Aerodynamic data banks for Clark-Y, NACA 4-digit and NACA 16-series airfoil families

Appendix I

ClarkY Program Listing

//CLARKY JOB (R230,006B,SO2,003,A7),'CLARKY' //*FORMAT PR,DDNAME=,JDE=JFMTI,FORMS=Illl //*XBM WATFIV //$OPTIONS NOLIST C C* * C* THIS PROGRAM WILL CALCULATE THE LIFT COEFFICIENT, DRAG, " C* AND MOMENT COEFFICIENT ABOUT THE QUARTER CHORD OR THE * C _ LEADING EDGE, COORDINATES FOR A CLAYK Y AIRFOIL SECTION C* C DIMENSION CL(25,25),CD(25,25),CLD(25,25),ALPHA(7),ALPHAO(21), &RN(25),CM(25,25) REAL HM(4),NCLD DATA HM/0.0,0oI_0.2,0o4/ DATA ALiPHA/-I.0,0.0,1o0,2o0,3o0,4o0,5.0/ DATA ALTUDE/10000o/ C C NOTE: CHORD MUST BE IN FEET C DATA CHORD/0.75/ DATA NUMACH/4/ DATA NUMALP/7/ DATA NCL/1/ DATA NCD/I/ C CALL ATMCON(ALTUDE,TEMP,PRES_DEN,VIS,WA) C C SPECIFY HERE THE KNOWN VALUE OF CLD OR TMAX C SET THE UNKNOWN VARIABLE (CLD OR (T/C)MAX) EQUAL TO ZERO C FOR EXAMPLE, NCLD=UNKNOWN VALUE OF CLD,T=KNOWN VALUE OF (T/C)MAX C NOTE: THIS CLD IS INCOMPRESSIBLE AND ONLY TO START THE CODE.

DATA NCLD/0o00/ C C IN ORDER TO BE CONSISTANT T IS NON-DIMENSIONAL C DATA T/0oll70/ C CALL CLTMAX(T,NCLD,ALPHLO,DNCLD) C C SPECIFY HERE THE DESIRE FOR CLARK - Y AIRFOIL SECTION COORDINATES C AND ITS MOMENTS OF INERTIA BY INDICATING "l" FOR "YES", AND "0" C FOR "NO" FOR PARAMETER "L" C FOR EXAMPLE, L=I DATA L/l/ CALL CYCOOR(L,CHORD,T) C WRITE(6,10) l0 FORMAT('l',/////////,56X,' .... ,1X,'LIMITATIONS',IX,' .... //) C C SPECIFY HERE THE DESIRE FOR MOMENT COEFFICIENTS - EITHER CM C ABOUT THE NOSE OR THE QUARTER CHORD - BY INDICATING "i" FOR C "CM ABOUT THE NOSE" AND "2" FOR "CM ABOUT THE QUARTER CHORD" C FOR THE PARAMETER _'M". IF CM IS NOT DESIRED, INDICATE "0" FOR C PARAMETER "M"o C FOR EXAMPLE, M=lo DATA M/2/ C DO 21 K=I,NUMACH C DO 42 J=I,NUMALP C RN(K)=DEN*HM(K)_WA*CHORD/VIS C ALPHAO(J)=ALPHA(J)-ALPHLO CALL CLCD(ALPHAO(J),T,HM(K),CL(K,J),CD(K,J),NCL_NCD) CLD(K_J)=CL(K,J)/CD(K,J) C CM(K,J)=CMFF(T,CL(K,J),M,HM(K)) C 42 CONTINUE C 21 CONTINUE J=0 IF(NUMACH.EQ.1) GO TO 44 NUMT=NUMACH DO 40 JJ=I,NUMACH WRITE(6,892) 892 FORMAT( 'l',//////////) WRITE (6,852) 852 FORMAT(' ',I4X,'*'olX,'CLARK Y SERIES AIRFOIL DATA BANK', &IX,'*',24X,'*',IX,'CLARK Y SERIES AIRFOIL DATA BANK',IX,'_'////) C WRITE (6,515) ALTUDE, ALTUDE 515 FORMAT(T20,'ALTITUDE = ',F10o4,1Xw'FEET'rT83,'ALTITUDE = ' &,FI0.4,1X, 'FEET'/) WRITE(6,117) CHORD,CHORD 117 FORMAT(T23,'CHORD = ',FI0.6,1X,'FEET'wT86,'CHORD = 'g &F10.6, IX, 'FEET'/) C IF(DNCLD.EQ.1.) GO TO 730 C WRITE(6,950) T,T,NCLD,NCLD 950 FORMAT(T20, '(T/C)MAX = '_F10o6g ' (S) _,T82s _(T/C)MAX = ', &F10.6,' (S)',//T25,'CLD = '_F10o6,T87,'CLD = ',FI0o6/) GO TO 100 C 730 CONTINUE WRITE(6,888) T_T,NCLD,NCLD 888 FORMAT(T20,'(T/C)MAX = '_F10o6_T83,_(T/C)MAX = ',FI0.6, &//T25, 'CLD = ',Fl0°6w ' (S) '_T88, 'CLD = ' wF10.6, ' (S) '/) C 100 CONTINUE WRITE (6,735) ALPHLO, ALPHLO 735 FORMAT(T21_'ALPHALO = ',F10o6glXw'DEG°'wT84, 'ALPHALO = 'w &F10.6,1X,'DEG.'/) WRITE(6,701) HM(J+l)_HM(J+2) 701 FORMAT(T20,'MACH NO. = ',FI0.6_T83,'MACH NO. = '_FI0.6/) C WRITE (6,729)RN (J+l) ,RN(J+2) 729 FORMAT(T16, 'REYNOLDS NO. = '_EI4o6,T79, 'REYNOLDS NO. = ' _E14 °6,//) C IF(M.EQ°2) GO TO 82 WRITE (6,555) 555 FORMAT(T10, 'ALPHA',T23, 'CL'wT35g 'CD',T45, 'CL/CD',T57 U 'CM(LED)' w &T73,'ALPHA',T86, 'CL',T98, 'CD'gTI08, 'CL/CD',T120, 'CM(LED) '/) GO TO 83 82 WRITE(6 _556) 556 FORMAT(TIOu 'ALPHA' _T23, 'CL' _T35, 'CD' ,T45, 'CL/CD' _T57 p 'CM(1/4) '_ &T73w'ALPHA',T86, 'CL',T98, "CD',T108, 'CL/CD',T120, 'CM(I/4) ') 83 CONTINUE C DO 41 N=lwNUMALP C WRITE(6_600) ALPHA(N)wCL(J+I,N),CD(J+I,N),CLD(J+I,N), &CM(J+I, N) ,ALPHA(N), CL (J+2, N) ,CD(J+2, N), CLD(J+2, N), CM(J+2, N) FORMAT(2 (LXw FI0.6,2X, FI0 o6 w 2X, FI0 °6,2X_ F10.6,2X, FI0.6) ) C CONTINUE C J=JJ*2 NUMT=NUMT-2 IF(NUMT.EQ°0) GO TO 33 IF(NUMToEQ.I) GO TO 44 40 CONTINUE 44 WRITE(6,579) 579 FORMAT('I'_//////////) WRITE(6,589) FORMAT(' ',14X,'*',lX,'CLARK Y SERIES AIRFOIL DATA BANK' &IX,'*'////) C WRITE(6,214) ALTUDE FORMAT(T20,'ALTITUDE = ',FI0.4,1X,'FEET'/) WRITE(6,339) CHORD FORMAT(T23,'CHORD = ',FI0.6,1X,'FEET') C IF(DNCLD.EQ.I.) GO TO 731 C WRITE(6,951) T,NCLD FORMAT(T20,'(T/C)MAX = (S)',//T25,'CLD = ',Fl0.6w' ',FI0o6/) GO TO 101 C CONTINUE WRITE(6,889) T,NCLD FORMAT(T20,'(T/C)MAX = ',F10o6_//T25,'CLD = ',FI0o6,' (S)'/) C i01 CONTINUE WRITE(6,736) ALPHLO FORMAT(T21,'ALPHLO = ',F10.6_IX,'DEGo'/) WRITE(6,702) HM(NUMACH) FORMAT(T20,'MACH NO. = ',F10.6/) C WRITE(6,912)RN(NUMACH) FORMAT(/TI6,'REYNOLDS NOo = 'FE14o6//) C IF(M.EQ.2) GO TO 84 WRITE(6,666) ,T57,'CM(LED)'/) 666 FORMAT(T10,'ALPHA',T23,'CL',T35,'CD'_T45,_CL/CD ' GO TO 85 WRITE(6,665) FORMAT(TI0,'ALPHA',T23, _CL',T35,'CD',T45,'CL/CD'rT57,'CM(1/4)'/) 85 CONTINUE C DO 66 N=I,NUMALP WRITE(6,250) ALPHA(N),CL(NUMACH,N),CD(NUMACH,N),CLD(NUMACH,N) _CM(NUMACH,N) 250 FORMAT(5X,F10.6,2X_F10.6,2X,F10o6_2XwF10.6w2X,FIO.6) 66 CONTINUE GO TO 33 33 WRITE(6,999) 999 FORMAT('I*w//////////) STOP END SUBROUTINE CLCD(ALPHAOrT,HM,CL,CD,NCL,NCD) C C HIGH-SPEED LIFT AND DRAG DATA C FOR _C PROPELLER PERFORMANCE CALCULATION C CLARK-Y SECTIONS C C C REFERENCES: = C C HAINES_ Ao B. AND MONAGHAN, Ro Jo, "HIGH SPEED LIFT * C AND DRAG DATA FOR PROPELLER PERFORMANCE CALCUALATIONS * C TIONS," R&M NO. 2036, BRITISH A. R. Co, 1945o * C C MACDOUGALL, A. Ro Co, "REVISED HIGH-SPEED LIFT AND C DRAG DATA FOR PROPELLER PERFORMANCE CALCULATIONS, °' * C R&M NO. 2474, BRITISH A. Ro Co, 1947.

C C ..............................................................

C = C USAGE: * C * C CALL CLCD(ALPHAO,T,HM,CL,CD,NCL,NCD) * C C DESCRIPTION 0_ PARAMETERS: " C * C CL = LIFT COEFFICIENT C CD = DRAG COEFFICIENT * C ALPHA = ANGLE OF ATTACK RELATIVE TO FREE STREAM (DEG.) " C ALPHAO = ANGLE OF ATTACK RELATIVE TO THE ZERO LIFT LINE C (DEGREES) C T = THICKNESS-CHORD RATIO WITH RESPECT TO LONGEST * C CHORD LINE C HM = MACH NUMBER C NCL = NCL .NE. 0 IF CL DESIRED C NCD = NCD .NE. 0 IF CD DESIRED C C_.oo.._...........o.o...o...,..,..o..o...._.oo.o.oo..o_oo.oooo _ Co,.o.o.......,,.................o.o,o..ooo_oooooooooo.o_©_oooo _ C IF(NCL.NE.0) CL=CLFF(ALPHAO,T,HM) IF(NCD.NE.0) CD=CDFF(T,ALPHAO,HM) RETURN END C C C C LIFT DATA " C C FUNCTION CLFF(ALPHAO,T,HM) C CLFF = LIFT COEFFICIENT C ALPHAO=ANGLE OF ATTACK RELATIVE TO THE ZERO LIFT LINE C T =THICKNESS-CHORD RATIO C IF(T.LT.0.16) GO TO 1 CLFF=ALPHAO*THKSLP(T,ALPHAO,HM) C THKSLP(T,HM) CALCULATES THE SLOPE OF THE LIFT CURVE C FOR THICK SECTIONS RETURN 1 AO=AOF(T,ALPHA0,HM) C AOF(T) CALCULATES SLOPE OF LOW-SPEED LIFT CURVE HML=HMLF(T,ALPHAO,HM) C HMLF(T,ALPHAO,HM) CALCULATES THE CRITICAL MACH NUMBER FOR C LIFT. (FUNCTION OF THICKNESS AND ANGLE OF ATTACK) H=HM-HML C CALCULATE INCOMPRESSIBLE LIFT COEFFICIENT CLO=AO*ALPHA0 C APPLY PRANDTL-GLAUERT CORRECTION IF(HM.LE.HML) CLFF=CLO/SQRT(I.-HM_HM) IF(H.LE.0.4) GO TO 2 2 IF(HM.GT.HML)CLFF=CLO/SQRT(1.-HML*HML)+CLSF(H) C CLSF(H) CALCULATES THE DIFFERENCE OF CL AT A MACH NUMBER C ABOVE THE CRITICAL FROM ITS CRITICAL VALUE.

RETURN END FUNCTION AOF(T,ALPHAO,HM) AOF= VALUE OF AO, SLOPE OF THE LOW SPEED LIFT CURVE T = THICKNESS-CHORD RATIO DIMENSION A(28),H(28),X(3),Y(3) C DATA IS FROM HAINES AND MONAGHAN, P_ 1174, TABLE #i C DATA A = SLOPE OF LOW-SPEED LIFT CURVE DATA A/0.I095, 0.1094, 0.1091, 0.1085, 0o1069, 0.1043_ 1 0.i017, 0o0991, 0.0999, 0.0999, 0o0999, 0°0998, 2 0.0996, 0.0992, 0.0987, 0.0980, 0o0972, 0.0962, 3 0.0950, 0.0936, 0.0920, 0°0902, 0.0881, 0.0858, 4 0.0832, 0°0804, 0°0773, 0.0738/ C DATA H = THICKNESS-CHORD RATIO DATA H/0.001,0.002,0.005,0.010,0.025,0.050_0o075,0o100,0oi10_ 1 0_120,0.130,0.140,0.150,0o160,0o170,0o180,0.190,0o200, 2 0.210,0.220,0.230,0.240,0.250,0.260,0o270,0.280,0.290, 3 0.300/ TCMAX=0.3 IF(T.GT.TCMAX) WRITE(6,30) T,TCMAX 30 FORMAT(' ',I9X,'T/C = ',FI0.6,' IS GREATER THAN (T/C)MAX = ', &F10.6,' OF FUNCTION AOF'/) N=2 AOF=0.1096 IF(T.EQ.0.) RETURN IS=I IL=IS+N-1 1 IF(IL.GE.28) GO TO 2 IF((T-H(IS))*(T-H(IL)).LE.0o) GO TO 3 IS=IL IL=IS+N-1 GO TO 1 2 IS=28-N+l IL=28 3 DO 4 I=IS,IL X(I-IS+I)=H(1) Y(I-IS+I)=A(1) 4 CONTINUE AOF=YLAGN(X,Y,N,T) RETURN END FUNCTION CLSF(H) CLSF=CLS H =M-ML DIMENSION C(40),S(40),X(3),Y(3) DATA IS FROM HAINES AND MONAGHANq P. 1176, TABLE #4 DATA C = LIFT COEFFICIENT DATA C/ 0.010, 0.017, 0.022, 0.025, 0.026, 0.025, 0.021, 1 0.015, 0.007,-0.002,-0.014,-0.027,-0.040,-0.054, 2 -0.070,-0o086,-0.I02,-0o119,-0.138,-0.157_-0.175_ 3 -0.193,-0°212,-0.231,-0.250,-0.270,-0.289,-0.307 w 4 -0.325_-0.344,-0.363_-0.381,o0.400,-0.417,-0.432, 5 -0.446,-0o459,-0.470,-0.478,-0.485/ DATA S = (M-ML), WHERE M=LOCAL MACH NO., AND ML=CRITICAL MACH NO.

FOR LIFT AT WHICH THE LIFT DEPARTS FROM THE GLAUERT LAW, VARIED WITH (T/C) AND ALPHAO DATA S/0o01,0o02,0.03,0.04,0°05w0.06_0.O7,0.08,0.09v0.10w 1 0oi1,0o12,0o13,0.14,0o15_0.16,0.17,0.18,0.19,0.20, 2 0o21,0oZ2,0o23_0°24,0.25,0o26,0.27,0o28,0o29,0.30, 3 0o31;0.32,0°33,0.34,0o35,0.36,0o37,0.38u0o39,0.40/ HMIN=0o01 HMAX=0_40 IF(H°LT.HMIN) WRITE(6wl0) HwHMIN i0 FORMAT(' ',19X_'H = M-ML = 'wFl0o6,' IS LESS THAN HMIN = _, &F10.6,' OF FUNCTION CLSF'/) IF(HoGT.HMAX) WRITE(6,20) H,HMAX FORMAT(' ',19X, °H = M-ML = ',F10.6,' IS GREATER THAN HMAX = ', &F10°6,' OF FUNCTION CLSF'/) N=3 IS=l IL=IS+N-1 IF(HoLE.S(IL)) GO TO 1 IL=40 IS=IL-N+l IF(H.GEoS(IS)) GO TO 1 IS=I IL=IS+N-1 2 IF(((H-S(IS))*(H-S(IL))).LEo0.) GO TO 1 IS=IL IL=IS+N-1 GO TO 2 1 DO 4 I=ISuIL X(I-IS+I)=S(1) Y(I-IS+I)=C(1) 4 CONTINUE CLSF=YLAGN(X_Y,N,H) RETURN END C FUNCTION THKSLP(T,ALPHA0,HM) C THKSLP = VALUE OF THE SLOPE OF THE LIFT CURVE OF THE C THICK SECTION C T = THICKNESS-CHORD RATIO C HM = SECTION MACH NUMBER C DIMENSION H(6),S(9),X(3),Y(3),U(3),V(3) DIMENSION AI5(6),A17(5),A19(4) DATA IS FROM HAINES AND MONAGHAN, P. 1176, TABLE #5 DATA 'A.NO°': 'A'=INVERSE SLOPE OF LOW=SPEED LIFT CURVE, '°NOo'= THICKNESS-CHORD RATIO DATA A15/9.2,8.95,8.7,8.4,8.0,7.9/ DATA A17/9.6,9o4,9.2,8.95, 8.8/ DATA A19/10.1,10.0,9.9,9.8/ DATA H = MACH NO.

DATA H/0.40,0.45,0.50,0.55,0.60,0.65/ DATA S = THICKNESS-CHORD RATIO DATA S/0.15,0.17,0.19,0.21,0°23,0.25,0°30,0.35,0.40/ TCMAX=0.40 HMAX=0°80 IF(T°GT.TCMAX) WRITE(6,33) T,TCMAX 33 FORMAT(' ',lgX,'T/C = ',F10.6,' IS GREATER THAN (T/C)MAX = ', &FI0o6,' OF FUNCTION THKSLP'/) IF(HM.GT.HMAX) WRITE(6,70) HMwHMAX 70 FORMAT(' ',IgX,'MACH NOo = ',FI0.6,' IS GREATER THAN MACH NO.'

&'(MAX) = ',FI0.6,' OF FUNCTION THKSLP'/) IF(HM.LTo0.3) GO TO 50 CALL OUT(9,2,IS,IL,S,T) CALL OUT(6,2,JS,JL,H,HM) U(1)=H(JS) U(2)=H(JL)

x(1)=s(Is)

X(2)=S(IL)

DO l0 I=IS,IL COMPUTED GO TO GO TO (15,17, 19,21,23,25,30,35,40),I 15 ANS=A15(1) IF(HM.LE.H(1) .GO TO 1 ANS=A15(6) GO TO 1 IF(HM°GE.H(6) V(1)=A15(JS) V(2)=A15(JL) GO TO 2 17 ANS=AI7(1) IF(MMoLEoH(1) GO TO 1 ANS=A17(5) IF(HMoGE.H(5) GO TO 1 V(1)=A17(JS) V(2)=A17(JL) GO TO 2 19 ANS=AIg(1) IF(HM.LEoH,(1) GO TO 1 ANS=A19(4) IF(HMoGE.H(4) GO TO 1 V(1)=A19(JS) V(2)=A19(JL) GO TO 2 21 ANS=10o5 GO TO 1 23 ANS=I0o9 GO TO 1 25 ANS=IIo4 GO TO 1 30 ANS=I3°6 GO TO 1 35 ANS=Igo2 GO TO 1 40 ANS=30o0 GO TO 1 2 ANS=YLAGN(U,V,2,HM) 1 Y(I-IS+I)=ANS l0 CONTINUE THKSLF=I./YLAGN(X,Y,2,T) RETURN 50 THKSLP=AOF(T,ALPHAOrHM) RETURN END FUNCTION HMLF(T,ALPHAO,HM) C HMLF = ML C T = THICKNESS-CHORD RATIO C ALPHAO = ANGLE OF ATTACK RELATIVE TO THE ZERO LIFT LINE C (DEGREES) C DIMENSION A(17),B(25),C(Z5;17),X(3),Y(3),U(3),V(3), 1 E(6,10),F(10),G(6) DATA IS FROM HAINES AND MONAGHAN, P. 1175, TABLE #3 • DATA A = ALPHAO = ANGLE OF ATTACK WITH RESPECT TO ZERO LIFT LINE DATA A/3o,3.5,4o,4.5,5.,5°5,6.,6o5,7.,7.5,8_,8.5,9., 1 9.5,10.,i0.5,11o/ DATA B = THICKNESS-CHORD RATIO DATA B/0.04,0.045,0.05,0°055,0.06,0.065,0.07,0°075,0.08F 1 0.085,0.09,0.095,0.10,0.105,0.11,0.I15,0.12,0.125,0.13, 2 0.135,0.14,0°145,0.15,0.155,0.16/ DATA C = CIRTICAL MACH NO. FOR LIFT AT WHICH THE LIFT DEPARTS FROM THE GLAUERT LAW, VARIED WITH (T/C) AND ALPHAO DATA (C(I,1),I=l,25)/ 1 0o879,0.858,0.83125,0.8125,0.79125,0.7775,0.765, 1 0.751,0.742,0.732,0.723,0.713,0.704,0o695,0.686_0.677, i 0.669,0o660,0.651_0.643,0.635,0.627,0.618,0.610_0.603/ DATA(C(I,2),I=l,25)/ 2 0.874,0.852,0.828,0.807,0o790,0.775,0.764,0.751,0.742, 2 0.732,0.723,0°713,0o704,0o695,0.686,0.677,0.669,0.660, 2 0.651,0°643,0.635,0o627,0o618,0.610_0.603/ DATA (C(I,3),I=1,25)/ 3 0.867,0.846,0.825,0.804e0.7875,0o773,0.765,0o749,0.740, 3 0.730,0.721,0.711,0.702,0°694,0.685f0.676,0.668,0.658, 3 0.649,0o641,0.633,0.625,0.616,0.608,0 .601/ DATA (C(I,4),I=1,25)/ 4 0.859,0.838,0.817,0.798,0o78125,0o768 ,0.756,0°745,0°735, 4 0.725,0.716,0.707_0°698,0o689,0.680,0 .671,0.663,0.654,

4 0.645,0.637,0.628,0°620w0.611,0.603,0 .s961

DATA (C(I,5),I=l,25)/ 5 0°848_0°828,0.807,0.789;0.774,0.761,0 .749,0.738w0.728, 5 0.718,0.709,0.699,0o689,0o680,0.671,0 .663,0.654,0°646,

.SSSl

5 0.637s0.627,0o618w0o612,0.602,0.593,0 DATA (C(I,6),I=I,25)/ 6 0.836,0°817,0.797v0.780,0o765_0o752,0 .740,0.729,0.719, 6 0o709_0o699,0o689F0o679_0o669,0.660,0 .650,0.641,0.631v

6 0o621,0.611,0o600_0.589,0°578,0o568,0 .559/

DATA (C(I,7)_I=I,25)/ 7 0°823,0o805,0°787,0o771,0o755,0.742,0 .730,0.719,0o707, 7 0o697_0o687,0.675_0o666,0o656o0o646,0.635_0.625,0o614, 7 0o603,0.591,0.579r0o567,0.555u0°543,0o532/ DATA (C(lw8),I=l,25)/ 8 0o808g0o792,0.775w0o760_0o744,0o731,0.718,0.706,0°695u 8 0.684,0.674w0.663_0°652,0°641_0o629,0o618_0.607,0.595, 8 0.584,0o572w0o560,0°548,0.536_0.524,0.513/ DATA (C(I,9)_I=1,25)/ 9 0.794,0o778_0o762,0.745,0.730,0o717,0.704,0.691,0.679, 9 0.667_0o657g0o646,0o635,0o623,0o611,0.600,0.588,0.577, 9 0o565,0°553,0o541,0.530,0o518s0o507,0.496/ DATA (C(I,10),I=l,25)/ $ 0o781_0o765,0o748,0.731,0o716_0.702,0o689e0.676,0o663, $ 0.651,0o640,0.628,0.617,0o605u0.593,0°582,0.570,0.558, $ 0o546,0_533_0°523,0°513,0.502,0o492,0°483/ DATA (C(I,11),I=l,25)/ 1 0o768,0o752_0.734u0o717_0o701,0.687,0°673,0.661,0.648, 1 0o635,0o622_0.611_0o599,0.587,0o575,0.563,0.551,0.539, 1 0o528,0o517,0.507v0.498,0o489_0.479rO.470/ DATA (C(I,12),I=l_25)/ 2 0o755,0o739,0.720_0.703,0o685,0.670,0.656r0°644,0o631, 2 0o618,0o606,0.593,0.580,0o568,0.556_0.545_0.534,0.523w 2 0.513,0o503,0.493r0o484,0.474,0o466w0.457/ DATA (C(I,13),I=i,25)/ 3 0.742,0.726,0.706,0.689,0.667,0.652,0o638,0.626,0.613, 3 0.601,0.588,0.575,0.563,0.551,0.539,0.528,0.518,0.508, 3 0.498,0.489,0.479,0.471,0°462,0.454,0.446/ DATA (C(I,14),I=l,25)/ 4 0.729,0.713,0.692,0.675,0o647,0.633,0_620,0.608,0.595, 4 0.583,0.570,0.558,0.546,0.535,0.524,0.513,0.503,0.494, 4 0.484,0°475,0.467,0.460,0.453,0.446,0°439/ DATA (C(I,15),I=l,25)/ 5 0.716,0.700,0.678,0.661,0.625,0.613,0.601,0°589w0.576_ 5 0.564,0.552,0.541,0o530,0o519,0.509,0.499_0o490,0°481, 5 0o473,0.465,0.458,0.451,0.445,0.438_0.432/ DATA (C(I,16),I=l,25)/ 6 0.703,0.687,0.664,0.647,0.601,0.592,0.582,0o570_0o558, 6 0.547,0.536,0.526,0.516,0°505,0.496,0.487,0o479,0.471, 6 0.463_0.457,0.450,0.444,0o439,0.432,0°426/ DATA (C(I,17),I=1,25)/ 7 0.690,0.674,0.650,0.633,0o575,0.570,0.564,0o552,0o541, 7 0.531,0.521,0.511,0.502,0o493,0.485,0o477,0.470,0o463, 7 0.456,0.450,0.445,0.439,0.433,0.427,0o422/ DATA IS FROM MACDOUGALL, PPo 1032-33, TABLES 1A&B DATA F = ALPHAO = ANGLE OF ATTACK WITH RESPECT TO ZERO LIFT LINE DATA F/-1.5,-i°,-0.5,0.,0.5,1.,i.5,2.,2o5,3./ DATA G = THICKNESS-CHORD RATIO DATA G/0.045,0o05_0.055,0o06,0.065,0.07/ DATA E = CIRTICAL MACH NO. FOR DRAG AT WHICH THE DRAG DEPARTS FROM ITS LOW-SPEED VALUE DATA ((E(I,II),I=l,6),II=l,5)/ 1 0.584w0o593,0o603w0.613,0.625,0.638, 2 0o586,0o601,0.610,0.62125,0.63125,0.64375, 3 0o603,0.61875,0.63125,0.64,0o65875,0.6662, 4 0.64625,0.6620,0.67425,0.6875,0.69375,0.696875, 5 0.7,0.7125w0o725,0.73525,0.73125,0.73125/ DATA ((E(I,II),I=l,6),II=6,10)/ 6 0o775,0.775,0.775,0°77625,0o7575,0o75w 7 0.8125,0.80625,0.778125,0.7775,0.76875,0°7593, 8 0°840,0o82125,0.805,0o7875,0.776,0.765_ 9 0o852,0°827,0°80875,0.790,0.775_0.7656, 1 0.858,0o83125,0o8125,0.79125,0.7775,0.765/ TCMIN=0.04 TCMAX=0.16 ALOMIN=-I.5 ALOMAX=llo0 IF(T.LToTCMIN) WRITE(6,21) T,TCMIN 21 FORMAT(' ',lgX,'T/C = ',FI0.6,' IS LESS THAN (T/C)MIN = 'iF10.6_ &' OF FUNCTION HMLF'/) IF(ToGT.TCMAX) WRITE(6_30) T,TCMAX 30 FORMAT(' ',IgX,'T/C = 'qFl0.6,' IS GREATER THAN (T/C)MAX = '_ &FI0.6,' OF FUNCTION HMLF'/) IF(ALPHAO.LT.ALOMIN) WRITE(6_40) ALPHAO,ALOMIN 40 FORMAT(' ',I9X,'ALPHAO = ALPHA-ALPHLO = '_Fl0o6w' IS LESS THAN', &' ALPHAOMIN = 'wF10.6,' OF FUNCTION HMLF'/) IF(ALPHAOoGToALOMAX) WRITE(6,50) ALPHAO,ALOMAX 50 FORMAT(' '_19X,'ALPHAO = ALPHA-ALPHLO = 'wF10o6,' IS GREATER'F &' THAN ALPHAOMAX = ',F10o6w' OF FUNCTION HMLF'/) IF(ALPHAO .LTo3.) GO TO 12 IMPROV=I IF(IMPROV.EQo0) GO TO 12 AL=ALPHAO IF(ALPHAO.LE.3.) ALPHAO=3.

N=Z IS=I IL=IS+N-1 IF(ToLEoB(IL)) GO TO 2 IL=25 IS=IL-N+l IF(T.GEoB(IS)) GO TO 2 IS=l IL=IS+N-1 3 IF((T-B(IS))*(T-B(IL))oLE.0o) GO TO 2 IS=IL IL=IS+N-1 GO TO 3 2 IF(ALPHAO .GT. 3.) GO TO 4 DO 5 I=IS,IL X(I-IS+I)=B(I) Y(I-IS+I)=C(I,1) 5 CONTINUE GO TO 6 4 JS=I JL=JS+N-1 IF(ALPHAO.LEoA(JL)) GO TO 7 JL=I7 JS=JL-N+I IF(ALPHAOoGE.A(JS)) GO TO 7 JS=I JL=JS+N-I 8 IF((ALPHAO-A(JS))_(ALPHAO-A(JL)).LE.0o) GO TO 7 JS=JL JL=JS+N-I GO TO 8 7 DO 9 J=JS,JL U(J-JS+I)=A(J) 9 CONTINUE DO l0 I=IS,IL X(I-IS+I)=B(I) DO ii J=JSwJL V(J-JS+I)=C(I,J) ll CONTINUE Y(I-IS+I)=YLAGN(U,VwN,ALPHAO) l0 CONTINUE 6 HMLF=YLAGN(X,Y_N_T) ALPHAO=AL RETURN 12 IF(ALPHAO.GT. -1o5) GO TO 13 HMLF=Oo549359-0o001148*(T_I00o) 1 +0.001968"(T*100.)_'2 RETURN 13 N=2 IS=l IL=IS+N-I IF(ToLEoG(IL)) GO TO 14 IL=6 IS=IL-N+l IF(ToGEoG(IS)) GO TO 14 IS=l IL=IS+N-I 15 IF((T-G(IS))_(T-G(IL)).LE.0.) GO TO 14 IS=IL IL=IS+N-1 GO TO 15 14 JS=I JL=JS+N-1 16 IF((ALPHAO-F(JS))_(ALPHAO-F(JL)).LEo0.) GO TO 17 JS=JL JL=JS+N-1 GO TO 16 17 DO 18 J=JS_JL U(J=JS+l)=F(J) 18 CONTINUE DO 19 I=IS,IL X(I-IS+I)=G(I) DO 20 J=JS,JL V(J-JS+I)=E(I_J) 20 CONTINUE Y(I-IS+I)=YLAGN(U,V_NNALPHAO) 19 CONTINUE HMLF=YLAGN(X,Y,NwT) RETURN END C C C DRAG DATA C C FUNCTION CDFF(T,ALPHAO,HM) DIMENSION A(15),X(3),Y(3) DATA A = THICKNESS-CHORD RATIO DATA A/0.09,0.1,0.11,0.12,0.13,0o14,0.15v0o16, 1 0.17,0.19,0.21,0.23,0.25,0.30,0.35/ TCMIN=0.09 TCMAX=0.35 IF(T.LT.TCMIN) WRITE(6,20) T,TCMIN 20 FORMAT(' ',lgX,'T/C = ',F10.6,' IS LESS THAN (T/C)MIN = 'uF10°6f &' OF FUNCTION CDFF'/) IF(T.GT.TCMAX) WRITE(6,31) T,TCMAX 31 FORMAT(' ',lgX,'T/C = ',F10.6,' IS GREATER THAN (T/C)MAX = _ &FI0.6,' OF FUNCTION CDFF'/) IF(T.GT. 0o16) GO TO 1 IF((T.GT.0.09) .AND. (ALFHAO.GT.5o)) GO TO 1 CDO=BOF(T,ALPHAO,HM)*COF(T,ALPHAO,HM) HMD=HMDF(T,ALPHAO,HM) CDS=0.

H=HM-HMD IF(HoGT. 0.) CDS=CDSF(T,ALPHAO,HM,H) IF(H.LE.0.4) GO TO 5 5 CDFF=CDO+CDS RETURN 1 N=2 IS=I IL=IS+N-I IF(ToLE.A(IL)) GO TO 2 IL=15 IS=IL-N+I IF(ToGE.A(IS)) GO TO 2 IS=I IL=IS+N-I 3 IF((T-A(IS))"(T-A(IL))oLEo0°) GO TO 2 IS=IL IL=IS+N-I GO TO 3 2 DO 4 I=IS,IL J=I-IS+l X(J)=A(I) ALOMIN=3.0 ALOMAX=ll.0 HMAX=lo0 IF(ALPHAO.LT.ALOMIN) WRITE(6_40) ALPHAO,ALOMIN 40 FORMAT(' ',I9X,'ALPHAO = ALPHA-ALFHLO = _,FI0o6,' IS LESS', &' THAN ALPHAOMIN = ',F10°6,' OF FUNCTION CDFF'/) IF(ALPHAOoGT°ALOMAX) WRITE(6,50) ALPHAO,ALOMAX 50 FORMAT(' ',lgX,'ALPHAO = ALPHA-ALFHLO = 'gFl0o6w' IS GREATER', &' THAN ALPHAOMAX = ',F10o6, _ OF FUNCTION CDFF'/) IF(HMoGT.HMAX) WRITE(6,65) HM,HMAX 65 FORMAT(' °,IgX,'MACH NO° = ',F10o6_ ' IS GREATER THAN MACH NOo'_ &_(MAX) = 'wFl0.6,' OF FUNCTION CDFF'/) GO TO (9,10,11,12,13,14,15,16,17,19921, 1 23,25,30_35)gI DATA 'CD°NO.F': 'CD' = DRAG COEFFICIENT, '.NO.' = THICKNESS-CHORD RATIO 9 Y(J)=CD9F(T,ALPHAO,HM) GO TO 4 i0 Y(J)=CD10F(T,ALPHAOvHM) GO TO 4 ll Y(J)=CDIIF(T,ALPHAO,HM) GO TO 4 12 Y(J)=CDIZF(T,ALPHAO_HM) GO TO 4 13 Y(J)=CDI3F(T,ALPHAO,HM) GO TO 4 14 Y(J)=CD14F(T,ALPHAO,HM) GO TO 4 15 Y(J)=CD15F(TgALPHAO,HM) GO TO 4 16 Y(J)=CD16F(T,ALPHAO,HM) GO TO 4 17 Y(J)=CDI7F(T,ALPHAO,HM) GO TO 4 19 Y(J)=CDIgF(T,ALPHAOrHM) GO TO 4 21 Y(J)=CD21F(T,ALPHAO,HM) GO TO 4 23 Y(J)=CD23F(T,ALPHAO,HM) GO TO 4 25 Y(J)=CD25F(T,ALPHAO,HM) GO TO 4 30 Y(J)=CD30F(T,ALPHAO,HM) GO TO 4 35 Y(J)=CD35F(T,ALPHAO,HM) 4 CONTINUE CDFF=YLAGN(X,Y,NpT) RETURN END FUNCTION BOF(T,ALPHAO,HM) C BOF=BO C ALPHAO=EFFECTIVE ANGLE OF ATTACK C DIMENSION A(51),B(51),X(3),Y(3) C DATA IS FROM HAINES AND MONAGHAN, P. 1177, TABLE #6 C DATA A = ALFHAO = ANGLE OF ATTACK WITH RESPECT TO ZERO LIFT LINE DATA A/-2.0,-io8,-1.6,-1.4,-1o2,-i.0, -0.8,-0.6,-0.4, 1 -0.2,0o0,0o2,0.4,0.6,0.8,1o0,1.2,1.4,1.6,1.8,2.0,2.2, 2 2.4,2.6_2.8,3.0,3o2_3o4,3o6w3.8,4.0,4.2,4.4,4.6,4.8,5o0, 3 5o2,5.4,5.6,5.8,6.0,6o2,6.4_6.6,6.8,7o0,7.2,7o4,7.6,7.8, ¢ 8.0/ C C DATA B = FACTOR EXPRESSING DEPENDENCE OF LOW-SPEED DRAG ON C INCIDENCE (ALPHAO) DATA B/i.131,i.114,1.098,1.082,1o067_i.054,1.041,1.030, 1 1o019vlo009,1_000,0o994,0.987,0°983,0.979,0o976,0.974, 2 0.973,0.972,0.971,0.972,0.974,0.976,0.978,0.980,0.982, 3 0.985,0.989,0.994,0.999,1.005,1.012,1.020,i.028,1.037, 4 1.047,1o057ri.067,1o078,1_090,ioi03,1.i17,1.132,1o147 , 5_1.162,1o179,1.197,1o216,1o235,1o255_io276/ ALOMIN=-2o0 ALOMAX=8.0 IF(ALPHAO.LT.ALOMIN) WRITE(6,40) ALPHAO,ALOMIN 40 FORMAT(' ',I9X,'ALPHAO = ALPHA-ALPHLO = 'wF10o6,' IS LESS', &' THAN ALPHAOMIN = ',F10o6w' OF FUNCTION BOF'/) IF(ALPMAOoGToALOMAX) WRITE(6,50) ALPHAO,ALOMAX 50 FORMAT(' ',19X,'ALPHAO = ALPHA-ALPHLO = ',FI0.6,' IS GREATER', &' THAN ALPHAOMAX = ',F10o6,' OF FUNCTION BOF'/) C N=3 IS=I IL=IS+N-I IF(ALPHAO.LE.A(IL)) GO TO 1 IL=51 IS=IL-N+l IF(ALPHAO.GE.A(IS)) GO TO 1 IS=I IL=IS+N-I Z IF((ALPHAO-A(IL))_(ALFHAO-A(IS)) oLEo 0.) GO TO 1 IS=IL IL=IS+N-1 GO TO 2 1 DO 3 I=IS,IL X(I-IS+I)=A(I) Y(I-IS+I)=B(1) 3 CONTINUE BOF=YLAGN(X,Y,N,ALPHAO) RETURN END C FUNCTION COF(T,ALPHAO,MM) C COF=CO C T=THICKNESS-CHORD RATIO C DIMENSION A(Z7),B(27),X(3),Y(3) C DATA IS FROM HAINES AND MONAGHAN_ P.i177, TABLE @7 C DATA A = THICKNESS-CHORD RATIO DATA A/.03, .035, .04, .045, .05, .055, .06, .065, 1 .07, .075, .08, .085, .09, .095, .i0, .105, °ll, o115, 2 .12, .125, .13, .135, .14, .145, .15, .155, .16/ DATA B = FACTOR EXPRESSING DEPENDENCE OF LOW-SPEED DRAG ON THICKNESS DATA B/0.00745,0.00753,0.00761,0.00770,0.00780,0o00790, 1 0.00800,0.00810,0.00820,0.00830,0.00840,0.00851,0.00862, 2 0.00874,0.00886,0.00898,0.00910,0.00921,0.00932,0°00944, 3 0°00957,0.00970,0.00983,0.00997,0.01010,0.01025,0.01040/ TCMIN=0.03 TCMAX=O.16 IF(ToLT.TCMIN) WRITE(6,20) T,TCMIN 20 FORMAT(' ',19X,'T/C = ',FI0.6,' IS LESS THAN (T/C)MIN = ',FI0.6, &' OF FUNCTION COF'/) IF(T.GToTCMAX) WRITE(6,30) T,TCMAX 30 FORMAT(' ',I9X,'T/C = ',FI0.6,' IS GREATER THAN (T/C)MAX = ', &FI0.6,' OF FUNCTION COF'/) N=2 IS=I IL=IS+N-1 IF(ToLEoA(IL)) GO TO 1 IL=27 IS=IL-N+l IF(ToGE.A(IS)) GO TO 1 IS=l IL=IS+N-I 2 IF((T-A(IL))*(T-A(IS)) oLEo 0o) GO TO 1 IS=IL IL=IS+N-I GO TO 2 1 DO 3 I=IS,IL X(I-IS+l)=A(I) Y(I-IS+l)=B(I) 3 CONTINUE COF=YLAGN(X,Y,N,T) RETURN END C FUNCTION CDSF(T,ALPHAO,HMgH) C CDSF=CDS C H=M-MD C DIMENSION A(40),B(40),X(3),Y(3) C DATA IS FROM MACDOUGALL, Po 1033, TABLE @2 C DATA A = (M-MD), WHERE M=LOCAL MACH NO°, MD= CRITICAL MACH NO.

C FOR DRAG AT WHICH DRAG DEPARTS FROM ITS LOW-SPEED VALUE DATA A/0.01,0.02,0.03,0.04,0o05,0.06,0.07,0.08,0o09, 1 0oI0,0.11,0.12,0.13,0.1490o15_0o16,0o17,0o18,0o19, 2 0°20,0o21,0o22,0.23,0.24,0.25,0o26a0o27,0.28,0.29, 3 0o30,0.31,0.32,0.33,0°34,0o35,0o36,0.37,0.38,0.39, 4 O.4O/ DATA B = DRAG COEFFICIENT DATA B/0.0001,0,0009_0.0022_0.0040,0.0063,0.0091,0o0122, 1 0o0154g0.0187,0.0221q0.0255,0.0288,0.0322,0o0356,0o0389_ 2 0.0423,0.0456,0.0490,0o0524,0.0557,0.0591,0.0625,0.0658, 3 0o0692g0o0726,0o0759,0.0793_0.0826,0.0860,0.0894,0.0927, 4 0o0961e0o0995,0o1028,0oi062,0.1096,0.1129,0.i163,0.1196, 5 0o1230/ HMIN=0o01 HMAX=0.40 IF(HoLT.HMIN) WRITE(6,10) H,HMIN l0 FORMAT(' ',19X,'H = M-MD = 'vFl0o6,' IS LESS THAN HMIN = _ &FI0.6,' OF FUNCTION CDSF'/) IF(H.GT.HMAX) WRITE(6,20) H,HMAX 20 FORMAT(' ',19Xw'H = M-MD = 'wF10o6,' IS GREATER THAN HMAX = &F10o6,' OF FUNCTION CDSF'/) N=2 IS=I IL=IS+N-1 IF(HM.LE.A(IL)) GO TO 1 IL=40 IS=IL-N+I IF(HM.GE.A(IS)) GO TO 1 IS=I IL=IS+N-I 2 IF((HM-A(IL))*(HM-A(IS)) .LE° 0o) GO TO 1 IS=IL IL=IS+N-I GO TO 2 1 DO 3 !=IS,IL X(I-IS+I)=A(I) Y(I-IS+I)=B(I) 3 CONTINUE CDSF=YLAGN(X,Y,N,H) RETURN END FUNCTION HMDF(T,ALPHAO,HM) HMDF=MD ALPHAO=EFFECTIVE ANGLE OF ATTACK T=THICKNESS-CHORD RATIO DIMENSION A(18),B(13),C(13,18),U(3),V(3),X(3),Y(3) DATA IS FROM MACDOUGALL, PP.1032-33, TABLES #lA&B DATA A = ALPHAO = ANGLE OF ATTACK WITH RESPECT TO ZERO LIFT LINE DATA A/-1.5,-lo0,-0.5_0.,0o5,1o0,1.5F2°0,2.5,3.0, 1 3°5,4.0,4.5,5.0,5°5,6.0,6.5,7°0/ DATA B = THICKNESS-CHORD RATIO DATA B/.045, .05w .06, .07g .08, .09, .i0, oli, i .12, .13, .14, .15, °16/ DATA C = CRITICAL MACH NO. FOR DRAG AT WHICH THE DRAG DEPARTS FROM ITS LOW-SPEED VALUE DATA (C(I_I),I=I,13)/ 1 0.718,0.705,0.674,0.627, i 0.620,0.5915,0.560,0.5255,0.5015,0.4715o 1 0.4435,0.412,0.378/ DATA (C(I,2),I=I,13)/ 2 0.763,0.749,0.718,0.675, 2 0.6575,0.629,0.599,0.5705,0.5425,0.514,0.487, 2 0.4575,0.4265/ DATA (C(I,3),I=I,13)/ 3 0.800,0.785,0.755,0.715, 3 0°690,0.5525,0.634,0.5065,0.5795, 3 0.5525,0.5265,0.499,0.471/ DATA (C(I 4),I=i,13)/ 4 0.820,0.811,0.782,0.750,0o728,0.709w0.691,0 674, 4 0o658,0.643,0.629,0;614,0.600/ DATA (C(I 5) I=I,13)/ 5 0o810,0.817,0°800,0.774,0.750,0.728,0.709,0 690, 5 0.672,0.656,0o640,0°625,0.613/ DATA (C(I 6) i=I,13)/ 6 0.787,0.805,0.808,0.790,0.768,0°746,0.725,0 705, 6 0.685,0o567,0.551,0.637,0.625/ DATA (C(I 7) I=i,13)/ 7 0°752,0.785,0°805,0.799,0.776,0.755,0.735,0 715,0.696, 7 0°678,0°661,0o647,0o637/ DATA (C(I 8) I=i,13)/ 8 0o735,0.761,0o796_0.800,0.774,0.752,0.732_0 715, 8 0o698,0.582,0.667,0.655,0.646/ DATA (C(I,9) I=i,13)/ 9 0o707w0o735,0°779,0.795,0.766,0o741,0.715,0 599,0°684, 9 0o671,0°662,0o654w0.648/ DATA (C(I,10) I=i,13)/ $ 0o680,0.707,0o756,0.781,0.752,0.724,0.697,0 681, $ 0°667,0°657_0°650,0.643,0°637/ DATA (C(I,II) I=i,13)/ 1 0o651_0o680,0°731,0.761,0.733,0.705,0°678,0 662,0.648, 1 0o639,0o632,0°626,0o621/ DATA (C(I,12) I=i,13)/ 2 0.621,0o650,0o702,0°737,0.713,0.684,0.660,0 644_ 2 0°630,0o620,0°611,0.605,0.600/ DATA (C(I,13) I=l,13)/ 3 0o593,0.620,0o671,0.708,0.590,0°672,0.642_0 626,0.612, 3 0.602,0.593,0.586,0.580/ DATA (C(I,14),I=I,13)/ 4 0.565,0.591,0.641,0o679,0.663,0.641,0°625,0o610, 4 0.597,0.587,0.580,0.574,0.570/ DATA (C(I,15),I=l,13)/ 5 0.537,0.563, 0.611, 0.649, 5 0.6605,0.6715,0.6825,0.6935, 5 0.7055,0.7185,0.734,0.7495,0.7665/ DATA (C(I,16),I=l,13)/ 6 0.509,0.535, 0°583, 0.620, 6 0.6325,0.646,0.6595,0.671,0.6835, 6 0.6965,0.713,0o729,0.747/ DATA (C(I,17),!=l,13)/ 7 0.481,0.507, 0°556, 0.590, 7 0.601,0°614,0o627,0.636,0.646v 7 0.656w0.6705,0.684,0.700/ DATA (C(I,i8),I=l,13)/ 8 0°453,0.479, 0.529, 0.564, 8 0.5735,0.588,0.6025,0o611,0.6205, 8 0.6295,0.644,0.657,0°673/ TCMIN=0.045 TCMAX=0.16 ALOMIN=-I.5 ALOMAX=7o0 IF(T.LT.TCMIN) WRITE(6,20) T,TCMIN 20 FORMAT(' ',IgX,'T/C = ',F10.6,' IS LESS THAN (T/C)MIN = ',F10.6, &' OF FUNCTION HMDF'/) IF(T.GT.TCMAX) WRITE(6,30) T,TCMAX 30 FORMAT(' ',IgX,'T/C = ',FIOo6,' IS GREATER THAN (T/C)MAX = ', &F10.6,' OF FUNCTION HMDF'/) IF(ALPHAO.LToABOMIN) WRITE(6,40) ALPHAO,ALOMIN 40 FORMAT(' ',lgXF'ALPHAO = ALPHA-ALPHLO = ',FI0o6,' IS LESS', &' THAN ALPHAOMIN = ',FI0.6,' OF FUNCTION HMDF'/) IF(ALPHAO.GT.ALOMAX) WRITE(6,50) ALPHAO,ALOMAX 50 FORMAT(' ',lgX,'ALPHAO = ALPHA-ALPHL0 = ',FI0.6,'IS GREATER', &' THAN ALPHAOMAX = ',F10.6,' OF FUNCTION HMDF'/) N=2 IS=I IL=IS+N-I IF(ToLEoB(IL)) GO TO 1 IL=I3 IS=IL-N+I IF(T.GEoB(IS)) GO TO 1 IS=I IL=IS+N-I 2 IF((T-B(IS))"(T-B(IL)) oLEo0o) GO TO 1 IS=IL IL=IS+N-I GO TO 2 1 JS=l JL=JS+N-I IF(ALPHAOoLE.A(JL)) GO TO 3 JL=18 JS=JL-N+l IF(ALPHAO.GEoA(JS)) GO TO 3 JS=I JL=JS+N-I 4 IF((ALPHAO-A(JS))=(ALPHAO-A(JL))oLEo0o) GO TO 3 JS=JL JL=JS+N-1 GO TO 4 3 DO 5 J=JS,JL U(J-JS+l)=A(J) 5 CONTINUE DO 6 I=ISgIL X(I-IS+i)=B(1) DO 7 J=JS_JL V(J-JS+I)=C(I,J) 7 CONTINUE Y(I-IS+I)=YLAGN(U_V,N,ALPHAO) 6 CONTINUE HMDF=YLAGN(X,Y,N,T) RETURN END C C C FUNCTION CD9F(T,ALPHAO,HM) DIMENSION AO(4),MM5(7),HM6(7),HM7(7),HM8(7), $ CD5(7),CD6(7),CD7(7)fCD8(7) DIMENSION HM3(1),HM4(1),HM9(1),MM10(1),HMII(1), 1 CD3(1),CD4(1),CD9(1),CDI0(1),CDII(1) C DATA IS FROM MACDOUGALL, P. !036, FIG. 5 C DATA AO = ALPHAO = ALGLE OF ATTACK WITH RESPECT TO ZERO LIFT LINE C DATA 'HM.NO.': 'HM' = MACH NO., '.NO.' = MACH NO.*10 C DATA 'CD.NO.': 'CD' = DRAG COEFFICIENT, '.NO.' = MACM N0.*10 DATA A0/5.,6.,7.,8./ DATA HM5/0.6545, 0.66364, 0.67273, 0.68182, 0.7, $ 0.8, 0.9/ DATA CD5/0.00909, 0.00982, 0.01091, 0.01327, 0o01818, S 0.05018, 0.08545/ DATA HM6/0.62727, 0.63636, 0.64545, 0.65455, 0.7, $ 0.8, 0.9/ DATA CD6/0.00945, 0.01, 0.01091, 0.01273, 0.02727, $ 0.06182, 0.i/ DATA HM7/0.60909, 0.61818, 0.62727, 0.63636, $ 0.7, 0.8, 0.9/ DATA CD7/0.01073, 0.01109, 0.01273, 0.01455, $ 0.03655, 0.07636, 0.12273/ DATA HM8/0.6, 0.60909, 0.61818, 0°62727, 0.7, $ 0.8, 0.9/ DATA CD8/0.01273, 0.01455, 0.01636, 0.01818, $ 0.04682, 0.09455, 0.14764/ CD9F=CDTHKF(T,ALPHA0,MM,AO,4, 1 HM5,HM6rHM7,MM8,HM3,HM4,HM9,MMI0,HMII, 2 CD5,CD6,CD7,CD8,CD3,CD4,CD9,CDI0,CDII, 3 7,7,7,7,0,0,0,0,0) RETURN END FUNCTION CDIOF(T,ALPHA0,HM) DIMENSION AO(7),HM5(10),CD5(10),MM6(10)wCD6(10), 1 HM7(10),CD7(10),HMS(10),CD8(10),HM9(10),CD9(10), 2 HM10(12),CD10(12),HMll(12)rCDll(12) DIMENSION HM3(1),HM4(1),CD3(1),CD4(1) DATA IS FROM MACDOUGALL, P. 1036, FIG. 6 DATA A0/5.,6.,7.,8.,9.,10.,i1./ DATA HM5/.62, .63, .64 v .65_ .66, .67, .7, .8, °9, 1./ DATA CD5/o0086, .009, .01, .0109, .013, .0158, .024g 1 .058, o0906, .124/ DATA HM6/.6, o61, .62, .63, .64, °65, .7,o8,°9,1./ DATA CD6/.0094, .01, .0108, .012, .0138, .016, o03, 1 .065, .105, .149/ DATA HM7/.58, °59, .60, .61_ .62, .63, .7, .8, .gu i./ DATA CD7/.01, .0104_ .011, .0121, .0141, .018, .04, 1 .078, o128, o184/ DATA HM8/.57, .58, .59, .60, .61, .62, .7, °8, .9, .97/ DATA CD8/.0112g .012, .0136, .016, .019, .0222, .05, 1 °098, o154, °2/ DATA HMg/ °54, .55, .56, .57, .58, .59, .7, .8, .9w.91/ DATA CDg/.012, .0128, .0138, .016, .018, .0216, .067_ 1 .1224v o192, .2/ DATA HMI0/.52, .53, .54, .55, .56, .57, .58, .59_ .6, .7, 1 .8, .86/ DATA CD10/.014,.0142,.016,.017,.0198,.022,.026, 1 .03, .034r .086v .151, .2/ DATA HMII/o5, .51, .52, .53, .54_ .55w .56, .57, .6, o7, 1 .8, .82/ DATA CDII/.016, .01618, .0164, .0176, °02u .023, .0262, 1 o03_ .045, .103, .178, .2/ CDIOF=CDTHKF(TgALPHAOpHM,AOw7, 1 HM5,HM6,HM7,HM8,HMg,HM10,HMI1,HM3IHM4, 2 CD5,CD6,CD7,CD8,CD9,CDI0,CDll,CD3,CD4, 3 i0,i0,i0,I0,i0,12,12,0,0) RETURN END FUNCTION CDIIF(T,ALPHAO,HM) DIMENSION AO(6),HM5(9),CD5(9),HM6(9),CD6(9), 1 HM7(9),CD7(9),MM8(9),CD8(9),HMg(II),CDg(ll), 2 HMI0(9),CDI0(9) DIMENSION HM3(1),HM4(1),HMII(1),CD3(1),CD4(1), 1 CDll(1) DATA IS FROM MACDOUGALL,P. I037, FIG. 7 DATA AO/5 ,6.,7.,8.,9.,10./ DATA HM5/ 62727, .63636, .64545,.65455, .66364, °67273, 1 7, .8, 9/ DATA CD5/ 00903, .01, .01109, .01291, .01545, .01855w 1 02727, .06182, .09818/ DATA HM6/ 6, .60909, .61818, .62727, .63636, .64545, 1 7, .8, .9/ DATA CD6/ 00964 .01, .01091, .01209, .01455, .01636, 1 03327, .06909, .ll018/ DATA HM7/ 5727_ .58182, .59091, .6, .60909, .61818, 1 7, .8, .9/ DATA CD7/ 01036 .01064, .011, .01182, .01345, .01545, 1 04364, .08545, .134/ DATA HMS/ 56364 .57273, .58182, .59091, .6, .60909, °7, 2 8, °9/ DATA CDS/ 01091 .01136, .01273, .01455, °01636, .01909, 1 05455, .10455, .16273/ DATA MMg/ 53636 .54545, .55454, .56364, .57273, o58182, 1 6, .64545, .7,.8,.88182/ DATA CDg/ 01182 .01218, .01273, .01427, .01636, o01864, 1 02491, .03291, .07091, .12909, .18/ DATA HM10/.52727 .53636, .54545, .55454, .56364,.6, 1 64545, .7, .8/ DATA CD10/.01273 .01309, .01455, .01636, .02, .0360, 1 06, .08909, .15636/ CDIIF=CDTHKF(T,ALPHAO,HM,AO,6, 1 HM5,HM6,HM7,HM8,HMg,HM10,HMll,HM3,HM4, 2 CD5,CD6,CD7,CD8,CDg,CD10wCDll,CD3,CD4, 3 9,9,9,9,11,9,0,0,0) RETURN END FUNCTION CD12F(T,ALPHAO,HM) DIMENSION AO(6),HM5(10),CDS(10),HM6(ll),CD6(ll), 1 MM7(ll),CD7(ll),HMS(ll),CDS(ll),HM9(ll),CD9(ll), 2 HM10(12),CD10(12) DIMENSION HM3(1),MM4(1),HMll(1),CD3(1),CD4(1),CDll(1) DATA IS FROM MACDOUGAL, Po 1037, FIG. 8 DATA A0/5.,6o,7.,8.,9.,I0./ DATA HM5/.59, °6, .61, .62, .63, .64, .65, °7, .8, .9/ DATA CD5/.0099, .01020, .01140, .013, .015, o017, .0198, 1 °034, .066, .10/ DATA HM6/.57, .58, .59, .6, .61, .62, .63, .64, o7_ .8, °9/ DATA CD6/.0102,.011, .012, .013, .0147, .0164, .018, .02, 1 °038, .074, .i150/ DATA HM7/.55, .56, .57, .58, .59, .60, .61, .65, .7, .8, .9/ DATA CD7/.0112, o0114, .012, .0136, .0156, .0169, .019, o03, 1 .048, .0886, .14/ DATA HM8/.54, .55, .56, .57, .58, .59, .6, .65, .7, .8, .9/ DATA CD8/.012, .0122, .014, .015, .0179, .02, .0221, .04, .06, 1 oll, .168/ DATA HM9/.52, .53v .54, .55, .56, .57, .6, .65, .7w .8, .9/ DATA CD9/.012, .013, .014, .016, .018, .02, .03, .05, .074, 1 o1302, .20/ DATA HM10/.51, .52, .53, .54, .55, .56, .57r .6, .65, .7, o8,.85/ DATA CDI0/.014, .0144, .016, .018, °02, .0237, .026, .04_ .0638, 1 o092w .158, .20/ CD12F=CDTHKF(T,ALPHAO,HM,AO,6, 1 HM5rHM6,HM7,HM8,HM9,HMI0,HMll,HM3,HM4, 2 CD5wCD6,CD7,CD8,CD9,CDI0,CDll,CD3,CD4, 3 I0,i1,ii,ii,ii,12,0,0,0) RETURN END FUNCTION CDI3F(T,ALPHAOeHM) DIMENSION AO(6),HM5(5),CD5(5),HM6(8),CD6(8),HM7(8),CD7(8), 1 HMS(9),CD8(9),HM9(9),CD9(9),HM10(8),CD10(8) DIMENSION HM3(1),HM4(1),HMII(1),CD3(1),CD4(1),CDll(1) DATA IS FROM MACDOUGALL, P.1038, FIG. 9 DATA AO/5., 6., 7., 8., 9., i0./ DATA HM5/.58, .59, .6, .7, .9/ DATA CD5/.01, .0102, .011, .038, .1027/ DATA HM6/.57, .58, .59, .6, .63, .7, .8, .9/ DATA CD6/.0103, .011, .012, .014, .02, .042, .078, .12/ DATA HM7/.56, .57, .58, .59, .6, .7, .8, .9/ DATA CD7/.0112, .012, .0134, .0154, .018, .05, .096, .146/ DATA HM8/.54, .55, .56, .57, .58, .6, .7, .8, .9/ DATA CD8/.012, .013, .014, .016, .018, .0254, .064, .114,o174/ DATA HM9/.52, .53, .54, .55, .56, .6, .7, .8, .9/ DATA CD9/.0132, .0139, .0142, .016, .018, .034, .078, 1 .1362, .2/ DATA HMI0/.51, .52, .53, .54, .6, .7, .8_ .845/ DATA CDI0/.014, .01416, .016, .02, .042, .092, .1622, .2/ CDI3F=CDTHKF(T,ALPHAO,HM,AO,6, 1 HM5,HM6,HM7,HM8,HM9,HMI0,HMll,HM3,HM4, 2 CD5,CD6,CD7,CD8,CD9,CD10,CDll,CD3,CD4, 3 5,8,8,9,9,8,0,0,0) RETURN END FUNCTION CD14F(T,ALPHAO,HM) DIMENSION AO(6),HM5(7),CD5(7),HM6(8),CD6(8),HM7(9)FCD7(9), 1 HM8(9),CD8(9),HM9(9),CD9(9),HM10(8),CD10(8) DIMENSION HM3(1),HM4(1),HMII(1),CD3(1),CD4(1),CDII(1) DATA IS FROM MACDOUGALL, P. 1038, FIG. l0 DATA AO/5.,6.,7.,8.,9.,10./ DATA HM5/.58, .59, .6, .61, .7, .8, .9/ DATA CD5/.OI, .01018, .0112, .014, .04, .074, .1079/ DATA HM6/.57, .58, .59, .6, .61, .7, .8, .9/ DATA CD6/.0108, o012, .014, .0156, .018, .047_ .084, .128/ DATA HM7/.55, .56, .57, .58, .59r .6, .7, .8, .9/ DATA CD7/.0114, .012, .0132, .0156, .018, .02, .058e .102, 1 .1526/ DATA HM8/.53, .54, .55, .56, .57, .6v .7, .8, .9/ DATA CD8/.012, .0128, .014_ .016, .02, .0286, .07, .12, .1822/ DATA MM9/.51, .52, .53, .54, .55, .6, .7, .8, .88/ DATA CD9/.0136, .0138, .0144, .016, .02, .038, .082, .1424, .2/ DATA HMI0/.5, .51, .52_ .53, .6, .7, °8, .84/ DATA CDI0/.014, .0144, .016, .018, .048, .098, o166r .2/ CD14F=CDTHKF(T,ALPHAO,HM,AO,6, 1 HM5rHM6,HM7,HM8,HM9,HMI0,HMII,HM3,HM4, 2 CD5,CD6wCD7,CD8,CD9,CD10,CDll,CD3,CD4, 3 7,8,9,9,9,8,0,0,0) RETURN END FUNCTION CDI5F(T,ALPHAO,HM) DIMENSION AO(6),MM5(7),CD5(7),HM6(9),CD6(9),HM7(10),CD7(10), 1 HMS(I1),CDS(ll),HM9(9),CD9(9),HM10(10),CDI0(10) DIMENSION HM3(1),HM4(1),HMII(1),CD3(1)gCD4(1)oCDll(1) DATA IS FROM MACDOUGALL, P.1039, FIGo Ii DATA AO/5o_ 6._ 7., 8o, 9., 10./ DATA HM5/.57, .58, °59, .6, .7, .8, .9/ DATA CD5/.01, .0104_ .0114; .013, .042, .076, oll/ DATA HM6/°55, .56, .57, °58, .59, .6, °7, °8, .9/ DATA CD6/o0104, .0108, .012, .014, .016, .018, .05, .09, .1334/ DATA HM7/°53, °54, .55, .56, .57, .58, .6w .7, .8, .9/ DATA CD7/.0113, o012, .0124, .014, o016, .02, .025, .062, 1 .106, .16/ DATA HM8/o51, .52, .53u .54, .55, .56, .57, .6, .7, .8, .9/ DATA CD8/.012_ o0122, .014, .015, .0172, .02, .022, .032, 1 °07378, .126, .19/ DATA HM9/o5, .51, °52, .53, .54, .6, .7, .8, .87/ DATA CD9/.0134, .0136, .014, .016, .02, .04, .086, .148, .2/ DATA HMI0/.5, .51, .52, .53, .54_ .55_ .6, .7, .8, .835/ DATA CD10/.0147, .0155_ .017, .02, °024, .028, °0496, .1032, 1 .172, °2/ CDI5F=CDTHKF(T,ALPHAO,HM,AO,6, 1 HM5,HM6,HM7,HM8,HM9,HMIO,HMII,HM3,HM4, 2 CD5,CD6,CD7,CD8,CDg,CDI0,CDII,CD3,CD4, 3 7,9,10,11,9,10,0,0,0) RETURN END FUNCTION CDI6F(T,ALPHAO,HM) DIMENSION AO(7),HM5(6),CD5(6),HM6(9),CD6(9),HM7(10),CD7(10), 1 HM8(ll),CD8(ll),HM9(10),CD9(10),HM10(ll),CDI0(II),HMII(I1), 2 CDII(II) DIMENSION HM3(1),HM4(1),CD3(1),CD4(1) DATA IS FROM HAINES AND MONAGHAN, P. 1187, FIG. 8 DATA AO/5., 6., 7., 8., 9., 10., ii./ DATA HM5/.55, .56667, .5833, .6, .65, .9/ DATA CD5/.01083, .01233, .015, .01833, .03333, .118/ DATA HM6/.51667, .53333, .55, .56667, .6, .65, o7, .8, °9/ DATA CD6/.01167, .01267, .015, .01833w .02667, .0425, °06, 1 .10167, .14783/ DATA HM7/.4833, .5, .51667, .53333, .55, .6, .65, °7, .8, .9/ DATA CD7/.01217, .01267, .015, .01742, .02167, .03333, .05167, 1 °07033, .11833, .178/ DATA HM8/.46667, .48333, .5, °51667, .55, .6, .65, .7, .75, 1 .8, .9/ DATA CD8/.01283, .013333, .01575, .01942, o02708, .04333, °06, 1 .08267, .105, .13667, .20192/ DATA HM9/.46667, .48333, .5, .5333, .55, .6, .7, .75, °8, 1 °89417/ DATA CD9/.01333, .01583w .01933, .02667u .0315, .04833, .095, 1 o12167, .15733, °23/ DATA HM10/.4625, .48333, .5, .525, .55w °6, .65, °7, .75, 1 .8, .85833/ DATA CD10/o015, .01867, .02217, .03, .03708, .05667, .0815, 1 .ll, .14217, .18133, .23/ DATA HMI1/.45, .45833, °46667, .5, °525, .6, .65, o7g .75, 1 .8, .81667/ DATA CDll/.01667, .01717, .01917, .02667, .03667, o06617, 1 .09367, .12633, .165, .212, .23/ CDI6F=CDTHKF(T,ALPHAO,HM,AO,7, 1 HM5,HM6,HM7,HM8,HM9,HMI0,HMll,HM3,HM4, 2 CD5,CD6,CD7,CD8,CD9,CDI0,CDIlrCD3,CD4, 3 6,9,10,11,10,11,11,0,0) RETURN END FUNCTION CDI7F(T,ALPHAO,HM) DIMENSION AO(9),HM3(4),CD3(4),HM4(7),CD4(7),CD5(6),HM5(6), 1 HM6(8),CD6(8),HM7(8),CD7(8),HM8(8),CDS(8),HMg(ll)gCD9(ll), 2 HM10(9)wCD10(9),HMII(10),CDII(10) DATA IS FROM HAINES AND MONAGHAN, P. 1188, FIG. 9 DATA AO/3., 4°, 5., 6., 7., 8., 9o, I0., ll./ DATA HM3/o64, °65, .7, .8/ DATA CD3/.01, .011, .027, .068/ DATA HM4/.59, o6, .62, .63, .65, .7, °8/ DATA CD4/.01, .011, .013, .015, .021, .0275, .08/ DATA HM5/o57, .58, .6, .65, .7, .8/ DATA CD5/.01125, .012, .01545, .0325, .0525, .095/ DATA HM6/.54, o55, °56, .57, .58, _6, o61, .8/ DATA CD6/o01225, .0125, o015, .016, .0195, .025, .02975, .ll/ DATA HM7/o52, .53, .54, .55, .57, .6_ .75, °8/ DATA CD7/.014, .015, .0154, .018, .025, .0355, .1035, .130/ DATA HM8/.5, .51, .52, .53, o55, .6, °7, °8/ DATA CD8/.015, o016, o017, °02, .025,.044, .095, .1475/ DATA HM9/o49, .5, .51, .53, o55f °57, .6, .65, .7, .75, .8/ DATA CD9/.01625, .0175, o02 W °025, .0315, .04, .052, .075, 1 o1025, .13375, .1675/ DATA HMI0/o47, °48, .5, .52, .55_ °6, .65, .7, .8/ DATA CDI0/o0175, o01875, .022, o0275, .03875, °06, .086, .1185, 1 o19/ DATA HMll/.46, °47, .5, .52, .55, °6, .65, .7, .75, °8/ DATA CDli/.01925, .02, .026, °034, .045, .07, .I, .135, o1965, 1 o2175/ CDI7F=CDTHKF(T,ALPHAO,HM,AO,9_ 1 HM3,HM4,HM5,HM6,HM7,HM8_HMg,HM10,HMll, 2 CD3_CD4,CD5,CD6,CD7,CDS,CD9,CD10_CDll, 3 4,7,6,8,8,8,1199,10) RETURN END FUNCTION CD19F (T, ALPHAO, HM) DIMENSION AO(9),HM3(6),CD3(6),HM4(6),CD4(6),HM5(5),CD5(5), 1 HM6(7),CD6(7),HM7(7),CD7(7),HM8(8),CD8(8),HMg(9)rCD9(9), 2 HM10(9),CD10(9),HMll(9),CDll(9) DATA IS FROM HAINES AND MONAGHAN, P. 1188, FIG. l0 DATA AO/3., 4., 5., 6., 7., 8., 9., I0., ii./ DATA HM3/.59, .61, .63, .65, .67, .8/ DATA CD3/.01, .0105, .01425, .02, .0275, .0925/ DATA HM4/.56, .59, .61, .63, .65, .8/ DATA CD4/.0105, .012, .01575, .02175, .03, .1025/ DATA HM5/.54, .56, .59, .61, .8/ DATA CD5/.0125_ .014, .0175, .0245, .11625/ DATA HM6/.51, .54, .56, .59, .61, .75, .8/ DATA CD6/.014, .015, .0175, .025, .034, .1085, o1355/ DATA HM7/.49, .51, .54, .56, .59, .75, .8/ DATA CD7/.015, .0154, .02, .025, .035, .124, .1515/ DATA HM8/.47, .49, .51, .54_ .56, .59, .75, .8/ DATA CD8/.016, .0175, .02, .025, .0315, .045r .1385, .171/ DATA HM9/.45, .47, .49, .51, .54, .56, .59,.75, .8/ DATA CD9/.0175, .01925, .02025, .025, .032, .04, .055, .1505, 1 .1875/ DATA HM10/.45, .47, .49, .51, .54, .56, .59, .75, .8/ DATA CDI0/.01925, .02125, .025, .03, .04, .049, .065, .17, 1 .2085/ DATA HMll/.45, .47, .49, .51, .54, .56, .59, .75, .8/ DATA CDll/.02, .02475, .0295, .035, .0465, .059, .0754, o19125_ 1 °236/ CD19 F =CDTHKF (T, AL PHAO, HM, AO, 9, 1 HM3, HM4, HM5, HM6, HM7, HM8, HM9, HMI0, HMll, 2 CD3, CD4, CD5, CD6, CD7, CD8, CDg, CDI0, CDll, 3 6,6,5,7,7,8,9,9,9) RETURN END FUNCTION CD21F(T,ALPHAO,HM) DIMENSION AO(9),HM3(6),CD3(6),HM4(6),CD4(6),HM5(6),CD5(6), 1 HM6(7) _CD6(7), HM7(6),CD7(6),HM8(7),CD8(7),HM9(7),CD9(7), 2 HM10(6),CD10(6),HMll(7),CDll(7) DATA IS FROM HAINES AND MONAGHAN, P. 1189, FIG. ll DATA AO/3., 4., 5., 6., 7., 8., 9°, 10., Iio/ DATA HM3/.57, .6, .62, .65, .67, .8/ DATA CD3/.01425r .015, .018, .026, .035, .ll/ DATA HM4/.56, .58, .6, .64, .72, .8/ DATA CD4/.01425, .0155, .01925, .0305, .075, .125/ DATA HM5/.52, .55, .58, .6, °65, .8/ DATA CD5/.01425, .015, .02, .025, .045, .1405/ DATA HM6/.5, °55, o575, °6, °65, .7, °8/ DATA CD6/.015, .02 v .025, _0335, .057, .0895, _1625/ DATA HM7/.47-, .5, o55, .6, .65, .8/ DATA CD7/.016, .018, .0255v °0425, .0705, .18/ DATA HM8/.45_ .48, .5, .55, .6_ °65, .8/ DATA CD8/.0175, o01975, .021, .0345, .0515, .084, .195/ DATA HM9/.45, .48r °52, .57 e .62, .7, °8/ DATA CD9/.0195, .022, .03045,.05, .075, o1305, .214/ DATA HM10/.44, .48, .5, .55, .65, °8/ DATA CDI0/.02, .025, .03, o0505, oli, .231/ DATA HMll/.43, °45, °48, .55, .61, .71, .8/ DATA CDll/.022, °0235, .03, .06, .i, .175, .26/ CD21F=CDTHKF (T, A L PHAO _ HM, AO, 9, 1 HM3, HM4, HM5, HM6, HM7, HM8, HM9, HMI0, HMll, 2 CD3, CD4, CD5, CD6 e CD7, CD8, CD9, CDI0, CDll, 3 6,6,6,7,6,7,7,6,7) RETURN END FUNCTION CD23F(T,ALPHAO,HM) DIMENSION AO(9)_HM3(9),CD3(9),HM4(8),CD4(8),HM5(9),CD5(9)w 1 HM6(9),CD6(9),HM7(9),CD7(9),HM8(9),CD8(9),HM9(9),CD9(9)v 2 HM10(9),CD10(9),HMII(9),CDII(9) DATA IS FROM HAINES AND MONAGHAN, P. I189, FIG. 12 DATA A0/3., 4.p 5., 6., 7., 8., 9., i0., ii.

DATA HM3/.55, .58, .6, .63, .65, .68, .7, .7 , .8/ DATA CD3/.013, .015, .017, .025, .03075, .045, .056, .09,.129/ DATA HM4/.53, .56, 58, .6, .63, .67, .71, .8/ DATA CD4/.013, .015, .0175, .02075, .03, .05, .075, .145/ DATA HM5/.48, .52, 55, .58, .6, .64, .69, .75, .8/ DATA CD5/.013, .015, .0165, .2, .02545, .039, .075, .12, .161/ DATA HM6/.49, .52, 55, .59, .6, .63, .67, .735, .8/ DATA CD6/.015, .017, .0204, .03, .034, .0495, .075, .125, .181/ DATA HM7/.4, .45, .5, .54, .58, .6, .66, .71, .8/ DATA CD7/.0155, .016, .02, .025, .035, .043, .08, .12, .205/ DATA HM8/.4, .45, .5, .53, °55, .58, .6, .71, °8/ DATA CD8/.016, .0175, .02425, .03i .035, .045, .0535, .135_ .222/ DATA HMg/.4, .45, .485, .55, .57, .6, .65, .71, .75/ DATA CD9/.0175, .02, .025, .043, .0505, °06625, .10075, .152, 1 .192/ DATA HMI0/.4, .42, .45, .5, .54, .585, .63, .69, .73/ DATA CD10/.0195, .02, .02325, .035, .05, .075, .105, .155, .19/ DATA HMII/.4, .43, .47, .5, .55, .58, .64, .72, .8/ DATA CDll/.0204, .025, .03, .0445, .07, .09, .135, .205, o281/ CD23F=CDTHKF(T,ALPHA0,HM,A0,9, 1 HM3,HM4,HM5,HM6wHM7wHM8gHM9,HM10,HMll, 2 CD3,CD4,CD5,CD6,CD7,CD8,CD9pCDI0,CDII, 3 9,8,9,9,9,9,9,9,9) RETURN END C FUNCTION CD25F(T,ALPHA0,HM) DIMENSION AO(9),HM3(8)wCD3(8),HM4(9),CD4(9),HM5(8),CD5(8), 1 HM6(8),CD6(8),HM7(9),CD7(9),HM8(9),CD8(9),HM9(9),CD9(9), 2 HMI0(8),CD10(8),HMll(7),CDII(7) DATA IS FROM HAINES AND MONAGHAN, P. ll90, FIG. 13 DATA AO/3., 4., 5., 6., 7., 8., 9., i0., Ii./ DATA HM3/.55,.58, .6, .624, .65, .68, .75, .8/ DATA CD3/.015, .0165, .02, .025, .0325, .05, .i, .1454/ DATA HM4/.52_ .55, .58, .6, .64, .65, .68, .76, .8/ DATA CD4/°015, .0155, .02, .02425, .0355, .04, .06, .125, .166/ DATA HM5/.5, .56, °59, .62, .65, .71, .75, .8/ DATA CD5/.015, .02, .025, .035, .05, .095, .135, .19/ DATA HM6/.46, .51, .55, .6, .63, .67, .725, .8/ DATA CD6/.015, o0175, .0235, .035, .05, .0775, .125, .2125/ DATA HM7/.4, .45, .5, .55, .59, .63, .68, .76_ .8/ DATA CD7/.0155_ .017, .0205, .03, .04, .06, .1, °18, .233/ DATA HM8/.4, .45, .5, °55e o59, .61, .65, .74, .8/ DATA CD8/.0175, .02w .025, °035, .05, .06, °0825, .18, .25/ DATA HM9/.4, .43, .47, °5, °55, .58, .61_ .67, .8/ DATA CD9/.0195, .02, .025, °03, .045, .0555, .075, .126, .2675/ DATA HM10/.4, o44, .49_ °53, .58, .65, .73, .8/ DATA CD10/.02, .025, .035, °04975, .076, .132, .207, .285/ DATA HMll/.4,.46, .5, .55_ .62, .71 w .8/ DATA CDII/.021, .035, .05, °078, .13, .215, .305/ CD25F=CDTHKF(T,ALPHAO,HM,A0,9, 1 HM3,HM4wHM5,HM6,HM7_HM8,HM9,HM10,HMII , 2 CD3,CD4wCD5,CD6,CD7,CD8,CD9,CD10,CDll, 3 8,9,8,8,999,9,8,7) RETURN END FUNCTION CD30F(T,ALPHAO,HM) DIMENSION AO(9),HM3(9),CD3(9),HM4(8),CD4(8),HM5(8),CD5(8), 1 HM6(9)_CD6(9),HM7(8),CD7(8),HM8(10),CD8(10),HM9(8),CD9(8), 2 HM10(8),CDI0(8),HMll(7),CDII(7) DATA IS FROM HAINES AND MONAGHAN e P.1190, FIG. 14 DATA AO/3o, 4., 5., 6°, 7o, 8., 9°_ i0., ll./ DATA HM3/.4, .55, .585, .63, .65, .69, .735, .76, .78/ DATA CD3/.015, o018, .02, .03, .037, .06o .i, .13, .16/ DATA HM4/.4, .53, .59s .64, .68, .72, .757, .8/ DATA CD4/.015, .018, .024, .04, .065, o102e .15_ .22/ DATA HM5/.4_ .51, .57, .62, °65, .7, .74, .8/ DATA CD5/.015, o018, .025, .04, .055, .l_ .15, .25/ DATA HM6/.4, .5, .55, .6, .64, .66_ .7_ .78, .8/ DATA CD6/.016, .02, °025, .0395, .06, o077, o12, .24_ °275/ DATA HM7/.46, .53, .58, .62, .65, °7, °74, .8/ DATA CD7/.02, o03, .04, .059, .081e .14, .199_ °3/ DATA HM8/.4, .45, .5, .55, .6, .68, °665, .7, .75, .8/ DATA CD8/.02, .021, .03, .041, .061, °082, o12, .165, °24, .33/ DATA HM9/.4, .45, .5, .55, .6, .65, .72, °8/ DATA CD9/.02, .025, .033, .05, .08, .133, .22, _35/ DATA HMI0/o4, .46, .5, .54, .59, .65, .73, .8/ DATA CDI0/.02,.03, .04, .06, .1, .16, .2608, .365/ DATA HMll/.4, .45, .5, .56, .61, .72, .8/ DATA CDII/.021, .035, .06f .105, .15, °277, .381/ CD30F=CDTHKF(T,ALPHAO,HM,AO,9, 1 HM3,HM4,HM5,HM6,HM7,HMS,HM9,HMIO,HMll_ 2 CD3,CD4,CD5,CD6,CD7,CD8,CD9,CD10,CDll, 3 9,8,8,9,8,10,8,8,7) RETURN END FUNCTION CD35F(T,ALPHAO,HM) DIMENSION AO(9),HM3(9),CD3(9),HM4(7)sCD4(7),HM5(8),CD5(8)_ 1 HM6(8),CD6(8),HM7(8),CD7(8),HMS(8),CD8(8),HMg(8)fCDg(8)F 2 HM10(7),CD10(7),HMll(8),CDII(8) DATA IS FROM HAINES AND MONAGHAN, P. i191, FIG. 15 DATA A0/3o,4o, 5., 6., 7., 8°, 9., i0., llo/ DATA HM3/.57 .6, .62, .65, .68, .71, .75, °78, °8/ DATA CD3/.02 .025, .0308, .042, °06, °09, o15, .205, °25/ DATA HM4/.55 .6, .65, .68, °705, °76, .8/ DATA CD4/o02 .029, °05, .075, .I, °19, °28/ DATA HM5/o53 .58, .63, .67, .7, °73, °78_ .8/ DATA CD5/.02 .028, .05, .08, olll, .16u °26, o312/ DATA HM6/o52 .565, .6, .63, .67, .71, °75, .8/ DATA CD6/o02 .03, .043, .06, oi, o15, .22, .342/ DATA HM7/.48 o54o .59, °62, °65, °7, o74_ .8/ DATA CD7/.02 °03, .05w .07, o095, o156, °23, °375/ DATA HM8/.46 .54, .59w .62, .65, .7, o75w °8/ DATA CD8/.02, .036, .06, .085, .112, o188, °29, .405/ DATA HM9/.43, .46, .52_ .564, 06, °65, °75_ °8/ DATA CD9/o02, °025, .04, o06, .088, o144, °325, .43/ DATA HM10/.4, .45, °5, .55, .6, .7,°8/ DATA CDI0/.02, .03, .05, .079, .12, .27, °45/ DATA HMll/.4, .44_ .48, .538, .587, °68, .77, °8/ DATA CDll/°021, .04, °059, oi, .15, .28, °42, °47/ CD35F=CDTHKF(T,ALPMAO,HM,AO,9, 1 HM3,HM4,HM5,HM6,HM7,HM8,HM9pHM10,HMll, 2 CD3,CD4eCD5,CD6,CD7,CD8,CD9,CDI0,CDll, 3 9,7,8,8,8,8,8_7,8) RETURN END C C C C FUNCTION CDTHKF(T,ALPHA0,HM,AO,NA, 1 HM1,HM2,HM3,HM4,HM5,HM6,HM7,HMS,HM9, 2 CD1,CD2,CD3,CD4,CD5,CD6,CD7,CD8,CD9, 3 NI,N2,N3,N4,N5,N6_N7,N8,N9) DIMENSION AO(1),HMI(1),HM2(1),HM3(1),HM4(1),HM5(1),HM6(1), 1 HM7(1),HM8(1),HM9(1)wCDI(1),CD2(1)wCD3(1),CD4(1),CD5(1), 2 CD6(1),CD7(1),CD8(1),CD9(1) DIMENSION X(Z),Y(2) ALP=ALPHAO IF(ALPoLEoAO(1)) ALP=AO(1) N=2 CALL OUT(NA,N,IS,IL,AO,ALP) DO 30 I=IS,15 X(I-IS+I)=AO(1) GO TO (1,2,3,4,5_6,7,8,9),I 1 ANS=GETF(N1,N,HM1,CDI,T,ALPHAO,HM) GO TO 20 2 ANS=GETF(N2,N,HM2,CD2,T,ALPHAO,HM) GO TO 20 3 ANS=GETF(N3,N,HM3,CD3,T,ALPHAO,HM) GO TO 2O 4 ANS=GETF(N4,N,HM4,CD4,T,ALPHAO,HM) GO TO 20 5 ANS=GETF(N5,N,HM5_CD5,T_ALPHAO,HM) GO TO 20 6 ANS=GETF(N6,N,HM6,CD6,T,ALPHAO,HM) GO TO 20 7 ANS=GETF(N7,N,HM7,CD7,T,ALPHAO,HM) GO TO 20 8 ANS=GETF(N8,N,HM8,CD8,T,ALPHAO,HM) GO TO 20 9 ANS=GETF(Ng,N,HM9,CD9,T,ALPHAO,HM) 20 Y(I-IS+l)= ANS 30 CONTINUE CDTHKF=YLAGN(X,Y,NwALP) RETURN END FUNCTION GETF(NMAX,N,XHM,YCD,T,ALPHAO,HM) DIMENSION XHM(1),YCD(1),U(3),V(3) IF(HM.GToXHM(1)) GO TO 1 GETF=YCD(1) RETURN CALL OUT(NMAX,N,JS,JL,XHM,HM) DO 2 J=JS,JL U(J-JS+l)=XHM(J) V(J-JS+l)=YCD(J) CONTINUE GETF=YLAGN(U,V,NwHM) RETURN END SUBROUTINE OUT(NMAX_N,IS,IL,Y,X) DIMENSION Y(1) IS=l IL=IS+N-1 IF(X°LE.Y(IL)) RETURN IL=NMAX IS=IL-N+l IF(X.GEoY(IS)) RETURN IS=l IL=IS+N-I IF((X-Y(IS))*(X-Y(IL))oLEo 0o) RETURN IS=IL GO TO 1 END FUNCTION YLAGN(X,Y_NwZ) C C PERFORMS THE LAGRANGE INTERPOLATION C DIMENSION X(1),Y(1) SUM=0o DO 1 l=lwN S=Io DO2 J=lpN IF(JoEQoI) GO TO 2 S=S*(Z-X(J))/(X(1)-X(J)) 2 CONTINUE SUM=SUM+S_Y(I) 1 CONTINUE YLAGN=SUM RETURN C C ..............................................................

C C END OF INFORMATION * C END C C C C SUBROUTINE ATMCON(ALTUDE,TEMP_PRES,DENwVIS,WA ) C

6O

ALTUDE=ALTUDE".3048 SLOPE=-.0065 TEMP=288oI6+SLOPE"ALTUDE EXP=2.718281828 TSEA=288°I6 PSEA=I01325.

PRESI=22700.

GRAV=9.82 R=288.

POWER=GRAV/(SLOPE*R) PRES=PSEA*(1/(TEMP/TSEA))**POWER IF(ALTUDE.LE.I1000.) GO TO 1 PRES=PRESI"EXP**(-GRAV/(R*216o66)_(ALTUDE-11000°)) TEMP=216.66 WA=SQRT(1.4*R*TEMP)/o3048 TEMP=(TEMP-273.15)*9/5+491o67 VIS=.35*(TEMP/492.)*"I.5"(690/(TEMP+I98.))_.000001 PRES=PRES*2116.2/PSEA DEN=PRES/(1718.*TEMP) ALTUDE=ALTUDE/o3048 RETURN END C C SUBROUTINE CLTMAX(T,NCLDrALPHLO,DNCLD) C * C DESIGN LIFT COEFFICIENT WITH RESPECT TO MAXIMUM C THICKNESS AND VISE VERSA FOR CLARK-Y SECTIONS * C C C REFERENCE: NACA TR 628 C ..............................................................

C * C USAGE: * C CALL CLTMAX(T,ALPHA,HM_HML,HMD_ALPHLO_NCLD,T) * C * C DESCRIPTION OF PARAMETERS: * C C ALPHLO = ANGLE OF ATTACK AT ZERO LIFT (DEGREES) C TMAX = MAXIMUM THICKNESS - CHORD RATIO C AOI = SECTION LIFT - CURVE SLOPE (DEGREES) * C C C DATA IS FROM NACA TR 628 C DATA ALPHLO/-2.9,-3.6,-4.5,-6.2,-7.6,-9o3/ C DATA TMAX/0.06,0.08_0o10,0oI4,0.18,0o22/ C DATA CLD/0.2993_0o3642,0.4461,0.5902,0.6944,0.8950/ C DALO(L)=ALPHLO(L),L=I_6 C AOI=DCL/DALO=O.1096*(1-(T/C)MAX(L))/(1-(T/C)MAX(L))**2)_".5 C THUS, CLD=(DCL/DALO)*ABS(DALO)=AOI*ABS(DALO) C PLOTTING CLD VERSUS (T/C)MAX SHOWS LINEAR RELATIONSHIP DIMENSION ALPHAO(21) REAL NCLD IF(NCLD.NEo0.) GO TO i00 C C EQUATION OF LINE CLD VERSUS (T/C)MAX: CLD=0.0328125(T/C)MAX+0.234 C TCMIN=O.06 TCMAX=0.22 IF(ToLToTCMIN) WRITE(6,20) T,TCMIN 20 FORMAT(' '_19X,'T/C = ',F10°6, IS LESS THAN (T/C)MIN = ',FI0o6_ &' OF SUBROUTINE CLTMAX'/) IF(ToGT.TCMAX) WRITE(6,30) T,TCMAX 30 FORMAT(' ';19X,'T/C = ',F10o6, IS GREATER THAN (T/C)MAX = ', &Fl0o6,' OF SUBROUTINE CLTMAX'/) NCLD=(-0.16879+SQRT(0.02849+0.496405_T))/0.2482025 AOI=AOIOF(T) C AOIOF(T) CALCULATES SLOPE OF LOW-SPEED LIFT CURVE ALPHLO=NCLD/(-AOI) DNCLD=0o GO TO 889 i00 CONTINUE CLDMIN=0.30 CLDMAX=0.90 IF(NCLD.LT.CLDMIN) WRITE(6",90) NCLD,CLDMIN 90 FORMAT(' ',29X,'CLD = ',FI0.6,' IS LESS THAN CLDMIN = ',F10.6/) IF(NCLD.GToCLDMAX) WRITE(6,105) NCLD,CLDMAX 105 FORMAT(' ',29X,'CLD = ',FI0o6,' IS GREATER THAN CLDMAX = ',FI0.6/) IF(NCLD.GE.0.0) T=0.1241*NCLD**2+0.16879*NCLD IF(NCLD.LE.0.0) T=0°1241*NCLD"*2+0.16879*NCLD AOI=AOIOF(T) ALPHLO=NCLD/(-AOI) DNCLD=lo GO TO 889 889 RETURN END FUNCTION AOIOF(T) AOIOF = VALUE OF A0, SLOPE OF THE LOW SPEED LIFT CURVE T = MAXIMUM THICKNESS-CHORD RATIO DIMENSION A(6)fH(6),X(3),Y(3) DATA IS CALCULATED FROM THE GIVEN INFORMATION FROM NACA TR 628 DATA A = SLOPE OF LOW-SPEED LIFT CURVE DATA A/0.1032,0o1012,0.0991,0.0952,0.0914,0.0876/ DATA H = MAXIMUM THICKNESS-CHORD RATIO DATA H/0.06,0.08,0.10,0o14_0.18,0o22/ N=2 AOIOF=0o1096 IF(T.LTo0o06) RETURN IS=l IL=IS+N-1 1 IF(IL.GE°6) GO TO 2 IF((T-H(IS))*(T-H(IL))oLE.0o) GO TO 3 IS=IL IL=IS+N-1 GO TO 1 2 IS=6-N+I !L=6 3 DO 4 I=IS,IL X(I-IS+I)=H(I) Y(I-IS+l)=A(I) 4 CONTINUE AOIOF=YLAGN(X,YwN,T) RETURN END FUNCTION CMFF(T,CL,M_HM) C * C MOMENT COEFFICIENTS C ABOUT THE QUARTER CHORD AND ABOUT THE LEADING EDGE C FOR CLARK - Y SECTIONS * C * Co.oo,**.°°o,**,,**o®,ooo°o******o©.oo,o°..,**,....***°***,***° _ Coo°_o,._°,,o.o,oo,o..o°,o©_***,,o.ooo°°...°,.°,°®oo.°..°.,o... _ C C TCMIN=0.05 TCMAX=0.25 IF(T.LT.TCMIN) WRITE(6,10) T_TCMIN l0 FORMAT(' ',IgX,'T/C = ',F10.6_' IS LESS THAN (T/C)MIN = ', &F10o6,' OF FUNCTION CMFF'/) IF(ToGT.TCMAX) WRITE(6,20) T,TCMAX 20 FORMAT(' ',IgX,'T/C = '_FI0.6,' IS GREATER THAN (T/C)MAX = ' &F10o6_' OF FUNCTION CMFF'/) IF(MoEQol) GO TO 1 IF(M.EQo2) GO TO 2 IF(M.EQo0) GO TO 3 C DATA IS FROM NCSTATE PROGRAM C DATA ALPHA = ANGLE OF ATTACK RELATIVE TO THE FREESTREAM C DATA "CMLE.NO.": "CMLE" = MOMENT COEFFICIENT ABOUT THE C LEADING EDGE C ".NO." = THICKNESS-T0-CHORD RATIO C DATA "CMQC.NO.": "CMQC" = MOMENT COEFFICIENT ABOUT THE C QUARTER CHORD C ".NO." = THICKNESS-TO-CHORD RATIO C PLOTTING CM VERSUS CL AT VARYING THICKNESS-TO-CHORD RATIO, C SHOWS QUADRATIC RELATIONSHIP.

C DATA ALPHA /-4,-2,0,2,4,6,8/ C DATA CMLE5 /.0158,-.0506,-.0814,-o1232,-.1776,-.2247,-.27Z4/ C DATA CMQC5 /-.0306,-°0387,-.0306,-°0272,-.0306,-.0308,-.0327/ C DATA CMLEI0 /-.0692,- 1124,-.1588,-.2131,-.2693w-.3184,-.3635/ C DATA CMQCI0 /-.0627,- 0545,-.0579,-.0610,-o0659,-.0679,-.0688/ C DATA CMLEI5 /-.1580,- 2064,-.2513,-.3060,-o3600,-.4136,-°4740/ C DATA CMQC!5 /-.0959r- 0945,-.0940,-.0988,-.1028,-.1071,-_i158/ C DATA CMLE20 /-.2463,- 2961,-.3359,-.3985,-.4642,-.5266,-o5872/ C DATA CMQC20 /-.1279,- 1282,-.1272,-°1366,-o1468,-o1553,-.1653/ C DATA CMLE25 /-.3239,- 3869,-o4429,-°5037,-.5698q-°6389,-.6996/ C DATA CMQCI_i5 /-.1550,- 1643,-°1700,-o1799,-.1902,-.2055_-.2159/ 1 CONTINUE CMLE=T**2*(-.3065*CL+.875)-T*(.1514*CL+.705)-.23993*CL+6.25/100000 CMLEMX=-.02654*CL**2-.35847*CL-.09792 IF(CMLE.LT.CMLEMX) WRITE(6,105) CMLE,CMLEMX 105 FORMAT(' ',I9X,'CMLE = ',FI0°6,' IS GREATER THAN CMLEMAX = ', &F10.6,' OF FUNCTION CMFF'/) CMFF=CMLE/SQRT(I-HM**2) GO TO 3 2 CONTINUE CMQC=(-o4¢*CL+l.15)*T**2-(o0993*CL+.785)_T+.0036*CL+.00638 CMQCMX=-.02545*CL**2-°lI281*CL+o09972 IF(CMQC.LToCMQCMX) WRITE(6,110) CMQCvCMQCMX ii0 FORMAT(' ',IPX,'CMQC = ',FI0.6,' IS GREATER THAN CMQCMAX = ', &F10.6,' OF FUNCTION CMFF°/) CMFF=CMQC/SQRT(1-HM**2) 3 RETURN END C C SUBROUTINE CYCOOR(L,CHORD,T) * THIS ROUTINE WILL GIVE DIMENSIONS AND SECTION PROP * * -ERTIES FOR A FLAT FACED CLARK-Y AIRFIOL SECTION FOR ANY * * GIVEN THICKNESS AND REFERENCE CHORD° IT ALSO CALCULATES * THE MOMENT OF INERTIA FOR THE MAJOR AND MINOR AXES° * * THE INPUT UNITS WILL CORRESPOND WITH THE OUTPUT UNITSg * * HOWEVER THE COORDINATES ARE NON-DIMENSIONAL WITH * * THE RESPECT TO THE REFERENCE CHORD. THE UPPER AND LOWER * X-COORDINATES ARE THE SAME° DIMENSION X(14),YU(14),YL(14),YUI(13),YLI(13) DATA YU1/.294,.55, o665,.808,.959,1.0,.985_.93,.83_.685,.523,°338,o

&_13/

REAL IMAJOR,IMINOR IF(LoEQ.0) GO TO 5 550 FORMAT('I',//////////////) 500 FORMAT( _ _,45X,'***',lX,'CLARK-Y A_RFOIL COORDINATES',IX, '_**', &//' ',39X,'X-COORDINATES',5X_'Y-COOR UPPER',6X,'Y-COOR LOWER'/) 600 FORMAT(' ',39X_FI0o6,8X,FI0.6,SX_F10.6) 601 FORMAT(_O',//,43X,'*"*'_lX,'CLARK-Y AIRFOIL DIMENSIONS IN FT.', &iX,'***',//,' ',39X_X-COORDINATES',5X,'Y-COORD UPPER',6X, &'Y-COORD LOWER',/) 700 FORMAT(' ',5(/),43X,'(T/C)MAX',7X,'CHORD(FT)',8X,'AREA(FT**2)', &/41X,F10°6,6X,FI0.6,7X,F10.6)

8OO

FORMAT(' _,5(/),53X,'MAJOR',I2X,'MINOR',/53X,'MOMENT',IIX_'MOMENT', &/52X,'INERTIA',IOX,'INERTIA',/49X,FIO.5,7X,FlO°5,/53X,'IN**4', &I2X_'IN**4') THICK=T IMAJOR=.0418*CHORD**4*THICK IMINOR=o0454*CHORD**4*THICK**3 YLl(1)=YUl(1) YLl(2)=ol31 YL1(3)=.0824 YLI(4)=.038 YL1(5)=.0067 DO 1 I=6,13 1 YLI(I)=0.0 X(1)=0.0 X(2)=.0025 X(3)=.025 X(4)=2"X(3) DO 2 I=l,10 2 X(I+4)=FLOAT(I)/10.

RADLE=.015*CHORD RADTE=.086=THICK AREA=.7245*CHORD*THICK YU(1)=YUI(1)'THICK YL(1)=YLI(1)*THICK DX=RADLE-X(2) DY=SQRT(RADLE**2-DX**2) YU(2)=YU(1)+DY YL(2)=YL(1)-DY DO 3 I=3,14 YU(1)=YUI(I-I)*THICK 3 YL(1)=YLI(I-I)*THICK NUMPTS=14 WRITE(6,550) WRITE(6q500) WRITE(6,600) (X(1),YU(I),YL(I ,I=I,NUMPTS) WRITE(6,601) DO 4 I=I,NUMPTS X(1)=X(I)*CHORD YU(1)=YU(I)*CHORD YL(1)=YL(1)*CHORD 4 WRITE(6,600)X(1),YU(1),YL(I) WRITE(6,700)THICK,CHORD_AREA WRITE(6,800)IMAJOR, IMINOR 5 RETURN END C C //$DATA C C

Appendix II ClarkY Program Cases Case 1 Input/Output //CLARKY dOB (R230,OOGB,SO2oOO3,AT)o'CLARKY' //aMAIN USER=R2305AT,DRG=XERDX //*FORMAT PR,DDNAME=,JDE=JFMTI,FORMS=IIIi //*XBM WATFIV C C* THIS PROGRAM WILL CALCULATE THE LIFT COEFFICIENT, DRAG, * C* AND MOMENT COEFFICIENT ABOUT THE QUARTER CHORD OR THE * C* LEADING EDGE, COORDINATES FOR A CLAYK Y AIRFOIL SECTION * C * , C i DIMENSION CL(25,25),CD(25,25),CLD(25,25)oALPHA(7),ALPHAO(21)o &RN(25),CM(25,25) 2 REAL HM(4),NCLD 3 DATA HM/O.O,O.l,O,2,0.4/ 4 DATA ALPHA/-I.O,O.Oo 1.0,2.0,3.0o4.0,5.0/ 5 DATA ALTUDE/IO000./ C C NOTE: CHORD MUST BE IN FEET C B DATA CHORD/O.?5/ 7 DATA NUMACH/4/ B DATA NUMALP/7/ 9 DATA NCL/I/ I0 DATA NCD/I/ C 11 CALL ATMCON(ALTUDE,TEMPoPRES_DENoVIS,WA) -.j C C SPECIFY HERE THE KNOWN VALUE OF CLD OR TMAX C SET THE UNKNOWN VARIABLE (CLD OR (T/C)MAX) EQUAL TO ZERO C FOR EXAMPLE° NCLD=UNKNOWN VALUE OF CLD,T=KNOWN VALUE OF (T/C)MAX C NOTE: THIS CLD IS INCOMPRESSIBLE AND ONLY TO START THE CODE° 12 DATA NCLD/O.O0/ C C IN ORDER TO BE CONSISTANT T IS NON-DIMENSIONAL C 13 DATA T/0.11?O/ C 14 CALL CLTMAX(T,NCLD,ALPHLO,DNCLD) C C SPECIFY HERE THE DESIRE FOR CLARK - Y AIRFOIL SECTION COORDINATES C AND ITS MOMENTS OF INERTIA BY INDICATING "I" FOR "YES", AND "0" C FOR "NO" FOR PARAMETER "L" C FOR EXAMPLE, L=I 15 DATA L/i/ 16 CALL CYCOOR(L,CHORDoT) C 17 WR!TE(G,IO) 18 10 FORMAT('I',/////////,56X,'***',IX,'LIMITATIONS',IX,'**_'//) C C SPECIFY HERE THE DESIRE FOR MOMENT COEFFICIENTS - EITHER CM C ABOUT THE NOSE OR THE QUARTER CHORD - BY INDICATING "I" FOR C "CM ABOUT THE NOSE" AND "2" FOR "CM ABOUT THE QUARTER CHORD" C FOR THE PARAMETER "M". IF CM IS NOT DESIRED, INDICATE "0" FOR C PARAMETER "M".

C FOR EXAMPLE, M=I.

t9 DATA M/2/ 000000"0 9_6600"0 O000_L'O 000000"0 6_96_0"0 0009L9"0 000000"0 868_0"0 000009"0 000000"0 60|090'0 000_'0 000000"0 _88_L0"0 0000_'0 000000°0 L09_80"0 O00_LS"O 000000"0 _8_980"0 000008"0 000000"0 09LL80"O 000_'0 88_000"0 _80"0 0000_0 _88800"0 _060LO'O O00GLO'O _8_LO0 0 _g8_O 0 O0_L80 0 _6_0"0 _9_8_0"0 O_L8_O'O _6_0_0 0 _0_80"0 _LS_O0 0 86LG_O'O 86L_0"0 000000"0 _3M07 06000-A _3ddN 06003-I $31_Nlf16000-X *** "I_ NI SNO_ISN3_IO -]IO_BIV A->I6vq3 *** 000000 0 _8_0"0 000000'_ 000000"0 9_$680"0 000006'0 000000"0 &B&_90"O 000008"0 000000'0 _P_O80"O O0000L'O CO 000000"0 O_L60"O 000009'0 000000"0 0_880_'0 000005"0 000000"0 9_9_'0 O000Q_'O 000000"0 O00L_'O 000008"0 _8LO00"O 80_l'0 00000_'0 9_00"0 989_60"0 00000_'0 _9600"0 908LLO'O 000090"0 L_8_O'O 0_8_90"0 0009_0"0 L_SL_O'O 69_0'0 009_00"0 868_80'0 868_80'0 000000"0 _3_07 6003-A _3dd_ _OOO-A S31VNIOBOOO-X *** S3IVNI06003 310_IV A-_V73 **_

(T/C)MAX CHORD(FT) AREA(FT_2)

O.ii7000 0.750000 0.063575

MAdOR

MINOR

MOMENT MOMENT

INERTIA INERTIA

0.00155 0.00002

IN_4

IN_4 q_

CLARK Y SERIES AIRFOIL DATA BANK * CLARK Y SERIES AIRFOIL DATA BANK *

ALTITUDE = 9999.9960 FEET ALTITUDE = 9999.9960 FEET CHORD : 0.?50000 FEET CHORD = 0.750000 FEET (T/C)MAX = 0. II?000 (S) (T/C)MAX = 0.117000 (S) CLD = 0.505381 CLD = 0.505381 ALPHALO = -5.t86451 DEG. ' ALPHALO = -5.186451 DEG.

MACH NO. = 0.000000 MACH NO. = 0.100000 REYNOLDS NO. = O.O00000E O0 REYNOLDS NO. = 0.411794E 06 ",,4 ALPHA CL CD CL/CD CM(I/4) ALPHA CL CD CM(l/4) CL/CD -1.000000 0.418226 0.009360 44.680600 -0.0?5595 -I.000000 0.420333 0.009360 44.905680 -0.076005 0.000000 0.518126 0.009712 53.347590 -0.076998 0,000000 0.520736 0.009712 53.616340 -0.077422 1.000000 0.618026 0.010203 60.574240 -0.0?8400 1.000000 0.621140 0.010203 60.8?9400 -0.078839 2.000000 0.717926 0.011083 64.7?6260 -0.079803 2.000000 0.?21543 0.011083 65.102600 -0.080256 3.000000 0.817826 0.011724 69.757200 -0.081206 3.000000 0.821946 0.011724 ?0.108620 -0.081673 4.000000 0.917726 0.012258 74.86?980 -0.082609 4.000000 0.922349 0.012258 75.245140 -0.083090 5.000000 1.017626 0.013931 73.04?980 -0.084011 5.000000 1.022752 0.013931 ?3.415930 -0.084507 * CLARK Y SERIES AIRFOIL DATA BANK CLARK Y SERIES AIRFOIL DATA BANK ALTITUDE = 9999.9960 FEET ALTITUDE = 9999.9960 FEET CHORD = 0.750000 FEET CHORD = 0.750000 FEET (T/C)MAX = 0.117000 (S) (T/C)MAX = 0.117000 (S) CLD = 0.505381 CLD = 0.505381 ALPHALO = -5.18645i DEG. ALPHALO = -5.186451 DEG.

MACH NO. = 0.200000 MACH NO. = 0.400000 REYNOLDS NO. = 0.823587E 06 REYNOLDS NO. = 0. i64717E 07 ALPHA CL CD CL/CD CM(I/4) ALPHA CL CD CL/CD CM(I/4) -1.000000 0.426850 0.009360 45.601940 -0.077277 -1.000000 0.456322 0.009360 48.750530 -0.083064 0.000000 0.528810 0.009712 54.447640 -0.078738 0.000000 0.565322 0.009712 58.206980 -0.084734 1.000000 0.630770 0.010203 61.823330 -0.080200 1.000000 0.674322 0.010203 66.091910 -0.086404 2.000000 0.732730 0.011083 66.111990 -0.081661 2.000000 0.783321 0.011083 70.676690 -0.088074 3.000000 0.834690 0.011724 71.195640 -0.083122 3.000000 0.892321 0.011724 76.111350 -0.089744 4.000000 1.001321 0.012258 81.687630 -0.091414 4.000000 0.936650 0.012258 76.411800 -0.084583 5.000000 1.038610 0.013931 74.554260 -0.086044 5.000000 1.110320 0.013931 79.701840 -0.093084 Case 2 Input/Output //CLARKY JOB (R230oOO6B_SO2oOO3,AT),'CLARKY' //*MAIN USER=R2305A?,ORG=XEROX //_FORMAT PR,DDNAME=,dDE=dFMTI,FORMS=11_I //_XBM WATFIV C C* * C* THIS PROGRAM WILL CALCULATE THE LIFT COEFFICIENT, DRAG, * C* AND _OMENT COEFFICIENT ABOUT THE QUARTER CHORD OR THE * C* LEADING EDGE, COORDINATES FOR A CLAYK Y AIRFOIL SECTION * C • C DIMENSION CL(25o25),CD(25,25),CLD(25,25),ALPHA(7),ALPHAO(21), &RN(25),CM(25o25) 2 REAL HM(2),NCLD DATA HM/0.6,0o85/ DATA ALPHA/-2.0,O.O,2.0,4.0,6.0,B.O, IO.O/ DATA ALTUDE/iO000./ C C NOTE: CHORD MUST BE IN FEET C \ 6 DATA CHORD/0.75/ DATA NUMACH/2/ DATA NU_ALP/7/ DATA NCL/I/ DATA NCD/I/ .C ...j CALL ATMCON(ALTUDE,TE_P,PRESoDEN,VIS,WA) oJ C C SPECIFY HERE THE KNOWN VALUE OF CLD OR TMAX C SET THE UNKNOWN VARIABLE (CLD OR (T/C)MAX) EQUAL TO ZERO C FOR EXAMPLE_ NCLD=UNKNOWN VALUE OF CLDoT=KNOWN VALUE OF (T/C)_AX C NOTE: THIS CLD IS INCOMPRESSIBLE AND ONLY TO START THE CODE.

t2 DATA NCLD/O.O0/ C C IN ORDER TO BE CONSISTANT T IS NON-DIMENSIONAL C DATA T/0.30/ C 14 CALL CLTMAX(T,NCLD,ALPHLO,DNCLD) C C SPECIFY HERE THE DESIRE FOR CLARK - Y AIRFOIL SECTION COORDINATES C AND ITS _OMENTS OF INERTIA BY INDICATING "1" FOR "YES", AND "0" C FOR "NO" FOR PARAMETER "L" C FOR EXAMPLE, L=I DATA L/I/ t6 CALL CYCOOR(L,CHORD,T) C '17 WRITE(G,10) 10 FORMAT('I',/////////,56X,'***',_X,'LIMITATIONS',IX,'***'//) C C SPECIFY HERE THE DESIRE FOR MOMENT COEFFICIENTS - EITHER CM C ABOUT THE NOSE OR THE QUARTER CHORD - BY INDICATING "I" FOR C "C_ ABOUT THE NOSE" AND "2" FOR "CM ABOUT THE QUARTER CHORD" C FOR THE PARAMETER "M". IF CM IS NOT DESIRED, INDICATE "0" FOR C PARAMETER "M".

C FOR EXAMPLE, _=I.

19 DATA M/2/ 000000"0 9_P9_0'0 O000_L'O 000000"0 O_09LO'O O00_L9"O 000000"0 9L9L_'O 000009'0 000000'0 _9_'0 000_9"0 000000"0 0_L98_'0 O000gV'O 000000'0 0_60_'0 0009L8'0 000000"0 9_9_'0 000008"0 000000"0 0009_'0 0009_'0 809_00"0 9LLg_'O 00009_'0 099800"0 008_8L'0 O009LO'O 0_98L0"0 9_96V_'0 O0_LSO'O 9L_6EO'O 09L8_'0 09L8_0"0 L_8090"0 89_L0"0 9L8_00"0 09_990"0 09_990"0 000000"0 63MOH G_OO3-A 63ddN U_OOD-A S31VNIQ_OOD-X *** '1_ NI SNOISNB_IO IIO_B!V A-N_Vl3 *** 000000"0 006880"0 000000"_ 000000"0 OOP_O_'O 000006"0 000000"0 00699_'0 000008"0 000000"0 00990_'0 O0000L'O 000000'0 O006V_'O 000009'0 000000"0 O006L_'O 000009"0 000000"0 00996_'0 00000_'0 000000"0 000008"0 000008"0 050_00'0 OOLLS_'O 00000_°0 00_0"0 O0_P_'O 00000_'0 O_L_O'O 00966_'0 000090"0 00_680"0 00099_'0 0009_0'0 6_80"0 _L_960"0 009_00"0 00_880"0 00_880"0 000000"0 63_07 _O00-A 83ddn BOOD-A S31VNIO6OOD-X *** S3iVNI06003 910_BIV A-NBV93 **_

(T/C)MAX CHORD(FT) AREA(FT_2)

0.300000 0.750000 0.163012 MAdOR MINOR MOMENT MOMENT INERTIA INERTIA 0.00397 0.00039 IN**4 IN*_4 .,..j *** LIMITATIONS *** T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.177439 IS GREATER THAN CMQCMAX = -0,004924 OF FUNCTION CMFF ALPHAO = ALPHA-ALPHLO = 12.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 12o712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0,187114 IS GREATER THAN CMQCMAX = -0.027959 OF FUNCTION CMFF ALPHAO = ALPHA-ALPHLO = 14.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 14.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION COFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF ,,,j CMQC = -0.196789 IS GREATER THAN CMQCMAX = -0.052096 OF FUNCTION CMFF oh ALPHAO = ALPHA-ALPHLO = 16.712020 IS GREATER THAN ALPHAOMAX = 1t.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 16.712020 IS GREATER THAN ALPHAOMAX : 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.206464 IS GREATER THAN CMQCMAX = -0.077333 OF FUNCTION CMFF ALPHAO = ALPHA-ALPHLO = 18.7i2020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION COFF ALPHAO = ALPHA-ALPHLO = 18.?12020 IS GREATER THAN ALPHAOMAX = 11,000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.216139 IS GREATER THAN CMQCMAX = -0.103671 OF FUNCTION CMFF ALPHAO = ALPHA-ALPHLO = 20.?12020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 20.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.225814 IS GREATER THAN CMQCMAX = -0.131110 OF FUNCTION CMFF ALPHAO = ALPHA-ALPHLO = 22.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION COFF ALPHAO = ALPHA-ALPHLO = 22.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.235489 IS GREATER THAN CMQCMAX = -0,159650 OF FUNCTION CMFF MACH NO. = 0.850000 IS GREATER THAN MACH NO.(MAX) : 0.800000 OF FUNCTION THKSLP T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.177439 IS GREATER THAN CMQCMAX = -0.004924 OF FUNCTION CMFF MACH NO. = 0.850000 IS GREATER THAN MACH NO.(MAX) = 0,800000 OF FUNCTION THKSLP ALPHAO = ALPHA-ALPHLO = 12,712020 IS GREATER THAN ALPHAOMAX = II.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 12.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0o187114 IS GREATER THAN CMQCMAX = -0.027959 OF FUNCTION CNFF MACH NO, = 0.850000 IS GREATER THAN MACH NO,(MAX) = 0.800000 OF FUNCTION THKSLP ALPHAO = ALPHA-ALPHLO = 14.712020 IS GREATER THAN ALPHAOMAX = il.O00000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = i4.7i2020 IS GREATER THAN ALPHAOMAX = II.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.196789 IS GREATER THAN CMQCMAX = -0.052096 OF FUNCTION CMFF _j _j MACH NO. = 0.850000 IS GREATER THAN MACH NO.(MAX) = 0.800000 OF FUNCTION THKSLP ALPHAO = ALPHA-ALPHLO = 16.712020 IS GREATER THAN ALPHAOMAX = ll.O00000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 16.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0,300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.206464 IS GREATER THAN CMQCMAX = -0.07J333 OF FUNCTION CMFF MACH NO. = 0.850000 IS GREATER THAN MACH NO.(MAX) = 0.800000 OF FUNCTION THKSLP ALPHAO = ALPHA-ALPHLO = t8.7t2020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 18.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.216139 IS GREATER THAN CMQCMAX : -0.103671 OF FUNCTION CMFF MACH NO. = 0.850000 IS GREATER THAN MACH NO.(MAX) = 0.800000 OF FUNCTION THKSLP ALPHAO = ALPHA-ALPHLO = 20.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF ALPHAO = ALPHA-ALPHLO = 20.712020 iS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.225814 IS GREATER THAN CMQCMAX = -0.131110 OF FUNCTION CMFF

MACH NO.= 0.850000 IS GREATER THAN MACH NO.(MAX) = 0.800000 OFFUNCTION THKSLP

ALPHAO = ALPHA-ALPHLO = 22.712020 IS GREATER THAN ALPHAOMAX = 11.000000 OF FUNCTION CDFF

ALPHAO = ALPHA-ALPHLO = 22.712020 IS GREATER THAN ALPHAOMAX = li.O00000 OF FUNCTION CDFF T/C = 0.300000 IS GREATER THAN (T/C)MAX = 0.250000 OF FUNCTION CMFF CMQC = -0.235489 IS GREATER THAN CMQCNAX = -0.159650 OF FUNCTION CMFF Oo CLARK Y SERIES AIRFOIL DATA BANK CLARK Y SERIES AIRFOIL DATA BANK * ALTITUDE = 9999.9960 FEET ALTITUDE = 9999.9960 FEET CHORD = 0.750000 FEET CHORD = 0.750000 FEET (T/C)MAX = 0.300000 (S) (T/C)MAX : 0.300000 (S) CLD = 1.016961 CLD = 1.016961 ALPHALO = -12.712020 DEG.

ALPHALO = -12.712020 DEG.

MACH NO. = 0.600000 MACH NO. = 0.850000 REYNOLDS NO. = 0.247076E 07 REYNOLDS NO. = 0.350024E 07 ALPHA CL CD CL/CD CM(I/4) ALPHA CL CD CL/CD CM(1/4) ",4 LO -2.000000 0.787648 0.132073 5.963749 -0.221799 -2.000000 0.787648 0.444107 t.773553 -0,336836 0.000000 0.934707 0.194073 4.816274 -0.233893 0.000000 0.934707 0.457249 2.044195 -0.355202 2.000000 1.081765 0,256073 4.224447 -0.245987 2.000000 1.081765 0.470393 2.299704 -0.373568 4.000000 t.228824 0.318072 3.863345 -0,258080 4.000000 1.228824 0.483535 2.541334 -0.391934 6.000000 1.375882 0.380072 3,620055 -0.270174 6.000000 1.375882 0.496678 2.770166 -0.410301 8.000000 t.522942 0.442072 3.445008 -0.282268 8.000000 t.522942 0.509821 2.987208 -0.428667 10.000000 1.670000 0,504071 3.313024 -0.294362 10.000000 1.670000 0.522964 3.193339 -0.447033 II.NACA 4-DIGIT AIRFOIL DATA BANK 1. Introduction With the advent o£ the NACA 4-digit family of airfoils, a convenient and systematic method of design was created, treating separately the camber and thickness distributions. For example, the airfoil thickness distribution for the NACA 4-digit family was obtained by uncambering airfoils such as the Gottingen 398 and the Clark-Y. The designation of the NACA 4-digit airfoil family is related to the section geometry where the first integer indicates the maximum value of the mean line ordinate Yc in percent of the chord. The second number indicates the distance from the leading edge to the location of the maximum camber, and the last two digits indicate the thickness of the section in % chord. The NACA 4-digit data bank computer program listed in Appendix I provides lift, drag, and moment coefficients about the airfoil quarter chord or leading edge. The coordinates for these NACA 4-digit airfoils have the maximum camber located at mid-chord, and therefore have the designation X5XX. The data base for the computer code has been derived from the study of McCormick, et.al. (I), and the airfoil coordinates and moment coefficients are calculated using the method of dacobs, et.al.(2). It should be noted that a] ] interpolation and extrapolation is done by the Lagrangian method in subroutine LINEAR.

The current data bank has been compared to the airfoil analysis code of Smetana, et.a]. (3), with the results given in Table I. As noted, the absolute difference between the theoretical predictions of= Smetana et.al, and the NACA 4-digit airf=oil data bank is acceptable with an average deviation of 6.4% f=or all cases.

2. Input The User may speci f=y any a i rf=oi 1 of = the NACA 4-di g i t f=am i 1y which has the maximum camber at the mid-chord position. A maximum of= tO values of (t/C)ma x may be specified, and either the maximum mean line ordinate in per cent of chord (Z), or the design 1 if=t coefficient (Cld) can be evaluated at any one time.

A compl ere 1 i sting of input parameters and associated descriptions is given in Table If. It may be noted that the Reynolds number may be suppl led by the variable, RE, or may be computed f=rom CHORD, MACH, and ALT specif=ied in the input. In this case, the variable RE must be set to 0.0, and any value between 4XiO 5 to 1XI0 7 based on airf=oil chord is computed.

3o Main Program The main program routes the various input parameters to the subroutines, with the computations From the subroutines returned to the main program and output° There are, however, several parameters that are computed in the main program. For example, to obtain C 1 and C d it is necessary to initially obtain the optimum lift coef=ficient, Clopt, given by the equation: II-I Clopt : Z C(Re) D((t/c)max)

where Z is the (y/c) percentage of maximum camber. The Reynolds

number function (C(Re)) and thickness function (D(t/C)ma x) For optimum lift coefficient are expressed as: II-2 C(Re) = -14.0(AtoglO(Re)-6.O) + 24.5 iI-3 D((t/c)max) = -3.8438((t/c)max) + 1.0 The drag coefficient is then computed by summing the increments due to lift not being optimum, camber, thickness, and Reynolds number.

When the lift coefficient is not optimum, the increase in drag is found through the parameter, X, given as: C l - Clopt X = II-4 Clmax- Clopt This Factor is translated to a &C d by Figure I in subroutine CDL.

The effects of camber and thickness are found in subroutine CDMN, and the effects of Reynolds number (E(Re)) are obtained in RECD finally yielding: Cdmin = Cdmin ! E(Re) II-5 The drag coefficient is then found as a sum of these effects, ioe., C d = Cdmin + AC d i I-6 The lift coefficient is a result of the angle of attack, camber, and (t/C)ma x. The design lift coefficient is either given as an input parameter or found from the maximum camber

parameter, Z, in subroutine CLDVSZ. The lift-curve slope is

computed by a series of IF statements for various (t/C)ma x values: dC 1 t-(t/c)max II-7 A 0 - 1 d_ y l-((t/c)max) A o is prescribed by the value of (t/C)ma x as follows: (t/C)ma x Ao 20% 0.1321 20%-17% 0.1216 16%-14% 0.1175 13%-11% 0.1134 10%-08% 0.1043 07%-05% 0.1039 < 05% 0.1021 The increment of 1 ift due to angle of attack is then calculated by : dC 1 AC 1 = u_ e I [-8 d_ and is corrected for compressibi 1 ity effects by the Prandtl- Glauert correction factor: I I-9 (aCl)comp = (ACl)inc /V 1-'_ Final ly, the lift coefficient is found by: II-lO C 1 = C 1 + AC 1 The remainder of the main program consists of: CALL statements for various subroutines and output statements for the data.

4. Subroutine ATMCON ATMCON calculates the temperature, pressure, speed of sound, density, and viscosity for a specified altitude using the empirical equations of Minzer, et.al.(4) as given by Anderson (5).

These equations have been curve fit from the available data off the ARDC 1959 standard atmosphere (4), and divide the atmosphere into two regions,i.e., from sea level to 1 1,000 meters, and 11,000 to 25,000 meters. These equations are given as: Sea level to 1 tzO00 meters.

Tamp = 288. 16 - 0.0065 h I I-11 P = (101325)/(1/(Temp/288. 16) )-5.2457 II-12 qr e 11,000 meters to 25z000 meters.

Tamp = 216.66 11-13 P = (22,703.59)exp(0.0001547(h-ll,000)) II-14 where h is in meters, Temperature is in "K,and pressure P is in N/m 2. The values of P and temperature are converted by; Temp = (Temp - 273.15) 9/5 + 491.67 I 1-15 P = 2116.2 P/101325 II-16 where Temp and P are now in units of "R and lbs/ft 2, respectively. Values of density, viscosity, and speed of sound are then calculated by; Density = (Pressure)/(1718)(Temp) 11-17 Viscosity=B.5x 10 -7 (Temp/492)l-5(690/(Temp+198)) I 1-18 Speed of Sound = (403.2)(Temp)/0.3047 II-19

V '

where density is on lb-ft2/sec 4, viscosity in lb-sec/ft 2, and speed of: sound in Ft/sec.

5. Subroutine CLDVSZ Subroutine CLDVSZ finds the maximum camber ,Z, if the design lift coefficient, Cld, is input, or will obtain Cld if Z is input given (t/C)ma x. The tabular data contained in the subroutine are ffor C1d values of 0.2, 0.4, 0.6, and 0.8, and for maximum camber values of 0.02, 0.04, 0.06, 0.08. Data are also contained for (t/C)max values of 4, 6, 9, 12, and 18 percent. If any of the required input correspond to values not listed above, subroutine LINEAR will interpolate between or extrapolate beyond the tabular data.

The data for these relationships were obtained using the airfoil analysis program of Smetana, et.al.(3)o Sweeps were made for different values of Cld and Z for various (t/C)ma x values.

Also, different values of Reynolds number were investigated and shown to have a minimal effect on Cld , therefore Reynolds number was not included as a function of the Cid, Z relationship.

6. Subroutine MAXCL The maximum lift coefficient is estimated as a function of the maximum camber Z and the thickness of the airfoil, (t/C)ma x- The tabulated data in this subroutine were obtained by taking the values given in Figure 2, i.e., Clmax versus (t/C)max for various Z values, as given by McCormick (1) . The Eppler airfoil analysis code (6) was also used to partially verify the results contained in the data bank.

7. Subroutine CDL

Subroutine CDL finds the eFFect of 1 iFt on the drag

coefficient. The data was tabulated From Figure 1 For which the

eFFects oF Z were included, and when necessary interpolated using subroutine LINEAR.

8. Subroutine CDMN The minimum drag coeFFicient For Reynolds numbers between 6XIO 5 and IXlO 7 are calculated in the CDMN subroutine. LINEAR is used to interpolate between the tabulated data For 6 values oF camber and 12 values of (t/C)ma x contained within the computer code. These data were taken from Figure 3 and expanded using Smetana, et°al. (3).

9. Subroutine RECD.

Subroutine RECD tabulates the data contained in Figure 4 to add the Reynolds number effects to the minimum drag coefficient.

The value obtained is multiplied in the main program by the minimum drag coeFFicient Found previously in CDMN to obtain CDMIN. The Reynolds number effects are such that Reynolds numbers lower than 6X10 5 increase the minimum drag while Reynolds numbers greater than 5XIO 6 lower the minimum drag.

tO. Subroutine FDCOOR This subroutine calculates the y/c dimensions oF a NACA 4- digit airfoil section. The Following equations are used in the computation, and the symbols are defined as: II _0 X u = X - Yt sin 8 II-21 Yu = Yc - Yt cos e II-22 x I = x + YI sin e II-23 Y1 = Yc + Yt cos e where ; e tan -I (dYc/dxc) X u - abscissa of a point on the airfoil upper surface X I - abscissa of a point on the airfoi I lower surface X c - abscissa of point on the mean line Yc - ordinate of point on the mean line Yu - ordinate of point on the upper surface of a wing section YI - ordinate of point on the upper surface of a wing sect ion Yt - ordinate of point on the surface off a symmetrical section X u and X 1 are at a common chordw i se 1 coat ion. Yt, nondimensional ized by the chord represents the ordinate of the symmetrical thickness distribution found by the equation: Yt (t/c)max (0.2969 X - 0.1260 X - 0.3516 X 2 + 0.2843 X 3 c 0.20 - 0oi015 X 4) II-24 where t is the non-dimensional maximum thickness expressed as a fract i on of the chord. The Iead i ng edge radi us nondimensionel ized by the chord is defined by: r t = I.I019 ((t/c)max) 2 11-25 C

The shape of the mean line is expressed analytically as two

parabol ic arcs that are tangent at the maximum camber

location (T) , and are expressed as: (Forward of the maximum ordinate) Z Yc - p2 ( 2 P X X 2) 11-26 (Aft of the maximum ordinate) Z Yc - ((I-2 P) + 2 P X - X 2) I1-27 (l-p2) Z is the maximum ordinate of the mean line as defined earlier, and P is the chordwise position of the maximum ordinate which has been fixed at 0.5. The y-dimensions are computed at 14 locations to calculate the moment coefficient by subroutine QCCM.

11. Subroutine QCCM With the coordinates generated in FDCOOR, the moment coefficient is Found by applying a method developed by Pankhurst (8) uti 1 izing the airFoi 1 coordinates. The quarter chord moment coefficient is found by the summation: Cmc/4 = ZB ( Yu + YI) II-28 where the coefficient B is defined in Table [II as a Function of the non-dimensional chordwise location, X° The moment coefficient about the leading edge of the airfoi 1 is found From the equet ion: Cml e = Cmc/4 - 0°25 C 1 II-29

The effects of compressibility are accounted for by the Prandtl-

Glauert factor, i.e., (Cmc/4,1e)inc II-30 (Cmc/4)comp = ! - M2" 12 Subroutine FDCR Subroutine FDCR employs the same equations as subroutine FDCOOR. However, 53 stations along the airfoil chord are computed if desired and given in tabular form in the output. This subroutine has been added to allow the User to obtain a detailed set of airfoil coordinates for later use in the airfoil analyses codes of Eppler(6) and Smetana, et.al. (3).

I3. Subroutine AREA This subroutine finds the area, coordinates of the centroid and moments of inertia for the NACA 4-digit airfoil cross section under study. The subroutine employs a trapezoidal integration scheme to find the cross sectional area. The moments of inertia are found by utilizing: le IMAJOR = S Y2 dA (in 4) li-31 te le IMINOR = # X 2 dA (in 4) [[-32 te 14. Limitations The following limits are suggested to guide the User for proper utilization of the NACA 4-digit airfoil data bank. These limitations can be exceeded slightly with minimal error, however caution must be exercised as to the extent these limitations are violated. The Reynolds number for which the airfoil data bank is valid ranges from 4XI05 to lOX106, and maximum Z values of less than O.09.The maximum camber relationship is governed by limits of Cld and (t/C)ma x as given in subroutine CLDVSZo The flags appear as: (1) REYNOLDS NUMBER=O.5OOOOOE 04 IS LESS THAN RE(MIN) = 0.400E 06 (2) LIMITATIONS FOR MACH NO. = 0.90 (3) MAX. CAMBER = 0.I0 IS GREATER THAN Y/C(MAX) = 0°90 FOR CLD = 0.90 AND T/C = 0.12 15. Output A sample case is given in Appendix II to show how the code is used, and corresponds to an angle-of-attack sweep from -tO to 8 degrees in increments of 2 degrees at a Mach number of 0.I9.

The Full output was selected to show the capabilities and output Format of the computer code.

9O

REFERENCES

1. McCormick, B.W., Eisenhuth, d.J., and Lynn,J.E., "A Study of

Torpedo Propellers" - Part I and II, March 1956.

2. dacobs, E.N., Ward, K.E., and Pinkerton, R.M., "The Characteristics of 78 Related Airfoil Sections From Tests in the Variable - Density Wind Tunnel", NACA Report No. 460, 1933.

3. Smetana, F.O., 5ummey, D.C., Smith, N.S., and Carden, R.K., "Light Aircraft Lift, Drag, and Moment Prediction - A Review and Analysis", NASA CR-2523, May 1975.

4. Minzner, R.A., Champoin, K.S.W., and Pond, H.L., "The ARDC Model Atmosphere", Air Force Cambridge Research Center Report No.

TR-59-267, 1959.

5. Anderson, Jr.,J.Do, Introduction to Fliqht, McGraw-Hill Book Company, 1978.

6. Eppler, R.,and Sommers, D.M., "A Computer Program for the design and Analysis of Low-Speed Airfoils", NASA TM-80210, August ! 980.

7. Abbott,IoH., and yon, Doenhoff, A.E., TheTh_@_g_E_of Winq Sections, Dover Publ ications, 1959.

8. Pankhurst, R.C., "A Method for the Rapid Evaluation of G]auert's Expressions For the Angle of Zero Lift and the Moment at Zero Lift", R.& M. No.1914, British ARC, 1944.

Table I. Percent Difference NACA X5XX Data in Comparison of et. al. Airfoil Bank and Smetana, Analysis Code (eef. 3).

H DRAG COEFFICIENT, CD -.T LIFT COEFFICIENT, C L O CJ

o

_2 ° 0 ° 2 ° 6 ° I0 ° o 2 ° 6 ° I0 ° -2 ° m_ z 9.5 * -4.5 0.3 4.4 0.3 * 0.01 3.12 3.7 50,2 -I.0 -0.8 0°2 3.6 9.7 5.9 1.7 * 0o01 1.50 4.2 63.3 16.1 * 5.8 20.0 5.9 0.6 * 2.3 70.4 2504 0.01 3.12 -0°6 0°2 1.4 I0.I 9.3 6,1 2.0 * 1.4 157.6 2506 0.01 1.50 4.9 * 8,7 34.7 6.0 0.8 * 2506 0,01 3.12 -I.I 123o5 -0.9 -0.3 1.8 9.3 8.8 3°9 1.2 * 0°8 190o8 2509 O.O1 1.50 -4.9 -12,4 -0°3 25°6 3.9 4.0 * =2.3 -76°3 8.5 2512 0.01 1.50 6.1 3°5 5°4 53.1 7.0 2_4 2.1 * O.Ol 3.12 =4.4 125.1 5.0 3.0 8.0 2.0 m 18o0 -7.0 3.0 0.5 * 2512 0.40 2.91 -I0.I * -26.8 * -12.5 -i.I 15.6 -5.5 -164o5 2515 0.70 3.00 8.1 0.4 4.4 -I.I 8o2 -6°9 112o2 2.3 4.1 * 2518 0.01 1.50 22.8 32.7 35.8 56.9 5.9 0.4 0o2 * 2518 0.01 3o12 -9° 2 96° 8 1.0 -3.0 * -2.0 8.0 0o0 1o5 2.0 - 87°0 O o20 1 o46 -34.8 * -50.3 19.2 -0.2 21.3 * 22.7 °236.2 2521 0 o70 I. O0 7.8 * -3.0 3.9 =13o9 -3.3 4.2 0.60 4.00 -3.5 -31.2 -20.8 m -30.9 -29.0 -10o2 -3°9 18.1 3521 0.60 2.00 13 o9 -35. I -53.0 * -34°6 -85.3 4°0 11.2 * 0.01 3.12 6.4 12.5 -1.3 0,0 806 O, I 4°6 3°7 3°0 * 0.01 1.50 2.4 14.7 11.7 * 14.3 21.9 3°0 1.6 * 4504 0.01 3.12 1.7 13.2 -1o9 =3.0 0.2 -O.l 7.4 5.3 * 0.01 1.50 9.0 Ioi 21.8 * 6.9 * 0°5 22.6 4.3 3°5 * 4506 0.01 3o12 -1.4 19o8 -7.6 -6°4 5.2 -1.7 19o7 14o6 8°8 * 0.01 1.50 0.6 46°4 Table Io (c0nt) tn DRAG COEFFICIENT, C D LIFT COEFFICIENT, C L o o -,I" _2 ° 0 ° 2 o 6 ° i0 ° _2 ° 0 o 2 = 6 ° i0 o 5.9 * 10.8 23.4 * * -11.3 -5.2 1.4 4.37 -5.8 -6.6 4509 0.60 3.1 -0.6 1o7 38.3 * 9.6 6°6 4512 0.01 1.50 -0.7 27.3 12.9 21.8 36.2 22.0 53.6 * 3.12 -2.3 25.1 10.2 7°7 5°3 4512 0.01 0.0 * 2.0 21.0 -2.0 1.0 4512 0.40 2.91 * 3.0 * -4.0 -Io0 -5°8 -i.I 6.1 26.0 * I o50 0.4 8.8 4.3 1o9 3.0 4518 0o01 15.8 16.6 24.4 34.7 * 3.4 -0.9 =1,6 0.2 4518 O.O1 3.12 -4.1 * -8.0 15.0 -2.0 -1.4 -0.5 0°5 -1.5 1.46 * 2.0 * 4518 O.2O * 19.8 3.3 * -7°7 =2°6 -0.7 8.4 5506 0.40 3.00 -2°2 -5°3 * * 31.6 24.2 -9.8 -9oi =5ol -1.6 25.6 5512 0.40 4.00 ,4.9 -9.7 * -3.3 0.3 0.8 ioi * 2.6 7°4 3ol 2°0 4.0 * 6504 0.01 1o50 11o9 * 37.3 38.9 * I o4 4.8 * -0°2 1o9 * 6504 0.01 3.12 4.9 6.6 * -0.I -0.8 -0.I 4.6 * 6506 0.01 1o50 104 12.3 6.0 21.7 - 22.9 40.9 * 6506 0.01 3.12 -0oi 10o3 * 2_0 4°4 * -3.5 -7.4 1.8 11.3 * 12o2 7.8 * 6509 0o01 1.50 0o8 28°0 16o3 3.8 * 16.6 125.0-14.6 6509 0.30 3°00 =3°5 12o9 * lo3 1.9 2.9 6509 0.50 3°64 -2oi -1o3 * -6.1 -3o0 -0.5 5.1 * 6.3 -14.0 * 6512 0o01 0°9 0o9 * -ioi 0.i -0.7 25.5 * 1o50 -0oi 2.7 0.0 6512 0o01 3o12 -1o5 -0.I =2.1 -2.2 0°9 1803 23.6 42.4 27.4 * 6515 0°30 * -10.5 -7o4 -3.4 -0.6 • 5°4 10.9 -24.4 2.00 -5.6 -13.4 6521 0.30 Io00 -3.3 2°8 * -0.4 -004 1.8 -15.1 • -3.6 -5.8 -18.1 6521 0.30 2.18 -5.3 -1.8 * -3.3 -2.7 -0°5 5.1 * 20.0 13.7 -4.3 8504 0o01 1.50 2.0 3.9 2.3 2.0 5.2 1.0 -1.5 0.9 0.6 * 8506 0o01 1.7 -1o3 0.6 -0.4 * 1.50 Io8 5.0 2°3 i o5 5.0 36.5 37.1 82.7 45.5 * 8506 0001 3o12 0°7 2.6 0o0 -Io2 3.7 ' _ Table I. (cont) (_ DRAG COEFFICIENT, C D LIFT COEFFICIENT, C L o o u N O i0 ° -2 ° 0 ° 2 ° 6 ° i0 ° _2 ° 0 o 2 ° 6 ° _ Z -0. I * * =0.i 1.2 Ioi 1.50 0.9 5.0 2.3 -0.5 -0.7 8509 0.01 5.3 * * =io4 -0.3 3.4 8512 0.01 1.50 0.7 5.3 2.2 1o6 1o4 6.2 * * 17.4 38.7 39o4 8512 0.01 3.12 -0.7 2.4 0.5 -0.9 1.2 4.7 * * 0.7 0°4 0°4 8518 0.01 1.50 0.8 6.4 2.4 0°7 1.4 18.7 -9.2 5.9 9.6 8,5 13.3 IAVG. % DEV. I 3.3 6.4 6.1 4.5 3.4 NOTE: *Airfoil analysis codes yielded unrealistic values or did not run.

Table II. NACA 4-Digit Airfoil Data Bank Input Parameters.

ALPHA Angle(s)-of-Attack.

NUMALP Number of Alphas.

CLD Design Lift Coefficient.

NZRCLD Number of values of CLD or Z to be ca]culatedo TC Maximum Thickness-to-Chord ratio.

NUMTC Number of Thickness-to-Chord values to be calculated.

CHORD Input in dimensions of feet, which is used for calculation of Reynolds Number.

MACH Mach Number (Free-Stream).

RE Reynolds Number. For calculation based on Mach number, Altitude, and Chord set RE=O.O.

ALTITUDE Geometric Altitude in Feet.

MCP Moment CoeEficinet Parameter =0, if moment coefficients are not desired.

=1, for moment coefficient about the quarter- chord.

=2, for moment coefficient about the leading- edge.

=3, For all moment coefficients.

ACP Air#oil Coordinates Parameter :0, of Air#oil Coordinates are not desired.

:I, for the Airfil dection coordinates.

CAMP Camber Parameter =0, if CLD is input and is calculated.

:1, i# Z is input and CLD is calculated.

Table III. Constants for Moment Coefficient Calculation.

X B 0.0 -0.119 0.025 -0.156 0.05 -0.104 0.1 -0.124 0.2 -0.074 0.3 -0.009 0.4 0.045 0.5 0.101 0.6 0.170 0.7 0.273 0.8 0.477 0.9 0.786 0.95 3.026 1.00 -4.289 © o,-I ¢o .,-q (I) o r..)

bO C=I C_ .,-i .... /;i _ _ (D 0 0_.-4 p_ °,-.t •r-t o,-t *,-4 o I o • o,-4 _0 T'7 T7 ,-I °,---I .% .,--I m t!

bO °,-i | ,i *'i_ _ L_ 0

.*iii

_ 0 _ Q', :!

..o _:,,1 0 .,-4 o. i, °,-4 O0 oo o_ _,:r ii *-x.o e_ o _co ,1 •,..4 _1 t_4 _a I_II t!

,_H H _'* I-E _;; !ii o , oJ _2,_ ill bO ._-i 0.007 5 Figure 3.

Minimum Drag Coefficients for Four-Digit Airfoils for a Reynolds Number between 6 x IO _ and 5 x 10 .

r E °_--I .r-I o cr o z ....S q£ _J o o .;} s% o e °,-I 0 _,-I o _-_ o r._ L3 • ' o f_ h0 ...4

Appendix - I

NACA 4-Digit Program Listing

i01

//FDBANKA JOB (R205,011C,S02,002,A7),'NACA4DM' //*XBM WATFIV //$OPTIONS NOLIST C C C C C C THIS PROGRAM WILL CALCULATE THE LIFT COEFFICIENT, * C C DRAG COEFFICIENT, MOMENT COEFFICIENT ABOUT THE w C C • QUARTER-CHORD OR THE LEADING EDGE, AND THE COORDIN- C C • ATES OF A NACA FOUR-DIGIT AIRFOIL SECTION WITH THE * C C • MAXIMUM CAMBER AT THE MID-CHORD POSITION * C C C C THE DATA BASE FOR THIS ROUTINE IS FROM: MCCORMICK,B.Wo,EISENHUTH,J.J., C LYNN,J E.; "A STUDY OF TORPEDO PROPELLERS - PART I" 1956. THE C EQUATIONS AND GRAPHS CONTAINED IN CHAPTER TWO(2) FORM THE BASIS FOR C THE CL AND CD CALCULATIONS• MOMENT COEFFICIENT AND AIRFOIL COORDINATES C ARE CALCULATED USING EQUATIONS FROM: ABBOTT,I.H.,VONDOENHOFF,A.Eo; C "THEORY OF WING SECTIONS", 1958. SPECIFIC EQUATIONS OR GRAPHS ARE C REFERRED TO WITHIN THE PROGRAM AND AT THE BEGINNING OF EACH SUBROUTINE• C C C ALPHA = ANGLE OF ATTACK C C CLD = DESIGN LIFT COEFFICIENT C C Z = Y/C PERCENTAGE VALUE OF MAXIMUM CAMBER C C TC = MAXIMUM THICKNESS TO CHORD RATIO C C CHORD = LONGEST CHORD LENGTH (FEET) C C MACH = MACH NUMBER C C ALT = ALTITUDE (FEET) C C RE = REYNOLD'S NUMBER C C CMC4 = MOMENT COEFFICIENT ABOUT THE QUARTER-CHORD C C CMLE = MOMENT COEFFICIENT ABOUT THE LEADING EDGE C C LERAD = LEADING EDGE RADIUS (NON-DIMENSIONALIZED BY THE CHORD) C C NUMAL P = NUMBER OF ALPHA"S SPECIFIED C C NZRCLD = NUMBER OF Z_S OR CLD_S SPECIFIED C C NUMTC = NUMBER OF TC'S SPECIFIED C C NUMACH = NUMBER OF MACH NUMBERS SPECIFIED C C MCP = MOMENT COEFFICIENT PARAMETER C 0, IF MOMENT COEFFICIENTS ARE NOT DESIRED C l, FOR THE MOMENT COEFFICIENT ABOUT THE QUARTER-CHORD C = 2_ FOR THE MOMENT COEFFICIENT ABOUT THE LEADING EDGE C 3, FOR ALL THE MOMENT COEFFICIENTS C C ACP = AIRFOIL COORDINATES PARAMETER C 0, IF AIRFOIL COORDINATES ARE NOT DESIRED C i, FOR THE AIRFOIL SECTION COORDINATES C C CAMP = CAMBER PARAMETER C 0, IF CLD IS INPUT AND Z IS CALCULATED C = l, IF Z IS INPUT AND CLD IS CALCULATED C C

I02

SPECIFY CLD OR Z, AND NZRCLD; DELETE THE OTHER ONE FROM DATA BUT DIMENSION THEM BOTH EQUALLY REAL ALPHA(10),CLD(1,1),Z(1,1),TC(1),MACH(1), &LERAD(10,10),CL(10,10,10),CD(10,10,10),CLMAX(10,10),CMC4(10,10)_ &CMLE(IO,10,10),XU(10,10,53),YU(10,10,53),XL(10,10_53), &YL(10,10,53),X(10,10,10),TC0(13),BT(13),IMAJ,IMIN INTEGER ACP, CAMP DATA ALPHA / -i0.0,-8.0,-6.0,-4.0,-2o0,0o0,2°0,4o0,6o0,8°0/ DATA NUMALP / i0 / DATA CLD / 0.2 / DATA NZRCLD / 1 / DATA TC / 0.120 / DATA NUMTC / 1 / DATA CHORD /io0/ DATA MACM / 0°50/ DATA NUMACH / 1 / C SET RE = 0.0 FOR CALCULATION OF RE BASED ON MACH, ALT AND CHORD DATA RE / 0.0/ DATA ALT / i0000.0/ DATA MCP / 3 / DATA ACP / 1 / DATA CAMP / 0 / C END OF INPUT DATA XMEAN = 0.5 REY= RE C DO 19 M1 = i, NUMACH DO 21 N = I, NZRCLD DO 24 N1 = i, NUMTC DO 31 NN = i, NUMALP C IF (REY .GT. 0.0) GO TO 88 CALL ATMCON(ALT,DEN,VIS,WA) OMACH = MACM(MI) IF (MACH(M1) .EQ. 0.0) MACM(M1) = 0.05 VEL = MACH(MI)*WA RE = DEN*VEL*CHORD/VIS MACH(MI) = OMACH C 88 CAMB = CAMP CALL CLDVSZ( CAMB, TC(N1), CLD(N_N1), Z(N,NI) ) C CRE = REYNOLDS NO. FUNCTION FOR OPTIMUM LIFT COEFFICIENT -- C FROM FIG. 2-48, MCCORMICK CRE = -14o0*(ALOG!O(RE)-6o0)+24o250 C DTC = THICKNESS FUNCTION FOR OPTIMUM LIFT COEFFICIENT -- C FROM FIG. 2-49, MCCORMICK DTC = -3o84375*TC(NI)+I C CLOPT FROM EQ. 2-44, MCCORMICK CLOPT = Z(N,NI)*CRE_DTC CALL MAXCL(Z(N,NI), TC(NI), CLMX ) IF (ALPHA(NN)oEQo 0.0) GO TO 40 IF (TC(NI) oGEo .20) DCLDAL = .1321*(I-TC(NI))/SQRT(I-TC(NI)_2) IF (TC(NI) oLT° .20) DCLDAL = .1216*(I-TC(NI))/SQRT(I-TC(NI)**2) IF (TC(NI) .LT..17) DCLDAL = .II75_(I-TC(NI))/SQRT(I-TC(NI)*-2) IF (TC(NI) .LT. o14) DCLDAL = olI34*(I-TC(NI))/SQRT(I-TC(NI)*_2) IF (TC(NI) .LT. oli) DCLDAL = oI043*(I-TC(NI))/SQRT(I-TC(NI)**2) IF (TC(NI) .LT..08) DCLDAL = °I039*(I-TC(NI))/SQRT(I-TC(NI)_*2) IF (TC(NI) .LT..05) DCLDAL = oI021*(I-TC(NI))/SQRT(I-TC(NI)-*2) DCLDAL = DCLDAL/SQRT(1-MACH(M1)_2) DELCL = DCLDAL*ALPMA(NN) GO TO 50 40 DELCL = 0o0 50 CONTINUE CL(NN_N,N1) = CLD(N,NI)+DELCL C C X FROM EQo 2-45, MCCORMICK X = (CL -CLOPT)/(CLMX - CLOPT) X(NN,N,NI) = (CL(NN,N,N1)-CLOPT)/(CLMX-CLOPT) CALL CDL(X(NN,N,NI), Z(N,N1), TC(NI), DELCD ) CALL CDMN( Z(N,NI)e TC(NI), CDMN1 ) CALL RECD ( RE, ERE ) C CDMIN FROM EQ. 2-46, MCCORMICK CDMIN = CDMNI*ERE CD(NN,N,NI) = CDMIN + DELCD IF(NN .GT. i) GO TO 12 CALL FDCOOR( Z,NZRCLD,TC(NI),YU,YL,N,N1 ) 12 CONTINUE IF (MCP .EQ. 0) GO TO 14 CALL QCCM(CMC4,YU, YL, N, N, NN, MACH(M1) F CMLEg CL, N1, Z(NrNI) 14 CONTINUE 31 CONTINUE IF(ACP .EQ. 0) GO TO 24 CALL FDCR( Z,NZRCLD,TC(NI),XU,XL,YU,YL,LERAD,NUMACS,N,N1 ) CALL AREA( XU,YU,XL,YL,AT,XREF,YREF,IMAJ,IMIN,N,NI,CHORD ) 24 CONTINUE 21 CONTINUE C C WRITE(6,260) MACH(MI) 260 FORMAT('I',T43,'* LIMITATIONS FOR MACH NOo = ',F6.4,' 3,//) IF(RE .LT. 4.0E05) WRITE(6,261) RE 261 FORMAT(T5,'REYNOLDS NO. = ',E12o6,' IS LESS THAN RE(MIN) &= 0.400E 06') IF(RE .GT. 0.10E08) WRITE(6,262) RE 262 FORMAT(T5,'REYNOLDS NO. = ',E12°6,' IS GREATER THAN RE(MAX) &= 0.100E 08' ) DO 263 I = I,NZRCLD DO 264 ll = leNUMTC IF(Z(I,I1) .GT. 0.09) WRITE(6,265) Z(I,I1), CLD(I,I1), TC(II) 265 FORMAT(T5,'MAX. CAMBER = ',FI0o6, ' IS GREATER THAN Y/C(MAX) &= 0.090 FOR CLD = ',F10.6,'AND T/C = ',F10o6) 264 CONTINUE 263 CONTINUE WRITE(6,271) FORMAT('-',T53, '" END LIMITATIONS *'///) WRITE(6,999) 999 FORMAT('I') DO ll L = 1,NZRCLD NTC = NUMTC DO lll L1 = 1,NUMTC,2 IF (ACP oEQ. 0) GO TO 5 IF (NUMTC .EQo i) GO TO 800 IF (CAMP .EQ. l) GO TO 41 WRITE(6,15) 15 FORMAT('-',9X,'* NACA 4-DIGIT SERIES AIRFOIL COORDINATES _', &I8X,'* NACA 4-DIGIT SERIES AIRFOIL COORDINATES "'///) GO TO 13 41 IZ = Z(L,LI)*I01 IZP = Z(L,Ll+l)*101 ITC = TC(L1)*I01 ITCP = TC(LI+I)*I01 IF(ITCP oLTo i0) WRITE(6,43) IZ,ITC_IZP_ITCP IF(ITCP oGEo 10) WRITE(6,42) IZ,ITCvIZP,ITCP 42 FORMAT('I_,2(14X, '* NACA ',ll,'5',I2w' AIRFOIL COORDINATES *',gx) 43 FORMAT('I',2(14X, '* NACA',I2,'50',II,' AIRFOIL COORDINATES _',9X) 13 CONTINUE WRITE(6,25) CLD(L,L1), CLD(L,LI+I) 25 FORMAT('-'_T30_°CLD = ',FI0.6,T92,'CLD = 'eFl0.6/) WRITE(6935) TC(L1)w TC(LI+I) 35 FORMAT(T25,'(T/C)MAX = ',F10o6,T87,'(T/C)MAX = ',F10.6/) WRITE(6,36) LERAD(L,LI)_ LERAD(L,LI+I) 36 FORMAT(T28,'LERAD = ',FI0.6_T90,'LERAD = ',F10o6/) WRITE(6,45) XMEAN, XMEAN 45 FORMAT(T9,'X/C VALUE OF MAX. CAMBER = ',F10.6,T71, &'X/C VALUE OF MAX° CAMBER = ',F10o6/) WRITE(6,55) Z(L,L1), Z(L,LI+I) 55 FORMAT(T9,'Y/C VALUE OF MAX° CAMBER = ',F10.6,T71, &'Y/C VALUE OF MAX. CAMBER = ',FI0o6//) WRITE(6,65) FORMAT(T13_'XUPPER',T25, 'YUPPER'_T37g'XLOWERE,T49,'YLOWER', &T76_'XUPPER',T88,'YUPPER',T100,'XLOWER',TlI2,'YLOWER'/) C DO 66 M = l, NUMACS WRITE(6,75) XU(L,LI_M)_YU(L,L1,M),XL(L,LI,M),YL(LoL1,M), &XU(L_LI+I,M),YU(L,LI+I,M),XL(L,LI+I,M)vYL(L,LI+IvM) 75 FORMAT(2(9X,FI0.6,2X,FIO.6N2X,F10.6u2X,FI0o6,8X)) 66 CONTINUE GO TO 99 800 IF (ACP .EQ. 0) GO TO 900 K1 = NUMTC IF (CAMP °EQ. i) GO TO 141 WRITE(6,115) 115 FORMAT('-',9X, '_ NACA 4-DIGIT SERIES AIRFOIL COORDINATES _'///) GO TO 113 141 IZ = Z(L,KI)*101 ITC = TC(K1)*101 IF(ITC .GE. i0) WRITE(6,142) IZ,ITC IF(ITC .LT. i0) WRITE(6,114) IZ,ITC 142 FORMAT('I'yI4X,'* NACA ',II,'5',I2,' AIRFOIL COORDINATES _') 114 FORMAT('I'_I4X,'* NACA ',II,'S0',Ii,' AIRFOIL COORDINATES *') 113 CONTINUE WRITE(6,999) WRITE(6,125) CLD(L,K1) FORMAT('-',T30,'CLD = ',FI0o6/) WRITE(6,135) TC(K1) FORMAT(T25,'(T/C)MAX = 'wFl0.6/) WRITE(6,136) LERAD(L,EI) FORMAT(T28,'LERAD = ',FI0.6/) WRITE(6,145) XMEAN FORMAT(T9,'X/C VALUE OF MAX. CAMBER = ',F10°6/) WRITE(6,155) Z(L,K1) FORMAT(T9,'Y/C VALUE OF MAX. CAMBER = ',F10.6//) WRITE(6,165) FORMAT(TI3,'XUPPER'wT25,'YUPPER',T37,'XLOWER',T49,'YLOWER'/) C DO 166 M = l, NUMACS WRITE(6,175) XII(L,KI_M),YU(L,KI,M),XL(L,KI,M),YL(L,K1,M) FORMAT(9X,F10.6,2X,F10.6,2X,FI0.6,2X,F10.6) 166 CONTINUE C GO TO 900 5 IF (NUMTC .EQ. i) GO TO 900 99 WRITE(6,100) 100 FORMAT('-',IIX, _* NACA 4-DIGIT SERIES AIRFOIL DATA BANK _', &20X,'* NACA 4-DIGIT SERIES AIRFOIL DATA BANK "') IF (CAMP oEQ. 0) GO TO 104 IZ = Z(L,LI)*IOI IZP = Z(L,LI+I)*I01 ITC = TC(L1)*I01 ITCP = TC(LI+I)*I01 IF(ITCP oLTo i0) WRITE(6,108) IZ,ITC,IZP,ITCP IF(ITCP oGEo i0) WRITE(6,105) IZ,ITC,IZP,ITCP 105 FORMAT(2(25Xw _" NACA 'oIl_'5',I2,' *tul4X)) 108 FORMAT(2(25X,'* NACA ',Ii,'50'_II,' *',14X)) 104 CONTINUE WRITE(6,200) CLD(L,LI), CLD(LgLI+I) 200 FORMAT(///_T25_CLD = ',FI0.6,T87,'CLD = '_FI0.6/) WRITE(6,300) TC(LI)_ TC(Ll+l) 300 FORMAT(T20,t(T/C)MAX = t,FI0.6,T82,'(T/C)MAX = ',FI0.6/) WRITE(6,301) MACH(M1) e MACH(M1) 301 FORMAT(T20,'MACH NO. = ',FI0.6,T82_'MACH NO. = ',F10o6/) WRITE(6g400) RE, RE 400 FORMAT(T16,'REYNOLDS NO. = ',E14.6,T79,'REYNOLDS NO. = ' &,El4.6/) IF (MCP .EQ. 0) GO TO 101 IF (MCP .EQ. 2) GO TO i01 WRITE(6,500) CMC4(L,L1), CMC4(L,LI+I) 500 FORMAT(T24,'CMC4 = ',F10.6,T86,'CMC4 = ',FI0o6//) i01 CONTINUE IF (MCP oEQ° 2) GO TO 501 IF (MCP oEQ. 3) GO TO 501 WRITE(6,600) 600 FORMAT(T20,'ALPHA',T33w_CL',T45,_CD,,T83 ,ALPHA, T96, &'CL',T108,'CD_/) GO TO 107 501 WRITE(6u601) 601 FORMAT(T13v'ALPHA'vT26_'CL'wT38,'CD',T49_,CMLE,eT76 ' &'ALPHA',T89,'CLgpT101,_CD',TII2,'CMLE,/) 107 CONTINUE C DO i0 J = i, NUMALP

I05

IF (MCP .EQ. 2) GO TO 106 IF (MCP .EQ. 3) GO TO 106 WRITE(6,802) ALPHA(J),CL(J,L,LI),CD(J,L_L1),ALPHA(J), &CL(J,L,LI+I),CD(J,L,LI+I) 802 FORMAT(2(15X,FI0.6,2X,FI0.6,2X,FI0o6,15X)) GO TO i0 106 WRITE(6,801) ALPHA(J),CL(J,L,LI),CD(JNL,LI),CMLE(JeL,LI)g &ALPHA(J),CL(J,L,LI+I),CD(J,L,LI+I)NCMLE(JvL,LI+I) 801 FORMAT(2(SX,F10.6,2X,FI0.6_2X,FI0.6,2X,FI0.6,9X)) l0 CONTINUE NTC = NTC - 2 IF (NTC .EQ. 0) GO TO ii IF (NTC °EQ. i) GO TO 800 lll CONTINUE 900 K1 = NUMTC WRITE(6,901) 901 FORMAT('-',IIX,'* NACA 4-DIGIT SERIES AIRFOIL DATA BANK _') IF (CAMP .EQo 0) GO TO 902 IZ = Z(L,K1)*I01 ITC = TC(KI)*101 IF(ITC oLTo i0) WRITE(6_903) IZ,ITC IF(ITC oGE. i0) WRITE(6,920) IZ,ITC 903 FORMAT(25X,'* NACA ',II,'50',Ii,' *') 920 FORMAT(25X,'* NACA _,Ii,'5',I2_' _') 902 CONTINUE WRITE(6,904) CLD(L,K1) 904 FORMAT(///,T25,'CLD = 'vF10°6/) WRITE(6,906) TC(K1) 906 FORMAT(T20,'(T/C)MAX = ',FI0o6/) WRITE(6,907) MACH(M1) 907 FORMAT(T20,'MACH NO. = '_FI0o6/) WRITE(6,910) RE 910 FORMAT(TI6N'REYNOLDS NO° = ',E14o6/) WRITE(6,708)AT,XREF,YREF 708 FORMAT(T24,'AREA = ',F10o6,' IN**2'o/,T19w'XCENTRIOD = ,,F10.6, IN''/,TI9,'YCENTRIOD = ',FI0.6,' IN'n/) WRITE(6,709)IMAJ,IMIN 709 FORMAT(T22,'IMAJOR = ",F10.3_ _ IN"_4',/,T22,'IMINOR = 'sFl0o7, *IN**4',/) IF (MCP .EQ. 0) GO TO 908 IF (MCP .EQo 2) GO TO 908 WRITE(6,909) CMC4(L,K1) 909 FORMAT(T24,'CMC4 = ',F10.6//) 908 CONTINUE IF (MCP oEQ. 2) GO TO 911 IF (MCP oEQo 3) GO TO 911 WRITE(6,912) 912 FORMAT(T20,'ALPHA',T33,'CL'_T45,_CD_/) GO TO 913 WRITE(6,914) FORMAT(T13,'ALPHA',T26,'CL',T38w_CD_,T49,'CMLE'/) 913 CONTINUE C DO 919 J = l, NUMALP IF (MCP .EQo 2) GO TO 916 IF (MCP .EQ. 3) GO TO 916 WRITE(6,gl7) ALPHA(J),CL(JfL,KI)uCD(J,L_KI) FORMAT(15X,F10o6,2X,F10.6,2X,F10.6) GO TO 915 WRITE(6,918) ALPHA(J)_CL(J,L,K1),CD(J,L,KI),CMLE(J,LNK1) FORMAT(SXwF10o6,2X,FI0.6,2X,F10o6,2X,F10o6) 915 CONTINUE 919 CONTINUE ll CONTINUE 19 CONTINUE WRITE(6,999) STOP END SUBROUTINE ATMCON FINDS PARAMETERS AT GIVEN ALTITUDE SUBROUTINE ATMCON(ALT_DENeVIS,WA) ALT = ALT*.3048 SLOPE = -.0065 TEMP = 288.16+SLOPE*ALT EXP = 2.718281828 TSEA = 288.16 PSEA = 101325.

PRESI = 22700.

GRAV = 9.82 R = 288.

POWER = GRAV/(SLOPE*R) PRES = PSEA*(1/(TEMP/TSEA))_*POWER IF(ALT .LE. ll000.) GO TO 4 PRES = PRESl*EXP**(-GRAV/(R*216o66)"(ALT-11000o)) TEMP = 216.66 4 WA = SQRT(I.4*R*TEMP)/.3048 TEMP = (TEMP-273.15)*9/5+491.67 VIS = .35*(TEMP/492.)**I.5*(690/(TEMP+I98=))_o000001 PRES = PRES*2116.2/PSEA DEN = PRES/(1718.*TEMP) ALT = ALT/.3048 RETURN END C C SUBROUTINE CLDVSZ CALCULATES DESIGN LIFT COEFFICIENT IF C CAMBER IS INPUT OR VICE VERSA SUBROUTINE CLDVSZ( CAMP F TC, CLD N Z ) DIMENSION CLDATA(5,4),ZDATA(5,4),ZI(4),CLDI(4),TCI(5), &CLD02(5),CLD04(5),CLD06(5),CLD08(5)gZ2(5),Z4(5),Z6(5), &ZS(5),ZADATA(4),CLDTA(4) EQUIVALENCE(CLDATA(I,I), CLD02 ) EQUIVALENCE(CLDATA(Ip2), CLD04 ) EQUIVALENCE(CLDATA(1,3), CLD06 ) EQUIVALENCE(CLDATA(1,4), CLD08 ) C EQUIVALENCE(ZDATA(I,1), Z2 ) EQUIVALENCE(ZDATA(1,2), Z4 ) EQUIVALENCE(ZDATA(lw3), Z6 ) EQUIVALENCE(ZDATA(1,4), Z8 ) C DATA ZI / 0°02,0.04,0.06,0.08 / DATA CLDI / 0.2,0.4,0.6,0o8 / DATA TCI / 0.04,0.06,0.09,0.12,0.18 / DATA CLD02 / .225537,.235576g.246819,.256079_.265394 / DATA CLD04 / .455984,.48389,°547405,°52539,.489006 / DATA CLD06 / .672912,.707067,o786416,.691206_.6380 / DATA CLD08 / .892327N.899246,.906358,.930514w o843705 / C DATA Z2 / .0195,.0186go0175,.0168,.0160 / DATA Z4 / .0370,.0360,.0350,.0340_.0330 / DATA Z6 / .0550,.0540,.0530,.0520_.0530 / DATA Z8 / o0730,.0720, o0710,.0700,.0760 / C IF (CAMP .EQ° I) GO TO i0 DO 20 I = 1,4 CALL LINEAR(5,TCI,ZDATA(IwI)_TC_ZADATA(I)) CONTINUE CALL LINEAR(4,CLDI,ZADATA,CLD,Z) GO TO 30 i0 CONTINUE DO 40 J = 1,4 CALL LINEAR(5,TCI,CLDATA(I,J),TC,CLDTA(J)) CONTINUE CALL LINEAR(4,ZI,CLDTA,Z,CLD) RETURN END C C SUBROUTINE MAXCL ESTIMATES CL(MAX) TO AID IN FINDING C THE DRAG COEFFICIENT INCREASE DUE TO THICKNESS SUBROUTINE MAXCL(Z, TC, CLMX ) REAL LDATA(7,5),LADATA(5),ZI(5)_TCI(7) DIMENSION CLM00(7)_ CLM02(7), CLM04(7)_ CLM06(7)F CLM08(7) EQUIVALENCE (LDATA(Igl), CLM00) EQUIVALENCE (LDATA(I,2), CLM02) EQUIVALENCE (LDATA(I_3)p CLM04) EQUIVALENCE (LDATA(I_4), CLM06) EQUIVALENCE (LDATA(I,5), CLM08) C DATA Zl / 0.0,0.02,0.04,0.06w0.08 / DATA TC1 / 0.03,.06,.09, °12,.15,.18, °21 / DATA CLM00 / 1.4,1o3,1.4,1.4,1.4,1.4,1.4 / DATA CLM02 / 1.5,1.4,1.5,1.5,1.4,1.4_1.3 / DATA CLM04 / 1.65,1o6,1o7,1.7,1.65,1.6_1.55 / DATA CLM06 / 1.8,1.9,1.9,1.8,1o7,1.8,1.65 / DATA CLM08 / 2.0,2.1,2.1w2.0,1.9,1.8,1°7 / C DO 130 IA = i, 5 CALL LINEAR( 7 r TCI, LDATA(IwIA), TC_ LADATA(IA) 130 CONTINUE CALL LINEAR( 5, Z1, LADATA, Z, CLMX ) RETURN END SUBROUTINE CDL FINDS THE EFFECT OF LIFT COEFFICIENT ON DRAG COEFFICIENT -- FROM FIG. 2-52, MCCORMICK (PLUS INCORPORATION OF T/C(MAX)) SUBROUTINE CDL( X, Z, TC, DELCD ) DIMENSION DCD(17,4,5),DECD(5),DLCD(4),ZP(4)_TCP(5)fXP(17)w &X2(9),X4(II),X6(12),X8(17) DIMENSION DCD204(9),DCD206(9),DCD209(9),DCD212(9),DCD218(9), &DCD404(I1),DCD406(ll),DCD409(ll),DCD412(I1),DCD418(ll), &DCD604(12),DCD606(12),DCD609(12),DCD612(12)_DCD618(12), &DCD804(17),DCD806(17),DCD809(17)_DCD812(17),DCD818(17) EQUIVALENCE (DCD(I,I,I), DCD204) EQUIVALENCE (DCD(I,1,2), DCD206) EQUIVALENCE (DCD(I_I_3), DCD209) EQUIVALENCE (DCD(I,1,4), DCD212) EQUIVALENCE (DCD(1F1,5) , DCD218) EQUIVALENCE (DCD(1,2,1), DCD404) EQUIVALENCE (DCD(1,2,2)g DCD406) EQUIVALENCE (DCD(lw2,3) , DCD409) EQUIVALENCE (DCD(Ig2,4), DCD412) EQUIVALENCE (DCD(1,2,5), DCD418) EQUIVALENCE (DCD(lf3,1), DCD604) EQUIVALENCE (DCD(I_3,2), DCD606) EQUIVALENCE (DCD(I,3,3), DCD609) EQUIVALENCE (DCD(I,3,4), DCD612) EQUIVALENCE (DCD(I,3,5), DCD618) EQUIVALENCE (DCD(1,4w1) , DCD804) EQUIVALENCE (DCD(lw4_2), DCD806) EQUIVALENCE (DCD(I,4,3), DCDS09) EQUIVALENCE (DCD(I,4,4), DCD812) EQUIVALENCE (DCD(I_4,5)f DCD818) DATA ZP / 0o02,0.04,0.06_0.08 / DATA TCP / 0.04, o06_ °09eo12_.18 / DATA X2 / -0.3,-.2v-ol,0o,olgo2w.3,.4v.5 / DATA X4 / -0oLw-.4,-o3_-_2g-ol,0._olg.2w.3,°4,.5 / DATA X6 / -0.7,-o6w-o5_-o4,-o3,-o2,-olF0.,ol,o2w.3,.4 / DATA X8 / -i°1,-1o0,-.9,-o8,-.7,-.6,-.5,-.4,-.3,-.2_-.i,0., 01,o2, o3w o4,o5 / DATA DCD204 / .00065,.0003,0.,0.,.0003,.00065f.0011,

&o0017_o0025 /

DATA DCD206 / .0009,.00035,.0001,0.,.00025,o0008,.0018,

&o0032, o0046 /

DATA DCD209 / .0014w.0006,.0002_.0002r.0006,.0012,.0026,

&o0042g.0058 /

DATA DCD212 / .0014g.0008,.0003,.0002,.0001,0.,.0015_

&o0036,.0058 /

DATA DCD218 / .0021,.0018u.0013_0.,.O01w.0015, .0019,

/

&.0023,.0041 DATA DCD404 / .0008, o00045,°0002,.0001_0.,.00015,.0004,.0008, &°0015,.0022,.0030 / DATA DCD406 / .0016,.0013 ,.001,°00065_.0002,0.,.0006,.0017, &.003,.0044,.0059 / DATA DCD409 / .001,.0007, .0005,.0002,0.,0.,0.,.0008, &.0021,.0036,.0052 / DATA DCD412 / .0012,.0007 ,.0004,.0002,.0005,0.,.0001,°0003p &.0022,.0040,.0066 / DATA DCD418 / .0042,.0037 ,.0032,.0026,.002, o0008,.0001,.0001_ &.0018,.0032,.0051 / DATA DCD604 / .0013,.0011, .001,.0011,.0013,.0016,.0021,_0028w &.0037,.0047,.0057,.0067 / DATA DCD606 / .0015,.0014, .00135,.0013,.0013,.0013N.00135,°0018, &.0027,.0042,.0062,.008 / DATA DCD609 / .0005,.0004, .00045,.0006,.0007,.0003, o0003,.0009, &.001,.0018,.0032,.005 / DATA DCD612 / .0020,.0018, .0016f.0013,.001, o0008,.0005,.00045, &.001,.0028,.0039,.0053 / DATA DCD618 / .0021,.0019, • 0015_.0011,.0009, o001,.0015,.0012, &.0015,.0020,.0040,.0054 / C DATA DCD804 / .0030,.0029,.0028,.0027,.00275e.003,o0034,.004_ &.0049,.0057,.0066,°0074,.0082,°009,.0098v°0106,.0113 / DATA DCD806 / .0025,.0023,.0024,o0028_.0032,.0034,.003,.0025, &.0024,.003,oO045,.006,.0075,.009w.0105,oO12_.0135 / DATA DCD809 / .0005,.0006,.0007,.0008eo001_.0012,.0016,.0019, &-0023,.0027,-0031,.0035,.0038,.0041,.0044,°0047w.0049 / DATA DCD812 / .0013,.0012,.001, o0008wo0007wo0006,.0005_ o00045, &.0004,.00035,.0004,.0007r.0023w.0038r _0041,.0044,.0047 / DATA DCD818 / .0005,.0004,.0003,.0002_.0001w0°_0.,0., °0001o &-0002,.00025,.0006,.0012,.003Fo0035,.0038, o0047 / DO 102 I = 1,4 DO 103 J = I,5 IF (I .EQ. i) CALL LINEAR (9NX2,DCD(I,I_J)_X,DECD(J)) IF (I .EQ. 2) CALL LINEAR (lloX4,DCD(1,I,J),X,DECD(J)) IF (I .EQo 3) CALL LINEAR (12,X6,DCD(I,I,J)_X,DECD(J)) IF (I .EQ_ 4) CALL LINEAR (17,X8rDCD(INI,J)_XwDECD(J)) I03 CONTINUE CALL LINEAR( 5, TCF, DECD, TC, DLCD(I) ) CONTINUE CALL LINEAR( 4, ZP, DLCDw Z, DELCD ) RETURN END SUBROUTINE CDMN FINDS THE MINIMUM DRAG COEFFICIENT FOR 6E05 < RE < 5E06 FROM FIG. 2-53o MCCORMICK SUBROUTINE CDMN( Z, TC, CDMNI ) REAL DMDATA(12,6), MNDATA(6)_ Z3(6), TC2(12) DIMENSION CDM00(12), CDM02(12), CDM04(12), CDM06(12), & CDM08(12), CDMI0(12), CDMI2(12) EQUIVALENCE (DMDATA(I,I), CDM00) EQUIVALENCE (DMDATA(I,2), CDM02) EQUIVALENCE (DMDATA(I,3), CDM04) EQUIVALENCE (DMDATA(Iv4), CDM06) EQUIVALENCE (DMDATA(1,5), CDM08) EQUIVALENCE (DMDATA(1,6)s CDM10) DATA Z3 / 0.0a.02_.04,.06,.08,o10 / DATA TC2 / o02r o04,°06,.08,.i0,.12,.14,.16,.18,.20,.22,°24 / DATA CDM00 / .00465_.00478,.0049,.00515,.0055,.00565,.00578, &.0064_o0069,.0074,°00765_.00865 / DATA CDM02 / o005,.0051w.0054,°0058,.0062,.0067u.0069 ' &o0076_.0083_.0086,.0089,.0092 / DATA CDM04 / o0056,.00569,°00545,.00661,.0071u.00785,.0081g &.0084w.O088,.009_°0092_.00953 / DATA CDM06 / .0048,.0052,.006,.0065,.0073_.0081,.0083, &o0084,o0091,.0094v.0097w.0103 / DATA CDM08 / .0046,.0049,.0057,.0070, o00793_.00851,.0089v &o0092,.00973,.0103,.0107,.0111 / DATA CDMI0 / o0085g.009_.00903_.00948_.00952,.010,.01003, &.01053,°01103,.01107,.01203,.01253 / DO 170 IE = i_6 CALL LINEAR 12, TC2, DMDATA(I,IE), TC, MNDATA(IE) ) 170 CONTINUE CALL LINEAR 6, Z3, MNDATA, Z, CDMNI ) RETURN END SUBROUTINE RECD FINDS THE EFFECT OF REYNOLDS NO. ON MINIMUM DRAG COEFFICIENT -- FROM FIG. 2-54, MCCORMICK SUBROUTINE RECD( RE, ERE ) DIMENSION R(9), ER(9) DATA R / I.E 5, 1.5E 5, 2.E 5, 3.E 5, 4oE 5, 5oE 5_ 6oE 5_ &6oE 6, 8.E 6 / DATA ER / 3.8,2.8,2.2,1.6,1o3,1.1,1.0,1.0,.95 / CALL LINEAR( 9, R, ER, RE, ERE ) RETURN END SUBROUTINE FDCOOR FINDS THE Y-DIMENSIONS OF A NACA 4-DIGIT AIRFOIL SECTION IN ORDER TO CALCULATE THE MOMENT COEFFICIENT -- -- FROM EQS. 6ol-6.4, ABBOTT & VONDOENHOFF SUBROUTINE FDCOOR( YMEAN,NZRCLD,TCMAX,YU,YLfIO,N1 ) REAL X2(14),YC(14),YMEAN(NZRCLD),SLOPE(14),THICK(14)_ &YU(10,10,14),YL(10,10,14) DATA X2 /0°,.025,.05,.l,.2, o3,.4,oLe.6,.7,.8r.gf o95ulo0 / XMEAN = 0.5 C NUMPTS = 14 DO 2 I = 1,NUMPTS IF(X2(I) °GT° XMEAN) GO TO 1 YC(I) =YMEAN(IO)/XMEAN**2*(2*XMEAN*X2(I)-X2(I)**2) GO TO 2 1 YC(I) =YMEAN(IO)/(1-XMEAN)**2*(I-2_XMEAN+2*XMEAN_X2(1)-X2(I)**2) 2 CONTINUE NUM = NUMPTS-I DO 6 JJ = 2,NUM SLOPE(JJ) = (YC(JJ+I)-YC(JJ-I) )/(X2(JJ+l)-X2(JJ-1) ) 6 CONTINUE SLOPE(l) = (YC(2)-YC(1) )/(X2(2)-X2(1) ) SLOPE(NUMPTS) = (YC(NUMPTS)-YC(NUM) )/(X2(NUMPTS)-X2(NUM) ) DO 3 MM = 1,NUMPTS THICK(MM) =(TCMAX/.2)*(SQRT(X2(MM))*.2969-X2(MM)*.126 &-X2(MM)**2*o3516+X2(MM)**3*o2843-X2(MM)**4"°IOI5) THETA = ATAN(SLOPE(MM)) YU(IO,N1,MM) =YC(MM)+THICK(MM)*COS(TMETA) YL(IO,N1,MM) =YC(MM)-THICK(MM)*COS(THETA) 3 CONTINUE RETURN END C SUBROUTINE QCCM FINDS THE MOMENT COEFFICIENT ABOUT C THE QUARTER-CHORD USING THE METHOD ON PAGE 72, ABBOTT & VONDOENHOFF SUBROUTINE QCCM( CMC4, YUF YL, IG, N, NN, MACH, CMLE, CL, Nl_ Z ) REAL MACH DIMENSION BI(14),X3(14),CMC4(IO_I0),CMLE(10,10,10),CL(10,10,10), &YU(10_I0,14),YL(10,10,14) DATA X3 / 0.0,.025,.05,o1,°2, o3,.4,.5,°6,.7,.8,.9,.95,1.0 / DATA B1 / -o119,-o156,-.104,-o124,-.074,-.009,.045,.101, &o170,o273_o477, o786,3.026,-4.289 / C CMC4(IG,NI) = 0.0 DO 23 IGG = 1,14 CMC4(IGwN1) = CMC4(IG,NI)+BI(IGG)"(YU(IG,NlwIGG)+YL(IG_NI_IGG)) 23 CONTINUE CMC4(IG,N1) = -(CMC4(IGuN1)-(.25_Z+.005)) CMLE(NN,IG,N1) = CMC4(IG,N1)-.25_CL(NN,N,NI) CMLE(NN_IG,NI) = CMLE(NN,IG,NI)/SQRT(I-MACH**2) CMC4(IG,NI) = CMC4(IG_N1)/SQRT(1-MACH**2) RETURN END ii0 SUBROUTINE FDCR FINDS THE DIMENSIONS OF A NACA 4-DIGIT AIRFOIL SECTION -- FROM EQS. 6.1-6.4, ABBOTT & VONDOENHOFF SUBROUTINE FDCR(YMEAN,NZRCLD,TCMAX,XU,XL,YU,YL,LERAD, &NUMACS,IO,NI) REAL LERAD(10,10),X2(53),YC(53),YMEAN(NZRCLD),SLOPE(53), &XU(10,10u53),XL(10,10,53),YU(10vI0,53),YL(10,10,53) DATA X2 / 0.,.01,.02,.03,.04,.05,.06,.07_.08,°09,°igo125w &.15,.175,.2o.225,.25,.275,.3,.325,.35,.375,.4,.425u°45,o475_o5, &.525,.55,.575,.6,.625,.65,.675,.7,.725,.75, o775_°8wo825wo85_ &.875,.gw.91,.92,.93,°94,.95,.96,°97,°98,.99,1o0 / XMEAN = 0°5 NUMACS = 53 DO 7 I = I,NUMACS IF(X2(I) °GT. XMEAN) GO TO 8 YC(I) =YMEAN(IO)/XMEAN_*2_(2*XMEAN*X2(I)-X2(I)_2) GO TO 9 8 YC(I) =YMEAN(IO)/(1-XMEAN)_*2"(1-2*XMEAN+2_XMEAN_X2(I)-X2(I)_-2) 9 CONTINUE 7 CONTINUE NUM = NUMACS-I DO 16 JJ = 2,NUM SLOPE(JJ) = (YC(JJ+I)-YC(JJ-I) )/(X2(JJ+I)-X2(JJ-1) ) 16 CONTINUE SLOPE(l) = (YC(2)-YC(1) )/(X2(2)-X2(1) ) SLOPE(NUMACS) = (YC(NUMACS)-YC(NUM) )/(X2(NUMACS)-X2(NUM) ) DO 17 MM = 1,NUMACS THICK =(TCMAX/.2)*(SQRT(X2(MM))*o2969-X2(MM)*oI26 &-X2(MM)**2*°3516+X2(MM)**3_o2843-X2(MM)**4_.I015) IF(MM .EQ. NUMACS) THICK = 0.0 THETA = ATAN(SLOPE(MM)) XU(I0,NI,MM) =X2(MM)-THICK*SIN(THETA) YU(IO,N1,MM) =YC(MM)+THICK*COS(TMETA) XL(IO,N1,MM) =X2(MM)+THICK*SIN(THETA) YL(IO,N1,MM) =YC(MM)-THICK*COS(TMETA) 17 CONTINUE LERAD(IO,NI) =I°1019"TCMAX*_2 RETURN END SUBROUTINE LINEAR INTERPOLATES LINEARLY BETWEEN POINTS SUBROUTINE LINEAR( NU, XIN, YIN_ XOUT, YOUT ) DIMENSION XIN(NU), YIN(NU) INTEGER F NM1 = NU-I F = 1 C TEST FOR OFF LOW END IF(XOUT .LTo XIN(1)) GO TO ll0 F = NM1 C TEST FOR OFF HIGH END IF(XOUT .GT. XIN(NU)) GO TO ii0 C IN RANGE DO 120 II = 2wNM1 F = II-i IF(XOUT .LE. XIN(II)) GO TO ii0 120 CONTINUE F = NM1 C SLOPE INTERCEPT FORMULA ll0 CONTINUE IP1 = F+I SLP = (YIN(IP1)-YIN(F))/(XIN(IP1)-XIN(F)) B2 = YIN(F)-XIN(F)_SLP YOUT = SLP"XOUT+B2 RETURN END C SUBROUTINE AREA FINDS AREA , COORDINATES OF CENTROID , C AND MOMENTS OF INERTIA ABOUT PRINCIPLE AXES SUBROUTINE AREA(XUwYU,XL,YL,AT,XREFsYREF,IMAJwIMIN,IO,NIwCHORD ) REAL IMAJ,IMIN DIMENSION AU(53),DXU(53),XMU(53),YMU(53)wYPU(53) DIMENSION AL(53)qDXL(53),XML(53),YML(53)wYPL(53) DIMENSION A(53),DX(53),XM(53),YM(53),YP(53) DIMENSION XU(10,10w53),YU(10w10w53)wXL(10,10_53),YL(10,10,53)

iii

DATA AUP,ALP,AP,XAU,XAL,XA,YAU,YAL,YA/9*0o0/ IMAJ=0.0 IMIN=0.0 ISTEP=0 NUMPTS=53 DO 700 I=I,NUMPTS J=I+l IF(ISTEP.EQ.I)GO TO 702 IF(IoEQ.NUMPTS-1)GO TO 720 IF(YL(IO,NI,J+I).GT.0.0)GO TO 702 720 DXU(I)=XU(IO,NI,J)-XU(IO,NI,I) DXL(I)=XL(IO,NI,J)-XL(I0,NI,I) XMU(I)=(XU(IO,NI,J)+XU(IO,NI,I))/2 XML(I)=(XL(IO,N1,J)+XL(IO,NI,I))/2 YMU(I)=(YU(IO,N1,J)+YU(IO,NI,I))/2 YML(I)=ABS((YL(IO,N1,J)+YL(IO,NI,I))/2) YPU(I)=YMU(I)/2 YPL(I)=-YML(1)/2 AU(I)=DXU(1)*YMU(1) AL(I)=DXL(I)*YML(1) AUP=AUP+AU(I) ALP=ALP+AL(1) XAU=XAU+AU(I)*XMU(1) XAL=XAL+AL(I)*XML(I) YAU=YAU+AU(I)*YPU(I) YAL=YAL+AL(1)*YPL(I) A(I)=0.0 GO TO 703 702 XPI=(XU(IO,NI,I)+XL(IO,NI,I))/2 XP2=(XU(IO,N1,J)+XL(IO,N1,J))/2 DX(I)=XP2-XP1 XM(I)=(XPI+XP2)/2 YM(I)=(YU(IO,NI,J)-YL(IO,NI,J)+YU(IO,NI,I)-YL(IO,NI_I))/2 YP(I)=(YU(IO,NI,J)+YL(IO,NI,J)+YU(IO,NI,I)+YL(IO,NI,I))/4 A(1)=DX(I)*YM(I) XA=XA+A(1)*XM(I) YA=YA+A(I)*YP(1) AP=AP+A(I) ISTEP=I 703 IF(IoEQ.NUMPTS-I)GO TO 704 700 CONTINUE 704 AT=AUP+ALP+AP XREF=(XAU+XAL+XA)/AT YREF=(YAU+YAL+YA)/AT CHORD=CHORD*12.0 AT=AT*CHORD**2 XREF=XREF*CHORD YREF=YREF*CHORD ISTEP=0 K=NUMPTS-1 DO 707 I=luK IF(ISTEPoEQol)GO TO 706 IF(A(I)oGTo0.0)GO TO 706 DIMIU=(DXU(I)*YMU(I)**3)/12+AU(I)_(ypu(I)-YREF)_*2 DIMIL=(DXL(I)*YML(1)'_3)/12+AL(I)_(ypL(I)-YREF)"_2 IMIN=IMIN+DIMIU+DIMIL DIMAU=(YMU(1)*DXU(I)"*3)/12+AU(I)*(XMU(I)-XREF)*"2 DIMAL=(YML(I)*DXL(I)"*3)/12+AL(I)*(XML(I)-XREF)_2 IMAJ=IMAJ+DIMAU+DIMAL GO TO 707 706 DIMAJ=(YM(I)*DX(I)**3)/12+A(I)"(XM(I)-XREF)**2 DIMIN=(DX(I)_YM(I)_*3)/12+A(1)_(yp(1)-YREF)*"2 IMAJ=IMAJ+DIMAJ IMIN=IMIN+DIMIN ISTEP=I 707 CONTINUE IMAJ=IMAJ*CHORD*_4o0 IMIN=IMIN*CHORD**4o0 RETURN END //$DATA

IISSTOP

Appendix II

NACA 4-Digit Program Case

Input/Output

Input File

DATA ALPHA / -10.0,-8o0,-6.0,-4o0g-2o0_0o0,2.0,4o0_6o0eS.0/ DATA NUMALP / l0 / DATA

CLD / 0.2 /

DATA NZRCLD / 1 / DATA TC / 0o120 / DATA NUMTC / 1 / DATA CHORD /1.0/ DATA MACH / 0.50/ DATA NUMACH / 1 / C SET RE = 0.0 FOR CALCULATION OF RE BASED ON MACH, ALT AND CHORD DATA RE / 0.0/ DATA ALT / 10000°0/ DATA MCP / 3 / DATA ACP / 1 / DATA CAMP / 0 /

Output File

* NACA 4-DIGIT SERIES AIRFOIL COORDINATES * CLD = O.2OOOO0 (T/C)MAX = 0.120000 LERAD = 0.015867 X/C VALUE OF MAX. CAMBER = 0.500000 Y/C VALUE OF MAX° CAMBER = 0.016800 XUPPER YUPPER XLOWER YLOWER 0°000000 -0.000000 0.000000 -0.000000 0o017666 0 008880 0.011120 -0 016335 0.024866 0 018481 0.021519 -0 022232 0.030300 0 028210 0.031790 -0 026389 0°034796 0 038008 0.041992 -0 029635 0 047854 0.038674 0.052146 -0 032290 0 057735 0.042099 0.062265 -0 034519 0 067642 0.045169 0.072358 -0 036420 0.047950 0.077572 0.082427 -0 038058 0.050485 0.087521 0.092479 -0 039478 0.052811 0°097533 0.102467 -0 040715 0.057840 0o122455 0.127545 -0 043140 0.061960 0.147488 0.152512 -0 044824 0.065337 0.172570 0°177430 -0 045933 0.068081 0,197688 0o202311 -0.046577 0.070274 0°222836 0o227164 -0.046838 0.071979 0.248005 0.251995 -0.046779 0.073243 0°273190 0.276_810 -0°0_6447 0.298387 0.074107 0.301613 -0.045884 0°323592 0.074604 0.326408 -0.045120 0.348801 0 074762 0o351199 -0.044186 0.374011 0 074604 0.375989 -0°043104 0 074153 0.399220 0°400780 -0o041897 0 073425 0°424425 0°425575 -0.040581 0 072438 0°449625 0.450375 -0.039174 0 071205 0°474817 0o475183 -0.037689 0 069740 0.500000 0.500000 -0.036140 0 068053 0.525172 0.524828 -0°034538 0 066155 0.550333 0.549667 -0°032891 0 064054 0.575480 0°574520 -0.031210 0 061757 0.600613 0°599387 -0°029502 0°059273 0°625731 0.624269 -0.027773 0.056605 0.650833 0.649167 -0.026029 0°675918 0.053758 0.674082 -0.024274 0°700984 0°050738 0.699015 -0.022514 0.726033 0.047546 0.723967 -0,020750 0°751061 0°044185 0.748939 -0.018985 0.776070 0.040657 0°773930 -0o017221 0.801057 0.036962 0.798943 -0.015458 0°033100 0o826022 0.823978 -0.013696 0.029071 0°850964 0°849036 -0o011935 0.875883 0.024873 0°874117 -0.010173 0.020505 0°900763 0.899237 -0,008409 0.018708 0.910728 0.909272 -0.007701 0.920674 0°016885 0.919326 -0.006993 0.015033 0.930616 0°929384 -0.006283 0o013152 0.940554 0°939446 -0.005572 0.011243 0.950487 0o949513 -0.004859 0.009305 0.960416 0.959584 -0o004144 0.007338 0°970340 0°969660 -0.003426 0°980260 0°005341 0°979740 -0.002706 0.003314 0.990174 0.989826 -0o00!_84 0.000000 1.000000 io000000 -0o000000

Output File

* NACA 4-DIGIT SERIES AIRFOIL DATA BANK _" CLD = 0.200000 (T/C)MAX = 0o120000 MACH NO. = 0.500000 REYNOLDS NO. = 0.274529E 07 AREA = 11.828390 IN_*2 XCENTRIOD = 5.048587 IN YCENTRIOD = 0.153324 IN IMAJOR : 36573.010 IN*_4 IMINOR = 35.0840600 IN**4 CMC4 = -0.050110 ALPHA CL CD CMLE -i0.000000 -0.960685 0.011524 0.227216 -8.000000 -0.728548 0.010441 0.160204 -6.000000 -0°496411 0°009357 0°093192 -4.000000 -0.264274 0.008250 0.026179 -2.000000 -0°032137 0.007105 -0.040833 0.000000 0°200000 0.006728 -0°107845 2o000000 0o432137 0.006530 -0.174857 4.000000 0°664274 0.009618 -0.241869 6.000000 0.896411 0.013376 -0.308881 8o000000 1o128548 0.017133 -0°375893

IlI NACA-16 AIRFOIL DATA BANK

1. Introduction

The NACA 16-series airfoils were designed for use at.

transonic Mach numbers, and are particularly adaptable to the

outer radii of propet let systems. These airfoi Is were designed

to raise the Mach number at which the "compressibility burble"

appears, and hence control the onset of drag divergence. This

problem was originally discovered in the early 1940"s when the

requirement for higher aircraft velocities was real ized. The

reduction in drag was attained by decreasing the induced velocity

near the leading edge of the airfoi ] and increasing the induced

velocity over the rear segment of the airfoi 1, which resulted in

a constant value of the pressure distribution over the majority

of the wing section.

The NACA-16 series airfoil is designated by 16-XXX, with the

first digit representing the lift coefficient at zero degree

angle-of-attack (Cld), and the last two digits designating the

maximum thickness in percent of chord of the airfoi I.

The computer program for the NACA 16-series airfoi l

databank, contained in Appendix I, was derived from publications

by Cooper(1) and the Curtiss-Wright Corporation(2). The program

uses tables and plots from these papers to compute the

coefficients of lift, drag, and moment about the quarter chord.

Values of these aerodynamic coefficients from the existing

databank were compared with the output from the airfoil analysis

computer code of Smetana et.al. (3) and found to be acceptable as

indicated in Table I, with an average deviation of 1.93_.

Limits exist with the NACA 16-series airfoil data bank

computer program. Flags have been installed where a limitation

is exceeded, and appear in the "Limitations" category in the

printed output. These limitations will be discussed in detail in

the following Sections.

2 o ! nput.

The code has been arranged to compute up to i5 angles-of-

attack and 15 different Mach numbers with properly dimensioned

arrays. Essential ly, the airfoi l is dictated by the

specification of the design lift coefficient (Cld), the maximum

thickness to chord ratio ((t/c)max), and the airfoi I chord in

feet. A I ist of input parameters is described in Table I I and

provided in Appendix I I for the sample case. Other input

parameters dictate the amount of computer output desired,

including compressibi 1 ity effects and other factors to be

discussed later.

3. Main Program.

The main program is designed as an operating system to route

the variables to the various subroutines described in the ensuing

Sections. The output is passed back to the main program and

output.

4. Subroutine ATMCON.

ATMCON calculates the temperature, pressure, speed of sound,

density, and viscosity for a speciffied altitude using the

empirical equations o6 Minzer, et.al. (3) as given by Anderson (4).

These equations have been curve fit from the avai]able data of

the ARDC 1959 standard atmosphere (3), and divide the atmosphere

into two regions, i.e., from sea level to 11,000 meters, and

1t,000 to 25,000 meters. These equations are given as: Sea level to 11,000 meters.

Temp = 288.16- 0.0065 h III-i

P = (lO1325)/(I/(Temp/288.16)) -5-2457 III-2

11,000 meters to 25_000 meters.

Temp = 216.66 III-3

P = (22,700)exp(0.0001547(h-ll,000)) III-4

where h is in meters, Temperature is in "K, and pressure is in

N/m 2. The values of P and Temp are converted by;

Temp = (Temp - 273.15) 9/5 + 491.67 III-5

P = 2116.2 P/101325 III-6

where Temp and P are now in units °R and lbs/ft 2, respectively.

Values of density, viscosity, and speed of sound are then

calculated by:

0ensity = (Pressure)/(lTt8)(Temp) II[-T

Viscosity = 3.5 x 10-7 III-8

Speed of Sound = (403o2)(Temp)/0.3047 III-9

V '

where density is in lb-ft2/sec 4, viscosity in lb-sec/ft 2, and

speed of sound in ft/sec°

5. Subrut ine CLCD

Subrout i ne CLCD ca I cu 1 ates the sect i on 1 i ft and drag

coefficients for a NACA-16 series airfoil. The database for this

subroutine has beentaken from graphical descriptions of data as

found in Cooper(i).

The lift curve slope (dCl/de) is computed for the case of

subsonic or supersonic Mach number. For the subsonic case,

compressibility effects are taken into account by the application

of the Prandtl-Glauert Factor (1) The lift-curve slope is then

found by one of the following equations:

Incompressible Lift Curve S]o__op__e

dC l .t096(i-(t/c)max)

Ill-tO

-- = (deg -i )

de V l-(t/c)max2 '

Compressible Subsonic Lift Curve

dC 1 .tO96(l-(t/c)max)

= (deg -i ) III-11

de Vl-(M+(t/c)max2)

Su_Mloersonic Lift Curve Slo__

dC l .0698

= ( deg- 1 ) III-12

de M 2 - I

V '

and the lift coefficient, utilizing the lift-curve slope is found

by :

dC l

C l - e III-13

d(l

The drag coefficient can be obtained from an algorithm

contained in Cooper (1) in which the drag is characterized by the

sum of flour components, i.e., the basic drag coefficient (Cdo),

the increment due to lift (Cdi), the increment due to camber

(Cdd), and the increment due to skin friction (Cdf). Using

Figure I and knowing the difference between the lift coefficient

and the design lift coefficient, and the corrected airfoil section Mach number (Ms) given by: MX M s = III-15 0.9 - (t/c)max The drag due to lift the parameter ACd/(Cl-Cld )2 is Found.

(Cd]) may then be calculated by: AC d Cd] = (Cl-Cld)2 (Cl-Cld) 2 llI-I6 The skin friction drag (CdF) is obtained by specifying From the Reynolds number and the radial blade location (X=r/R). The radial location on the propeller blade indicated a strong effect on the extent of laminar run of each airfoil section, and has been quantized by Cooper(l)(Figure 2). Thus the skin friction drag coefficient (Cdf) is found graphically in Figure 3, and curve Fit For the airfoil databank, The drag due to camber (Cdd) represents the increase in the minimum basic drag of cambered NACA 16-series airfoils over that of an uncambered section as given in Figure 4. The data were obtained from two-dimensional NACA tests which extended to Mach 0.8. Above Math 0.8 and in supersonic Flow, the effects of camber are known to be small and Cdd approaches zero.

Finally, the basic drag coefficient (Cdo) is given in Figure 5 as a function of (t/c)max and section Mach number (Mx).

This relationship was obtained by Hoerner (5) From low speed wind tunnel tests of NACA-16 series airfoil sections.

These four drag contributions are summed to obtain the total drag coefficient of the airfoil section: III-17 C d = Cdo + Cdf + Cdl + Cdd 6. Moment Coefficient The moment coefficent is obtained from tables acquired from Lindsey, et.al. (6). These tables were generated from the results of wind tunnel tests of 24 related airfoil sections over a Mach number range of 0.3 to 0°75. A typical plot is shown in Figure 6.

The tables are arranged in matrix form for Cld values of 0.0, 0.1, 0.3, and 0.5, at Mach numbers of 0.3, 0.45, 0.6, 0.7, and 0.75 with thickness ratios of 0.02, 0.06, 0.09, 0.12, O.tS, 0.21 and 0.30. These data are contained in Function Subroutines designated CMXXX, where a Lagrangian interpolation scheme obtains the desired airfoil quarter chord moment coefficient From the available information. However, this value can easily be transformed to the moment coefficient about the airfoil leading edge by: III-8 Cml e = Cmq c - 0.25 C I 7. Subroutine NI6COOR The airfoil coordinates and other pertinent airfoil information is computed, if desired, in this subroutine where: 0.489 (t/c)max 2 = Ill-19

L-E-radius

Chord III-20 Area =0.7396( 1 +0.00544 Cld2)(t/c)max Chord III-21 Mx =0.03335( I +0.00196 Cld 2) Cid (t/c)max Chord 2 + 0.01775( 1 +0.1332 Cld2) Cld (t/c)max 3 111-22 My =0.3569( 1 +0.00458 CldC)(t/c)max Chord 2 Ix=0.04476( 1 -0.00182Cld2)(t/c)max 3 Chord + III-23 0.00009358( 1 +0.02013 Cld 2) Cld 2 (t/c)max Chord 3 Iy =0.04221( 1 +0.01287 Cld 2) (t/c)max Chord 3 III-24 The moments, M x and My, and the moments of inertia Ix and ly are computed about the respective axes. The airfoil coordinates are computed from empirically derived Tables that define the airfoil shape along with the given (t/c)max and given Cld. The equations are given as: III-25 A = CtCld Chord + C 2 Cld (t/c)max2/Chord III-26 B = C 3 (t/c)max + C4Cld 2 (t/c)max with the coefficients C l, C 2, C 3, and C 4 specified in Table Ill as a function of chord location. The coordinates are then calcualted by: 2 A III-27 YU - Chord A - B III-28 Yl - Chord and Y] is the airfoil where Yu is the upper airfoil coordinate, lower coordinate for a given x/c location.

8. Limitations As stated earlier, some limitations exist in the computer program, and when exceeded, flags are contained in the program output to indicate to the User what value has been exceeded. It is to be noted that a Mach number of 0.0 is not allowed, and the program has difficulty handling negative angles of attack of large magnitude at high Mach numbers for thick airfoils. The f=lags appear as: (a) "T/C= 30 IS GREATER THAN (T/C)MAX= 26 FOR THE LIFT CURVE SLOPE" (b) "(CL-CLD)=.9ISGREATERTHAN (CL-CLD)(MAX)=.8FOR DRAG DUE TO L I FT" (c) "CLD= .8 IF GREATER THAN CLDMAX= o6 FOR DRAG DUE TO CAMBER" (d) "T/C= .40 IS GREATER THAN (T/C)MAX= °30 FOR THE BASIC DRAG" (e) "MACH NO.= .95 IS GREATER THAN (T/C)MAX=.35FORTHE MOMENT COEFFICIENT" (f) "T/C= .40 IS GREATER THAN (T/C) MAX= ,35 FOR THE MOMENT COEFF IC ! ENT" (g) "CL= 1.6 IS GREATER THAN CLMAX= 1.3 FOR THE MOMENT COEFF!CIENT" (h)"CLD=,90F GREATER THAN CLDMAX=.8FOR THE MOMENT COEFF !C[ ENT" (i) "ANGLE= 10.0 IS GREATER THAN MAX ANGLE= 9.0" (j) "MACH N0,=,951S GREATER THAN MACH NOo(MAX)=,9FOR SUBSONIC SPEED" 9. Sample Case A sample case with the corresponding input and output is

provided in Appendix II tonindi:cate how the NACA 16-series

airfoil data_bank computer code may be utilized. The complete

output selection for the sample c,_se::..was chosen to show the full capabilities off the databank ,_ode.-- __ d_,--:.

REFERENCES 1. Cooper, J.P,, "The "Linearized Inflow" Propeller Strip Analysis", WADC TR 56-615, February 1957.

2. Enos, T., and Borst, H.V., "Propeller Performance Analysis Aerodynamic Characteristics NACA 16 Series Airfoils" - Part l and If, December t948.

3. Smetana, F.O., Summey, D.C., Smith, N.S., and Carden, R.K., "Light Aircraft Lift, Drag, and Moment Prediction - A Review and Analysis", NASA CR-2523, May 1975.

4. Minzner, R.A., Champoin, K.S.W., and Pond, H.L., "The ARDC Model Atmosphere", Air Force Cambridge Research Center Report No.

TR-59-267, 1959.

5. Anderson, Jr.,J.D., Introduction to Fliqht, McGraw-Hi] I Book Company, 1978.

6 Hoerner, S. F., Aerodynamic Drag, Otterbien Press, Dayton, Ohio, I951.

7. Lindsey, W. F., Stevenson, D.B., and Daley, B.N., "Aeronautical Characteristics OF 24 NACA I6-Series Airfoi ls at Mach Numbers Between 0.3 and 0.8", NACA TN 1546, December t947.

8. Abbott,I.H., and von, Doenhoff, A.E., Theory of Wing Sections, Dover Publ ications, t959.

Table Io Comparison Cases for NACA-16 Airfoil Data Bank°

(t/c)

Mach a Actual Values NACA-16 Values a %C l A %C d max No. (deg) C1 C d C] C d (Cld = 0. i) 0°04 0.45 0 0.1147 0.0056 0.1146 0.0008 1.31 -31.50 0.04 0.45 2 0.3583 0.0071 0.3560 0.0107 0.64 -33.88 0.06 0.45 0 0.Ii00 0.0005 0.1160 0.0008 -5.22 -30.72 0.06 0.45 2 0.3527 0.0081 0.3556 0.0111 -0.81 -27.10 0.06 0.70 0 0o1400 0.0075 0.1536 0.0174 -8.86 -56.59 0.06 0.70 2 0.5181 0.0159 0.4706 0.0221 10.09 -28.17 0.09 0.45 0 0.1007 0.0065 0.1184 0.0090 -14.87 -28.74 0.09 0.45 2 0.3359 0.0090 0.3553 0.0116 -5.47 -21.20 0.09 0.70 0 0.1330 0.0083 0.1625 0.0238 -18.14 -65.09 0.09 0.70 2 0.4690 0.1914 0.4878 0.0287 -3.85 -33.52 Cld = 0.3 0.02 0.70 0 0.4761 0.0072 0.4322 0.0073 10.14 -2.16 0.02 0°70 2 0.7842 0.0139 0.7418 0.0153 5.71 -8.47 0.04 0.45 0 0.3135 0.0139 0.7418 0.0073 -8.82 -23.45 0.04 0.45 2 0.5741 0.0093 0.5852 0.0105 -2.42 -11.73 0.04 0.70 0 0.4691 0.0070 0.4456 0.0074 5.26 -6.88 0.04 0.70 2 0.7911 0.0161 0.7585 0.0160 4.30 0.59 0.06 0.45 0 0.3135 0.0050 0.3482 0.0075 -9.95 -33.18 0.06 0.45 2 0.5599 0.0098 0.5877 0.0180 -4.73 -9.20 0.06 0.70 0 0.4621 0.0088 0.4608 0.0078 0.28 11.82 0.06 0.70 2 0.7981 0.0182 0.7778 0.1711 2.61 6.45 0.09 0.45 0 0.2855 0.0065 0.3550 0.0079 -19.57 -17.65 0.09 0.45 2 0.5262 0.0110 0.5920 0.0112 -ii.i0 -2.37 0.09 0.70 0 0.4060 0.4873 0.0086 -16.68 0.09 0.70 2 0.7415 0.0182 0.8127 0.0191 -8.68 -5.13 Table II, NACA-16 Series Input List, M Mach Number ANGLE Angle of Attack ALTUDE Geometric Altitude (in Feet) CHORD Chord (Feet) TC Maximum Thickness to Chord ratio CLD Design Lift Coefficient ICL Lift Coefficient Parameter 0 = Incompressible Lift Coefficient ! = Compressible Lift Coefficient ICD Drag Coefficient Parameter 0 = Incompressible Drag Coefficient i = Compressible Drag Coefficient X Radial Location on the Propeller (r/R) NUMACH Number of Mach Numbers NUMALP Number of Alphas IFORM Output Format Control Moment Coefficient Parameter MP 0 = No Moment Computed t = Moment Coefficient about Leading Edge 2= Moment CoefFicientaboutQuarter Chord Airfoil Coordinates Parameter 0 = No Coordinates Computed t = Airfoil Coordinates Computed Table III. Airfoil Coordinate Coefficients.

Chordwise C I C 2 C 3 C 4 Station i 0.00930 0.12720 0°15044 0.00639 2 0.01580 0.09653 0.20911 0.00574 3 0°02587 0.06600 0.28811 0.00440 4 0.03982 0.03473 0.38867 0°00237 5 0.04861 0.01461 0.45144 0.00103 6 0.05356 0.00394 0.48789 0.00025 7 0.05516 0.00000 0.50000 0.00000 8 0.65356 0.00447 0.48622 0°00025 9 0.04861 0.01895 0.43911 0.00100 10 0.03982 0.04400 0.34989 0.00021 11 0.02587 0.05961 0.20978 0.00321 12 0.0158 0.05469 0.11789 0.00324 i I

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Appendix - I

NACA 16-Series Program Listing

//NACAI6 JOB (R205,011C,S02,002,A7),'CAMBA' //*XBM WATFIV * PROGRAM TO CALCULATE THE LIFT, DRAG, AND " W * MOMENTS FOR NACA 16-SERIES AIRFOILS THIS PROGRAM CALCULATES THE LIFT COEFFICIENTS DRAG COEFFI- CIENTS, LIFT-TO-DRAG RATIOS, AND MOMENT COEFFICIENTS FOR NACA 16-SERIES AIRFOILS. IT IS WRITTEN IN FORTRAN G-l, ORIGANALLY FOR USE ON A HARRIS /6 COMPUTER. THE USER WILL HAVE TO DEVLEOP A ROUTINE FOR READING IN THE INPUT THAT IS COMPATIBLE WITH HIS OR HER SYSTEM. SOME LIM- ITATIONS DO EXIST IN THE PROGRAM° A MACH NUMBER OF 0o0 IS NOT ALLOWABLE. ALSO, THE PROGRAM HAS TROUBLE HANDLING NEGATIVE ANGLES OF ATTACK OF LARGE MAGNITUDE AT HIGH MACH NUMBERS FOR THICK AIRFOILS.

INPUT LIST ICD DRAG COEFFICIENT COMPRESSIBILTY CHECK FACTOR 0_ GIVES INCOMPRESSIBLE DRAG COEFFICIENT l, GIVES COMPRESSSIBLE DRAG COEFFICIENT ICL = LIFT COEFFICIENT COMPRESSIBILITY CHECK FACTOR 0, FOR AN INCOMPRESSIBLE LIFT COEFFICIENT = l, FOR A COMPRESSIBLE LIFT COEFFICIENT IFORM = CHECK PARAMETER WHICH CONTROLS FORMAT OF OUTPUT 0, GIVES ALL OF THE INCREMENTS IN THE DRAG i, GIVES TABULAR OUTPUT OF CL AND CD AT EACH ALPHA ONE TABLE FOR EACH MACH NUMBER NUMALP = NUMBER OF ALPHAS SPECIFIED (INTERGER) UP TO 15 NUMACH = NUMBER OF MACH NUMBERS (INTEGER) UP TO 15 CLD = DESIGN LIFT COEFFICIENT THICKNESS TO CHORD RATIO TC = CHORD = CHORD LENGTH (FEET) ALTUDE = ALTITUDE (FEET) M = MACH NUMBER(S) ANGLE = ANGLE(S) OF ATTACK REFERENCED FROM THE LONGEST CHORD (DEGREES) X = RADIAL LOCATION MP = MOMENT COEFFICIENT PARAMETER = 0, IF THE MOMENT COEFFICIENTS ARE NOT DESIRED = l, FOR THE MOMENT COEFFICIENT ABOUT THE LEADING EDGE = 2, FOR THE MOMENT COEFFICIENT ABOUT THE QUARTER CHORD AIRFOIL COORDINATES PARAMETER 0, IF THE COORDINATES ARE NOT DESIRED i, GIVES THE AIRFOIL SECTION COORDINATES AND ITS MOMENTS OF INERTIA C C SUBROUTINE ATMCON C C THIS SUBROUTINE IS VERY STRAIGHT FORWARD. GIVEN AN ALTITUDE, THE C SUBROUTINE CALCULATES THE TEMPERATURE, PRESSURE, DENSITY, VISCOSITYF C AND SPEED OF SOUND AT THAT ALTITUDE.

C C C C SUBROUTINE N16COR C C THIS SUBROUTINE CALCULATES THE DIMENSIONS AND SECTION PROPERTIES C FOR A (SOLID SECTION) NACA 16-SERIES AIRFOIL SECTION FOR ANY C GIVEN THICKNESS, CHORD, AND DESIGN LIFT COEFFICIENT. IF A C DESIGN LIFT COEFFICIENT IS NOT KNOWN BUT THE AREA, TC, AND C CHORD IS, THEN THE CLD WILL BE OUTPUT. THE ROUTINE ALSO CAL- C CULATES THE MOMENT OF INERTIA FOR THE MAJOR (X) AND MINOR C (Y) AXES. SEVERAL OTHER PROPERTIES OF THE NACA 16-SERIES ARE C CALCULATED, BUT ARE NOT OUTPUT UNLESS DESIRED. THEY ARE C DEFINED BELOW° ALSO NOTE THAT THE COORDINATES ARE NON-DIMEN- C SIONAL WITH RESPECT TO THE CHORD r AND THE X UPPER AND LOWER C ARE THE SAME.

C LERAD = LEADING EDGE RADIUS OF AIRFOIL C TERAD = TRAILING EDGE RADIUS OF AIRFOIL C MY = MOMENT ABOUT THE Y AXIS C MX = MOMENT ABOUT THE X AXiS C IYC = MOMENT OF INERTIA ABOUT Y CENTROIDAL AXIS C IXC = MOMENT OF INERTIA ABOUT X CENTROIDAL AXIS C C C C SUBROUTINE CLCD C C C C SUBROUTINE CLCD CALCULATES THE SECTION LIFT AND DRAG COEFFICIENTS FOR A C NACA 16-SERIES AIRFOIL. THE DATA BASE FOR THIS SUBROUTINE IS FROM: C COOPER, Jo L., "THE 'LINEARIZED INFLOW' PROPELLER ANALYSIS" WADC TR 56-516, C 1957. THE EQUATIONS AND GRAPHS CONTAINED IN THIS REPORT FORM THE BASIS C FOR ALL FURTHER DISCUSSION.

C C C CALCULATION OF CL (SEE COOPER, Po 14) C C A. FOR SUBSONIC SECTION VELOCITIES: C C CL= ALPHA*DCLDA WHERE: C C DCLDA=.1096_(1-XTC)/SQRT(1-XTC*_2) C AND ALPHA IS SPECIFIED IN INPUT C C B. FOR SUPERSONIC SECTION VELOCITIES: C C DCLDA=.0698/SQRT(XM**2-1) C XM= LOCAL MACH NUMBER C C AND CL=ALPHA*DCLDA C C C C C C CALCULATION OF CD C C THE DRAG COEFFICIENT IS CALCULATED IN FOUR INCREMENTS: BASIC DRAG C COEFFICIENT(CDZERO);THE INCREMENT DUE TO LIFT(CDLIFT); THE INCREMENT C DUE TO CAMBER(CDCAMB);AND THE INCREMENT DUE TO SKIN FRICTION(CDFRIC).

C C C C BASIC DRAG COEFFICIENT: C C C DATA FOR CALCULATION OF CDZERO IS TAKEN FROM FIG 12, P.31 IN COOPER.

THIS IS A PLOT OF CDZERO -VS- MACH NUMBER AS A FUNCTION OF THICKNESS.

C C GIVEN A THICKNESS AND A MACH NUMBER, THE PROGRAM CALCULATES THE DRAG- C DIVERGENCE MACH NUMBER BY LINEAR INTERPOLATION, AND TESTS TO SEE IF THE SPECIFIED MACH NUMBER IS ABOVE OR BELOW THE DRAG DIVERGENCE MACH NUMBER.

C IT THEN CALCULATES CDZERO ACCORDINGLY.

C C A. FOR SUBSONIC SECTION VELOCITIES: C C C THE SUBROUTINE PERFORMS A LINEAR INTERPOLATION IF THE LOCAL MACH IS C BELOW THE DRAG DIVERGENCE MACH NUMBER,OR USES A POLYNOMIAL CURVE FIT FOR LOCAL MACH NUMBERS ABOVE THE DRAG DIVERGENCE MACH NUMBER.

C C C C B. FOR SUPERSONIC SECTION VELOCITIES: C C THE SUBROUTINE USES A POLYNOMIAL CURVE FIT ON THE SUPERSONIC PORTION C OF THE CURVE TO ARRIVE AT A VALUE FOR CDZEROo C C C _**NOTE***=* C IF THE THICKNESS IS LESS THAN _03 OR IF CDZERO IS NEGATIVE_ THEN C CDZERO IS SET EQUAL TO 0.0.

C C C C C C C C C C C CALCULATION OF CDLIFT C C C DATA FOR CDLIFT CALCULATION COMES FROM FIGURE 9A_ P.26 IN COOPER° C C FIRST: C C DELTA=(CL-XCLI) C C THEN IT CALCULATES XMXT, THE WEIGHTED MACH NUMBER C C XMXT=XM/(.9-XTC) C C THEN IT CALCULATES DELCD USING THE FORMULA AT THE TOP OF FIGURE 9A.

C C DELCD=(XMXT_*2-XMXT-.1765)_(-o4397"DELTA**2+ol173"DELTA-.0938) C C NEXT, TESTM IS CALCULATED. TESTM IS THE VALUE OF XMXT ON THE LINE C LABELED LIMA WHICH CORRESPONDS TO THE VALUE OF DELCD JUST CALCULATED° C OBTAINED° C C TESTM=(DELCD-.03)_(o9-o875)/(.03-o08)+o9 C C IF THE VALUE OF XMXT IS GREATER THAN TESTM, THE EQUATION ABOVE DOES NOT HOLD° THEN THE VALUE OF DELCD IS ARRIVED AT BY USING A 6TH C DEGREE POLYNOMIAL CURVE FIT TO FIND THE SLOPE OF THE PLOT. THEN: C C C DELCD=SLOPE=(XMXT-1.011111)+o0911111 C C THEN THE SUBROUTINE TESTS IF YOU HAVE A SUPERSONIC MACH NUMBER.

C IF SO: C C DELCD= SQRT(XM_"2-1)/4 AND C DELTA= CL C C ONCE DELTA AND CL HAVE BEEN CALCULATED IN THE PROPER MANNER, C CDLIFT IS GIVEN BY: C C CDLIFT=DELCD_DELTA"_2 C C C CALCULATION OF CDFRIC THE COEFFICIENT OF DRAG DUE TO FRICTION IS A FUNCTION OF REYNOLDS NUMBER AND PERCENT LAMINAR FLOW; AND IS CALCULATED USNG FIGURES 10A AND 10B , PP.28-9 IN COOPER° FIGURE 10B IS A CURVE OF PERCENT LAMINAR FLOW -VS- RADIAL LOCATION° FROM THIS CURVE THE SUBROUTINE FINDS THE PERCENT LAMINAR FLOW OVER THE AIRFOIL (PLAM) BY A 2ND. DEGREE POLYNOMIAL CURVE FIT.

PLAM=(33.+l./3.)*XR**2+(8o+I./3.)*XR+I7.0 THEN THE REYNOLDS NUMBER FOR THE AIRFOIL IS CALCULATED BY: XRN=DEN*XM*WA*CHORD/VIS WHEN WE HAVE REYNOLDS NUMBER AND PERCENT LAMINAR FLOW, CDFRIC IS CALCULATED FROM: CDFRIC=2.65/SQRT(XRN)+(IOO-PLAM)/PLAM"(°944/DLOGlO(XRN)*"2.65/SQRT( &SQRT(XRN)) ***NOTE**** THIS IS FOUND ON P. 25 IN COOPER CALCULATION OF CDCAMB CDCAMB, 'THE DRAG DUE TO CAMBER REPRESENTS THE INCREASE IN THE MINIMUM BASIC DRAG COEFFICIENT OF CAMBERED NACA 16-SERIES AIRFOILS OVER THAT OF THE UNCAMBERED AIRFOILS OF THE SAME SERIES'- COOPER CDCAMB IS CALCULATED FROM FIGURE ll, Po30 IN COOPER. THIS IS A PLOT OF CDCAMB -VS- XMXT AS FUNCTION OF CLD.

THE SUBROUTINE PERFORMS A SERIES OF LINEAR INTERPOLATIONS TO FIND THE PROPER CDCAMB AT A SPECIFIED XMXT FOR A SPECIFIED CLD.

CALCULATION OF MOMENT COEFFICIENTS ABOUT THE QUARTER CHORD (CMQC) DATA TABLES FOR THE MOMENT COEFFICIENTS ABOUT THE QUARTER CHORD ARE SET UP FOR CLDS' OF 0.0, 0.1, Oo3w AND 0°5 AT MACH NUMBERS OF 0.3, 0°45, 0°6, 0°7, AND 0°75 WITH THICKNESS RATIOS OF °02, .06, °09, °12, .15v °21, AND .30. A LAGRANGIAN INTER- POLATION ROUTINE INTERPOLATES BETWEEN THE TABLES TO OBTAIN THE DESIRED MOMENT COEFFICIENT. THE DATA TABLES ARE EXTRACTED FROM LINDSEYw W.F., D.Bo STEVENSON_ AND BERNARD N. DALEY, "AERODYNA- MIC CHARACTERISTICS OF 24 NACA 16-SERIES AIRFOILS AT MACH NUMBERS BETWEEN 0.3 AND 0.8" NACA TN1546, FIG. 7o9, PP. 57-7Z.

ABOUT THE LEADING EDGE (CMLE) THE MOMENT COEFFICIENT ABOUT THE LEADING EDGE IS TRANSFORMED FROM THE QUARTER CHORD WITH THE FOLLOWING EQUATION: CMLE = CMQC-0.25_CL DIMENSION CLF(30,30),CDL(30,30),CDFR(30,30),CDC(30,30),CDF(30,30) DIMENSION CDZ(30,30),CM(30,30),RLD(30,30) DIMENSION ANGLE(3),ANG(30) DIMENSION RN(30) REAL MXMACH REAL M(3) DATA M/0.3,0.5,0o7/ DATA ANGLE/0.0,2.0,4°0/ DATA ALTUDE/0./ DATA CHORD/I.000/ DATA TC/0.15/ DATA CLD/0.2/ DATA ICL/I/ DATA ICD/I/ DATA X/.50/ DATA NUMACH/3/ DATA NUMALP/3/ DATA IFORM/1/ DATA MP/I/ DATA L/l/ CALL ATMCON(ALTUDE,TEMP,PRES_DEN,VIStWA) ALPHAO=-CLD/(0.1096*SQRT((I+TC)/(I-TC))) CALL N16COR(L,CHORDuTC,CLD,AREA) CALL TEST(TC,MXMACH) WRITE(6,10) l0 FORMAT('I',56X, '"** LIMITATIONS _'//) DO 21 K=I,NUMACH C 36 DO 42 J=I,NUMALP C ANG(J)=ANGLE(J)-ALPHA0 C CALL CLCD(M(K),ANG(J)_CLF(K,J),CDF(K,J),ICL_ICD,CHORD_TCrRN(K) &,CLD,X,WA,VIS,DEN,CDFR(K,J),CDL(K,J)_CDC(K_J),CDZ(K,J)) RLD(K,J) = CLF(K,J)/CDF(K,J) IF(MPoEQo0) GO TO 5 HMIN=0.3 MMAX=0_75 TCMIN=0.02 TCMAX=0o30 CLFMIN=-0o3 CLFMAX=lo0 IF(M(K).LT.HMIN) WRITE(6,22) M(K),HMIN 22 FORMAT(' ,9X,'MACM NO. = '_F10.6,' IS LESS THAN MACH', &' NO.(MIN) = '_FI0o6,' FOR THE MOMENT COEFFICIENT'/) IF(M(K) oGToHMAX) WRITE(6,31) M(K),HMAX 31 FORMAT(' ,9X,'MACH NO° = '_F10o6, " IS GREATER THAN MACM NO°' &,'(MAX) = ',FI0o6,' FOR THE MOMENT COEFFICIENT'/) IF(TCoLT.TCMIN) WRITE(6w43) TC,TCMIN 43 FORMAT( _ ,gX,'T/C = '_FI0o6,' IS LESS THAN (T/C)MIN = '_ &Fl0o6w " FOR THE MOMENT COEFFICIENT'/) IF(TC.GToTCMAX) WRITE(6,50) TC,TCMAX 50 FORMAT(' ,gX, tT/C = '_F10o6,' IS GREATER THAN (T/C)MAX = ', &F10o6,' FOR THE MOMENT COEFFICIENT'/) IF(CLF(K,J).LToCLFMIN) WRITE(6,60) CLF(K,J),CLFMIN 60 FORMAT(' ,9X,'CL = [vF10o6v' IS LESS THAN CLMIN = ',FI0o6, &' FOR THE MOMENT COEFFICIENT'/) IF(CLF(KfJ)oGT.CLFMAX) WRITE(6,65) CLF(K,J),CLFMAX 65 FORMAT(' ,gx,'CL = ',F10.6_' IS GREATER THAN CLMAX = ',Fl0.6r &' FOR THE MOMENT COEFFICIENT'/) CMOQC=CMOFF(M(K),TC,CLF(K,J)) CMIQC=CMIFF(M(K),TC,CLF(K,J)) CM3QC=CM3FF(M(K),TC,CLF(K,J)) CM5QC=CM5FF(M(K),TC,CLF(K,J)) C VARIABLE 'CMoN0.QC': 'CM' = MOMENT COEFFICIENT C '°NO.' = DESIGN LIFT COEFFICIENT _ l0 C 'QC t = QUARTER CHORD CLDMIN=0.0 CLDMAX=0o5 IF(CLD.LToCLDMIN) WRITE(6,55) CLD_CLDMIN 55 FORMAT(' ',9X,'CLD = vFl0o6, IS LESS THAN CLDMIN = ',F10o6_

&' FOR THE MOMENT COEFFICIENT'/)

IF(CLD.LE.0.1) GO TO4

IF(CLD.LE.0.3) GO TO1

IF(CLD.LE.0.5) GO TO2

WRITE(6,70) CLD,CLDMAX

' tFl0o6_

70 FORMAT(' ',gX,'CLD= ',F10.6,' IS GREATER THAN CLDMAX =

&' FOR THE MOMENT COEFFICIENT'/)

GO TO2

4 YI=CMIQC-CMOQC

Xl=0.1

X2=CLD

Y2=YI*X2/X1

GO TO3

1 YI=CM3QC-CMIQC

Xl=0°2

X2=CLD-0°I

Y2=YI*X2/X1

GO TO3

2 YI=CM5QC-CM3QC

XI=0.2

X2=CLD-0.3

Y2=YI*X2/Xl

3 CM(K,J)=Y2

IF(MP°EQ°I) CM(K,J)=CM(K,J)-0o25"CLF(K,J)

5 IF(MPoEQ.0) CM(K,J)=0o0

IF(TC°GT.0.1) GO TO 281

IF(M(K)°LT.0o5) GO TO 281 IF(M(K).GE.1.0) ALTEST=999.99 CALL AOAT(M(K),ALTEST,K) IF(ANGLE(J).GT.ALTEST) WRITE(6_20) ANGLE(J),ALTEST 20 FORMAT(' ',9X_'ANGLE = ',FI0.6,' IS GREATER THAN MAX°', &'ANGLE = ',F10.6/) 281 IF(M(K).LT°MXMACM) GO TO 42 IF(M(K) oGE.I.0) GO TO 42 WRITE(6,30) M(K),MXMACH 30 FORMAT(' ',9X,'MACM NO. = ',FI0o6,' IS GREATER THAN MACH NO°'_ &'(MAX) = ',FI0o6,' FOR SUBSONIC SPEED'/) CONTINUE 21 CONTINUE IF(IFORM.EQol) GO TO 53 DO 87 KK=I,NUMACH DO 88 LL=IwNUMALP WRITE(6,254) FORMAT('I'_39X,'*',lX,'NACA 16,6 SERIES AIRFOIL DATA BANK',

_lx,'*'llll)

WRITE(6,900) CLD,ALPHAO,TC,M(KK),ANGLE(LL),ALTUDE 90O FORMAT(30X,'INPUT PARAMETERS'/25X,32('_') &/25X,'_,30Xu'*'/25X,'*',30X,'*'/25X, V*°r5X &,'CLD=',F10.7,11X,'*'/25X,'*',30X,'*'/25X,'_',30X &,'*'/25X,'"',5X,'ALPHAL0='wF10o7,gX,'*'/ &25X,'*',30X,'*'/25X,'*',30X &,'_'/25Xv'*',5X,'T/C=',F10o7,11Xr'*'/25Xr '"', &30X,'"'/25X,'*',30XF'_'/25X_'"',5X,_MACH =', &FI0o7_10X,'*'/25X,'*',30X,'*'/25X,'*',30X, '"' &/25X,'*' 5X,'ALPHA=',F10.7,9X_'"'/25X, '*t, f '/25X,' 30X,'*'/25X,'*_5X,'ALTITUDE =' , &30Xu '_ *', &FI0.3,6X,'_'/25Xw_*',30Xr'_'/25X,'*',30X,'*'/25X,32('_')) WRITE(6,99) CLF(KK,LL) 99 FORMAT(20X,'LIFT COEFFICIENT='_F10o6///) WRITE(6,100) CDL(KK,LL) 100 FORMAT(20X_'INCREMENT IN DRAG COEFFICIENT DUE TO LIFT='_F10°6) WRITE(6,101) CDFR(KK,LL) i01 FORMAT(///20X,'INCREMENT IN DRAG COEFFICIENT DUE TO FRICTION=', &FI0.6) WRITE(6,102) CDC(KK,LL) 102 FORMAT(///20X,'INCREMENT IN DRAG COEFFICINT DUE TO CAMBER=',FI0o6) WRITE(6,103) CDZ(KK,LL) 103 FORMAT(///2OX,'BASIC DRAG COEFFICIENT=',F10o6) WRITE(6,104) CDF(KK,LL) FORMAT(///2OX,'TOTAL DRAG COEFFICIENT=',F10.6) C CONTINUE C C CONTINUE C 53 CONTINUE C J=0 IF(NUMACH.EQ.1) GO TO 44 NUMT=NUMACH DO 40 JJ=I,NUMACH WRITE(6,852) FORMAT('I',IIX,'* NACA 16,6 SERIES AIRFOIL DATA BANK _',22X, &'* NACA 16,6 SERIES AIRFOIL DATA BANK "'////) WRITE(6,515) ALTUDE,ALTUDE FORMAT(T20,'ALTITUDE = ',F10.4,1X,'FEET',T83,'ALTITUDE = ', &FI0.4,1X,'FEET'/) WRITE(6,117) CHORD,CHORD ll7 FORMAT(T23,'CHORD = ',F10.6,1X_'FEET',T86,'CHORD = ', &FI0.6,1X,'FEET'/) WRITE(6,701) TC,TC,CLD,CLD FORMAT(T20,'(T/C)MAX = ',FI0o6uT82, '(T/C)MAX = ',F10.6, &//T25,'CLD = ',F10.6,T87,'CLD = ',F10o6/) WRITE(6,283) ALPHAO,ALPHAO FORMAT(T21,'ALPHAL0 = ',FI0.6,1X,'DEG.',T84,'ALPHAL0 = ', &FI0.6,1X,'DEGo'/) WRITE(6,700) M(J+I),M(J+2) FORMAT(T20,'MACH NO. = ',F10.6,T83,'MACH NOo = ',FI0.6/) WRITE(6,729)RN(J+l),RN(J+2) FORMAT(T16,'REYNOLDS NO. = ',E14.6,T79, _REYNOLDS NO. = ', &El4.6,1/) C IF(MPoEQo2) GO TO 82 WRITE(6,555) FORMAT(TI0v'ALPHA'FT23, 'CL',T35,'CD',T45,'CL/CD',T57,'CM(LED ) ' &,T73,'ALPHA',T86,'CL',T98,'CD',T108,'CL/CD',T120,'CM(LED)'/) GO TO 83 WRITE(6,556) FORMAT(TI0,'ALPHA',T23,'CL',T35,'CD',T45,'CL/CD'wT57,'CM(1/4)' &_T73,'ALPHA',T86,'CL',T98N'CD',TI08,'CL/CD',T120,'CM(I/4)') C CONTINUE DO 41 N=I,NUMALP C WRITE(6,600) ANGLE(N),CLF(J+I,N),CDF(J+I,N),RLD(J+I_N)_CM(J+lvN) &wANGLE(N),CLF(J+2,N),CDF(J+2FN),RLD(J+2gN),CM(J+2,N) 60O FORMAT(2(5X,F10.6,2X,F10.6,2X,FI0.6,2X,FI0.6,2X,FI0.6)) C 41 CONTINUE C J=JJ_2 NUMT=NUMT-2 IF(NUMToEQ.0) GO TO 33 IF(NUMToEQ.I) GO TO 44 40 CONTINUE 44 WRITE(6,589) 589 FORMAT('I',39Xw'*',lXw'NACA 16_6 SERIES AIRFOIL DATA BANK', &lX,'*'//I/) WRITE(6,214) ALTUDE 214 FORMAT(Tll,'ALTITUDE = ',F10o4,IX_'FEET'/) WRITE(6,339) CHORD FORMAT(TI4,'CHORD =',FI0.6,1X,'FEET') WRITE(6,152) TC FORMAT(/Tll,'(T/C)MAX = ',F10o6/) WRITE(6,151) CLD FORMAT(T16,'CLD = ',F10.6/) WRITE(6,888) ALPHAO FORMAT(T12, 'ALPHAL0 = ',FI0.6/) WRITE(6,150) M(NUMACH) FORMAT(Tll,'MACH NO. = ',FI0.6/) WRITE(6,912)RN(NUMACH) FORMAT(/T7,'REYNOLDS NO° = ',FI0.6//) C IF(MP.EQ.2) GO TO 84 WRITE(6,666) 666 FORMAT(TIO,'ALPHA',T23,'CL',T35,'CD',T45,'CL/CD',T571'CM(LED)'/) GO TO 85 WRITE(6,665) FORMAT(TI0,'ALPHA',T23,'CL',T35,'CD',T45,'CL/CD'_T57,'CM(1/4)'/) C CONTINUE 85 DO 66 N=I,NUMALP WRITE(6_250) ANGLE(N),CLF(NUMACHwN),CDF(NUMACH,N)_RLD(NUMACH, &N),CM(NUMACH,N) 25O FORMAT(5X,F10.6,2X,F10.6,2X,F10.6,2X,FI0.6,2XIF10o6) 66 CONTINUE C GO TO 33 C 33 WRITE(6,999) 999 FORMAT('1') STOP END SUBROUTINE CLCD(XM_ALPHA,CL,CD,ICL,ICD,CHORD,XTC,XRN,XCLI,XR &wWA,VIS,DEN,CDFRIC_CDLIFT,CDCAMB,CDZERO) DIMENSION CDD(6),CLIT(6)_A(6),B(6),C(6)_D(6),E(6),F(6),G(6) DIMENSION TB(ll),DMACH(I1),CD0(ll),CD01(6),TBI(6),AA(6),BB(6) DIMENSION CC(6),DD(6),EE(6),FF(6) DOUBLE PRECISION AA,BBwCC,DD,EE,FF DATA A/1°325276,°i024011,.2890272,.5288957,1.177606,2o125449/ DATA B/-5o133061N-°0976595,-o2461832g-.0205697v-.2953677,o1974199/ DATA C/8o412967F-o2752136,-o8075892,-2.787452,-5.423342,-11.9608/ DATA D/-7o325109,.5574539,1o52008194.335364,8.694619,18.21422/ DATA E/3o522405,-o3924382,-1o018046,-2_761126,-5o583289,-iio50479/ DATA F/-,8777567,o1226128,.3042805,.8093843,1o64263,3°357388/ DATA G/.087806w-.0140459,-.0334875,-.0889465,-olS14412,-.3697504/ DATA TB/°031_.0625,.if.1375, o175v o2125,.25_.2875w.325,o3625_.4/ DATA CD0/0o0, o00025, o00065_°0013,.0022,.0033,.00465,.0861, &o0078_°01wo013/ DATA DMACH/.9_.84,o79_.75, °72,.7w o68w °665_o65,.6375,.62/ DATA AA/-5o834527753w-lo45916514_8o3327673,2°6038473,-o10428842,.2 &08297374/ DATA BB/37.09086074_9o58857686g-51°4547602,-16.2479854,.78201755,- &1o2497732/ DATA CC/-94.01887327e-25o1902339_126°241026,40°198068,-2.2988001_2 &o94734747/ DATA DD/l18.8401952,33.12056567,-153o736709w-49.206188_3o3320883,- &3o39928973/ DATA EE/-74.98024889r-21o858250,g2°8384573,29.7250413,-2.3960093, &1.903809351/ DATA FF/18.94459392_5.83350647,-22.1932814,-7.0552833,.689991999,- &o408891283/ PLAM=(33o+l./3.)*XR**2+(8.+I./3.)*XR+17o0 TCMIN=0°02 TCMAX=0°30 IF(XTCoLT.TCMIN) WRITE(6,21) XTC,TCMIN Zl FORMAT( _ ',9Xv _T/C = ',F10.6,' IS LESS THAN (T/C)MIN = '_F10.6, &' FOR THE LIFT CURVE SLOPE'/) IF(XTCoGT.TCMAX) WRITE(6,30) XTCgTCMAX FORMAT(' ',gX,'T/C = '_FI0o6,' IS GREATER THAN (T/C)MAX = ',

&FI0.6,' FOR THE LIFT CURVE SLOPE'/)

IF(XM.LT.I.0) GO TO 1 DCLDA=.O698/SQRT(XMW*2-1) GO TO 2 1 IF(ICL.EQ.0) DCLDA=.1096*(I-XTC)/SQRT(I-XTC'*2) IF(ICL.EQ.0) GO TO 2 DCLDA=.lO96/SQRT(I-(XM)**2) IF((XM+XTC).GE.I.0) GO TO 2 DCLDA=.1096*(1.-XTC)/SQRT(1-(XM+XTC)"_2) 2 CL=ALPHA*DCLDA XRN=DEN*XM"WA*CHORD/VIS C XRN=3000000.0 IS THIS SUPPOSE TO BE HERE? --- WINTER C IF(ICD.EQ.0) RETURN DELTA=CL-XCLI XMXT=XM/(.9-XTC) DELCD=(XMXT**2-XMXT-.1765)_(-o4397*DELTA"_2+ol173_DELTA-_0938) TESTM=(DELCD-.03)*(.9-.875)/(.03-o08)+o9 IF(XMXT.GT.TESTM) GO TO 3 GO TO 4 3 SLOPE=-lI7.218415"DELTA**6+321.890357*DELTA"*5-332.087766*DELTA"_4 &+I51.8614153*DELTA**3-24.597998"DELTA"*2-2.6451615*DELTA+Io48 DELCD=SLOPE*(XMXT-1.011111)+°0911111 4 IF(XM.GE.1.0) DELCD=SQRT(XM**2-1)/4o IF(XMoGE.1.0) DELTA=CL CLDMX=0.8 IF(DELTA.GToCLDMX) WRITE(6,40) DELTA,CLDMX 40 FORMAT(' ',9X,'(CL-CLD) = ',FI0.6,' IS GREATER THAN (CL-CLD)'t &'(MAX.) = ',FI0.6,' FOR DRAG DUE TO LIFT'/) CDLIFT=DELCD*DELTA**2 IF(CDLIFT.LT.0o0) CDLIFT=0.0 CDFRIC=2.65/SQRT(XRN)+(lOO-PLAM)/lOOo_(o944/(ALOGIO(XRN)_"2o6)-2o6 &S/SQRT(XRN)) IF(XMXT.GT.1.0) GO TO 8 DO 5 I=i,6 CDD(I)=A(I)*XMXT*"6+B(1)_XMXT**5+C(1)"XMXT_*4+D(1)_XMXT_"3+E(I)*XM &XT**2+F(I)*XMXT+G(1) 5 CLIT(I)=FLOAT(I)/10.+ol SUM=Oo0 DO 7 IX=l,6 S=CDD(IX) DO 6 JX=l,6 IF(JX.EQ.IX) GO TO 6 S=S*(XCLI-CLIT(JX))/(CLIT(IX)-CLIT(JX)) 6 CONTINUE SUM=SUM+S 7 CONTINUE CLDMIN=0o0 CLDMAX=0o7 IF(XCLI.LToCLDMIN) WRITE(6,50) XCLI,CLDMIN 50 FORMAT(' '_gx,'CLD = 'wF10o6,' IS LESS THAN CLDMIN = ',F10o6, &' FOR DRAG DUE TO CAMBER'/) IF(XCLIoGT.CLDMAX) WRITE(6_60) XCLIwCLDMAX 60 FORMAT(' ',gx,'CLD = ',F10.6,' IS GREATER THAN CLDMAX = _,F10.6, &' FOR DRAG DUE TO CAMBER'/) CDCAMB=SUM IF(CDCAMBoGT.0.0) GO TO 9 8 CDCAMB=0o0 9 IF(XMoGEo.95) GO TO 14 IF(XTCoLE.o03) GO TO 19 SUM=0o0 DO ll IX=l,ll S=CDO(IX) DO i0 JX=l,ll IF(JXoEQ°IX) GO TO i0 S=S*(XTC-TB(JX))/(TB(IX)-TB(JX)) i0 CONTINUE SUM=SUM+S ii CONTINUE CDZERO=SUM

SUM=0.0

DO 13 IX=l,ll S=DMACH(IX) DO 12 JX=l,ll IF(JXoEQ.IX) GO TO 12 S=S*(XTC-TB(JX))/(TB(IX)-TB(JX)) 12 CONTINUE SUM=SUM+S 13 CONTINUE DIVMAC=SUM IF(XM.LE.DIVMAC) GO TO 18 XCHANG=.7Z25+(XM-DIVMAC) YCHANG=CDZERO-.O023845 CDZERO=-3773Z.79544*XCHANG"*5+I43059.1078*XCHANG**4-216835.3262"XC &HANG**3+164241°3211*XCHANG**2-62170.O9813*XCHANG+9408.610638+YCHAN _G GO TO 18 14 DO 15 I=l,6 CD01(I)=AA(I)"XM"*5+BB(I)'XM**4+CC(I)_XM_"3+DD(I)"XM*_2+EE(1)"XM+F

_F(1)

15 TBI(I)=FLOAT(I)/100o SUM=Oo0 DO 17 IX=I_6 S=CDOI(IX) DO 16 JX=l,6 IF(JXoEQolX) GO TO 16 S=S"(XTC-TBI(JX))/(TBI(IX)-TBI(JX)) 16 CONTINUE SUM=SUM+S 17 CONTINUE CDZERO=SUM 18 IF(CDZEROoLTo0o0) CDZERO=0°0 GO TO 20 19 CDZERO=0o0 TCMIN=0o02 TCMAX=0o40 IF(XTCoLT°TCMIN) WRITE(6,70) XTC;TCMIN 70 FORMAT(' '_gX,'T/C = ',F10.6,' IS LESS THAN (T/C)MIN = ', &F10o6t' FOR THE BASIC DRAG'/) IF(XTCoGToTCMAX) WRITE(6,80) XTC,TCMAX 80 FORMAT(' ',9X,'T/C = ',F10o6,' IS GREATER THAN (T/C)MAX = _, &F10.6e' FOR THE BASIC DRAG'/) 20 CD=CDLIFT+CDFRIC+CDCAMB+CDZERO IF(ICLoEQ.0) CD=CDFRIC XRN=XRN/1000000° RETURN END C C C C DATA FOR MOMENT COEFFICIENT ABOUT THE QUARTER CHORD C C C FUNCTION CMOFF(M,TC,CLF) DIMENSION A(5),X(3),Y(3) REAL M C DATA A = MACH NO° DATA A/0.3,0.45,0o6,0o7w0o75/ N=2 IS=I IL=IS+N-I IF(MoLEoA(IL)) GO TO 2 IL=2 IS=IL-N+I IF(M_GEoA(IS)) GO TO 2 IS=I IL=IS+N-I 3 IF((M-A(IS))_(M-A(IL))oLE.0.0) GO TO 2 IS=IL IL=IS+N-1 GO TO 3 2 DO 4 I=IS,IL J=I-IS+I X(J)=A(I) GO TO (30,45,60,70,75),I DATA 'CM.NO.': 'CM' = MOMENT COEFFICIENT ABOUT THE QUARTER CHORD '.N0o'= CLD*I0 AND MACH NUMBER*100 3O Y(J)=CM030(M,TC,CLF) GO TO 4 45 Y(J)=CMO45(M,TC,CLF) GO TO 4 Y(J)=CM060(M,TC,CLF) GO TO 4 Y(J)=CM070(M,TC,CLF) GO TO 4 75 Y(J)=CM075(M,TC,CLF) 4 CONTINUE CMOFF=YLAGN(X,YFN,M) RETURN END FUNCTION CM030(M_TC,CLF) DIMENSION T(7),CL2(II),CM2(ll),CL6(II),CM6(il),CL9(ll),CM9(ll)w &CLI2(ll),CM12(ll),CL15(10),CMIL(10),CL21(9),CM21(9),CL30(5), &CM30(5) REAL M DATA IS FROM NACA TN1546, PP.57-72, FIG. 7-9 DATA T = TC = THICKNESS RATIO DATA 'CLoNO.': 'CL'=LIFT COEFFICIENT, '.NO.'=THICKNESS RATIO*100 DATA 'CM.NO.': 'CM'=MOMENT COEFFICIENT ABOUT THE QUARTER CHORD, '.NO.'=THICKNESS RATIO*100 DATA T/0°02,0o06_0.09v0o12,0.15,0.21,0.30/ DATA CL2/-0.1,0o0r0.1o0.2,0o3w0o4r0oL,0.6,0o7,0.8,0og/ DATA CM2/-.0135_-.00825,-.01775,-.015,-o007,-.0055,0.01525, 002,0o0235,-.016,-.04925/ DATA CL6/-0°1,0o0,0o1_0.2,0.3,0o4,0.5,0.6,0.7,0°8,0o9/ DATA CM6/-.0135,-.01575,-.011,-.00375,-.0025,-o007r-o00075 e 0012,0o011,-.0055,0.02525/ DATA CLg/-0.1,0.0,0.1,0.2,0o3t0o4,0oL,0o6,0°7,0.8,0og/ DATA CM9/-.0135,-.005,-o001,0.003,0.005,0.00925,0.0035,0.00975, 0006,0o0085f0.057/ DATA CLI2/-0ol,0o0,0ol,0.2,0.3,0°4,0.5,0o6,0.7,0o8r0.9/ DATA CM12/0.003,0.00925,0.009,0.009,0°017,0.046,0.0315,0.0275, 00185,0°0365,0°063/ DATA CL15/0.0,0°I,0.2_0o3,0.4,0.5,0.6,0.7,0.8,0.9/ DATA CM15/0o001f0.004,0.0105,0.039,0.09,0.097,0.061,0.061, 007,0o053/ DATA CL21/-0.1_0o0,0ol_0.2_0.3,0o4,0oLv0o6,0.7/ DATA CM21/0.005w0.01125u0o015,0.019,0.094w0.064,0.123_0o204f 0109/ DATA CL30/-0oI,0.0,0ol,0_2,0°3/ DATA CM30/-o022f0.013,0.0305,0o0565w0.167/ CM030=CMTHKF(M,TC,CLF,T,7wCL2wCL6,CL9,CL12,CL15,CL21,CL30_CM2, &CM6_CMg,CMI2_CM15,CM21,CM30olI,11,11_IlfI0,9_5) RETURN END FUNCTION CM045(M,TC,CLF) DIMENSION T(7),CL2(I1)_CM2(I1),CL6(ll),CM6(II)_CL9(ll),CM9(ll), &CLI2(ll),CM12(ll),CL15(10)wCM15(10),CL21(9),CM21(9),CL30(5)_ &CM30(5) REAL M DATA T/0.02,0.06,0.09,0.12,0°15,0.21,0.30/ DATA CL2/-0ol,0.0,0ol_0o2w0.3r0.4,0o5F0o6_0o7,0.St0°9/ DATA CM2/-o0035,0.012,0o011,-.005,-o006,-.01,-o008,0.0085,0.019, &-°05,-o03675/ DATA CL6/-0.1,0.0F0.1v0o2,0.3,0.4_0.5,0.6,0o7,0.8,0o9/ DATA CM6/-o01175,-o003,0.003,0.0275,0.0,0.002,0.00625_0.0045, 0012,-.0225,0.013/ DATA CL9/-0oI,0.0,0.I,0.2,0.3,0o4_0o5,0o6,0.7,0.8,0.9/ DATA CM9/-°01475,-o012,0°0,0.00625,0.012w0.024,0.02475,0.02, 00175,0.01225,0.038/ DATA CL12/-0.I,0.0,0.1,0.2,0.3,0o4,0.5,0.6,0.7,0o8,0o9/ DATA CM12/-.011,0.012,-.002,0.005,0.028,0.074,0.097,0o053_0o047, 0054,0.032/ DATA CL15/0.0,0.I,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9/ DATA CM15/0.011,0.006,0.013,0.062,0.112,0.107,0.084,0o0845_ 0084,0.0785/ DATA CL21/-0.1,0o0,0.1,0.2,0.3,0.4,0.5v0.6,0.7/ DATA CM21/O.0005,0.0075,0.02,0.08225,0o135,0o085,0o236w0.191,

0158/

DATA CL30/-0oi,0.0,0.I,0.2,0o3/ DATA CM30/-.01425,0.00925,0.0405,0.179,0.216/ CM045=CMTHKF(M,TCrCLF,T,7wCL2,CL6,CL9,CL12,CL15,CL21FCL30_CM2_ &CM6,CMg,CM12wCM15,CM21,CM30gll,ll,llwll,10,9,5) RETURN END FUNCTION CMO60(M_TC,CLF) DIMENSION T(7),CL2(ll),CM2(ll),CL6(10),CM6(10),CL9(ll)oCM9(ll)_ &CL12(10),CM12(10)NCLlS(ll),CM15(ll)_CL21(10),CM21(10),CL30(4), &CM30(4) REAL M DATA T/0o02,0o06w0.09,0o12r0.15_0o21,0o30/ DATA CL2/-0oi,0.0,0ol,0.2,0.3,0o4,0o5,0°6,0.7,0°8,0o9/ DATA CM2/0o034,0o063o0o004,0.023_0.01,0.004,-°023,-.017, 000875,-.0415,-o049/ DATA CL6/-0ol,0.0,0olr0.2,0.3,0o4,0.5,0.6,0°7,0.8/ DATA CM6/0o002,-oQO2w0.002,0.004,0.008,0.009,0.01w0.01225,0o014_ 0014/ DATA cLg/-0.1w0.0,0.1v0o2,0o3,0.4,0.5,0.6,0.7,O°8,0.9/ DATA CMg/-.01375w0.004_0.003,0.006,0.015_0o03075t0.046,0.046, 0035w0.053,0.0395/ DATA CL12/-0.1w0o0g0ol,0°2_0.3w0o4_0.5w0.6,0°7,0.8/ DATA CM12/0o001,0.0305,0.02,0.01475w0.O405,0.088,0.108,0o1005u 0082_0ol/ DATA CL15/-0.1,0.0,0.1,0.2e0o3,0o4,0.5,0.6,0.7_0.8,0.9/ DATA CM15/0o032,0.031,0o0187,0o013,0o0525,0.13625,0o16875, 01275,0o11625,0o1225,0o0985/ DATA CL21/-0.1;OoOwOol,O.2,0o3,0o4,0o5,0.6,0o7,0.8/ DATA CM21/-.013,-.009,0.0725,0.102,0.06275,0.0975,0.284,0.273, 0239,0o196/ DATA CL30/-0.1,0o0,0.1,0o2/ DATA CM30/-o033,-°028,0o142,0.213/ CM060=CMTHKF(M,TCFCLF_T,7,CL2,CL6_CLg,CL12eCL15,CL21,CL30,CM2, &CM6,CMg,CM12,CM15,CM21,CM30,11,10,11,10,11,10r4) RETURN END FUNCTION CM070(M,TC,CLF) DIMENSION T(5),CL2(10)qCM2(10),CL6(10),CM6(10),cLg(10),CMg(10), &CL12(9)wCM12(9),CL15(8),CMI5(8) DIMENSION CL21(1),CL30(1),CM21(1),CM30(1) REAL M DATA T/0.02,0.06,0.09_0°12,0.15/ DATA CL2/-0.1,0.090ol_0o2_0.3,0o4,0o5,0.6,0o7_OoS/ DATA CM2/0.0145,-.022,-o008,0.025,0.038,0.024,0.024,0.004, 0002,-°026/ DATA CL6/-0.I,0°0,0o1_0.2,0o3,0o4,0o5,0o6,0.7,0o8/ DATA CM6/-.015,-.008,-°00225,0°0125_0o022,0.024,0.0255,0.0255, 0023,0.019/ DATA CLg/-0.1,0.0,0.1v0.2,0.3f0o4,0o5v0o6,0o7,0o8/ DATA CM9/-o02,0.004,0.002,0.009,0.012,0.023v0.059,0°0165, 003375,0°0485/ DATA CL12/-0oi,0.0,0ol,0o2,0.3,0o4,0.5,0.6,0o7/ DATA CMI2/0o009,0.026,0.031N0o031,0.021F0o0465,0.031,0.046,0.073/ DATA CL15/0.0,0.1,0.2,0.3,0.4,0.5,0.6,0o7/ DATA CM15/0o083,0.02375,0.0185,0.037,0o108,0.002,-.011,-.0275/ CM070=CMTNKF(MwTC,CLF,T_5,CL2_CL6,CLg,CL12,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CM15,CM21,CM30,10,10,10,9,8,0,0) RETURN END FUNCTION CM075(M,TC,CLF) DIMENSION T(3),CL2(8),CM2(8),CL6(9),CM6(9),CL9(8),CM9(8) DIMENSION CL12(1),CL15(1),CL21(1),CL30(1),CMI2(1),CM15(1), &CM21(1),CM30(1) REAL M DATA T/0.02,0.06,0.09/ DATA CL2/-0.I,0.0,0.1,0.2_0.3,0.4,0.5,0.6/ DATA CM2/0.008,0.1675e0.0425,-.01,0.0125,0o02,0.7,0.69/ DATA CL6/-0.1,0o0,0ol,0.2,0.3,0.4,0.5v0o6,0o7/ DATA CM6/-.01125,-.0015,0.00375,0.014,0.027,0.0305,0.007,0.012 F 0014/ DATA CL9/-0.1,0.0,0.1,0o2,0.3,0o4_0.5,0.6/ DATA CM9/-.021,0.0185r0.0495,0.0565,0.056,0.0615,0.052,0o052/ CM075=CMTHKF(M,TC,CLF,T,3,CL2,CL6,CLg,CLI2,CL15,CL21,CL30,CM2, &CM6,CM9,CMI2,CM15,CM21,CM30,8,9,8,0,0,0,0) RETURN END FUNCTION CMIFF(M,TC,CLF) DIMENSION A(5),X(3),Y(3) REAL M DATA A/0o3,0°45,0o6,0o7g0o75/ N=2 IS=I IL=IS+N-I IF(MoLEoA(IL)) GO TO 2 IL=2 IS=IL-N+I IF(MoGE.A(IS)) GO TO 2 IS=l IL=IS+N-I 3 IF((M-A(IS))W(M-A(IL))oLEo0o0) GO TO 2 IS=IL IL=IS+N-I GO TO 3 2 DO 4 I=IS,IL J=I-IS+I X(J)=A(I) GO TO (30,45,60,70u75)_I 30 Y(J)=CM130(M_TC,CLF) GO TO 4 45 Y(J)=CM145(M,TC,CLF) GO TO 4 60 Y(J)=CM160(M,TC,CLF) GO TO 4 70 Y(J)=CM170(M,TC;CLF) GO TO 4 75 Y(J)=CM175(M,TC,CLF) 4 CONTINUE CMIFF=YLAGN(X,Y,N,M) RETURN END FUNCTION CMI30(M,TC,CLF) DIMENSION T(7)gCL2(10),CM2(10),CL6(13),CM6(13),CL9(13),CM9(13)_ &CL12(10)wCM12(10)gCL15(15),CM15(15)FCL21(5),CM21(5)sCL30(ll)_ &CM30(I1) REAL M DATA T/.02,.06,.09,.12,.15,.21,.30/ DATA CL2/-0ol,0o0g0ol_0o2,0o3,0o4,0.5,0.6,0°7,0o8/ DATA CM2/-o03,-.034_-.0406,-.037w-o032v-o0275,-.02_-o0075 , &-°005,-.025/ DATA CL6/-0.1,0.0,0.1,0.2,0.3,0.4,0.5,0o55,0.6,0.65,0.7,0o75, O8/ DATA CM6/-.03w-o0275_-.025,-.0Z25,-o02_-°02,-_0175,-.015t-o0075w &-o005,-.005,-.008,-o0125/ DATA CL9/-0.1,0.0w0ol_0.2,0o3_0°4,0o5,0.6v0.7,0.725,0.75o 0775,0.8/ DATA CM9/-.03,-.0225,-.0175,-Oo015,-.0125,-o0i,-o01,-.0075,-o005, &-.005,-.001,0.0,0.0/ DATA CL12/-0.1,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8/ DATA CM12/-.023,-.0175,-.0144,-.0112,-.005,0o0115,0.012, 0012,0o01,0.021/ DATA CL15/-0.i,0.0,0.1,0.2,0.225,0o25,0.275,0.3,0o35,0.4,0.425, 05,0.6,0.7_0.8/ DATA CM15/-.0175,-.0125,-.01,-.0075,-o005,-.0025,0.0,0.0075, 00225,0.04,0.0475,0.0475,0.0475,0.045,0.045/ DATA CL21/-0.I,0o0,0.1,0o2,0.3/ DATA CM21/-.0175,-.0025,0.003,0.0085,0.056/ DATA CL30/-0.1,-0.05,0.0,0.1,0.15,0.2,0o225,0.25,0.2625,0.275,0o3/ DATA CM30/-.0175,0.0,0.0125,0.0275,0.035,0o05,0.0625r0.0875, 01175,0.1325,0.14/ CM130=CMTHKF(M,TC,CLF,T,7,CL2,CL6,CL9,CL12,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CMI5,CM21wCM30,10,13,13,10,15,5,11) RETURN END FUNCTION CM145(MwTC,CLF) DIMENSION T(7),CL2(10),CM2(10),CL6(15),CM6(15),CLg(10),CMg(10), &CLI2(10),CM12(10)vCLIS(16),CMI5(16),CL21(5),CM21(5),CL30(10), &CM30(10) REAL M DATA T/.02,.06,.09,o12,.15,.21,.30/ DATA CL2/-0.1,0o0w0.1,0o2,0.3_0o4,0.5,0.6,0.7w0.8/ DATA CMZ/-o0275,-o0175,-o0225,-.036,-.035,-.0325,-.03v-.0225, &-°00625,-o05/ DATA CL6/-0.I,-0.05,0o0,0ol,0.2,0.3,0o4,0.5,0.6,0.625,0.675,0.7, 0725,0.75,0.8/ DATA CM6/-.033,-o0285,-.025,-.0225,-.O21w-.02F-.0175,-°015,-.013, &-°01,-.006,-.005_-o0075,-.01,-o025/ DATA CL9/-0ol,0o0,0ol,0.2,0.3,0o4,0o5,0°6,0o7,0.8/ DATA CM9/_o035,-o03_-.0225,-o015,-.01,-o0025,0.0_0o001,0.001,0o0/ DATA CL12/-0ol,0o0,0.1,0o2,0.3,0.4F0o5,0.6,0.7,0.8/ DATA CM12/-o035,-o025,-.02375,-o0165,0.00125,0.029,0.04675, 00295,0.0265,0.0295/ DATA CL15/-0ol,0.0,0.1,0o2,0.225,0o25,0o275,0.3,0°325,0.35,0.4, 045,0o5,0o6,0o7,0o8/ DATA CM15/-.0225,-o02,-o0125,-o005,-o005,0.0,0.005,0.0175,0.0325, 004,0.0525,0o0575,0o06,0.0625,0.0625,0.0625/ DATA CL21/-0ol,0o0,0.1,0o2,0o3/ DATA CM21/-.0145,-.005,0.007,0.0475,0.08125/ DATA CL30/-0.1,0o0,0ol,0.15,0.1625,0.175,0.18,0.185,0.2,0o3/ DATA CM30/-o01,0°0125,0.0375,0o0625,0o0675,0.085,0.1,0.14, 01525,0.1825/ CM145=CMTHKF(M,TC,CLF,T,7,CL2,CL6,CL9,CL12,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CMI5,CM21,CM30vl0,15,10,10,16,5,10) RETURN END FUNCTION CMI60(MoTC,CLF) DIMENSION T(7)vCL2(10),CM2(10),CL6(10),CM6(10),CL9(10),CMg(10), &CL12(10),CM12(10),CL15(lS),CM15(15)wCL21(4),CM21(4),CL30(14), &CM30(14) REAL M DATA T/0.02,0o06,0.09,0_12,0.15,0o21,0o30/ DATA CL2/-0ol,0o0v0ol,0o2,0o3,0.4,0o5,0o6,0o7,0oS/ DATA CM2/-o005,-o007,-o025,-.025,-°025,-.0285,-.04,-.035, &-.0235,-.0535/ DATA CL6/-O.I,O.O,0.1,O.2,0o3,0.4,0o5,0o6,Oo7wO.8/ DATA CM6/-.03,-0.275,-.025,-.0225,-°02,-.0175,-o015,-.01r &-o0075,-o005/ DATA cLg/-0°l,0.0,0.1,0.2,0°3,0o4,0.5,0o6F0o65,0.7/ DATA CM9/-.039,-.03,-.025,-o02_-.0125,-o0025,0.009,0.015, 0015,0o0125/ DATA CL12/-0.1,0o0,0ol,0.2,0.3,0o4,0.5,0.6,0.7,0o8/ DATA CM12/-o035,-°025,-.02375,-o0165,0.00125,0o029,0.04675, 0055,0o05275,0.068/ DATA CL15/-0.I,0.0,0.I,0.2,0.25,0.27,0.3,0o335,0o365,0o4,0.45, 05,0.6,0.7,0.8/ DATA CM15/-.029,-.02,-.015,-.0075,-.0025,0o0,0o015,0.0375,0o05, 00625,0.0725,0.08,0.09,0.0925,0.0925/ DATA CL21/-0.1,0.0,0.1,0.2/ DATA CM21/-°023,-.01575,-.0335,-.058/ DATA CL30/-0.1,0.0,0.03,0.03,0.04,0.05,0.07,0o08,0o09,0ol, 0115,0.125,0.15,0.2/ DATA CM30/-.015,-.01,-.009,0.04,0.0575,0o0675,0.075,0.08,0.I, 013,0.1625,0.1725,0.1825,0.19/ CMI60=CMTMKF(M,TC,CLF,T,7,CL2,CL6,CL9,CLI2,CLI5,CL21,CL30,CM2, &CM6,CM9,CMI2,CMI5,CM21,CM30,10,10,10,10,15,4,14) RETURN END FUNCTION CMI70(M,TC,CLF) DIMENSION T(5),CL2(7),CM2(7),CL6(9),CM6(9),CLg(ll)_CM9(ll), &CLI2(6),CMI2(6),CLIL(10),CMI5(10) DIMENSION CL21(1),CL30(1),CM21(1),CM30(1) REAL M DATA T/0.02_0.06,0.09,0o12,0.15/ DATA CL2/-0ol,0.0,0.1F0o2,0.3,0o4,0o5/ DATA CM2/-.016,-°037,-o0325,-o02625,-.01875,-.01875,-.01875/ DATA CL6/-0ol,0.0,0.I,0.2,0o3,0.4,0.5,0o6,0.7/ DATA CM6/-°04,-o035,-.031,-.024,-.018,-.016,-.012,-.012,-.012/ DATA CLg/-0.1w-0o05,0o0,0ol,0.2,0o3_0o36,0.4,0.44,0.472,0.5/ DATA CMg/-.048,-o04,-o034,-.028,-.02v-.016,-.014,-.01,-o006,

00,0.008/

DATA CL12/-0.i,0o0,0.1,0_2,0.3,0.4/ DATA CM12/-.039,-.028,-o02075_-o0125,-.0085_0.0055/ DATA CL15/-0.i,0o0,0.1,0o2,0.26,0.3,0o325,0.35,0.375,0.4/ DATA CM15/-.03,-.02,-.012,-.002,0.0,0.008,0.012,0.018,0°03,

oo461

CM170=CMTHKF(M,TC,CLF,T,5,CL2,CL6wCL9,CL12,CL15,CL21,CL30,CM2w &CM6wCM9,CMI2,CM!5,CM21,CM30N7,9,11,6,10,0,0) RETURN END FUNCTION CMI75(M,TC,CLF) DIMENSION T(3),CL2(6),CM2(6),CL6(7),CM6(7),CL9(9),CM9(9) DIMENSION CL12(1),CL15(1)wCL21(1),CL30(1),CM12(1),CM15(1) v &CM21(1),CM30(1) REAL M DATA T/0.02,0.06,0.09/ DATA CL2/-0.I,0o0_0.I,0o2,0o3,0o4/ DATA CM2/-o0373,-o0383,-o0373,-o0289,-.0175,-o0061/ DATA CL6/-0o2,-0.I,0o0,0oi,0o2,0o3,0o4/ DATA CM6/-o05,-.044w-o037,-.032,-.026,-o02,-.014/ DATA CL9/-0.I,0.0,0.05,0oI,0o2_0.3,0.4,0o5,0o6/ DATA CM9/-°049,-.036,-.032,-o028,-o024,-o022,-°02,-o02,-.021/ CMI75=CMTHKF(M,TC,CLF,T,3,CL2,CL6fCL9,CLI2,CLI5,CL21,CL30,CM2, &CM6,CM9,CMI2,CMI5,CM21,CM30,6,7,9,0,0,0,0) RETURN END FUNCTION CM3FF(M,TC_CLF) DIMENSION A(5)gX(3),Y(3) REAL M DATA A/0.3,0.45,0.6,0.7,0o75/ N=2 IS=I IL=IS+N-I IF(MoLE.A(IL)) GO TO 2 1L=2 IS=IL-N+I IF(M.GEoA(IS)) GO TO 2 iS=l IL=IS+N-I 3 IF<(M-A(IS))*(MQA(IL)).LE.0.0 GO TO 2 IS=IL IL=IS+N-I GO TO 3 2 DO 4 I=IS,IL J=I-IS+l X(J)=A(I) GO TO (30,45,60,70,75),I 30 Y(J)=CM330(M,TC,CLF) GO TO ¢ 45 Y(J)=CM345(M,TC,CLF) GO TO 4 60 Y(J)=CM360(M,TC,CLF) GO TO 4 70 Y(J)=CM370(M,TC,CLF) GO TO 4 75 Y(J)=CM375(M,TC,CLF) 4 CONTINUE CM3FF=YLAGN(X,Y,N,M) RETURN END FUNCTION CM330(M,TC,CLF) DIMENSION T(6),CL2(ll),CM2(ll),CL6(15),CM6(15),CL9(13 ,CM9(13), &CL12(15),CMI2(15),CL15(19)wCMIS(19),CL21(16),CM21(16) DIMENSION CL30(1),CM30(1) REAL M DATA T/0.02,0.06,0.09,0olZ,0o15,0.21/ DATA CL2/-0ol,0.0,0.1,0o2F0o3_0o4r0.5r0o6,0o7,0.8,0og/ DATA CM2/-.0625,-.08065,-.082,-.0785,-.07675,-.07125,-o0785, &-.05875,-.05875,-.0445,-.0625/ DATA CL6/-0°1,0.0,0.1,0o2,0o3,0.4,0°45,0o5,0o55,0.6,0°65,0o7, 075,0o8,0.9/ DATA CM6/-.0625,-°06,-.06,-o06_-_0575,-o055,-.0575,-°0575,-o0525w &-.05,-°045,-o04,-o035,~.0325,-o03/ DATA CL9/-0.1,0o0,0ol,0.2,0°3,0.4,0.5,0.55,0.6,0.65_0.7,0o8,0o9/ DATA CM9/-.0625,-.0575,-°055,-.0525,-.05,-o05,-o0425,-.0425, &-.0425,-.04,-°03,-.0225,-.0125/ DATA CL12/-0ol,0.0,0o1_0.2_0.3,0.4,0.425_0.45,0.5o0o55,0o6,0.7, 075,0°8,0.9/ DATA CM12/-.075,-o0675,-o06,-o0525,-.05,-.0475,-.0475,-.045, &-.0325_-.0275,-o025,-.0175,-o015v-.01,0°0/ DATA CL15/0°0,0.05,0.1w0o2,0o3,0.4,0.45,0.5,0_517,0o533,0o55, 0567,0.583,0.6e0o7,0.75,0o8,0o85,0o9/ DATA CM15/-o05r-o05,-.0475e-_045,-.0425,-o035,-.0325,-.025_ &-o02,-°01,0o005,0.0075,0.01,0.01w0o0075,0o005,0.005,0o01,0.0125/ DATA CL21/-0.i,-0.075,0o0,0ol,0.2,0.3,0o4_0.433,0.467,0o483, 05,0o508,0.517,0o533,0o6,0o7/ DATA CM21/-o0625,-.035,-o03_-°0Z25,-.015,-.01,0.0,0.0,0.0,0.0!5, 0025,0o0575,0o07_0o0725,0o065,0.0525/ CM330=CMTHKF(M,TC,CLFwTf6,CL2,CL6_CL9_CL12,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CM15,CM21,CM30,11pl5_13,15,19,16,0) RETURN END FUNCTION CM345(M,TC,CLF) DIMENSION T(6),CL2(ll),CM2(ll),CL6(12),CM6(12),CLg(15),CMg(15), &CLI2(18),CM12(18),CL15(20),CMI5(20),CL21(15),CM21(15) DIMENSION CL30(1),CM30(1) REAL M DATA T/0.02,0o06,0.09,0.12,0.15,0.21/ DATA CL2/-Ool,O.O,Ool_O°2vO.3,0o4,0.5,0.6,0o7,0o8,0.9/ DATA CM2/-°075,-.07,-.077,-.08625,-.08125,-.0755f-.0735,-.069, &-o05925,-o05625,-.07/ DATA CL6/-0ol_0°0,0ol,0.2w0.3,0o4,0o5,0.6r0.7,0_8,0.85,0°9/ DATA CM6/-o075,-.07,-o07,-.0675,-.065,-°0625,-.06w-o0525,-.045, &-o04,-.036,-o04/ DATA CLg/-0.1,0.0r0o05,0.1,0.2,0.25,0o3rO.4,0.475,0o5,0.6,0.7, 08,0°85,0°9/ DATA CM9/-.075,-o07,-.07,-.0675,-.06,-.055,-.056,-.055,-o0525_ ...... • ....... : • i•_ i •if: ¸• • ....................

&-.05,-.04,-.034,-.0275,-.025,-.02/ DATA CL12/-0.I,0.0,0.I,0.2,0.25,0.3,0.4,0.433,0._67,0.5,0o525, 055,0.575,0.6,0.7,0.8,0.883,0.9/ DATA CM12/-.0825,-.08,-.0675,-.06,-.055,-o0525,-.05,-.0525, &-.0475,-.04,-.034,-.0275,-.024,-.02,-.015,-.0125,-.01,-°0075/ DATA CL15/0.0,0.05,0.1r0.125,0.15,0o2,0.3,0o4,0.45fO.475w0.5, 0525,0.55,0.567,0.583,0.6,0.7,0.783,0.8,0.9/ DATA CM15/-.0775,-.065,-o055,-.05,-.0475,-.045,-.0425,-o0375, &-.0325,-.03,-.0225,-.01,-.005,0.015,0.0175_0o0175,0.0175,0.02, 0022,0.0275/ DATA CL21/-0.I,0.0,0.I_0.2,0.3,0.38,0.4,0.425,0.45,0o475,0o5, 0525,0.55,0.6,0.7/ DATA CM21/-.0425,-.03,-.0225,-.0125f-o0025o0.005;0o01,0o025,0o05, 0065,0.075,0.08,0o0825,0.0825,0.0825/ CM345=CMTHKF(M,TC,CLF,T,6,CL2,CL6,CL9,CLI2,CLI5,CL21,CL30,CM2, &CM6,CM9,CMI2,CMI5,CM21,CM30,11,12,15,18,20,15,0) RETURN END FUNCTION CM360(MeTC,CLF) DIMENSION T(6),CL2(12),CM2(12),CL6(15),CM6(15),CLg(13),CM9(13), &CL12(17),CMI2(17),CLIS(22),CMI5(22),CL21(17),CM21(17) DIMENSION CL30(1),CM30(1) REAL M DATA T/0.02,0.06,0.09,0.12,0.15,0.21/ DATA CL2/-0.1,0.0,0.1,0.2,0.3,0.4,0.5,0o6,0.7,0.8f0.grl.0/ DATA CM2/-o082,-.077,-.0786q-.095,-.095,-.0875,-.0775,-.07375, &-.0775,-°081,-.07,-o122/ DATA CL6/-0.1,0.0,0.I,0.2,0o3,0°4,0.5,0o6_0.7,0°8,0o9,0.94286, 097145,0o9857,1.0/ DATA CM6/-.082,-.08036,-.0786,-.0768,-.075,-.0714,-o06786, &-°0607,-.0536,-°0464,-.0375,-o0357,-.0393,-.04286,-.05/ DATA CL9/-0.1,0.0,0.i,0.2,0.3,0.4_0o5,0o55,0.6,0.7,0o8,0°9,1o0/ DATA CM9/-o0893,-.0875,-o0786,-o0714,-.06786_-°0643,-.0607, &-.O571,-o05,-.0339,-o0214,-.0143,-.0089/ DATA CL12/-0.i,0.0,0.1,0°2,0o25,0o3,0o4,0o475,0°5,0°55,0.6, 065,0o7,0.75,0.8w0o875,0.9/ DATA CM12/-.107,-.0982,-.0857,-.075,-.0714,-.06786_-.0643, &-.0589,-.0536,-o04286,-.0286,-.01786,-.007,-.0036,0-0,0.00536, OOO7/ DATA CL15/-0.1,0.0g0.1,0.157,0.1786w0.2,0.2286,0.3,0o4,0°45, 05,0o5286,0o557,0.5857F0.6,0o6143,0.65,0o7,0.75,0o8,0o9,1o0/ DATA CM15/-.15,-.l125,-o0786,-o0589,-o0536,-.05w-°0464,-.0464, &-o0446,-.04286,-.0357,-.02857,-.01786,0.0,0.0143,0.025,0.032, 00357,0o0357,0o0357,0.0339,0.0286/ DATA CL21/-0oi,0.0,0°I,0.2,0.3,0o4,0o4143,0o4357,0o457,0o4786, 05,0.55,0o6_0o6286,0°7,0o75,0o8/ DATA CM21/-.04286,-o0286_-.0232,-o0143,0o0w0.01786,0.0286, 006786,0.0857,0.09286,0.1,0o107,0ol125,0.1143,0.1125w0o1089w 01/ CM360=CMTHKF(M,TC,CLF,T,6,CL2wCL6fCL9wCL12,CL15wCLZ1,CL30,CM2, &CM6,CMg,CM12FCM15,CM21,CM30,12_I5,13,17,22,17_0) RETURN END FUNCTION CM370(M,TC,CLF) DIMENSION T(5),CL2(II),CM2(ll),CL6(14),CM6(14),CLg(13)wCMg(13), &CLI2(9),CM12(9),CL15(ll),CM15(ll) DIMENSION CL21(1)gCL30(1),CM21(1),CM30(1) REAL M DATA T/0o02,0o06,0.09,0.12v0o15/ DATA CL2/-0ol_0o0,0°l,0.2w0.3,0.4_0o5,0°6,0.7,0o8,0og/ DATA CM2/-.076,-°072,-.0875,-.098_-o095Q-.094,-.093,-o086,-o087, &-.097,-.0997/ DATA CL6/-0.2,-0.1,0.0,0.I,0.2,0.3,0.4,0.5,0.6,0.65,0.7,0.8, 085,0.9/ DATA CM6/-.08958,-.08958w-.0875_-o0875_-o0854,-.0854,-o0833_ &-o0833,-.08125,-.08125,-.0792,-.075,-.0729,-°0667/ DATA CLg/-0o2,-0ol,0o0,0.1,0.2w0o3F0°4,0o5,0o6_0.7w0.75v0.8w0.9/ DATA CM9/-.1083,-.i042,-.i,-o0875_-.0792,-.0771,-.075,-.075, &-.075,-.0667,-.06458,-.0583,-.0417/ DATA CL12/-0.I,0.0,0.I,0.2,0o3,0.4,0.5,0.6,0.7/ DATA CM12/-.1333,-.l1458,-.0958r-.08125,-°0667,-o0625,-.0583, &-.0521,-.0417/ DATA CL15/0.0,0.1,0.133,0.167,0.2,0.3,0.4,0.5,0.55,0.6,0.7/ DATA CM15/-.15,-.08125,-.0625,-.05,-.0458,-o0417,-.0417, &-.0458,-.0479,-.0479,-.05/ CM370=CMTHKF(M,TC,CLFwT,5,CL2,CL6,CLg,CLI2,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CMI5,CM21,CM30,11,14,13,9,11,0_0) RETURN END C C C FUNCTION CM375(M,TC,CLF) DIMENSION T(3),CL2(8),CM2(8),CL6(ll),CM6(ll),CLg(10),CM9(10) DIMENSION CLI2(1),CL15(1),CL21(1)eCL30(1),CM12(1),CM15(1), &CM21(1),CM30(1) REAL M DATA T/0.02,0.06,0.09/ DATA CL2/-0.I,0.0,0.1,0.2,0.3,0o4,0o5,0.6/ DATA CM2/-.129,-.1333,-°ll,-.l,-.1057,-o1062w-o09935,-o1002/ DATA CL6/-0.3,-0.2,-O.1,0.0,0ol,0.2,0o3,0o4,0o5,0o6v0o7/ DATA CM6/-.i083,-o1083,-.1083,-.i0625,-o1042,-.1,-oi,-.0979, &-o09375,-o0917,-o09375/ DATA cLg/-0.3,-0.2,-0.1,0.0,0.1,0.2,0.3w0.4,0°5_0.6/ DATA CM9/-.1083,-oi083,-.1042,-.i,-oi,-ol,-o0958,-°0917, &-o08958,-.0854/ CM375=CMTHKF(M,TC,CLF,T,3,CL2_CL6,CL9_CL12_CL15uCL21,CL30,CM2, &CM6,CMg,CM12,CM15,CM21,CM30,8,11,10,0_0wO,0) RETURN END FUNCTION CM5FF(M,TC,CLF) DIMENSION A(5),X(3),Y(3) REAL M DATA A/0o3_0o45,0o6,0.7_0.75/ N=2 IS=I IL=IS+N-I IF(MoLE.A(IL)) GO TO 2 IL=2 IS=IL-N+I IF(MoGEoA(IS)) GO TO 2 IS=I IL=IS+N-1 3 IF((M-A(IS))"(M-A(IL))oLEo0o0) GO TO 2 IS=IL IL=IS+N-I GO TO 3 2 DO 4 I=IS,IL J=l-IS+l X(J)=A(I) GO TO (30,45_60,70,75),I 30 Y(J)=CM530(M,TC,CLF) GO TO 4 45 Y(J)=CM545(M,TC,CLF) GO TO 4 60 Y(J)=CM560(M,TCwCLF) GO TO 4 70 Y(J)=CM570(MwTC,CLF) GO TO 4 75 Y(J)=CM575(M,TC,CLF) 4 CONTINUE CM5FF=YLAGN(XrY,N,M) RETURN END C C C FUNCTION CM530(M,TC,CLF) DIMENSION T(7)wCL2(II),CM2(ll),CL6(16),CM6(16),CLg(14),CMg(14), ..... i iiiiiii ............. : ...............................................

/

&CLI2(18),CM12(18),CL15(15),CM15(15),CL21(14),CM21(14),CL30(ll), &CM30(I1) REAL M DATA T/0.02,0.06,0.09,0.12,0.15,0.21,0o30/ DATA CL2/0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0/ DATA CM2/-.i06,-.i0625,-.i135,-.i135,-.i135,-.1135,-.136, &-.1495,-.09,-.0715,-.061/ DATA CL6/0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.625,0.65,0o675v0oT,0o725, 075,0.8,0.9,1.0/ DATA CM6/-.10625,-.10625,-.i042,-°i042,-.10625,-oi0625,-.10625, &-.i0625,-.1021,-.i,-.0917,-.0833,-.0771,-o075,-.0667,-.0625/ DATA CLg/0.0,0.1,0.Z,0.3_0.4,0.5,0.6,0o625,0.675,0o7,0o725,0.8, 09,1.0/ DATA CMg/-.1083,-.10625,-.1021,-.l,-.l,-.l,B.09375,-.0917, &-.0792,-o0708,-.0667,-.0625,-.0583,-o0542/ DATA CL12/0.0,O.l,0.2,0o3,0.35,0.4,0.5,0.575,0.6v0.625,0.65, 0675,0.7,0.75,0.8,0.9,0.95,1.0/ DATA CM12/-.1125,-.i083,-.1042,-.0979,-.09375,-o0917,-o0917, &-.0896,-.0875,-.0854,-o0833,-o075,-.0708,-o05,-o0458,-o0417, &-.0375,-.03125/ DATA CL15/0.0,0.I,0.2,0.3,0.4,0.5,0°55,0o6,0.65,0.7,0.75,0.8, 085,0o9,1.0/ DATA CM15/-.I167,-.I021,-.0896,-.0833,-o0792,-.0729,-o0667, &-.0604,-.0542,-.0396,-.0292,-o0208,-.0167,-.0146t-.0146/ DATA CL21/0.0,0.I,0.2,0.3,0.4,0.5,0.55,0.6,0.65,0o683,0o7, 0717,0.75,0.8/ DATA CM21/-o0575,-.055,-.05,-.0475,-.0425w-o04,-.035,-o0275, &-.0125,0.0075,0.015,0.0225,0.0275,0o03/ DATA CL30/-0.1,-0.05,0.0,0.I,0.2,0.3,0.35,0.4,0.45,0.475,0.5/ DATA CM30/0.0,0.00625,0.0104,0.0167,0.025,0.0333,0o0375,0.0417, 00521,0.0583,0.0667/ CM530=CMTHKF(M,TC,CLF,T,7,CL2,CL6,CL9,CL12,CL15,CL21,CL30,CM2, &CM6,CM9,CM12,CM15,CM21,CM30,11,16,14,18,15,14,11) RETURN END FUNCTION CM545(MrTCeCLF) DIMENSION T(7),CL2(ll),CM2(ll),CL6(15),CM6(15),CLg(14),CMg(14), &CLI2(14),CMI2(14),CLI5(17),CM15(17)wCL21(13),CM21(13),CL30(9), &CM30(9) REAL M DATA T/0°02,0.06,0.09,0.12,0.15,0.21,0o30/ DATA CL2/0.0,0.1,0.2,0.3,0.4,0o5_0.6,0o7,0o8,0o9,1.0/ DATA CM2/-.1167,-.i146,-.1125,-.116,-.124,-o117,-o13,-.128, &-.i04,-.092,-.084/ DATA CL6/0.0,0.1,0.2w0o3,0.4,0.5,0o6,0o6333,0.675,0.7,0.75, 0775_0o8,0.9,1.0/ DATA CM6/-.l167,-.l146,-.l146,-ol125_-°l125_-.l125,-.l125w &-.1104,-oi083,-.1,-.0896,-o0833,-.0792,-.075,-o0667/ DATA CL9/0.0,0.1,0.2,0.3,0o4,0o5,0o6,0o625_0.675_0.7,0o75, 08,0.9F1.0/ DATA CMg/-.l167,-ol146,-ol146_-o1083,-o10625,-o1042r-ol,-ol, &-.0875,-.08125,-.0667,-o0604,-.0583w-.0521/ DATA CL12/0.0,0.1,0o2,0.3,0.4w0°5,0o55,0.6,0.65o0.7,0.75,0o8 ,

085,0o9/

DATA CM12/-ol167,-°l125,-o1083_-o10Zl_-.lw-.0958_-o0917,-.0875, &-o0792,-.06875w-.0542,-o0417,-o0333,-°0333/ DATA CL15/0.0,0.1,Oo2v0o25,0o3,0.4,0o5v0o6,0.625,0o65r0.675, 07,0o725,0o8_0o900o95,1o0/ DATA CM15/-o125w-ol146,-.l_-.0917,-o0854,-o08125,-o075,-.06875, &-.0667w-o0583,-o05,-o0333_-.025,-.0167,-o00625_0.0,0o0/ DATA CL21/0olt0.133,0o2,0o3w0o4,0.5,0o55,0.6,0.625_0.65,0.675 , 07,0°8/ DATA CM21/-.06,-o05f-.0475,-o0425_-.04,-.0325,-o0225,-.01,0.0, 001,0.025,0.0325_0o0375/ DATA CL30/-0.1,-0.075,-0.05,0.0,0.1,0.2,0o3F0.35_0o4/ DATA CM30/0.0083,0o0146,0.01875,0.025,0.0271,0.0458,0.05083, 005125g0o075/ CM545=CMTHKF(M,TC,CLF,T,7,CL2,CL6,CL9,CL12,CL15,CL21,CL30,CM2, &CM6,CMg,CM12,CMIS,CM21,CM30,11,15,14,14,17,13,9) RETURN END FUNCTION CM560(M,TC,CLF) DIMENSION T(7),CL2(10),CM2(10),CL6(14 ,CM6(14),CLg(18),CMg(18), &CL12(17),CMI2(17),CLI5(19),CM15(19),CL21(13),CMZl(13),CL30(ll), &CM30(ll) REAL M DATA T/0.02,0.06,0.09,0.12,0.15,0.21,0.30/ DATA CL2/0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0o9/ DATA CM2/-.1065,-.126,-.I16,-.129,-.132,-.13,-o114,-.1245, &-o1765,-.084/ DATA CL6/-0.1,-0.05,0.0,0.i,0.2,0.3,0.4_0.5,0.6,0o7,0.75,0o8, 0825,0.85/ DATA CM6/-.1229,-.1271,-.1292,-.13125,-o13125,-.1292,-.1292, &-.1271,-.125,-.1229,-.i167,-.i083,-°i021,-.0958/ DATA CL9/0.0,0ol,0o2,0.3,0.4,0.5,0.6,0.65,0.675,0o7,0.725,0.75, 0775,0.8,0.825,0°85,0.875,0.9/ DATA CMg/-.1375,-.1333,-.13125,-.1292,-.1229w-.1208,-o1229, &-o1229,-o1208,-.I167,-.10625,-.0917,-o0792,-.0708,-o0625, &-o05625,-.0521,-.05/ DATA CL12/0.0,0.I,0.2,0.275,0.3,0.35,0.4,0o433,0.5,0o55,0.6, 0675,0o7,0.75,0.775,0.8,0.85/ DATA CM12/-o1375,-.1333,-.125,-.1208,-o1167,-.i125,-oli04, &-o1083,-.i0625,-.i0417,-.1021,-.i,-.0979,-.0833,-.0708,-.0583, &-o0417/ DATA CL15/0.0,0°I,0.2,0.225,0.25,0.3,0.325,0.4,0.5,0.6,0o65, 0675,0o7,0.725r0o75,0.775,0.8,0.85,0.9/ DATA CM15/-o15_-o1375,-.125,-.1208,-.1125,-°0917,-.0875,-o0833, &-.0792,-.075,-.0708,-.06875,-.06458,-o0542,-.0417,-.025, &-°01875,-.0125,-o0083/ DATA CL21/0oI,0o2,0o3,0.4,0o45,0.5,0.55,0o6,0.625,0.65,0.7,0°8,

O9/

DATA CM21/-.0542,-.05,-.0417,-.0354,-.0333,-.025,-.01458, 00042,0o01458,0.0208,0.0271,0.0354,0.0417/ DATA CL30/-0.3,-0.2,-0.1,0_0,0.05,0_lv0.125,0.2,0.25,0.3,0°4/ DATA CM30/0o0333,0.04375,0.0542,0.0625,0°06875,0.0833,0.0875, 01,0.1,0.1,0.1021/ CM560=CMTHKF(M,TC,CLF,T,7,CL2,CL6,CL9FCLI2,CLI5,CL21,CL30,CM2, &CM6,CM9,CMI2,CMI5,CM21,CM30,10,1¢,I8,17,19,13,11> RETURN END FUNCTION CM570(M,TC,CLF) DIMENSION T(6),CL2(9),CM2(9),CL6(7),CM6(7),CL9(9),CM9(9),CL12(9), &CM12(9)wCL15(14),CM15(14),CL21(ll),CM21(ll) DIMENSION CL30(1)wCM30(1) REAL M DATA T/0.02,0o06,0o09,0o12,0.15,0.21/ DATA CL2/0o0,0.1,0.2,0o3,0o4,0o5,0o6,0.7,0.8/ DATA CM2/-o2175,-o2,-.101,-ollg-o1415w-o14,-.145,-.146,-o144/ DATA CL6/0o2,0o3,0o4,0o5,0o6,0o7,0o8/ DATA CM6/-.1479,-.1458,-o1458,-o1458,-.1417,-.1417,-.1375/ DATA CL9/0.0,0ol,0o2,0.3,0.4,0.5,0_6,0o7,0.8/ DATA CM9/-.1583,-o1542,-o1521,-o1458,-o14375,-o1417,-.1354, &-o1333,-.1292/ DATA CLlZ/0o0,0olv0.2,0o3,0.4,0.5,0.6,0o7,0.8/ DATA CM12/-o1542,-o145,-o14,-o1275_-o1175,-o1175,-oi175, &-ol175,-ol15/ DATA CL15/0o0,0°i,0.15,0o175,0.2,0o225_0o25,0.275,0.2917,0o3, 04,0o5,0°6,0o7/ DATA CM15/-o17,-.16,-o155,-o1525,-o15,-.145w-.13,-.ll,-°l,-.09, &-o085_-.0775,-.0725,-o065/ DATA CL21/-0o2,-0ol,0.0,0.025,0.05,0.075,0ol,0.125,0.175,0.2r0.3/ DATA CM21/-.04,-.0325,-°025_-.02,-o0175,-.01,0.0,0.01,0.0225, 0025,0.0375/ CM570=CMTHKF(M,TC,CLF,T,6,CL2,CL6,CLg,CL12,CL15,CL21,CL30,CM2, &CM6,CM9,CM12,CM15,CM21,CM30,9,7,9,9,14,11,0) RETURN END : :i::: ..... H .............

C FUNCTION CM575(M,TC,CLF) DIMENSION T(5),CL2(8),CM2(8),CL6(8),CM6(8),CLg(10),CM9(10), &CL12(9),CMI2(9),CL15(8),CM15(8) DIMENSION CL21(1),CL30(1),CM21(1),CM30(1) REAL M DATA T/0.O2,0.06,0.0g,0.12,0.15/ DATA CL2/0.0,0.I,0.2,0.3,0.4,0.5,0o6,0.7/ DATA CM2/0.318,0.24625,-.4565,-.4625,-.633,-.633q-.633,-.524/ DATA CL6/0.2,0.3,0.4,0.5,0.6,0.65,0.7,0.8/ DATA CM6/-.1575,-o1575,-.16,-.16,-.16,-o1625,-°165,-.1725/ DATA CLg/0.0,0ol,0.2w0.3,0.4,0o5,0.55,0.6,0.65,0o7/ DATA CM9/-.0708,-.0708,-.0667,-.0646,-.0625f-.0625,-.0604, &-.0583,-.0521,-.0458/ DATA CL12/-0.1,0o0,0.1,0.2,0o3,0o4,0.5,0.6,0.7/ DATA CM12/-.16,-.1525,-.145,-o135,-.125,-.115,-.105,-ol,-o085/ DATA CL15/-0.05,0.0,0.I,0.2,0.3,0.35,0.4,0o5/ DATA CM15/-°09375,-.08958,-.075,-°0625,-.0479,-.0417,-.0375, &-.0333/ CM575=CMTHKF(M,TC,CLF,T,5,CL2rCL6,CLg,CL12,CLI5,CL21,CL30,CM2_ &CM6,CMg,CM12,CMI5,CM21,CM30,8,8,10,9,8,0,0) RETURN END C C C FUNCTION CMTHKF(M,TC,CLF,T,NA,CLI,CL2,CL3,CL4,CL5,CL6,CL7,CM1, &CM2,CM3,CM4,CM5,CM6,CM7,N1,N2,N3,N4,N5,N6,N7) DIMENSION T(1),CLI(1)fCL2(1),CL3(1),CL4(1),CL5(1),CL6(1),CL7(1), &CMI(1),CM2(1),CM3(1)wCM4(1),CM5(1),CM6(1),CM7(1) DIMENSION X(2),Y(2) REAL M TCR=TC IF(TCR.LE.T(1)) TCR=T(1) N=2 CALL OUT(NArN,IS,IL,T,TCR) DO 30 I=IS,IL X(I-IS+I)=T(I) GO TO (1,2,3_4,5,6,7),I 1 ANS=GETF(N1,N,CL1,CM1,M,TCfCLF) GO TO 20 2 ANS=GETF(N2,N,CL2,CM2,MrTCwCLF) GO TO 20 3 ANS=GETF(N3,N,CL3,CM3,M,TC,CLF) GO TO 20 4 ANS=GETF(N4,N_CL4,CM4,M,TC,CLF) GO TO 20 5 ANS=GETF(N5,NvCLS,CM5,M,TC_CLF) GO TO 20 6 ANS=GETF(N6,N,CL6,CM6,M,TC,CLF) GO TO 20 7 ANS=GETF(N7,N,CL7,CM7,M,TC,CLF) 20 Y(I-IS+I)=ANS 30 CONTINUE CMTHKF=YLAGN(X,Y,N,TCR) RETURN END FUNCTION GETF(NMAX,N,XCL,YCM,M,TCvCLF) DIMENSION XCL(1)uYCM(1)_U(3),V(3) REAL M IF(CLFoGToXCL(1)) GO TO 1 GETF=YCM(1) RETURN CALL OUT(NMAX_N,JS,JL,XCLrCLF) DO 2 J=JS,JL U(J-JS+I)=XCL(J) V(J-JS+I)=YCM(J) CONTINUE GETF=YLAGN(U,V,N,CLF) RETURN END SUBROUTINE OUT(NMAX,N,IS,IL,Y,X) DIMENSION Y(1) IS=I IL=IS+N-I IF(X.LE.Y(IL)) RETURN IL=NMAX IS=IL-N+I IF(X.GE.Y(IS)) RETURN IS=l IL=IS+N-I IF((X-Y(IS))"(X-Y(IL)).LEo0.0) RETURN IS=IL GO TO 1 END FUNCTION YLAGN(X,Y,N,Z) C C PERFORMS THE LAGRANGE INTERPOLATION C DIMENSION X(1),Y(1) SUM=0°0 DO 1 I=l,N S=l.0 DO 2 J=I,N IF(JoEQ°I) GO TO 2 S=S'(Z-X(J))/(X(1)-X(J)) 2 CONTINUE SUM=SUM+S"Y(I) 1 CONTINUE YLAGN=SUM RETURN END C C ....................................................................

C C END OF DATA INFORMATION C SUBROUTINE ATMCON(ALTUDE,TEMPwPRES,DEN,VIS_WA) ALTUDE=ALTUDE*o3048 SLOPE=-o0065 TEMP=288.16+SLOPE*ALTUDE EXP=2.718281828 TSEA=288oI6 PSEA=I01325° PRESI=22700.

GRAV=9.82 R=288.

POWER=GRAV/(SLOPE*R) PRES=PSEA*(I/(TEMP/TSEA))_*POWER IF(ALTUDE°LEolI000.) GO TO 1 PRES=PRESI*EXP"*(-GRAV/(R*216o66)_(ALTUDE-11000.)) TEMP=216.66 WA=SQRT(1.4*R*TEMP)/.3048 TEMP=(TEMP-273o15)_9/5+491o67 VIS=o35*(TEMP/492o)"*l.5*(690/(TEMP+198.))_°000001 PRES=PRES*2116.2/PSEA DEN=PRES/(1718o*TEMP) ALTUDE=ALTUDE/.3048 RETURN END SUBROUTINE TEST(TC,MXMACH) INTEGER THL REAL MMACH(4) REAL MXMACH DATA MMACH/0o845,0.770,0o700,0o625/ 3 S=0.7143 THL=INT(TC*I0) DELTHI= TC-(THL/10o) TNL=THL+I MXMACH=MMACH(THL)-DELTHI*S RETURN END SUBROUTINE AOAT(MvALTEST,K) REAL M DIMENSION ALL(5) DATA ALL/18o667g14o5f10o4,6o2_2o03/ S=-41_667 IF(M.GEolo0) RETURN MM=INT(M"10.)-4 DEL=M-(INT(M"10o)/10o) ALTEST=ALL(MM)+DEL*S RETURN END SUBROUTINE N16COR(L,CHORD_TC,CLDwAREA) DIMENSION X(14),YU(14),YL(14)_CI(12),C2(12),C3(12),C4(12) DATA CI/o0093, o0158f.02587,°03982,.04861,.05356,.05516,o05356, &o04861,.03982,.02587,.0158/ DATA C2/o1272, o09653,.066,o03473,.01461,.00394,0.0,.00447,.01895g &o0449 °05961, o05469/ DATA C3/o15044_o20911go28811,.38867,.45144,.48789,.5, o48622, &o43911,.34989v o20978N oi1789/ DATA C4/.00639_.00574,.0044,.00237,o00103,.00025,0.0,.00025_ o001_ &o00213,.00321,.00324/ REAL LERAD,IXC,IYC,MY,MX IF(LoEQ°0) RETURN THICK=TC LERAD=o489"THICK*_2/CHORD TERAD=o01*THICK SLOPE=.62234*CLD AREA=o7396*(l+.00544*CLD**2)*THICK*CHORD MY=o3569"(I+o00458*CLD**2)*THICK*CHORD_*2 MX=o03335*(I+.00196*CLD**2)*CLD*THICK*CHORD**2+.01775*(l+.I332*CLD "2)*CLD*THICK**3 IYC=.04221*(l+o01287*CLD*"2)*THICK*CHORD**3 IXC=o04476*(I-o00182*CLD"*2)*THICK"*3_CHORD+.00009358*(I+.02013*CL &D**2)*CLD**2*TNICK*CHORD**3 THETA=ATAN(SLOPE) DYI=LERAD"SIN(THETA) x(1)=0o0 YU(1)=DY1 YL(1)=DY1 X(2)=o025*CHORD X(3)=2"X(2) DO 1 I=lu9 1 X(I+3)=FLOAT(I)/10*CHORD X(13)=o95*CHORD X(14)=CHORD DO 2 I=l,12 COMI=CI(I)*CLD"CHORD+C2(1)*CLD*THICK_2/CHORD COM2=C3(I)*THICK+C4(1)*CLD**2"THICK YU(I+I)=2"COMI 2 YL(I+I)=COMI-COM2 DY2=TERAD*SIN(THETA) YU(14)=DY2 YL(14)=0.0 NUMPTS=14 WRITE(6,500) 500 FORMAT('I',45X, '*"_ NACA-16 AIRFOIL DIMENSIONS "*_'_//' _, &39X,'X-COORDINATES',5X,'Y-COOR UPPER',6X,'Y-COOR LOWER'/) DO 3 I=I,NUMPTS X(I)=X(I)/CHORD YU(I)=YU(I)/CHORD YL(I)=YL(I)/CHORD IF(CLD.NE.0.0) GO TO 3 YU(I)=-YL(I) 3 WRITE(6u600) X(I),YU(I),YL(I) 600 FORMAT(' ',39X,FI0.6,SX,FI0o6,8X,FI0o6) WRITE(6,700) THICK,CHORD,AREA 700 FORMAT(' ',5(/),40X,'(T/C)MAX',7X,'CHORD(FT)',8X, 'AREA(FT*_2) ', &/38X,F10.6,6X,F10o6,7X,F10o6) WRITE(6,800) IXC,IYC 800 FORMAT(' ',5(/),50X,'MAJOR',12X, 'MINOR',/50X,'MOMENT',IIX, &'MOMENT',/49X,'INERTIA',IOX, _INERTIA',/46X,FI0.5,7X,FI0.5) RETURN END //$DATA //$STOP

Appendix II

NACA 16-Series Program Case

Input/Output

6 REAL M(3) 7 DATA M/0o3,0.5_0.7/ 8 DATA ANGLE/0.0,2.0,4.0/ 9 DATA ALTUDE/0o/ i0 DATA CHORD/lo000/ ii DATA TC/0ol5/ 12 DATA CLD/0.2/ ,13 DATA ICLlll 14 DATA ICDIll 15 DATA Xlo50/ 16 DATA NUMACH/3/ 17 DATA NUMALP/3/ 18 DATA IFORM/1/ 19 DATA SP/1/ 2O DATA L/l/

*** NACA-16 AIRFOIL DIMENSIONS ***

X-COORDINATES Y-COOR UPPER Y-COOR LOWER

0.000000 0.000110 0.000110

0.025000 0.004336 -0,003863 0,050000 0,007280 -0.004736 0.100000 0.011853 -0,005607 0.200000 0.018195 -0.006454 0.300000 0.022191 -0.006964 0.400000 0.024442 -0.007295 0.500000 0.025170 -0.007415 0.600000 0.024443 -0.007228 0.700000 0.022195 -0.006469 0.800000 0.018202 -0.004899 0.900000 0.011848 -0.002474 0.950000 0.007249 -0.00i098 1.000000 O.O0005G 0.000000 (T/C)MAX CHORD(FT) AREA(FT*_2) 0.040000 1.000000 0.029592 i-..= L,.)

MAJOR MINOR MOMENT MOMENT INERTIA INERTIA 0.00000 0.00169

*** LIMITATIONS ***

u7 86_8L_'0- 08LOL_'_E £_[_0"0 08£886"0 000000"_ L£O90_'O- OL#£#_'£C 9090_O'O C6_#_L'O 0OOOOO'# #_OBP_'O- O968OL'6£ 980800"0 £BL_8#'O 000000"_ O8£_81"O- OO_9C_'E£ O_L_O'O OEL£_9"O O00000"_ 9_9060'O- O9_81£'8# O#££OO'0 868_#_'O 000000"0 88_'O- O8Og_g'g£ L98£OO'O O98_8"O OOOO00"0 (O31)_D 03/73 OO 7D VHdqV (037)_3 03/70 OD 73 VHd7V _O 3£#9L_8"O = "ON SG7ONA3a _O 369960£'0 = "ON SOTONA3a OOOO£#'O = "ON HDV_ OOOOOL'O = "ON HDV_ "930 OOOOOO'_- = O7VHdqV "930 OOOOOO'_- = OqVHdqV

o_B_ao = o73 O£_8_'O = oqo

0000#0"0 = XV_(3/1)

oooo#oo = xv_(3/z)

1333 OOOOOO'[ = Q_OHD 133_ OOOOOO'_ = OaOH3 133_ 0000"O = 3on1117v 1333 OOOO'O = 3ORlI17V NNV8 VlVO 7103_IV $31_3S 9'9['VDVN _ • NNV8 VlVfl 7103B[V S31_3S 9'9_ VOVN

* NACA 16,6SERIES AIRFOIL DATA BANK *

ALTITUDE = 0.0000 FEET CHORD = 1.000000 FEET (T/C)MAX = 0.040000 CLD = 0.228150 ALPHALO = -2.000000 MACH NO. = 0.700000 REYNOLDS NO. = 5.096695 ALPHA CL CD CL/OD CM(LED) 0.000000 0.312880 0.005867 53.323080 -0.112138 2.000000 0.625720 0.011710 53.436300 -0.182580 4.000000 0.938580 0.044125 2_.2707B0 -0._73298

F_

o',