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LAUNCH.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LAUNCH
* Problem:
* ********
* The objective function to be minimized represents the total cost of
* the development and launching of a 3 stages space launching vehicle.
* Constraints are imposed on physical interrelations between the variables
* and performance.
* The problem is highly non-convex.
* Source:
* B. Rush, J. Bracken and G. McCormick,
* "A nonliner programming model for launch vehicle design and costing",
* Operations Research, pp. 185-210, 1967.
* SIF input: P. Driscoll, Virginia Tech., April 1993,
* corrected and simplified by Ph. L. Toint, May 1993.
* classification OOR2-MY-25-28
VARIABLES
AW1 $ stage 1 airframe weight (Kpounds)
IW1 $ stage 1 total inert weigh (Kpounds)
MF1 $ stage 1 mass fraction
TT1 $ stage 1 total thrust (Kpounds)
PW1 $ stage 1 propellant weight (Kpounds)
ET1 $ stage 1 engine thrust (Kpounds)
S1L $ stage 1 length (feet)
AW2 $ stage 2 airframe weight (Kpounds)
IW2 $ stage 2 total inert weigh (Kpounds)
MF2 $ stage 2 mass fraction
TT2 $ stage 2 total thrust (Kpounds)
PW2 $ stage 2 propellant weight (Kpounds)
ET2 $ stage 2 engine thrust (Kpounds)
S2L $ stage 2 length (feet)
AW3 $ stage 3 airframe weight (Kpounds)
IW3 $ stage 3 total inert weigh (Kpounds)
MF3 $ stage 3 mass fraction
TT3 $ stage 3 total thrust (Kpounds)
PW3 $ stage 3 propellant weight (Kpounds)
ET3 $ stage 3 engine thrust (Kpounds)
S3L $ stage 3 length (feet)
INW $ instrument weight (Kpounds)
BT1 $ stage 1 burn time (secs)
BT2 $ stage 2 burn time (secs)
BT3 $ stage 3 burn time (secs)
GROUPS
* Cost of stage 1
XN STA1 ET1 0.0002587
XN STA1 'SCALE' 1.0D+8
* Cost of stage 2
XN STA2 ET2 0.0002587
XN STA2 'SCALE' 1.0D+8
* Cost of stage 3
XN STA3 ET3 0.001958
XN STA3 'SCALE' 1.0D+8
* Instrumentation cost
XN INST INW 47.040096
XN INST 'SCALE' 1.0D+8
* Launch operating costs
XN LAUN PW1 0.003 PW2 0.003
XN LAUN PW3 0.003
*XN LAUN 'SCALE' 0.039215686
XN LAUN 'SCALE' 39215686.0
* Relations between airframe weights and inert weights
XE SGTH1 AW1 2.0 IW1 -1.0
XE SGTH3 IW2 0.6 AW2 -1.0
XE SGTH5 IW3 0.7 AW3 -1.0
* Definition of stage mass fractions
* Relation between stage thrust and single engine thrust
XE SGTH2 ET1 5.0 TT1 -1.0
XE SGTH4 ET2 5.0 TT2 -1.0
XE SGTH6 TT3 1.0 ET3 -1.0
* Constraints on structural integrity (stage weight vs propellant weight)
XG SGSI1A PW1 1.0 IW1 -12.0
XL SGSI1B PW1 1.0 IW1 -17.0
XG SGSI2A PW2 1.0 IW2 -10.0
XL SGSI2B PW2 1.0 IW2 -13.0
XG SGSI3A PW3 1.0 IW3 -7.0
XL SGSI3B PW3 1.0 IW3 -10.0
* Constraints expression the ratio of thrust to initial weight for a given
* payload
XG TTIW1A TT1 1.0 IW1 -1.2
XG TTIW1A PW1 -1.2 IW2 -1.2
XG TTIW1A PW2 -1.2 IW3 -1.2
XG TTIW1A PW3 -1.2 INW -1.2
XL TTIW1B TT1 1.0 IW1 -1.4
XL TTIW1B PW1 -1.4 IW2 -1.4
XL TTIW1B PW2 -1.4 IW3 -1.4
XL TTIW1B PW3 -1.4 INW -1.4
XG TTIW2A TT2 1.0 IW2 -0.6
XG TTIW2A PW2 -0.6 IW3 -0.6
XG TTIW2A PW3 -0.6 INW -0.6
XL TTIW2B TT2 1.0 IW2 -0.75
XL TTIW2B PW2 -0.75 IW3 -0.75
XL TTIW2B PW3 -0.75 INW -0.75
XG TTIW3A TT3 1.0 IW3 -0.7
XG TTIW3A PW3 -0.7 INW -0.7
XL TTIW3B TT3 1.0 IW3 -0.9
XL TTIW3B PW3 -0.9 INW -0.9
* Constraints on the stage mass fraction of the 3 stages
XE SMF1 MF1 20.0 IW1 -1.0
XE SMF1 IW2 -1.0 PW2 -1.0
XE SMF1 IW3 -1.0 PW3 -1.0
XE SMF1 INW -1.0
XE SMF2 MF2 20.0 IW2 -1.0
XE SMF2 IW3 -1.0 PW3 -1.0
XE SMF2 INW -1.0
XE SMF3 MF3 20.0 IW3 -1.0
XE SMF3 INW -1.0
* Constraints on the specific impulse
XG SI1A PW1 -240.0
XL SI1B PW1 -290.0
XG SI2A PW2 -240.0
XL SI2B PW2 -290.0
XG SI3A PW3 -340.0
XL SI3B PW3 -375.0
* Total vehicle launch constraint
XG GLGCON
CONSTANTS
* Objective function
LAUNCH STA1 247.963 $ Stage 1
LAUNCH STA2 247.963 $ Stage 2
LAUNCH STA3 32.591 $ Stage 3
LAUNCH INST 35.5 $ Instrumentation
* Constraints
LAUNCH TTIW1A 24.0 $ thrust to initial weight
LAUNCH TTIW1B 28.0
LAUNCH TTIW2A 12.0
LAUNCH TTIW2B 15.0
LAUNCH TTIW3A 14.0
LAUNCH TTIW3B 18.0
LAUNCH SMF1 20.0 $ stage mass fraction
LAUNCH SMF2 20.0
LAUNCH SMF3 20.0
LAUNCH GLGCON 35000.0 $ total launch performance
RANGES
LAUNCH GLGCON 15000.0 $ total launch performance
BOUNDS
XL LAUNCH 'DEFAULT' 1.0D-8
XU LAUNCH 'DEFAULT' 1.0D+4
XL LAUNCH S1L 125.0 $ length of stage 1
XU LAUNCH S1L 150.0
XL LAUNCH S2L 75.0 $ length of stage 2
XU LAUNCH S2L 100.0
XL LAUNCH S3L 50.0 $ length of stage 3
XU LAUNCH S3L 70.0
XL LAUNCH MF1 0.25 $ good design constraints
XU LAUNCH MF1 0.30
XL LAUNCH MF2 0.24
XU LAUNCH MF2 0.29
XL LAUNCH MF3 0.16
XU LAUNCH MF3 0.21
XL LAUNCH INW 2.5 $ bound on intrument unit weight
XU LAUNCH INW 4.0
START POINT
* The starting point is very close to feasible
XV LAUNCH AW1 68.0
XV LAUNCH IW1 136.0
XV LAUNCH MF1 0.29988744
XV LAUNCH TT1 3733.0
XV LAUNCH PW1 2177.0
XV LAUNCH ET1 746.6
XV LAUNCH S1L 125.0
XV LAUNCH AW2 28.2
XV LAUNCH IW2 47.0
XV LAUNCH MF2 0.28939109
XV LAUNCH TT2 480.0
XV LAUNCH PW2 566.0
XV LAUNCH ET2 96.0
XV LAUNCH S2L 75.0
XV LAUNCH AW3 11.2
XV LAUNCH IW3 16.0
XV LAUNCH MF3 0.20980926
XV LAUNCH TT3 129.0
XV LAUNCH PW3 145.0
XV LAUNCH ET3 129.0
XV LAUNCH S3L 50.0
XV LAUNCH INW 2.5
XV LAUNCH BT1 155.0
XV LAUNCH BT2 314.0
XV LAUNCH BT3 403.0
ELEMENT TYPE
EV PROD1 VA VB
EV PROD1 VC VD
EV PROD1 VE
EV POWER XX
EP POWER PWR SC
EV PROD2 VA VB
EV PROD2 VC VD
EV X7Y X Y1
EV X7Y Y2 Y3
EV X7Y Y4 Y5
EV X7Y Y6 Y7
IV X7Y XX YY
EV X5Y X Y1
EV X5Y Y2 Y3
EV X5Y Y4 Y5
IV X5Y XX YY
EV X3Y X Y1
EV X3Y Y2 Y3
IV X3Y XX YY
EV 2PR X Y
EV BIG1 LH TH
EV BIG1 LL V1
ELEMENT USES
* Elements for stage 1 modelling
* a) airframe R&D
T XPROD1 PROD1
V XPROD1 VA AW1
V XPROD1 VB IW1
V XPROD1 VC MF1
V XPROD1 VD TT1
V XPROD1 VE PW1
* b) LOX/RP propulsion R&D
T XPF POWER
V XPF XX ET1
P XPF PWR -0.146
P XPF SC 1000.0
T XPG POWER
V XPG XX ET1
P XPG PWR 0.648
P XPG SC 1000.0
* c) airframe production unit
T XPROD2 PROD2
V XPROD2 VA AW1
V XPROD2 VB MF1
V XPROD2 VC PW1
V XPROD2 VD S1L
* d) LOX/RP propulsion production of 5 engines
T XPL POWER
V XPL XX ET1
P XPL PWR 0.736
P XPL SC 1000.0
T XPM POWER
V XPM XX ET1
P XPM PWR -0.229
P XPM SC 1000.0
* Elements for stage 2 modelling
* a) airframe R&D
T XPROD3 PROD1
V XPROD3 VA AW2
V XPROD3 VB IW2
V XPROD3 VC MF2
V XPROD3 VD TT2
V XPROD3 VE PW2
* b) LOX/RP propulsion R&D
T X2PF POWER
V X2PF XX ET2
P X2PF PWR -0.146
P X2PF SC 1000.0
T X2PG POWER
V X2PG XX ET2
P X2PG PWR 0.648
P X2PG SC 1000.0
* c) airframe production unit
T XPROD4 PROD2
V XPROD4 VA AW2
V XPROD4 VB MF2
V XPROD4 VC PW2
V XPROD4 VD S2L
* d) LOX/RP propulsion production of 5 engines
T X2PL POWER
V X2PL XX ET2
P X2PL PWR 0.736
P X2PL SC 1000.0
T X2PM POWER
V X2PM XX ET2
P X2PM PWR -0.229
P X2PM SC 1000.0
* Elements for stage 3 modelling
* a) airframe R&D
T XPROD5 PROD1
V XPROD5 VA AW3
V XPROD5 VB IW3
V XPROD5 VC MF3
V XPROD5 VD TT3
V XPROD5 VE PW3
* b) LOX/RP propulsion R&D
T XQF POWER
V XQF XX ET3
P XQF PWR 0.539
P XQF SC 1000.0
T XQG POWER
V XQG XX ET3
P XQG PWR 0.772
P XQG SC 1000.0
* c) airframe production unit
T XPROD6 PROD2
V XPROD6 VA AW3
V XPROD6 VB MF3
V XPROD6 VC PW3
V XPROD6 VD S3L
* d) LOX/RP propulsion production of 1 engine
T XQL POWER
V XQL XX ET3
P XQL PWR -1.33
P XQL SC 100.0
T XQM POWER
V XQM XX ET3
P XQM PWR 0.498
P XQM SC 100.0
* Elements for constraints on the stage mass fraction
T SMFE1 X7Y
V SMFE1 X MF1
V SMFE1 Y1 IW1
V SMFE1 Y2 PW1
V SMFE1 Y3 IW2
V SMFE1 Y4 PW2
V SMFE1 Y5 IW3
V SMFE1 Y6 PW3
V SMFE1 Y7 INW
T SMFE2 X5Y
V SMFE2 X MF2
V SMFE2 Y1 IW2
V SMFE2 Y2 PW2
V SMFE2 Y3 IW3
V SMFE2 Y4 PW3
V SMFE2 Y5 INW
T SMFE3 X3Y
V SMFE3 X MF3
V SMFE3 Y1 IW3
V SMFE3 Y2 PW3
V SMFE3 Y3 INW
* Constraints on specific impulse
T TT1BT1 2PR
V TT1BT1 X TT1
V TT1BT1 Y BT1
T TT2BT2 2PR
V TT2BT2 X TT2
V TT2BT2 Y BT2
T TT3BT3 2PR
V TT3BT3 X TT3
V TT3BT3 Y BT3
* Total launch constraint
T XBIG11 BIG1
V XBIG11 LH TT1
V XBIG11 TH BT1
V XBIG11 LL PW1
V XBIG11 V1 MF1
T XBIG12 BIG1
V XBIG12 LH TT2
V XBIG12 TH BT2
V XBIG12 LL PW2
V XBIG12 V1 MF2
T XBIG13 BIG1
V XBIG13 LH TT3
V XBIG13 TH BT3
V XBIG13 LL PW3
V XBIG13 V1 MF3
GROUP TYPE
GV SUMM TERMS
GROUP USES
E STA1 XPROD1 5272.77
E STA1 XPF 160.909 XPG 282.874
E STA1 XPROD2 0.64570846
E STA1 XPL 31.136196 XPM 12.092112
E STA2 XPROD3 5272.77
E STA2 X2PF 160.909 X2PG 282.874
E STA2 XPROD4 0.64570846
E STA1 X2PL 31.136196 X2PM 12.092112
E STA3 XPROD5 5272.77
E STA3 XQF 181.806 XQG 232.57
E STA3 XPROD6 0.49783215
E STA3 XQL -0.22424514 XQM 20.708238
T LAUN SUMM
E SMF1 SMFE1
E SMF2 SMFE2
E SMF3 SMFE3
E SI1A TT1BT1
E SI1B TT1BT1
E SI2A TT2BT2
E SI2B TT2BT2
E SI3A TT3BT3
E SI3B TT3BT3
E GLGCON XBIG11 -32.0 XBIG12 -32.0
E GLGCON XBIG13 -32.0
OBJECT BOUND
LO LAUNCH 0.0
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LAUNCH
TEMPORARIES
R SCPWR
R LG
M LOG
R EA
R VA0
R VA1
R VA2
R EB
R VB0
R VB1
R VB2
R EC
R VC0
R VC1
R VC2
R ED
R VD0
R VD1
R VD2
R EE
R VE0
R VE1
R VE2
INDIVIDUALS
T BIG1
A LG LOG( V1 )
F (LH * TH * LG) / LL
G V1 (LH * TH ) / ( V1 * LL)
G LH (TH * LG) / LL
G TH (LH * LG) / LL
G LL - ( LH * TH * LG ) / ( LL ** 2 )
H V1 V1 - ( LH * TH ) / ( LL * V1 ** 2 )
H V1 LH TH / ( V1 * LL )
H V1 TH LH / ( V1 * LL )
H V1 LL - ( LH * TH ) / ( LL ** 2 * V1 )
H LH TH LG / LL
H LH LL - TH * LG / LL **2
H TH LL - LH * LG / LL ** 2
H LL LL 2.0 * (LH * TH * LG) / (LL ** 3.0)
T PROD1
A EA 1.2781
A VA0 VA ** EA
A VA1 EA * VA ** ( EA - 1.0 )
A VA2 EA * ( EA - 1.0 ) * VA ** ( EA - 2.0 )
A EB -0.1959
A VB0 VB ** EB
A VB1 EB * VB ** ( EB - 1.0 )
A VB2 EB * ( EB - 1.0 ) * VB ** ( EB - 2.0 )
A EC 2.4242
A VC0 VC ** EC
A VC1 EC * VC ** ( EC - 1.0 )
A VC2 EC * ( EC - 1.0 ) * VC ** ( EC - 2.0 )
A ED 0.38745
A VD0 VD ** ED
A VD1 ED * VD ** ( ED - 1.0 )
A VD2 ED * ( ED - 1.0 ) * VD ** ( ED - 2.0 )
A EE 0.9904
A VE0 VE ** EE
A VE1 EE * VE ** ( EE - 1.0 )
A VE2 EE * ( EE - 1.0 ) * VE ** ( EE - 2.0 )
F VA0 * VB0 * VC0 * VD0 * VE0
G VA VA1 * VB0 * VC0 * VD0 * VE0
G VB VA0 * VB1 * VC0 * VD0 * VE0
G VC VA0 * VB0 * VC1 * VD0 * VE0
G VD VA0 * VB0 * VC0 * VD1 * VE0
G VE VA0 * VB0 * VC0 * VD0 * VE1
H VA VA VA2 * VB0 * VC0 * VD0 * VE0
H VA VB VA1 * VB1 * VC0 * VD0 * VE0
H VA VC VA1 * VB0 * VC1 * VD0 * VE0
H VA VD VA1 * VB0 * VC0 * VD1 * VE0
H VA VE VA1 * VB0 * VC0 * VD0 * VE1
H VB VB VA0 * VB2 * VC0 * VD0 * VE0
H VB VC VA0 * VB1 * VC1 * VD0 * VE0
H VB VD VA0 * VB1 * VC0 * VD1 * VE0
H VB VE VA0 * VB1 * VC0 * VD0 * VE1
H VC VC VA0 * VB0 * VC2 * VD0 * VE0
H VC VD VA0 * VB0 * VC1 * VD1 * VE0
H VC VE VA0 * VB0 * VC1 * VD0 * VE1
H VD VD VA0 * VB0 * VC0 * VD2 * VE0
H VD VE VA0 * VB0 * VC0 * VD1 * VE1
H VE VE VA0 * VB0 * VC0 * VD0 * VE2
T PROD2
A EA 0.3322
A VA0 VA ** EA
A VA1 EA * VA ** ( EA - 1.0 )
A VA2 EA * ( EA - 1.0 ) * VA ** ( EA - 2.0 )
A EB -1.5935
A VB0 VB ** EB
A VB1 EB * VB ** ( EB - 1. 0)
A VB2 EB * ( EB - 1.0 ) * VB ** ( EB - 2.0 )
A EC 0.2363
A VC0 VC ** EC
A VC1 EC * VC ** ( EC - 1.0 )
A VC2 EC * ( EC - 1.0 ) * VC ** ( EC - 2.0 )
A ED 0.1079
A VD0 VD ** ED
A VD1 ED * VD ** ( ED - 1.0 )
A VD2 ED * ( ED - 1.0 ) * VD ** ( ED - 2.0 )
F VA0 * VB0 * VC0 * VD0
G VA VA1 * VB0 * VC0 * VD0
G VB VA0 * VB1 * VC0 * VD0
G VC VA0 * VB0 * VC1 * VD0
G VD VA0 * VB0 * VC0 * VD1
H VA VA VA2 * VB0 * VC0 * VD0
H VA VB VA1 * VB1 * VC0 * VD0
H VA VC VA1 * VB0 * VC1 * VD0
H VA VD VA1 * VB0 * VC0 * VD1
H VB VB VA0 * VB2 * VC0 * VD0
H VB VC VA0 * VB1 * VC1 * VD0
H VB VD VA0 * VB1 * VC0 * VD1
H VC VC VA0 * VB0 * VC2 * VD0
H VC VD VA0 * VB0 * VC1 * VD1
H VD VD VA0 * VB0 * VC0 * VD2
T POWER
A SCPWR PWR / ( SC ** PWR )
F (XX / SC) ** PWR
G XX SCPWR * XX ** ( PWR - 1.0 )
H XX XX SCPWR*( PWR - 1.0 )*XX**( PWR - 2.0 )
T X7Y
R XX X 1.0
R YY Y1 1.0 Y2 1.0
R YY Y3 1.0 Y4 1.0
R YY Y5 1.0 Y6 1.0
R YY Y7 1.0
F XX * YY
G XX YY
G YY XX
H XX YY 1.0
T X5Y
R XX X 1.0
R YY Y1 1.0 Y2 1.0
R YY Y3 1.0 Y4 1.0
R YY Y5 1.0
F XX * YY
G XX YY
G YY XX
H XX YY 1.0
T X3Y
R XX X 1.0
R YY Y1 1.0 Y2 1.0
R YY Y3 1.0
F XX * YY
G XX YY
G YY XX
H XX YY 1.0
T 2PR
F X * Y
G X Y
G Y X
H X Y 1.0
ENDATA
*********************
* SET UP THE GROUPS *
* ROUTINE *
*********************
GROUPS LAUNCH
INDIVIDUALS
T SUMM
F TERMS** 0.460
G 0.460 * TERMS**(-0.540)
H -0.2484 * TERMS**(-1.540)
ENDATA