-t-_÷ ÷÷÷ I I CONVERGENCE RATE AT N = 1150 IS 1.01043 1
I
÷++÷4-_÷ +4-÷+÷÷ ÷÷q-4.÷÷÷÷q-4--k 4-k+++÷÷÷_÷4-++÷÷÷÷q-4P÷+-1-÷4-e-l.4-÷÷+ 1160 •255E-07 0 1.37796 .03703 -.13151 .14483 .04736 -.00951 .824E-06 28 1170 .270E-07 0 1.37926 •03726 - .13201 .14548 .04_0 -.00960 .733E-06 27
6O
1180 •554E-07 0 1.38124 .03764 -•13279 .14640 .047?7 -.00974 .141E-05 186 23 1190 .736E-07 0 1•38359 •03800 -•13356 •14728 .04831 -.00985 .178E-05 27 2 1200 .909E-07 0 1•38620 •03838 -.13439 • 14827 .04872 -.00998 .195E-05 26 2 ......................................................
max CFL = 1396•172 at j,k = 210 2 dt used = 1.55414E-02 0 N RESIDUAL S-S PTS CL CD CM CLF CDF CMF MAX RES]D AT J K 1210 •903E-07 0 1.38901 •03868 -.13512 .14908 .04705 -.01007 .162E-05 25 2 1220 •845E-07 0 I•39138 •03873 -.13549 • 14946 .04922 -.01009 .121E-05 190 31 1230 .753E-07 O 1.39320 .03862 -.13559 • 14954 .04926 -.01007 .111E-05 190 31 1240 •640E-07 0 1.39475 .03848 -.13567 • 14965 .04932 -.01008 .101E-05 187 31 1250 •545E-07 0 1•39625 •03840 .13585 • 14992 •04943 -.01011 .817E-06 5 ÷÷÷+÷÷÷÷÷÷_+÷÷÷÷÷÷÷÷÷+÷4_1"÷+_+_*--I-_4_÷÷÷÷_÷÷÷÷÷÷4-_÷+÷÷÷÷ g iS 1.00559 I CONVERGENCE RATE AT 1250 I
I
÷+÷-F+÷÷J_'F+÷÷÷÷÷÷4_k÷÷÷÷÷_4-,F÷÷÷÷÷÷÷R-F÷4_÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷ 1260 .517E-07 0 1.39765 .03835 -.13605 .15018 .04954 -.01013 .697E-06 191 32 1270 .501E-07 0 1.39879 .03827 -•13616 .15032 .04959 -.01014 .678E-06 210 43 1280 .427E-07 0 1.39967 .03818 -.13622 .15039 .04961 -.01014 .647E-06 13 2 1290 .367E-07 0 1.40044 .03812 -.13629 .15048 .04964 -.01015 .70_-06 11 2 1300 .319E-07 0 1.40111 .0_ -.13636 •15057 .04967 -.01016 .562E-06 9 2 ......................................................
max CFL = 1396.112 at j,k = 2 2 I 0 N RESIDUAL S-S PTS CL CO CM ELF COF CMF MAX RESID AT J 1310 .257E-07 0 1.40171 .03802 -.13642 .15065 .04970 -.01016 .524E-06 3 1320 •215E-07 0 1.40222 .03797 -•13646 •15072 .04971 -.01017 .400E-06 202 1330 .179E-07 0 1•40269 .03794 -•13651 .15078 .04973 -.01017 .291E-06 8 1340 .145E-07 0 1.40312 •03791 -.13657 .15085 .04975 -.01018 .351E-06 11 1350 •132E-07 0 1•40352 .03789 -.13662 • 15092 .04977 -.01018 .329E-06 202 ÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷÷'F4_÷÷÷÷÷_÷÷÷_÷_"('÷÷_÷÷÷÷÷÷÷÷4-4-÷÷÷÷÷÷÷ N ]S o 98_8_ J CONVERGENCE RATE AT 1350 J
I
÷÷÷÷÷÷÷÷÷÷÷÷_÷÷÷÷÷÷÷÷÷÷÷+_lk÷÷÷÷÷+_÷÷_÷÷4-k÷÷÷÷÷_÷÷÷÷÷÷÷ 1360 •124E-07 0 1.40390 .03788 -•13667 .15098 .04979 -.01019 .267E-06 204 1370 .108E-07 0 1•40425 •03787 -.13672 .15104 .04981 -.01019 .193E-06 207 1380 •963E-08 0 1•40460 •03786 -•13677 .15110 .04983 -.01019 .16_-06 208 1390 •895E-08 0 1.40494 .03785 -.13682 .15116 .04985 -.01020 .155E-06 11 1400 •826E-08 0 1.40527 •03785 -•13686 •15122 .04987 -.01020 .145E-06 10 ......................................................
I
max CFL = 1396.088 at j,k = 2 2 dt used = 1.55414E-02
I
......................................................
0 N RESIDUAL S-S PTS CL CD CM CLF CDF CMF MAX RES%D AT J K 1410 .777E-08 0 1.40559 •03784 -•13691 •15128 .04989 -.01021 .131E'06 204 2 1420 .789E-08 0 1.40589 •03783 -•13696 .15133 • 04990 ".01021 .142E'06 209 49 1430 .733E-08 0 1.40619 .03783 -.13700 •15138 .04992 ".01021 .111E'06 207 2 1440 .674E-08 0 1•40647 .03782 -•13704 .15142 .04993 ".01022 .110E'06 209 49 1450 .667E-08 0 1.40673 .03781 -•13708 .15147 .04995 -.01022 .145E-06 210 49 ÷÷÷+÷÷÷÷÷÷÷÷'Ik'I_÷÷÷÷4--I-4_F4-1_4-_÷4-_4_4-_+4-4-÷-F-F_÷÷4-+÷_-(.
N iS I CONVERGENCE RATE AT 1450 I
I
÷+'F4_k÷÷÷++÷÷4"k÷÷÷÷÷÷_÷÷4-+4-1_÷4-t_4_÷_÷+_k÷4--I-÷÷÷÷÷÷÷÷ 1460 .614E-08 0 1.40698 •03781 -.13711 .15151 .04996 -.01022 .897E-07 210 49 1470 .591E-08 0 1•40722 .03780 -•13714 .15155 .04997 -.01022 .682E-07 208 49 1480 •577E-08 0 1.40743 .03779 -.13717 .15158 .04998 49 -.01023 .900E-07 5 1490 .607E-08 0 1.40764 .03778 -.13720 .15161 .04999 -.01023 .135E-06 2 48 1500 •553E-08 0 1.40783 .03778 -•13722 .15164 .05000 -.01023 •975E-07 208 49 .....................................................
I
max CFL = 1396.079 at j,k = 210 2 dt used = 1.55414E-02
I
.....................................................
0 N RESIDUAL S-S PTS CL CD CM ELF CDF CNF MAX RESID AT J K 1510 •567E-08 0 1.40801 •03777 -•13725 .15167 .05001 -.01023 .143E-06 209 49 1520 .499E-08 0 1.40818 .03776 -.13727 .15170 • 05002 -.01023 .612E-07 6 69 1530 •503E-08 0 1.40834 .03776 -.13729 •15172 .05002 -.01024 .695E-07 6 49 1540 .515E-08 0 1•40849 .03775 -•13731 .15175 .05003 -.01024 .729E-07 207 49 1550 •516E-08 0 1.40863 . 03775 -.13733 .15177 .05004 -.01024 .137E-06
I
CONVERGENCE RATE AT N = 1550 15 ,9974426 +++÷ ++++++ +÷÷++++_+++++++++++++ +++++++++÷+++÷+++++++_ 1560 .485E- 08 0 1 •40876 .03775 - •13735 .15179 .05005 -.01024 .836E-07 2 1570 •492E-08 0 1 •40889 •03774 - •13737 .15181 .05005 -.01024 .847E-07 209 1580 • 468E -08 0 1 •40900 •03774 -. 13738 .15183 .0501)6 -.01024 • 739E- 07 1590 •530E-08 0 1 •40910 .03773 -. 13739 .15185 .05006 -.01024 • 195E- 06 1600 •475E-08 0 1•40921 •03773 -•13741 .15186 .05007 -.01024 • 135E-06 5 COEFficient of pressure 31 1 • 0000000 • 1976698 32 .9930729 .0225722 33 .9850137 • 1595531 34 .9762082 .1144295 35 .9666984 • 1687549 36 .9564199 • 1663821 37 .9453421 • 1936772 38 .9334201 .2016548 39 .9206188 • 2223480 40 • 9069042 • 2366361 41 •8922454 .2571344 42 .8766187 .2782969 43 •8600070 •3005058 44 • 8423987 .3302305 45 .8237941 •3598284 46 .8041884 .3925751 47 .7836373 • 4765949 48 .7620977 .5205188 49 .7395216 .4705587 50 • 7162625 .4155749 51 •6921651 .3788_11 52 .6673404 • 3391788 53 .6418810 .3109129 54 • 6158789 • 2863236 55 .5894457 • 2661 092 56 .5626972 .2486024 57 .5357551 .2340002 58 • 5087454 .2212392 59 • 4817948 .2107866 60 •4550291 •2025214 61 • 4285712 .1964115 62 • 4025388 .1921010 63 .377O421 .1901899 64 •3521819 .1905778 65 •3280495 .1932818 66 .3047241 • 1987540 67 • 2822732 • 2066578 68 .2607519 .2172277 69 • 2402028 • 2305753 70 .2206565 • 2467764 71 • 2021326 • 2664876 72 • 1846395 • 2891960 73 •1681751 .3145422 74 • 1527298 .3428932 75 • 1382864 .3745063 76 • 1248212 • 4O93344 77 •1123040 .4466507 78 • 1007013 .4867579 79 .0899777 .5301293 80 • 0800938 .5757127 81 • 0710071 .6230747 82 .0626777 .6721492 83 • 0550648 • 7226353 84 •0481294 • 7738953 85 .0418311 .8249471 86 .0361316 .8742657 87 • 0309914 .921)4015 88 • 0263783 .9615760 89 .0222581 ,9951571 90 .0186007 1.0182440 91 •0153761 1. O27O920 92 •0125537 1.0180302 93 •0101089 .9867784 94 •0080119 • 9299932 95 • 0O62356 .8447264 96 • 0047548 .7298673 97 .0035399 • 5869638 98 .0025609 .4192306 99 • O017891 •2315082 100 •0011962 • 0303605 101 .0007552 -. 1 ?62679 102 • 0004397 - .3811764 103 • 0002251 -. 5815095 104 • 0000911 -. 7751365 105 .0000208 -. 9605599 106 • 0000000 -1.1376113 10 7 .0000208 -1.306&818 108 .0000912 - 1.4887952 109 • 0002255 -1.6933,175 110 • 0004408 - 1.9132767 111 •0007578 -2,1464539 •0012013 -2.3823452 113 •0017983 -2.6085486 • 0025762 -2.8182993 .0035640 -3.0056195 • 0047909 -3.1599729 .00628T7 - 3.2708972 • 0080845 -3.336O431 • 0102071 -3.]622341 • 0126837 -3 •3532281 .0155445 -3.3109827 .0188150 - 3.2460959 123 .0225270 - 3.1638274 124 • 0267111 -3.0672112 •0313989 -2.9637392 126 .0366252 -2.8573716 127 .0424241 - 2. ?528203 128 • 0488564 -2.6498480 .0559019 -2.5463214 • 0636625 - 2.4437711 .0721588 - 2.3442833 • 0814332 - 2.2499397 133 .0915277 -2.1616180 • 1024867 - 2.0759907 135 .1143510 -1.9910361 136 .1271574 - 1.9103333 • 1409415 - 1.8336240 138 • 1557347 - 1.7584276 139 • 1715616 - 1.6852927 140 • 1884401 - 1.6152563 • 2063808 - 1.5486089 142 •2253858 - 1.4835045 .2454458 -I.4194115 .2665406 - 1 3578078 .2886381 - 1.2984681 146 .3116934 -1.2417207 .3356489 - 1.1872449 •3604338 -1.1349101 .3859650 - 1.0852556 .4121469 - 1.0378520 151 • 4388741 - .9932848 152 .4660311 - .9524528 .4934950 - .9143247 .5211375 -. 8796726 155 .5488279 - .8488069 .5764338 - .8234314 .6038248 - .8019454 .6308747 -. 7892146 .6574623 - .7810572 160 • 6834 794 -. 7922194 161 .7088125 - .8178418 162 .7334155 -. 8909938 .7570487 -. 9686529 • 7792703 - .8885443 165 .7997717 - .6502506 •8191265 - .4437802 .8375918 -. 3385127 .8550543 - •2532743 169 • 6715389 -. 1841083 170 .8870492 -• 1316468 .9015961 - .0881486 .9152075 -.0530056 .9279145 -. 0252402 •9397448 - .0013473 .9507378 .0156183 • 9609281 • 0332537 .9703661 .0382416 .9790709 .0571448 .9871352 .0361109 .9944184 .1219511 • O000000 • 0338233 PRESSURE CL = 1.40885 CD = 2.82631E-02 CM = -.137439 FRICTION CL = 3.55404E-04 CO = 9.46539E-03 C.M = 3.09680E-05 TOTAL CL = 1.40921 CO = 3.77285E-02 CM = -.137408 PRESSURE CLF = .1520771 CDF = 4.90500E-02 CMF = -1.02668E-02 FRICTION CLFV = -2.14973E-04 CDFV = 1.01651E-03 CMFV = 2.20656E-05
I
TOTAL CLF = .1518621 CDF = 5.00(_5E-02 CMF = -1.02448E-02
I
++++++++++÷+++++ ViscOUS Output _+++++++++++++ 0 j x t_ yplus(k=2) uptus(k=2) Y • 776041E+00 31 1.0000 -_0653 -.635939E-04 .7666871E+00 32 .9931 -.0661 -.108517E-03 .101146E+01 .100122E+01 33 .9850 -.0655 -.180186E-03 .130510E+01 .128739E+01 34 .9762 -.0647 -.1M556E-03 .123986E+01 .122206E+01 .122031E+01 .1202821E+01 35 .9667 -.0638 -.157048E-03 36 .9564 -.0628 -.147108E-03 .118149E+01 .116429E+01 37 .9453 -.0617 -.144293E-03 .117044E+01 .115322E+01 .115217E+01 .113488E+01 38 .9334 -.0605 -.139752E-03 39 .9206 -.0592 -.137477E-03 .114443E+01 .1127131E+01 .113795E÷01 .112047E+01 40 .9069 -.0578 -.135917E-03 41 .8922 -.0562 -.141409E-03 .116191E+01 .114384E+01 42 .8766 -.0545 -.156119E-03 .122071E+01 .12011_+01 43 .8600 -.0526 -.153115E-03 .121024E+01 .119058E+01 44 .8424 -.0506 -.144502E-03 .117614E+01 .115648E+01 45 .8238 -.0483 -.135222E-03 .113934E+01 .112026E+01 .I_+01 .107954E+01 46 .8042 -.04_ -.125317E-03 47 .7836 -.0432 -.962405E-04 .96_5E+00 .947115E+00 48 .7621 -.0408 -.526986E-04 .713943E÷00 .706588_E+00 49 .7395 -.0418 -.401502E-04 .622520E÷00 .613814E+00 50 .7163 -.0450 -.620060E-04 .772466E+00 .758622E÷00 51 .6922 -.0479 -.856853E-04 .907558E÷00 .892519E+00 52 ._73 -.0508 -.100399E-03 .980516E+00 .964535E+00 53 .6419 -.0536 -.111528E-03 .103242S÷01 .I01610E+01 54 .6159 -.0564 -.120229E-03 .107179E+01 .105553E÷01 55 .5894 -.0591 -.127640E-03 .110432E+01 .108825E+01 56 .5627 -.0617 -.134077E-03 .113107E÷01 .111521E÷01 57 .5358 -.0641 -.13_;)33E-03 .115473E+01 .113916E+01 56 .5087 -.06_ -.145180E-03 .117613E+01 .116097E+01 .119529£+01 .118054E+01 59 .4818 -.0685 -.150023E-03 60 .4550 -.0703 -.154711E-03 .121308E+01 .119875E+01 61 .4286 -.0719 -.158908E-03 .122952E+01 ,121565E+01 62 .4025 -.0732 -.162702E-03 .124452E+01 .121115E+01 63 .3770 -.0743 -.166603E-03 .125909E+01 .124603E+01 6/, .3522 -.0750 -.1700871E-03 .1272_E+01 .125958E+01 65 .3280 -.0755 -.173275E-03 .128368E+01 .127096E÷01 66 .3047 -.0757 -.176208E-03 .129400E+01 .128189E+01 67 .2823 -.0756 -.178796E-03 .130449£÷01 .129159E+01 68 .2608 -.0752 -.181161E-03 .131414E+01 .130092E+01 69 .2402 -.0745 -. 183147E-03 .132101E'_01 .130701E*01 70 .2207 -.0736 - .184876E-03 .132808E+01 .131304E÷01 71 .2021 - .0724 -.186643E-03 .133564E+01 .131921E+01 72 .1846 -.0710 -.187162E-03 .133695E+01 .131850E+01 73 .1682 -.0694 -.187352E-03 .133895E+01 .131828E+01 .134220E+01 .131880E÷01 74 .1527 -.0676 -.187694E-03 .134181E+01 .131498E÷01 75 .1383 -.0656 -.187061E-03 .133690E+01 .130587E+01 76 .1248 -.0635 -.185551E-03 77 .1123 -.0613 -.183639E-03 .133103E+01 .12952_E+01 78 .1007 -.0590 -.181161E-03 .132386E+01 .128252E÷01 .131406E+01 .126633E+01 79 .0900 -.0566 -.177904E-03 80 .0801 -.0542 -.172811E-03 .129615E+01 .124124E+01 81 .0710 -.0516 -.1(_656E-03 .127446£+01 .121173E+01 82 .0627 -.0491 -.160232E-03 .125163E+01 .117994E÷01 83 .0551 -.0465 -.152625E-03 .122270E+01 .114095E+01 84 .0481 -.0439 -.142973E-03 .118547E+01 .109300E+01 85 .0418 -.0414 -.131401E-03 .113779E+01 .105427E+01 86 .0361 -.0388 -.117691E-03 .107866E+01 .964564E+00 87 .0310 -.0362 -.101775Eo03 .100402E+01 .880424E+00 88 .0264 -.0337 -.830%_E-04 .90_+00 ._639E÷00 89 .0223 -.0311 -.607348E-04 .776965E+00 .647264E÷00 90 .0186 -.0287 -.340160E-04 .581885E÷00 .4(:_862E÷00 91 .0154 -.0262 -.2020171E-05 .141800E÷00 .111429E+00 .603972E+00 -.4447V4E+O0 92 .0125 -.0218 .366831E-04 .909654E+00 -.632753E÷00 93 .0101 -.0215 .833337'E-04 94 .0080 -.0192 .138326E-03 .117018E+01 -.760383E+00 95 .0062 -.0171 .201374E-03 .140872E+01 -.843897E÷00 96 .0047 -.0150 .270504E-03 .162780E+01 -.885128E÷00 97 .0035 -.0130 .3434q3E-03 .1827_÷01 -.886853E+00 98 .0026 -.0111 .418601E-03 .200881E+01 -.853715E+00 99 .001B -.0093 .493607E-03 .217066E+01 -.790004E÷00 100 .0012 -.0076 .565574E-03 .231124E+01 -.700253E+00 101 .0007 -.0061 .631870E*03 .242059E÷01 -.591920E+00 102 .0004 -.0046 .692161E-03 .252892E+01 -.474750E+00 103 .0002 -.0033 .747421E-03 .261356E+01 -.355163E+00 .2MTOIE+01 -.236237E+00 104 .0001 -.0021 .798564E-03 105 .0000 -.0010 .846083E-03 .275133E+01 -.119989E+00 106 .0000 .0000 .B83708E-03 .279792E+01 -.275861E'02 107 .0000 .0010 .912100E-03 .282915E+01 .117956E+00 108 .0001 .0021 .9425191E-03 .286138E+01 .246295E+00 .289387E+01 .3&8178E+O0 109 .0002 .0033 .975255E-03 110 .0004 .00_ .100833E-02 .292376E+01 .544129E÷00 111 .0007 .0061 .103809E-02 .294600E÷01 .713528E+00 .L:_5495E÷01 .891830E+00 112 .0012 .0076 .105965E-02 113 .0018 .0093 .107183E-02 .295061E+01 .107131E+01 114 .0026 .0111 .107457E-02 .293399S+01 .124539E+01 115 .0036 .0130 .106607E-02 .290_,7E÷01 .140881E+01 116 .0048 • 0150 . 104450E-02 .285823E+01 .155544E+01 117 .0063 • 0171 . 101257E-02 .280215E+01 .168116E+01 118 •0081 .0193 .980055E-03 .274878E+01 .178969E+01 .0102 .0216 •934190E-03 .268036E+01 .186882E+01 120 •0127 • 0240 .886940E - 03 .261006E+01 .192765E+01 121 .0155 .0264 •842155E-03 .254559E+01 .197238E+01 122 .0188 • 0288 .7946971E-03 .247676E+01 .199759E+01 123 .0225 •0313 .750503E-03 .241303E+01 .201281E+01 124 •0267 •0339 .709366E- 03 .235242E+01 .201794E+01 125 •0314 .0364 .670627E-03 .229446E+01 .20146TE+01 126 .0366 • 0390 .635945E-03 .224162E+01 .200693E+01 127 .0424 .0416 • 606276E-03 .219634E+01 .199907E+01 128 .0488 .0442 .577276E-03 .215009E+01 .198474E+01 129 •0559 .0468 • 550965E-03 .210721E+01 .1<_853E+01 •0637 .0494 .525754E-03 .206457E+01 .194817E+01 .0722 .0520 . 502476E-03 .202557E+01 .192770E+01 132 •0814 .0545 .483603E- 03 .1_150E+01 .190868E÷01 133 .0915 .0570 .464314E-03 .195823E÷01 .188853E+01 134 1025 .0594 .446319E-03 .192450E+01 .186579E+01 135 1143 .0617 .429450E- 03 .189245E+01 .184278E+01 1272 .0639 .413284E- 03 • 186148E+01 .181931E+01 137 1409 .0660 .398455E- 03 .183192E÷01 .179606E+01 138 1557 .0680 .384091E-03 .180201E÷01 .177119E÷01 139 1716 • 0697 .3698491E- 03 .177295E+01 .174627E+01 140 .1884 .0713 .357165E-03 .174600E+01 .172263E+01 .2064 .0727 .345030E-03 .171966E+01 .169885E÷01 142 •2254 .0738 .332698E-03 .169205E+01 .167320E+01 143 •2454 .0747 .321044E-03 .166524E+01 .164788E÷01 144 .2665 .0753 .310075E-03 .164017E+01 .162377E+01 145 .2886 • 0756 .299549E- 03 • 161422E+01 .159829E+01 146 •3117 .0757 .289610E-03 • 159038E+01 .157485E÷01 .3356 • 0754 .280364E- 03 • 156761E+01 .155211E+01 148 •3604 .0748 .271458E-03 .154407E÷01 .152828E+01 149 .3860 .0739 •262845E-03 .152247E+01 .150644E+01 150 •4121 .0728 .255027E-03 .150245E+01 .148605E+01 151 .4389 .0713 .248248E-03 .148401E+01 .14670_+01 152 .4660 .06_ .241912E-03 .146655E+01 •I_0E+01 •4935 .0676 .236129E-03 .145022E+01 .143200E+01 154 •5211 .0654 .231276E-03 .143641E+01 .141743E+01 .5488 .0630 .227579E-03 .142646E+01 .14_E+01 156 .5764 •0604 .224946E -03 .141_9E+01 .139932E+01 157 .6038 .0577 .223664E-03 .141723E+01 .13962_+01 •6309 • 0548 .224094E -03 .141745E+01 .139548E+01 .6575 .0519 .227261E-03 .142947E+01 .140675E+01 160 .6835 • 0489 • 23376_- 03 .144896E+01 .142491E+01 161 .7088 .0458 .251442E-03 .150141E+01 .147643E+01 .75334 • 0430 .287176E- 03 .160039E+01 .157009E+01 163 .7571 • 0392 .292355E - 03 .161184E÷01 .156013E+01 164 .7793 .0331 .21_6E-03 .138318E+01 .129898E+01 165 .7998 • 0249 .929618E - 04 .916899E+00 .839018E+00 166 •8191 .0166 - .112894E-05 .101792E+00 ".922492E'01 .8376 .0088 -. 110688E- 04 .318313E+00 ".289871E+00 168 .8551 .0013 -. 108427E-04 .317569E+00 ".288871E+00 169 .8715 -.0058 -.12551C_E-04 .3415591E÷00 ".310265E+00 170 .8871 - .0126 -.152909E-04 .377351E+00 -.342186E÷00 171 .9016 -.0190 -.186413E-04 .417490E*00 ".378111E+00 172 •9152 -.0250 -.216986E-04 .450432E+00 ".407524E+00 173 .9279 -.0307 -.244931E-04 .480001E+00 ".433956E+00 174 •9397 - . 0360 - . 266489E- 04 .502177E+00 -.453620E*00 •95O7 -.0409 -.289123E-04 .521884E+00 -.470800E+00 176 .9609 -.0456 -.310040E-04 .541315E+00 ".487892E+00 177 • 9704 -.0499 -.369735E-04 .590858E+00 ".531918E÷00 178 •9791 -.0539 -.471181E-04 .668336E+00 ".601460E+00 179 •9871 - .0575 -.785861E-04 .862953E+00 -.773126E+00 180 • 9944 - .0611 -.112292E-03 .103862E+01 -.882394E+00 181 1.0000 -.0653 -.127941E-03 .110702E+01 -.991692E+00 ÷÷÷÷÷+÷÷÷÷-1_÷÷'÷÷÷,#_÷,4_÷÷÷÷+÷4-+4._IP//-P÷÷÷+4.÷÷÷÷÷_÷
Appendix 5
Appendix 5
Listing of "CREATE" Code and COM File
PROGRAH CREATE PARAMETER (HALF:20, NNCH:13) REAL NACH(NHCH), ALPHA(HALF ) CHARACTER* 10 FNAME CHARACTER*2 A.q4 NNCH) CHARACTER'*] AA(NALF) DATA HACH/.20, .30, :_ 0.45, °50, .55, .60, .65, .70, .75, & .80, .85, '40' '45' '50','55','60' '65' $70','75', DATA AN /'20',•30•, 90,. / , , , & '80'•'85', DATA ALPHA/-%.,.-4.,-3.,-2.,-1., O.O, 1.,2.,3.,4.,5., & 6.,7.,8. •9., 10.,11., 12.,13.,14./ DATA AA/ 'MOS•,•HO4t,tHO3',sHO2',•HOl',°OOO', , I • • C • • • t • , t • I & P01 P02 , P03 , P04 , POS , P06 , POT ,'P08', & 'P09' : 'PIO', 'PI I ', 'P12', 'P13', 'P14' / OPEN ( 11, F l LE= a sweep, com', STATUS= ' UNKNOUN ' ) URITE (11,100) e#l/birVcsh' 100 fo_--'t (alO) WRITE 411,*) 'hostrla_' WRITE (11,*) 'date' WRITE (11,*) 'time' ILtITE (11, =) 'dr e WRITE 411,*) *# ........... " .................................... ' k_ITE 411,*) 'cp header.,x, |oads.tb[' URITE (11,'7 'cp base-nacaOO15.grd grid.dat, URITE (11,*) '# ................................................ ' DO 10 IN : 1 , NMCH DO 10 IA : 1 a HALF ¢ahm fnall_:' base. ,//AN( IN)//' - '//AA4 [A) ,name= AN( IN)//'" "//AA( IA)//". in' I_ITE (11,*) Itime nice ÷10 ', & '/hprs7/tS36345/NA ! N/arc2d/arc2d <', ,name cahm WRITE (11,'7 ,my arc2d run.out out.a/JmKim)J/*-,//aa(ia) t.I_ITE (11,*) 'llV arc2d run, out *,am(im)//'-*l/aa4ia)//*.ou¢' WRITE 411,*) *c(mpress-e.out* ',JRITE (11,*) *cat ftr_9 >>Loads.*b** _ITE (110") ,rm ctcd.dat sotn.dat rest.dat ftn99' MRITE (11,*) '# ......................... - ...................... ' OPEN ( 10, F I LE:frlame, STATUS=*UNKNK_M' ) "URITE (10,*) *%INPUTS FSNACH:',NACH(]H), &', ALPHA=',ALPHA()A),e, RE= 3000000, HETH=3,' MRITE (10,*) ' JHAX: 211. IOIAX: S0, JTAILI: 31, JTAIL2: 181,' MRITE 410,*) * TIUUISLO= O.Oa TRANSUP= O.0, RESTART:FALSEa* _ITE (10,*) ' DIS4X= 0.64• D%S4T: 0.64, DIS2X: 0., DIS2Y: 0.,' ',,/RITE (10,*) * IPRINT:IO, ]READ= 2, STORE: TRUE, ISPEC=I,' MRITE (10,*) ' 6CA%RF: TRUE, CIRCUL: FALSE, PERIODIC= FALSE,* URITE (10,*) ' VISCOUS= TRUE, TURBULNT: TRUE, V|SX|= TRUE,' URITE 410,*) ' NP = 100000, NPCP=100000, JACDT:la ]SAVE:IOO00 S' WRITE (10,,*') "$F|NFO XLIH:O.7_, XNINGE:O.75, IFLAG:I,' URITE 410,*) ' FANG=,0. S t MRITE (10,*) *ISEQUAL [F %%EQUAL GT I, DTISEQ : II=I,%SEQUAL' ',_ITE 410,'7 a3' WRITE (10,*) 'JMXI, IO(X%, %ENDS, DTISEQ, DTMINS' MRITE (10, _) '211, 50, 350, 1.0, 0.0' _RITE 410,*) '211, 50, SOD, 3.0, 0.0 a WRITE (10,*) •211, 50, 750, 5.0, 0.0' CLOSE 410) !0 CONT %HUE URITE (11,*) *hostname, WRITE (11,*) *date* '_RITE (11,*) 't_me' I_ITE (11, t) *df* _ITE 411,*) *exit' CLOSE (11) STOP 888 END #!lbin/csh hostname date time df sleep 12600 # ................................................ HPRI03 cp header.txt toads.tb[ ....................
time nice +10 IhprsTIts36_51NAIMlarc2dlarc2d <20oMO5.in my arc2d run.out 20-MO5.out conlpress-*, oqJt cat ftn99 >>loads.tb[ re ctcd.dat sotn.dat rest.dat ftr_9 # ................................................
time nice +10 /hprs7/ts36345/MAIM/arc2d/arc2d <20-MO4.in my arc2d run.out 20-MO4.out compress-*, out cat ftn99 >>toads.tbt re ctcd.dat sotn.dat rest.dat ftn99 # ................................................
t =me nl ce +10 /hprs7/ts]6345/MA! M/arc2d/arc2d <20-M03° in my arc2d run.out 20-NO3.out compress-*.out cat ftn99 >> toads, tbt re clcd.dat sotn.dat rest.dat ftn99 # ................................................
t lme nl ce +10 /hprsT/ts36_5/MA I N/arc2d/arc2d <20-M02. i n my arc2d run.out 20-MO2.out compress-*, out cat ftn99 >>loads.tbt rm ctcd.dat soin.dat rest.dat fin99 # ................................................
time nice +10 /hprsT/ts36345/RAIN/arc2d/arc2d <20-HOl.in my arc2d ru_.out 20-NOl.out compress-*. OUt cat ftng9 >>Loads.tbl re clcd.dat soln.dat rest.dat ftn_ # ................................................
time mce +10 /hprsT/ts36345/MAlN/arc2d/arc2d <20-O00.in my arc2d run.out 20-O00.out compress-*, out cat ftn99 >>toads.tbt re ctcd.dat sotn.dat rest.dat ftn99 # ................................................
time mce +10 /hprsT/ts36345/W_lN/arc2d/arc2d <20-P01. in mv arc2d run.out 20-POl.out compress-*, out cat ftn99 >>toads.tbt re ctcd.dat sotn.dat rest.dat ftn99 # ................................................
time nice +10 /hprsT/tsT_S/l_lN/arc2d/arc2d <20-PO2.in my arc2d run.out 20-PO2.out compress-*, out cat ftn_ >>toads.tbt re cLcd.dat soln.dat rest.dat ftn99 # ................................................
time nice +10 /hprs7/ts_5/RAIN/arc2d/arc2d <20-PO3.in my arc2d run.out 20-PO3°out compress-*, out cat fin99 >>toads.tbt re ctcd.dat sotn.dat rest.dat fin99 # ................................................
time nice +10 /hprsT/ts30345/MAIN/arc2d/arc2d <20-PO4.in my arc2d run.out 20-PO4.out compr ess-*, out cat ftn99 >>toads.tbt re clcd.dat soLn.dat rest.dat ftn_ # ................................................
time nice +10 /hprsT/ts]6345/NAlN/arc2d/arc2d <20-POS.in my arc2d run.out 20-PO5.out compress-*, out cat ftn99 >>toads.tbl rm ctcd.dat sotn.dat rest.dat ftn99 # ................................................
time nice +10 /hprsT/ts36345/NAIN/arc2d/arc2d <20-PO6.in my arc2d run.out 20-POO.out coN1pr ess-*, out cat fin99 >>|oads.tbl re ctcd.dat sotn.dat rest.dat ftn99 # ................................................
time nice +10 /hprsT/ts36345/HAIN/arc2d/arc2d <20-PO7.in my arc2d run.out 20-PO7.out compress-*, out cat ftn_ >>toads.tbt rm clcd.dat soln.dat rest.dat fin99 # ................................................
time nlce +10 /hprs7/ts36345/MA!N/arc2d/arc2d <20-POS.in my arc2d run.out 20-P_.out compress-*, out cat ftn99 >>loads.tbl rm cLcd.dat soln.dat rest.dat fin99 time mce +10 Ihprs71ts363/+511(AIMlarcEdlarcEd <20-PO9.in mv arc2d run.out 20-PO9.out compress-*, out cat ftn99 >>toads.tbt rm ctcd.dat sotn.dat rest.dat ftn99 time nice +10 IhprsTIts_5/NAtNlarcEd/accPd <20-P10. in my arced run.out 20-PlO.out compress-* .out cat ftn99 >>[oads.tb{ rm ctcd.dat sotn.dat rest.dat ftn99 ........................ . .......................
time mce +10 /hprsT/ts36345/HA]N/arcEd/arc2d <20-Pll. in my arced run.out 20-Pll.out COelllDress-*. ou¢ cat ftn99 >>loads.tbt rm ctcd.dat sotn.dat rest.dat ftn99 ................................................
time race +10 /hprsT/ts36345/RAlM/arcEd/arcEd <EO-P12. in my arced run.out 20-PIE.out compress TM . out cat ftn99 >>Loads.tbt rm ctcd.dat sotn.dat rest.dat ftn99 # ................................................
time n=ce +10 /hprsT/ts36345/RAlMlarcEd/arc2d <EO-P13. =n my arced run.out EO-P13.out c(:MIIpress-*, out cat ftn99 >>toads.tbt rm ctcd.dat sotn.dat rest.dat ftn99 ................................................
time nice +10 /hprs7/ts36345/NAlN/arc2d/arcEd <EO-P14.in my arced run.out 20-P14.out compress-* .out cat ftn99 >>toads.tbt rm cLcd.dat sotn.dat rest.dat ftn99 ................................................
time nice +10 /hprsZ/ts36_S/HAlN/arcEd/arc2d <30-NOS.in my arced run.out 30-MOS.out co_press TM . out cat ftn99 >>toads.tb[ rm c[cd.dat sotn.dat rest.dat ftn99 ................................................
time nice +10 /hprsT/ts36345/HA[N/arcEd/arcEd <30-HO4.in my arced run.out 30-MO4.out compress -= . out cat ftn99 >>toads.tbL rm ctcd.dat sotn.dat rest.dat ftn99 ................................................
time nice +10 /hprsT/ts36345/NAiN/arcEd/arcEd <30-HO3.in my arced run.out 30-HO3.out conlpr ess TM .out cat ftn99 >>toads.tb[ rm ctcd.dat sotn.dat rest.dat ftn99 _... .............................................
time nice +10 /hprsT/ts36345/NAIN/arc2d/arc2d <30-NO2. in mv arced run.out 30-NOE.out ..... .....
#ime n+ce +10 Ihprs71tpll_St It41_ItUarczdlarczd <30 p01 in ,tv_ arc2 d run.out 30-PU]- -= out compress • ' -'-t --o ftn99 >>loaaS._ -_t dat ftn99 .......
%.+: ++-+oo--
comP "> oads tbt tn99 > [ " t ftn99 cat f _ dat soLn._t rest.da ........... - .................. - ....... . °" i'_ Ct_U+ #: ;+ n_ce" ;10 /hprST/+ts3363&ouSt/l_ltl/arc;')d/arcEd <30 P03 in arc2d_run, tout +u-r--- compress . ou, ..... +-t cat ftn99 >>_oau=._ -+t dat ftn99 rm ctcd dat soLn.Oam r=+ - #" . _ +_n +hnrsTitS3631+5114AINlarcEdlarcEd time n_ce "'_,t_ 30-PO4.out mv arc_o ._-.- :- c(:_l_pess = .OU_: cat ftn99 >>toads.tb[ rm c[cd.dat soln.dat rest.dat ftn99 time nice +10 /hprs7/ts36345/HA[N/arc2d/arc2d <30-POS.in my arc2d run.out 30-POS.out c_press-*, out cat ftn99 >>koads.tbl rm ctcd.dat sotn.dat rest.chat ftn99 ................................................
time mce +10 /hprsT/ts36345/NA%N/arc2d/arc2d <30-POO. in my arc2d run.out 30-PO6.out co_>ress-* . out cat ftn99 >>toads.tbl rm ctcd.dat sotn.dat rest.dat ftn99 t_me nice +10 /hprsT/ts36345/MAZtl/arc2d/arc2d <30-PO7.1n nw arc2d run.out 30-POT.out compress TM . out cat ftn_ >>[oads.tbl rm c[cd.dat soln.dat rest.dat ftn99 ................................................
t ime m ce +10 /hprs7/ts363_5/NA| N/arc2d/arc2d <]O-P08. in my arc2d run.out 30-POS.out compress-*, out cat ftn99 >>toads.tbl rm ctcd.dat sotn.dat rest.dat ftn99 ................................................
time race +10 /hprsTIts363_S/NAZN/arc2d/arc2d <3O-POg. in my arc2d run.out 30-PO9.out compress-*, out cat ftn99 >>toads. tbt rm c[cd.dat so[n.dat rest.dat ftn99 ...... T .........................................
time mce +10 /hprsT/ts36345/MAIN/arcZdlarc2d <30-PlO.in my arc2d run.out 30-PlO.out compress-*, out cat ftn99 >>loads.tb( rm c|cd.dat sotn.dat rest.dat ftn99 ................................................
time nice +10 /hprsT/ts]6345/NAiN/arc2d/arc2d <30-P11.in my arc2d run.out 30-Pll.out compress-*. OUt cat ftr_9 >>[oads.tb[ r_ clcd.dat so[n.dat rest.dat ftr_9 ................................................
time nice +10 Ihprs7/ts]6_5/HA]N/arc2d/arc2d <30-P12.in my arc2d run.out 30-P12.out compress-* .OUt cat ftn99 >>loads.tbl rm ctcd.dat soln.dat rest.dat ftn99 ................................................
time n_ce +10 /hprs7/ts36345/HAiN/arc2dlarc2d <30-P13.in my arc2d run.out 30-P13.out compress"*. OUt cat ftn99 >>[oads.tb[ rm ctcd.dat sotn.dat rest.dat ftr_9 ................................................
time nice +10 /hprs7/ts36345/NAIN/arc2d/arc2d <30-P14.in my arc2d run.out 30-P14.out co_ress-*, out cat ftn99 >>[oads.tb[ re, ctcd.dat sotn.dat rest.dat ftn99 ................................................
hostname date time df exi t
Appendix 6
Appendix 6
Sample "LOADS.TBL" File
NNACH ................ DELTA = +10.0 DEGREES NACH ALFA CL CD CM CLF (:OF CleF .2000 -14.0000 -•8663 • 0245 -. 1161 • 0542 -. 0065 - • 0043 • 2000 -13.0000 -.7(_1 .0221 -.1154 .0576 - .0058 ".0045 .2000 -12•0000 -.6641 .0201 -.1146 • 0610 - .0050 - .0046 • 2000 -11.0000 -.5615 • 0183 -.1136 .0641 - .0_0 - .0047 .2000 -10•0000 -.4504 • 0169 -.1125 .0669 - .0028 - .0048 • 2000 °9.0000 -•3535 • 0157 -•1115 .0700 - .0016 - .0049 .2000 -8•0000 -•2483 .0148 -.1104 • 0730 -.0003 - .0050 .2000 -7.0000 -.1411 .0142 -.1096 .0762 .0012 - .0052 • 2000 -6.0000 -•0334 • 0138 -.1088 .07V4 • 0027 - • 0054 .2000 -5•0000 •0748 • 0137 -.1080 • 0827 .0044 - .0055 .2000 -4.0000 .1_ .0138 -. 1071 .0858 .0062 - .0057 • 2000 -3.0000 .2914 • 0142 - .1062 .0889 .0080 - .0059 .2000 -2•0000 .3994 .0148 -•1052 .0918 .0100 - .0061 • 2000 -1.0000 .5072 • 0157 -. 1040 • 0947 .0120 - .0063 .2000 .0000 .6142 .0168 - .1027 .G973 .0140 - .0065 • 2000 1.0000 .7202 .0182 -.1011 .0996 .0160 - .0067 • 2000 2.0000 .8251 .0199 - .0994 .1018 .0181 - .0068 .2000 3.0000 .9288 • 0217 - .0974 .1036 .0202 - .0070 .2000 4.0000 1.0310 • 0239 - ._1 .1052 .0223 -.0071 .2000 5.0000 1•1316 • 0263 -. 0926 .1065 .0244 - .0073 .2000 6.0000 1.2301 .0290 - .0897 • 1075 .0265 ".0074 .2000 7•0000 1.3262 • 0319 - .0865 .1082 .0286 - .0076 • 2000 8.0000 1.4199 • 0351 - .O_O • 1087 .0306 - .0077 .2000 9.0000 1.5108 .0387 -. 0792 .1089 .0326 - .0079 .2000 10•0000 1.5974 .0426 - .0749 .1087 .0346 - .0080 .2000 11.0000 1.6806 •0468 -•0703 .1085 .0366 - .0082 • 2000 12.0000 1.7577 " •0514 -.0651 • 1077 .0385 - .0084 • 2000 13.0000 1.8273 •0503 -.0592 • 1067 .0405 - .0085 • 2000 14. 0000 1.8872 .0617 -.0524 .1049 .0422 -.0087 .3000 - 14 • 0000 - .8855 .0259 -. 1212 .0560 -.0069 - .0045 .3000 -13•0000 - •7829 .0231 - .1200 .0595 - .0062 - .0047 .3000 -12.0000 -.6778 .0206 - .1190 .0631 - .0054 - .00_ • 3000 -11•0000 -.5745 .0187 -.1173 • 0657 -. 0043 -. 0049 • 3000 - 10•0000 - •4712 .0170 -.1154 .0680 - .0031 - .0049 .3000 -9.0000 - •3614 .0156 -.1148 .07'19 -.0019 - .0051 • 3000 -8•0000 - •2550 .0146 - •1134 • 0745 - .0005 - .0051 .3000 -7.0000 -•1463 .0139 -.1123 .0776 .0010 - .0053 .3000 -6• 0000 - .0368 .0134 -.1114 .0808 .0026 -.0054 • 3000 - 5.0000 .0726 .0133 -.1103 .0838 .0042 -.0056 • 3000 - 4.0000 .1830 .0135 -.1095 .0870 .0060 -.0058 .3000 -3.0000 •2930 .0140 - .1084 .0900 .0079 -.0059 .3000 - 2.0000 .4029 .0147 -.1073 .0929 .0098 -.0061 .3000 -1.0000 .5122 .0158 -.1060 .0956 .0118 -.0063 • 3000 .0000 • 6208 .0171 -.1046 .0980 .0138 -.0065 .3000 1.0000 .7285 .0188 - .1028 .1003 • 0159 -•0066 .3000 2.0000 .8353 .0207 -.1009 .1023 .0179 -.0(0)8 • 3000 3.0000 .9408 .0230 -.0986 .1040 .0200 -•0069 .3000 4. 0000 1.0450 .0255 -.0960 .1055 .0221 -.0071 .3000 5.0000 1.1474 .0283 - .0930 .1066 .0242 -.0072 .3000 6.00O0 1.2480 .0315 -.0897 .1075 .0262 -.0073 • 3000 7.0000 1.3462 .0349 -.0859 .1081 .0282 -.0075 • 3000 8.0000 1.4421 .0387 -.0818 .1004 .0302 -.0076 .3000 9. 0000 1 • 5343 .0428 -.OTTO .1083 .0321 -.0077 • 3000 10.0000 1.6229 .0472 -.0717 .1080 .0340 -.0079 • 3000 11.0000 1.7075 .0520 - .0659 .1074 .0358 - .0080 .3000 12.0000 1.7821 .0570 -.0588 - .1059 .0375 - .0081 .3000 13.0000 1.8521 .0625 -.0513 .1042 .0391 - .0083 .3000 14.0000 1.9057 .0685 - .0421 .1017 .0406 - .0083 .4000 - 14.0000 - .9102 .0285 -. 1320 .0602 - .0072 - .0049 .4000 "13.0000 ".8111 • 0247 -. 1288 .0629 - .0067 - .0050 .4000 ' 12.0000 ".7055 .0218 -.1259 .0655 - .0058 - .0050 .4000 "11.0000 ".5962 .0194 -.1239 .0687 - .0047 - .0051 .4000 - 10•0000 - .4874 • 0174 - .1217 .0715 - .0035 - .0051 .4000 -9.0000 -. 3T?'6 .0158 - .1198 • 0742 - .0022 - .0052 .4000 -8.0000 - .2666 • 0145 -.1181 .0770 - .0007 - .0053 .4000 - 7.0000 - .1549 .0137 " .1167 • 0799 .0008 - .0054 .4000 -6.0000 - .0429 .0132 -.1153 .0828 .0024 - .0055 .4000 -5.0000 •0692 .0130 - .1139 .0855 .0041 - .0056 .4000 -4.0000 .1_ • 0132 - .1131 .0889 .0059 - .0058 .4000 -3.0000 .2968 .0138 -.1119 .0917 .0078 - .0059 .4000 -2.0000 .4096 .0147 - .1106 .0944 .0097 -.0061 .4000 - 1.0000 .5220 .01_ - .1_1 ._9 .0117 - .0063 • 4000 .0000 • 6335 .0176 - .1073 .0992 .0137 - .0004 • 4000 1.0000 .7444 .0196 -.1052 .1012 .0157 - .0066 • 4000 2 • 0000 .8543 .0219 - .I028 .1030 .0178 - .0067 .4000 3.0000 .9631 .0246 -.1000 .1045 .0198 - .0068 .4000 4.0000 1.0704 .0276 - .0967 .1057 .0218 - .0070 • 4000 5.0000 1 •1763 .0310 - .0928 .1066 .0238 - •0071 • 4000 6. 0000 1 . 2799 .0347 - .0883 .1071 .0258 - .0072 .4000 7.0000 1.3815 .0388 - .0831 .1073 .0277 - .0073 • 4000 8.0000 1.4794 • 0434 - .0769 .1071 .0295 - .0075 .4000 9.0000 1.5628 .0487 - .0682 .1049 .0308 - .0075 .4000 10. 0000 1.6_44 • 0563 -. 0549 .0993 .0316 - .0074 • 4000 11.0000 1.6055 .0655 - .0389 .0919 .0324 - .0072 • 4000 12.0000 1.5755 .0757 - .0233 .0856 .0343 - .0071 • 4 000 13 . 0000 1 . 5397 .0932 - .0178 .0875 .039S - .0079 .4500 -14.0000 - •8560 • 0380 -.1408 .O645 - .0043 -.0055 .4500 -13•0000 - .6050 .0283 -.1580 .0674 - .0061 -.0055 •4500 -12.0000 -• 7206 .0229 -.1328 .0684 - .0059 -.0053 •4500 -11.0000 - .6123 •0199 -.1291 .0710 - .0049 -.0053 •4500 -10.0000 - •5014 •0177 -.1260 .0734 -. 0037 -.OO53 •4500 -9.0000 - .3889 .0159 -.1236 .0760 - .0023 -.0053 .4500 -8.0000 - .2755 .0146 -.1215 .0787 - .0009 -.0054 •4500 -7•0000 -.1613 .0136 -.1197 .0815 .0007 -.0054 .4500 -6.0000 -. 0465 .0131 -•1182 .0843 .0023 - .OO55 .4500 -5.0000 .0689 .0129 -.1169 .0872 .0041 - .0057 .4500 -4.0000 .1811 .0132 -.1149 .0892 •0058 -.0_7 .4500 -3•0000 •2992 .0138 -.1141 .0927 .0077 -.0059 .4500 -2•0000 .4121 .0148 -•1122 .0947 .0096 -.0060 .4500 -1.0000 .5266 .0162 -•1105 .0971 •0116 -.0062 .4500 •0000 .6402 .0180 -.1085 .0992 .0136 -.0063 •4500 1.0000 .7556 .0202 -.1066 .1015 ,0156 -.0065 .4500 2.0000 .8678 .0227 -.1058 .1031 .0176 -.0066 .4500 3.0000 • 9789 .0256 .I005 • 1044 .0196 -.0067 .4500 4.0000 1 • 0890 .0290 -.0965 • 1054 .0216 -.0069 .4500 5.0000 1 • 1973 .0327 -.0918 .1060 .0235 -. 0070 .4500 6•0000 1.3012 • 0369 -.0858 • 1061 .0253 -. 0071 .4500 7.0000 1.4007 .0417 -.0781 .1051 • 0269 -. 0071 .4500 8.0000 1.4634 .0485 -.0(552 .1002 .0278 -.00_ .4500 9.0000 1.4901 .0576 -.0494 • 0929 • 0284 -.0_ .4500 10.0000 1.4831 .0678 -.0327 • 0859 • 0296 -.0067 •4500 11.0000 .0790 -.0185 -.0067 1.4522 .0808 .0320 2O .5000 -14.0000 - .7531 .0547 1424 .0641 • 0024 -.0054 .5000 -13.0000 -.7384 • 0399 1471 .0721 - .0024 -.0061 .5000 -12•0000 - .6947 .0290 1444 . O750 - .0046 -•0061 .5000 -11•0000 - .6226 .0218 1379 .0749 - .0049 -.0057 .5000 -10.0000 -.5194 .0182 1323 .0759 - .0039 -.0055 .5000 -9.0000 - •4043 .0162 1285 .0_I - .0025 -.0054 :.1258 .5000 -8.0000 - • 2873 .0147 .0807 - .0010 -.OO55 .5006 -7.0000 -. 1699 •0136 -•1235 .0833 .0006 -.OO55 .5000 -6.0000 - .0518 -.1217 -.0056 .0130 •0860 .0022 •5000 -5•0000 •0649 .0128 -.1197 .0883 .0040 -.0057 .5000 -4•0000 •1822 •0131 -.1180 .0907 .0058 -.0057 .5000 -3.0000 .3012 .0138 -.1166 .0935 .0077 -.0059 .5000 -2.0000 •4185 .0149 -.1149 .0958 .0096 -.0060 •5000 -I•0000 .5384 .0165 -.1135 .0986 .0116 -.0062 .5000 •0000 .6554 .0185 -.1112 .1005 .0136 -.0063 .5000 1.0000 .7717 .0209 -.1085 • 1022 .0155 -.0064 .5000 2.0000 .8872 • 0237 -.1052 .1035 .0175 -.00_ .5000 3.0000 1.0019 • 0270 -.1011 -.0067 .1045 .0194 •5000 4.0000 1.1154 .0307 " . 0960 • 1052 .0213 -.0068 .5000 5.0000 1•2115 .0342 -.0865 .1018 .0220 -.0064 •5500 -13.0000 - •6360 .0566 -.1484 .0727 .0044 -.0060 .5500 -12.0000 -. 6301 •0418 -.1541 .0808 - .0008 -.0067 .5500 -11.0000 - .5868 .0301 -•1511 .0828 - .0030 -.0066 .5500 -10.0000 - •5193 .0217 -.1438 .0819 - .0034 -.0061 .5500 -9.0000 - .4227 •0170 -.1363 .0813 - .0027 -.0057 •5500 -8.0000 - •3044 .0149 -.1315 .0829 -.0012 -.0056 •5500 -7.0000 -•1614 .0137 -.1285 •0856 •0004 -.0056 .5500 -6.OOOO - •0606 •0130 -.1258 .0877 .0021 -.0056 •5500 -5.0000 .0128 .0907 .0635 -.1242 .0039 -.0058 .5500 -4.0000 • 1859 .0131 -.1225 .0932 .0058 -.0059 .5500 -3.0000 .3081 .0139 -.1207 .0956 .0077 -.0060 .55OO -2.0000 .4299 .0152 -.1188 .09T'/ •0096 -.0061 •5500 -1.0000 .5512 •0169 -.1166 .0996 .0115 -.0062.
.5500 .0000 .6722 .0191 -.1139 .1013 .0135 -.0063 .5500 1.0000 .0218 -.1106 -.0064 .7927 .1026 .0154 .5500 2.0000 •9121 .0250 -.1063 •1035 .0172 -.0065 .5500 3.0000 I• 0322 • 0287 - .1008 • 1042 .0191 -.0066 .6000 -11.0000 - •5173 .0449 -.1593 .0898 .0012 -.00_ .6000 -10.0000 -. 4753 .0325 - .1568 .0910 -.0010 -.0071 .6000 • 0228 - .1499 .0892 - .0017 -.0065 -9.0000 - •4103 •6000 -8.0000 -.1414 .0872 - .3199 .0165 - .0012 -.0059 .6000 -7.0000 - .2008 .0140 -.1350 .0877 .OO02 -.0057 .6000 .0131 .0907 -6.0000 - • 0692 -.1321 .0020 -.OO58 .6000 -5.0000 • 0590 .0129 -.1295 • 0930 .0038 -.0058 .6000 -4.0000 • 1867 .0132 -.1274 • 0952 .0057 -.0_9 .60OO -3.0000 •3140 .0141 -.1253 .0972 .0076 -.0059 .6OOO -2.0000 .4408 .0155 -.1230 .0990 .0095 -.0060 .6000 .1005 -1.0000 .5672 .0175 -.1203 .0114 -.0061 .6000 •0000 •6939 .0200 -.1170 .1016 .0132 -.0061 .6000 1.0000 .8207 .0232 -.1125 .1024 .0150 -.0062 .6500 -10.0000 -. 39 72 • 0492 -•1617 .0995 .0037 -.0078 .6500 -.1604 •0994 .0010 -.OO75 -9.0000 -. 3649 • 0366 .6500 -8•0000 -. 2982 .0258 -.1545 .0964 .0003 -.OO69 .6500 -7.0000 -.2055 .01_ -.1474 • 0940 .0006 -.0062 .6500 -.0883 .0138 -•1403 .0931 -.0058 -6.0000 .0018 .6500 -5.0000 •0503 .0131 -.1366 ._5 .0037 -.0058 .6500 -4.0000 .1861 .0135 -.1337 •0973 .0055 -.0058 .6500 -3.0000 .3204 .0145 -.1311 .0074 -.0059 .6500 -2.0000 • 4548 .0161 -.1283 •1000 .0093 -.0059 .6500 -I.0000 • 5893 .0185 -.1248 • 1008 .0110 -.0059 •6500 .0000 .7246 •0215 -.1198 .1010 .0127 -.0059 .6500 1.0000 .8509 .0265 -.1110 .0984 .0138 -.0058 .7000 -9.0000 - .2363 .0456 -.1354 • 0786 •0006 -.0059 .moo -8.0000 -.2455 .0428 -.1602 .1077 • OO36 .7000 -.0077 -7•0000 -. 1832 .0312 -.1560 • 1056 .0024 •_ -.00_ -6.0000 - .0828 .0213 -.1522 .1010 .0027 .?ooo -.00_ -5.0000 • 0389 .0154 -.1475 .0_, .0037 ._ -.0059 -4.0000 .1796 .0141 -.1425 .0993 • 0053 .7ooo -.0057 -3•0000 .3260 .0152 -.1386 .0996 •0071 .moo -2.0000 -.0057 .6726 .0173 -.1346 .0995 .0087 •_oo -.0056 -1.0000 .6148 .0213 -.1289 .0966 .0098 .7000 -.0055 .0000 .7431 .0288 -.1232 .0892 .0099 .moo -.0051 1.o000 .8594 • 0407 -.1204 .0811 .0098 •7000 -.0047 2.0000 .9450 .0551 -.1153 .0730 .0102 9 -.00_.
. _00 -7.0000 .2031 .0498 -.2156 .1579 .0445 . _0o -.0114 -6.0000 - .0943 .0426 -.I_Q .10_ .0053 ._0o -.0065 -5.0000 .0165 .0302 -.14T3 .1018 .0047 ._00 -.0060 -4.0000 • 1576 .0217 -.1486 .0992 .0053 -.0056 . _00 -3.0000 .3335 .0187 -.1517 .0945 • _00 .0054 -.0052 -2.0000 .5047 • 0240 -.1580 ._16 .0042 • _00 -.0045 -1.0000 .62_ .0347 -.1599 .0714 .0042 ._00 -.0040 .0000 .6969 .0461 -.1498 .0630 • 0056 • _00 -.0_5 1.0000 .73_ .0574 -.1332 .0554 .0077 9 -.0031 •_O0 -7.0000 .20"_1 .0498 -.2156 .1579 .0445 ._ -.0114 -6.0000 - .0943 .0426 -.14_ .1046 •0053 -.0_5 •_ -5•0000 .0165 • 0302 -.1473 .1018 .0047 ._ -.0060 -4.0000 .1576 .0217 -.1486 .0992 • 0053 ._00 -.0056 -3.0000 .3335 •0187 -.1517 .0945 • 0054 •_00 -.0_2 -2.0000 .5047 .0240 -.1580 • 0816 .0042 ._ ".0045 -1•0000 .6266 .0347 -.15_ .0714 .0042 ._00 -.0040 •0000 .6949 -0461 -.1498 .0630 .0056 •_ -.0_5 1. o000 .7334 .0574 -.1332 .0554 .0077 9 -.0_1 .8500 -7.0000 .2031 .0498 -.2156 .1579 .0445 .85_ -.0114 -6.0000 - .0943 .0426 -.1464 • 1046 .0053 •8500 -.0065 -5.0000 .0165 •0302 -.1473 .1018 .0047 -.0060 .85_ -4.0000 .1576 .0217 -.1486 .0992 .0053 .8500 -.0056 -3•0000 .3335 •0187 -.1517 .0945 .0054 .8500 -.0_2 -2.0000 .5047 • 0240 -.1580 .0816 .0042 .85_ - .0045 -1 •0000 .6266 .0347 -.1599 .0714 .0042 .8500 -. 0040 • 00o0 .6949 .0461 -.1498 .06_ .0056 .85_ -.0035 1.0000 •7334 .0574 -.1332 .0554 .0077 9 -.0031 ._00 -7.0000 .2031 .0498 -.2156 .1579 .04,Q5 .9000 -.0114 -6.0000 - .0943 .0426 -.1444 .1046 .0053 . _00 -.0065 -5.0000 .0165 .0302 -.1473 • 1018 .0047 ".0060 -4.0000 .1576 .0217 *.1486 .0992 ._ .0053 -.0_6 -3.OO0O .3335 .0187 -.1517 .0945 •9_0 • 0054 -2.0000 -._52 .5047 .0240 -.1580 .0816 . _00 .0042 -.0045 -1.0000 .6266 .0347 -.1599 .0714 .0042 ._00 -.0040 .0000 .6949 .0461 -.1498 .0630 .0056 . _00 -.0035 1.0o00 .7334 .0574 -.1332 .0554 .00T7 -.0031
Appendix 7
Appendix 7
C81 Tables For All Airfoils
(Flap deflections; 0.0 +/-5, +/-10, +/-15,+/-20 degrees)
AIRF iNTERPOLATED DATA 156115611561 NACA-0015 BASELINE (D=O.O DEGS.)
• 0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 .6500 • 7'000 .7'500 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 -170.00 .7_,52 .T452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 .7452 - 160.00 .6471 .6471 .6471 .6471 .6471 .6471 .6471 .6471 . _-+ 71 .6471 .6471 .6471 .6471 •6471 .6471 -140.00 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 -120.00 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7548 .7348 .7548 -110.00 .4823 .4823 •4823 .4823 .4823 .4823 .4823 .4823 .4823 .4823 °4823 .4823 .4823 .4823 •4823 -100.00 .2097 .2097 .2097 .2097 ,2097 .2097 .2097 •2097 .2097 • 2097 .2097 .2097 .2097 .2097 .2097 -t)O.O0 -.0627 -.0627 -.0627 -.0627 -.0627 -.0627 -.0627 -.0627 -.0627 -.0627 - . 0627 - .0627 -.0627 - .0627 -. 0627 - 80. O0 - •3352 -.3352 - .3352 -.3352 - . 3352 -.3352 - • 3352 -.3352 -.3352 - • 3352 -.3352 -.3352 - .3352 - .3352 -.3352 - 70. O0 -. 6077 -. 6077 -. 6077 -. 6077 -. 6077 -. 6077 -. 6077 - .6077 -. 6077 - .6077 - .6077 - .6077 - .6077 - .6077 - .6077 - 60.00 -.8802 - • 8802 -.8802 - • 8802 -. 8802 - .8802 -. 8802 -. 8802 -. 8802 -.8802 -.8802 -.8802 - .8802 -.8802 -.8802 • 50.00-1 . 1528-1 . 1528-1 . 1528-1 . 1528-1 . 1528" 1.1528-1 . 1528 - 1.1528-1 . 1528 - 1.1528-1 . 1528-1 . 1528-1 . 1526-1 . 1528-1.1528 -30.00 -.9900 -.9900 -.9950-1.0050-1.0100-1.0150-1.0150-1.0150-1.0150 - 1 . 0150 -. 9450 - . 9300 - . 9200 -. 9100 -.9100 - 21. 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8O
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2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 100.00 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2°0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 110.00 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 120.00 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 140.00 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 160.00 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 • 3020 .3020 .3020 .3020 .3020 .3020 170.00 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 180.00 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 • 0220 .0220 .0220 .0220 .0220 .0220 .0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 .6500 .7000 .7500 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 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.3990 .3f_0 -50.00 .2827 .2827 .2893 .2973 .3033 .3093 .3163 .3233 .3283 • 3333 .3427 .3513 .3583 .3653 .3653 -30.00 .1740 .1740 .1840 .1960 .2050 .2140 .2245 .2350 .2425 .2500 .2640 .2770 .2875 .2980 .2980 -21.00 .I009 .I009 .1066 .1160 .1233 .1306 .1368 .1430 .1493 •1556 .1699 .1974 .2101 .2229 .2229 -16.00 .0730 .0730 .0780 .0860 .0915 .0970 .1025 .1080 .1125 • 1170 .1370 .1760 .1880 .2000 .2000 -15.00 .0540 .0540 .0650 .0730 .0785 .0840 .0905 .0970 .1040 .1110 .1330 .1730 .1840 .1950 .1950 -14.00 -.0692 -.0692 -.0746 -.0888 -.0934 -.0083 .0463 .0616 .0756 .0908 .I065 .1371 .1469 .1568 .1568 -13.00 -.0678 -.0678 -.0724 -.0836 -.0947 -.0975 -.0116 .0150 .0374 .0630 .0674 .0818 .0905 .0992 .0992 -12.00 -.0664 -.0664 -.0704 -.0788 -.0891 -.1004 -.0682 -.0334 -.0031 .0329 .0243 .0199 .0274 .0349 .0349 -11.00 ".0651 -.0651 -.0687 -.0754 -.0823 -.0952 -.1058 -.0786 -.0434 .0023 -.0200 -.0442 -.0379 -.0316 -.0316 -10.00 -.0638 -.0638 -.0667 -.0724 -.0773 -.0871 -.1009 -.1082 -.0807 -.0283 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9O
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O0 .0140 .0140 .0137 .0135 .0135 .0135 .0135 •0137 .0151 .0245 .0420 .0546 .0546 .0546 .0546 6.00 .0147 .0147 .0146 .0146 .0146 .0147 .0149 .0155 .0210 .0358 .0257 .0673 .0675 .0674 .0674 7.00 .0157 .0157 .0157 .0159 .0161 • 0164 .0169 .0196 .0307 .0488 .0319 .0873 .0878 .0677 .0877 8•00 .0170 .0170 .0172 .0177 .0180 .0186 .0200 .0276 .0434 .0693 .0550 .1099 .1108 .1105 .1105 9.00 .0185 .0185 .0190 .0198 .0204 .0214 .0264 .0390 .0576 .0937 .0835 .1334 .1346 .1343 .1343 10.00 .0203 .0203 .0211 .0223 .0232 .0264 .0363 .0528 .08Z8 .1193 .1137 .1573 .1588 .1584 .1584 11.00 .0224 • 0224 .0349 .0491 .0823 .1133 .0236 .0253 .0271 .1452 .1444 .1812 .1832 .1827 .1827 12.00 .0249 .0249 .0265 .0288 .0341 .0468 .0853 .1191 .1453 .1712 .1753 .2052 .2077 .2073 .2073 13.00 •0276 .0276 .0297 .0336 .0448 .0628 .1321 .1576 .1775 .1972 .2059 .2292 .2325 .2328 .2328 14.00 .0308 .0308 .0333 .0423 .0598 .1360 .1798 .1956 .2092 .2230 .2358 .2533 .2583 .2605 .2605 15.00 .1112 .1112 .I_6 .1666 .1995 .2124 .2210 .2296 ,2387 .2482 .2634 • 2776 .2868 .2948 .2948 16.00 .1602 .1602 .1862 .2126 .2254 .2381 .2460 .2539 .2621 .2706 .2848 .2998 .3161 .3346 .3346 21.00 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3350 .3400 .3400 .3320 30.00 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 50.00 1.3920 I.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 60.00 1.6620 1 .(_20 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 70.00 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 80.00 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.96,?.0 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 I ._20 90. O0 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 100.00 2°0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 110.00 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 120.00 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 140.00 1.0420 1 •0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 160.00 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 170.00 •1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 • 1320 .1320 .1320 .1320 180.00 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 .6500 .7000 .7300 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 • 0000 .0000 .0000 .0000 .0000 - 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.0154 -.0014 .0337 .0475 .0622 12.00 .0250 .0250 • 0206 .0000 .0845 •1141 • 1533 .1616 • 1700 1700 11 •00 •0284 .0250 .0109 - •0060 -.0192 .0142 .0302 .047'2 ..0284 .1532 • 1608 1608 .0750 •1071 .1457 .0053 -.0105 -.0033 •0134 .0323 10.00 .0316 .0316 •0289 •0207 .0655 .1001 • 1380 .1448 .1515 1515 -9.00 •0344 •0344 .0325 .0272 .0175 .0009 - .0120 -.0015 .01F9 .0560 .0931 • 1304 .1363 .1422 .1422 .0371 .0358 .0320 .0275 .0142 -.0016 -.0085 .0056 -8•00 .0371 .1278 •1329 .1329 •0466 .0861 .1227 -7.00 .0395 .0395 • 0386 .0363 • 0336 .0269 .0114 .0008 .0013 •0378 •0791 .1150 .1193 .1236 •123 -6.00 •0415 .0415 .0411 .0398 .0382 .0353 • 0253 •0115 .0118 .0308 .0724 • 1074 .1109 •1144 .1144 -5.00 .0434 •0434 •0435 .0429 .0419 • 0405 • 0367 •0244 •0193 .0298 •0663 .0999 .I026 •1052 • 1052 .0453 •0456 .0455 .0452 .0448 • 0433 •0374 .0279 -4•00 .0453 .0621 .0927 .0946 • 0964 .0964 .0389 .0479 .0463 .0386 -3.00 .0469 •0469 .0474 •0477 • 0480 .0481 •0433 .0638 .0864 .0876 .0887 .0887 -2•00 • 0483 .0483 •0490 .0497 .0503 •0509 • 0514 •0516 .0491 .0474 •07"37 • 0828 .0833 •0837 •0837 - 1.00 .0496 •0496 •0506 .0516 .0519 • 0533 .0543 .0554 .0560 .0541 • 0738 •0869 .0869 • 0869 • 0869 .0509 .0509 .0519 .0527 .0541 • 0552 .0567 .0583 .0603 .00 .0613 .0720 .1004 .1004 .1004 • 1004 1.00 .0521 .0521 .0532 .0548 •0559 .0571 .0588 .0609 .0635 .0668 .0731 .0991 .0991 •099 1 .0991 2.00 .0532 .0532 .0544 .0563 • 0575 •0591 .0609 .0633 .0_5 .0710 • 0782 •0956 •0956 .0956 •0956 .0545 .0559 .0578 .0592 •0609 .0631 .0660 .0700 3.00 .0545 .0948 •0948 •0948 .0764 .0834 .0948 .0630 4.00 .0558 .0558 .0571 .0595 .0610 .0658 .0691 .0742 .0821 .0841 .0867 .0821 .0821 .0821 • 5•00 •0571 •0571 • 0587 .0612 .0631 .0657 .0686 .0729 .0812 .0918 .0905 •2405 .2405 .2405 •2405 6.00 .0586 • 0586 .0602 .0629 •0654 •0682 .0720 .0783 .0911 •0969 .1587 .3033 .3027 •3020 .3020 7.00 .0599 .0599 .0619 .0653 .0675 .0712 .0763 .0871 .0994 .2808 .2791 .2791 •1006 • 1726 •2824 .0675 .0705 .0746 .0828 ._69 .1048 8•00 .0613 .0613 •0634 •0846 •1463 .2324 .2296 .2269 • 2269 9.00 •0625 • 0625 .0651 .0698 •0736 • 0796 .0924 .1047 •1055 •0580 .1073 .1722 .1683 .1644 .1644 10.00 .0638 .0638 • 0667 .0724 .0773 .0871 .1000 .1082 .O807 .1036 • 0985 •0985 •0283 •0642 • 1087 11.00 .0651 • 0651 • 0687 .0754 •0823 •0952 .1058 .0786 .0434 -.0023 .02 O0 .0442 .0379 .0316 .0316 12.00 •0664 .0664 •0704 .0788 .0891 • 1004 .0682 .0334 .0031 -.0329 -. 0243 - .0199 -.0274 -. 0349 -. 0349 •0678 .0724 .0836 .0947 • 0975 .0116 -.0150 -.0374 13.00 .0678 -.0992 -.0992 -.0630 - .0674 -.0818 -.0905 14.00 •0692 • 0692 • 0746 .0888 •0934 • 0083 -.0463 - . 0616 - . 0756 .O9O8 -. 1065 -.1371 -.1469 -. 1568 -.1568 15.00 •0540 -• 0540 - • 0650 -.0750 -. 0785 - . 0840 -. 0905 - . 0970 - . 1040 .1110 -• 1330 - .1730 -.I_0 -. 1950 -. 1950 -. 0780 -.0860 - .0915 -.0970 -.1025 -.1080 -.1125 16.00 •0730 .0730 •1170 .1370 -. 1760 -.I_0 -. 2000 - .2000 21.00 •1009 •1009 -.I066 -.1160 -. 1233 -. 1306 -.1368 -•1430 - .1493 -•2101 - .2229 -.2229 .1556 .1699 -. 1974 - •2050 -. 2140 -.2245 -. 2350 -. 2425 30. O0 .1740 •1740 -.1840 -.1960 -. 2980 .2500 .2640 -. 2770 -.2875 -.2980 50•00 ,2827 •2827 -. 2893 -.2973 -. 3033 -.3093 -.3163 - .3233 - .3283 .3333 .3427 -.3513 -.3583 - .3653 - .3653 60. O0 .3370 •3370 -.3420 -.3480 -.3525 -. 3570 -.3623 - .3675 - . 3713 .3750 .3820 -.3885 -.3938 -. 3990 - .3990 -.3987 - .4017 -.4047 -.4082 -.4117 -.4142 70. O0 .3913 .3913 -. 3947 .4167 .4213 - .4257 -.4292 -.4327 -. 4327 80. O0 .4457 •4457 - .4473 -.4493 - .4508 -.4523 -.4541 -.4558 -.4571 -•4646 -. 4663 -•4663 .4583 .4607 -. 4628 90. 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.1187 .1343 .1417 .1560 .1707 .1784 .1804 .1801 .1801 -8.00 .0351 .0351 .0387 .0434 .0485 .0812 .1025 .1196 .1265 •1416 .1563 .1629 .1646 .1644 .1644 -7.00 .0319 .0319 .0349 .0388 .0417 .0634 .0864 .I048 .1113 • 1272 .1419 .1474 .1489 .1487 .1487 -6.00 .0290 .0290 .0315 .0347 .0369 .0466 .0704 .0900 .0962 .1128 .1274 .1320 .1331 .1330 .1330 -5.00 .0263 .0263 .0283 .0310 .0327 .0342 .0546 .0753 .0811 • 0985 .1130 .1165 .1174 .1173 .1173 -4.00 .0239 .0239 .0255 .0276 .0290 .0307 .0398 .0607 .0660 .0841 .0986 .I011 .1017 .1016 .1016 -3.00 .0217 .0217 .0230 .0246 .0256 .0270 .0287 .0463 .0512 .0697 .08_3 .0858 .0862 .0861 .0861 -2.00 .0199 .0199 .0207 .0219 .0227 .0237 .0250 .0330 .0374 • 0551 .0704 .0709 .0711 .0711 .0711 -I.00 .0182 .0182 .0188 .0196 .0202 .0209 .0218 .0232 .0265 .0407 .0574 .0574 .0574 .0574 .0574 .00 .0168 .0168 .0171 .0176 .0180 .0185 .0191 .0200 .0215 • 0288 .0461 .0461 .0461 .0461 .0461 1.00 .0157 .0157 .0158 .0160 .0162 .0165 .0169 .0175 .0185 • 0213 .0347 .0347 .0347 .0347 .0347 2.00 .0148 .0148 ,0147 .0147 .0148 .0149 .0152 .0155 .0161 .0173 .0240 .0240 .0240 .0240 .0240 3.00 .0142 .0142 .0140 .0138 .0138 .0138 .0139 .0141 .0145 • 0152 .0187 .0187 .0187 .0187 .0187 4.00 .0138 .0138 .0135 .0132 .0132 .0131 .0131 .0132 .0135 .0141 .0217 .0217 .0217 .0217 .0217 5.00 .0137 .0137 .0133 .0130 .0129 .0128 .0128 .0129 .0131 .0154 .0302 .0302 .0302 .0302 .0302 6.00 .0138 .0138 .0134 .0132 .0131 .0130 .0130 .0131 .0138 • 0213 .0426 .0426 .0426 .0426 .0426 7.00 .0142 .0142 .0139 .0137 .0136 .0136 .0137 .0140 .0178 • 0312 .0498 .0498 .0498 .0498 ,0498 8.00 .0148 .0148 .0146 .0145 .0146 .0147 .0149 .0165 .0258 • 0428 .0681 .0692 .0695 .0694 .0694 9.00 .0157 .0157 .0156 .0158 .0159 .0162 .0170 .0228 .0366 .0456 .0938 .0965 .0973 .0972 .0972 10.00 .0169 .0169 .0170 .0174 .0177 .0182 .0217 .0325 .0492 .0679 .1218 .1265 .1277 .1276 ,1276 11.00 .0183 .01_ .0187 .0194 .01_ .0218 .0301 .0449 .0796 .1021 .1506 .1573 .1590 .1589 .1589 12.00 .0201 .0201 .0206 .0218 .0229 .0290 .0418 .0829 .1194 • 1398 .1797 .1883 ,1907 .1907 .1907 13.00 .0221 .0221 .0231 .0247 .0283 .0399 .0566 .1339 .1616 .1782 .2086 .2191 .2224 .2230 .2230 14.00 .0245 .0245 .0259 .0285 .0380 .0547 .1369 .1860 .2030 • 2155 .2369 .2494 .2544 .2568 .2568 15.00 .1112 .1112 .1546 .1866 .1995 .2124 .2210 .2296 .2387 .2482 .2634 .2T;'6 .2868 .2948 .2948 16.00 .1602 .1602 .1862 .2126 .2254 .2381 .2460 .2539 .2621 .2706 .2848 .2998 .3161 .3346 .3346 21.00 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3350 .3400 .3400 30.00 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 50.00 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 60.00 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 70.00 1.6420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.6420 1.8420 1.6420 1.8420 1.8420 1.8420 1.8420 1.6420 80.00 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 90.00 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2,0220 2.0220 2.0220 100.00 2.0220 2.0220 2,0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 110.00 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 120.00 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520.1.6520 1.6520 1.6520 1.6520 1.6520 140.00 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 160.00 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 170.00 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 180.00 .0220 .0220 .0220 .0220 ,0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 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2.0220 2.0220 2.0220 2.0220 2,0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2,0220 100.00 2,0220 2.0220 2.0220 2.0220 2.0220 2,0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2,0220 110.00 1.8520 1.8520 1.8520 1.8520 1.8520 1,8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1,8520 1,8520 120.00 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1,6520 140.00 1.0420 1.0420 1.0420 1.0420 1.0420 1,0420 1.0420 1.0420 1.0420 1.0420 1.0420 1,0420 1.0420 1.0420 1.0420 160.00 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 170.00 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .]320 .1320 .1320 .1320 ,1320 180.00 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 ,0220 .0220 .0220 .0220 .0000 .2000 .3000 .4000 .4500 ,5000 .5500 .6000 .6500 .7000 .7500 .8000 .8500 .9000 1,0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 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.3320 .3320 .3320 .3320 .3320 .3320 .3320 .3320 .3350 .3400 .3400 30.00 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 .5620 50.00 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 1.3920 60.00 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 1.6620 70.00 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 1.8420 80.00 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 1.9620 90.00 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 100.00 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 2.0220 110.00 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 1.8520 120.00 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 1.6520 140.00 1.0420 1.0420 1.0420 1.0420 1.8420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 1.0420 160.00 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 .3020 • 3020 .3020 .3020 .3020 .3020 .3020 170.00 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 .1320 • 1320 .1320 .1320 .1320 .1320 .1320 180.00 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 .0220 • 0220 .0220 .0220 .0220 .0220 .0220 • 0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 .6500 .7000 .7500 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .OODO .0000 .0000 .0000 .0000 .0000 .0000 -170.00 .4000 .4000 .4000 .4000 .4000 .4000 .4000 .4000 .4000 • 4000 .4000 .4000 .4000 .4000 .4000 -160.00 .30DO .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 .3000 -140.00 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 .4600 -120.00 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 -110.00 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 -100.00 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 -90.00 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 .5000 -80.00 .4457 .4457 .4473 .4493 .4508 .4523 .4541 .4558 .4571 • 4583 .4607 .4628 .4646 .4663 .4663 -70.00 .3913 .3913 .3947 .3987 .4017 .4047 .4082 .4117 .4142 • 4167 .4213 .4257 .4292 .4327 .4327 -60.00 .3370 .3370 .3420 .3480 .3525 .3570 .3623 .3675 .3713 .3750 .3820 .3885 .3938 .3990 .3990 -50.00 .2827 .2827 .2893 .2973 .3033 .3093 .3163 .3233 .3283 • 3333 .3427 .3513 .3583 .3653 .3653 -30.00 .1740 .1740 .1840 .1960 .2050 .2140 .2245 .2350 .2425 .2500 .2640 .2770 .2875 .2980 .2980 -21.00 .1009 .1009 .1066 .1160 .1233 .1306 .1368 .1430 .1493 .1556 .1699 .1974 .2101 .2229 .2229 -16.00 .0730 .0730 .0780 .0860 .0915 .0970 .1025 .1080 .1125 .1170 .1370 .1760 .1880 .2000 .2000 -15.00 .0540 .0540 .0650 .0730 .0785 .0840 .0905 .0970 .1040 .1110 .1330 .1730 .1840 .1950 .1950 -14.00 .0938 .0938 .0868 .0715 .0763 .0820 .0887 .0945 .1027 .1110 .1335 .1730 .1833 .1935 .1935 -13.00 .0914 .0914 .1043 .0768 .0809 .0867 .0928 .0976 .I061 .1145 .1366 .1749 .1845 .1942 .1942 -12.00 .0992 .0992 .1139 .0842 .0876 .0935 .0988 .1028 .1111 .1194 .1407 .1774 .1866 .1958 .1958 -11.00 .1057 .I057 .1057 .0921 .0951 .I010 .I054 .I088 .1168 .1248 .1452 .1802 .1889 .1976 .1976 -10.00 .1188 .1188 .1110 .1003 .1028 .1087 .1122 .1152 .1228 1304 .1498 .1831 .1913 .1996 .1996 -9.00 1339 .1339 .1197 .I085 .1105 .1164 .1190 .1216 .1288 1360 .1544 .1860 .1938 .2017 .2017 -8.00 1436 .1436 .1279 .1167 .1183 .1242 .1259 .1281 .1349 1417 .1591 .1889 .1963 .2037 .2037 -7.00 1525 .1525 .1361 .1250 .1261 .1320 .1327 .1346 .1410 1474 .1638 .1918 .1988 .2058 .2058 -6.00 1608 .1608 .1442 .1332 .1340 .1398 .1396 .1411 .1471 .1531 .1685 .1948 .2013 .2079 .2079 -5.00 .1713 .1713 .1523 .1414 .1418 .1476 .1464 .1476 .1532 .1588 1731 .1977 .2038 .2090 .2099 -4.00 .1784 1784 .1604 .1497 .1496 .1554 .1533 .1541 .1593 .1645 1778 .2006 .2063 .2120 .2120 -3.00 .1846 1846 .1685 .1579 .1574 .1632 .1602 .1606 .1654 .1702 1825 .2036 .2088 .2141 .2141 -2.00 .1900 1900 .1766 .1662 .1652 .1710 .1670 .1671 .1715 .1760 1872 .2065 .2113 .2161 .2161 -1.00 .1944 1944 .1847 .1744 .1730 .1788 .1739 .1736 .1776 .1817 1919 .2095 .2138 .2182 .2182 .00 .1987 1987 .1927 .1826 .1808 .1866 .1807 .1801 .1837 •1874 1966 .2124 .2163 .2203 .2203 1.00 .2012 .2012 .2003 .1908 .1886 .1943 .1876 .186(5 .1898 .1931 .2013 .2153 .2188 .2223 .2223 2.00 .2043 .2043 .2065 .1988 .1964 .2021 .1946 .1931 .1959 .1988 .2060 .2183 .2213 .2244 .2244 3.00 .2071 .2071 .2098 .2064 .2041 .2097 .2018 .1996 .2021 .2045 .2106 .2212 .2238 .2265 .2265 4.00 .2095 .2095 .2127 .2132 .2115 .2170 .2098 .2061 .2082 .2102 .2153 .2242 .2264 .2285 .2285 5.00 .2112 .2112 .2147 .2193 .2185 .2232 .2190 .2126 .2143 .2159 .2200 .2271 .2289 .2306 .2306 6.00 .2130 .2130 .2167 .2216 .2247 .2273 .2268 .2191 .2203 •2216 .2247 .2300 .2314 .2327 .2327 7.00 ,2138 .2138 .2177 .2237 .2273 .2304 .2316 .2255 .2264 •2272 .2294 .2330 .2339 .2348 .2348 8.00 .2142 .2142 .2184 .2249 .2287 .2324 .2353 .2318 .232.3 .2328 .2340 .2360 .2366 .2371 .2371 9.00 .2144 .2144 .2187 .2255 .2297 .2339 .2377 .2377 .2379 .2381 .2385 .2392 .2394 .2395 .2395 10.00 .2143 .2143 .2190 .2258 .2301 .2351 .2399 .2427 .2427 •2427 .2427 .2427 .2427 .2427 .2427 11.00 .2140 .2140 .2183 .2260 .2305 .2_2 .2428 .2431 .2431 .2431 .2431 .2431 .2431 .2431 .2431 12.00 .2134 .2134 .2187 .2261 .2309 .2378 .2446 .2395 .2395 •2395 .2395 .2395 .2395 .2395 .2395 13.00 .2127 .2127 .2177 .2259 .1428 J2390 .2426 .2309 .2.309 .2309 .2309 .2309 .2309 .2309 .2309 14.00 .2116 .2116 .2173 .2259 .0166 .2382 .2376 .0680 .0641 .0601 .0488 .0288 .0235 .0182 .0182 15.00 -.0540 -.0540 -.0650 -.0730 -.0785 -.0840 -.0905 -.0970 -.1040 -.1110 -.1330 -.1730 -.1840 -.1950 -.1950 16. 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.0000 .0000 .0000 .0000 .0000 .2000 .3000 .4000 .4500 .5000 .5500 .6000 .6500 .7000 .7500 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 • 0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -170.00 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -160.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .O000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -140.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -120.00 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -110.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -I00.00 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -90.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 -80.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 • 0000 .0000 -70.00 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -60.00 .0000 ".0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -50.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -30.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -21.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 •0000 .0000 -16.00 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 m " O O O 0 .0000 -15.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -14.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -13.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -12.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -11.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -I0.00 .0000 .0000 .0000 .0000 o0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -9.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -8.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -7.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -6.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -5.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -4.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 °0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -3.00 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 • 0000 .0000 -2.00 .0000 .0000 • 0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -I.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 1.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 2.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 3.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 ,0_0 .0000 .0000 .0000 .0000 .0000 .0000 4.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 5.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 6.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 7.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 8.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 9.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 • 0000 .0000 .0000 .0000 .0000 .0000 10.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 11.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 12.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 ,0000 .0000 13.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 14.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 15.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 16.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 21.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 30.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 •0000 .0000 .0000 .0000 .0000 .0000 50.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000".0000 .0000 .0000 .0000 .0000 .0000 .0000 60.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 • 0000 .0000 .0000 .0000 .0000 .0000 70.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 80.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 90.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 ._00 .0000 •0000 .0000 .0000 .0000 .0000 .0000 100.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 110.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 120.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 140.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 ".0000 • 0000 .0000 .0000 .0000 .0000 .0000 I_,00 .0000 .0000 .0000 .0000 °0000 .0000 .00(]0 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 170.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .2000 .3000 .4000 .4500 .SO00 .5500 .6000 .6500 • 7000 .7500 .8000 .8500 .9000 1.0000 -180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 -170.00 .0008 .0008 .0009 .0006 .0006 .0007 .0006 .000(5 .0006 .0006 .0006 .0006 .0006 .0006 .0006 -160.00 .0017 .0017 .0018 .0013 .0013 .0013 .0012 .0012 .0012 • 0012 .0012 .0012 .0012 .0012 .0012 -140.00 .0034 .0034 .0036 .0026 .0025 .0026 .0023 .0024 .0024 .0024 .0024 .0024 .0024 .0024 .0024 -120.00 .0051 .0051 .0054 .0038 .0038 .0040 .0035 .0035 .0035 • 0035 .0035 .0035 .0035 .0035 .0035 -110.00 .0059 .0059 .0063 .0045 .0044 .0046 .0041 .0041 .0041 .0041 .0041 .0041 .0041 .0041 .0041 -100.00 .0067 .0067 .0072 .0051 .0050 .0053 .0047 .0047 .0047 .0047 .0047 .0047 .0047 .0047 .0047 -90.00 .0076 .0076 .0081 .0058 .0057 .0059 .0053 .0053 .0053 • 0053 .0053 .0053 .0053 .0053 .0053 -80.00 .0084 .0084 .00990 .0064 .0063 .0066 .0059 .0059 .0059 .0059 .0059 .0059 .0059 .0059 .0059 -70.00 .0093 .0093 .0099 .0070 .0069 .0073 .0065 .0065 .0065 .0065 .0065 .0065 .0065 .0065 .0065 -60.00 .0101 .0101 .0108 .0077 .0076 .0079 .0070 .0071 .0071 .0071 .0071 .0071 .0071 .0071 .0071 -50.00 .0110 .0110 .0117 .0083 .0082 .0086 .0076 .0077 .0077 .0077 .0077 .0077 .0077 .0077 .0077 -30.00 .0127 .0127 .0135 .0096 .0095 .00_ .008,8, .0_ .00_ .0088 .0088 .0088 .0088 .0088 .0088 -21.00 .0134 .0134 .0143 .0102 .0100 .0105 .0093 .0094 .0094 •0094 .0094 .0094 .0094 .0094 .0094 -16.00 .0138 .0138 .0147 .0105 .0103 .0108 ,0096 .0097 .0097 .0097 .0097 .0097 .0097 .0097 .0097 -15.00 .0139 .0139 .0148 .0105 .0104 .0109 .0097 .0097 .0097 .0097 .0097 .0097 .0097 .0097 .0097 -14.00 .0140 .0140 .0149 .0106 .0105 .0109 .0097 .0098 .0098 .0098 .0098 .0098 .0098 .0098 .0098 -13.00 .0121 .0121 .0151 .0107 .0105 .0110 .0098 .0098 .0098 .0098 .0098 .0098 .0098 .0098 .0098 -12.00 .0119 .0119 .0149 .0107 .0106 .0111 .0099 .0099 .0099 .0099 .0099 .0099 .0099 .0099 .0099 -11.00 .0117 .0117 .0117 .0108 .0107 .0111 .0099 .0100 .0100 .0100 .0100 .0100 .0100 .0100 .0100 -10.00 .0119 .0119 .0114 .0109 .0107 .0112 .0100 .0100 .0100 .0100 .0100 .0100 .0100 .0100 .0100 -9.00 .0125 .0125 .0115 .0109 .0108 .0113 .0100 .0101 .0101 .0101 .0101 .0101 .0101 .0101 .0101 -8.00 .0126 .0126 .0116 .0110 .0108 .0113 .0101 .0101 .0101 .0101 .0101 .0101 .0101 .0101 .0101 -7.00 .0127 .0127 .0118 .0111 .0109 .0114 .0102 .0102 ,0102 .0102 .0102 .0102 .0102 .0102 .0102 -6.00 .0128 .0128 .0119 .0111 .0110 .0115 .0102 .0103 .0103 •0103 .0103 .0103 .0103 .0103 .0103 -5.00 .0131 .0131 .0120 .0112 .0110 .0115 .0103 .0103 .0103 .0103 .0103 .0103 .0103 .0103 .0103 -4.00 .0132 .0132 .0122 .0113 .0111 .0116 .0103 .0104 .0104 .0104 .0104 .0104 .0104 .0104 .0104 -3.00 .0133 .0133 .0123 .0113 .0112 .0117 .0104 .0104 .0104 • 0104 .0104 .0104 .0104 .0104 .0104 -2.00 .0133 .0133 .0124 .0114 .0112 .0117 .0104 .0105 .0105 .0105 .0105 .0105 .0105 .0105 .0105 -1.00 .0133 .0133 .0125 .0114 .0113 .0118 .0105 .0106 .0106 .0106 .0106 .0106 .0106 .0106 .0106 .00 .0132 .0132 .0126 .0115 .0113 .0119 .0106 .0106 .0106 .0106 .0106 .0106 .0106 .0106 .0106 1.00 .0131 .0131 .0128 .0116 .0114 .0119 .0106 .0107 .0107 .0107 .0107 .0107 .0107 .0107 .0107 2.00 .0130 .0130 .0129 .0116 .0115 .0120 .0107 .0107 .0107 • 0107 .0107 .0107 .0107 .0107 .0107 3.00 ,0129 .0129 .0128 .0117 .0115 .0121 .0107 .0108 .0108 .0108 .0108 .0108 .0108 .0108 .0108 4.00 .0129 .0129 .0128 .0121 .0116 .0121 .0108 .0108 .0108 .0108 .0108 .0108 .0108 .0108 .0108 5.00 .0127 .0127 .0127 .0126 .0120 .0122 .0113 .0109 .0109 •0109 .0109 .0109 .0109 .01_ .0109 6.00 .0126 .0126 .0126 .0125 .0124 .0122 .0117 .0110 .0110 •0110 .0110 .0110 .0110 .0110 .0110 7.00 .0124 .0124 .0124 .0124 .0124 .0122 .0118 .0110 .0110 .0110 .0110 .0110 .0110 .0110 .0110 8.00 .0122 .0122 .0122 .0123 .0123 .0121 .0119 .0111 .0111 .0111 .0111 .0111 .0111 .0111 .0111 9.00 .0120 .0120 .0120 .0121 .0121 .0120 .0118 .0111 .0111 • 0111 .0111 .0111 .0111 .0111 .0111 10.00 .0118 .0118 .0119 .0119 .0119 .0119 .0117 .0112 .0112 • 0112 .0112 .0112 .0112 .0112 .0112 11.00 .0115 .0115 .0115 .0117 .0117 .0118 .0117 .0110 .0110 .0110 .0110 .0110 .0110 .0110 .0110 12.00 .0113 .0113 .0115 .0115 .0116 .0117 .0115 .0106 .0106 .0106 .0106 .0106 .0106 .0106 .0106 13.00 .0110 .0110 .0112 .0113 .0115 .0115 .0113 .0099 .0099 .0099 .0099 .0099 .0099 .0099 .0099 14.00 .0108 .0108 .0110 .0111 .0115 .0113 .0110 .0098 .0098 .0098 .0098 .0098 .0098 .0098 .0098 15.00 .0107 .0107 .0109 .0110 .0114 .0112 .0109 .0098 .0098 .0098 .0098 .0098 .0098 .0098 .0098 16.00 .0107 .0107 .0109 .0110 .0113 .0112 .0109 .0097 .0097 .0097 .0097 .0097 .0097 .0097 .0097 21.00 .0103 .0103 .0105 .0106 .0110 .0108 .0105 .0094 .0094 .0094 .0094 .0094 .0094 .0094 .0094 30.00 .0098 .0098 .0099 .0100 .0104 .0102 .0099 .0089 .0089 •0089 .0089 .0089 .0089 .0089 .0089 50.00 .0085 .0085 .0086 .0087 .0090 .0088 .0086 .0077 .0077 .0077 .00_ .007-/ .0077 .0077 .0077 60.00 .0078 .0078 .0080 .0080 .0083 .0082 .0080 .0071 .0071 .0071 .0071 .0071 .0071 .0071 .0071 70.00 .0072 .0072 .0073 .0074 .0076 .0075 .0073 .0065 .0065 .0065 .0065 .0065 .0065 .0065 .0065 80.00 .0065 .0065 .0066 .0067 .0069 .0068 .0066 .0059 .0059 .0059 .0059 .0059 .0059 .0059 .0059 90.00 .0059 .0059 .0060 .0060 .0062 .0061 .0060 .0053 .0053 .0053 .0053 .0053 .0053 .0053 .0053 100.00 .0052 .0052 .0053 .0053 .0055 .0054 .0053 .0047 .0047 .0047 .0047 .0047 .0047 .0047 .0047 110.00 .0046 .0046 .0046 .0047 .0048 .0048 .0046 .0041 .0041 .0041 .0041 .0041 .0041 .0041 .0041 120.00 .0039 .0039 .0040 .0040 .0041 .0041 .0040 .0036 .0036 • 0036 .0036 .0036 .0036 .0036 .0036 140.00 .0026 .0026 .0027 .0027 .0028 .0027 .0027 .0024 .0024 .0024 .0024 .0024 .0024 .0024 .0024 160.00 .0013 .0013 .0013 .0013 .0014 .0014 .0013 .0012 .0012 • 0012 .0012 .0012 .0012 .0012 .0012 170.00 .0007 .0007 .0007 .0007 .0007 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0006 .0006 .0006 180.00 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000 .0000
Appendix 8
Appendix 8
Listing of "UTIL" Code
PROGRAM UTIL C ............................ ° ...... " ................................ " ......... C C THIS PROGRAM CONTAINS A HUNBER OF UTILITIES WHICH FACILITATE THE C C GENERATION OF 2-0 AIRFOIL AEROOYNANICS DATA TABLES IN C-81 FORMAT C C ............................................ " .............................. _--C C WRITTEN BY C C OR. AHNED A. HASSAN C C MCDONNELL DOUGLAS HELICOPTER SYSTEMS C C MESA, ARIZONA 85205 C C (602) 891-6069 C C .................................................. " ........................... C PARAMETER (1M=15,, IA=IO0) COMMON /AHM4/8ASE, NULT, AL FNAX, AL FM[ N LOGICAL BASE,NULT BASE : .FALSE.
NULT : . FALSE.
ALFRAX = 15.0 ALFMIM : -15.0 [IdRT : 1 CALL COMBINE (I_RT) CALL PCLCDCJ4 CALL FILL1 CALL BLEND CALL OUTC81 STOP 777 ENO SUgROUTINE COMBINE (IURT) PARAMETER (IM-'-15, IA:IO0) COMMON /AHM1/ MCL(IM)wANGCL(|A),CL(IM,,IA),NMCL,NANGCL,CLF{IM, IA), MCM(IM).ANGCM(IA),CM(IM, IA) ,NMCM,NANGCM,CHF( IN, IA) **CONRON MCD(IN),ANGCD( IA),CO(IM, IA),NMCD,NAMGCD,CDF(IM, Ik), /AHMS/ IDENT, IDENT2,tDUNA(IM) REAL NCL oMCD, NCN CHARACTER*30 IOENTt ]DENT2 C .......................... ° ...... "-" ...... " ..... " ............................. C C BEGIN SEGMENT TO READ IN C81 TABLES C C ........ " .......... " ...... " ...... " .......... "-°-" ...... "-" ...... °'" ...... " .... C OPEN (12,FILE='nacaO012-1.c81 s, FOI_-IFORNATTED',STATUS=eUMKNOi4N ') OPEN (13, Fi LE=enacaO012-2.c81 p, FORM= e FORMATTED' ,STATUS=IUNKNOWII _ ) OPEN ( 14, FILE='nacaO012-].c81 ', FORM= t FORMATTED _ ,STATUS=eUNKNOMN a ) READ (13,101) IDENT,NMCL,NANGCL,NMCD,NANGCO,NMCN,NANGCN, |DENT2 READ (12,101) IDENT,NMCL,NANGCL,MNCD,NANGCD,MNCM,MANGOt, IDENT2 NMCL = NMCL + 5 NMCD : NMCD + 5 NMCM : NMCM ÷ 5 |F ([_IRT.EQ.1) THEN WRITE(I/*, 101) IDENT,NMCL,NANGCL,)_ICDoNANGCD,NNCMeNANGCN, IDENT2 ENDIF C ........ ° ................. " ............... " ..................... ° .............
C READ CL VALUES C C ........ ° ................. " ........ " ...... ° ..... " ............... " ............. C READ (12,102) (MCL(1),I:I,IO) READ (1],102) (MCL(I),I=ll,NMCL) IF (]WRT.EQ.1) THEN WRITE (1/,.102) (MCL(I),I=I,NMCL) ENDIF DO 200 IANG=I,NANGCL DO 199 IMO=I,NMCL,9 IMI:IMO IMF--MIN( IMO+B,MNCL ) IF (IMO .EQ. 1) THEN READ (12,103) ANGCL(IANG),(CL(IMI,IANG),IMI:IMI,IMF) IF (IWRT.EQ.I) THEN WRITE (1/% 10]) ANGCL ( IANG), (CL( IN1, |ANG), IHl=lMI, IMF) END [ F ELSE READ (12,102) (CL(IM1 , IANG) , ]M1=10,10) READ (13,103) ANGCL(IANG),(CL(IMl,iAMG),IMl=ll,IMF) IF (IURT.EQ.1) THEN _ITE (14,102) (CLCIMI,IANG),IMI:IMI,IMF) ENDI F EMOIF 199 CONTINUE 200 CONTI HUE C .......................... ° ............... " ..... " ...... ° ...................... C C READ CO VALUES C C ................... " ............................................ " ........ " .... C READ (12,102) (MCD(I),I=I,IO) READ (13,102) (MCD(1),Z=ll,HNCD) IF (I_RT.EQ.1) THEN '_ITE (14,102) (MCD(I),I=I,NHCD) EMDIF DO 300 IANG=I,NANGCD D0299 IMO=I,NMCD,9 ]MI=INO IMF=MIN(IMO+8,NNCD) IF (IHO .EQ. 1) THEN READ (12,103) ANGCD(IANG),(CD(IMI,IANG),IMI=IHI,IMF) IF (|WRT.EQ.1) THEN I.IRITE (14,103) ANGCD(IANG),(CD(iMI,IANG),IMI=]M|,IMF) ENDIF ELSE READ (12,102) (CO(IMI,IANG),INI=IO, IO) READ (15,10]) ANGCD(IANG),(CD(IMl,IANG),iM1=11,%MF) IF (IMRT.EQ.1) THEM WRITE (14,102) (CD(IMI,IANG),IMI=[M|,IMF) ENDIF EMDIF 299 CONT] HUE 300 CONT|MUE C .............................................................. " ............... C C READ 014 VALUES C C .............................................................................. C READ (12,102) (MCH([),]=I,IO) READ (13,102) (MCM(Z),I=ll,NMCH) IF (I_RT.EQ.1) THEN WRITE(14,102) (MCM(I),I=I,NNCM) ENDIF DO 400 IANG = 1,NANGCM DO 399 IMO=leNMCH,9 IMI=JMO IMF=MiN(IMO÷8.NMCM) IF (]MO .EQ. 1) THEN READ (12,103) ANGCM(IANG),(CM([MI,IANG),IMI=IM[,IMF) IF (]i./RT.EQ.1) THEN WRITE (14,10]) ANGCM(%ANG),(CM(|MI,|ANG),]MI=|M[,IMF) ENDIF ELSE READ 412,102) (C14(IN1,IANG),IN1=10,10) READ (13,103) ANGCM(IANG),(CH(IMlaIANG),IMl=ll,IMF) IF (IWRT.EQ.1) THEN WRITE (14,102) (CM(IMI,IAHG),IMI=IMI,IMF) ENDIF ENDIF 399 CONTINUE 400 CONTINUE CLOSE (12) CLOSE (13) CLOSE 414) c WRITE (66,500) 4(CL(|,J),J=I,NANGCL),]=I,NMCL) c _R]TE (66, _) c WRITE (66,500) ((C/)(|,J),J=I,NANGCD),]=I,NMCO) c IgRI TE (66,*) c MR%TE (66,500) ((CM(I,J).J=I,NANGCN),[=I,NMCI4) c MR%TE (66,*) 101 FORHAT(A]O.612.A30) 102 FORNAT(TX,9FT.4) 103 FORHAT(F7.2,9FT.4] 500 FORRAT ((SX,'* ',8(F7.4,1N,))) RETURN END SUBROUTINE PCLCDCM C .............................................................................. C C THIS SUflROUT|NE HANDLES THE PREDICTED AEROOYNAHIC COEFF%CIENTS C C .............................................................................. C PARAMETER (]M=15,]A=lO0) CO_N /AHH2/ PCL(]M,]A)o PCO(]M,]A), PCH(]M, ZA), * PCLF(IM,IA),PCOF(IN, IA).PCHF(IN,IA), * AOA(IA),MACH(IN) REAL MACH C(_4MON /AHM4/ BASE,MULT,ALFNAX,ALFM[N LOGICAL BASE,NULT OPEN (1S,FILE=°LOADS.TBL',FORM='FORHATTED',STATUS='OLD s ) I l e I OPEN 416, FILE='LOADS.OUT ',FORM= FORMATTED ,STATUS= UNKNC_M ) C .............................................................................. C C READ THE PREDICTED VALUES FOR EACH NACH NUMBER C C .............................................................................. C READ (15,*) READ (15,*) NHACH READ (15,*) DO 20 M = 2 , NMACH - 1 READ (15,*) NAOA DO 21N = 1 , NAOA READ (15,*) MACH(R),AOA(N),PCL(M,N),PCD(N,N),PCM(M,N), * PCLF(M,N),PCOF(M,N),PCHF(M,N) 21 CONTINUE C "'° .......................................................... " ................ C C THE FOLLOWING STATEMENTS ARE ONLY APPLICABLE TO THE SYMMETRIC C C BASELINE (I.E., UNFLAPPED) NACA-O015 AIRFOIL C C''" ........................................................................... C IF (BASE) THEN NALFA : 2 * NAOA - 1 ELSE NALFA = NAOA END XF |,'RITE(16,600) NALFA IF (BASE) THEN DO Z2 N = NAOA , 2 , -1 WRITE (16,601) NACH(N),-AOA(N),-PCL(N,N),PCD(M,N),-PCM(M,N), * "PCLF(M,N),PCDF(M,N),'PCHF(M,N) 22 CONTINUE END IF DO 23 N : 1 , NAOA WRITE (16,601) NACH(M),AOA(N)rPCL(M,N),PCD(M,N),PCM(N,N) , * PCLF(M,N),PCDF(M,N),PCHF(M,N) 23 CONTINUE 20 CONTINUE CLOSE (15) CLOSE (16) 600 FORMAT (SX,13) 601 FORMAT (FT.4,2X, F6.2,6(2X,FT.4)) RETURN END SUBROUTINE FILL1 PARAMETER (IM=15,IA=IO0) C ..................................... - ........................................ C C THIS SUBROUTINE REPLACES THE NACA-O012 AEROOYNAMICSCOEFFICIENTS C C _ITH THE PREDICTED VALUES IN THE ANGLE OF ATTACK AND MACH NUMBER C C RANGES FOR THE PRED|CTIONS C C ............................ - ................................... - ............. C COH_ /AHM1/ NCL(IM),ANGCL(IA),CL(IM,IA),NMCL,NANGCL,CLF(IM,]A), * MCD(]N),ANGCD(IA)_CD(IN, IA).NMCD,NANGCD.CDF(IM, IA), * MCN(]M),ANGCH(IA),ON(IM, IA),NMCM,NANGCH,CHF(IM,[A) COMMON /AHH2/ PCL([M, IA), PCD(]M, IA), PCM(]M,|A), * PCLF(]M, IA),PCDF(IN, IA),PCHF(IM,|A), * AOA(]A)rNACH(IN) CoNIqON /AHN3/ IDENToIDENT2,1DUNA(IM) COFg40N /AHH4/ BASE,NULT,ALFNAX,ALFMIN LOGICAL BASE,NULT CHARACTER*30 IDENT,IDENT2 REAL MCL,ROD,MCIq,NACH OPEN (16, FILE='LOADS.OUT',FORM=tFORRATTED',STATUS=IUNIOIOUN ' ) C .......................................... - ................................... C C FOR THE AIRFOIL COEFFICIENTS C C ..... " ................... *--o ................................... *--- .......... C C FIRST ZERO OUT ALL VALUES ]N THE ANGLE OF ATTACK ANDMACH NUMBER C C RANGES FOR THE PRED]CTED DATA. TH]S ENABLES SEE|NG MORE CLEARLY C C THE VALUES TO BE O6TAINED THROUGH INTERPOLATION C C ......................... _--* ....... - ..... ---- ................................ C C FOR THE FLAP COEFFICIENTS C C ..... " ............................................... - .......... - ............. C C ZERO OUT ALL TABLE VALUES SINCE NO VALUES FOR THE NACA-O012 AIRFOIL C C ARE KNOll4 C C ..... -°-- ..................................................................... C OO29N = 1 , NMCL DO 29 ] = 1 , NANGCL CLF(M,I) = 0.0 COF(M,I) = 0.0 CHF(R,I) = 0.0 IF (ANGCL(I).GT.ALFN|N.AND.ANGCL(I).LT.ALFMAX) THEN CL(Ms]) = 0.0 CO(H,I) = 0.0 CN(MtI) = 0.0 END !F 29 CONTINUE C ................................................................ ---- .......... C C START REPLACING THE NACA-O012 A!RFO|L DATA WITH THE PREDICTED VALUES C C ......................... " ........................... " .......... "--" .......... C C NOTE: C C THE PREO|CTEO DRAG VALUES FOR THE INTEGRAL FLAP ARE NOT ACCURATE SINCE C C THEY DO NOT TAKE INTO ACCOUNT THE CONTRIBUTION OF THE FLAP'S LEADING C C EDGE WHICH IS BURIED |NTO THE AIRFOIL SECTION. THIS APPROXIMATION %S C C MADE TO ALLOt,/ FOR MOOELING OF THE FLAPPED AIRFOIL AS A SINGLE ELEMENT C C AIRFOIL. FOR A TWO-ELEMENT AIRFOIL, THE PREDICTED DRAG VALUES FOR THE C C FLAP ELEMENT SHOULD BE USED SINCE THEY ARE RELATIVELY ACCURATE. C C .............................................................................. C DO 27 M = 2 , NNCL - 1 READ (16, t) NALFA IDI.J_CM) = NALFA DO 26 J = 1 , NALFA READ (16,*) DUN,AOA(J),PCL(N,J),PCD(H,J),PCM(M,J), * PCLF(N,J),PCDF(N,J),PCHF(N,J) DO 25 I = 1 , MANGCL IF (ANGCL([).EQ.AOA(J) ) THEN CL(M,I) = PCL(N,J) CD(M,]) = PCD(M,J) CM(M,I) = PCM(M,J) CLF(N,I) = PCLF(N,J) CHF(M,I) = PCHF(M,J) IF (NULT) THEN CDF(N,I) = PCDF(M,J) END IF END IF 25 CONTINUE 26 CONTINUE 27 CONTINUE IDUHA(1) = ]DUHA(2) IDUHA(NMCL) = IDUKA(NMCL-1) C .............................................................................. C C FILL ARRAY VALUES FOR MINF=O AND MINF=I.0 C C .............................................................................. C DO 28 I = 1 , NANGCL CL(1,I) = CL(2, I) CD(1,1) CDC2, I) CM(1,[) CN(2,I) CLF(1,I) CLF(2,]) CDF(1,1) = CDF(2, I) CHF(1,1) CHF(2,1) CL(NNCL,I) = CL(NNCL-I,I) CD(NMCL,I) = CD(NMCL-I,I) CM(NMCL,I) = CN(NMCL-I,I) CLF(NMCL,I) CLFCNMCL-I,I) CDF(NMCL,I) = CDFCNMCL'I,I) CHF(NMCL,I) = CHF(NNCL-I,I) 28 CONT! HUE C ............................................................... _ .............. C C PRINT FOR CHECKOUT PRIOR TO INTERPOLATION C C .............................................................................. C WRITE (77,*) ' SECTIONAL LIFT VALUES • WRITE (77,110) (NCL(M),H=I,NMCL) DO 31 I = 1 . NANGCL WRITE (77,10_) ANGCL(I),(CL(M,I),M=I,NNCL) 31 CONTINUE WRITE (77,*) WRITE (7-/',*) ' SECTIONAL DRAG VALUES WRITE (77,110) (NCL(N),N=I,NNCL) DO 32 I = 1 , NAHGCL WRITE (77,100) ANGCL(I),(CD(N,I),M=I,NMCL) ]2 CONTINUE WRITE (77, t) I,_ITE (77,*) ' SECTIONAL NOMEHT VALUES i URITE (T[,110) (MCL(N),N=I,NHCL) DO 33 I = 1 , NANGCL WRITE (77,100) ANGCL(I),(C...M(M,I),M=I,NNCL) CONTINUE WRITE (77,*) _]TE (77,*) * FLAP LIFT VALUES WRITE (77,110) (MCL(N),M=I,NMCL) DO ]4 I = 1 , NANGCL WRITE (77,100) ANGCL(I),(CLF(M,I),N=I,NMCL) CONTINUE tA_ITE (77,*) WRITE (77,*) ' FLAP DRAG VALUES t/RITE (77,110) (NCL(N),M=I,NMCL) DO 35 I = I , NANGCL WRITE (77,100) ANGCL(I),(CDF(N,I),N=I,NMCL) ]5 CONTINUE WRITE (77,*) _ITE (77,*) ' FLAP HINGE VALUES WRITE (77,110) (NCL(N),N=I,NNCL) DO ]6 ] = 1 , NANGCL WRITE (77,100) ANGCL(I)o(CHF(M,I),N=I,NMCL) CONTINUE 100 FORMAT (F6.1,15(IX,F7.4)) 110 FORMAT (6X, 15(1X, F7.4)) 101 FORHAT (/L30,612./_0) 102 FORMAT(TX,9FT.4) 103 FORNAT(FT. 2,9F7.4) 500 FORMAT ((SX, e* ',8(F7.4,1H,))) CLOSE (16) RETURN ENO SUBROUT ] NE OUTC81 PARAMETER (IN=15, ]A=IO0) C ................ " ............................................................. C C THIS SUBROUTINE f_RITES THE FINAL C81 DATA TABLES WITH THE FITTED C C DATA FOR THE NAIN AIRFO]L SECTION AND FOR THE FLAP C C THIS SUBROUTINE ALSO GENERATES A DATA FILE SUITABLE FOR PLOTTING C C ON A NACTINTOSH C .C014_ /AHM1/ MCL(IN),ANGCL(IA),CL(IN, IA),NHCL,NANGCL,CLF(IM,IA), MCD(IM),ANGCD(IA), I_( ]H, [A), NNCD, NANGCD, CDF(IH, IA), * MCM( IN), ANGCM( ! A) ,CM( IN, |A), NMCM, NANGCM,CHF ( IK, IAt COMMON /AHM2/ PCL(IM, IA), PC::D(IM, IA)e PCM(IM, IA), * PCLF(IM, IA),PCDF(IH, IA), PCHF( IN, IA), * AOA(IA) ,HACK([M) CQI_ /AHNI/ IDENT,IDENT2, IDUNA(IM) CHARACTER*30 IDENT, IDENT2 REAL NCL,MCD,HCM,MACH OPEN (19,FILE:amain.c81 ', FORM:' FORMATTED', STATUS='UNKNO_/N' ) OPEN (20, FILE = ' f Lap. c81 ', FORM= _ FORMATTED ', STATUS=' UNKNO_ ' ) C--" ..................... " ............. ° ........................ " .............. C C FILL IN CL VALUES C C .............................................................................. C URITE (19,101) IDENT,NNCL,NANGCL,NHCJ),NANGCD,NMCH,NANGCH, IDENT2 WRITE (19,102) (MCL(I),I:I,NNCL) _ITE (20,101) IOENT,NNCL.NANGCLeNNCD,NANGCD,NMCH,NANGCM, ]DENT2 WRITE (20,102) (HCL(I),i=I,NNCL) DO 200 IANG=I,NANGCL DO 199 INO=I,NNCL,9 [NI:IMQ IMF=MIM(]NO+8,NHCL) IF (]MO .EQ. 1) THEN WRITE(19,103) ANGCL(]ANG) f ( CL( IN1, ]ANG), IMl=XMI, |HF) WRITE(20,103) ANGCL(IANG), (CLF(IH1, IANG), IHl=IMI, IMF) ELSE klRITE(19,102) (CL(IMI,IANG),INI=IMI,IHF) k)RI TE (20,102) (CLF( IN1 • ]AMG), ZMl=IM], IMF) ENDIF 199 CONTINUE 200 CONT 1 HUE C .............................................................................. C C FILL IN C1) VALUES C C ..................................................................... "''' ..... C WRITE (19,102) (Hr...D(]), i:I,NNCO) WRITE (20,102) (MCD(I),I=I,NMCO) DO 300 ]ANG=I,NANGCD DO 299 IMO=I,NNCO,9 INI=lMO ]NF:NIM(INO+8,NMCD) IF (IHO .EO. 1) THEN t,/RITE(19,103) ANGCO( IANG),( CO(IN1, IANG), IMI:IMI, |NF) WRITE(Z0,103) ANGOD(IANG), (COF(IM1, IANG), IMI=IMI, [MF) ELSE _RITE(19,102) (CD(IMI,IANG),INI=INI,INF) WITE(20,102) (CDF( I1(1, IANG), INl=lH[, INF) ENDIF 299 CONT 1 HUE 300 CONT I NUE C .............................................................................. C C FILL IN CN VALUES C C ..... ° .... " .............................. " .................................... C WRITE(19,102) (NCM(I), 1 :I,NMCH) WR]TE(20,102) (NC)f( [ ). I=1 ,NNCH) DO 400 IANG = 1,NANGCN DO 399 IMO:I,NMCM,9 INl:lNO |MF:MIN( I MO+8, NMCM) IF (IHO .EQ. 1) THEN URITE(19,103) ANGCM(IANG),( CH(IM1, IANG), |Ml=lMI, IMF) I_RITE(20,103) ANGCH(IANG), (CltF( 1M1, IANG), IMI=IMI, INF) ELSE _1TE(19,102) (CM(IHI,IANG),iMI=THI,IMF) _tRI TE(20,102) (CHF(IN1, IANG), IHl=lNI, IHF) ENDIF 399 CONTINUE 400 CONTINUE C ................................... ° .......................................... C C PRINT TABLES FOR HAC PLOTTING C C .............................................................................. C DO 31 = 1 , NANGCL I/RITE (88,100) ANGCL( I ), (CL(N, I ) .N=l, NMCL) 31 CONTI NUE WRITE (88, t) DO 32 1 . NANGCL I/RITE (88,106) ANGCL( I ), (CD(N, I ),N=l ,NMCL) 32 CONT I NUE I/RITE (88, t) DO 3] = 1 , NANGCL I/RITE (88,100) ANGCL(I ), (CM(M, l ),M=l ,NNCL) 33 CONTINUE WRITE (88, t) DO 34 = 1 , NANGCL I/RITE (88,100) ANGCL(I),(CLF(N, I),N=I,MHCL) CONT[ NUE I/RITE (88, t) DO 35 = 1 , NANGCL I/R I TE (88,100) ANGCL( [ ), (CgF(N, I ) ,N=l s NMCL) 35 CONT I NUE I/R I TE (88,_) DO ]6 1 . NANGCL I/R I TE (8;, 106) ANGCL( ] ), (CHF(M, ] ),N=l, NNCL) 36 CONT ! NUE 100 FORMAT (1X, F7.1,15(1X, F7.4)) 101 'FORMAT(_O. 6% 2._0) 102 FORMAT (TX,,9F7.4) 103 FORNAT(F7.2,9F7.4) 500 FORMAT ((5X,'* ',8(FT.4,1H,))) CLOSE (19) CLOSE (20) RETURN END SUBROUTINE BLEND PARAMETER (IH=15, ]A=IO0) C .............................................................................. C C THIS SUBROUTINE BLENDS IN THE NACA-O012 EXPERIMENTAL VALUES I/ITH C C THE PREDICTED VALUES. IT ALSO INTERPOLATES FOR THE UMKNOI/N AERO C C COEFFICIENTS FOR A GIVEN NACH NUMBER AT ALL THE USER DEFINED ANGLES C C OF ATTACK C C .............................................................................. C COMMON /ANN1/ MCL( ]N),rANGCL( ]A),,CL( IN, [A) ,NMCL,NANGCL,CLF ( IN, IA), * MCD(IN) rANGCD( |A),CO( IN, |A), NMCD, NANGCD,CDF ( IN,, I A) .
* MCN(IN),ANGCM(IA),CN(IN, IA), NMCM, NAMGCM, CHF(IH, %A) COMMON /AHN3/ ]DENT, IDENT2, IDUMA(IM) DIMENSION DUN( IO0).DUNCL (100), DUNCD ( IO0).DUNCN(100) DIMENSION DMCL F(IO0), DMCDF( IO0)rDMCHF (I00) DII'_ENSION BB(IOO),Y| (100) ,YP(100), YPP(100) DIMENSION ANG(IO0) CHARACTER*30 ]DENT,]DENT2 REAL MCL, MCD,,MCH DEBUG = 1.0 r" .............................................................................. C C DEBUG IS A FLAG USED TO OUTPUT A FILE TO UN|T 44 TO CHECK TI_E C C ORDERING OF THE COMBINED EXPERINENTAL-PRED|CTED DATA PRIOR TO C C THE INTERPOLATION PROCESS FOR A GIVEN NACH NUMBER AND ANGLE OF C C ATTACK C t" .............................................................................. C IF (DEBUG.EQ.O.O) THEN NSTART = 9 NEND = 9 ELSE NSTART = 1 MEND = NMCL END ] F DO 10 M = MSTART , MEND NPNTS = 16 + IDUMA(H) + 16 DO 11 I = 1 , 16 DUH(I ) = ANGCL(I) DUMCL(I) = CL(M,I) DUHCD(I) = CD(N_I) DUMCH(I) = CH(M,I) IF (NULT) THEN DMCLF(I) = CLF(N,I) DMCDF(]) = CDF(R,I) DMCHF(%) = CHF(M,I) ELSE ANG(1) = ANGCL(1) DHCLF(1) = CLF(N, 1) DHCDF(1 ) CDF(M, I ) DNCHF(1) = CHF(N,1) END IF 11 CONTINUE K = 16 L = 1 DO 12 ] = 17 , 45 C IF (CL(N,I).EQ.O.O.AND.ANGCL(1).NE.O.O) GO TO 12 For baseline onty IF (CL(H,I).EQ.O.O) GO TO 12 K=K+I DUN(K) = ANGCL(I) DUNCL(K) = CL(N,I) DUHCD(K) = CD(N,I) DUNCN(K) = C)I(N,I) IF (NULT) THEM DNCLF(K) = CLF(N,I) DNCDF(K) = COF(N,I) DNCHF(K) = CHF(N,I) ELSE L=L÷I ANG(L) = ANGCL(I) DNCLF(L) : CLF(H,I) DHCDF(L) : CDF(M,I) DHCHF(L) = CHF(N,I) END IF CONTINUE 12 DO 1_ ] = 46 , NANGCL DUN(K+1) = ANGCL(I ) DUHCL(K+I) = CL(N,I) DL_4CD(K+I) = CI)(N,I) DUNCM(K+I) = CH(M,I) IF (HULT) THEN DMCLF(K+I) = CLF(N,I) DMCDF(K+I ) = CDF(M, l ) DNCHF(K÷I) : CHF(M,I) ELSE ANGCL+I ) = ANGCL(NANGCL) DHCLF(L+I) = CLF(N,NANGCL) DNCDF(L+I) = CDF(N,NANGCL) OMCHF(L+I) = CHF(M,NANGCL) END IF K=K+I 13 CONT I HUE LP1 = L + I IF (DEBUG.EQ.I.O) THEM C _IIE (44,*) NPNTS C DO 150 I = 1 , NPNTS C WRITE (44,1;)0) ],DUR(Z),DURCL(]) C150 CONTINUE C WRITE (44,*) c URITE (44,'*) LP1 c DO 150 I = 1 , LP1 c RITE (44,120) [,ANGCI),DNCLF(I) c 150 CON T I HUE c MRITE (44,*) 120 FORMAT (SX, ' l =', 13,5X, 'AOA=', F6.1,SX, 'CLF=', F7.4) END I F KIOC = NANGCL ST = I0.0 C ......... ° ....................................................... " ..... _ ...... C C INTERPOLATE FOR AIRFOIL SECTIONAL LIFT VALUES C C .............................................................. °--° ............ C CALL TSPLINE (DUM,DUHCL,NPNTS,BB,ST, 1,KKK,AMGCL,YI,YP,YPP,XINT) DO 15 N = 1 , KKK CL(N,N) = YI(N) 15 CONTINUE C ................................................... ° .......................... C C INTERPOLATE FOR AIRFO;L SECTIONAL DRAG VALUES C C ............................... " .............................................. C CALL TSPLINE (DUH,DUHCD,NPNTS,BB,ST, 1,KKK,ANGCL,YI,YP,YPP,XINT) DO 16 N : 1 , KKK CO(M,N) = YI(N) 16 CONTINUE C ................................................... _ .......................... C C INTERPOLATE FOR AIRFOIL PITCHING I¢OHENT VALUES C C ......... ° .................................................................... C CALL TSPLINE (DU_I,DUIqCN,NPNTS,RB,ST, 1,KKK,AMGCL,YI,YP,YPP,XIHT) DO 17' N = I , KKK CH(ReN) = YI(N) 1T CONT | HUE C ......... ° .................................................... ° ............... C C FLAP CHARACTERISTICS C C ............................... " .............................................. C IF (RJLT) THEN C ............ " ............................................................. -o--C C *************** FOR A NULTI-ELERENT AIRFOIL ****************** C C .............................................................................. C C INTERPOLATE FOR FLAP SECTIONAL LIFT VALUES C C NOTE: FLAP SECTIONAL LIFT IS NC_RHALIZED BY THE AIRFOIL*S (I.E., NOT C C THE FLAPeS) CHORD LENGTH. C C ..................................................................... " ........ C CALL TSPLINE (DUM,DRCLF,NPNTS,BB,ST,I,KKK,ANGCL,Y[,YP,YPP,X]NT) DO 18 N = I , KKK CLF(N,N) = YI(N) 1B CORTINUE C .............................................................................. C C INTERPOLATE FOR FLAP SECTIONAL DRAG VALUES C C NOTE: FLAP SECTIONAL DRAG IS NORV.ALIZED BY THE AIRFOIL'S (I.E., NOT C C THE FLAP'S) CHORD LENGTH. C C .............................................................................. C CALL TSPLINE (DIJM,DMCDF,NPNTS,BR,ST,1,KKK,ANGCL,YI,YP,YPP,XINT) DO 19 N = I o KKK CDF(M,N) = YI(N) 19 CONTINUE C .............................................................................. C C INTERPOLATE FOR FLAP HINGE t_4ENT VALUES C C NOTE: FLAP HINGE MOMENT IS NORNALIZED BY THE AIRFOIL'S (I.E.o MOT C C THE FLAPeS) CHORD LENGTH. C C .......................................... * ................................... C CALL TSPLINE (DUN_DNCHF,NPNTS,BB,ST,1,KKK,ANGCL,YI,YP,YPP,XINT) DO 20 N : 1 , KKK CHF(M,N) = YI(N) 20 CONTINUE ELSE WRITE (44,*) WRITE (44,*) LP1 DO 111L = 1 , LP1 WRITE (44,112) L,ANG(L),DMCLF(L),DHCHF(L) 111 CONTINUE WRITE (44,*) 112 FORMAT (SX,'L=',I3,SX,*ANG=',F6.1,SX,aCLF=_,F7.4,SX,'CHF=',F7.4) C .............................................................................. C C ************ FOR A SINGLE ELENENT FLAPPED AIRFOIL .t****t******** C C SPECIAL TREATMENT C C .......................... " ................................................... C C INTERPOLATE FOR FLAP SECTIONAL LIFT VALUES C C HAD TO ADJUST TENSION PARAMETER FOR SPLINE FITTING TO WORK PROPERLY C C ..................................................... ? ........................ C C ST=I.0 C CALL TSPLINE (ANG,DNCLF,LPI,BB,ST,I,KKK,ANGCL,YI,YP,YPP,XINT) C DO 21N = 1 , KKK C CLF(N,N) = ¥I(N) C21 CONTINUE DO 21N = 1 , KKK DO 23 L = 1 , LPI-1 IF (ANGCL(N).GE.ANG(L).AND.ANGCL(N).LE.ANG(L+I)) THEN A1 = ABS(ANGCL(N) - AMG(L) ) B1 = ABS(ANG(L+I) - ANG(L) ) CLF(M,N) = DMCLF(L) + (DMCLF(L+I) - DNCLF(L) ) * A1/B1 CHF(M,N) = DNCHF(L) + (DMCHF(L+I) - DNCHF(L) ) * AI/B1 END IF 23 CONTINUE 21 CONT I RUE C .............................................................................. C C INTERPOLATE FOR FLAP HINGE MIONENT VALUES C C NOTE: FLAP HINGE MOMENT IS NORMALIZED BY THE AIRFOIL'S ([.E., NOT C C THE FLAPSS) CHORD LENGTH. C C .............................................................................. C C CALL TSPLINE (ANG,DMCHF,LPI,BBoST,1,KKKoANGCL,YI,YP,YPP,XINT) C DO 22 N = I , KKK C CHF(N,N) = YI(N) C22 CONTINUE END IF C ................ _ ............................................................. C C END MACH NUMBER DO LOOP C C ..................... ° ........................................................ C 10 CONTINUE 100 FORMAT (SX, tN=',I3,SX,_AOA=_,F6.1,SX,'CL=',FT.4) RETURN END SUBROUTINE TSPLINE (X,Y,N,B,SToIOP,NP,XI,YI,YPoYPP,XINT) C .............................................................................. C C TENSION AND CUBIC SPLINE CURVE FIT PROGRAH C C .............................................................................. C C SOURCE FOR THE SUBROUTINE WAS TAKEN FROM A FORTRAN CODE BY TEX JONES C C OF THE NASA LANGLEY RESEARCH CENTER C C .............................................................................. C C X AND Y - INPUT TABLE. C C N - NUMBER OF INPUT VALUES OF X AND Y. C C B - SOLUTION VECTOR (SECOND DERIVATIVE AT INPUT VALUES OF X AND Y. C C ST - TENSION PARAMETER. C C IOP - COMPUTING OPTION. C C =0 COMPUTE YI,YP,AND YPP AT NP EQUALLY SPACED VALUES C C OF XI BETWEEN X(1) AND X(N) C C =1 COMPUTE YI,YP,AND YPP AT NP INPUT VALUES OF X| C C NP " NUMBER OF INPUT VALUES OF XI. C C XI - INPUT TABLE OF INTERPOLATION VALUES OF X BETWEEN X(1) C C AND X(N). C C YI - INTERPOLATED TABLE OF ¥ VALUES. C C YP - INTERPOLATED TABLE OF FIRST DERIVATIVE VALUES. C C YPP - INTERPOLATED TABLE OF SECOND DERIVATIVE VALUES. C C X]NT - VALUE OF INTEGRAL OF Y BETWEEN X(1) AND X(N). C C ....... ° ................................................. * ............ - ...... -C DIMENSION X(N),Y(N),B(65),XIC65),YI(65),YP(65),YPP(65) C A IS DUMMY STORAGE VECTOR. DIMENSION A(IO*N).
DIMENSION A(6SO) M =N-1 NI=N+I N2=NI+N N3=N2+N N4=N3÷N NS=N4+N M6=NS÷N NT=N6+N NB=N7+N N9=NB+N T=ST*FLOAT(N'I)/(X(N)-X(1)) C .............................................................................. C C LOAD MATRIX ROWS 2 THRU N-1 C C .......... _ ................................................................... C DO 11=l,H HZ=X(I+I)'X(I) IF(ST.EQ.O.O) A(I)=H2/6.
IF(ST.NE.D.O) A(I)=(I./H2"T/SINH(TtH2))/(T*T) K=_'N+I A(K)=A(I) IF(I.EQ,1) GO TO 1 K=K÷N HI=X(I)-X(]-I) [F(ST.EQ.O.O) A(K)=(H2÷H1)/3.
IF(ST.NE.O.D) A(K)=(T*COSH(T*H1)/SINH(TtH1)-I./HI+T*COSH(T*H2)/SIN 1H(TtN2)-I./H2)/(TtT) K=K÷N A(K)=(Y(I÷I)-Y(]))/H2-(Y(%)-Y(%-I))/H1 I CONTINUE C LOAD NATR]X ROWS I AND N C C .............................................................................. C A(N)=- .5 A(N2)=- .5 A(N3)=I.0 A(N4-1)=1.0 A(N4)=O.O A(N5-1)=OoO C ...................................................................... ° ....... C C SOLVE TRIDIAGONAL MATRIX C C .............................................................................. C A(NT)=A(N3) A(NB)=A(N4)/A(N3) A(N9)=A(N2)/A(N3) DO 6 1=2,N 11=1-I 12=1-2 A(NT+]I)=A(N3+I1)-A(I1)*A(N_o-]2) IF(].EQ°N) GO TO 4 A(Ng÷]I)=A(N2÷I1)/A(N?+il) 6 A(NB+I1)=(A(N4+I1)-A(Z1)*A(NB÷I2))/A(NT+I1) A(N6-1)=A(Ng-1) DO 5 l=l,N !1=N6-1-1 I2=N-I 13=12-1 5 A(II)=A(NS+I3)'A(Ng÷I3)*A(]I+I) K=O DO 6 ]=I,N I1=i-1 A(N6+K)=A(NS+I1) 6 K=K+I A(N)=A(N3-2) C LOAD SOLUTION INTO VECTOR B C C ....... " ................................ " ..................................... C DO 7 I=I,N i1=N6+[-1 7 B(I)=A(]I) C ....... ° ................................................. " .................... C C COMPUTE Y,YP,YPP AT DESIRED X VALUES C C ....... " ...................................................................... C IF (NP.LE.O) RETURN IF (IOP.EQ.O) GO TO 13
REPORT DOCUMENTATION PAGE Fo_._p_o_a
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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
May 1999 Contractor Report
4. TITLE AND SUutHLE 5. FUNDING NUMBERS
Predicted Aerodynamic Characteristics of a NACA 0015 Airfoil Having a
25% Integral-Type Trailing Edge Flap NAS 1-20096 Task 6
WU 538-07-14-10
6. AUTHOR(S)
Ahmed Hassan
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
The Boeing Company REPORT NUMBER
Mesa, Arizona
9. SPONSORING/MONiTOHING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCY REPORT NUMBER
National Aeronautics and Space Administration
NASA/CR-1999-209328
Langley Research Center
Hampton, VA 23681-2199
11. SUPPLEMENTARY NO, _S
Langley Technical Monitor: Henry E. Jones
12a. DISTRIBUTION/AVAILABILITY STA;_MENT 12b. DISTRIBUTION CODE
Unclassified-Unlimited
Subject Category 01 Distribution: Nonstandard
Availability: NASA CASI (301) 621-0390
13. ABSTRACT (M_-l_,um 200 words) Using the two-dimensional ARC2D Navier-Stokes flow solver analyses were conducted to predict the sectional aerodynamic characteristics of the flapped NACA-001 5 airfoil section. To facilitate the analyses and the generation of the computational grids, the airfoil with the deflected trailing edge flap was treated as a single element airfoil with no allowance for a gap between the flap's leading edge and the base of the forward portion of the airfoil. Gen- eration of the 0-type computational grids was accomplished using the HYGRID hyperbolic grid generation pro- gram. Results were obtained for a wide range of Mach numbers, angles of attack and flap deflections. The predicted sectional lift, drag and pitching moment values for the airfoil were then cast in tabular format (C81) to be used in lifting-line helicopter rotor aerodynamic performance calculations. Similar were also generated for the flap. Math- ematical expressions providing the variation of the sectional lift and pitching moment coefficients for the airfoil and for the flap as a function of flap chord length and flap deflection angle were derived within the context of thin airfoil theory. The airfoirs sectional drag coefficient were derived using the ARC2D drag predictions for equiva- lent two dimensional flow conditions.
14. SUBJECT TERMS IRS. NUMBER OF PAGES
Noise Reduction, Airfoils, Blade-Vortex Interaction
16. PRICE CODE
A08
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF REPORT OF THIS PAGE OF ABSTRACT OF ABSTRACT
Unclassified
Unclassified
Unclassified
UL
NSN 7540-01-280-$500 Standard Form 298 (Rev. 249) Presonbad by ANSi Std. Z39-18 298-102 GO TO 14 13 DELTAX=(X(H)-X(1))/FLOAT(NP-1) XX(1)=X(1) DO 15 ]=2,NP 15 X[([)=X]([-1)+DELTAX 14 CONT[NUE DO 8 ]=ltNP P=XI(I) DO 9 K=2,N KI=K-1 [F((P.GE.X(K1)).AND.(P.LE.X(K))) GO TO 10 GO TO 9 10 JI=K1 JZ=K 9 CONTINUE H=X(J2)-X{J1) ]F(ST.EQ.O.O) GO TO 11 SINHT=SINH(T*H) Y]([)=B(J1)t(S]XX(Tt(X(J2)-P))/(T_T*S]XHT)-(X(J2)-P)/(HWT*T))÷B(J2 1)=(SINH(T*(P-X(J1)))/(TtTWSINHT)-(P-X(J1))/(H*TtT))+(Y(J1)m(X{J2) - 2P)+Y(J2)*(P-X(J1)))/X YP(1):B(J1)*(1./(H*T*T)-COSH(T*(X(J2)-P))/(TeSZNHT))÷B(J2)W(COSH(T I*(P-X(J1)))/(TtSINHT)'I./(H*T*T))+(Y(J2)-Y(J1))/X YPP(I):B(J1)+SINH(Tt(X(J2)'P))/S|NXT+B(J2)wS|NX(Ta(P'X(J1)))/S]NHT GO TO 8 11 YI(X)=B(J1)t((X(J2)-P)t*3/(6.tH)-(X(JZ)-p)tH/6.)+B(J2)*((P-XCJ1)) t I*3/(6.*H}-(P-X(J1))*H/6.)+(Y(J1)t(X(JZ)-P)÷Y(J2)t(p-x(J1)))/H YP{X)=B(J1)*(H/6.-(X(J2)-p)t*2/(2.*H))+B(J2)*((P-X(J1))**2/(2.tH) - 1H/6.)+(Y(JZ)-Y(J1))/H YPP(I)=B(J1)t(XCJ2)-P)/H+B(J2)t(p-x(J1))/H 8 CONTINUE C .............................................................................. C C COMPUTE INTEGRAL OF Y BETWEEN X(1) AND X(N) C C .............................................................................. C XINT=O.O DO 12 I=2,X H=X(I)-X(]-I) XINT=X]NT+(Y(I)+Y([-1))*H/2.
]F(ST.EO.O.O)XINT=XINT-(B(])+B(I-1))*X**3/24.
]F(ST.NE.O.O)X]NT=XINT-(B([)+B(]-I))t(C1.-COSH(T*X))/(T**3*S]XH{T* 1H))+H/(Z.*T*T)) 12 CONTINUE RETURN END