ASTP [SA-210) LAUNCH VEHICLE OPERATIONAL FLIGHT TRAJECTORY . - Ibiblio
https://ntrs.nasa.gov/search.jsp?R 19760004113 2017-10-31T12:25:30 00:00Z Contract WAS8-4016 Apollo/Soyuz Test Project ASTP [SA-210) LAUNCH VEHICLE OPERATIONAL FLIGHT TRAJECTORY DISPERSION ANALY SlS VOLUME I
i I TECHNICAL NOTE DRL 444-V4a ASTP (SA-210) LAUNCH VEHIrLE OPERATIONAL FLIGKT TRAJECTORY DISPERSION ANALYSIS VOLUME I A p r i l 4 , 1975 CONTRACT NAS 8-4016 APOLLO/SOYUZTEST PROJECT FLIGHT TECHNOLOGY BRANCH CHRYSLER CORPORATION SPACE DIVISION Prepared by: N. W. Williams, G. W. Klug and F. A. Ransom Approved by: Performance and Mission Analysis Group ,ED. 3 R. D. T a y l o r , 'Managing Engineer F l i g h t e c h a n i c ss e c t i o n & Swider, Manager Technology Branch ,,d ' J &/dL//. R. H. Ross, Deputy P r o j e c t Manager Vehicle Systems
FOREWORD This document i s Data Requirements L i s t (DRL) Item 444-V4a. It is Volume I of t h e two volume documentation required f b r t h e ASTP (SA-210) Launch Vehicle Operational F l i g h t Trajectory Dispersion Analysis under Contract NAS 8-4016, Schedule 11, Modification MSFC-1, Amendment 199. a s s o c i a t e d Guidance Hardware Error Analysis i s documented s e p a r a t e l y , The AS Volume 11, because it contains c l a s s i f i e d m a t e r i a l . Acknowledgements a r e made t o the personnel of Marshall Space F l i g h t Center SA&I-EL24 f o r t h e i r a s s i s t a n c e and cooperation.
TABLE OF CONTENTS Pag e . TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . DEFINITIONS AND SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . 0 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 2.0 DISCUSSION . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 M i s s i o n D e s c r i p t i o n . . . . . . . . . . . . . . . . . . . . 2.2 Launch V e h i c l e and T r a j e c t o r y D e s c r i p t i o n . . . . . . . . . 2.2.1 L a u n c h v e h i c l e . . . . . . . . . . . . . . . . . . . 2.2.2 F l i g h t Environment . . . . . . . . . . . . . . . . . 2.2.3 F l i g h t Sequence of E v e n t s . . . . . . . . . . . . . 2.3 D i s p e r s i o n E r r o r S o u r c e s . . . . . . . . . . . FOREWORD 2.4 3.0 4.0 5.0 T r a j e c t o r y D i s p e r s i o n and A n a l y t i c a l P r o c e d u r e s . 3.1 T r a j e c t o r y D i s p e r s i o n s . . . . . . . . . . . . 3.2 S-IVB S t a g e F l i g h t Performance Reserve . . . . GOVERNMENT FURNISHED DOCUMENTATION . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . . . . RESULTS DISTRIBUTION . i ii iii iv 1 4 5 5 5 5 6 6 7 8
LIST OF TABLES Table . Events . . . . . . . . . . . . . . . . . . . 1 V e h i c l e Weight Breakdown 16 2 F l i g h t Sequence of 17 3 Three Sigma Tolerances 4 . T r a j e c t o r y D i s p e r s i o n s a t S-IB/S-Ivs S e p a r a t i o n , S-IB Propul ;ion/Non-Propulsion Three Sigma Deviations . . . . . . . . 20 T r a j e c t o r y Dispersions a t S-IB/S-IVB S e p a r a t i o n , S-IVB Propulsion/Non-Propulsion Three Sigma Deviations 25 T r a j e c t o r y Dispersion Envelope a t S-IBIS-IVB S e p a r a t i o n , Combined S-IB and S-IVB S t a g e Three Sigma Deviations . 30 T r a j e c t o r y Dispersions a t O r b i t I n s e r t i o n , S-IB Propulsion/Non-Propulsion Three Sigma Deviations . 35 T r a j e c t o r y Dispersions a t O r b i t I n s e r t i o n , S-IVB Propulsion/ on-TropulsionThree Sigma Deviations . 43 . 18 T r a j e c t o r y D i s p e r s i o n Envelope a t O r b i t I n s e r t i o n , Combined S-IB, S-IVB S t a g e and IMUThree Sigma Deviations 51 Three Sigma F l i g h t Envelope of P e r t i n e n t Design Parameters, F i r s t Stage F l i g h t 58 . . Performance T r a d e - o f f s a t S-IB/S-IVB S e p a r a t i o n . . . . . . . . 60 . 61 Performance T r a d e - o f f s a t O r b i t I n s e r t i o n Large Guidance P l a t f o r m Azimuth Misalignment E f f e c t s a t OrbitInsertion . S-IVB S t a g e F l i g h t Perf orrnance Reserve . . . . . . . . . . . . . 62 63
DEFINITIONS AND SYMBOLS Aerodynamic Heating Indicator qVr 1 dt I q dynafiic pressure Vr :relatSve velocity a t tota! :angle of a t t a c k ;- Aerodynamic Load I n d i c a t o r Product of dynamic press.,re 3nd sngle of a t t a c k . Altitude Vehicle a l t i t u d e above t h e reference e l l i p s o i d measured aiong the geocentric position vector. Angle of Attack, Pitch Angle between the p i t c h ?lane compocent of t h e r e l a t i v e velocity vector and the o n g i t u d i n a l axis of t h e vehicle, measured poaitive nose up. Apogee Altitude Apogee height of t h e osculating conic above t h e reference e l l i p s o i d , referenced t o t h e e q u a t o r i a l radius, 6378165 m t e r s . Attitude Command Eulerian angle command,derived by t h e guidance system and transmitted t o t h e c o n t r o l system. Attitude Error Difference between t h e vehicle a t t i t u d e ( p i t c h , yaw and r o l l Eulerian angles) and t h e vehicie a t t i t u d e command. Axial Force Component of t h e r e s u l t a n t aerodynamic force along the vehicle longitudinal axis (X axis of PASCS h ) , measured p o s i t i v e toward t h e nose of t h e vehicle. Descending Node Argumsnt Angle meaaured i n t h e e q u a t o r i a l plane between t h e o r b i t descending node and t h e space fixed launch meridian defined a t Guidance Reference Release. Component of t h e r e s u l t a n t aerodynamic force along t h e relatLve velocity vector. meerured p o s i t i v e opposite t o t h e v e l o c i t vector. Dynsmic Pressure 4 x ( s i t y x) (Relative
KBFINITIONS AND SYMBOLS (CONT ' D) Earbh Fixed Cross Range Ye component of PUCS 10 position vector. E a r t h Fixed F l i g h t Path Angle Angle between the e a r t h fixed v e l o c i t y vector and t h e e a r t h fuced geocentric p a s i t i o n vector (PASCS 11) , measured p o s i t i v e downrange from t h e p o s i t i o n vector. Earth Fixed Position Position vector/cornponents i n an earth-fuced pad-centered plumbline coor. -.;late system. The Xe a x i s i s c o i n c i d e r twith t k e reference e l l i p s o i d normal, p o s i t i v e upward. The Ze a x i s i s p a r a l l e l to the earth-fixed ainling azimuth and i s p o s i t i v e downrange. The Ye d s comp l e t e s a r i g h t handed s y s t c n . ( p S l . 510) E a r t h Fixed Velocity Velocity vector/components i n FASCS 10. E a r t h Fixed Velocity Magnitude ie2 fe Z i " L Le Eccentricity E c c e n t r i c i t y of t h e osculating conic. F l i g h t Azimuth Angle d e f i n i n g o r i e n t a t i o n of t h e space f i x e d coordinate system downrange a x i s , Zs, a t Guidance Reference Release, measured p o s i t i v e e a s t of n o r t h i n plane normal t o t h e space f i x e d X s axls. Geocentric Declination Angle between t h e geocentric r a d i u s vector and the t r u e e q u a t o r i a l plane, measured p o s i t i v e north of t h e equator. Geodetic Latitude Angle between t h e reference e l l i p s o i d normal through t h e point of i n t e r e s t and the t r u e e q u a t o r i a l plane, measured p o s i t i v e north of the equator. Ground Range Surface distance from launch s i t e t o t h e subvehicle point, p o s i t i v e e a s t (0" 1800). Inclination Angle between the instantaneous f l i g h t plane and t h e e q u a t o r i a l plane. I n e r t i a l Range Angle Angle between t h e instantaneous space f i x e d p o s i t i o n vector and t h e space fixed p o s i t i o n vector a t Guidance Reference Release. -
DEFINITIONS AND SYMBOLS (COW ' D) Longitude Angle between the Greenwich meridian plane and t h e projection of the geocentric poeit i o n v e c t o r i n the e q u a t o r i a l plane, measured p o s i t i v e e a s t of Greenwich. Longitudinal Acceleration That p a r t of t h e t o t a l measurable a c c e l e r a t i o n d i r e c t e d along t h e longitudinal a x i s of t h e vehicle. Mach Number ( R e l a t i v e Velocity) Ma88 Mass of t h e v e h i c l e . Navigation Coordinate System This system is i d e n t i c a l t o PASCS 13 with i d e a l navigation. Normal Force Magnitude of t h e r e s u l t a n t aerodynamic f o r c e normal t o t h e v e h i c l e longitudinal a x i s , and i n t h e plane defined by t h a t a x i s and t h e r e l a t i v e v e l o c i t y vector. Perigee A l t i t u d e Perigee height of t h e o s c u l a t i n g conic above t h e reference e l l i p s o i d , referenced t o t h e e q u a t o r i a l r a d i u s , 6378165 meters, Period Period of t h e o s c u l a t i n g conic. P i t c h , Yaw, Roll ( I n e r t i a l ) Eulerian angles of v e h i c l e a t t i t u d e measured with respect t o t h e space fixed coordinate system. Vehicle a t t i t u d e is defined by t h e ordered r o t a t i o n of p i t c h , yaw, and r o l l . (See i l l u s t r a t i o n ) Radius Space fixed poeition v e c t o r magnitude, Range Surface d i s t a n c e from launch r i t e t o t h e eub-vehicle p o i n t , p o a i t i v e e a r t (0' 180'). Relative Vehicle A t t i t u d e P i t c h , yaw and r o l l angles of t h e v e h i c l e i n a n e a r t h r e l a t i v e system. The r o l l urir ir t h e p r o j e c t i o n of t h e v e l o c i t y v e c t o r i n the l o c a l horizontal plane; t h e yaw a x i r i e i n t h e l o c a l v e r t i c a l plane, p o s i t i v e toward the c e n t e r of t h e e a r t h ; t h e p i t c h a x i s complrtw a r i g h t handed syetem. Vehicle a t t i t u d e lm defined by ordered r o t a t i o n - p i t c h , yaw and roll. f (Local Speed of Sound) -
Launch Mecidkn Pitch Yaw Rol I
Relative Velocity Velocity r e l a t i v e t o t h e atmoephere ( i n cludee wind v e l o c i t y ) . Semi-Ma j o t Axis Length of t h e chord i n t h e o r b i t plane connecting t h e apogee and the perigee of t h e o s c u l a t i n g conic. Space Fixed Croee Range Ya component of PASCS 13 p o s i t i o n v e c t o r . Space Fixed F l i g h t Path Angle Angle between t h e apace fixed v e l o c i t y v e c t o r and t h e radius v e c t o r (PASCS 13), measured p o e i t i v e downrange from radius vector. Space Fixed Position Poaltlon vector/componente i n a space fixed e a r t h centered, plumbline coordinate system defined a t Guide-ce Reference Releare. The Xe a x l e i a p a r a l l e l t o t h e reference e l l i p e o i d n o r m 1 which paesee througb t h e launch s i t e . The 2s a x i s i s p a r a l l e l t o , and p o e i t i v e i n t h e same d i r e c t i o n as, t h e earth-f ixed f i r i n g azimuth. The Y s u l r c m p l e t e e t h e r i g h t handed aystem. Thir is Project Apollo Standard Coordinate System 13. (PASCS 13). Space Fixed Velocity Velocity vector/components in PASCS 13. T Space Fixed Velocity Magnitude 28 T ime Inst8ntaneous f l i g h t time referenced t o f irst mu: '22. Three Sigma ( 3 6 ) Three standard deviations. Thrus t T o t a l e f f e c t i v e t h r u s t magnitude, True Anomaly Angular dieplacement of t h e v e h i c l e C.C. from t h e perigee, measured i n t h e d i r e c t i o n of t h e motion. Velocity Vector Azimuth The angle between t h e v e l o c i t y v e c t o r proj e c t i o n on t h e e a r t h ' s a u r f r c e and truo north. viii
Vehicle Weight Inetantaneoue t o t a l vehicle weight. Y 4 Position Vector Vehicle c. 8. dieplacement component8 in a apace fixed, r i g h t handed, t a r g e t coordinate ayetem with i t 8 o r i g i n a t t h e center of t h e earth. The Xq a x i r parser through t h e descending node of t h e orbit plane. The 24 axis l i e 8 i n t h e desired o r b i t plane 90' downrange from t h e & axis. The Y4 a x i s completes a r i g h t handed eyetem and i e perpendicular t o t h e orbit plane.
' DEFINITION AND SYMBOLS (CONT D) AFETR A i r Force Eastern Test Range AFB A i r Force Base AH1 Aerodynamic Heating l n d i c u t o r APS Auxiliary Propulsion S y s t n , APSO Apollo Soyuz Program O f f i c c AS Apollo Saturn ASTP Apollo Soyuz Test Project B- 7 T r a j e c t o r y Data Tape C C-Band Radar S t a t i o n s c/o Cut off CS Command System CCSD Chrysler Corporation Space D i i s i o n C .G. Center of Gravity CM Command Moduie CSM Command and Service Modules DELTA ( ) (AP) Increment Parameter I n c e m e n t DIA Vehicle Diameter DM Docking Module DRL Data Requirements L i s t ECF End Conditions of F l i g h t EMR Engine Mixture Ratio F Average Longitudinal Sea Level Thrust F PR F l i g h t Performence Reserve FT F l i g h t Technology 8 Acceleration of Gravity a t Sea L w e i (9.80665 rn/sec*)
' DEFINITIONS AND SVME3LS ( CONT D) GCS Guldance Cutoff S i g n a l GET Ground Elapsed Time Government Furnished Documentation Gaseous Hydrogen Greenwich Mean "me GRR Guidance Reference Release GSFC Goddard Space F l i g h t Center H- 1 S-IB Stage Engine Inclination IBM I n t e r n a t i o n a l Business Machines Corp. IECO Inboard Engine Cutoff S i g n a l G IM I t e r a t i v e Guidance Mode Inertia Measurement Unit S p e c i f i c Impulsc? Instrument Unit S-IVB Stage Enginp Kennedy Spacef 1i g h t Center LAC Loss of A t t l t u d e Control LC Launch Complex LES Launch Escape S y t e m LH2 Liquid Hydrogen LMSC/ HREC Lockheed M i s s i l e s and Space Company/Huntsville Research and Engineering Center LOX Liquid Oxygen LSA Level Sensor Actuation LVDC Launch Vehicle D i g i t a l Computer
DEFINITIONS AND SYMBOLS (CONT ' D) L/V Launch Vehicle LWC Launch Wi dowClosing LWO Launch Window Opening MDAC McDonnell Douglas A i r c r a f t Corporation MSFC Marshall Space F l i g h t Center NASA National Aeronautics and Space A d m i n i s t r a t i o n Liquid Nitrogen Not Applicable Non-Dimens iona 1 NPV Non-Propulsive Vent OECO Outboard Engine Cutoff S i g n a l Orbit I n s e r t ion Operat iona 1 T r a j e c t o r y PASCS P r o j e c t Apollo Standard Coordinate System POT Preliminary Operational F l i g h t Trajectory PSF ; psf Pounds Per Square Foot 9 Dynamic P r e s s u r e RP- 1 S-IB P r o p e l l a n t RS S Root-Sum-Square S-IB F i r s t S t a g e of t h e S a t u r n I B Launch V e h i c l e S-IU S a t u r n U u n c h Vehicle Instrument Vehicle Second Stage of t h e S a t u r n I B Launch V e h i c l e Saturn Spacecraft xii
DEFINITIONS AND SYMBOLS (CONT 'D) SIGMA ( o ) (2) Standard Deviation Summation of SLA Spacecraft Launch Adapter SM Service Module STA Vehicle S t a t i o n Location T Telemetry S t a t i o n s ; Time Base One Time Time Base Zero Time Base One Time Base Two Time Base Three lime Base Four Technical Note UHF Ultra High Frequency USA United S t a t e s of America Union of Soviet S o c i a l i s t Republics VHF Very High Frequency Flowrate xiii
SUMMARY This r e p o r t p r e s e n t s t h e ASTP (SA-210) Launch V e h i c l e Operatiorla1 F l i g h t T r a j e c t o r y (OT) t h r e e sigma ( 3 r ) f l i g h t parameter envelopes, t h e S-IVB S t a g e F l i g h t Performance Reserve (FPR) , t h e S-IB s t a g e design parameter envelopes, and p e r t i n e n t t r a d e - o f f f a c t o r s . The ASTP (SA-210) Launch Vehicle 500 Pound Launch Window Opening O p e r a t i o n a l F l i g h t T r a j e c t o r y was u t i l i z e d a s t h e nominal f o r t h i s a n a l y s i s . The f l i g h t envelopes p r e s e n t e d a r e t h e r e s u l t s of s t a t i s t i c a l comb i n a t i o n s o f p e r t u r b a t i o n e f f e c t s , eniploying t h e Root-Sum-Square (RSS) technique. Concise summaries of p e r t i n e n t t r a j e c t o r y parameter d i s p e r s i o n s a t S-IBIS-IVB S e p a r a t i o n a n d O r b i t I n s e r t i o n (01) f o l l o w . S-IBIS-IVB Sep. F l i g h t Time ( s e c ) Radius (m) Space Fixed V e l o c i t y (m/sec) Space Fixed P a t h Angle (deg) RS S - -RSS - 2.82 2.65 2050. 46.10 1.872 2303. 41.82 1.776 Orbit I n s e r t i o n RS S 10.99 505. -RSS 10.46 502. 2.47 2.46 0.018 0.018 Ground Range (m) 4646. 3607. 40192. 38336. E a r t h Fixed Cross Range (m) 4002. 2377. 4928. 5125. I n c l i n a t i o n (deg) ----- Descending Node Argument (deg) ----- --------- 0.019 0.019 0.019 0.019
Three sigma ( S I T ) v a r i a t i o n s i n t h e e s t a b l i s h m e n t s of t h e Launch V e h i c l e D i g i t a l Computer (LVDC) time bases T2, T 3 , and T4 a r e d i s p l a y e d i n t h e following t a b l e . Also included a r e t h e 3 0 v a r i a t i o n s i n t h e time t h a t dynamic p r e s s u r e ( q ) d e c r e a s e s t o one pound p e r s q u a r e f o o t ( p s f ) . The time bases i n i t i a t e independent event sequences and q 5 1 psf is a primary Launch Escape System (LES) j e t t i s o n i n g c r i t e r i o n . T 3 'Lime of q 1 psf (sec) T3 (se) T4 (sec) RSS ( ) 2.70 2.82 10.99 3.37 RSS (-) 2.53 2.65 10.46 4.83 T2 (sec) The 3 6 d e v i a t i o n s i n 5-2 engine i g n i t i o n and Engine Mixture R a t i o (EMR) s h i f t times a r e t h e same a s t h o s e shown f o r T3, s i n c e t h e y a r e programmed T3 events. The S - I V B s t a g e t h r e e sigma F l i g h t Performance Reserve (FPR) r e q u i r e ments f o r t h i s launch a r e 1172 pounds of LOX and 683 pounds of LH2. This FPR i s considered t o be v a l i d a t any p o i n t i n t h e p r e s c r i b e d 500 pound launch window, s i n c e a p r e v i o u s a n a l y s i s h a s e s t a b l i s h e d t h a t FPR v a r i a t i o n w i t h i n a l a r g e r 700 pound launch window is l e s s t h a n 50 pounds. U t i l i z i n g t h e s e FPR d a t a , t h e t a b l e on t h e f o l l o w i n g page p r o v i d e s a n assessment of t h e S-IVB r e s i d u a l p r o p e l l a n t s p r e d i c t e d f o r t h e nominal m i s s i o n . The nominal launch time i s 2.84 minutes p r i o r t o t h e p l a n a r f l i g h t o p p o r t u n i t y , consequently, 9 6 pounds of t h e 500 pound launch window p r o p e l l a n t a l l o c a t i o n a r e r e q u i r e d f o r yaw s t e e r i n g t o t h e p r e s c r i b e d t a r g e t c o n d i t i o n s .
LOX (Pounds) LH2 (Pounds) Total (Pounds) T o t ; l on board a t GCS (1);;nutscable (2)Total Available 3 s i :ma FPR a l l o c a t i o n 1172 Remc 1.ning launch window a l l o c a t i o n ( 4 . 8 . 1 EMR) 334 - Total allocation Excess a v a i l a b l e over a l l o c a t i o n Excess useable a t 4 . 8 : l EMR Excess b i a s 683 1855 70 - 404 - 1506 7 53 22 59 2 62 91 3 53 2 62 - 0 55 - 36 317 36 (1) Unuseable determined by MSFCIMDAC t o a s s u r e t h e required 6.7 m/sec d e p l e t i o n cutoff t h r u s t decay v e l o c i t y increment. (2) T o t a l ; " a i l a b l e LH2 includes a 460 pound b i a s . The preceding t a b l e is a modification of t h e r e s i d u a l p r o p e l l a n t assessment provided i n t h e ASTP (SA-210) OT documentation, using t h e a c t u a l FPR generated in this a n a l y s i .
SECTION 1 INTRODUCTION Launch v e h i c l e performance i s p r e d i c t a b l e only b i t h i n c e r t a i n t o l e r a n c e s . T h e r e f o r e , d e v i a t i o n s from a p r e d i c t e d launch v e h i c l e t r a j e c t o r y a r e expected. I n o r d e r t o e s t a b l i s h r e a l i s t i c d e v i a t i o n l i m i t s f o r t h e ASTP (SA-210) Launch Vehicle O p e r a t i o n a l F l i g h t T r a j e c t o r y , a d i s p e r s i o n a n a l y s i s has been conducted and i s documented i n t h i s r e p o r t . The nominal t r a j e c t o r y p r e s c r i b e d f o r t h i s a n a l y s i s is t h e ASTP (SA-210) Launch Vehicle 500 Pound Launch Window Opening OT. T h i s t r a j e c t o r y is docu- mented i n Reference 1. The e r r o r s o u r c e s considered a r e t h o s e a s s o c i a t e d w i t h p r e d i c t i o n s of v e h i c l e c h a r a c t e r i s t i c s , v e h i c l e systems performances, and f l i g h t environment. The nominal v e h i c l e , t h e boost t r a j e c t o r y s i m u l a t i o n s , t h e e r r o r s o u r c e s , t h e a n a l y t i c procedures u t i l i z e d , and t h e r e s u l t s a r e d i s c u s s e d i n t h e f o l l o w i n g sections. Launch v e h i c l e guidance system i n a c c u r a c i e s were determined from t h e guidance e r r o r a n a l y s i s , which i s documented i n Volume I1 of t h i s p u b l i c a t i o n (Reference 2 ) . These d a t a a r e composed of i n d i v i d u a l e r r o r s o u r c e t r a j e c t o r y e f f e c t s , which a r e s t a t i s t i c a l l y combined t o provide t r a j e c t o r y parameter d i s p e r s i o n envelopes. F i x e d time s t a t e v a r i a b l e c a r d s a r e provided w i t h Volume I1 t o f a c i l i t a t e o r b i t a l t r a j e c t o r y d i s p e r s i o n a n a l y s e s .
SECTION 2 DISCUSS ION 2.1 Mission D e s c r i p t i o n The Apollo Soyuz T e s t P r o j e c t (ASTP) i s a j o i n t USA and USSR v e n t u r e c o n s i s t i n g of s e p a r a t e Apollo and Soyue s p a c e c r a f t launches f o r an e a r t h o r b i t rendezvous and docking. The Soyuz w i l l be launched f i r s t on J u l y 15, 1975 and i n s e r t e d i n t o a 1881228 km. (101.5/123.1 n.mi.) a t 51.78 degrees. e a r t h o r b i t inclined Subsequently, t h e Soyuz o r b i t w i l l be c i r c u l a r i z e d a t 225 km. (121.5 n.mi.). Approximately 75 hours a f t e r t h e Soyuz launch, t h e Apollo s p a c e c r a f t w i l l be launched and i n s e r t e d i n t o a 1501167 krn. (81/90 n . m i . ) e a r t h o r b i t c o p l a n a r 5 t ht h e Soyuz o r b i t . and dock w i t h t h e Soyuz. The Apollo w i l l t h e n rendezvous The two s p a c e c r a f t w i l l remain docked f o r approxi- mately two days, d u r i n g which time t h e crews w i l l exchange v i s i t s and operat i o n a l procedures. A f t e r a d d i t i o n a l docking t e s t s , t h e s p a c e c r a f t w i l l s e p a r a t e and conduct independent a c t i v i t i e s . The Soyuz w i l l d e o r b i t approxi- mately 46 hours a f t e r t h e i n i t i a l undocking, and t h e Apollo w i l l remain i n o r b i t , conducting experiments, f o r f i v e a d d i t i o n a l days. Launch Vehicle and T r a j e c t o r y D e s c r i p t i o n 2.2 The launch v e h i c l e and t y p i c a l t r a j e c t o r i e s a r e d e s c r i b e d i n Reference 1. F e a t u r e s p e r t i n e n t t o t h i s a n a l y s i s a r e d i s c u s s e d i n t h e f o l l o w i n g sub- sections. Associated d i s p e r s i o n d a t a a r e d i s c u s s e d i n s u S s e c t i o n s 2.3 and 2.4. 2.2.1 Launch Vehicle The Apollo launch v e h i c l e i s S a t u r n I B 210. It i s composed of t h e
S-IE-10 f i r s t s t a g e , a n i n t e r s t a g e , t h e S-IVB-210 second s t a g e , and t h e S-IU-210 Instrument Unit. and the Major s p a c e c r a f t elements a r e t h e 0 1 - 111 C o l . Module, SM- 111 S e r v i c e Module, t h e SLA- 18 S p a c e c r a f t Launch AdapLer anil t h e u !-2 Dockin& bioaule. A Launch Escape Systelkl (LES) completes t h e space v e h i c l e . A v e h i c i e weight breakdown is presented i n Table 1. 2.2.2 -F !i g h t Environment The 1963 P a t r i c k A i r Force Base atmosphere model, defined i n Reference 3, i s t h e nominal atmosphere used i n t h i s a n a l y s i s . The nominal wind i s t h e J u l y mean p r o f i l e from Reference 4 supplemented by compatible d a t a from Reference 5 f o r a l t i t u d e s g r e a t e r t h a n 2 7 k i l o m e t e r s . 2.2.3 F l i g h t Sequence of Events The nominal f l i g h t sequence of e v e n t s , f o r t h i s a n a l y s i s , i s presented i n Table 2 . O f f nominal p r o p u l s i o n systems performances produce s i g n i f i c a n t sequence changes. Of primary i n t e r e s t a r e t h e e v e n t s which e s t a b l i s h Launch Vehicle D i g i t a l Computer (LVDC) time b a s e s and t h u s t h e subsequent e v e n t s dependert on t h e s e time bases. A d i s c u s s i o n of p e r t i n e n t time bases and associated events follows. 1) Time Base 2 (T2) - E s t a b l i s h e d by S-IB s t a g e p r o p e l l a n t l e v e l s e n s o r a c t u a t i o n i f a downrange v e l o c i t y 1 500 mlsec e x i s t s . S i g n i f i c a n t dependent e v e n t s a r e Inboard Engine Cut-Of f S i g n a l (IECO), i n t e r c o n n e c t i o n of t h r u s t O.K. s w i t c h e s and f u e l d e p l e t i o n probe arming. 2) Time Base 3 (T3) - E s t a b l i s h e d when a n Outboard Engine Cut-Off S i g n a l (OECO) i s r e c e i v e d by t h e LVDC due t o e i t h e r UIX o r f u e l
d e p l e t i o n ; o r , by a backup LVDC s i g n a l i n i t i a t e d 13.00 seconds of Time Base 2 . a f t e r establishment P e r t i n e n t dependent e v e n t s a r e u l l a g e r o c k e t f i r i n g , S-IB r e t r o - r o c k e t f i r i n g , S-IBIS-IVB s e p a r a t i o n s i g n a l , 5-2 engine s t a r t s i g n a l , I G M guidance i n i t i a t i o n , and Engine Mixture R a t i o (DIK) changes. 3) Time Base 4 (T4) - I n i t i a t e d approximately 0 . 2 seconds a f t e r Guidance Cutoff S i g n a l (GCS). I n t h i s a n a l y s i s , GCS i s r e - ceived when t h e S-IVB s t a g e o b t a i n s t h e t a r g e t v e l o c i t y l e s s t h e p r e d i c t e d v e l o c i t y increment from 5-2 t h r u s t decay. The s i g n i f i - c a n t e v e n t s subsequent t o T4 a r e t h e preplanned o r b i t a 1 maneuvers and S-IVB s t a g e v e n t i n g s . It should be noted t h a t T 2 and T3 e s t a b l i s h m e n t s a r e nominally de- pendent upon p r o p e l l a n t l e v e l s e n s o r a c t u a t i o n s and p r o p e l l a n t d e p l e t i o n detection. T h e r e f o r e , e s t a b l i s h m e n t s of t h e s e time bases a r e v e r y s e n s i t i v e t o p r o p u l s i o n system p e r t u r b a t i o n s , which a f f e c t p r o p e l l a n t f l o w r a t e , and thus, tank level h i s t o r i e s , 2.3 Dispersion E r r o r Sources V e h i c l e manufacturing t o l e r a n c e s , p r e d i c t e d system performance i n - a c c u r a c i e s , f l i g h t environment anomalies, and guidance hardware i n a c c u r a c i e s a r e s o u r c e s of e r r o r s which s i g n i f i c a n t l y a f f e c t t r a j e c t o r y p r e d i c t i o n s . To f a c i l i t a t e s t a t i s t i c a l a n a l y s e s o f such e r r o r e f f e c t s , t h r e e sigma t o l e r a n c e s have been e s t a b l i s h e d . The t h r e e sigma t o l e r a n c e s considered i n t h i s a n a l y s i s , w i t h corresponding r e f e r e n c e s , a r e d i s p l a y e d i n Table 3.
The LOX and RP-1 d e n s i t y c a s e s presented h e r e i n were g e e r a t efrom d J u l y propulsion p r e d i c t i o n s u t i l i z i n g t h e t a p e s d e l i n e a t e d i n Reference 11. The t h r e e sig11:a wind d a t a u t i l i z e d a r e t h e Reference 5 annual wind p r o f i l e s . 2.4 T r a j e c t o r y Dispersions and A n a l y t i c a l Procedures T l et r a j e c t o r y parameter p e r t u r b a t i o n s r t s u l t i n gfrolr t h i s a n a l y s i s a r e a s s u i etdo be rantlom, independent, a n d normally d i s t r i b u t e d . These a s s u n p t i o n sallow a p p l i c a t i o n of t h e Root-Sum-Square (RSS) s t a t i s t i c a l con2b i n a t i o n method t o produce a r e a s o n a b l e t r a ; e c t o r y d i s p e r s i o n envelope. Dispersed t r a j e c t o r i e s were generated w i t h each of t h e ttlree sigma t o l e r a n c e s d e l i n e a t e d i n Table 3. E f f e c t s on p e r t i n e n t t r a j e c t o r y parameters a t S-IB/S-IVB s t a g e s e p a r a t i o n and o r b i t i n s e r t i o n were determined and combined a s follows: RSS - ,/- RSS AP JZ( '; perturbed parameter ; where - nominal parameter. These RSS v a l u e s d e f i n e a r e a s o n a b l e t h r e e sigma f l i g h t envelope f o r t h e ASTP (SA-210) Launch V e h i c l e O p e r a t i o n a l F l i g h t T r a j e c t o r y . In a similar manner, u t i l i z i n g t r a j e c t o r y d i s p e r s i o n d a t a , t h e S-IVB F l i g h t Performance Reserve (FPR), r e q u i r e d t o o f f s e t t h e combined t h r e e sigma d e v i a t i o n s , was determined, i n S e c t i o n 3. T h i s FPR and o t h e r t r a j e c t o r y d i s p e r s i o n r e s u l t s a r e p r e s e n t e d
SECTION 3 RESULTS 3.1 Trajectory Dispersions T r a j e c t o r y d i s p e r s i o n d a t a a r e presented f o r two e v e n t s , S-IBIS-IVB s t a g e s e p a r a t on and o r b i t i n s e r t i o n . Table 4 p r e s e n t s t h r e e sigma t r a - j e c t o r y parameter d e v i a t i o n s produced a t S-IBIS-IVB s e p a r a t i o n by t h e S-IB s t a g e p r o p u l s i o n , non-propulsion, and f l i g h t environment p e r t u r b a t i o n s . Table 5 p r o v i d e s s i m i l a r d a t a derived from S-IVB s t a g e p e r t u r b a t i o n s . 7 and 8 d i s p l a y corresponding d a t a a t o r b i t i n s e r t i o n . both - t h r e e 'Fables I n t h e cvent t h a t sigma p e r t u r b a t i o n s of t h e same e r r o r s o u r c e produce e f f e c t s w i t h l i k e a l g e b r a i c s i g n , only t h e l a r g e r e f f e c t i s included i n t h e RSS. Tables 6 and 9 d i s p l a y p r e d i c t e d t h r e e sigma f l i g h t envelopes a t S-IBIS-IVB s e p a r a t i o n and a t o r b i t i n s e r t i o n , r e s p e c t i v e l y . These envelopes a r e t h e root-sum-square of t h e p r e v i o u s l y mentioned e r r o r s o u r c e group e f f e c t s with t h e RSS of t h e I n e r t i a l Measurement Unit (IMU) e r r o r e f f e c t s included i n Table 9 . I n d i v i d u a l IMU e r r o r e f f e c t s a r e provided i n Reference 2 . R e s u l t s of t
Flight Trajectory (OT) three sigma (3r) flight parameter envelopes, the S-IVB Stage Flight Performance Reserve (FPR) , the S-IB stage design parameter envelopes, and pertinent trade-off factors. The ASTP (SA-210) Launch Vehicle 500 Pound Launch Window Opening Operational Flight Trajectory was utilized as the nominal for this analysis.
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HLK-HD5 5 943 320 515 200 360 cont. 36 40 210 30 20 HLK-RHD5 5 943 320 515 200 360 cont. 36 80 21030 20 HLK-EH5 5 795 210 96 460 180 14 25 210 12 9.5 HLK-40400 5 1425 410 760 240 360 cont. 75 150 210 45 30 HLK CRA6 6 1500 280 600 150 360 cont. 36 32 210 28 14.5 HLK-HD6W 6 1120 280 515 380 360 cont. 36 30 210 29 21
On February 22, 2013, NASA announced that it had assigned a fourth Delta 2 to launch the Ice, Cloud and Land Elevation Satellite (ICESat)-2 into near polar obit from Vandenberg AFB, a launch then scheduled for July 2016. A firm fixed-price launch service task order was awarded for the Delta 7320-10C launch under the
Artificial Intelligence and the Modern Productivity Paradox: A Clash of Expectations and Statistics Erik Brynjolfsson, Daniel Rock, and Chad Syverson NBER Working Paper No. 24001 November 2017 JEL No. D2,O3,O4 ABSTRACT We live in an age of paradox. Systems using artificial intelligence match or surpass human level performance in more and more domains, leveraging rapid advances in other .
