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Appendix E GUIDANCE EQUATIONS E-1/2 Appendix E GUIDANCE EQUATIONS E-1/2 Appendix E GUIDANCE EQUATIONS L INTRODUCTION This appendix describes the operational IGS guidance equations. In general, these equations have been derived in Appendix A and in ref- erences 1 through 7 listed in Appendix H. Certain portions of the guidance equations are presented which have specific application to the GEMINI IGS and have not been derived in the refer- enced documents. A discussion of the IGS equations as implemented in the simulation has been included in this appendix to present the simulation oper- ation in moredetail. Il. DESCRIPTION OF IGS ASCENT GUIDANCE OPERATION This section defines the operation of the Ascent Guidance equations dur- ing launch. Numbers in parentheses refer to areas or blocks in the Ascent Math Flow Diagrams (Figures E-1A and E-1B). See Table E-I for the definitions of symbols. The platform is aligned as described in Appendix A. The word "eontinuously"' when used in the discussion of computer operations means that the information is updated at approximately 0. 5-sec. intervals. A. FROM START TO PLATFORM RELEASE The computer will first be turned to the Ascent mode. All quantities which require initialization are contained in block A102. Agena ephemeris data will be inserted into the computer approximately 60 sec.prior to launch. This information will be continuously updated (A112) and will be used to de- fine the azimuth orientation of the platform X-axis with respect to East (y) and the angle between the orbit plane and the launch site (8). The initial conditions on the spacecraft velocity along platform axis (A117) and the initial platform roll gimbal angle @y - A116) wiil also be computed continuously. At approximately 30 sec. prior to launch, the platform will be released from torquing.* The guidance system is now in the inertial mode. *As of 28 January 1963, this time — 30 sec. prior to launch — is not definite and may eventually be "time of engine ignition." I 9 8 I 7 ih : 6 | 5 4 I 3 2 I 1 REVISIONS sym [enara novice DESCRIPTION pate [ewx] arprovat A RELEASED URfea MALCIra B RELEASE WTTe : FROM Aus A226 & 280 SLOW LOOP (2 SAMPLES/ SEC) oe EROMUEYEC All4 A153 PLATFORM COMPUTE All RELEASED fee SIN #COS ACCELEROMETER DI 36 A132 : Oe to, SUBROUTINE ae At = AttAts | (Fx, Fy, Fe) ANS Ats:0 Al48 | A\54 TO Or. = On Nzo= SIN Ye SIMULATIONBoE Le2 - Ori + On Na =COS ¥COSO, oes cy Yer = Vw N2r=SIN Od Allé PH AIS3 pacaraia Wa =Wae 6Y4=SOn26Q.2O ASCENT Ny = SIN § RteX? +2472 f N 2=COS ho = " Bees ° R 2 =VRE a£ Nes =COS*,b SINGb Te=175 A¥y=AQy=A@y-O INITIALIZATION @n=Cs-X¥+90 aK aa -— : Vir*O Go = 40-0 LC 4A, 4C,4D4E,4F+ ¢ ‘ eg [tse-% To Biase GOStsceeee Uae61-0 LCtc. 4B- _—*18,204 GeeCOS82COSsCaCO |AII7 aé A202 A155 ASG _ AIST AISB VatVin VyuzO . LC 2\,24,+ SdOe SINS Sake [este -t}* ta-% Dart tant X= Ko Ko= Vai 2 = cS A = ByAo Y=Vo Le Son Ze2 Ver A\SO §Ww:0 Zo Tus 100 A227 x= Yat AN Eee Alél : a Qu =Qo B= Oy n==Vx sti At -At,=0 Alls ag: Aso Dw = Dw + Ki (COS*8.)‘COS *8(AL) nw =71.25 "fee. | me | le On = OntGn AL Ou=O0 te * tz O@n- 90° Beeogek. cosy (At) Yun +K’s SIN YA) Vatisny = Wai Vycieny = Vi A\S\ TO Veti-n = Vee Vans te x 102 Ce Vai: Vai 1Aa X = X+B X(t) A106 Z=Z+AZ (tu) READ Tg A\52 A\35 AX=-AnZo Vai. = Vai) FadaBt AértAn Xo Wi = Vy (inn tFy-Sy AL Vai = Vein tFe-32At Ale4 [ eeu A\36 | X#X4 (Vat Vari ‘= “Poom All2 Al25 Ye Y+(WitWeda) : A232 COMPUTE G-R= (G-2)+Abt (Re-W’) tar -Ce Ze Z +(e tVorieahe A Ale7 cost COS (9-2), S/IN(D-11) lAQa =i SINS+ SIN 8(K5 HGSIN OKA ney, CALCULATE SIN SIN ¥= + SIN COS(O-R) hereeres | een . a= 3) 1 *Du-1-25 ATR COS On oe sas (+ 6 ta-Ce-ATR Be SET- BY DCS SIN Yn COS Wy S/N @-S2) ————_ WHEN UP DAG SIN &=-a,COSL+a,SINL COMMAND . cos y+|->pSIN2% RECEIVED A\68 e AI39 Allo A126 YE-PCOSOn COMPUTER aaa OP oat RUNNING ON is= y=-GSIN Pw DO-05 - [ee eee. A\66 + On -On + Ou Ab On=6u+6nu At Wn = Yu t¥n At Uae Al46 A169 ~Veur-Va" CALCULATE Vxup - Xo S¥n=Y¥n At! ; A\47 SOn=On AU Al2e Wat = Weir (Vye= Vr) SOx =On AX! Vaue = VxCi- 1S t (Vxi- Vx (é-1)) Viz Vel+ (V2/-Vaur) Veue = Vz (t-\)6t (Vzi- Vz(i-)) Vxi = Vi + (Vie -Vaur) : Vove WirtWi- Vv (i-1)) XIOS i A129 [ease ASCENT Tosve Ty Tu +50 | | | | ee a eS Eee Ee Eas LIST OF MATERIAL OR PARTS LIST UNLESS NOTED BREAK CORNERS DESIGNED cATE INTERNATIONAL BUSINESS MACHINES CORP, OUTSIDE MIN MAX FEDERAL SYSTEMS DIVISION ACEClandaions AnD ocenaaoesl| Set CLK ae papEmAnisORAyEs WEN VORES22 EET en x: rea BeesWetFacaanee on bop GEMINI COMPUTER DECIMALS DECIMALS ANctes]} GROS MATH FLOW DIAGRAM DRAWING CHECK ASCENT ; per] ASTOstet U2: = 2= faaro | EE DESIGNa APPROVAL CODE IDENT NO.| SIZE pA} ay dered anese F J62- 564-002 re TREAT| s SCALE wr : [sneer 40F9 I 3 I 8 I 7 I 6 T 5 I 4 I 3 I 2 | 1 Figure E-1A. GEMINI Computer Math Flow Diagram Ascent E-4 I 9 | 8 7 l o l = l = 1 1 = _L O° a REVISIONS N SYM JENGRG NOTICE) DESCRIPTION DATE Tenx APPROVAL 2 A RELEASE Titel Paton € B RELEASE Tufes| > N xe} ASCENT FAST LOOP gE A\55 Al49 a Aze7 Bin SIN”(RNac-RNes~ Neo) — BeOS A2is SIN AY =Nny Nze- nyNes- Nzo 1 V EVKEE HV AY =Sinay (14+ SINZAY_) |_| Veve wt: WGOST = A25\ I A2ZOs VeryVytNyVyt Ve 4) TO ZERO Vp=(VkX+Vy Y+Ve2)(R™) A2l6 > i ie A252 Pre-nxX+ny V+ Z Sep =3-(w'\?7R Yo =By-AY GIMBAL ANGLE SUBROUTINE 4 =Bn"-Bm x105 (fat.SsDEFINED 4 ¢ az30 A2I7 7 i =z = YWru = Yd Az58& x105 oe Wa) on ade ca . Te: Wiel-stu On= Oo > Du = De -90) Qr=QuWn™! Oe = Qu (i+ UST)" | feo! (0 +90) A253 Gp =-5lAn +e) . Dei=DetS Du Suey 2% AZ4S GEMINI Wre=VeLt+SWn GQsv dyihear) Baeon (3 VOUTS/DEGREE) SFA Orit+SOn : = =— Sy |+vaw(LEFT) + PIT boaaay [mca ee esas Boe D%AQ , A; BY -Y, = Fp a SIN Agn = Ger Ar AREO+30° AD? = On 2 gn 3(5|N Aan\+ (SIN gre) AG*O, Or, J A244 LIMIT ALTITUDE ya2i9 = A232 ERROR SIGNAL AIG7 To “t-te KBs] $ TOF A256 LV SINB= z¥2 2 Me eS 1A¥./ < 20 = Ddy= +(N248 +A) +ROLLCC Ww) B= Sina +58) IDSs} < 2O Aviv +(Na, AB + Nez AY)- Yd |+¥AW (LEFT) aay \" AG: +(Nes AS - Nag A¥)- Od |+ PITCHOOWN) . a N-1 = Q Qn == Qe- Sas | : Wa -1 = Ww Aer Qe? Os-KYye | A2s7 LIMIT ALTITUDE SIN -s VePVrVi oweie T: SINT(I+SIN #T7/6) COMPUTE COSINE T A220 Avi s ce | oe - es ee IAeuls GP AV=Ve-V+\, *Va Al53 Sra = Nee" PAB Ar Sit ; GUIDANCE A221 Srp =-AsVP*- SR cess = A\e *AV-a¢8Tu Kio = [C*T6*(Ge--5)] Qu = AV(C'Y' Ke= Re-R+Te Ve (Qg-!) a V/DEGREE) AQ=Qn-Qn-y Wor = Ke Kio A247 Ae __————t Ki =-Pa + Te Va(Qe-/) Rie A249 acer rere, A208 Wyy = Ki Kio AVxb = Vga= Ag Sra s Wa eWn-inll e +AQ + 72 (AGE 1Ys (AQ))3 ED oieAVyb =Vop=Aq Sr By = Va /AVe Bn =Bgn +&+ To (Qe~1) Wer | A209 By = Br ~Te(Q-l) yy A235 Tomes A268 Ko SINT Eero <eD B * . 24 - Vg? Vq- AU Ks A223 A270 j EXIT A210 Wee aw Ser (C*) oo ASCENT A269 P = (-\W*- Wg *Wer) FAST LOOP 1.5- & AS,,= O = AY= O 7 ADv= O A2i2 Aec4 ‘TO A260 Vat =Vg - 1854E Ks x105 2 2 x J &Tuuw = (Vag e+ + Vag) (Ag) - gere) 10S Vac (Ae Bag (& ASCENT Aal32 200-% + | A2ZZ25 : ms 1823*QeToMea ((B EAEWeptSgrV2 ieee ty(oe Peete (oreirnine.ne. Artsinicarion'|| aasies Lael[ LIST OF MATERIAL OR PARTS LIST UNLESS NOTED BREAK CORNEAS DESIGNED DATE INTERNATIONAL BUSINESS MACHINES CORP. A226 OUTSIDE MIN MAX FEDERAL SYSTEMS DIVISION INSIDE x NEW YORK 22. ET ‘ALL DIMENSIONS AND TOLERANCES DESIGN CHECK 590 MADISON AVE. A APPLY TO FINISHED PART A= (an-T)2+(23, VeVe)2I| ASS UNLESS OTHE SPECIFIED DIMENSIONS, ARE IN INCHES TOLER, ANCE ON ee4 eee DECIMALS2 PLACE DECIMALS3 PLAC ANGLES DRAWN. ChomenaBeT 15-44 "CEMATHMINFLOWCOMPUTERDIAGRAM VAENa- AACAT DRAWING CHECK i i aeeg| Aen z Chie DESIGN APPROVAL CODE IDENT NO.] SIZE ‘ 2 TT eda bad “ssn” F [62-54-0020 g SCALE WT sneer 5 OF @ _ eae i 8 7 I 6 T 5 I 4 | 3 2 | 1 Table E-1 SYMBOLS FOR MATH FLOW A, ALPHABETIC (CAPITAL) A3 Stored constant used to inhibit spacecraft yaw angle computation. A4 Stored constant used to limit spacecraft allowable yaw angle. As =a 23/9 v2p Ag = dva/aV Sensitivity coefficients used for Spacecraft Insertion Velocity Adjustment Evaluated at A7 = drg/OR perigee, -1 Ag 8 = [aralav | Pp Ag = [ arp/av] “1 Same as above only evaluated at apogee. a C* Effective exhaust velocity. Initial eastward velocity at launch point due to Cy earth rate, C5 Constant used to define orientation of spacecraft Yp axis; with respect to east, while vehicle is on the launch pad.
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