APPENDIX A
APPENDIX A REGRESSION ANALYSIS FOR NONLINEAR PRESSURE FUNCTIONS The requirements for determining the coefficients for the polynomial expansion for the inlet nonlinear pressure functions are outlined in this section. The effort involves selecting the form of the expansion and obtaining a least squares fit of the data for the range of interest. To date these computations were performed separately although a general program could be prepared to compute all necessary coefficients in sequence and output them in a punched card form suitable for use in the 8400 digital computer program.
The necessary mathematical steps are outlined in the following paragraphs.
The polynomial expansions of the pressure variables were obtained from wind tunnel data which are functions of five independent variables. Two vari- ables were considered to be primary ones, Wic 6sp, to be fitted with greater , accuracy, and the remaining variables, aw, 8, M, were considered secondary and were fitted less accurately. Polynomials of prescribed form were fitted to the data using a least square criterion. A factor to be accounted for in the curve-fitting process was that the range for which the inlet variables (wic, 6sp) were needed varied with flight condition. A double interpolation of a portion of the polynomial coefficients was also required since, in general, the expansions were made relative to nominal conditions which were different from the original data conditions.
The complete polynomial expansion for either the pressure recovery or signal pressure function, P, was expressed in the following form by the substitution of equation (36) into equation (34) or (35) imax 3max P 0, ,M ) C i..ww i6 w o c sp i=0 j=0 j k maxR max max 6 cijkWicsp ij kw C + i=0 j=0 £=1 + C. w. AM
SC1im
i=0 A-4840 is made relative to nominal flight condition of Note that the expansion angle of attack is defined 0, and M = M . Also, the incremental Nw = awo, 8 = o was made to expand the - aWo. As previously discussed, provision as a = , w inlet condition.
about any convenient average variables, wic and 6sp, inlet are given in Table 1.
for each pressure function The upper summation limits the following was separated into procedure for obtaining the coefficients The steps.
linear regression for the two primary first step was to perform a The tunnel data were of c , 8, M for which wind wic and 6sp, for values variables, w equation (Al), denoted the first summation in Hence, the form of available.
unknown coeffi- equation for the to determine the regression by Pl, was used Cij(aw, 8, M).
cients (A2) MW c(J)sp(J) (aw , Cii = 8, M, J) 1 iawl j=o i=o where 8, M) J = 1 . N(a , w of data points used to determine The value, N(cs , , M), is the number for each constant (w ,, M) M) as a function of wic and sp Pa(Ow, , condition.
the a and M the Cij coefficients in The second step was to interpolate Both linear (using two values of aw and M .
directions to selected nominal 0 o inter- values per direction) and quadratic (using three values per direction) variations in the coeffi- depended upon the were used. The choice polations M directions. An available single cients between data points in the , and w applied as follows.
program was successively direction interpolation Cij( , M) C ij(aw , M ) C.ij (aO 8, M) _+ Cij (Cw , 8, M C.( 1 , M) Cij(w , N) where the subscript o refers to the selected nominal value of the M or aw variable.
A-4840 for the primary vari- The third step was to perform a linear regression variables, a, 8, M, as indicated by the ables with each of the secondary expan- summations in equation (Al). The resulting second, third, and fourth previous conditions selected in the relative to the nominal sions were made equations for a variable, the regression For instance, for the interpolation.
as follows: Cijk coefficients were the unknown
i j
max max 2 ( A 3 ) ( J ) c(J)6j (J)ak , , , Mo)wi P2, k=l i=o j=o where J = 1 N(O, Mo) used to determine is the number of data points The quantity, N(O, Mo), 6p, and a.
M) as a function of wic, P (a, 0, following equation.
0, Mo, J) was computed from the The function, P (t, ) (A4) - P(aw , 0 M', 0, Mo, 0, M' J) P'(aw, P2(a, 0, Mo, J), were determined through P1(tw, 0, Mo, J) and Pl(awo, The functions, use of the first summation given in equation (Al) and the appropriate Cij J) is the equation for Pl(awo, 0, Me, coefficients. For instance, max max , 0, Mo)w (J)6sp(J) (AS) P w o, 0, M , J = i]C i=0 j=0 for the 8 and M was used to obtain the expansions A similar procedure (Al).
variables in equation 28 A-4840
APPENDIX
B APPENDIX SIMULATION PROGRAM LISTING of the YFl2 of the computer program for the representation A listing in this section.
system dynamics is provided aircraft motions and propulsion is given in Table 2. Listings of A list of the principal fortran variables such as an executive in the execution of the simulation other subroutines used numerical integration provides overall control, and monitoring program, which programs are not included.
sequence.
listing are used in the following The subprograms shown in the for use initial quantities are calculated In subroutine SETUP, the necessary step is controlled of the simulation. Each integration in subsequent portions the subroutines for the LOOPl. This subroutine calls, in turn, by subroutine CONTRL (SAS), and AIRFRM.
the simulation - INLET, ENGINE, various parts of the dynamic equations the necessary constants for In each of these subroutines, subroutines are made to the appropriate integration are calculated and calls subroutines which are descriptions of several additional when needed. Brief follows.
called in the listing are as to be used in the calculates the coefficients ZXFORM - This subroutine coefficients and as a function of transfer function z-transform integration integration interval.
and time multi- This subroutine is used in scaling, biasing, XFERDA - analog recorders.
plexing signals to be output to of the equation of MGRATE - This subroutine is the initialization portion
to be integrated, order of
integration method. The number of variables
motion
size are established.
integration, and step for an integration computes and stores results GRATON - This subroutine integration method.
for the equations-of-motion interval and speed of sound is a tabulation of density ARDC62 - This subroutine 1962 ARDC atmosphere.
versus altitude for the variable.
This function supplies limits for an indicated VALLMT - is as follows.
listing for the aircraft equations The computer A-4840 29 I C TITLE srTUP 2 SUSROUTINE SETUP 3 C 4 CHOMMON /BLKI / IMODE .IDT olTTIES *DT NT 5 1 TIME ,D2R o1D 6 C 7 eMMN /9LK2 / UB oVB SWB .PR e,0 8 1. Pa ,PHIR ,THETQ oPSIR *PHI .THET 9 2. PSI DMH 9ETA sALFA .BETAP *ALFAR 10 3. ALT .ANY oANZ oCLS -CL.A .CLDR 11 4. CLB9P .CL~SP ,CLRG E CLPg .CNq ,CNDA 5. CN:R .CNrP ,CNFlnS . CNp .C"PR .ELTAA 6. DELTAE DELTAP .r2Z . 772 PS7 *PT27 14 7. 7SP(.)
,DBP(2) **l2s PLA(2) o.AnJC(2) ,P-MM(2) 15 30 T(2) WECI(') DO-3F 16 C CeHMMN /BLK3 / CDZ CtAl I CnA2 oCL7 .CLAI 18 10 CZ .CHAI CYA2 . PF arnwP .C)DSP 19 2 CL. !C .CLFDP LF"SP ,CLFrB 0.Ac?7 VZ 2C 3* AREA ,XtASS .Ce .VSPAN ,G YYT 21 4, XT ,XLT .XAJT.XNT oxlY .YIYY 22 5. XlZZ XIXZ o.tY9 CyF oCy' ,CLA, 23 6. -'1R A rC%: HTF Cfle nP L tS ,CLPRS 24 '. CLP3S ,CLDlA rTLDPS .~LDPPS CLSSeS , S 25 N' rN*PS ,CNWBS ANuec gyDRS .CN'WS - NDSe C 27 CbHMMN /1LKS / XKPP .Xr O oYKQ2 .XKP ,YKRN 28 1. TCI aTC2 .TCNI eTC1t ,TC?' .TCD21 r 29 2. TCD22 sTCN- .W NA -7A WN 7E 30 3. WP .7pR *T11 T12 *TI4 -SP 31 4. ZSP STEI .TP? ,TE4 .TF~1 .TEN2 32 5. TED2 oTID4 TID' .TIil C 34 CeIMON / SLK7 / G1IA Gl .GGIC G2A 35 1 G2R SG2C .2 .F G2H 2. G21 ,G2J .K ' L .GA .G38 3. GAA ,G4e .4 .4 .G4E F G4F 38 4. GSA .GSR ,G1C .6A .G7f ,r7R 5. G7C .G77 . A rp .GAC o18D 40 6. GSE .GSF .S'; .r8; Gs81 oG8J 7. G6K SG6L 42 C 43 COMMON /BLK8 / G9A ,G99 sGQC ,Gg9 *G9E to G9 * GIOA r1I1A ,G119 ,Gi s *G11D 2 G1IIE SGllF ,GIIG Gt1ZA 'C129 jG4A 3. 0149 GI14C .G14- *G14E .GIdF .G15A 4 c-15 .G15 .ts15 *GI6A .G163 *GL6C 5. 0,6D0 .GIE .,16 .1j6G .10H WCI7A 6. 017p 1GI7C MGI S .GI8P .G13t 50 7. GISA 0G19 ?G20A .G20P 51 C 52 COHMMN /BLKIO/ GNI(17) F9RI(17) Zt1(17) Zf1l(l17) CN2(4d) 53 1 A2ND(4) .B2ND(4) ,Ze21(4) *2022(41 ZI121(A) .Z122(4) C COMMON /BLKII/ ALFAZ oALFAZR SPZ .4ICZ ODBPZ 56 1p THETZ ,DEZ .PBIC .031C aROIC .PHiIC 57 2. THEIC .PSIIC .9Dic .ETATI 4&LFA!C s.LTIC 58 3. ICDSPI2) aDSPICI2) nSPlIC(2).CBP(7) .DRPIC(2) .RPDIC(2) 4d ICRPM(2) .RPHIC2) AJIC(2) ,ICJ(2) AJrICc~ ) *AJCDIC(2) 5 IWF499(2). I2. WCFI),~wFPPJ2 1WFPIC IrPSAS .PSASI 6. PSADIC tICGSAS Q SASIC SICRSAS OPSASIC .kSADtC 62 7.
RSAli L JSA21C I.!A .DAIC Y.A ?C *ICDE 63 as DEIC .TElCt .100IR onIC DRIC Xw9 9. Z9 .YXa .ALT?
65 C C CIMENSIeN ISRD(l) C DATA NUMI/17/,NUM2/4/.18PDd4*0/ 70 C 71 ID01 C DT=.01*IDT 74 C 75 C INITIALIZE 76 C TIME=O.0 78 c PBOPBIC*D2R OBuQBIC*D2R 8I RB.RBlC*D2R c 83 PHI! .PHI IC 84 PH!R *PHI*D2R 'MET TNEIC 86 THETR-THET*1D2R PST *PSI!C 88 PSIR .PSI*32R 89 C 90 DM -OMIC BETA aeETAIC 9? BETAR =RETA*02R 93 ALFA ALFAIC 94 AVfAR .ALFA~fl2R 95 ALFAZR-ALFA!.029 C 98 VB-BETAP*VZ We-ALFAP*VZ 100 C ALT-ALTIC 102 c
103 C 0tIAkT1TIES RELATFO Tl REFrPVrN^.E ~UI
C Ps! *-(G9A.G99.DSP!. C+9~SP+G9+*~ S7*WI!C!Z.WIC! p 106 C 107 PT2Z--(Gl15A.G15q.DSP:. (1 15tCIG5fl*nS!) *W?(r71 108 C 109 DSJI-ALFAZ*ALFAZ 11c rDSU2.ALFAZ* 'SU1 III G27 *02A*DSU2,G2B*:OSIJI4G2C*ALFA7 112 C 113 DSJ3A9SfALFA7-G7A) fSU4-PSU7.0SU3 DSU5.oSU3*!ISUA 116 G7Z -G7fl.DSuS.G7C*flS'J4+G7D*DSlJl 117 C 118 C STABILITY nERIVATIVES CeNVERTE7I FLIPI eTASILITY AWES Te RAfly AXES 119 c 120 CALFAZwC(lS(ALFAZR) 121 SALFAZ.S!N(ALFAZR) 12?
CALF72-CALFAZ*CALFAZ 123 SALFZ2.SALFAZ*SALFAZ
nSU6 -ICNPBS*CLR99p.SALrAZ*CALFA7-
125 DSU7 ICLPgS-CNRBS,*SALFAZ*CALFAZ 126 C CN9 -CNBS*CALFAZ+CLBS*SALFA7 128 CLS =CLBS*CALFA!-CNBS.SALFAZ CNRP .CLPBS.SALFZ2+CNPAS*CALrZ2+DSU6 130 CLPB .- CNPB$.SALrZ22CLRqS.CALF721 SU7 131 CNP9 -CLRBS*SALF!2.CJP!S*CALF!2nSj7 132 CLPB UCWPS*SALF72.CLPBSOCALFZ2-DSUJ6 CNDR mCNDR$.CALFAZ*CL3RS.SALAZi 134 CLDR -CLDRS.CALFAZ-CN!DAS*SALFAZ 135 CNDA OCNDAS*CALr*AZ*CLflAS*SALFAZ 136 CIDA CLDAS.CALFAZ-CN!)AS*SALFAZ 137 CNDBP -CNDOPS*CALrAZ.CLDBPS*SALFAZ 138 CLDBP -CLDBPS*CALFAI-CNrAPS*SALFAZ 139 CNO)SP .CIDSPS*CALFAZ*CLrSPS*SALFAZ 140 CLDSP sCLDSPS*CALrA!-CNtSPS*SALFAZ 141 C 142 C Z.TPANSreRM SETUP C 144 GNI(1I -T14/TT2-1.
145 FRIll) at./T12 C GNI(2) I1./TII 148 I~l)*./TII 149 C ISO GNI(3 a1./TE3 151 FRIM3 a1./TE3 152 C 153 0141(4) al./TEI FRII4) a1./TEI c 156 GNI(s) 01 /TEd 01.1YE4 1137 FRI(13) 150 c 159 GN1461 -I.IYEDI IGO FRI(o) ol./YEDI 101 C GNIM TEMUM2-1.
103 FRIM olo/TED2 Lod c 165 Gt4iial -- XKPP/Yct FRI(S) 0I./TCj C 160 GNI(9) oXKQCoYCNI/YCDI AGO FRI(9) MI./YCDI 170 C 171 GNM01,XK0Q/7CDI 172 FRICIO)-I./TCDI 173 c 17d GN1911)QXK020(1.-TCN2/TCn2l)/(TCD21-YCD22) 179 FPMI)ol 17CD21 IYO C 177 GlilII2$-YK02PIYCN2/TCD22-1.)/(TCr2i-TCD221 1178 FRI(12)al./TCD22 IY9 C 180 GNL(13),VKRR 191 PRI(13101./YCN3 C 103 G1qI1I6)-YKRWf7C2 led (rRI(14)-I,/TC2 las c ISO GP4111F)ol./TIDA 107 FRI(15)11./TIDA ISO c 189 GNI(IO)-l./TTD9 190 FRI(j6)-I./TjPB GNIII?),I./TIDM 193 FPlfi7)ol.fTfDH 194 C 195 GN2(0 oWNSPOWNSP 196 A20(l),2. 2SPnWNSP 197 02MUMaWNSPOWNSP 198 C GN2(V -WNAOWNA 200 A2NDf2)m2.*ZA0WNA 201 62MD(2)-WNAaWNA c 203 GN2(3) mWNEOWNE 204 42ND(2)a2.0?EaWNE 205 P20(3)mWNEoWNE 2OG c GN2(4) WNRoWMR A2ND(4)-2.aZRoWNR 209 P2NDIA)awNRoWNP 210 c 211 c CALL ZXFORM(NUMI.GNI FRI ZOI 711,NUM2#104!.PN2.A2N".l9Nro 213 2-e21a7e22o7V2IoZT2!!o2T) c 219 RETURN 216 C END 8 8 I C TITLE L P1 SUReUTINE LOOP C COMMeN /9LKI / IMeDE .IDT &ITIMES .DT .NDT 5 1. TIME ,D2R .1D 6 C COMMtN /PLK2 / US VR #WB .9P .04 a . 9 OPHIR .THETO &PSPR OPHI .THET 9 2. PSI .DM .aETA .ALrA .9BEAR .ALFAQ 10 3. ALT .ANY .ANZ .CL9 .CLA .CLDR I1 4. CLDPP *CLOSP .CLQR .CLPP .CN .CNDA 12 o5 CNDR DCNRP .C9SP .CNp P Ce .nELTAA 13 6. DELTAE .DELTAP .G2Z r.7Z OPSZ ,PT2Z Id 7, MPP2) .DaB(2) D.T2S(2 *PLA(2) .1 (2) ,FPMH(') 8. T(2) wEC1(2) .PFA 16 C 17 CeMMeN /RLK3 / CDZ ,CrAI .IIA2 .CL? .CLAI I1 C47 rCMAI ,CHA C:De .Cvn P cDDSO 19 2. CLFDP .CLrFDB .CLFnSP .CLFB ,OAp? .vz 20 3. AREA .XMASS .CHel) .SPAN G rYXT 21 4. XZT .XLT XT NT .Xyxt .(XIYY 22 5. XI2Z OxIYZ .?Y3 ,CYrP .CYP9 CLA9 23 6. C'A .CM ,C nv .CalOP ,CLCS aCLPOS 24 7 CL~PS .CL:AS ,C L!C CLCPS .CL7S"S .CIBS 25 . CNPRS .CNRBS r JAAF 5 rP. .CP .S ,CJlDS 26 C 27 COMMON /BLK5 / XKPP .XKO0 y.n2 .XVml I<KRN 28 to TCI .TC2 ,TCNI .TC"? ' TC'\ ,TcD21 29 2. TCC22 .TCN . ~ZJA .Z .W'F ,7F 30 3. wNR .ZR .Tit .T2 .Tld qJSP 31 4a 73P .TEI .7 T4 .Tlr .TEN2 32 5. TE 2 .TID1 ,T9 .T17 33 C N CeMMO / aLK7 / GIA .ClO .CIC .GIA 35 la C2R *G2C G2 E , ?? .G2?! '!'
36 2. G21 .G2J .G2K PC2L rC .G3B r 37 3. G4A G4B rGdC .,4D .G4 r4F 38 4. GSA .G5: .G5C . 6A .GYA .78 5. & G7C .G7 ' .G .3 .G a .aSD 40 6. C8E vG8F .G8G 1"S t .j GlsJ 41 7, G8K .G8L 42 C 43 COrMN /BLK8 / 94A .G99 .G9C G097 ,G9E 1* Gr GICA GIIA sGit! # G1C r11l 45 2 0 IE ,CGIr rlit Gl2A .G121 .14dA 46 3. G14 .eGI4C .014' . CIE .GIde ,c15A 47 4. C150 , G15 .G15, Gi6A .G 01 .016C 48 5.
i60D G1rC .016F , 160 .C1*H .0174 49 6. C 17 170 .G18. .GIAR .1JC G7. G019A Gl1n ,G204 .G2 C 51 C 52 COMM8N /BLKIO/ GNI(17) .Fq1(17) Z.71(17) *711(17) ,bN2(A) 53 to A2Nn(4) .B2Nn4) 7!21(4) .?22M(4) *l7114) .712714) 54 C COnMMN /BLKII/ ALFAZ .ALFAZR .DSP7 WIC7 !9iPZ 56 1* THETT .DEZ P3tC .CBIC *RlT .PHITC 57 2. THEIC APSII ,riMIc .ETAIC ,ALFAIC .ALTIC 58 3. ICDSP(2) .DSPYC(2) .flSpD!C2ct9P(!8 ) DBTICt) .CRPPDIC(2) 59 4, ICRPh(2) .RPMIC(2) ICAJ(2) .AJIC(2) .AJrIC(2) JCDIC(2) 5. IOWPAa(|,WFA5IC( .ICwef(2).WFDDIC(2).I S .)r SASIC 61 6& PSADIC ICQSAS .0SA3!C tIVAS OSASIC .PSADIC 62 7. RSA llC RSA2I~C ICDA .AiC DIC ICDE 63 8& PEIC IEIC .IC3R .0RIC DRIC Ox9 9. 7; .XM3 .ALT!
65 C 66 C 67 DI;IENSION 7AMPLA(2),SLOPLA(2)*PLALMT(2).IPLA(2). IwP*A(2) 68 C 69 DATA SLOPLA/0.,0./OPLALT/0..C./.IPLA/0.r/ 7C C 71 C 72 C INPUT SIGNALS 73 C De 13 1-1.2 75 RAfMPLA(I)-SLOPLA(I)*TI9E 76 IF fRAMPLA(II.CT.PLALMTlEil -AMPLA(flsPLAL"T(f) 77 PLA(I) sIPLA(1)*RAMPLA(I) RPMM(I) O0.0 79 AJCII) 0.0 10 CONTINUE C 82 CALL INLET 83 C 84 CALL ENGINE 85 C 86 CALL CaNTRL 87 C 88 CALL AtRFRM 89 C 90 CALL XFFRtA(MeSDEIWOFe 0) 91 C 92 IF (IMHDE.GT.0) TIINHMTIHEDT 93 C 94 RETURN 95 C 98 EN3n I c TITLE INLET 2 SURUT1NV- INLET a C 4 COM3N /PLKI / IMODE al:)T *ITIMES &TIT ,NrT 5 Is TIME .02R '1 C 7COMMON /BLK2 / US 'Va .I%9 Op~i '~ I* 1. r3 .PHIR .THETQ #PS!R *PI .THET 9 2. P1 'Dm .BETA .ALFA *RFTAR .*LFAR 10 3. ALT *ANY .ANZ r Ll; CLrA *CLDP 11.d C.09' DCLDSP .CLR2 C LP3 .CNO .C'DA
12 5. IR . C,,4 D a . C4 r *cit .C:*iq . ci*P 9 .OELTAA
13 So DELTAE DfELTAP .. zz . !lj .ps? .T27 14 7. fspc2 aDSP(2) .PT23(2) #PLA(2) .Ajt-e) ,PPM4( ') 16 C 17 COMMIN /RLK5 IXKPP .xKoo #XK02 .XKR? Y'4 I$ Is CIl .TC2 .TCIl pTCOI .TCW' T1C21 19 2. TC022 , TWOJ ,101A ?2A , #JNEz 3. WNR MZR T11 .T12 T1d .Isp 21 4, !SP .TEI .TE7 *TEA .Trr .TCN2 22 S. TED' .TIDA .TI1 .T I Dl 23 C 24 Ce.9MON /9LK6/ XKIS SXK(6 VXKIO1 .KI XKTI X15 25 Is XI16 .XK119 )CK120 )(KI23 26 C 27 CfOMf.N / BLK7 / GIA .GIR Glr, .G1r G2A 28 to C2P .G7C .G2E ,G r .02C sG2H 2. C-2! G2J .0-lK *C2L .G3A .(39 30 3. OdA .,^48 r,4C t~4" C04F rAF 31 A, G3A .0SB *Gsc G6A GY7A G78 32 5. 7C G07T GSA4 .G39 .68n .080 33 6. G BE G08F F. VGb1 .G61 .G8J 7. G3K G08L 35 ' eCeMMON /BLeK8 /G9A fogq .CGC 'G11 G9E '7 Is G9F .GICA *O1IA #*0'11B #lI a01 .1 I1, 38 2.& C E .011r G110 CI VA r'12-S .14A 39 3. 014D .014C .oi,) .014E .0147 *.15IA 40 4, G158 G015C .015n C016A .0163 .(716C 41 S. 016D .GI6E 6016F .016r Gje5H Gl'7A 42 6& r'17? *.17C GIAA .1A3 Gljs A3 7. G19k 'G19-1 G204k *G?OC 45 COMMIN /ILK10/ GN1(17 F7RI(17) .ZOI(17) PZII7) t0N2[A) 46 1.
APNI(4 .921n(4) .7e?114) *782?(41 .ZTPI(4) .7127(4) 47 r 48 C1eMMON /BL'(11/ ALFAZ .ALFAZR rsp? .WTr7 :)RP7 49 le THETZ ICEZ #01C 0381C *?qJc P"HTIC so 2. THEIC OPS!IC .CMJCc a3ETAIC *ALWATC .ALYIC 3. ICISP(2) . SPIC(2i -,SPOI.-(2',jcrop(z,.fF'12 .'8Pl1c(2) 52 4. 1! RlM (2) *RPMIC(P) .ICAJ(Z) . AJ IC (!: . AJ'!C(2) AJC'(,) 53 50 IPAlE?).4F6RIC(2).
IcwrPc(2l..jF7"IC('). 10 .0AS . 3ASIC 5A 6. PsAric .ICJSAS .CSASIC .IcpsAs .PSASIC p.'SArC 55 7. RSAIJZ: .RSA21C oIc*DA #71 .s'I ICDE 56 8. 1E
IC c SP0IC MICDP ~ .'I C flprTc oxq
57 9v z~ F Xt1 0 3 ALTZ 59 C 60 DIMENSION DSP! (2).0SP1P42).D)SPIPPE2).OSPTSC2).1801SP(,) 61 1.DOUTi2I.120UTP I2).DOUTPP(2.P8C( ).PS(2)." E(') 62 2.X5D(2).C9-1 (2p.DBp2(2 ' isPPP(2) 64 4.Ptll2.),G44I2.wC2).08C(2).92.-3 101()G3)042 65 5.G 195(2) . 1612) !G17 (2)C'lA (2) . C^0(2) ,T) Il ()anc . EC (2) 66 c 67 c 68 ALFAT.ZOl (15$*ALFATZI11 15).ALrA 69 C 70 nflTATZe1(16).2ETAT4ZI1E16)*nETA 71 C 72 DMTl7tSIl1).DMT+ZI 1CI7)*!F" 73 C 74 nflGA9SfAN7)-G3B 75 IF (0JG1.Ly.0.0) DG1.0.3 76 G3-G3A*flG1 77 G6*G6A*DG1 79 GI2w(GI2A*G128oALFAh0ALFA fGSOALrATOALFAZ 82 C 83 nG2-"A8S(VGQ5'GA) 84 DG3c0G2aDG2 as fC4'-DG2*DG3 86 G7mG7B8flG4*'7C*DG3oG7fl*tC2-G77 87 C 88 fG6*DG5eDG5 89' flG7,!lG5SI1G6 90 C2GAD?,.8D6GCCSf74(2*G+?*G*2~r~2 91 1 .(r,2!.0G7oC2JoG6+",K*G5",:L)..nMT).DvT 02 C 93 &I9mcG1 9A#^-l9R0M?*OM 94 C 95 fG8-(G1A.ABS(9ETAT ,C19) *RETAT&PFTAT 96 0C90'EG)COA85t ETAT) .01J)) 4TATPFtTAT 97 IF (BETAT) 100.101.101 g8 130 C.1(1)MOG8 go G142)-'1G9 100 G(4 TO 102 l0t 101 r1(1)orlrG9 102 G1(2)flG8 103 102 coNr1NUE C 10s flG.10d1)ETA 106 0C10(2).--BETA 107 DC11-8FTA*8EVA £08 IDG12=ALFA*ALFA 109 C I10 PT3-XK123*DQBAR III WEC2-XK120.CM 112 C 113 DO1001~.
114 C 117 fSPISpCI)-0Sp?S(1) c
Ito ~ 1 IF IOVEI 201.2,202
120 201 IF 1C"3SP(1).E0.0) GO re 202 £21 C 122 flSPW1 =OSPC(I) 123 reuTP(1) =OSPI(U-DSP7 124 BOJTPP(1)=tD8UTPc1)-VSPnIC£1)*nT 125 Ge T~t 203 126 C 127 202 () 128 1 ZI-?24I1.DSPIP(I) 120 C fSPU k=DOUT( T )DSPZ 131 C 132 D0UTPPII)*DeUTPjj) 113 DPUTP(1) -DOUTIJ) 134 C 135 :!03 DSPIP(1)OflSP!(£) 136 C E()ECf)W2 138 nWICIf) wXKI5*rBp(I)+WECf1H 140 c
141 flW(I£=Z81c2).DW( )I ~.1(?).0WIP(I
142 nwipmI-DwIlI, DW!CtI)mDW(I)*WIC7 145 C 146 0SC( I )G2-XKI 10*G (I)G C 148 G4(1)u(G4AAG48*.DSP( I)4GCCtWICtI )).ALFA 149 1 *(4*4*$t)I;4'DI~)*11 151 G(1I(GAG6*0)SP(U)G5C*WIC(T))*rMI C 1541 8I 156 c 157 G9( I IOG9A*09S:DSP( I .(r9C*Gr1DSP(TI+( G9E,'nQFwnSP(I) )*DWI C(I)) C 160 PS( 1 wG4( I )G5( I )G8( I 2G9( I) 161 C 162 flE(I)0SUI)+PS2-PSC(I2 16:3 c 16A X50(I)-XKI6*DE(I2 165 C 166 IF (I"IDE) 211.2.212 167 11 1 IFfCDP(12.E0.0) Gft TO 212 168 C 169 E1OP(I2 wDSPIC(T2 DSP2(1).T14.XSDfl)-T12.tLnP C(1) 171 fl6'1f1-0Pfl-DBP2fl) 172 GO To 213 C 174 212 fBP(I)wD8PIlI2,X5D(1)*CT 175 DFlP2g I 2201(1 2.00P2( I11 1(12 .X5D( 1) 176 C 178 c 179 213 DflPR(! )-(DBP(1 2.DeP?)*17.4 180 C G14(1).(n1dAG148.DSP(1).G1An.DW!CrI)).ALrA 182 1 4(S14f+lG4E*nsi()*G14r*fWICI1[2CI2: 183 C 184 G19tI2.G15AG15lSDPCI2.(Gl5C4+1trn.SP'(T),*IWIC(1) 186 G61G6,1B0~![Gf()(1t1f~lD ))Y1*~5 187 1 *IFDPII)0~(I~)"I( 188 C 189 G17(II.(GI7AGl76.flSP(I).Gl7r*Ow1C(1I).1W 190 C P72(t)-G14(1)*GI5(1 )+GI(1)+GI7(f) 192 C 193 PT2S~l)-PT3*PT2(1)*PT2Z.C19 194 C 195 r.1l( I )DSP I )#GIOA.VI 196 C20.(GC'0AC20S*ALFA)*ALFA 197 C.
110,112.112 198 IF (D)G1O(tI) 199 110 IF(G110'DGII-G10(1)+C^IIF+G20) 11121110115 200 111 GI1(1).GIIA+GIIF'CGIl 201 GO TO 114 202 112 IF(GIID*DGI1-GI0(I)+GIlE+G20)) 113.113.115 203 113 C11(I1.GI1A 204 114 DGI3.GI0(t)-G118 205 IF (DG13.GE.0.0) G1I(1)8011(11.OIIC*DG13 206 C 207 G13(11=YKKI6.DSP(t)*DM 208 !WCU(UIIlt.G12.C3(1)-XKII5n 209 D)wC(1)=DW!C(I).flwICU(I2 210 IF (DICfI)2 It-5.115.116 211 115 GIS(1)-0.0 212 GO TO 1000 116 G18t1)uG18A.DWCE1).G188.SI1 (G1.5C*0JWrC)) 21A C 21S 1000 CONTINUE 216 r 217 2 RETURN 218 C 219 END I C TITLE !NCINF 2 SUBROUTINE ENC9INE 3 C 4 COMMON /BLKI / IMenE 6 [nT #IT!MES n1T *NDT 5 lo TIME a D2P 11) G C 7COMMON /BLK2 / UB 'v ,Ppn R 8 o Re DPHIR THETP OY ,PH? .THET 9 20 PST OD" ETA tALlrA ,Rf?AP ALFAQ 10 3., ALT oANY .At!Z .CLO oCL!rA oCLDR it 4o CLDBP .CLDSP o-%RP7 rLPP .CNA rNDItA 12 50 c NIR " Crtflp , C!" n s; o.Cup? .CHJP! nE:LTAA 13 69 DELTAE ,DEL~T.F I(27 . ;" ,ps? OPT27 14 70 nsp(l) 00rPc(2) OT2S(n) oPLAC.") PAJC'l lpM'"(11~ L6 17 COMMON /SLK5 /XKPP pXKQ' .)KO2 ,XKCP .'QKRN to It VCi I TC2 , TCN1 0 TC*0 I tTCN2 , TCD21 20 tCU22 oTC)N3 W'IA a.7A ' 7 20 1o a "IR o ZR Tit PTIP T714 .WNSP 21 4a ZSP vTEI VTE3 *TF4 T71 .TFN2 22 50 TE1D2 aTIDA T I r)2 aT I rlf 23 C 24 COMMON /9LK9 /XKE3 XVE4 PXKE7 ,XK~l XK' 25 l. XKE10 oXKEII .,XrEt? -)KF1 ' I ,YKEIN 26 20 XKE16 DXKE17 X~KE18 Xf19 .I2 2?
C 28 COMMON /BLKIO/ GNI(I7) .FPI(1 ) P2 1(17 .ZTI(17) .GN2(4) 29 t A2Nr)(4) oB,11)D4) It~2j(41 .'PP7(4) .7111(4) ,7127(4) 30 C 31 COMMON /BLKII/ ALFAZ .ALPA7; .1SP7 ,WIC7 1)-3P7 352 to TETZ ,flIZ *9!,IC *ODIC .Rplc .0 iIC 33 2. THEIC apsilc .)MI 1 T A I C .AL7ATC .ALTIC 35 4, ICRPM(2) *RPMIC(2) .ICAj(2) ,AIIC(-) .A~~' AJCIIC(2) 36 So ICWA02)oWFA3I1'(2)pIC 1CwPl(1 . ,F 1 2?).1 Gm , A, S OSASTC 37 6. FS:C ISA~ AS!: .1cpsAs P~SAS!C #PCAIC AG 9. z D t ,;ALT7 41 C 42 C A3 DIMENSION PTA! (2I.PT41P(2),PTA(2),PT4PI2).PLAP(2)ePmT(2).RPMIP(2) C £7 C 48 DO 1000 Im1,2 49 P74I(I) -. XKEI8*PT2S(1[oXKEI'*FRPMU) 50 PT4!P( I)=,5o(3.oPT41 (I)-PT4I0(I)) 51 C 52 PT4(1)oZe115)oPT4(11)-ZI1(5IPT4!P(I) 53 C 54 P741P(I)=.PT41(I) 55 C 56 RPMI(I)XKE9WFPB(I)e.XKEII.AJII)-XKE12WrA'(1)-Y0.IP2(1l so C so IF (IMODE) 182000*2 1 IF (ICRPM(Ik.EQ.0) GO TO 2 61 C 62 RPM(I)mRPNIC(l) 63 GO To 64 C 65 2 RPM(I )-Ze1Ae)RPM(I).ZIlc4)*PP"1I1 I) 66 C 67 3 RPmIPII)wRPMI(I) 68 C 69, WEC1(I)OXKE4*RPM(Il C
71 RPMP( I) .'.5*(RPMP( I ~oRPM( I))
72 RP"MMp(I)u.5e3.eRPMM(I)-RPMMPfI)) 73 C 74 AJI(I).QXKE3a(RPmmP I )-RP4-P(I)) 75 C RPMP(I) -RPM(I) 77 RPMMP4I)mRPMM(I) 65£T 3 gal 3 W£ a(iNlINGO 0001 GaT 3a Cc Q. Q5 611 3 ITT -J 601 3 901 CI'lIIV4M(I)dI~diM CZ S01 3 pot 3 Z01 ti)3iddam-(i)djm OUT 3 66 ZOO0O£'1Z (3aQWII1 4 6 0 96 41 )c I d.A4o~I I I9c4j.VA)G( I )dI 90M S6 tII1.ccaPTNXI)Vld*GI3AX- tI1164M CT P6 3 £6 (I)3rv*( I).LarfvU ICC, Z6 3 16 (I )cv. i) Trv- I).Lnorv 06 (zI,~IL1Iz(I)?v.(siQL 69 .LUEIIC.(I1t- iIrv at 3 49 CI 4;j QqC 99 (I31~u (I)ICv se £1 04, as oor3'Ir)C 1 11 09 D £TOOO£'11 l(QWI) Al 0.4 j 84 C e~qRL I C TITLE 2 SUBROUTINE CONTRL C /BLKI / 1I15DE ADT &ITIHES *DTW) COMMOI~N TIME OD2R of:) to 6 C COMMO8N /RLK2 / US 'VR Wct O~pp .3 THET PHIR DTHRER PAS7T PHT & to RN3 oPE'TA ,AtrA BEPTA:; ALFAR 9 2o PSI '0m 3. ALT' ANY 0AN17 ,CLP ,CCA .CLDR rNDA aCLDSP .CLQR: -rLPq rNr.
it do CLDBP 'C'40n nELTAA 5D CNOP .CND~m .CNlS- C.!Oq T2 DFLTAE ,flELTAR m,27 r~77 PS7 13 6.
,AjCI() .M14' 7. VSPe2) ,OBPf1 .PT2S(2) LLArl)) 16 C PSASL o TSA SU ,QSASL o 1u 17 C1MM /EPLK4 / P5451U AS ASL 18 1. ORIL PRS ASl!
19 C 22 C Wl7, r-IP7 23 CeNMN /PLKII/ ALFA7 ,ALFA7P ,r 'P7 .C4 r . Ic R-Ic . PH I I 24 1 . TH-ETZ oDEZ , P;" r crT4 c ,ALFATC ALTCr 25 2. THEIC .PSIIC ,n:il".
,Y2.. 0C 0. s !D ItrOt IcVsmfl) ODSOICi2) 26 30
.Air v:(;>. i jcn ~(P)
4. ICQPW (2I , o!PMIC1I .ICA:(7) . J! C IC c PSA!Iy P SA 1. 1C 'C.IS6; IA-1, . TC ; 1 . p AS A 29 -5.
.ICDE 7. PsAIIC R~SA!r ,IC7)A pATC DOA11C 32 9. ?F3 X .ALT 33 C* eT v as C C rrF T', RILI1TINE UTILTY vac EyPLA!NATIPI'. OF VALL11T 37 C 38 f" * 39 C do C POLL SAS 41 C 42 PSDEG =PTn/n2R 43 PR)r-5(.PD(-3EP 44 C 45 IF (IMOt) 1.100p2 46 1 IF (ICPSAS.EQ.D) GO Te 2 47 C PSAS-PSASIC 49 POU~vPSA3
so ~ Go TOI
51 C 52 2 POUTZe()PeUT+Z!IC6PBOEGP 53 C 54 PSASoVALLMT(PRUToRSASUoPSASL) 55 C 56 3 PBIGP.PDEG 57 C PITCH SAS ( lie IC P~evIflEr 58 C 59 C 60 QSDEG =2B/92P 08B121 =.5*g3.Q9EG-0ZlEGP) 62 n!nEGPm0~lEG 63 09341 -VALLMT1QR1.0911'J.Q0TL) 64 C o~Z61(9)ogeUT1,GN1I?). ('m2t-'lF121O) 65 QOUTI 66 Q8121F=QP121 67 C 68 08UT2 .&(0oUT+1(0'R2 69 C OOUT.7 .Ze(11)*GDUT3+711(1 1)*!-'Td!
71 C (j2I'C.;jA 72 t 0UT4 -O!6(12)*eUT49Z11 73 C 74 GOJneTI+0T+Q)J3r(l T 75 C 76 QSAS=VALLMT()eUT.QSASU.C'SASL) 77 C C YAW SAS 79 C
s0 ~ RSlEQ -R/2R
81 ROT -. 5*(3.*RaflEG-RBOEGP) 82 RR3EGPmR9DEG 83 C 8d ANYPw.5*(3.*ANY.ANYP) 85 C 86 IF flMOD!3 21.100.22 87 21 IF (ICPSAS.Eo.r%) GO TO ;12 88 c 89 QSAS -PSALIC#PSA21C 90 QeT-RA~ 91 RftNJ? lA2?fC 92 GO To23 93 c 94 22 ReUT1!8± ( 13).ReUTIQN1( I*PT-qP 95 P~UT2.!tl14).RO)UT2,Z1JflA).ANYO 96 QeUT *T".UT14RlIJT2 97 C 98 0SAS-V4LLMIT(Rf4UT.PSASU.RSASLl 99 C 100 23 PRIR:Q1 101 ANYP.A!jy 102 C 103 C AILERON ANGLE 104 r 105 DAT m.5.(oSASP+05Ss) 106 OsAsfl!pSAs 107 C I0 17s IF lmeF) 31,1110.32 109 31 Ir UICflA.Eo.0) G1 rA! 72 C 112 nAOPP wDELTAA-9AD!C.71I' 113 nIAP =P5S-PtOA0ICTT li4 GO Te ?3 115 C C eP*)5 I1o nAIP mnfl 120 C 33 DA;IP-DELTAA 122 C 123 C ELEVATOR ANGLE 124 C 125 DET =.S*(0SASP+0SAS) 126 OSASPOQRAS 127 C 128 IF (1Me0E) 41.100#42 129 At IF (ICDE.Ef).0) GO TO 42 130 C DELTAEDFIC 132 DEIPP =DELTAE-DEDIC*Dy 133 GO TO 43 C 135 42 LTEZ2g p. ()1 P.!, 3.E.!23DP C DE Pp-DEep 138 C 139 43 DFOP=DELTAE 1AO nE!PnDEI 141 C 142 DETLaDFLTAEODEZ 143 C 144 C RUDDER ANGLE 145 C 146 DR! 9.S.(SASP*RSAS) RSASP.PSAS 148 r 149 IF (IMODE) 51,100.52 150 51 IF (ICDR.EO*01 GO TO 52 151 C 152 DELTARUDRIC 153 DROPP uDELTAR-I3RDtC*DT !)RIP ERSAS-PSAfl1C*DT GO T!' 5!
156 C 157 52 DELTARoZ021()*DROPZ6022(4)*DPIPP+ZI21(4)*DRIe7722d(4)DRIP 158 C 159 DROPPmfRep 16C DR!P -RIT 161 c 162 53 DROePDELTAR 163 C 16a 100 RETURN 165 C 166 END I C TITLE A I RFP~t SUB~ROUTINE 41RFRM 3 C COtMON /SLKI / 1110DE I "I o .T VIES .n!
N!)T 5 1. TIME *D2P .
6 C 7 COMMON /RiLI2 / US .V3 Wppp '0 8 1 . P9 s*PHI R TPETP .PSIR APPT #THET 9 2. PSI .:)m oerTA ,ALF4 i 1FTA* .ALFAR 10 3D ALT .ANY & ANZ -CLP .CLrA oCLDP 11 4. CL D930 .CLDiSP CL01 CLPR . C"e A .C14DA '5, Cl ,jDo CNDsP *C11sp rCNQP *CNP0t *nELTAA 6. DELTAE DnEL TAR .127 GC77 0 ' DT727 14 7. DSP12) DOP (:! .pTf2j2 .I'LA(21 *AJC(2) I QPM' (1) 16 C 17 COMMOtN /8LK3 /CD7 . C" I f:7 rA? 2 *CL .%LAl 19 2. CLrij .CLFDLiP . C L F) . CIF. F .pAt' .V7 20 3. A tE A , X fA 5S .CHf-p & sP'N .GYX 21 do K7T mXLT YMHT . YNT .. <Ivy .'qYY 53. XI!! .YIXZ . c y . C Y ! p DC y 3 FLAP 23 6. C41AZ . cI0 o .Cinr , : W '' *CM rLPI'; 24 7. CLP;S .CLDAI; .CL' I . CLDES -CLrSoS .Ckjss 25 X8. cipt CcP~ DN zss .cr A CP S .C N7S .C~jDspq 26 c 0 7 27 Ce4MON /gLKIII ALFAZ .ALF47 'rSP .": i'~P7 28 1& TiiETZ E af~ .P'3r s C .RrPH I 29 2A THEIC apsIic . 1t1 D FETAJ jiALFAIC .ALTIC 33 6. PSAnIC .Irr.sA^, .( *~A 7 1C 0 .I rAe RQeasr PSI ?47. PSAJ1C vPSA2I!C .ICLA .:Arc PArTC IIc DE 35 8o DF71 C DED Ir oicn- AT~ic It1 r. VP )(I. Zfl *X 37 C 38 C rI ME NS8 I NgFFER (60) C 41 IO&TA NVAD/10 /.INTORD/2/ 42 C C 44 IF (IM6f0F) 1.100.?
45 C C INTPIcATI&N Rf-UTINE SETUP C 48 1 CALL MOAENATiUF:~ti-r-iF.ol!
49 C so C 51 CALL At DC62IALTZSPS5).lI.4P) 52 InRAP? m.5*Rl-O*VZ*VZ C 54 qUANI -gSARZ*AREA/XMASS OUAN2 -ALPAZP*VZ CUAN3 -SPAN/(2.*VZ) 57 OUANA -=Q7APZ'0UAN3 58 QUANS NAQEA*SPANJ/YXxX 59 OUAN6 -APEA*SPAN/YI7 60 OUAN7 vAPEA#C&JOft/XyYY VCUAN8 -CHOReD/2..VZI 62 GUAN9 s09AZ'?(jAN8 OUAN1OUOUA4;/V7 6A OUANII-XIXZ/X1XX 65 QUANI2uXIXZ/XIZZ 66 0UANj3wt..0UAN11.-lUA12 QUA1d2..'SP?
68 C 69 ALrA2 -ALFAZP*ALrAVq 70 CDAZ wCDZ.CtIAI.ALPATP*.DA;7ALFA2 71 CLAZ =CLZ+CLAI*ALPAZR 72 CMAZ .CMZCMAI*AL1'AZRCMAI.ALrA2 X~uOUAJ1.CD)AZ-OUAN.CLAZ*ALF&'Q 7A !!UOUAN41.CLA!40UAN1,*CIAZ*ALFA7S 75 CUkN17-G9AR7-CMAZ 76 C 77 fe TO 3 79 C INGATIDN 60 C 2 CALL GPATBNI UFR,; ,RVg,4,Q *Wp9* **tioo.Ri~rt 1. PHIflPHoTDTHEqPSTPPS!DALTlALT) 83 C 84 C 8s PM4T 0PHfR/02P THE? afl4EyP/fl2 87 PST ODSTP/nlp rma (1/968, 91 9ET4 09ETAR/D2R 92 ALFAR-W9/VZ ALFA -ALFAR/D2R 94 C 95 C 3 SP41 -SIN(PHIP) HETL-THFT7*THET DELALi'-ALT-bLTZ 99 C IOC CALL A~nC62(ALToSP~qNl,;Hfe) QBAR -. S*He*(VZ4+1i80., 102 rC9AP -0.3AQR-OPARZ 103 C 104 AWRPR =ALFAR.4ALFAP 105 C 108 nUANj5-n8AP0,AREA/X'iAS 107 AWRPP2-AWPPRbAWRPP CL-DOnlAPP~rA-W7P CLA-CL70CLAI*AWRPR C C SYMMETRIC CUA04TITIES C flRPS=SD!P(fl.DPP(2) D90S~r5Pc1).o5P(2)-,)UAN4 C 119 CASYMMt TRIC OUANT!TIES 120 C 121 flPAv09P(fl.V8P( ) 122 fSPA-DSPfj.fSpj2 TA -T(1,-T(2) 124 C 125 C DlRAG ANDl LIFT IN WIND AXES C DRAG UOUANIS*fCDA*CfDE*EL4AF&DcP*PS+CnflSP*CSOS) X~FIUN~tL+~oo)LA- LnPTSSC~)PDp 129 1 6OUA'~e*CLFQ9Q9 130 r 131 C ACCELERATIONS IN BODY AXES 132 C A1vXZ4 YB-DRAGs.XLlFT*AwPPR A~70BS4vWP-~F 136 A~0A5(8R CP9T CLD*LAPT CA*ETA l *DELTAR QUAM16-A6+XNToTA 0AIwV*BGS~+'A20 142 C tiRDOA1-QUAIlI*e02 G*TNJTRXVT*TS VelaA2+.CUA~l1A W91mA7*VZ*-lS+XZT*TS C, A! OQA7(UN0C4DW3-,IA,(-!
~~-!I%7'mR(m
1 *C'iE*PELAE4C IT)DnpSl+X-p C 1SO P~noA4+UAN1 1OOIJANJ16eXLT*TAS /' UA,\J13 QBDQA5+YMT*TS 4An0QUANI2*0qDoQUAl1,6 C I5d C ANGLF PATFS CF CHANGE C 156 bqlP St.I 159 C 16C C ALT1?UDF t ATE C AL~VOHTLDF-i*WPW-UN IV C N y APJfl ?-Z PFR c 166 ANYftVn-QUAJ18.44.RP))/G c 168 NIA!)V*R/ C
1-10 ~RFUR
C ENI
REFERENCES
1. Anon.: U. S. Standard Atmosphere,
1962. Available from Superintendent
of Documents, U. S. Government Printing Office, Washington, D. C.
2. Ralston, Anthony:
A First Course
in Numerical Analysis.
McGraw Hill, N. Y., 1965.
3. Neuman, Frank; and
Foster, John D.: Investigation of
a Digi'tal Automatic
Aircraft Landing
System in Turbulence. NASA TN D-6066, 1970.
A-4840
FOR INLET PRESSURE FUNCTIONS TABLE 1.-- LIMITS jmax max max
f(i
, 6sp , X
C.ijk 6cspX
i=O j= k= 1
Pressure Functions ima k x
max max max
1 1 fa(Wi c 6sp ) 6sp) fb(wic
6sp a) 1 1
f (w.
' sp 1 fa(ic
fb(wc, 6sp, 2 1 2
1 1 1 f a(wi , M) M) fb(wi, A-48 0 TABLE 2.- LIST OF FORTRAN QUANTITIES Airframe Quantity Fortran Units Description uUBD m/sec Forward acceleration v VBD m/sec Right acceleration wWBD m/sec Vertical acceleration u UB m/sec Forward velocity v VB m/sec Lateral velocity w WB m/sec Vertical velocity
PBD
rad/sec Roll
angular acceleration
q QBD rad/sec Pitch angular acceleration r RBD rad/sec Yaw angular acceleration Roll angular velocity p PB rad/sec q QB rad/sec Pitch angular velocity r RB rad/sec Yaw angular velocity p(o) PBIC deg/sec Roll angular velocity, I.C.
q(o) QBIC deg/sec Pitch angular velocity, I.C.
r(o) RBIC deg/sec Yaw angular velocity, I.C.
SPHID rad/sec
Roll rate
o THED rad/sec
Pitch rate
PSID rad/sec
Yaw rate
PHIR rad Roll angle Ae THETR rad Pitch angle
SPSIR
rad Yaw angle PHI deg Roll angle
A8
THET deg
Pitch angle
PSI deg Yaw angle
eo
THETZ deg
Pitch angle, reference
condition
THETTL deg
Total pitch angle
sin 4 SPHI ND Sine of roll angle 4(o) PHIIC deg Roll angle, I.C.
Ae(o)
THEIC deg
Pitch angle, I.C.
p(o) PSIIC deg Yaw angle, I.C.
A-4840
- Continued LIST OF FORTRAN QUANTITIES TABLE 2.- Airframe Description Fortran Units Quantity Mach number increment AM DM ND Mach number increment, I.C.
AM(o) DMIC ND angle 8 BETA deg Sideslip
Angle of attack
aALFA deg
angle 8 BETAR rad Sideslip of attack ALFAR rad Angle a angle, I.C.
deg Sideslip B(o) BETAIC attack, I.C.
deg Angle of c(o) ALFAIC condition reference of attack, deg Angle ALFAZ aWo ref. condition rad Angle of attack, aWo ALFAZR
Altitude rate
ALTD m/sec
f
Altitude ALT m h Altitude, I.C.
ALTIC m h(o) radians factor, degrees to rad/deg Conversion T/180 D2R pos.
inlet bypass actuator cm Symmetric bp DBPS s
spike position
cm Symmetric inlet
6sp DSPS
s
ND Incremental symmetric engine thrust
6ts TS
actuator
inlet bypass
cm Antisymmetric
DBPA
6bpa
position
spike position
Antisymmetric inlet
cm
6spa DSPA
engine thrust
6 Antisymmetric
ND
TA
ta
coefficient CDA ND Drag CD(c)
Lift coefficient
CLA ND
C L(a)
Pitching moment coefficient
C m(a) CMA ND
coefficient, I.C.
CDAZ ND Drag CD(o) coefficient, I.C.
CLAZ ND Lift
CL(o)
coefficient, I.C.
ND Pitching moment Cm(o) CMAZ A-4840
- Continued
TABLE 2.- LIST OF FORTRAN QUANTITIES
Airframe
Units Description
Quantity Fortran
CD(a)
order term in
ND Zero
CDZ
CDf
in CD(a)
order term
I/rad First
CDAI
CD,
in CD(a)
Second order term
I/rad
CDa CDA2
in CL(a)
ND Zero order term
CLZ
CLf
CL(a)
order term in
1/rad First
CLA1
CLa
Cmf CMZ ND Zero order term in C (a)
C (a)
order term in
1/rad First
CMA1
Cma
Cma2
CMA2 1/rad Second order term in C(a)
D/m DRAG m/sec Drag in stability axes
L/m XLIFT m/sec Lift in stability axes
derivative
Aerodynamic
CDDE I/deg
CD6
e
derivative
Aerodynamic
CDDBP i/cm
CD6bp
derivative
Aerodynamic
I/cm
CDDSP
CD6sp
Aerodynamic derivative
1/deg
e CLFDE
CL
derivative
1/cm Aerodynamic
CLFDBP
CL bp
derivative
1/cm Aerodynamic
CLFDSP
CL6sp
derivative
Aerodynamic
CLFQB 1/rad
CLq
Dynamic pressure
QBAR N/m
qv
Aqv DQBAR N/m Aq = qv - q reference cond.
N/m Dynamic pressure,
QBARZ
qv
°
V VZ m/sec Initial forward velocity
S AREA m Wing area
m XMASS kg Mass of vehicle
c CHORD m Mean aerodynamic chord
50 A-4840
TABLE
2.- LIST OF FORTRAN QUANTITIES - Continued
Airframe
Quantity
Fortran Units Description
b
SPAN m Wing span
kg/m Air density
p RHO
to gravity
G m/sec Acceleration due
g
X XZ m/sec Forward acceleration calculated for
ref. cond.
Z ZZ m/sec Downward acceleration
calculated for
o ref. cond.
for forward
Biased quantity
XB m/sec
Xb
acceleration
downward
Biased quantity for
ZB m/sec
Zb
acceleration
angular
Biased quantity for pitching
XMB rad/sec
Mb
acceleration
to thrust
m/sec Forward acceleration due
X6t XXT
Z6t XZT m/sec
Downward accel. due to thrust
L6t XLT rad/sec Rolling acceleration
due to thrust
M6t XMT rad/sec Pitching acceleration due
to thrust
N6t XNT rad/sec
Yawing acceleration due to thrust
Ixx XIXX kg m Rolling moment of inertia
Iyy
XIYY kg m Pitching moment of inertia
Izz
XIZZ kg m Yawing moment of inertia
m Product of inertia
Ixz XIXZ kg
derivative
Aerodynamic
1/deg
CYB
Cya
Cy r CYDR
1/deg Aerodynamic derivative
Cyr
CYRB l/rad Aerodynamic derivative
C£8
CLB 1/deg Aerodynamic derivative
Cjea CLAB 1/deg Aerodynamic derivative
CLDA I/deg Aerodynamic derivative
C£6a
A-4840
QUANTITIES - Continued
TABLE 2.- LISf OF FORTRAN
Airframe
Quantity Fortran Units Description
derivative
1/deg Aerodynamic
CLDR
CZ6
r
derivative
CZ6bp CLDBP I/cm Aerodynamic
1/cm Aerodynamic derivative
C6sp CLDSP
Aerodynamic derivative
Czr CLRB 1/rad
CLPB i/rad Aerodynamic derivative
Cp
1/rad Aerodynamic derivative
Cm CMAD
derivative
Cmq CMQB /rad Aerodynamic
Cm6e CMDE 1/deg Aerodynamic derivative
Cm6bp CMDBP I/cm Aerodynamic derivative
Cn CNB 1/deg Aerodynamic derivative
derivative
Aerodynamic
1/deg
CNDA
Cn6a
Cn CNDR I/deg Aerodynamic derivative
6 r
derivative
Aerodynamic
1/cm
CNDBP
Cndbp
derivative
i/cm Aerodynamic
CNDSP
Cn sp
Aerodynamic derivative
Cn CNRB S/rad
I/rad Aerodynamic derivative
Cnp CNPB
Ck CLBS 1/deg Aerodynamic derivative
C CLPBS 1/rad Aerodynamic derivative
s r
I/rad Aerodynamic derivative
Cr CLRBS
derivative 1/deg Aerodynamic CQ CLDAS
a
CG6r
CLDRS 1/deg Aerodynamic derivative
Cb
CLDBPS I/cm Aerodynamic derivative
52 A-484bp
52 A-4840 TABLE 2.- LIST OF FORTRAN QUANTITIES - Continued Airframe Quantity Fortran Units Description Cs CLDSPS 1/cm Aerodynamic derivative s sp sC CNBS I/deg Aerodynamic derivative Cnp CNPBS 1/degad Aerodynamic derivative derivative Aerodynamic 1/rad CNPBS
Cnr
s derivative Aerodynamic 1/rad Cnr CNRBS CS CNDAS i/deg Aerodynamic derivative a Cn6 CNDRS 1/deg Aerodynamic derivative
derivative
CNDRS 1/deg Aerodynamic
Cn6r
Cnb CNDBPS I/cm Aerodynamic derivative p s C6p CNDSPS I/cm Aerodynamic derivative
sp
cos aWo CALFAZ ND sin wo SALFAZ ND cos ao CALFZ2 ND sin2 cwo SALFZ2 ND n ANZ g Normal acceleration z DT sec Frame time
SAS Control
Roll SAS deg PSAS Psas qsas QSAS deg Pitch SAS.
rsas RSAS deg Yaw SAS
6a DELTAA deg Aileron angle A6e DELTAE deg Elevator angle 6r DELTAR deg Rudder angle de DETL deg Total elevator angle kpp XKPP sec SAS gain
limit
deg Psas upper
PSASU
Psas (U.L.)
limit Psas lower PSASL deg (L.L.)
Psas A-4840 - Continued LIST OF FORTRAN QUANTITIES TABLE 2.- SAS Control Fortran Units Description Quantity SAS gain kqq XKQQ sec XKQ2 sec SAS gain kq upper limit qsas Total deg QSASU qsas (U.L.)
lower limit Total qsas deg QSASL (L.L.)
qsas limit qsas upper Lagged deg QBIU (U.L.)
qsask limit qsas lower Lagged deg QBILL qsask (L.L.)
sec SAS gain krr XKRR XKRN deg/g SAS gain krn acceleration at nose ANY g Lateral nyn upper limit RSASU deg rsas rsas (U.L.)
lower limit deg rsas RSASL (L.L.)
rsas Time constant sec TC1 Tpl TC2 sec Time constant Tr2 sec Time constant Tq2 TCN1 sec Time constant Tql TCD1 constant TCN2 sec Time Tq TCD21 sec Time constant Tq3 TCD22 sec Time constant Tq3 TCN3 sec Time constant Trl velocity Roll angular deg/sec PBDEG P Pitch angular velocity q QBDEG deg/sec deg/sec Yaw angular velocity r RBDEG frequency for Undamped natural rad/sec WNA wna aileron servo servo ratio of aileron Damping ND ZA Pa frequency for Undamped natural rad/sec WNE Wne servo elevon of elevon servo ratio ND Damping ZE Pe natural frequency for wnr WNR rad/sec Undamped rudder servo servo of rudder Damping ratio ND ZR Pr A-4840 TABLE 2.- LIST OF FORTRAN QUANTITIES - Continued SAS Control Quantity Fortran Units Description Psas (o) PSASIC deg/sec I.C. for Psas qsas(O) QSASIC deg/sec I.C. for qsas I.C. for aileron a(O) DAIC deg deg I.C. for elevon e(o) DBIC for rudder deg I.C.
6r(O) DRIC condition for elevon e(o) DEZ deg Reference Psas(O) PSADIC deg/sec I.C. for psas rate isas(o) PSADIC deg/sec I.C. for rsas rate for aileron rate DADIC deg/sec I.C.
6a(o) e(o) DEDIC deg/sec I.C. for elevon rate I.C. for rudder rate DRDIC deg/sec 6r(o) rsasl o) RSAIIC deg I.C. for first part of rsas equation ( rsas2(o) RSA2IC deg I.C. for second part of rsas equation Inlet AMm DMT ND Measured increment of Mach number attack Measured angle of ALFAT deg am m BETAT deg Measured sideslip angle
6spo
DSPZ cm Reference condition
for inlet spike
Wico WICZ lb/sec Ref. condition for inlet airflow at ND Compensation for signal pressure Ps/Ptm o PSZ
reference condition
(Pt /Pto) PT2Z ND Compensation for pressure recovery at reference condition ND Command signal for bypass control (Ps/Ptm)c PSC
6sp
DSP cm Inlet spike
position
signal pressure
Ps/Pto PS ND Bypass
cm Bypass actuator position
A bp DBP
Total bypass actuator position
bp DBPR cm
A-4 40
TABLE 2.- LIST OF FORTRAN QUANTITIES - Continued Inlet Quantity Fortran Units Description actuator DBPZ cm Ref. condition for bypass bpo Awic DWIC kg/sec Inlet airflow Pt /Pto PT2 ND Inlet pressure recovery pressure recovery PT2S ND Incremental A(Pt/Pto ) f (m) G1 ND Spike $ bypass command function function G2 ND Bypass command fbp(a,Mm) ND Bypass command function fbp (nzm) G3 Signal pressure function G4 ND fb (ic,6sp,a)
ND Signal pressure function
fb(Wic,M) G5
Spike command function fsp(nzm) G6 in.
fsp (am) G7 in. Spike
command function
fb (ic,6sp,a) G8 ND Signal pressure function G9 ND Signal pressure function fb(wic,6sp)
Unstart boundary function
G10 in.
6sPd
fca(6sPd)+fca(B) G11 kg/sec Unstart boundary function
fca(a)
G12 kg/sec Unstart boundary function
fca(6spM)+kil5AM G13 kg/sec Unstart boundary
function
fa(Wic,6sp,a) G14 ND Pressure iecovery function
ND Pressure recovery function
fa(wic' sp) G15
, spS) G16 ND Pressure recovery function fa(Wic
Pressure recovery function
G17 ND
fa(Wic,M)
fd(wic) G18 cm-sec/kg Shockwave position function
fl(M) G19 ND Incremental
press. recovery function
fcs(a)
G20 in. Unstart boundary
function
Til TI1 sec Time constant
Ti2
TI2 sec
Time constant
Ti4
TI4
sec Time constant
ki5 XKI5
kg/cm-sec Bypass
loop gain
ki6 XKI6 cm Bypass loop gain A-4840 QUANTITIES - Continued 2.- LIST OF FORTRAN TABLE Inlet Description Units Quantity Fortran Bypass command gain XKI10 ND kil o Spike command gain cm ki12 XKI12 Unstart function gain XKIl5 kg/sec ki S function gain kg/cm-sec Unstart kil XKI16 cm Spike gain kil9 XKIl9 gain kg/sec Engine airflow ki2 XKI20 recovery gain pressure ND Incremental XKI23 ki23 servo freq. of spike rad/sec Undamped natural WNSP Wn servo ratio of spike ND Damping ZSP Psp sec Time constant TM TIDM sec Time constant T TIDB B sec Time constant Ta TIDA function command for bypass cond.
Ref.
ND G2Z fbp (awo0) function spike command cond. for cm Ref.
G7Z fsp(awo) for z-transform mode control ND I.C.
ICDSP integration z-transform mode control for ND I.C.
ICDBP integration position I.C. for spike cm DSPIC 6p(o) rate spike position cm/sec I.C. for DSPDIC 6sp(o) position I.C. for bypass cm DBPIC 6bp(o) rate bypass position I.C. for cm/sec DBPDIC bp() Engine deg Power level angle PLA PLA for exhaust nozzle signal Command cm AJC Ajc area
rotor
incremental engine
Command
%
RPMM
N
speed
speed
engine rotor
% Incremental
RPM
Nm
ratio pressure burner Primary ND PT4 Pt /Pto A-48 0
TABLE 2.- LIST OF FORTRAN QUANTITIES - Continued
Engine
Quantity Fortran Units Description
fuel flow
Incremental primary burner
%
WFPB
Wfpb
rate
rate
afterburner fuel flow
WFAB % Incremental
Wfab
AJ cm Incremental exhaust nozzle area
Aj
Incremental thrust
T %
t
WEC kg/sec Incremental airflow demanded by engine
Wec
Tel TE1 sec Time constant
Te TE3 sec Time constant
Te TE4 sec Time constant
TedI TED1 sec Time constant
Ten TEN2 sec Time constant
Ted2 TED2 sec Time constant
Ke XKE3 cm /%N Gain
Ke4 XKE4 (kg/sec)/%N Gain
Ke7 XKE7 %6t/cm Gain
Ke
XKE8 ND Gain
Ke9 XKE9 ND Gain
Ke10 XKE10 %6t/%wfpb Gain
Kell XKE11 1/cm Gain
Kel XKE12 ND Gain
Kel XKE13 l/%N Gain
Kei XKE14 %wfpb/%N Gain
Ke1 XKE15 %wfpb Gain
Kel XKE16
% t/%wfab Gain
Kel XKE17
%wfab/deg Gain
Kel8 XKE18 ND Gain Kel9 XKE19 %wfab Gain Ke2 O XKE20 %6t Gain ICRPM ND I.C. mode control for z-transform integration
N(O) RPMIC %N
I.C. for engine rotor speed
A-4840
QUANTITIES - Concluded TABLE 2.- LIST OF FORTRAN Engine Quantity Fortran Units Description ICAJ ND I.C. mode control for z-transform integration Aj (O) AJIC cm I.C. for exhaust nozzle area I.C. for exhaust nozzle area rate (0) AJDIC cm /sec Aj AJCDIC cm /sec I.C. for command exh. noz. area rate ND I.C. mode control for z-transform ICWFPB integration flow primary burner fuel %Wfpb I.C. for WFPBIC wfpb(O) ICWFAB ND I.C. mode control for z-transform integration afterburner fuel flow WFABIC %wfab I.C. for A-4840 Or oo Figure i.- Three-view drawing of the aircraft.
pSa ~1 e
- "Psas
inpi
Stlet
sI -rp L4 $
!
/P-o
N /P
Figure" ' 2.-r o
RpenIa Ee
n
tl ni ne sys t.ea
igueI 2-
propulsion system.
2.- Representation of aircraft
Figure
3 i 231 50 HEETS 5 SQUARE 50 SHEETS 5 SQUAR 4 2 382 4e 3 00 HTS SQUARE
aors a
ac,
Sbp de
sy sp 3t
7-,& p1roerlo
voi
n
,1 7qok I ,t
- Dor* Lf7
of Lft
p6 celera.2o S u W
L e pO F
Fore , i ' Forces e&
I _es > Sod~ ej in body aexes
EUl4Cr a nle
simulation.
Figure 3.- Airframe O0 BYPASS - MEASUREMENT BYPASS COMMAND tm COMMAND BYPASS CONTROL DYNAMICS I -: DYNAMICS + bp 6 + Ti 4 f m) ki 10ki O
1 ~r 5 13m) i t(1 + Ti 2 s)s
s L ----- - --
a 1 m fbp (awm, Mm) Ptm \Ptmm 1+T.,r //Wi: O
1 Arm ---- 7
DIFFUSER IM 1+TmsI DYNAMICS - SIGNAL PRESSURE Wi 1 + 1 -- I +i sps + 1 s
nm i bp (n~m
fbp ("1,)fb (Wic NP) 1+T '(FROM ENGINE J S---- - -L + ~+ I .
.
PRESSURE RECOVERY 7 t tt
S-
fb (Wic sp, a) a
SPIKE COMMAND % .
i. . P + (TO ENGINE) + .b ci, ,spl + .
ki 12
sp,
a,-f+ ( ic, '")
+ + sp (awm ib (wic, M) M 'a (Wic sp.)
a (Wic, M) ki 19 SPIKE DYNAMICS 1 I sp + sp spIm1 ++2 psp s s L + - - - 1I Wnsp ;p+ UNSTART CHARACTERISTICS I - - X, 0 L J fd (wic) UNSTART Wicu hsp o Ca 0a FI + ,pu r --- - fcf, (0 (cs (CL a + M "a (bsp, M + Ki 17 r pd hspd , I L w Figure 4.-Inlet block diagram.
+ +
i---- -}-Q~B
ke t9
aa 7t '
eI
r.ow I-I-
1 I
.TI .i • i- 1
Figure 5.- Engine block
diagram.