Commercial Launch Vehicle Design and Predictive Guidance Development Matthew R
THE UNIVERSITY OF ADELAIDE AUSTRALIA
School of
Mechanical Engineering
Commercial Launch Vehicle Design
and
Predictive Guidance Development
Matthew R. Tetlow
A thesis subrnitted in fulfilment of the requirements for the degree of Ph.D in Engineering on the 20th day ofJønuøry 2003 Contents
Abstract xvi
Statement of originality xvlu
Acknowledgements xtx
Nomenclature xx
Acronyms xxllt
L Introduction 1
1.1 Background 1
I.2 Objective 7
1.3 Practical application . 8
2 Literature Review 9
2.1 Launch vehicles to date 9
2.2 Propulsion systems 10 2.2.7 Chemical rocket propulsion
2.2.2 Air-breathingpropulsion
2.3 Vehicle design aspects
2.3.1 Vehicle configuration .
2.3.2 Number of stages/boosters
2.3.3 Vehicle layout
2.3.4 Recovery system
2.4 Orbital mechanics .
2.4.7 Mission requirements .
2.5 Launch sites
2.6 Ascent guidance
2.6.1 Open loop guidance
2.6.2 Closed loop guidance .
2.7 Flyback guidance systems
2.8 Conclusions from the literature review
3 Numerical Techniques
3.1 Simulationtechniques
3.7.1 Dynamicsmodelling
3.7.2 Propulsion modelling .
11 3.1.3 Mass modelling . .
3.1.4 Atmospheremodelling
3.1.4.1 Standard atmosphere models
3.1.4.2 MSISE atmosphere models
3.1.5 Wind modelling GIWM93)
3.1.6 Earth form modelling
3.1.6.1 Spherical Earth
3.1.6.2 Higher order models
3.7.7 Gravitation field modelling . .
3.I.1.1 Newtonian
3.7.1.2 Higher order models .
3.2 Optimisationtechniques
3.2.1 Gradient projection method
3.2.2 Sequential quadratic programming (NLPQL) . . . .
3.3 Steering model parameterisation
4 Software Description
4.1 Sensitivity analysis software
4.2 Vehicle design software
4.2.7 Simulation and optimisation
111 4.2.2 Propulsion model
4.2.3 Mass model .
4.2.4 Steering model parameterisation
4.3 Ascent guidance software
4.3.1 Virtual system
4.3.I.1 Virtualvehicle
4.3.7.2 Virtual environment
4.3.2 Guidance computer .
4.3.2.1 Guidance environment models
4.3.3 Steering modelparameterisation
4.3.4 Attitude controller
4.4 Flyback guidance software
4.4.1 Virtual system
4.4.7.1 Virtualvehicle
4.4.1.2 Virtual environment
4.4.2 Guidance computer
4.4.2.1 Vehicle models .
4.4.2.2 Environment models .
4.4.3 Steering modelparameterisation
lV 5 Sensitivity Analysis 100
5.1 Problemdescription 100
5.2 Nominal models 101
5.3 Results 101
5.3.1 Integration Verification 101
5.3.2 Modelling error sensitivity . 704
5.4 Sensitivity conclusion . l12
6 Launch Vehicle Design Investigation 113
6.1 Design choices 7r4
6.2 Mission analysis . 115
6.3 Reference mission tt7
6.4 Design concept 777
6.4.1 Propulsion 179
6.4.2 Aerodynamics t2l
6.4.3 Component masses 121
6.5 Staging condition results 722
6.6 Powered booster flyback results 123
6.6.1 Design choice for powered flyback concept 126
6.7 Unpowered booster flyback results 130
v 6.7.7 Design choice for unpowered flyback concept 132
6.8 Comparison 136
6.9 Summary and discussion 138
7 Predictive Guidance for Ascent 139
7.1 Introduction 139
7.2 Problemdescription 140
7.3 Vehicledescription l4l
7.4 Mission profile t42
7.5 Developmentobservations 142
7.6 Ascent guidance results 144
7.6.1 Gravitation model perturbation . 146
1.6.2 Atmosphere modelperturbation 148
1.6.3 V/ind model . 151
7.6.4 Steering parameter models r55
7.6.5 Guidance call intervals ls6
7.6.6 State errors (sensor errors) 158
1.6.7 Non-nominal atmosphereperturbations 160
1.6.8 Staging errors (staging point errors) 162
7.6.9 Thrust loss 163
7.6.70 Monte Carlo analysis 165
7.1 Summary and discussion 167
v1 I Predictive Guidance for Flyback 169
8.1 Introduction t69
8.2 Problem description . n0
8.3 Vehicle description 777
8.4 Mission profile llt
8.5 Developmentobservations 773
8.6 Flyback guidance results 776
8.6.1 Gravitation and atmosphere model 178
8.6.2 Wind model 182
8.6.3 State errors (sensor errors) 188
8.6.4 Guidance call intervals 189
8.6.5 Random wind variations 190
8.6.6 Initial condition effors (staging point errors) . . . . 193
8.6.7 Monte Carlo analysis . t96
8.7 Summary and discussion 200
9 Conclusions 203
9.7 Vehicle design 203
9.2 Guidance 204
9.2.1 Ascent guidance 20s
v11 9.2.2 Flyback guidance 206
9.3 Recommendations 201
9.4 Closing Remarks 207
Appendices 208
A Woomera weather 208
B US Standard atmosphere model 2t0
C MSISE93 atmosphere model 212
D HWM wind model 214
E Aerodynamic coefficient reference table 216
F Flyback-Monte Carlo (NE nom. wind) 218
References 220
v111 List of Figures
1.1 Kistler Kl (Kistler,2002) J
7.2 Expected yearly GEO payload market (2001-2010) (Middleton,1999) 4
1.3 Future launch market (Griner and Lyles, 1998) 6
2.1 Typical performance of a rocket engine (Huzel and Huang, 7992) 72
2.2 Linear Aerospike (NASA, 2002) 13
2.3 SSME on test stand (NAS A,2002) l4
2.4 Aerojet AJ26-60 (Kistler, 2OO2) t6
2.5 NASA X-vehicles 23
2.6 Orbit parameters 26
2.7 Angle description 28
3.1 Wing mass analysis data 51
3.2 Axes for gravitation derivation 58
3.3 Parameterisation using grid points 69
1X 3.4 Parameterisation using function coefficients lo
4.1 ATOPS parameterisation model 73
4.2 Virtual orbiter (Tetlow et a1., 2002) 7l
4.3 Program flow for ascent guidance (Tetlow et a1., 2002) 78
4.4 Virtual orbiter mass distribution 81
4.5 Typical grid type steering model for ascent 88
4.6 Program flow for flyback guidance 90
4.7 Flyback program structure 96
4.8 Typical steering model 99
5.1 Altitude vs Time for integration step comparison 702
5.2 Dynamic Pressure vs Time for integration step comparison 103
5.3 Sensitivity to specific impulse of first stage engine at sea level lo4
5.4 Sensitivity to specific impulse of first stage engine in vacuum 105
5.5 Sensitivity to specif,c impulse of second stage engine in vacuum 105 s.6 Sensitivity to mass flow rate of the first stage engine 106
5.7 Sensitivity to mass flow rate of the second stage engine 107
5.8 Sensitivity to gross lift off weight . 707
5.9 Sensitivity to initiation time of first roll manoeuvre 108
5.10 Sensitivity to final time of first ro11 manoeuvre . 108
x 5.11 Sensitivity to aerodynamic lift and drag coefficients 109
5.12 Sensitivity to constant atmospheric variation at all altitudes 110
5.13 Sensitivity to an atmospheric density increase between 40km and 60km 111
5.14 Sensitivity to an atmospheric density increase between 75km and 40km 111
6.1 Mission profile 118
6.2 Concept vehicle (Tetlow et al., 2007) 118
6.3 Staging condition comparison 723
6.4 Altitude profile 126
6.5 Velocity profile 127
6.6 Ground track 128
6.7 Booster flyback mission (post-staging) 129
6.8 Flyback control parameters 130
6.9 Altitude profile 132
6.10 Velocity profile 133
6.1I Ground track 134
6.12 Booster flyback mission (from staging) 135
6.13 Flyback control parameters 135
1.7 Ascent mission prof,le 142
7 .2 Sequence of virtual environmental variations 745
xl 7.3 Flight profile for the gravity perturbed case 147
1.4 Steering model for the gravity perturbed case t49
1.5 Flight profile for the atmosphere perturbed case. t49
7.6 Steering model for the atmosphere perturbed case 1s0
7.7 Flight profile for the tailwind case 152
7.8 Steering model for the tailwind case 152
7.9 Flight profile for the headwind case 153
7.10 Steering model for the headwind case 154
7.11 Altitude profile with sensor errors 159
7.12 Flight profile with sensor errors 159
7.13 Flight profile for the random atmospheric density and wind case l6t
7.14 Partial steering profile for the random atmospheric density and wind case 162
7.15 Monte Carlo result for final altitude t66
7.16 Monte Carlo result for flight path angle 166
8.1 Flyback mission profile 172
8.2 Sequence of virtual environmental variations 177
8.3 Flight profile for disturbed atmosphere and gravitation case 719
8.4 Steering model for disturbed atmosphere and gravitation case 181
8.5 Flight profile with South Westerly wind 183
xtl 8.6 Steering model with South'Westerly wind 18s
8.7 Flight profile with North Easterly wind 186
8.8 Steering model with North Easterly wind 188
8.9 Flight profile with random wind variation 19r
8.10 Steering model with random wind variation 192
8.11 Guided flight profile with initial condition effors 195
8.12 Steering model with initial condition effors 196
8.13 Monte Carlo result for flnal heading 198
8.14 Monte Carlo result for flight path angle 198
8.15 Monte Carlo result for velocity . 199
4.1 Wind data for'Woomera (BOM-Adelaide, 2002) 209
8.1 US Standard atmospheric density profile 2tt
C.l MSISE93 atmospheric density profile 2t3
D.1 HWM Southerly winds 214
D.2 HIVM'Westerly winds 215
E.1 Aerodynamic coefficient reference table 217
F.1 Monte Carlo result for heading 218
F.2 Monte Carlo result for flight path angle 279
F.3 Monte Carlo result for velocity 219
xI11 List of Tables
1.1 Current launch vehicle costs (Isakowitz,1995) 2
2.1 Current launch vehicles (Isakowitz, 1995) 10
2.2 Orbital velocities 27
6.1 Powered booster vehicle comparison . 124
6.2 Unpowered booster vehicle comparison 131
6.3 Mass breakdown for powered booster flyback concept vehicle 138
7.1 Constraint violations for the gravity perturbed case t4l
7.2 Constraint violations for the atmosphere perturbed case 1s0
7.3 Constraint violations for the tailwind case 153
7.4 Constraint violations for the headwind case 155
I .5 Performance with different parameter models 156
1.6 Performance with different guidance call intervals 158
7.7 Maximum sensor errors (source document is commercially sensitive) 158
xlv 7.8 Constraint violations for the random atmospheric density and wind case 161
7.9 Guidance performance with thrust errors 164
7.10 Error bounds for random variation 165
8.1 Maximum sensor effors (source document is commercially sensitive) . . . . . 188
8.2 Flight results for case with sensor effors 189
8.3 Performance with different guidance call intervals . 190
8.4 Staging condition errors 194
8.5 Maximum variation bounds for Monte Carlo analysis 797
xv Abstract
With the potential growth of the commercial space market, there is a demand for more effi- cient and cost effective launch services. These improvements to launch services would make
space more accessible to many industries, thereby encouraging the commercial space market to grow even further. Launch services can be improved by both better vehicle design and im- proved operations. In the present study alternative reusable launch vehicle design concepts
are investigated, and a robust guidance strategy developed for use on the ascent and flyback phases of flight.
Previous studies have investigated launch systems with unpowered and powered booster fly- back phases; however, few accessible studies have compared the two flyback concepts using the same mission. Although valuable information is obtained by optimising launch systems of a specific configuration, it is also useful to perform a comparison of launch systems with different conflgurations. This provides a clear indication of the performance constraints for each concept, thereby allowing the designer to weigh up the performance and operational lim- itations and generate an optimal launch vehicle design.
The design aspect of this study investigates the payload capability of two-stage fixed gross lift off weight vehicles using two different flyback strategies for the booster stage. The first concept vehicle uses air-breathing engines to perform a powered return flight to the launch site, while the second employs only aerodynamic forces to achieve flyback, hence returning
xvt unpowered. The software employs a trajectory optimiser to determine the optimum flight
path and propellant consumed. It then scales the vehicle size and mass to accommodate the
propellant tanks. A reference mission is used to compare launch vehicle payloads, assuming
launch from'Woomera Prohibited Area, South Australia. It is shown that the vehicle employing
a powered return flight for its booster stage is able to deliver considerably more payload than
the vehicle employing an unpowered booster return flight.
Most current guidance systems use an analytical process to generate steering commands for
the launch vehicle. Analytic systems have the advantage of being stable and require lower
computational power; however, they assume a simplified flight environment, making them sub
optimal or even unsuitable for certain flight phases. Another type of guidance system uses a
numerical approach to generate steering commands. These systems are prone to computational
instability and require more computational power than analytic methods. They do, however,
have the advantage of being able to include any environmental parameter that can be modelled.
Computer performance has increased dramatically over the past decade, making numerical
methods a feasible option. The second aspect of this study is thus to develop a numerical
guidance system that is robust enough for use in real-time, and to apply it to upper stage
ascent and booster flyback missions.
The so-called predictive guidance system works by integrating from the current state, along
the trajectory to the final state of the vehicle. It then compares the achieved final state to the required target state and calculates the target condition error. A parameterised non-linear
optimisation technique is then used to determine the new values of the optimisation parameters required to steer the vehicle from its current position and velocity to the desired position and velocity. Various causes of instability are identifled and then addressed using both numerical and heuristic methods. Once the guidance is operating for the nominal case, environmental and system perturbations are introduced to test robustness. The predictive guidance system is found to operate successfully and offer considerable robustness to environmental and system perturbations, in both the ascent and flyback phases of flight.
xv11
Acknowledgements
I would like to thank my supervisors Dr. Gerald Schneider, Dr. U.M. Schoettle and Dr.
Michael Evans for their support and guidance throughout my studies. I would also like to thank my fellow postgraduate students from the University of Adelaide and my colleagues from the Space Systems Institute at the University of Stuttgart, for their help and support.
My thanks also goes to the administrative staff at the School of Mechanical Engineering. In particular I would like to thank Billy Constantine for many hours of help sorting out my com- puter problems. I would like to thank the University of Adelaide and The Sir Ross and Sir
Keith Smith Fund for their financial support during my research.
I would especially like to thank my parents, Kay and Rod Tetlow for their continual support and understanding. They have always encouraged my scientific and engineering interests, and
I owe many of my achievements to their help and encouragement.
xlx Nomenclature
A= Atealmzf
D = Drag force [N]
F = Thrust [N]
Fv = Vacuum thrust [N]
F¡ = Ttrust and aerodynamic forces along the velocity vector [N]
Fy = Ttrust and aerodynamic forces in the direction to complete the orthogonal set [N]
F¿ = Thrust and aerodynamic forces in the local horizontal plane [N] g = Earth's gravitational acceleration lmf s2l go= Earth's gravitational acceleration at ground Levellmf s2) h = Altitude [m]
Irp = Specific impulse [s]
Ixx = Mass moment of inertia about the x-axis lkT.m2l
Ir, = Mass moment of inertia about the y-axis lkg.m2)
Izz = Mass moment of inertia about the z-axis lkT.m2l
xx L = Lift force [N]
m=Yehicle mass [fr8] me =Final vehicle mass [fr8] mo =Initial vehicle mass [frg]
M¿= Mass of the Earth [frg]
1\{" - Moment torque about the roll or x- axis ÍN.ml
I\4 = Moment torque about the pitch or y-axis lN.ml
Mz = Moment torque about the yaw or z- axis lN.m]
¿ = mass flow rate ÍkSlsl
P = Pressure lpa)
Rr= Radius of the Earth at the equator [m]
R¿ = Radius of the Earth at apointlml
Rp= Radius of the Earth at the poles [m] ra= Distance between the Earth and a spacecraft at apoapsis [m] rrr¡= Cylinder radius [m] rp= Distance between the Earth and a spacecraft at periapsis [rn] v = Vehicle velocity lmf s] cr = Angle of attack [']
ÂV = Velocity incrementlmlsl
xxl ô = Latirude [.]
e = Thrust angle ["]
T= Flight path angle ["]
l, = Longitude ["]
Ë = Bank angle ["]
p = Atmospheric density Iks/*31 or = Angular velocity of the Earth lradlsl
@v¡ = Vehicle angular velocity about the x-axis relative to the velocity co-ordinate system
lrad /sl oqy = Vehicle angular velocity about the y-axis relative to the velocity co-ordinate system [rad/sl
(t)v,z = Vehicle angular velocity about the z-axis relative to the velocity co-ordinate system lrad/sl o¡ = Vehicle angular velocity about the x-axis frad lsl rÙ = Vehicle angular velocity about the y-axis lrad /sl oz = Vehicle angular velocity about the z-axis lradlsl
I = Heading angle [']
xx11 Acronyms
DOF - Degrees of Freedom
COG - Centre of Gravity
CRV - Crew Return Vehicle
FESTIP - Future European space Transportation Investigation program
GEO - Geostationary Earth Orbit
GLOW - Gross Lifr offV/eight
GTO - Geosynchronous Transfer Orbit
HAC - Heading Alignment Cylinder
HWM - Horizontal Wind Model
IRS - Institut für Raumfahrtsysteme (Space Systems Institute), University of Stuttgart
LEO - Low Earth Orbit
LOX - Liquid Oxygen
LHz - Liquid Hydrogen
LTO - Low Earth Transfer Orbit
xx[11 MOD - Mission Operations Directorate (Space Shuttle)
MECO - Main Engine Cut-Off
NLP - Non-linear programming
SLI - Space Launch Initiative
SRB - Solid Rocket Booster (Space Shuttle)
SSME - Space Shuttle Main Engine
SSTO - Single Stage to Orbit
TAEM - Terminal Area Energy Management (space Shuttle entry guidance)
TPS - Thermal Protection System
TSTO - Two Stage to Orbit
xxlv Chapter 1 fntroduction
The work carried out in this thesis deals with issues involved in improving launch vehicle design and operations. Two main areas of research are addressed. The first is launch ve- hicle design, showing a comparison between powered and unpowered flyback of a booster.
The second is the development of a predictive guidance system, which will improve launcher flexibility and reduce the amount of pre-flight guidance analysis required for each launch.
1..1 Background
The end of the last decade saw a significant growth in the commercial space market. The growing use of computer networks for business and personal use, satellite phones and global positioning systems, as well as live television being broadcast across the world, resulted in an increased demand for satellite time. Since the late 1990's there has been a steady fall in the telecommunications satellite launch industry due to the excess of satellite bandwidth and the debt incurred to deliver the currently orbiting satellites (Butash, 2002). The forecast of satellite launches for the next decade has declined more than20Vo from forecasts in the year 2001. The market is, however, still expected to grow in future years. According to Wang et al. (1998),
1 1.1. Background 2
"satellite communications" \ryas a US$38.8 billion revenue market in 1998 and it is expected
to grow to over US$171 billion by the year 2007. Although this growrh is likely to be due
to the further expansion of the communications industry, a considerable amount of research
has also been performed showing a number of businesses, such as space tourism (Fatava and
Martineau, 2002) and inner solar system mining (Lee,20O2), that could thrive given access to
space. The major factor preventing this development from going forward is the extremely high
cost of current launch services (Mueller et al., 1993).
Launch vehicle Payload to LEO Payload ro GTO Estimated launch cost Anane 44L 9600 kg 4520kg US$90-110 million Ariane 5 18000 kg 6800 kg US$120 million Atlas IIAS 8640 kg 3606 kg US$95-105 million Atlas IIA 728Okg 3039 kg US$80-90 million Detta7925 5089 kg 1840 kg US$45-50 million H2 10500 kg 4000 kg US$150-190 million Proton D-1 20900 kg 5500 kg US$50-70 million Space Shuttle 24400kg 5900 kg US$300 million Titan IV 72640kg 8620 kg US$248 million Zenit l374Okg 5180 kg US$35-70 million Table 1.1: Cunent launch vehicle cosfs (Isakowitz, 1995)
As shown in Table 1.1, the cost of current launchers such as Ariane 5, the Japanese H-2 vehicle or Titan IV can be as high as US$248 million, while a single launch of the Space Shuttle could cost as much as US$300 million. Although still expensive, the Russian launchers are often thought to be slightly cheaper than their Western counterparts, as shown by the Proton and
Zenit costs in Table 1.1. Contrary to this, however, Soyuz-Fregat is said to be capable of delivering 5500frg of payload to a 450km circular orbit at a cost of between US$50-60 million
(Zak,20O2), which is no cheaper than several Western launchers. This may be influenced by the fact that Soyuz-Fregat is operated by Starsem, a French-Russian joint venture, hence the 'Western pricing standard.
The high cost of current launch vehicles is due to either their expendability or their require- ment for extensive refurbishment and pre-flight analysis before launch. This has prompted
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.1. Background J
Figure 1. 1 : Kistler Kl (Kistler, 2002)
much research into new design and operational procedures for the next generation of launch
vehicles. New launchers will require vast improvements over cunent vehicles with regard to
cost, reliability, safety and operations. This can only be achieved by improving technology in
the areas of propulsion systems, vehicle structures, guidance systems, vehicle operations and 'With materials. advances in technology, new designs will be needed to take advantage of these
technological developments. Although there is a push to reduce the recurring costs of current
expendable launch vehicles (Knauf et al., 2002), the only way to dramatically reduce launch
costs is to develop fully reusable systems. This would allow the cost of a launch system to
be recovered over a number of flights instead of a single flight, as is the case with expendable
launch vehicles (Wang et al., 1998).
With the view of reducing future launch costs, a number of investigations are being conducted worldwide on reusable launch systems. Reusable launch vehicle investigations in the USA include NASA s Space Launch Initiative (SLI), Boeing's X-37 andthe Kistler Kl (Figure 1.1).
An indication of the potential cost reduction achieved by re-usability is displayed by the Kistler
Kl. According to Chakroborty et al. (1998) it will cost US$17 million to deliver a 4.5tonne payload to LEO. This amounts to a 5O7o costreduction per launch, when compared to the Delta
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.1. Background 4
7925lawch vehicle (shown in Table 1.1), which has a similar payload capability. The cost reduction sought for the SLI program is to reduce launch costs to US$1000nb (Sietzen, 2002).
Nease (1998) suggested a strategy to reduce the annual operating costs of the Space Shuttle by
US$400 million, based on seven flights per year, by replacing the solid rocket boosters with reusable liquid flyback boosters. A number of studies are also being carried out in Europe, such as FESTIP (Future European Space Transportation Investigation Program) and FLTP (Future
Launch Transportation Program). FESTIP (1998) shows a move towards reusability by the
European Space Agency, with the recommended gradual development of the Ariane launch vehicle family to include two fully reusable stages.
20
<1814 kg lSls-4082 kg 4083-5443 kg 15 >5443 kg
Ø (l)
í) Ø 10 tt zci
5
0 0 2 3 Mass category
Figure 1.2: Expected yeafly GEO payload market (2001-2010) (Middleton, 1999)
An assessment of the yearly commercial payloads expected from the year 200I to year 2010, carried out by the Federal Aviation Administration (FAA), predicts that 767o of satellites launched into Low Earth Orbit (LEO) will have a mass less than 800kg (Middleton,1999).
The Geostationary Earth Orbit (GEO) market, shown in Figure I.2,will be dominated by two categories. It is expected that 36Vo of payloads will be between 1815kg - 4082k9 and 427o between 4082kg - 5443kg, with the FAA prediction also indicating a growth in the number of satellites above 5443k9. The remainder of the satellite market is expected to consist of
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.1. Background 5
payloads outside the afore mentioned ranges. The Teal group performed a similar study, fore-
casting the world satellite market for the next 3O-years (Caceres, 2003). This study, shows
the trend that satellite operators are moving away from large satellites (5 tonne approx.), such
as the Boeing Satellite Systems BSS-702s and the Loral 20:20, to smaller satellites such as
the Orbital Sciences Galaxy (1.7 tonne) satellite. At the same time, Alcatel Space Industries
and Astrium are proposing a 10 tonne Alphabus satellite, which could be available in the next few years. Boeing Satellite Systems seem to have recognised the shift in demand towards the smaller satellites, starting the development of a new medium-sized satellite base on the
855601 (Caceres, 2003).
Middleton (1999) states that although the number of satellites requiring launch has increased, so has the annual capacity of launch service providers. As a result, the excess of demand over supply that supported higher launch prices for years, is changing to an excess in supply. In the
LEO market, an average of 77 satellites per year Íìre expected to require launch over an eleven year period, while the launch capability is well over l00launches per year. The GEO market predicts a similar scenario, with 33 satellites expected to require launch each year over the eleven year period, while current launch companies are capable of providing 69 launches per year, with this number expected to rise to 80 by the year 2005. This shows that the potential number of launches exceeds the payload estimate by up to 1007o, suggesting that the launch vehicle market will become highly competitive, with only the cost effective launch services or those supported by government likely to survive.
An independent study conducted by Griner and Lyles (1998), illustrated in Figure 1.3, suggests there will be an exponential growth in the international payload market, provided there is a substantial reduction in launch costs. The time scale of this reference seems to be slightly optimistic;however, it does illustrate the potential growth in the commercial launch market if launch costs can be reduced. A more recent assessment of the commercial launch market, seen in de Selding (2001), has predicted a fall in the number of large (above 5000ftg) commercial satellites, from 30-35 per year, as predicted two years ago, to 20-35 per year. This suggests that
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.1. Background 6
Market Ëxpansion Potenlial Ë.DDO
t'- ^ l¡ h:leill urrti he;r';y f : 1.t.,lOD lt¡s] 5 QLI(ì il tjllr,1-Lite rrr0 Sniall i.:1.000 ¡bsl
4-C/ûtl >E Ð o. fi d 3.ùÐ0 t) L q -3 000 FY22 li I oÙ's¿tb 't.0ô0 FYü7 sl.00uilÞ
0 DuffBnl 5,C00 1_C'00 Ê0c ioO 40û 3rl0 200 100 5ù CoEl Þer Pound ($I1o Low Eanh OrÞlt
Figure 1.3: Future launch market (Griner and Lyles, 1998) the market will become more competitive and launch providers will have to seek new ways of reducing launch costs.
Clearly the launch vehicle market is expected to be highly competitive over the next 10 years, making it vitally important to produce a reliable low cost vehicle to compete in the market. All of the launchers currently available, bar the Space Shuttle, are expendable, making it difficult to reduce the vehicle cost significantly as the entire launch vehicle cost needs to be recovered in a single launch. One way to reduce launch cost is to produce a reusable launcher that can recover the vehicle cost over multiple launches instead of a single launch. The research in the present study will therefore include recovery and reuse of the entire launch vehicle.
Another area with the potential for improvement is launch vehicle operations, of which the guidance system is a part. Improved guidance systems would reduce the requirement for ex- tensive pre-flight trajectory analysis, thereby reducing the launch costs. It is also hoped that these guidance systems will allow more optimal trajectories to be flown, thereby reducing fuel requirements or possibly increasing payload capabilities. A study published in 1991 showed that NASA Mission Operations Directorate (MOD) spent over US$32 million on activities for
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.2. Objective 7
each Shuttle flight (Bordano etaI.,1997). MOD activities include staffing and associated facil-
ities for pre-flight trajectory analysis of upcoming Space Shuttle flights. Costs associated with
pre-flight analysis thus accounted for more than 727o of the 1991 estimated cost of US$258.4
million per flight. If a guidance system could be developed that did not require such extensive pre-flight analysis, it could reduce this 727o fraction of the Space Shuttle cost significantly.
1.2 Objective
As a contribution to the development of future launch vehicles, two aspects of launch systems were investigated in the present study. The first aspect of the study was the optimisation of the vehicle design. Currently, there are no multistage launch vehicles that have a return to launch site flight for the booster. Instead, the boosters are simply dropped after use and they fall back to the Earth, to be picked up by a recovery vehicle/vessel. The objective of this study was thus to design a commercial launch vehicle concept that uses a winged flyback booster, which returns to and lands at the launch site, so that no recovery vehicle/vessel is required.
More specifically, the objective was to compare two booster flyback missions: the first using air-breathing engines on the booster, and the second employing only aerodynamic forces to return to the launch site. The vehicle design was performed using software developed at the
Space Systems Institute in Stuttgart, German¡ for German space programs.
Guidance systems play an important role in payload delivery missions as they effect both per- formance and operations of the launch vehicle. During ascent the guidance system is required to command a near optimal flight trajectory thereby delivering the payload to the required orbit using the minimum amount of fuel. During re-entry and booster flyback, the guidance system is required to guide the vehicle to a specified landing point without exceeding heating and structural loads.
Current guidance systems require intensive pre-flight trajectory analysis, which adds consider- able cost (more thanT2Vo in the case of the Space Shuttle) to the mission. Ascent guidance sys-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 1.3. Practical application I tems that use position and velocity feedback are generally only applicable to exo-atmospheric flight phases, thereby having to rely on open loop guidance during atmospheric flight. This introduces operational constraints as launch has to be postponed if weather conditions are dif- ferent to models used during pre-flight analysis. The second aspect of the study was thus to develop and test a guidance system, capable of real-time guidance updates, while at the same time not requiring intensive pre-flight trajectory analysis. A numerical approach was chosen to enable modelling of atmospheric parameters, thereby allowing the guidance system to operate near-optimally in the atmospheric as well as exo-atmospheric flight phases.
L.3 Practicalapplication
This study will provide future launch vehicle designers with a guide to the optimal stage sizes for vehicles with a similar mission profile to the one being considered in the study. It can also be used to demonsfrate typical flight profiles of winged ascent launch vehicles in the upper stage ascent and booster flyback phases.
The predictive guidance system can be used on any curent or future launch vehicle. The software is in a modular format, making it easy to change system models and adapt it to different launch vehicles and target orbits. The IRS has proposed this predictive guidance system for use on future reusable launch systems investigated in the technology program called
Astra (Schoettle, 2002).
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 2
Literature Review
2.1 Launch vehicles to date
During the cold war, many launch vehicles such as Rokot, Soyuz, Titan and Atlas (Heppen- heimer, l99l) were developed as inter-continental ballistic missiles (ICBM's) or intermediate- range ballistic missiles (IRBM's) to carry nuclear warheads. They served as a stern reminder that any attack on the USA or the Soviet Union would be met with a devastating retaliation.
Some launch vehicles that were originally intended for military application have since been modified, to various degrees, to carry revenue generating, commercial payloads. An example of this is the Russian R-7 ICBM, which was developed into the now well-known Soyuz launch vehicle, which launched such spacecraft as Vostok and Voskho d (Zak,2002).
Two families of American launchers that are currently undergoing performance and general program improvements are the Atlas and Delta launch systems (Knauf et al., 2002). As part of the EELV (Evolved Expendable Launch Vehicle) program, these two families of launch vehicles are being improved in order to minimise recurring costs and to increase payload mass performance. The aim is to reduce the recurring operational costs by 25 - 50Vo compared to current systems (Knauf et a1., 2OO2).
9 2.2. Propulsion sysfems 10
Ex-military vehicles and purpose-built commercial launchers from more than six countries provide a considerable number of launch vehicles capable of launching commercial payloads 'With into orbit. manufacturing and processing facilities already in place, launch companies from these countries are able to offer highly competitive services in the commercial launch vehicle market. Table 2.1 shows the main launchers and their payload capabilities.
Launch Vehicle Propulsion System Payload LEO Payload GTO Ariane 44L Liquid main engines and boosters 9600 kg 4520ks Ariane V Liquid core and 2nd stages 18000 kg 6800 kg 2 solid rocket boosters PSLV Solid l"t and3'd stages 2900kg 6 solid strap on boosters. Liquid engines on2nd and4th stages GSLV Solid lsr stage with 4liquid 5000 kg boosters. Liquid 2nd and 3'd stages
H1 Liquid 1"r and 2nd stages 3200kg 1 100 kg 9 solid strap on boosters H2 Liquid 1rr and 2nd stages 10500 kg 4000 kg 2 solid strap on boosters Energia Liquid 7't ,2'd shges and boosters 88000 kg Soyuz 2 liquid stages, 4 liquid boosters 7000 kg Kosmos l"tand Znd stages liquid engines 1400 kg Proton 3 liquid stages, 6 liquid boosters 20900 kg 5500 kg Zenit3 3 liquid stages 13740kg 5180 kg Atlas II AS 2 liquid stages and liquid boosters 8640 kg 3606 kg Delta II Liquid I't ,2'd and 3'd stages 5089 kg 1840 kg 9 strap on solid boosters Space Shuttle 3 liquid engines and 244O0ks 5900 kg 2 solid rocket boosters Titan IV Liquid l"t and 2nd stages 12640kg 8620 kg 2 solid rocket boosters
Table 2.1: Cunent launch vehicles (Isakowitz, 1995)
2.2 Propulsion systems
The correct choice of the propulsion system is one of the most important decisions to be made when designing a rocket (Hammond ,2001). Various types of propulsion system, such as air-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 11 breathing propulsion, chemical rockets, electric propulsion, etc. are used depending on the flight phase. According to Griffin and French (1991), the single most important measure of engine performance is Specific Impulse (1ro), which they described as "the change in mo- mentum per unit mass of propellant consumed". Clearl¡ the higher the specific impulse, the higher the momentum transferred to the vehicle per mass of propellant consumed, therefore, the higher the payload capability for a fixed mass of propellant. This can be shown using the well known Tsiolkowsky Equation (Equation 2.1), where 1ro is specific impulse, go is gravity at sea Level, ms is the initial vehicle mass, m" isthe final vehicle mass and Âv is velocity incre- ment. For a constant propellant consumption, the higher the specific impulse, the higher the velocity increment. (*o\ Lv:: I'rgstnI r^,. (2.1) \* )
Another important measure of propulsion system performance is thrust. When a pressurised, high temperature gas is expanded adiabatically through a nozzle, the sensible energy of the gas is converted into kinetic energy, producing thrust (Kubota, 1934). This thrust (F) has two components, as shown in equation 2.2. The first is an impulse term defined by the product of the mass flow rate of propellant Qh) and the exit velocity (v"r). The second term is a pressure term that defines the pressure distribution in the propulsion system, using a simple integral of the pressure (P) over the interior surface area (A). The thrust generated needs to be sufficient to propel the vehicle when it is full of fuel, but not so high as to cause the vehicle to exceed its acceleration and heating limits, once its mass has reduced due to propellant consumption.
F : thvext f r.aa (2.2)
2.2.1 Chemical rocket propulsion
In chemical rocket propulsion systems, all of the substances required for combustion are stored on board the rocket in solid, liquid or gaseous form. The combustion products are expanded
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 12 through a nozzle, producing thrust. A typical thrust and 1ro variation with altitude is shown in Figure 2.1. For most launch vehicles using a fixed expansion ratio, the 1"o increases as atmospheric pressure decreases. An example of this is the Aerojet AJ26-59liquid oxygen
(LOX)-kerosene rocket engines, used on the first stage of the Kistler Kl launch vehicle. These engines have a fixed expansion ratio of 271 , and produce a specific impulse of 297 .2s at sea level and 331.3s in a vacuum (Chakroborty et a1., 1998). The reason for this is that part of the thrust force is generated by a pressure difference between the combustion chamber and the local atmosphere (Kubota, 1984). For a constant propellant flow rate and hence a con- stant combustion chamber pressure, the decrease in atmospheric pressure as altitude increases causes the thrust force to rise, thereby increasing the specific impulse.
!s"S Spçeitic ltfìfrul$Þ âî'Outtlt æ8 $
F lk) T Th.uçl *l CLrtolf
?79,ü)0 lh
{r 3ó $s s0 1æ 1S0 180 210 24Q {$ti Åltitudê {tt x ld}
Figure 2.1: Typical performance of a rocket engine (Huzel and Huang, 1992)
Nozzle design
An ideal nozzle is required to expand the combustion products from the chamber pressure to the local atmospheric pressure. Because the local atmospheric pressure changes as the vehicle ascends, tbe nozzle would have to continually change its expansion ratio if it were to operate optimally throughout the flight. Most nozzles, however, are only designed to operate optimally at one altitude, so operation at any other altitude results in either under- or over-expansion
l- 'Expansion ratio is equivalent to area ratio, which is defined as the ratio of exit area to throat area of a converging-div erging nozzle (Brown, 1 996).
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 13
(NASA, 2002). Because both over- and under-expansion cause losses in engine efficiency, it
is important to carefully consider the flight conditions of a propulsion system when designing
the nozzle.
The issue of over- and under-expansion has led to the development of dual position exhaust nozzles, which use a low expansion rutio nozzle at low altitudes. Once the atmospheric pres-
sure has dropped sufficiently, an extra section of nozzle slides down over the existing nozzle, thereby increasing its expansion ratio. An example of an engine with a dual position nozzle is the Pratt & Whitney RL 108, which is used on the Delta 3 and Delta 4 launch vehicles. An- other way to improve nozzle efficiency at different altitudes is to use a linear aerospike rocket engine (Hammond, 2001). It has a unique-wedge shaped design that causes the thrust plume to expand against the wedge on one side and against atmospheric pressure on the other. This allows the exhaust plume to widen as the atmospheric pressure decreases, thereby maintaining optimum performance at all altitudes (NASA, 2002). The Linear Aerospike engine that was to be used on the X-33 technology demonstrator is shown in Figure 2.2.It was estimated to have a sea level specific impulse of 339.9s and a vacuum specific impulse of 429.8s (NASA, 2002).
Figure 2.2: Linear Aerospike (NASA, 2002)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 14
Solid Rockets
Solid rocket motors use solid fuel stored inside the motor casing. The fuel is packed in a paste form and cured to a hard rubbery state at elevated temperatures (Hammond, 2001). The mixture burns violently when ignited, thereby creating hot gases, which expand down the nozzle to produce thrust. Solid fuelled rockets have the advantages of having a long storage life and requiring no cooling system or turbo machinery. Their reliability and storability make solid rockets well suited for military applications (Kubota, 1984).
Figure 2.3: SSME on test sfand (Nr{S,A,2002)
Although solid rocket motors can produce a large amount of thrust, they generally have a lower specific impulse than liquid fuelled rockets. Consider a Space Shuttle Main Engine
(SSME) shown in Figure 2.3.It produces L67MN of thrust at sea level and 363.2s of specific impulse, while a Space Shuttle Solid Rocket Booster (SRB) generates IL79MN of thrust but only 267.3s of specific impulse in a vacuum (Isakowitz, 1995). Most solid rocket motors also have the undesirable characteristic of not being able to be to shut down once ignited. The motors will generally burn until all of the propellant has been expended. Unlike liquid rockets, solid rockets cannot be throttled by varying the propellant mass flow rate into the combustion
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 15 chamber; instead, the thrust-time profile is varied by varying the cross-sectional area or core shape of the propellant. The greater the exposed surface area, the higher the mass burn-rate and hence thrust. By moulding portions of large and small exposed surface areas, the mass flow rate through the motor can be altered. The thrust generated by a solid rocket motor (F) is determined using Equation 2.3 (Schneider and Kelso, 2002),
F:A6prqlry (2.3)
where A¿ is the instantaneous grain surface area at the flame front, ps is the density of the unburned propellant grain,lro is the propellant specific impulse and q is the burn rate or speed at which the flame front is progressing.
Liquid Fuel Rockets
Liquid rockets use propellants stored in liquid form, which is either pressure fed or pumped into the combustion chamber. The two major classes of liquid propellant systems are mono- propellants and bipropellants; tripropellant systems (eg LOX, Kerosene and H) have been investigated, but are uncommon so will not be discussed.
Mono-propellant systems consist of a single substance that decomposes by means of a catalyst to produce high temperature and pressure gases. The propellant must be stable in a natural or controlled environment, yet should produce hot combustion or decomposition gases when fed through a catalyst. Mono-propellant systems have the advantage of simplicity with respect to storage and feed systems, however, their specific impulse is generally less than that of 'With bipropellant systems. current technology, mono-propellant rocket motors are limited to about 250s of specific impulse (Comelisse et al., 1979). Mono-propellant systems also do not produce enough thrust for launch purposes (Schoettle, 2002) and are therefore mainly used in secondary power sources such as turbo pump gas generators, auxiliary power drives and roll control jets (Huzel and Huang ,1992). Monopropellant propulsion systems are also widely
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 16
used on geostationary communications spacecraft for North-South station keeping and attitude control (Fortescue and Stark, 1995). Examples of mono-propellants are hydrogen peroxide and hydrazine which have specific impulse values of 165s and 195s respectively (Fortescue and
Stark, 1995). Bipropellant systems have an oxidiser and a fuel, which are stored separately.
The combination is mixed in the combustion chamber, where it ignites and produces thrust.
An important aspect of rocket design is the storage of the propellant required for the mission.
Storable propellants are those propellants that can be stored for long periods of time without any loss in performance. An example of a storable propellant is RP-l, which is a kerosene derived fuel. This fuel was used on the Saturn V launch vehicle (Isakowitz, 1995). Standard kerosene is also used as a fuel and was used in the Russian NK-33 and NK-43 engines for the
Russian lunar missions (Chakroborty et al., 1998). These already flight-qualified and exten- sively tested engines have been modified by Aerojet to produce tbe AJ26 series engines, which have improved performance and robustness (Chakroborty et al., 1998). Figure 2.4 shows a kerosene fuelled Aerqet AJ26-60 rocket motor.
Figure 2.4: Aerojet A126-60 (Kistler,2002)
Cryogenic propellants have very low boiling points (-145"C to -256"C ) at ambient pres- sures, as well as very low critical temperatures2 1- L2"C to -240"C ) (Huzel and Huang, 2The critical temperature of a pure substance is the maximum temperature at which the liquid and vapour
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysfems 17
1992), causing significant storage and handling difficulties. Elaborate insulation techniques
need to be employed to minimise losses due to boil-off, as well as the provision of an adequate
venting system to prevent gas build up. Cryogenic propellant rocket engines are attractive to
designers as they produce high specific impulse relative to storable propellants, however, the
structure required to contain the cryogenic propellants is generally heavier and more compli-
cated than that for storable propellants. An example of a cryogenic propellant combination
is liquid Hydrogen (LHù and liquid Oxygen (LOX), which is used in the SSME, rhe Vul-
cain (HM60) engine on Ariane V and theLBl rocket engine, which is used on the H2launch
vehicle (Isakowitz, 7995).
Another common bipropellant combination used for space propulsion systems is hypergolic
propellants. This propellant combination ignites spontaneously when the fuel comes into con-
tact with the oxidiser. Although this property greatly simplifies the problem of propellant
ignition (Huzel and Huang, 7992), unintentional mixing of fuel and oxidiser due to hardware
failures can cause violent explosions. Hypergolic fuels have been used extensively in the past
(Isakowitz, 1995), but due to their relatively low performance their use is becoming less com-
mon. An example of a launch vehicle which uses hypergolic propellants is Titan Iy which
uses N2O4 as an oxidiser and Aerozine-5O as fuel.
A propellant feed system is required to deliver the propellant from the on-board tanks to the
liquid fuelled rocket engine at the correct flow rate and pressure. The propellant can either be
forced into the engines by a high pressure gas (gas-pressurised), or it can be pumped to the
combustion chamber using a turbo pump (a compact machine including a turbine and a pump).
There is no simple rule for the choice between gas-pressurised and turbo pump feed systems.
However, rockets with smaller propellant volumes often use the gas-pressurised system as the weight penalty to strengthen the tanks is not significant compared to the complexity of a
turbo pump amangement (Huzel and Huang, 1992). Large, high thrust, long duration liquid propellant rocket engines, such as the SSME (thrust = l.67MN (Isakowitz, 1995), burn time phases can coexist in equilibrium (Moran and Shapiro, 1996).
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion sysúems 18
> 500s (Huzel and Huang, 7992)), generally use a turbo pump feed system as it lowers the weight of the tanks and raises the performance compared to that of a pressurised gas fed engine (Huzel and Huang, 7992). This has resulted in turbo pump fed propeltant systems being used in launch stages, as the vehicle is very heavy and requires high thrust. The upper stage propulsion systems often employ pressure fed systems as the vehicle weight is an order of magnitude lower than that of the launch stages. With advancements in high strength tank materials and small, reliable turbo pumps, the range of rockets suited to each system has expanded. This has resulted in combined systems being developed, which use pressurised tanks to minimise the turbo pump size. Pressurised propellant tanks are also used to provide structural stability for rockets (Schoettle, 2002).
2.2.2 Air-breathingpropulsion
The first stage of the Ariane I launch vehicle burns approximately l2\tonnes of fuel (f of which is oxidiser) to accelerate the vehicle to l500mfs (Mach 4.5) at an altitude of 30km
(Fortescue and Stark, 1995). This altitude and velocity is well within the operating limits of air- breathing propulsion, which could have a specific impulse of 6000s (and beyond), as opposed to the 278s of the Viking V engine used on the Ariane 1 to Ariane 4 launchers (Fortescue and
Stark, 1995). Even the most advanced rocket propulsion systems such as the Vulcain engine
(core stage or Ariane 5) and the SSME are restricted to a specific impulse of about 455s.
Such statistics provide good reason for investigating the use of air-breathing propulsion during launch.
Current turbo fan propulsion systems are limited to an operating speed of Mach 3.5 (Tanatsugu et al., 1985), however, NASA Lewis are working on a turbine jet engine capable of Mach 4
('Wilson, 2002). A drawback of turbine air-breathing propulsion systems is their low thrust- to-weight ratio (Schoettle, 1989). One of the more powerful turbojet engines is the Pratt &
Whitney PV/4098, which develops 436kN of thrust and weighs 7303kg (Jackson, 1998), giv-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.2. Propulsion systems 19
ing it a thrust-to-weight ratio of 59 .7 N I kg. By comparison, the Space Shuttle Main Engines develop l670kN of thrust and weigh only 3775k9 (Syromiatnikov, 7992), giving them a thrust- to-weight ratio of 526N lkg.
According to Schoettle (1989), ramjets are limited to an operating velocity of between Mach 1.5 and Mach 8 and produce 3000 - 4000s of specific impulse. The operating range of these engines, however, prevents them from being used during launch and also prevents them from being used at high staging velocities (around Mach l0 - 12 (Rahn and Schoettle, 1996)). Scramjet (supersonic combustion ramjet) propulsion systems are only in the development stages, but are expected to have an operating range of between Mach 5 and Mach l5 (Fortescue and Stark, 1995). According to Schoettle (2002), it is not worth using scramjets above Mach
12, due to limited thrust, however, even at Mach 12, Fortescue and Stark (1995) indicate that scramjets will have a specific impulse three times higher than that of current cryogenic rocket propulsion systems. Scramjet development is being conducted by the US Air Force, who are working on an actively cooled hydrocarbon fuelled scramjet ('Wilson, 2002).In Australia, the
University of Queensland's Centre for Hypersonics became the first research group to success- fully flight test a scramjet engine, and so are also actively involved in the development of high speed air-breathing propulsion systems.
As discussed before, the specific impulse of air-breathing engines can be an order of magnitude higher than that of rocket engines. The increased drag and substantially heavier systems, however, need to be considered when determining which propulsion system is best suited to a specific launch vehicle (Schoettle, 1989). Combination engines employing air-ejector-rocket- ramjet or scramjet-rocket propulsion appear to be attractive, but only with the use of advanced material technologies (Bekey, 1994). The concept of scramjet propulsion is in the development stage and has few working examples. For this reason, the use of these engines in a launch system would require high development costs, making them less viable for commercial launch vehicles.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3. Vehicle design aspects 20
2.3 Vehicle design aspects
Launch vehicle designs vary considerably depending on the intended purpose of the vehicle.
The mass of the payload, target orbit and trajectory flown will all need to be considered when choosing a suitable launcher. A number of design aspects will now be investigated and their effect on launch vehicle performance discussed.
2.3.1 Vehicle configuration
One of the first design decisions to make is whether the vehicle should fly in a parallel or a tandem configuration. Parallel configuration means that the stages are side-by-side and they operate at the same time. A tandem configuration is when the stages are above one another and they operate one at a time.
A parallel configuration has the advantage of not carrying idle rocket motors. The disadvantage of this strategy is that the vehicle often has a bigger frontal area than its equivalent tandem conflguration vehicle, due to the fact that the stages stand along-side each other. It is therefore subject to higher atmospheric drag. Parallel configuration vehicles also have the disadvantage of having engines on the orbiter that are required to operate in both the dense low altitudes and the near vacuum of higher altitudes. This causes higher losses due to non-optimal expansion ratios for a large portion of the flight. It can, however, be overcome by using dual position nozzles or even a Linear Aerospike engine (see Section3.7.2 for further explanation).
Tandem conf,guration vehicles, on the other hand, often experience less drag, but waste pay- load mass as they need to carry idle engines for the upper stages. The optimal trajectories for these two configurations would be significantly different. The parallel configuration would fly a steeper trajectory to get out of the atmosphere as quickly as possible, thereby minimising drag losses (Schoettle, 1996), while the tandem conf,guration could fly a shallower trajectory, thereby minimising gravity losses.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3. Vehicle design aspects 21
2.3,2 Number of stages/boosters
Launch vehicle design is highly dependent on the mission it is required to fly and the payload
mass it has to carry. Many launch vehicles are thus designed with multiple versions, to try
and match the performance requirements for a range of customers. For example, Ariane IV
may use a central core alone, or a central core augmented by either two or four solid or liquid
strap-on boosters (Isakowitz, 1995). This allows the vehicle to fly a range of different missions
without requiring redesign of the entire vehicle. The Boeing family of Delta (Boeing, 2002)
launchers and the Lockheed Martin family of Atlas (LMCO, 2OO2) launch vehicles use a sim-
ilar strategy of variable numbers of strap-on boosters, to try and capture more of the payload
market (Knauf et al., 2002). This strategy is easy to achieve with expendable vehicles as the
boosters are not recovered so, provided they are disposed of safely, it does not matter where
they land. A fully reusable vehicle, however, requires that all of its stages be recovered, so it
would be undesirable to have to recover four boosters as well as a central core. It is thus desir-
able to have as few stages as possible on a reusable vehicle, to simplify operational aspects of the mission.
There are a number of different opinions regarding the optimum number of stages for a launch
vehicle, when considering available technology. The velocity increment, Âv, that a launch
vehicle can produce can be computed using Equation 2.4 for a tandem configuration vehicle,
and Equation2.5 for a parallel conf,guration vehicle. Iro is the effective specific impulse, 96
is the gravitational potential on the Earth's surface, rh is the propellant mass flow rate, ms
the initial mass of the vehicle and m" the final vehicle mass after the burn. In Equation 2.4,
i represents the operating stage and n the total number of tandem stages on the vehicle. It should be noted that Equation 2.5 is only relevant for the flight phases in which the vehicle is flying in a parallel configuration, with j representing the number of different propulsion systems operating. Once the boosters separate from the orbiter, a second Âu component would need be calculated using Equation 2.4. rJsingthe Space Shuttle as an example, Equation2.5 would be used to calculate the Âv produced while operating under the SRB's and the SSME's
commercial Launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3. Vehicle design aspects 22 together. Equation 2.4 would then be used to calculate the remaining Av produced by the rest of the SSME burn and the Orbital Manoeuvring Sysrem (OMS) burn.
Avr: it,r,goJnYY (2.4)
Lrp: ,oL!0,:,!¡-¡n!l (2.s) Limi me
Expanding Equation 2.4 to "n" stages, it can be seen that the higher the number of stages, the higher the velocity increment for the same mass of propellant. This is, however, limited in practice, as the more stages in the tandem configuration, the more idle engines that need to be carried. More stages also implies more operational complexity as each stage needs to be tracked and possibly controlled to land in a particular area. The number of stages would therefore be kept to a minimum while still providing enough energy for mission success. More than 4 stages is uncommon for launch vehicles (Isakowitz, 1995).
The most efficient design with regard to operational issues is a Single Stage to Orbit (SSTO) vehicle, as only one stage needs to be recovered (Hammond, 2001). The problem with SSTO vehicles is that they require very light dry masses and trade structural weight for payload weight on a kilogram for kilogram basis. Many people argue that this makes SSTO vehicles too risky, however, recent technological advances indicate otherwise.
In the pre-shuttle era, propellant mass fraction, which is propellant mass divided by start mass minus payload, was limited to around 0.84 for a vehicle dry weight between ll\tonnes and
755tonnes. Therefore, using the average lro of engines of that time of around 375s (Isakowitz,
1995) it was not possible to attain LEO using one stage (Bekey, 1994). However, with the use of graphite composite materials for fuel tanks (as used on the now cancelled X-34 project shown in Figure 2.5(a) (Orbital, 2002), and the Kistler Kl (Mueller er al., 1993)) and struc- tures, aluminium-lithium for oxygen tanks and lightweight thermal protection systems, ve- hicles can now confidently be built with a propellant mass fraction of 0.89 for pressure fed propulsion systems and 0.94 for turbopump fed propulsion systems (Huzel and Huang ,1992).
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3. Vehicle design aspects 23
Even using the current Space Shuttle (SSME's) Main Engines with an average ^lro value of 437s (Schoettle, 1996), there is sufficient margin available to allow a SSTO vehicle to be built
with a design margin and still caffy a payload (Bekey, 1994). A reason that SSTO may be
considered too risky for a commercial launch company is the fact that the X-33 (Figure 2.5(b))
project was cancelled (Hammond, 2001).
(a) X-34 (Orbital,2002) (b) x-33 (LMCO,2002)
Figwe 2.5: NASA X-vehicles
2.3.3 Vehicle layout
'When the propellant and subsystem masses for a launch vehicle concept have been determined,
the vehicle layout needs to be examined. Propellant tanks are often the largest subsystems that
need to be "squeezed" into the launch vehicle. From a structural point of view, propellant
tanks should be spherical or at least cylindrical to have the best volume-to-mass ratio as well
as strength-to-mass ratio (Shigley, 1986). Spherical tanks are often, however, not practical, as
demonstrated by the X-33 fuel tanks, which were required to have a conical shape (LMCO,
2002) in order to fit into the triangular shape of the vehicle. Trade-offs need to be made when
designing launch vehicles in order to fit all of the required sub-systems into the vehicle and
still have space for payload.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3" Vehicle design aspects 24
MacConochie et al. (1989) suggest that a cylindrical body vehicle should be used as it could carry 40Vo more payload and have a 20Vo redaced lift-offweight when compared to the Space
Shuttle. MacConochie et al. (1989) further suggest that a reconfiguration of the vehicle lay- out could reduce vehicle weight. If the crew compartment was placed behind the hydrogen tank, there would be a "several thousand pound" overall weight reduction, because of reduced windshield and thermal protection system (TPS) weights. Layout is therefore also an important factor to consider when designing launch vehicles.
2.3.4 Recovery system
Reusable launch systems may reduce launch costs significantly by minimising hardware waste, but multistage reusable launchers will introduce a new problem of stage recovery. A number of studies have been performed which address recovery of the booster stages, showing a number of advantages and disadvantages for each strategy. The booster could be controlled to land at some specific point down range from which it could be recovered by road, sea or air. This is advantageous from a payload capability point of view as the booster would only be required to calry a small amount of fuel for the recovery mission. However, the operations for this concept would be more difficult as the booster would have to be carried back to the launch site over land or sea, requiring expensive equipment and many man hours. Relatively small boosters could be transported by air, but if the expended booster was very large, it would be impractical to transport it by air. Road or sea transport would be time consuming, thereby extending the refurbishment period considerably.
A second possibility is to have the booster fly back to the launch site instead of landing down range. This has the advantage of requiring very little recovery effort, but at the expense of payload. The booster would need to carry either extra fuel or aerodynamic surfaces or both for the recovery mission, taking up weight that could have been used for revenue generating payload. An example of a flyback mission is described in Mueller et al. (1998) for the Kistler
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.3. Vehicle design aspects 25
Kl (Figure 1.1). The K1 booster stage will re-ignite its centre main engine after staging, to
perform a flyback burn that will send it back to the launch site. The problem with firing a
rocket engine for the booster flyback is that it requires a large amount of propellant. Although
propellants are relatively cheap (Schoettle, 1996) an extra 75.5tonnes of propellant (Mueller
et a1., 1998) will need to be carried by the K1 until staging. Another example is shown in a
study conducted by McKinney (1986) where a fly-back booster would require 2\tonnes of fuel
for a flyback mission after stagin g llÙnmi away from the launch site.
To overcome the problem of heavy flyback fuel requirements, the booster could be fitted with
wings, thereby employing aerodynamic forces to achieve flyback. This has the advantage of
requiring only about 8.8tonnes of aerodynamic surfaces (Schoettle, 1996) for a similar gross
lift off weight (GLOW) launch vehicle. The disadvantage of this approach is rhat staging
would need to be performed at an early stage in the flight, typically around Mach 3 (powell
et al., 7991), thereby allowing the vehicle to safely glide back to the launch site. The problem
with staging early, according to Schoettle (1989), is that optimal staging conditions tend to
be at higher staging velocities, typically above Mach 10 (Tetlow et al., 2000). powell et al.
(1991), however, suggested that an un-powered strategy was optimal due to its significantly
simplified design and operation.
A slight variation on this strategy is to use air-breathing engines to assist the booster fly-
back' This would have the advantage of allowing the vehicle to stage at higher Mach numbers
(around Mach 10), which were found by Rahn et aI. (1999) to increase payload capability.
Instead of rocket engines, air-breathing engines would be used, which have an order of mag-
nitude higher specific impulse compared to rocket engines (Fortescue and Stark, 1995). The
trade-off would be whether the increase in payload, from staging at high Mach numbers, would
outweigh the payload losses incurred having to carry idle air-breathing engines during ascent.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.4. Orbital mechanics 26
2.4 Orbital mechanics
Satellites often need to be placed in specific orbits to be able to function as intended. In order
to place the payload in a specific orbit, an understanding of orbital mechanics is important as
the parameters that define an orbit are required as target conditions. Orbits around a central
body can be either circular, elliptic, parabolic orhyperbolic, depending on the mission (Brown,
1998). For example, circular and elliptic orbits are used for payloads that need to remain in a
fixed orbit around a central bod¡ such as communication satellites. Parabolic and hyperbolic
orbits are required for missions in which a body is required to escape the gravity of the central
body, as in interplanetary travel. This study will be concerned with circular and elliptic orbits only.
rp /.
Eorth Perigee Apogee
Figure 2.6: Orbit parameters
In a circular orbit, as the name suggests, the vehicle remains at a fixed radius around a central
body. In an elliptic orbit, the distance between the orbiting vehicle and the central body varies
between the 'þeriapsis", where the bodies are closest together, and the "apoapsis", where the
bodies are the furthest apart (see Figure 2.6). A circular orbit is an elliptic orbit in which the periapsis and apoapsis are at the same altitude. For this reason, only elliptical orbits will be
investigated, as the theory can also be applied to circular orbits.
v o (?-Ð (2.6)
The absolute velocity of a spacecraft at any point in an elliptical orbit (relative to a stationary
Earth) can be calculated using the general velocity equation shown in Equation 2.6, where Ç)
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.4. Orbital mechanics 27
is the product of the central body mass and its universal gravitational constant. For the Earth ç¿ hasthevalueof 398603.2km3fs2. risthedistancefromthecentreof thebodyand o:t where ro is the distance between the centres of the bodies at apoapsis andro the distance at periapsis (see Figure 2.6). Using the above equation a number of orbits were analysed and their periapsis and apoapsis velocities determined (see Table 2.2). It should be noted that if the orbital velocity is determined for two different orbits, then the difference between these two velocities is the ideal velocity increment required to change from one orbit to another, assuming they remain at the same inclination.
Orbitlkml vrlkmlsl vo lkmlsl 94x466 (LTO) 1.95661 7.52414 466 circ 7.$r5 7.6315 94x35862 (GTO) 10.3336 1.5862 466x3s862 (GTO) 10.0119 1.62218 35862 circ. (GEO) 3.0719 3.0779 Table 2.2: Orbital velocities
Three parameters that define the orbit of a launch vehicle at engine shut-down are Earth relative velocity, radius from the centre of the Earth and flight path angle. The flight path angle (y) is the angle between the velocity vector and the local horizontal, and so describes the direction of flight relative to the Earth's surface (see Figure 2.7). Also shown in figure 2.7 are the angle of attack (o), which is the angle between the direction of flight (or velocity vector) and the body axis, and the thrust vector angle (e), which is the angle between the thrust vector and the vehicle body axis.
The heading of a launch vehicle at orbit insertion will determine the orbit inclination. For example, the heading of a launch vehicle would be due East over the Equator if a 0" orbit inclination was required. In this study, a heading angle of 0" will be used for a due North heading. The heading will then increase in positive angle increments to the East and Negative 'West. angles to the This implies that a 90' (or -210") heading is due East and a -90" (or 270") heading is due West. Due South could either be 180'or -180". Although negative
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.4. Orbital mechanics 28
Figure 2.7: Angle description headings are not commonly used by the aviation industry (Schneider,2002), it was necessary in this case to allow easier numerical modelling.
Specific orbits are often required by certain payloads, so it is important for the launch vehicle to be able to deliver the payload with a high degree of accuracy. A simple calculation can be performed to show how a very slight error in orbit insertion conditions can result in a significant orbit error (Brown, 1998). Using the case of a non-rotating, spherical Earth, it can be shown that the perigee velocity for a 94x466km elliptical orbit is 7937 .8m/s. This means that a vehicle with an altitude of 94km, a velocity of 7937 .8m/s and a flight path angle of 0' would be in an 94x466km elliptical orbit, at perigee. If there was a slight error in the orbit insertion conditions, so that the vehicle was still inserted at 94km altitude with a velocity of
7937.8m1s, but with a flight path angle of 1o, the resulting orbit would be a 55.2x438.7km orbit. This results in a 47Vo enor in orbit perigee altitude, therefore, requiring a large on- orbit propulsive force to place the payload into the correct orbit. This suggests that an ascent guidance system should be capable of delivering a payload to orbit with high accuracy, to ensure it is inserted into the required orbit.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.4. Orbital mechanics 29
2.4.1 Mission requirements
The characteristic or mission velocity increment LVr¡ is the velocity increment required to
attain the desired orbit from the current state. It could be from ground to a transfer orbit or
from a parking orbit to another orbit. It is therefore the velocity increment which needs to be
produced by the launch vehicle to achieve orbit. LV"¡ comprises two components: the first
is a path independent, ideal velocity increment, and the second a number of path dependent
velocity losses. The ideal velocity increment LV¡¿ is calculated from vacuum thrust Fu and.
time varying mass m,between the initial (rr) and frnal (tr) times using Eqtation2.7.
îte D LV¡¿ I 2.¿t (2.7) - Jto m
The second component of LVr¡ is a series of velocity losses which are dependent on the trajec-
tory flown. It is the aim of the guidance system to minimise these losses, thereby maximising
the launch vehicle capability. Some of the velocity increment losses are due to drag LVp
(Equation 2.8), gravíty LVg, (Equation 2.9), engine back pressure LVtsp (Equation 2.ll) and,
thrust vectoring AVs (Equation 2.10), and are calculated between initial time to and final time r" (Schoettle,7996):
o^ LVp: ["" o, (2.8)
LVsr g.siny.dt (2.e)
(t - cos (a- e)) .dt (2.10) ^vE: l:"' i.
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 2.5. Launch sites 30
LVrsp: F(h)).dt (2.1r) I:"" )fr" -
where D is drag force, lø is vehicle mass, g is the Earth's gravitational acceleration, ü is angle
of attack, y is flight path angle, e is thrust vector angle and F is thrust force.
Engine specif,c impulse is not constant during the flight as it varies with altitude, as local atmospheric air pressure changes. Figure 2.1 shows the increase in specific impulse for a
typical rocket engine, as altitude increases. In order to accurately model the behaviour of the
propulsion systems, this variation needs to be calculated. It is achieved assuming a linear
relationship between atmospheric pressure p andspecific impulse using equation2.72:
Isp,h: Irp,, (Irr,, tro,rù . - - #, (2.12)
where subscript "v" denotes vacuum, "s1" denotes sea level and "h" denotes the value at alti- tude "h".
2.5 Launch sites
'When choosing a launch site, a number of different factors need to be considered. From a performance perspective, it is best to have a launch site close to the Equator, to harness as much of the Earth's rotational energy as possible. Because the equator is the furthest line from the Earth's axis of rotation, a body on the Equator will have the highest velocit¡ relative to the centre of the Earth. This means that if the vehicle is launched in an Easterly direction, the total velocity change required to achieve orbit will be less. For example, the absolute orbital velocity, relative to a stationary Earth, a for 466km circular orbit is 7 631 .5m I s (Brown,
1998)' The velocity that a vehicle starts with when launched Eastward from the Equator is
commercial launch vehícIe design and predictive guidance development Matthew R. Tetlow 2.5. Launch sites 31
about 460mls. This is a6.4Vo reduction in the total velocity change required, compared to
a stationary Earth. If it were launched from 31" Latitude, the initial velocity of the vehicle
relative to a stationary Earth would be about 4O0mf s, which is a 5.5Vo reduction in velocity.
If it were launched from 50' Latitude, the initial velocity of the vehicle relative to a stationary
Eath would be about 3o0mf s, which is only a 4Vo reduction in velocity. If it were launched
from the poles, there would be no velocity relative to the centre of the Earth so the launch
vehicle would have to provide the full 763lmls of velocity.
Although performance is an important factor when deciding on a launch site, there is also the
issue of safety. Clearly it is not acceptable to launch near densely populated areas as the risk of
casualties, in the event of a launch failure, is high. Many launch sites such as Kagoshima, Japan
(31.2"N), Kourou, French Guiana (5.2"N) and Cape Canaveral, USA (28.6'N) (Isakowitz,
1995) thus launch over the sea to avoid densely populated areas. This makes the recovery of
any expended stages more difficult than if they were dropped over land. Woomera, Australia
has the advantage of being in a very sparsely populated area with large expanses of empty
land surrounding it. This allows firstly, flight over sparsely populated areas and, secondly,
recovery of expended stages over land, thereby simplifying any recovery operations (Mueller
et al., 1998).
There are also factors such as political stability of the country which houses the launch site.
Launch vehicles are both expensive and dangerous pieces of hardware, so it is important to
ensure that they are not at risk of confiscation by rogue groups. Weather is another important
factor that needs to be considered when choosing a launch site. Storms and high winds can often cause costly launch delays (Bordano et al., 1991). It is therefore desirable to have a launch site that has favourable weather conditions.
Considering the factors discussed above,'Woomera, in South Australia, was chosen as a launch site for this study. Woomera was opened as a testing ground in the 1950's for the British Blue
Streak launcher, which later developed into the European launch vehicle Europa I (Isakowitz,
1995). In the 1960's, it was converted into a sounding rocket and munitions test range. Re-
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.6. Ascent guidance 32
'Woomera cently, there has been renewed interest in by a number of international aerospace
companies such as NASDA, Spacelift and Kistler Aerospace (Mueller et al., 1998). In the past 'Woomera two years has been used for a number of commercial projects such as the Hyshot
scramjet test flight and the Alflex project from NASDA, as well as the Japanese supersonic
test vehicle called National Experimental Supersonic Transport (NEXST). NASA is also con-
sidering using the remote parts of northern South Australia as a potential landing site for the
X-38 crew return vehicle (Burkhardt et a1.,1999).
Woomera's weather is well suited to launch operations as it has a dry stable climate. The
following data was taken from the Woomera Aerodrome and averaged out over the last 52
years (BOM,2002):'Woomerahas an average of 9.1 hours of sunshineper day with 161.1
clear days per year, 86.2 cloudy days and 50.1 rain days per year. The mean wind speed
is 16.9kmlå at 9.00am and 17.9kmlh at 3.00pm. In addition, Woomera has a comfortable
average relative humidity of 55Vo and an average maximum day time temperature of 25.5oC.
Further information about the average weather conditions can be seen in Appendix A (BOM- Adelaide,2002).
Although not on the equator, Woomera, at 31.15o South (BOM, 2002) is still at a suitable 'Woomera latitude to conduct launch activities. Launch from requires only a O.9Vo higher 'Woomera velocity increment, compared to a launch from the Equator. is also at a similar
distance from the equator as the Space Shuttle's primary launch site, Cape Canaveral, which
is at a latitude of 28.6' North (Isakowitz, 1995). The most attractive aspect of Woomera,
however, is its remoteness, which allows a range of launch azimuths over sparsely populated
areas, and the recovery of stages or experimental payloads over land.
2.6 Ascent guidance
Guiding a launch vehicle during ascent involves defining a desired trajectory and providing the flight controller with requested steering commands to guide the vehicle from a current point
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.6. Ascent guidance -t-t
to the desired point. There are many guidance methods available for modern launch vehicles,
depending on their application and the resources available to the designer. One method is to
use simple guidance, as employed by vehicles such as Zuni rockets (Lee et al., 1999) recently
donated to the Australian Space Research Institute (ASRD. Essentially the vehicle is aimed in
the desired direction and then fired along a rail. Provided the initial conditions are correct and
no severe environmental factors are encountered, such as wind, the projectile could reach its
desired position with considerable precision. The advantage of this method is that it is cheap
and simple with regard to both hardware requirements and pre-flight analysis.
More advanced guidance systems involve analysis and modelling of the launch vehicle to
determine the optimal trajectory, which is then converted into control parameters describing
the flight path. This more advanced guidance strategy can be broken down into two classes:
open loop guidance and close loop guidance (Bordano et a1., 1991). A number of different
launch vehicles' ascent guidance strategies will be discussed in the following sections on open-
loop and closed-loop guidance.
2.6.1 Open loop guidance
Open loop guidance is the technique used by most current launch vehicles during the atmo-
spheric flight phase (Bordano et a1., l99l). The reason for this is that the formulation of most
closed-loop ascent guidance systems makes them suited only to exo-atmospheric flight phases
(Calise et a1., 1998).
Prior to flight, a number of simulation runs are performed to determine the optimum trajectory
for a given range of environmental parameters. This trajectory is then broken down into a
schedule of events such as thrust vector angles or aerodynamic surface deflections. On the
day of launch, weather and other relevant data is collected (Bordano et a1., 1991) and used to
determined which optimum trajectory best suits the conditions on the day. That trajectory is then used in the form of a look-up table of various parameters which describe an open loop
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.6. Ascent guidance 34
trajectory. The guidance system is thus open loop and has no capability to correct the trajectory
if the vehicle starts to fly off-course.
The advantage of this strategy is that there are no convergence, stability or communication
problems that may occur using a real-time feedback guidance system. Provided the schedule
of control parameters matches the flight conditions, the vehicle could attain the required tar-
get conditions. A disadvantage of this strategy is that it requires the determination of many
optimum trajectories, prior to flight, using various perturbations in environmental parameters.
For example, each possible, or likely, atmospheric density profile will have a different set of
open loop control parameters describing a different trajectory. For each of these atmospheric
density profiles there is a family of optimum trajectories for variations in atmospheric winds.
Another disadvantage is that optimum flight trajectories change dramatically with changes in
vehicle mass and target orbit. For this reason, each new payload being carried requires a new
set of optimum trajectories to be determined.
The Space Shuttle uses an open loop guidance strategy during the atmospheric flight phase
while under the power of the SRB's (McHenry et a1., 1979). Prior to flight, a series of optimal
trajectories are calculated for a number of different atmospheric conditions. In the days before
launch and on the launch day, a series of meteorological balloons are released and tracked, us-
ing radar, to determine wind speed and azimuth at25mintervals (Bordano etal.,l99l). Using
the weather data, the trajectory which best suits the launch day weather conditions is chosen
to guide the vehicle to orbit. During the first stage operation, the trajectory is broken down
into a schedule of inertial pitch and yaw commands as a function of relative velocity. This
is essentially an open loop strategy, which is modified slightly to include a load relief feature
(Bordano et al., 1991). This involves measuring normal and lateral loading and comparing them to a pre-selected profile. An error signal is then added to the regular attitude and attitude rate error signals. According to Bordano et al. (1991), possible improvements to this method include "in-flight adaptive techniques which would continuously compute and steer an optimal flight path, taking into account dispersed environment and system performance".
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 2.6. Ascent guidance 35
From launch, the Shuttle performs a vertical flight, to clear the launch tower, followed by a manoeuvre to attain the correct orientation and flight azimuth. It then flies a programmed pitch rate in a"taiI down" orientation with the orbiter thrust 12" inclined to the vehicle's centre line
(Olson and Sunkel, 1983). This is used until SRB separation at approximately 2 mins. and
10 secs. after launch. The aim of this guidance phase is to guide the Shuttle through the high dynamic pressure region with minimum deviation from the planned structural load profile
(McHenry et al., 1979). Although the Shuttle has aerodynamic surfaces, steering control is achieved by gimballing the main engines. The elevons follow an open-loop position profile to avoid excessive hinge moment and wing bending (Olson and Sunkel, 1983). A closed loop elevon load relief feature is also available to command the elevons away from the open loop profile, based on actuator differential pressure (Olson and Sunkel, 1983). The main engines are throttled the during flight to remain below the maximum dynamic pressure o16}0tb I f tz in the atmospheric flight phase, and also to limit acceleration to 39 in the exo-atmospheric flight phase.
The Titan IV launch vehicle employs open loop guidance for the first 116s of the ascent flight, while under the power of the solid rocket motors (SRM's) (Rao et al., 7997). This flight phase, called stage 0, uses a body rate schedule that determines the attitude of the vehicle at any point during the flight. The flight phase includes an initial roll to the correct flight azimuth, followed by a constant pitching rate flight. Between 25 and 85 seconds of flight time, a load relief profile is flown (Rao et al.,1997). Although a closed loop attitude controller is used to attain the required thrust direction, the guidance is completely open loop.
2.6.2 Closed loop guidance
A different approach is to use a real time guidance strategy, which updates the control param- eters as the vehicle flies, thereby calculating new steering commands on-line. Closed loop guidance is usually used in the upper stage or exo-atmospheric flight phases. The Titan IV
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.6. Ascent guidance 36
uses closed loop guidance once the SRM's have been jettisoned (Rao et al., 1997). Once the
SRB's have been jettisoned, the Space Shuttle changes from open loop guidance to the closed
loop Powered Explicit Guidance (PEG). This software iteratively computes the thrust vector
pointing and turning rate, based on a linear tangent steering law (Bordano et al., 1991), to achieve an accurate orbit insertion.
Current closed-loop guidance systems, such as those used on the Space Shuttle (Bordano et al.,
1991) and on Pegasus Air-launched Space Booster (Rovner, lggl) use analytic solution meth-
ods to update steering parameters. Analytic techniques have the advantage of being stable, but
can often not include all the factors influencing the trajectory, such as aerodynamic and wind
forces (Leung and Calise, 1994). An approximation of the launch environment is thus used,
which can lead to the generation of sub-optimal trajectories (Leung and Calise, 1gg4).
Another way to generate steering commands is to use numerical methods. This approach gen-
erally employs non-linear programming or "multiple shooting" methods to generate steering
commands (Leung and Calise,7994). A problem with this strategy is that it requires high-
speed computers to perform the new trajectory calculation during the short time intervals. The
guidance problem therefore needs to be formulated in such a way as to be as computation-
ally efficient as possible while at the same time providing the required accuracy to generate a
near optimal trajectory. Numerical methods have the advantage of being able to include more factors affecting the trajectory, such as aerodynamic and wind forces, however, they are more
susceptible to computational instability. This instability arises from the numerical processes used to vary the steering parameters, which rely on gradient calculations.
The Space Shuttle PEG uses a prediction of range-to-go and velocity-to-go to calculate the required thrust direction. The thrust direction is calculated using Equation 2.13, where ?vp is the vector defining commanded thrust direction, l,u is the unit vector in the direction of velocity-to-be-gained, i is a vector perpendicular to Ir, representing the rate of change of l,¡
, / is current time and 4 is a time chosen so that the total velocity change is along the velocity- to-be-gained direction (McHenry et a1.,1979). Velocity-to-go is calculated by decrementing
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.6. Ascent guidance 37
the sensed (inertial sensors) velocity change from the total required velocity change. This is
then used to determine time-to-go, from which a number of thrust integrals can be determined.
Range-to-go and t¡ are then calculated, allowing the determination 1,, and i.
?rr:Ì"u+i(r-4) (2.13)
This guidance strategy typically takes two seconds for a single guidance calculation, once
convergence has been obtained (McHenry et al., 7979), and it guides the Shuttle up to about
40 seconds before the main engine cut off (MECO) position. During the last 40 seconds,
the MECO position constraint is released to avoid guidance and control divergence problems
(McHenry et a1., 1979). In this guidance phase, the velocity-to-go is simply determined by subtracting the current velocity from the required velocity.
The Space Shuttle PEG guidance system cannot be used during atmospheric flight as aerody-
namic forces are not included in the formulation. The PEG scheme is based on the zero-order
expansion of a Hamilton-Jacobi-Bellman equation and essentially assumes vehicle dynamics
in a vacuum over a flat Earth. An improvement, suggested by Feeley and Speyer (1994), is
to use a first-order expansion of the Hamilton-Jacobi-Bellman equation and thereby include
aerodynamic forces and a spherical Earth model in the problem.
An example of the attainable accuracy during an ascent mission is shown by the Ariane 5 'When launch vehicle (Isakowitz, 1995). launching into a 500km circular LEO, it can achieve an altitude accuracy of I4km, which is a mere O.87o enor. When launching into a 280x35786km
GTO, the attainable accuracy is tlkm at injection, which is an accuracy of about 0.35Vo. By the time apogee is reached, the potential error has grown to tl\\km.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.7. Flyback guidance sysfems 38
2.7 Flyback guidance systems
Currently, there are no operational flyback boosters, so direct comparison is difficult. However,
a number of studies investigating booster flyback have been conducted, and may be used for
comparison. Construction of the Kistler Kl launch vehicle has already begun (Cochran et al.,
1998) and it may become the first operational launch vehicle to include a flyback flight for its
booster stage of Launch Assist Platform (LAP). The LAP guidance system first reorientates the
booster and then fires the centre engine for approximately 30 seconds (Mueller et al., 1993).
This sends the K1 LAP into a parabolic trajectory towards the launch site, causing the vehicle
to land about 5km downrange from the launch site.
Although the Space Shuttle is not a booster, its re-entry trajectory was examined as it is the only
winged hypersonic vehicle available for comparison. The one significant difference between a
booster return flight and a Shuttle re-entry flight is that the Shuttle does not require a significant
heading change during re-entry. The Shuttle deorbits close to the required orbit plane and
therefore only has to maintain the correct heading with minor adjustments. A flyback booster,
on the other hand, requires a 1800 heading change during its flight.
As with the Space Shuttle ascent mission, weather balloons are released prior to deorbit, which
are tracked with radar to determine wind speeds and azimuth at25m intervals (Bordano et al.,
l99I). The control parameters are determined using a drag-vs-Earth-relative-velocity for Mach numbers above 10.5 (Harpold and Gavert, 1933). Below Mach 10.5, a drag-vs-energy profile is used. At an altitude of 70, O00ft and a velocity of 15}0ft /s, the Terminal Area Energy
Management (TAEM) guidance system starts (Ehlers and Kraemer, 7gl7), which controls the energy-vs-range profile. The TAEM guidance system aims to achieve an air speed of 290knots, an altitude of 10000/r and a flight path angle of -21" along a heading alignmenr cylinder (HAC) (Ehlers and Kraemer,7977). A HAC is an imaginary cylinder that is rangent to the runway. If the Shuttle can achieve a heading also tangent to the HAC, then it will simply require a constant radius turn to achieve the correct heading for landing. In this analytic
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.7. Flyback guidance systems 39
guidance system, the aerodynamic forces are modelled using a fixed aerodynamic coefficient (Czr) plus a term dependent on the current angle of attack (Cb (cr)), using the form shown in
Equation 2.14 (SchoettIe,20O2) (Although lift coefficient is shown; a similar equation is used for the drag coefficient).
Cr: Ch+C1(u) e.t4)
The TAEM re-entry guidance system is broken into 4 phases that are required to perform
specific manoeuvres during the mission. In phase 0, the orbiter flies S-turns to dissipate energy.
It flies at the maximum dynamic pressure and speed brake limits, in a direction away from
the HAC. A ground track predictor and an established range energy boundary are used to determine when enough energy has been dissipated, at which time the Shuttle returns to a
heading tangent to the HAC. Phase I is called the acquisition phase, during which the correct
heading is controlled, using roll reversals, to be tangent to the HAC. The energy is managed
by modulating the dynamic pressure in the supersonic flight regime and using a speed brake
in the subsonic regime. During phase 2 the orbiter is made to track the HAC before the pre-
final guidance phase starts. As was stated above, the TAEM guidance system uses energy
control to determine the range-to-go, which is required to determine the amount of energy to be dissipated. The mathematical formulation of the problem is described in detail by Ehlers and Kraemer (1977).
Another booster flyback concept, discussed in Naftel and Powell (1991), employed only aero- dynamic gliding forces to return to the launch site. The booster did not use propulsion during its flyback phase, but relied only on aerodynamic surfaces for both aerodynamic lift and atti- tude control. The flyback was broken down into six phases, namely: initial turn after staging manoeuvre, excess performance dissipation, HAC acquisition, heading alignment cylinder, ap- proach and flare, and touchdown. Only the first three phases were relevant for comparison, as the remaining flight phases were for final approach and landing, which was not considered in the current study.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.7. Flyback guidance sysfems 40
After staging, the booster had a Mach number of 2.78, a flight path angle of 30o, an altitude of
88287 ft and an angle of attack of - 10' (Naftel and Powell,l99l). Optimisation software was
used to generate a minimum time turn flight, with the maximum normal acceleration of 2.3g,
using the angle of attack as a function of Mach number, and roll angle as a function of heading
angle. In Phase 1 these profiles were followed, open loop, from the initial heading angle of
90o to the required heading angle of 210". Once the 210" heading angle was reached, Phase
2began. The vehicle rolled out to 0" roll angle, but was modulated by feedback to keep the
heading at 2l0o . The angle of attack profile continued along the schedule until a value of 6.5"
was reached, which was maintained until the end of Phase 2. Phase 3 consisted of a turn and
glide to the HAC, while the angle of attack was modulated around the value of 6.5' to keep the
booster's actual range equal to its potential range. In this flyback strategy, we see a similar type
of guidance strategy to the Shuttle re-entry flight. Again this strategy is adequate provided the
atmospheric conditions are similar to those used to generate the control schedules. It would,
however, require a significant amount of pre-flight analysis and would also be restricted to fly
only in the atmospheric conditions for which a trajectory schedule had been generated.
A numerical guidance method was proposed, by'Wallner et al. (1999), for the re-entry flight
of the X-38 Crew Return Vehicle (CRV). This predictive guidance system generated steering
commands, based on a completely new trajectory, which was calculated at discrete time inter-
vals, typically between one and five seconds (Wallner et a1., 1999). The steering commands
were determined using an optimisation process which generated a near optimal trajectory to
guide the vehicle from the current state to the target state.
If this guidance system is adopted by the X-38, it will be achieved using bank angle variations,
while following a predetermined angle of attack profile open loop. After a deorbit manoeuvre,
the guidance system will perform a trajectory optimisation to minimise control effort and total
stagnation point heat load while achieving the target landing point of Coober Pedy, Australia
(28.242"5latitude and 734.98' longitude) (Burkhardt et a1., 1999). Two bank angle values and two time grid points will be used as optimisation parameters. During this flight regime
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.8. Conclusions from the literature review 41
the guidance system will be supplying no guidance updates. The nominal entry point will be at an altitude of 121.92km, a velocity of 7897.58 mf s, a flight path angle of - 1.3", a latitude of 45.659"5 and a longitude of 34.986', after which the on-line guidance system will start.
V/hile the guidance system is updating the steering commands, the time grids will be fixed,
leaving only the two bank angle values as optimisation parameters. This flight segment will not use a full optimisation procedure, but instead will only vary the bank angle values so as to
achieve the target constraints. This will be done to reduce convergence time, thereby allowing
real-time guidance updates.
A slight variation to this scheme is discussed in Jits and'Walberg (2001), where a predictor-
corrector algorithm is coupled with heuristic rules to provide guidance updates. These heuristic
rules add robustness to the guidance scheme by providing guidance updates in the event of
predictor corrector instability, or when certain predetermined boundaries are exceeded.
2.8 Conclusions from the literature review
Vehicle design
The literature strongly suggests that the key to cost reduction in the space launch vehicle market is reusability. Currently, the commercial launch vehicle industry is heavily reliant on expendable launch vehicles, which are continually being upgraded. The question has to be posed, why reusable launch vehicles are not currently under development, considering the po- tential cost reductions. The reason for this may be the current level of technology. Consider that the only reusable launch vehicle, the Space Shuttle, is the most expensive vehicle to oper- ate and has already had two catastrophic failures. With current technology, the subsystems on the Space Shuttle (propulsion, TPS, etc) need to be carefully checked and repaired before each flight, especially as the Space Shuttle is a manned vehicle. If technology can be developed that allows launch vehicles to operate with a reliability more like a commercial aircraft, the
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.8. Conclusions from the literature review 42
costs of reusable launch vehicles may be reduced significantly, making them more attractive to
launch service providers. Clearly, Kistler Aerospace believes the level of technology is already
advanced enough to build an unmanned reusabre launch vehicle.
For a reusable vehicle to be a viable venture for a commercial launch company in the near
future, the use of proven and available technology would be suggested. Although SSTO al-
ready seems possible, the first launcher developed failed, making it too risky for a commercial
launch company' A two stage vehicle, however, imposes less risk. LOX/kerosene propulsion
systems seem to be well suited to commercial application as they have provided reliable launch
services (Chakroborty et al., 1998) for over 30 years. Kerosene is a high density storable fuel,
allowing the vehicle to have smaller fuel tanks than if liquid Hydrogen was used (Schoettle,
1996). Kerosene is also easier to handle than liquid Hydrogen, making launch operations eas-
ier and safer. Composite kerosene storage systems have already been produced (Mueller et al.,
1998) and (Orbital,2002), showing that this fuel allows a light strucrure ro be produced with
minimal development costs.
For the vehicle to be fully reusable, it is clear that all of the stages need to be recovered.
From an operational point of view, it would be easier if the booster landed at the launch site
as this would negate the need for a recovery system. It would also reduce the turn-around time as the booster could be prepared for the next flight as soon as it landed. Using the main rocket propulsion system to achieve flyback requires a large amount of flyback propellant to be stored on-board, which adds significant mass to the booster (Schoettle, 1996). The use of wings would, however, reduce this mass considerably by using aerodynamic forces to sup- port the booster's weight, instead of the propulsion system. Although there are currently no winged flyback boosters, there are many examples of aerodynamic flight through the atmo- sphere (Jackson, 1998), so this aspect of flight is well understood.
High staging Mach numbers have been shown to support higher payload capabilities (Rahn et al., 1999), however, booster flyback cannot be achieved unpowered from a staging velocity much above Mach 3 (Naftel and Powell, 7997). It thus appears useful to investigate the pay-
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.8. Conclusions from the literature rcview 43
load capabilities of two reusable launch vehicles using different flyback methods. This would
indicate if the improved payload capability from staging at high Mach numbers (around Mach
10) would outweigh the penalty incurred carrying idle air-breathing engines and flyback fuel
during ascent.
Guidance strategy
Considering the large orbital effors that would be produced by a 1o error in final flight path
angle (see Section2.4), an accurate ascent guidance system is required for orbit insertion. Cur-
rent launch vehicles use both open-loop and closed-loop guidance strategies to achieve orbit
(McHenry et al., 7979), both of which require considerable pre-flight analysis and atmospheric
measurement (Bordano et al., 1991). The costs associated with these operations are up to l2%o
of the cost of a launch (Bordano et al., 1991). Reducing the pre-flight trajectory analysis time,
using an on-line, predictive guidance strategy could reduce the launch costs significantly by
reducing the number of hours spent on pre-flight trajectory analysis.
Ascent guidance systems are typically open-loop during the atmospheric flight phase (Bordano
et al., 1991), as current closed-loop ascent guidance systems use analytic methods for guidance
updates. These analytic methods rely on simplified environment models (Leung and Calise,
1994), such as no aerodynamic forces, making them unsuitable for atmospheric flight phases.
This means that open-loop guidance has to be used until the actual aerodynamic forces become
small enough to be ignored. Another problem with both ascent and re-entry analytic methods is
that because of the model simplifications, they produce a sub-optimal solution to the guidance problem. Although numerical methods are perceived to be less robust than analytic methods
(Feeley and Speyer, 1994), they do have the advantage of being able to include any number of environmental parameters when determining steering commands. This allows them to generate optimal guidance solutions in any flight phase. They also do not require extensive pre-flight trajectory analysis as the guidance updates can account for non-nominal vehicle behaviour.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 2.8. Conclusions from the literature review 44
The gap in the literature thus seems to be that there is no closed-loop guidance system capable
of guiding a launch vehicle during its atmospheric flight ascent phase or booster flyback phase.
The development of a robust numerical guidance system for orbiter ascent and booster flyback
would therefore be a useful undertaking.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 3
Numerical Techniques
3.1. Simulationtechniques
Simulation is a valuable tool used to determine how a real system would behave under cer-
tain conditions. The simulation techniques used in this study comprise a number of numerical
models that are combined, in a modular layout, to produce a numerical model of the whole
system. Some of the models are in the form of differential equations, which require an inte-
gration technique, some are relatively simple functions, which require only simple evaluation,
and some are in the form of data, which require interpolation or curve fitting techniques. Var- ious aspects of system dynamics and operating environment need to be modelled to different degrees of accuracy depending on the application of the software. Higher accuracy modelling generally produces a more accurate solution, but at the expense of an increased computation load.
3.l.L Dynamicsmodelling
Rigid body dynamics are used in this study to investigate how real launch vehicles would be- have during flight. A rocket operating in three dimensional space can have both translational
45 3.1. Simulation techniques 46
and rotational motion. For a highly accurate model, all six degrees of freedom (DOF) need
to be considered, as they all contribute towards the dynamic behaviour of the launch vehicle.
When considering only the translational motion or trajectory of a launch vehicle, high accu-
racy can still be obtained by considering only the three translational degrees of freedom and
ignoring the rotational freedoms. This is due to the fact that rotational motion and translational
motion can be readily decoupled from each other (Burkhardt, 2000) and (Tetlow et al., 1999), 'When for flight performance and flight load analysis. considering vehicle attitude, however,
all six degrees of freedom need to be considered, as well as various couplings between the six freedoms.
The 3DOF dynamics model used in the present study was taken from Schoettle (1988) and
is expressed with respect to the horizontal or geocentric reference frame. This reference
frame coincides with the local horizontal frame, with the x-axis pointing towards north, the
z-axis pointing towards the centre of the Earth and the y-axis making up the orthogonal set
(Burkhardt,2000). Equations 3.1,3.2 and 3.3 represent the dynamics.
¡ : \ * r (ø¿cosiì)2 (s;ny- cosytanõcosy) (3.1)
Fy ! 2 y v + (a¿ c o siì) (cosy + c o s1¿t anõsiny) + 2a c o sõsiny c o sy (3.2) mv B *
x : s inys inõ 2a ¿ c o s õ (c o syt any t anõ)+ ! s in^¡c o syt anõ (3.3) :mvcosT ^,. +# vco.t\ - -
Equations 3.4,3.5 and 3.6 represent the kinematics. When Equation 3.7 is integrated, it deter- mines the instantaneous mass of the launch vehicle.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 47
(3.4)
(3.s)
| : vsinT (3.6)
ùv : tÌt ehicl e - p ro pel I ant (3.7)
In the above seven equations is v the vehicle velocity, relative to the rotating Earth, 7 is the
flight path angle (see Figure 2.7), X is the heading angle (see Section 2.4), or¿ is the Earth's
angular velocity, ô is the geocentric latitude, l, is the geographic longitude, and r is the radius
from the centre of the Earth. Forces Fr, Fy and F, are the perpendicular forces acting on the body, with F" acting along the velocity vector.
The 6DOF model used in the present study was taken from Burkhardt (2000). In addition to the seven equations shown above (equations 3.1 to 3.7),the 6DOF formulation includes rotational modelling. The rotational dynamics are represented by the Euler equations, which include angular acceleration about the vehicle body fixed axes, taken as the axes of major moments of inertia. The angular accelerations are given by Equations 3.8, 3.9 and 3.10 respectívely. M*,
M, and M, are the resultant moments on the body about the vehicle x,y and z axes respectively.
Io, Iyy and Iu are the mass moments of inertia about the vehicle's axes and {Ð", or, and oz are the angular velocities of the vehicle about its axes.
(3.8)
commercial launch vehícle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 48
My+ (Izz- Lç,) t rrr, oy (3.e) by
_ Mz* (Io- Irn)o'9 oJz (3.10) L,
The kinematics of the rotational motion are given by Equations 3.1 1,3.72 and 3.13. Equation 3.11 represents the time rate of change of angle of attack (cr), Equation3.l2represents the time rate of change of side slip (B), and Equation 3.13 represents the time rate of change of bank angle (p). Bank angle is a rotation or roll about the velocity vector, and side slip is an
angle describing the yaw motion of the vehicle. e,,x, o)r,y and tÐr. are the angular velocities of the x, y and z ¿xes relative to the velocity reference frame.
a: (ro, o¿y) oB,) + sinc;(,o-r- o,,.)] (3.1 1) - - #lcosc;(o" -
þ: sins"(rrl, + ú)r,") - cosa(@z- o¿.) (3.12)
1 p crl4¡) + sinu(tr,r- @¿.)] (3.13) cosþ lcosa(or, -
There are a number of ways of representing the dynamics of the vehicle. Although the un- derlying equations are always the same, the reference frame chosen will affect the equation representation' In the case where no wind is considered, the wind reference frame becomes the same as the velocity reference frame. This means that no transformations need to be per- formed to model the dynamics of the vehicle. In the case where wind is considered, the wind relative equations need to be transformed into the velocity reference frame using a transforma- tion matrix (Burkhardt, 2000).
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3"1. Simulation techniques 49
'When determining whether to use 3DOF models or 6DOF models, Zeiler et al. (1999) suggests
that adequate accuracy can be achieved using 3DOF dynamics models, when determining
aerodynamic and propulsive loading. A 6DOF model is, however, required when perform-
ing simulations which include control modelling. According to Rao et al. (1997), there is a
significant difference between the 6DOF and 3DOF simulations when launch site winds are
considered. The choice of dynamics model is thus driven by trading off computational loading
and required accuracy.
3.1.2 Propulsion modelling
As was discussed in Section 2.2 the performance of a rocket engine varies with changes in
atmospheric pressure. This variation is modelled as a linear variation between the specific im-
pulse at sea level and that in a vacuum. The formulation was taken from Schoettle (1996) and
is shown in Equation 2.12. The air-breathing propulsion system modelled here, was assumed
to have constant thrust and fuel mass flow rate. This assumption can be made as the engines operate at cruise conditions.
3.L.3 Mass modelling
If a specific vehicle's entire mass breakdown is known, it is not necessary to perform mass modelling; however, in preliminary design situations, a mass model is often required to provide an approximate mass budget for a concept vehicle. One method of obtaining an approximate mass breakdown is to use statistical mass data from current and previous launch vehicles as well as previous concept vehicle studies.
This statistical mass modelling uses an approximation technique to generate a continuous func- tion relating a component mass to a given property, as shown by Equation3.14. A and,B are the coefficients that define the function relating the mass of the subsystem to property x. The data
commercial launch vehicle design and predictive guidance development Matthew R. TetIow 3. l. Simulation techniques 50
used to generate the function can be chosen by the designer. This allows data that is perceived
to have a similar technology level to the vehicle being considered, to be used. The mass model
can also be scaled up or down, to represent a change in technology.
n n L*,:Lt,.*?, (3.14) i:1 i:t
A wing mass calculation will now be shown as an example. Figure 3.1 shows a number of
data points from previous concept vehicles, which were obtained from Glatt (1914) and Rahn (1998). The data points relate the wing mass (m*¡rs) to the vehicle landing mass (m¡on) via
a wing mass function (\.¡n), given by Equation 3.15. A least squares curve-fitting technique is then used generate to the coeff,cienfs Ar¡n, and Br¡rr as shown in Equation 3.74. Ara,¡rr
has the value 3792.2979, while B*¡r, has the value of 0.7214. By calculating the wing mass
function for the vehicle under consideration, an approximate wing mass can be calculated,
using Equation 3.16. F Çwing:- *1x10-9 .mhndn'b'S2troo, (3.15)
rnwins:3i92.29791ï/,;o (3.16)
where m¡or¿ is the vehicle landing mass, å the wing span, troo¡ the wing root thickness, n the allowable load factor during landing and s the wing reference area.
3.1.4 Atmosphere modetling
The atmosphere is complicated, unpredictable and is continually changing, making it ex- tremely difficult to model. Since the 1960's, scientists have been trying to develop numeri- cal models to simulate the atmosphere, but since "Mother Nature" is the driving force behind atmospheric parameters, their success has been limited. Empirical density models have im- proved little over the past 30 years (Marcos et al., 1994). Even with the latest atmosphere
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3. 1. Simulation techniques 51
1000 .:
Òo J¿
Ø 00 èo 5
l0
100 1000 r0000 Landing mass function*e-9 [kg.m^2]
Figure 3.1: Wing mass analysis data
models, the overall error in modelling atmospheric parameters is generally about l5To (Mar-
cos et a1.,7994). Models cunently in use are based on long term averages of recorded data and
cannot take into account local changes at any specific times. The data for empirical models
is generally based on satellite data or direct measurement of thermospheric composition and temperature.
Solar EUV radiation that originates from the solar chromosphere, transition region and corona is an important source of atmospheric heating (Marcos et al., 1gg4). The EUV varies with the 1l-year sunspot cycle, the27-day solar rotation and the solar zenithangle, as well as other shorter-term fluctuations. In addition, the atmospheric heating effects depend on latitude, local time and season. High latitude regions are subject to solar wind effects that interact with the
Earth's magnetosphere resulting in more atmospheric heating. Many of the newer atmosphere models include such variables as solar flux, geomagnetic activity, local time, day of year, latitude and longitude. The solar electromagnetic and auroral heating inputs are predicted by the Fro.z and Ko indices respectively. The Fro.z is measured by considering the amount of EUV not absorbed by the atmosphere. The Ku represents the global changes in geomagnetism and is based on data obtained from a network of mid-latitude magnetometer monitoring stations.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 52
Although the above parameters allow more accurate modelling of the nominal expected at-
mospheric conditions, local, low altitude variations such as air pressure, temperature and air
density cannot be easily accounted for. This causes the atmosphere model to be a likely source of inaccuracies.
3.1.4.1 Standard atmosphere models
Standard atmosphere models are single mappings of primary atmospheric properties with
changes in altitude. They are presented as tables of temperature, pressure, density and alti-
tude. A commonly used standard atmosphere model is the US Standard Atmosphere 1976,
which models the atmosphere from the Earth's surface to an altitude of 1000 km and.from the
Equator to a latitude of 45o (Regan and Anandakrishnan, 1993). The atmospheric density
variation with altitude for the US Standard Atmosphere (1976) is shown in Appendix B. The
model comprises 11 strata within which the atmospheric conditions are representable by a sin-
gle mathematical function. There are seven strata below 86km altitude, with the remaining
four representing altitudes up to 1000km. For the mathematical formulations of each strata,
the reader is referred to Regan and Anandakrishnan (1993).
The US Standard Atmosphere 1976 model meets the World Meteorological Organisation's
def,nition of a temperature, pressure and density representation of year-round mid-latitude conditions (Regan and Anandakrishnan, 1993). This model is thus considered suitable for modelling the atmospheric conditions around woomera, Australia.
3.1.4.2 MSISE atmosphere models
The MSISE (Mass-Spectrometer-Incoherent-Scatter) models attempt to simulate the natural temperature and density of the Earth's atmosphere from ground level to thermospheric heights.
From ground level up to an altitude of 20km, the models use averages of data obtained by the
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 3.1. Simulation techniques 53
National Meteorological Centre (USA). From 2okm to 72.5km, data is based on the Middle At-
mosphere Program (MAP) (Labitzke et a1., 1985) handbook of zonal average temperatures and
pressures. MAP is based on measurements of atmospheric structure by a number of satellites,
such as Nimbus 5,6 and 7 (Labitzke et a1., 1985). Above 72.5km,the models are basically re-
vised versions of previous MSISE models, with new data from recent Space Shuttle missions.
The MSISE93 model, which was released in 1993, uses solar flux, geomagnetic activit¡ local
time, day of year, latitude, longitude and various other parameters, to approximate the Earth,s
general atmospheric parameters. However, it still does not account for local short term weather changes around the globe. The atmospheric density profiles at a latitude of -31.5" for three different days are shown in Appendix C.
3.L.5 Wind modelling (HWM93)
As was discussedin section 3.1.4, atmosphericparameters are difficultto model as they are driven by the chaotic forces of "Mother Nature". Wind is particularly difficult to model as
there is a limited amount of data available to model neutral or average wind (Miller et al., 1990).
The Horizontal Wind Model from 1993 (HWM93) uses the HWM87 model for altitudes above
220km (NASA, 2002). HWM87 was developed from mass spectrometer measurements on board the Atmospheric Explorer-E (AE-E) and Dynamic Explorer-2 (DE-2) sarellires (Miller et a1., 1990). It also used optical measurements of the Doppler shift on theDE-2 satellite.
Using wind data from ground-based incoherent scatter radar and Fabry-Perot optical interfer- ometers, the wind model was extended down to l00km altitude. Finally, using MF/Iyleteor data the model was extended down to ground level (NAS A,2002).
The model calculates zonal and meridional winds for specific positions and times. It works by determining the expected magnetic conditions for a particular day and then determining wind
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 54 coefficients by fitting wind data to vector spherical harmonic base functions. An example of the nominal wind conditions generated by I{WM at a latitude of -31.5' are shown in Appendix D.
3.1.6 Earth form modelling
Earth form modelling is required to determine the shape of the Earth and its radius at any point on the globe. The accuracy with which this is done will determine the accuracy of the vehicle altitude calculation. In the models used in this study, the altitude is calculated by subtracting the Earth's radius from the distance between the Earth's centre and the vehicle's centre of gravity.
3.1.6.1 SphericalEarth
A relatively good approximation is to model the Earth as a sphere. This approximation in- cludes the curvature of the Earth, thereby making orbit calculations possible. It is also simple to apply and does not require intensive computation, as the radius of the Earth is a constant value. The spherical Earth model, howeve¡ does not account for changes in the Earth's radius due to the Earth's oblateness.
3.1.6.2 Higher order models
To improve the model of the shape of the Earth, a spheroidal model can be used. These models include an oblateness term (Regan and Anandakrishnan, 1993) to take the Earth's ellipticity into account. They are slightly more computationally intensive, but provide significantly more accurate approximations of the Earth's radius. This leads to better altitude calculations, partic- ularly when flying across different latitudes. The derivation that follows was taken from Regan and Anandakrishnan (1993).
Commercial launch vehicle design and predictive guidance development Matthew R. TetIow 3. 1. Simulation techniques 55
We can write the equation of an ellipse as:
X' Z' 4-4-',, -, (3.n)
where R, is the equatorial radius and Ro the polar radius. If we choose a point on the earth,s
surface, say (X,Z) then:
X : RBcos(Lro) (3.18)
Z: Rnsin(Lro) (3.1e)
where Lro is the geocentric latitude on the surface of the Earth, which is a line drawn from the
centre of the Earth to a point on the Earth's surface, and R¿ is the Earth's radius at point (X,Z).
Substituting them into the ellipse equation, we get:
^rl+.'+l:' (3.20)
By simplifying: R RE: (3.21) {'- f'- (#)'l'o,'r,"}
å= But the eccentricity of the Earth is defined as K: r.,r, e2x7o-2(Grirnn and ft - (t)'] French, l99l)
Expanding:
RE :o, + r," f{ roror," * ...... 1 (3.22) it Çror,
commercial launch vehicle design and predictive guidance development Matthew R. TetIow 3.1. Simulation techniques 56
Ignoring the higher order terms, we can approximate:
Rn N^" +lror'r,"f (3.23) ft
A problem that is encountered when implementing such a model is that the normal to the
Earth's surface no longer passes through the centre of the Earth. This means that the altitude
is either not perpendicular to the Earth's surface or, if it is, the perpendiculars will not pass
through the same point at the centre of the Earth. To overcome this problem, the state variable
can be changed from an altitude to a radius from the centre of the Earth. This will result in the
distance from the centre of the Earth to the space vehicle being coffect, however, the altitude
would still have a slight error. This eÍÍor, D, in the altitude was approximated, in Regan and
Anandakrishnan (1993), using altitude (å), Earth's radius (R¿), ellipticity (e) and laritude (¿),
as shown in Equation 3.24: D: e(r - #) sin(21) e.24)
3.1.7 Gravitation field modelling
A gravitation model is required to approximate the gravitational field around a central body.
Although the gravitational models can be applied to any planetary body, the Earth is the only
one considered in this study.
The simplest model is to use a constant value of gravitational acceleration for the vehicle's entire flight. This assumes there is no variation in gravitational potential with changes in altitude and position on the Earth. It is a relatively good approximation as the variation in gravitational potential is small (approx. O.l57o at 5km altitude and 37o at 700km altitude), particularly when the vehicle remains close to the Earth's surface. Due to the fact that the vehicles discussed in this thesis are orbital or at least high altitude vehicles, more complex models are necessary.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 57
3.1.7.1 Newtonian
The Newtonian gravitation model improves accuracy by including a variation of gravitation
potential with changes in altitude. It assumes the Earth is a sphere with uniformly distributed
mass. The gravitational potential at any point on the Earth is determined by Equation 3.25
(Regan and Anandakrishnan, 1993): {2m g p2 (3.2s)
again, O is the product of the Earth's gravitation constant and its mass, and has the value
3.986005x7Os km3 s2 (Regan and Anandakrishnan, 7gg3), m is the spacecraft mass and R the
distance from the centre of the Earth to the centre of the spacecraft. This model has the
advantage of being computationally efficient, while at the same time providing a variation in
the Earth's gravitation field as the spacecraft's altitude changes. It is particularly useful for
high orbits as the further the spacecraft is from the central body, the more the central body
behaves like a point mass.
3.1.7.2 Higher order models
For a more accurate estimation of the Earth's gravitational potential, higher order models can be used, which consider variations in altitude and latitude, using higher order functions. These models attempt to model the variation in mass distribution due to the oblateness of the Earth, thereby providing a more accurate calculation of the variation of gravitational potential with altitude, while at the same time determining a variation in gravitational potential with changes in position on the Earth's surface.
This derivation of the Earth's gravitational potential, taken from Regan and Anandakrishnan
(1993), accounts for the non-spherical mass distribution between the equator and the poles, but considers the polar axis to be an axis of symmetry.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3. 1. Simulation techniques 58
Z
Vehicle
X Y
Figure 3.2: Axes for gravitation derivation
Derivation
The gravitational potential due to the Earth, U, is given by the integral of Equation 3.26, over the entire Earth (see Figure 3.2).
dMn U:G (3.26) I lR- rl where G is the universal gravitation constant, dMB is a mass element, R is the vector between the centre of the Earth and the point under consideration and, r is the vector from the centre of the Earth to the mass element. be expanded using Legendre polynomials to 6-rL¡ "un t {ro¡'^(e)l+ fiPllcos(e)l+ (;)2 r2lcor(e)1.... (fi)" r,fcos(e)l} where:
Pslcos (e)l : l, Plfcos(e)l : cos(0), P2fcos(e)l : f,lZrot(2e) + 1l
P3lcos and (e)l : $ [scos (3e) + 3cos (0)]
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.1. Simulation techniques 59
The Earth's rotation will be ignored, as it has no gravitation effect on a body removed from
the Earth's surface. So expanding Equation3.26, the gravitational force at a distance R from
the centre of the Earth is given by:
gRllr"n*" u : * (cos(o)r. ¿Mø) * (3.27) + I*"Pr # 1."P2(cos(0)rz.dun)+ ]
or more compactly as:
r k U:9 L Po(cos(e)) ( dMn (3.28) R I,k:0 R )
Displaying the Legendre functions using the Rodriques generating function with r1 : cos (0):
r ak P¿ (rl) : 0f -r) (3.2e) 2kkt d\k
Also displaying the Associate Legendre polynomials using Rodriques functions:
Pio:(n,-1)*w (3.30)
The mass element must also be replaced by spherical variables as shown in Figure 3.2.
dM E - D (r, þ, t') r2 sin(þ) d rdþdtu (3.31)
where D is the density function. It can be shown that:
cos(O) : s in(þ) s in(Q) cos(}. - l) + cos(B) cos (Q) (3.32)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3. 1. Simulation techniques 60
Using this to replace cos(O), the potential, (J, becomes a summation of a series of integrals.
This integral summation is extremely difficult to solve, even if the density is constant. For this
reason, the solution was attempted using the equation for U, but assigning numerical constants
to the i terms, based on measurements, rather than attempting to solve the entire equation algebraically.
From the addition formula of spherical harmonics (Regan and Anandakrishnan, lg93),we can write
P¿ [cos(O)] : P¿ [cos(Q)]r¿ [cos(p)]+
, (t }ul rro o s (þ) Pi (O) (3.33) rr-{fr#'^ U - lc I þ,, I }
Due to the fact that we are assuming symmetry about the polar axis, the density function
becomes O(r,þ) and the summation teÍns in the above equation can be ignored. U can thus
be written as: (Griffin and French, 7997)
: ( u +F-]*ror,", 0) (3.34)
where:
: G os (þ) * |h¡p D (r, þ) r2 sin(B) drdþdtu (3.35)
For fr: 0,land ) 2,Equation3.34 can be written as:
u(R, O) : + [cos(Q)] G36) I I*"dMn fr,",çq¡ fr"no,(þ)dMø. F-#P¿
The first integral is simply the mass of the Earth. The second term is zero (Regan and Anan- dakrishnan, 7993), leaving :
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 3.1. Simulation techniques 61
u (R, Q) : . (3.31) ry _:y-ffinfcos(Q) l
If we let: (*)0, where R" is the radius of the Earth at *#": U^tt the equator, then U(R,Q) can be written as:
o,oroþ^(o)r} u(R,o) : +{' -å (*) (3.38)
where: lr:-H@)
The ,/ terms are known as Jeffery constants (Regan and Anandakrishnan, 1993). Previously,
numerical integration would have been used to determine these constants, however, today they
are evaluated using satellite observations. Physically, the Jz term represents the difference
between the equatorial and polar moments of inertia. It is often referred to as the oblateness term or the dynamical form factor. The values used for the Jeffrey constants were: J2:
1.08x10-3, Js : -2.54x10-6 and J4: -1.67x70-6 (Burkhardt, 2000).
The gravitation potential can be expanded to the nth degree depending on the accuracy re-
quired. In this case, a fourth order expansion was calculated, yielding: : r, -V -:r(*)' ¡2,o,'çq¡- lt - r, cos(Q) lscos2lq¡ rl {, (X) - o - ¡zs"o,o çq) 30cos2(0) + 11 e ss) ia (* ) - )
which is the variation in the gravitational potential with altitude, and
3GMn 80: sin(þ)cos{o) *}n sec(Q) r] p2 (¡) {"' (*) fscos2lq¡ - *turo(*)' ¡t,o,,çq¡ - t1 ) (3.40)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.2. Optimisation techniques 62
is the variation in gravitational potential as the angle of latitude changes. These higher order
models are more accurate than the Newtonian approximation, but are more computationally intensive
3.2 Optimisation techniques
With the exception of analytical solvers, there are generally two ways of solving flight path
optimisation problems: in the function space, using calculus of variation, and in the parameter
space, using non-linear programming (NLP) methods. The optimisation used in the present
study was all in the parameter space and therefore employed only NLp methods.
Optimisation deals with obtaining the best or optimal solution to a problem, once it has been
determined what a measure of good or bad is. This is done by defining a cost function which,
when minimised, produces an optimal solution relative to the problem description. There
are a number of different optimisation procedures available, some of which require gradient
information, while others do not. Some methods can also accommodate constraints which
allow the user to obtain a minimum cost function value while at the same time achieving other required state values. A good example of this is a launch vehicle ascent. The ascent trajectory is required to deliver the payload to a certain orbit i.e. specific velocity, flight path angle and altitude, while at the same time minimising the amount of fuel used during the mission.
Constraints can be in the form of equality or inequality constraints. Equality constraints are required to have a specific value, e.g. orbital altitude. Inequality constraints are those which have a boundary, and provided their value remains on the correct side of the boundary, they are free to have any value, e.g. dynamic pressure. The dynamic pressure is only required to be below the structural allowable dynamic pressure, however, how far below the limit is not important.
Two main types of non-linearprogramming routines ate " genetic algorithm,s" and "hill climbers"
The family of hill climbers often use gradient information to keep minimising the cost function
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.2. Optimisation techniques 63
until the minimum is reached. They have the advantage of high speed convergence, making
them well suited to real time application or other time critical situations. The problem with
hill climbers is that they will only find the nearest local minimum, which is not necessarily the
global minimum. It is therefore important to provide a hill climber with an initial guess that is
close to the absolute minimum in order for it to optimise to the global minimum.
Genetic algorithms do not rely on gradient information, instead they "intelligently" vary the
optimisation parameters to see which ones produce solutions with desirable properties. The
"good" solutions then "breed" with each other to produce pockets of "good" solutions which
then finally converge on the global minimum. These algorithms have the advantage of not
being restricted to local minima as no gradient information is used. The problem with genetic
algorithms is that they are extremely computationally intensive and are therefore not well suited to real-time computations.
Due to the fact that a real-time guidance system requires high computational speed, genetic
algorithms are not suitable. As a result, only hill climbing algorithms were used for this study.
The two optimisation routines used will now be discussed in more detail.
3.2.1 Gradient projection method
The gradient projection algorithm used in this study was initially developed by Speyer et al.
(1971) and then applied to a number of studies at the Space Systems Institute, University of Stuttgart, such as that carried out by Schoettle (19SS). It is a constrained optimisation algorithm, so is capable of performing an optimisation while at the same time conforming to constraints. The algorithm has two different processes available to calculate parameter updates. The first is a constraint restoration step that uses a Newton-Raphson method to change the parameters to satisfy the target constraints. The second is a minimisation step that varies the parameters to minimise a cost function.
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 3.2. Optimisation techniques 64
During an optimisation run, the restoration algorithm is first used to determine the parameter
set required to achieve the target constraints. Once the target constraints have been satisfied,
the constraint violations are relaxed to give the optimisation process freedom to vary the pa-
rameters. The optimisation algorithm generates an augmented cost function, which includes
the cost function in addition to the constraints. The constraints are scaled using a constant
Lagrange multiplier. The augmented cost function is then evaluated and differentiated with
respect to the parameters, to determine its gradient. The algorithm searches down the gradient
to the local minimum. To ensure that the minimum reached is the global minimum, the initial
parameter set is varied. This causes the minimisation technique to follow different paths to the
minimum, thereby preventing the algorithm from "getting stuck" in a local minimum.
The problem is formulated using Equation 3.41 (Schoettle, lggg):
minimize f (p) suchthat g(p):g (3.41)
while satisfying the governing equations (Equations 3.42 and3.43)
¿(t): Í(¿,,p,t) (3.42) and
t(to): xo (3.43)
f (p) teptesents the performance index and g(p) the vector of the required terminal boundary conditions. The functions /(p) and g(p) are evaluated as functions of the parameter set p, using a4th otderRunge-Kutta numerical integration technique to integrate the differential state equations' Starting from parameter value pk a varied, parameter ¿e+l i, calculated according to Equation 3.44
o!*t : pk +c,'k.{ : pk + Lpk e.44)
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.2. Optimisation techniques 65
where ct¿ is the step length taken along the search direction st for the l{h iteration. The Newton-
Raphson step length, which is a weighted sum of the squares of the parameter changes, is used
where c[fr has a value of one. üfr can also be varied between zeto andone to change the amount
by which the parameters are changed, thereby changing the size of the convergence region.
For the restoration cycle, pk is varied according to Equation 3.45
({rrr{)-' (3.4s) ^p!:ak,l': -"04{ {
where ¡t' is the diagonal weighting matrix and g\is the Jacobian matrix of partial derivatives given by : {r: #. i l...ng, j : l...np. ng is the number of constraints and np thenumber of parameters.
For the optimisation cycle, the search direction qfr (Equation3.46) is determined using an
augmented cost functio nt-,
,k : -HkFk- (3.46)
where Fk : Fk + )"' gk, showing that the constraint erors gk are considered as part of the
augmented cost function using aLagrange multiplier À. This weighting criteria is determined using Equation 3.47. r.- - ({,ú{)-'44ü e47)
The diagonal weighting matrix, 4k, begins as the identity matrix and is updated using the
Fletcher and Powell (1963) form of the Davidon update formula (Speyer et al., 1971). The update has the form shown in Equation 3.48:
LpLpr HAF ^AFTH H+NI-H+ (3.48) Lp_'LL, LEIHLL p
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.2. Optimisation techniques 66
3.2.2 Sequential quadratic programming (NLpQt)
Quadratic programming is an optimisation process that minimises a scalar cost function of the form shown in Equation3.49.
1 f@):a+þrd+ dr nd (3.4e) 2
wherellistheHessianorthematrix of 2'd partialderivatives of f(p),and,aandþareconstant vectors of dimension n (number of parameters).
NLPQL is a Fortran implementation of a sequential quadratic programming method, which
is used to solve constrained non-linear optimisation problems. The process works by gen-
erating a sequence of quadratic programming sub-problems which are solved successively
(Schittkowski, 1983). "/2" sequential, one-dimensional searches are performed along search
directions {q¡} i : I : n, to arrive at the minimum. This process is very computationally ef- ficient as the minimum is reached in a finite number of steps, which is determined by the dimension of the parameter vector p. The NLPQL algorithm used in the present study was based on the algorithm in schittkowski (1985 /6) andschittkowski (19g3).
The general non-linear optimisation problem considered was to: minimise f(p) subject to the equalityconstraints s¡@):0, j:1,..., m"andtheinequalityconstraintsgi(p) > 0, i :fttel
1, ...., m, where I artd g are continuously differentiable functions for j : r ; m. The resulting quadratic sub problem is shown in Equation s 3 .25 to 3.52.
minimise )o' Uo + v f (p)r d for (3.s0)
V s¡Ø)' d + s ¡@) : 0, j : 1, .....ffie, (3.s1)
v s¡Ø)' d + s¡@) > 0, j : tte t l, ..m (3.s2)
where p is the parameter set and H is asymmetric matrix that approximates the Hessian of the
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.2. Optimisation techniques 67
Lagrange function, shown in Equation 3.53
m L(p,u):f@)-L"¡s¡@) (3.s3) j:1
The next iteration is given by p_*.+t: h+ a¡Q¡, where Q¡, is from the solution of Equation set 3.25 to 3.52 and cr¿ is the step length parameter, which is designed to decrease the cost
function. If p is close to the solution, it could be assumed that some of the constraints would
be fully met (Schittkowski, 1983), however, the formulation of the problem thus far would
still require the computation of gradients for all the constraints. To enable more efficient
computation, the constraints are broken down into two groups as shown in Equations 3.30
and 3.56 (Schittkowski, 1983):
1- minimise H¿ +v (p)r d (3.s4) i¿'L f for v s¡@)' d + I j@_) {t} o, j € ri, (3.s5)
v s ¡Ø ¡)' d + s j(p_) > 0, j e xf (3.56)
There are now two disjoint sets of constraints: { is the set of active constraints including both equality and inequality constraints, and Kf is the set of inactive constraints. In order for this modification to perform satisfactorit¡ the choice of active and inactive constraints needs to be decided. Active constraints are those whose function values p are not positive or whose coresponding Lagrange muttipliêr r¡r: (rf , ..... ,vf) is greater than zero. Using the condition g (p_) ( j e, the situation for which s ¡ @) tends to zero is avoided, however, the linear constraints in Equations3.26,3.52,3.30 and 3.56 can become inconsistent even if the original problem is solvable (Schittkowski, 1983). To overcome this, an additional term ô is added, leading to an n* I dimensional sub-problem.
minimise Uo + v (p)r ¿ + (3.s7) )o' f )enõ2 ¡o, vs¡Ø)'d+ (1 - ô)s;(¿) {t} o, j € rî,, (3.s8)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.3. Steering model parameterisation 68
ve¡Ø¡)'d+s¡@) >0, j eKl, (3.5e)
0<ô<1 (3.60) ,. (dl-rBo-tut E¡ -t)2 (3.61) (I -ô¿-r)2 i[_rHt-út-t and B k-t : v st (A-r), ....,Y s^ (O_r) (3.62)
3.3 Steeringmodelparameterisation
Steering model parameterisation refers to how steering commands are broken down into an
optimisable parameter set. Because steering commands need to be provided to a launch ve-
hicle (or simulated launch vehicle) as a continuous function, an infinite number of steering
parameters could be employed to provide a different steering command for every fraction of
a second of flight time. This would result in an unrealistic optimisation problem for an on- board solution. It is therefore important to have enough steering parameters to generate a good approximation of a continuous steering model, while at the same time keeping the parameter number to a minimum. Parameterisation also has a significant effect on optimisation stability, as using a poorly parameterised steering model can result in stability problems for the optimi- sation routine. For example, using too few parameters in a flight phase that is highly sensitive to steering commands would result in variations in that parameter causing large changes to the trajectory. These changes would cause large gradients in the cost function, thereby caus- ing optimisation instabilities. Steering parameters can be modelled with respect to a number of different parameters such as time, velocity, Mach number or energy. In this study, a time reference was chosen for steering parameter modelling because of its simplicity. The two parameterisation models used in this study will now be discussed in more detail.
The first parameter model type uses a grid of parameter values at specific times, shown in
Figure 3.3. The parameters, shown by the circles in Figure 3.3, arc linearly interpolated to obtain the values between the grid points. Because of the linear interpolation there are no step
commercial Iaunch vehicle design and predictive guidance development Matthew R. Tetlow 3.3. Steering model parameterisation 69
o f (ú
o) o E ct ct fL
Time
Figure 3.3: Parameterisation using grid points
changes in the parameter model, making it suitable for generating steering commands. Using
a grid type parameter model, the values of the parameters at each grid point can easily be seen
on a graph (see Figure 3.3), as they occur at the points where the slope is discontinuous. The linear interpolation function used in this study is shown in Equation 3.63.
a(r) : 4+P#U-u) (3.63) tk+l - Ik
where r is the current flight time, p¿ is the parameter value for the léh parameter and /¿ the grid time for the Hh parameter. The values for p¡¡1 andt¡r¡lrepresent the parameter value and grid time for the k* I grid respectively.
The second steering model parameterisation uses the parameters as coefficients of a steering function, as shown in Figure 3.4. The parameters used in this parameter model are not phys- ical values such as angle of attack, but instead are coefficients of a high order (typically 2"d or 3'd order) function defining a steering profile. Generating a specific steering profile is thus difficult, as the parameters are not a direct representation of the steering command value. A well known formulation of this parameterisation is the "linear tangent law" given in Bryson and (1969). Ho Although the Bryson and Ho (1969) formulation assumes aplanar trajectory, a constant thrust profile and a flat Earth model, it is widely used (Schoettle, 1988), (Braudaway,
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 3.3. Steering model parameterisation 70
f(t)=¿142*5¡*" q) f E
c) q) E Lõ È(ú
Time
Figure 3.4: Parameterisation using function coefficients
1910) and (Dvornychenko, 1980). It is also used in real applications such as the Space Shut-
tle exo-atmospheric flight phase (McHenry et al., 1979) and the Pegasus air-launched space
booster (Rovner, 1991).
It should be noted that both parameter models are restricted to time boundaries, which are fixed for the flight. If for some reason the flight time is longer than expected, the steering commands could become unstable. The grid type parameter model boundary is defined by the last grid point. The guidance problem is undefined for flight times greater than the last parameter.
The function type model has an exponential behaviour so may command unrealistic steering commands when used outside of the expected time frame. This is generally not a problem as flight durations do not vary much, unless severe perturbations (eg. partial engine failure) are encountered. An example of a severe perturbation would be the partial loss of engine thrust during an ascent mission. This may dramatically increase the flight duration, in which case the parameterisation model would not be suitable.
commercial launch vehicle design and predictive guidance deveropment Matthew R. TetIow Chapter 4
Software f)escription
This section will describe the software used for each aspect of the study and the specific models
used. The first software description is that of the sensitivity analysis, followed by the design
aspect of the study, the ascent guidance and finally the flyback guidance.
4.1 Sensitivity analysis software
Before starting an investigation into trajectory optimisation, it is important to determine which environmental parameters have the largest influence over the trajectory. It is also important to determine the numerical accuracy required to achieve a solution that is representative of the real system. To that end, a sensitivity analysis was performed prior to the design and guidance investigations to gain a better understanding of the environmental and numerical effects.
The software used for the sensitivity analysis was called ATOPS. It was an ascent optimisation program that used a Fourth Order Runge-Kutta numerical integration technique to integrate a 3 Degree of Freedom (3DOF) dynamics model. ATOPS was only capable of determining planar trajectories, which implies no motion perpendicular to the orbit plane was considered.
The trajectory flown by many launch vehicles involves a "dog-leg" manoeuvre to change orbit
71 4.1. Sensitivity analysis software 72
plane, which requires a Av component perpendicular to the orbit plane. These could not be modelled using ATOPS.
The propulsion system was modelled using Equation 2.I, and aerodynamics were modelled
as a table of lift and drag coefflcients at different Mach numbers. The table of aerodynamic
coefficients was then interpolated to approximate the launch vehicle aerodynamics. A Standard
atmosphere model was used and the Earth was modelled as a rotating sphere with a Newtonian approximation of its gravitation field.
The task was formulated as a non-linear programming problem that was solved by a gradient
projection optimisation algorithm, accelerated by a Davidon-Fletcher-Powell scheme. The
optimisation parameters were a series of steering parameters that described the flight path of the vehicle.
I (Ð : -mfinat (4.1)
The cost function, shown by Equation 4.7, maximised the vehicle mass at the predefined final orbit condition, for a fixed gross lift offweight (GLOW).
Steering model parameterisation
The trajectory was broken down into flight phases that were either segments of zero angle of attack or segments of non-zero angle of attack. This varying orientation of the vehicle changed the direction of the velocity vector, thereby changing its flight path angle. The angular accel- eration of the velocity vector was brought about by a thrust force at an angle, o, to the velocity vector. Because it was assumed that the thrust angle was always parallel to the vehicle, the an- gle of attack of the vehicle, ü,, was used to generate thrust force components perpendicular to the flight direction. The trajectory was therefore governed by three parameters, which caused the required angular variations of the velocity vector. The first was a coefficient of angular acceleration and the other two were the coefficients of the steering law given by Equatio n 4.3.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.1. Sensitivity analysis software 73
Lineorised orcton steering commond \ \ T4
3
Pitch I2 Flight ot constont occel pitch rote TI
h
Figure 4.1: ATOPS parameterisation model
The trajectory was broken down into four time segments as shown in Figure 4.1. Between
launch and time Tl the vehicle flew with zero pitching angular velocity, so was flying vertically
upward (its physical application was to clear the launch tower). Between Tl and T2, the first parameter was used to generate a pitching moment. The steering command generated by this parameter was an angle of attack, shown by Equation 4.2.
u: ptQ -rÐ+;-r*H (4.2) r is the current flight time, pl is the first optimisation parameter, a is the angle of attack and y is the flight path angle. rdsr is the distance along the ground (ground track) and R¿ is the constant Earth radius. Between times T2 and T3 no further pitching torque was applied, so a constant angular velocity around the pitching axis was experienced (a:0). After time T3, a linear tangent steering law was used, given by Equation 4.3 (Bryson and Ho, 1969) to again introduce an angular acceleration.
s,: arctan(pt"+ Æ) -y (4.3) where Í: t -T3. p, and p3 are the optimisation parameters used to generate the angle of attack commands between flight times T3 andT4.
commercial launch vehicle design and predictive guidance development Matthew R. TetIow 4.2. Yehicle design software 74
4.2 Vehicle design software
The optimisation software used for the vehicle design study was called RTSOPT and it was
developed at the Space Systems Institute in Stuttgart, Germany. RTSOPT was verified and
tested on a range of different computation platforms including a CRAY multi-processor com-
puter and IBM RS6000 Unix stations. The software has been used in a co-operative University
project called Ariane X (Rahn et a1., 1999), as well as a number of undergraduate studies on
vehicles such as the Pioneer rocket plane (Roth, Ig99).
4.2.1 Simulation and optimisation
The simulation technique used in RTSOPT employed apoint mass, rigid body dynamic model.
The aerodynamics of the vehicle were modelled as a table of lift and drag coefficients for
given Mach numbers and angles of attack. These values were then interpolated, using a spline function, to produce a continuous function that described the aerodynamics of the vehicle. The
Earth was modelled as a rotating sphere with a Newtonian approximation of its gravitational field. A static atmosphere model similar to the US Standard atmosphere was employed with no wind model. The 3 Degree of Freedom (3DOF) dynamics equations were integrated using a 4th Order Runge-Kutta numerical integration technique. The task was formulated as a non- linear programming problem that was solved by a sequential quadratic optimisation algorithm, employing central difference gradient calculations.
4.2.2 Propulsion model
Speciflc impulse of rocket engines vary with local atmospheric air pressure (Hammond ,2001)
(see Figure 2.1). In order to accurately model the behaviour of the propulsion systems, this variation was modelled in RTSOPT assuming a linear relation between pressure and specific impulse using Eqtation 2. 12.
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 4.2. Vehicle design software 75
4.2.3 Mass model
Statistical mass modelling was employed, as described in Section 3.1.3,to calculate the vehicle
subsystem masses. Vehicle sizing was calculated from the amount of propellant required to
be stored in the vehicle's tanks, including a 4Vo propellant reserye. The propellant volume
was used to determine the propellant tank masses, which imply a fuselage mass. The process
continued iteratively until the whole mass budget had been approximated. An 8Zo mass margin
was also included to allow for modelling inaccuracies.
The mass of the fuel required for flyback of the powered return concept was calculated using
the relationship shown in Equation 4.4 (Schoettle, 1988):
o, : I (+P * ht - ¡, +,r,,tnff) (4.4)
Knowing the distance back to the launch site Âs, the initial mass (rn 1), starting velocity (v1) and altitude (å1), as well as the target velocity (vz) and altitude (h), the final mass of the vehicle
(mù could be calculated. Thus, the propellant consumed during flyback was the difference between the initial and final masses of the vehicle. This propellant volume was added to that required for ascent.
The payload mass of the GTO mission was calculated using the payload mass for the LEO mission as the initial mass (zs) for a kickstagel and payload combined. The payload mass was calculated by solving Equations 4.5 and 4.6 simultaneously. Equation 4.5 was used to obtain a function relating 26, which is the initial mass for the kickstage and payload combined, to m¡, which is the injected mass of the kickstage and payload combined. The difference betwe en m0 and m¡ is therefore the fuel consumed during the burn. Lv¡r¡ isthe velocity change required to change from a 466km circular orbit to a 466x35862km GTO, ge is the gravitational potential lA kickstage is a smaller rocket stage that propels the satellite to the required orbit, after it has separated from the main launch vehicle.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.2. Vehicle design software 76
on the Earth's surface and Iry is the specific impulse of the kickstage motor. Equation 4.6 was
used to relate the injected mass (n¡) and the initial mass (26) to the payload mass using the
kickstage's propellant mass fraction (().
^:þ¡ m0 ffiie goltp (4.s)
nn¡:ntpt+(1-Ç)mç (4.6)
4.2.4 Steering model parameterisation
The mission was broken into three flight phases which had different parameter sets and were
optimised independently to achieve a solution. Phase 1 was the ascent of the mated configu- ration and it employed three optimisation parameters to describe the flight profile. The three parameters used were thrust vector angle during pitching manoeuvre, duration of the pitching manoeuvre and the launch azimuth.
Phase 2 was the booster flyback and it was controlled by 16 optimisation parameters, the first
T2being angle of attack steering commands and the remaining four bank angle steering com- mands. A grid parameter model was used for both angle of attack and bank angle parameter- isation. These models were linearly interpolated to obtain steering parameter values between the grid points, as shown in Figure 3.3. The angle of attack and bank angle parameterisation was achieved using n : 12 angle of attack time grid points and m: 4 bank angle time grid points.
Finally, Phase 3 was the orbiter ascent flight and it was optimised with respect to f,ve angle of attack parameters. Again, the thrust was always aligned with the body, so angle of attack de- fined an angle between the velocity vector and the direction of thrust. The steering commands were in a grid type parameter model as shown in Figure 3.3. It should also be noted that in all
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 4.3. Ascent guidance software 77
flight phases the angle of attack changes were instantaneous, and so a "perfect controller" was
assumed.
4.3 Ascent guidance software
Guldo nce conputer
contnotler
onblten
Figure 4.2: Virtual orbiter (Tetlow et a1.,2002)
There are three main parts to the ascent guidance software, shown in Figure 4.2. The first is the system simulation environment, which represents the orbiter and a realistic environment in which it would fly. They will be referred to as the "virtual orbiter" and "virtual environment" or "virtual system" when considered together. The trajectory flown by the "virtual orbiter" will be referred to as the "virtual flight". The second part is the guidance system which generates steering commands for the virtual orbiter. The guidance system thus represents an on-board guidance computer and so will be referred to as the "guidance computer". Finally, the at- titude controller represents another on-board computer that converts the steering commands into flight control commands, in this case thrust vector angles.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance softwarc 78
Virtual vehicle Guidance Computer
models Perturbations Environment models Vehicle models Vehicle models Dynamics x x Command model Par Opt./Resr u generator e Anitude Controller Dynamics model
Figure 4.3: Program flow for ascent guidance (Tetlow et at., 2002)
Figure 4.3 shows the flow of information and commands between the virtual orbiter, guidance computer and the attitude controller. The virtual orbiter's trajectory was generated using a pa- rameterised steering model, which was updated at regular intervals by the guidance computer.
At every guidance call, information about position and velocity was given to the guidance computer, which used its own, simplified simulation model to propagate the trajectory to orbit and calculate the orbit enors. It then used a Newton-Raphson restoration technique to calcu- late the parameters required to generate a near-optimum trajectory from the current point to the required target orbit. These new parameters were then converted into steering commands
(in this case, angle of attack). The angle of attack commands were then given to the attitude controller, which converted the steering commands into thrust vector angles. These thrust vec- tor angles were given back to the virtual orbiter, which continued along its trajectory using the latest steering commands.
Perturbations in certain parameters were generated in the virtual system to simulate variations in the flight environment as well as uncertainties in the vehicle model. If the guidance com-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 79
puter and virtual system used the same models, then the virtual flight would not need guidance
updates as it would always follow the flight that the guidance computer expected it to. How-
ever, if for example, the guidance computer used a US Standard atmosphere model and the
virtual system used the MSISE93 atmosphere model, guidance updates would be required as
the slight differences in atmospheric density calculation would result in the virtual orbiter fly-
ing a slightly different trajectory to the one it was expected to fly by the guidance compurer.
The guidance computer would therefore need to continually change the steering commands,
as the trajectory flown in the virtual environment would not match the trajectory calculated by
the guidance computer in the previous prediction. The perturbations generated in the virtual
system could either be in the form of different environmental models in the guidance com-
puter and virtual environment, or random perturbations in certain parameters in the virtual envronment.
The models and numerical techniques used in the virtual system, guidance computer and atti-
tude controller will now be discussed in more detail.
4.3.1 Virtual system
As mentioned before, the virtual system was required to model the flight environment, ve- hicle dynamics and aerodynamics as accurately as possible. There was no restriction on its computation time, as it would be replaced by the actual vehicle in a real application. The sim- ulation model used in the virtual system was developed at the Space Systems Institute (IRS) in Stuttgart, Germany. A number of modifications had to be made to the IRS model as it did not model thrust or the rotation dynamics (Burkhardt et al., 1999). The modifications included modelling the propulsion forces, mass reduction due to propellant consumption, mass moment of inertia and position of centre of gravity, as well as the equations to model the rotational motion of the vehicle. Velocity was used as a stopping condition for the integration, so the target velocity was always achieved for the virtual flight.
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 4.3. Ascent guidance software 80
The 6DOF vehicle dynamics model used in the virtual system is shown in Section 3.7.1. A4th
order Runge-Kutta integration technique was used to integrate Equations 3.1 to 3.13 along the
flight path, to determine the position and velocity of the virtual orbiter at each guidance call.
An integration step size of 0.1s was used for this analysis. The reason for this was that the
smallest guidance call interval used was ls, and the attitude controller needed at least 10 times
that resolution to operate acceptably.
4.3.1.1 Virtual vehicle
The ascent propulsion system was modelled as shown in Section 3.1.2. The aerodynamic
properties of the orbiter were modelled as a table of lift and drag coefficients for different Mach
numbers and angles of attack. Part of the aerodynamics look-up table is shown in Appendix E.
These values were then interpolated using a 3-dimensional interpolation routine, to generate
an aerodynamics model. By providing the model with Mach number and angle of attack, the
values of the drag and lift coefficients were able to be calculated.
The control parameter received by the virtual orbiter was a thrust vector angle, e. In order
to determine its effect, the instantaneous mass properties of the virtual orbiter needed to be
calculated. The mass moment of inertia and centre of gravity (COG) were therefore calculated every second during the virtual flight. The mass moments of inertia with respect to the COG, about the three axes of the dry orbiter, (including the empty propellant tanks) were determined using Equations 4.7,4.8 and 4.9 (Roskam, 1999).
b"wRl^-) IxJ(vehicre (4.7) 4go
^-a I¿wRl I!!v"hicte (4.8) 4go
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 81
(ry)'*É, L"....ventcrc : (4.e) 4go
where å is wing span [/r], w is vehicle weight ltbl, t is fuselage length lftl and ge is rhe gravitational acceleration on the surface of the Earth lft ltzl. The parameters Rr, R, and R.
are non-dimensional radii of gyration2, which are specific to each aircraft configuration. The
resulting moments of inertia had the unit of slug.ft2, so were simply converted to kg.m2 for use in the software.
Some assumptions were made when determining the mass of the propellants. The propellants
were assumed to be cylindrical masses with flat ends, perpendicular to the longitudinal axis
of the virtual orbiter (as shown in Figure 4.4). The fuel and oxidiser tanks were considered as
separate cylindrical masses, to allow different mass flow rates from each tank to be modelled.
It also allowed the oxidiser tank to be at the propulsion system end of the virtual orbiter and
the fuel tank to be near the nose, thereby having a space between the two propellant masses.
r- lF
Poytood CIG Bose of vehicle
x
Figure 4.4: Vinual orbiter mass distribution
In order to calculate the COG, the dimensions of the tanks were required. The base position 2These are not classic radii ofgyration, but rather non-dimensionalised factors accounting for the configura- tion of the vehicle.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 82
for each tank was known and constant, as the propellant was always assumed to remain at the
bottom of the tank. The upper dimension of the unused propellant volume was calculated by
subtracting the propellant flow rate during the time interval from the initial propellant mass,
thereby working out the remaining propellant volume, and therefore propellant height. Con-
sideration also had to be given to the fact that the engines were throttleable, thereby causing
different amounts of propellant to be consumed during different time intervals.
when the propellant COG's and masses had been determined, Equation 4.10 was used to de-
termine the COG along the body fixed axes.
m¡uelTf uel I morxo* I m¿rT¿r l mpayloadxpayload X- (4.10) llltotal
Where X is the position of the COG along the longitudinal axis of the orbiter and the mx,
terms are the masses and positions of the COG along the longitudinal axis for each component
mass. The same equation was used to determine Y and Z, thercby giving the COG of the entire vehicle.
The mass moment of inertia for the propellants and the payload were calculated using the equations for a solid cylinder with flat ends (Equations 4.11 and 4.12). The formulation used was obtained from Meriam and Craige (1993).
ç:)*f,, (4.11)
1^1 Iyy : Irr: + md2 (4.12) Umrlr¡ 1
where m is the mass of the cylinde\ rcyt is the radius of the cylinder and, d is the distance from the COG of the object to its base. Once the COG and mass moments of inertia for
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 83
the sub-sections had been determined, the mass moment of inertia for the whole vehicle was
calculated. This was done using Equation 4.13. The example shows the calculation of the
mass moment of inertia about the longitudinal axis, but the same formula was used for the
other two axes.
n Io : L Io, -f m¡x? (4.13) i:1
During the virtual flight, Iy and I* of the whole vehicle (including dry vehicle, payload and
propellant tanks) decreased by a factor of seven, while 1o decreased by a factor of only three.
4.3.1.2 Virtual environment
The virtual environment model had a number of different environment models that could be
activated. A spheroidal Ealth model was used to determine the radius of the Earth (see Section
3.1.6) at a given latitude. The gravitational potential of the Earth was calculated using a 4t¿
order approximation model (see Section 3.7.7). The atmospheric parameters were either cal-
culated using the US Standard atmosphere (see Section3.7.4.1) or the MSISE93 atmosphere
model (see Section3.l.4.2), depending on the requirements of the virtual environment. A wind model was also available to model the primary atmospheric wind speed and direction at given
altitudes, dates, flight times, latitude, and longitude (see Section 3.1.5). The virtual environ- ment thus had the capability to switch between a number of environmental models, depending on what type of virtual flight environment was required.
The virtual system had the capability to introduce random variations in a number of parame- ters. First, a random number was generated between the values of 0 and 1. This number was then placed on a 3o bell-shaped distribution curve to obtain a number between -1 and 1 that fell within a 3o bell curve. These random numbers were then used to create perturbations in the virtual environment, to model non-nominal environmental variations. The random num- bers between -1 and I were multiplied by the wind vectors to model random gusts and wind
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 84
reversals. Random atmospheric density perturbations were introduced using the initial ran-
dom numbers between 0 and 1. These numbers were multiplied by 2 and then multiplied by
the atmospheric density, causing random atmospheric density variations between 0 and twice
the nominal value. In order to model navigation system errors, the random numbers between
-1 and I were multiplied by the maximum expected measurement errors and then added to
the states given to the guidance computer. This had the effect of introducing an error in the
measured state given to the guidance computer, thereby modelling navigation erors. The first
random number between -1 and 1 was also used to generate erïors in staging conditions. It
was multiplied by the maximum expected staging condition error, which was then added to the
nominal staging conditions to create a staging velocity, flight path angle and altitude error.
4.3.2 Guidance computer
Guidance commands needed to be computed in very short periods of time, while at the same
time having sufficient accuracy for realistic trajectory propagation. Instead of high accuracy
models that were specific to a time, geographic position or weather phenomenon, the guidance
system used reduced order dynamics models and environment models that were intended to be as nominal as possible. This allowed the guidance system to be used anywhere around the
Earth without requiring modification to the models.
The guidance simulation employed a simplified 3DOF dynamics model, and thus only mod- elled the translational degrees of freedom. The seven states used were: radius from the centre of the Earth, longitude, latitude, Earth relative velocity, flight path angle, heading and vehicle mass. A 4th order Runge-Kutta integration technique was used to integrate Equations 3.1 to
3.J , from the current position along the trajectory to the final position. V/ith the final position, the guidance computer was able to calculate the violations in the target constraints. It then determined appropriate changes to the steering parameter model to guide the virtual orbiter to the required orbit. The target constraints (S(p) in Equation 3.47) were an altitude of 94068m
Commercial launch vehicle design and pedictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 85
and a flight path angle of 0'
There were two steering parameter model update techniques within the guidance system. The
first was a gradient projection optimisation routine (see Section 3.2.1). This gradient projec-
tion algorithm generated steering parameters for the fuel minimum trajectory that satisfied the
altitude and flight path angle constraints. The cost function (Í(p) in Equation 3.41) was thus to minimise the fuel used during ascent and had the form f (p) : rltinítiat - mfinat.This opti- misation process was only used before the virtual flight began, when there was sufficient time
to calculate an optimum trajectory, without having to generate steering commands. In the real
application it could be performed in the short coast phase between main engine shut-down
of the first stage and ignition of the second stage. This trajectory optimisation could also be
performed prior to flight, however, performing it late in the open loop flight phase would al-
low a more accurate prediction of the actual staging conditions. This would allow the initial
trajectory optimisation to produce a more optimal trajectory, as a better approximation of the
staging conditions could be determined.
Once the virtual flight began, the parameter updates were performed using a Newton-Raphson restoration technique. The restoration technique dropped the fuel minimisation requirement and produced parameter updates that drove the altitude and flight path angle errors to zero. It therefore did not perform an optimisation with respect to fuel minimisation, but simply varied the parameters to drive the target constraint violations to zeîo. Although the restoration tech- nique did not optimise the trajectory with regard to the complete cost function (i.e. minimise fuel and achieve target constraints), Schoettle and Hillesheimer (1991) proved that the restora- tion procedure tries to drive the changes in the parameters to zero. This means that it tries to keep the parameters as close as possible to the original values, which produced an optimal tra- jectory with respect to the complete cost function. The restoration thus still retained a notion of optimality in its command generation.
In both the gradient projection and Newton-Raphson methods, the Earth relative velocity was used as a stopping condition for the integration. For this reason a velocity constraint was not
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 86
required as the correct velocity was always achieved. Essentially, the software determined what altitude and flight path angle errors would occur, as well as the injected mass in the case of the optimisation phase, at the required velocity. It then modified the steering parameters to
eliminate these errors and maximise the injection mass, in the optimisation case.
The guidance algorithm was only implemented in the ascent plane and therefore could not determine steering commands in the roll and yaw directions. As a result, the guidance system could not use heading as a target constraint and therefore could not control the heading angle. The numerical guidance strategy that is applied to the normal plane could easily be applied the to lateral plane, however, if no dogJeg manoeuvre is required during ascent, a simple controller could be used to maintain a zeÍo side slip flight condition instead. As a zero side
slip condition was assumed during the present study, no lateral guidance was required.
Again, the aerodynamic properties of the orbiter were modelled as a table of lift and drag coef-
ficients for different Mach numbers and angles of attack. These values were then interpolated
using a 3-dimensional interpolation routine, to generate an aerodynamics model.
4.3.2.1 Guidance environment models
The guidance computer simulation environment used a spheroidal Earth model with a Newto- nian approximation for the gravitation field (see Section 3.1.7). The atmospheric parameters were calculated using the US Standard atmosphere (see Section3.l.4.l) and wind effects were neglected.
4.3.3 Steering model parameterisation
In the ascent guidance investigation, both steering parameter models discussed in Section 4.2.4 were used. The first was a grid of angle of attack values at specific times, which were linearly
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 87
interpolated to obtain an angle of attack value for every flight time (see Sectio n 4.2.4and Fig- ure 3.3). A predetermined number of angle of attack parameters were used over the flight time of 255s. As each time grid point was passed during the virtual flight, its angle of attack param- eter no longer had any effect on the trajectory. For this reason, the parameters were ignored
once the flight time exceeded their time grid points. As a result, the number of optimisation
parameters decreased as the flight progressed.
In order to maintain stable computation, the flight time could not exceed the final grid point. If this were to occur, there would be more constraints than parameters and the guidance scheme would fail. It was therefore important to ensure that the flight duration did not exceed the final parameter by imposing a buffer region at the end of flight. This buffer had to be large enough to avoid exceeding the grid point in unexpected environmental parameters, but not so large as to minimise the effect of the final parameter. Another measure taken to prevent instability was to stop the guidance from being called after the last time grid point.
Figure 4.5 shows a typical grid type steering model for the ascent mission. The angle of attack parameters at each grid point, shown by the circles, were linearly interpolated to obtain an angle of attack profile for the entire virtual flight. The guidance computer used the current set of angle of attack parameters to propagate the trajectory and determine the expected orbit conditions. It then varied the parameters, thereby changing the entire angle of attack profile used by the virtual orbiter until the next guidance update. This current parameter set was used to generate the command angle of attack corresponding to the virtual orbiter's current flight time.
The second steering parameterisation used a function (see Figure 3.4) relating angle of attack to time (shown by Equation4.74).
C[ +T : arctqn(qt2 + bt + c) (4.14) where cr is angle of attack, l is flight path angle, r is ûme and a,b,c are the optimisation pa-
Commercial launch vehicle design and predictive guidance development Matthew R. Tet1ow 4.3. Ascent guidance software 88
t2
10
òo C) 8
J4 O cú (* 6
c) ö0 Ê 4
2
0 20 40 60 80 100 120 140 160 180 200 220 240 260 Time [s]
Figure 4.5: Typical grid type steering model for ascent
rameters. This formulation is similar to the one seen in Bryson and Ho (1969), except that they
used only two optimisation parameters. In the present study the third parameter was required
to avoid an undefined optimisation problem. This would have occurred if there were more
constraints (fuel minimisation being considered a constraint) than optimisation parameters.
Two parameters would have been sufficient for the guided phase of flight as the restoration
technique had only two constraints, however, the optimisation technique required a third pa- rameter. It should be noted that the three parameters always influenced the trajectory and were therefore always active. Contrary to the grid time parameterisation model, the number of optimisation parameters remained constant throughout the virtual flight.
4.3.4 Attitude controller
Although angle of attack is a useful parameter to use for guidance purposes, it needed to be converted into some other parameter that could be used as a steering command in a real appli- cation. In the case of powered ascent flight phases, thrust vectoring is often used to vary the vehicle attitude (Jackson et a1., 1998) and thereby attain a required angle of attack. An atti- tude controller was thus developed to change the angle of attack command from the guidance
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.3. Ascent guidance software 89
system, into a thrust vector command, which would cause the required attitude change.
The attitude controller was a regulator that used current angle of attack, current rate of change
of angle of attack and commanded angle of attack to generate a thrust vector angle that would
produce the required attitude change. The formulation is shown by Equation 4.15.
Fpilch: -koUa* - kalf adotal Natf aLcom (4.rs)
where Fpitrt, is the thrust required to pitch the orbiter over. The values katf a, katf ado¡ and, No¡¡o
are the gains used for current angle of attack, current angle of attack rate and commanded angle
of attack respectively. These gains were estimated, using Simulink, to achieve the required
performance. Although more control theory could have been used to optimise these gains, it
was decided to use the estimates, as a non-optimal attitude controller would further test the robustness of the guidance system.
Because the mass properties of the virtual orbiter changed by half an order of magnitude and the position of the COG shifted during flight, the gains had to be changed three times to maintain stable attitude control. This changing of the gains during flight is called gain scheduling and it is commonly used for control systems. An example of gain scheduling is shown in Buschek (1999) for roll controllers.
The control command required by the virtual orbiter was a thrust vector angle. The pitch thrust, Fpitch, therefore had to be converted into a thrust vector angle, using Equation 4.16.
( E: arcsin !t!t!\ (4.16) \Frotot / where e is the thrust vector angle and F¡o¡o¡ is the total thrust produced by the operating rocket engrnes
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 90
4.4 Flyback guidance software
Virtual vehicle Guidance Computer Environment models Perturbations Environmcnt models
Vehicle models Vehicle XX models Dynamics Co and Opt./Rest. rnodel tt generatol' Par
Dynamics model
Figure 4.6: Program flow for flyback guidance
The flyback guidance system is similar to the ascent guidance system described in Section
4.3, except that there is no attitude controller. The reason for this is that during flyback, attitude would be controlled by aerodynamic forces. This means that any attitude control modelling would require a highly accurate aerodynamic model. As one was not available, attitude control was not investigated and a"perfect controller" was assumed. This means that the virtual vehicle was assumed to achieve the commanded attitude without any time delay. As a possible future study, it may be useful to include a fixed time delay to approximate the delay of a controller.
There are thus only two parts to the flyback guidance software. The first is the system simu- lation environment, which again represents the booster and the environment in which it would fly. These components will be referred to as the "virtual booster" and "virtual environment" or "virtual system" when considered together. The trajectory flown by the "virtual booster " will be referred to as the "virtual flight". The second part of the flyback guidance software is
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow guidance 4.4. Flyback software 91
the guidance system, which generates steering commands for the virtual booster. The guid-
ance system thus represents an on-board guidance computer and so will be referred to as the "guidance computer".
Figure 4.6 shows the flow of information and commands between the virtual booster and the
guidance computer. The virtual booster's trajectory was generated using a parameterised steer-
ing model, which was updated at regular intervals by the guidance computer. At every guid-
ance call, information about position and velocity was given to the guidance computer, which
used its own, simplified simulation model to propagate the trajectory to an altitu de of l2km
and calculate the target condition errors. It then used a Newton-Raphson restoration technique
to calculate the steering parameters required to achieve the desired state. These new parame-
ters were then converted into steering commands and given back to the virtual booster, which
continued along its trajectory using the latest steering commands.
Random perturbations in certain parameters were generated in the virtual system to simulate the variation in the flight environment. This was done to determine if the guidance computer was robust enough to guide the booster if its simulation models differed from the virtual envi- ronment.
4.4.1 Virtual system
The virtual system was required to model the flight environment, vehicle dynamics and aero- dynamics of a real vehicle. The 6DOF dynamics equations used for the booster dynamics are shown in Section 3.1.1. A 4th order Runge-Kutta integration technique was used, with an integration step size of ls, to integrate along the flight path and determine the position and ve- locity of the virtual booster at each guidance call. The virtual environment had the capability to switch between a number of environmental models, such as atmosphere and wind models, depending on what type of flight environment was required.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 92
4.4.1.1 Virtualvehicle
An air-breathing propulsion system was used during the flyback mission between the altitudes
of 10 - l3km. The maximum thrust and maximum propellant flow rate were assumed to be 'When fixed for the duration of the flight. the engines were throttled, the mass flow rate was
assumed to vary linearly with the thrust. That is to say that if the thrust were reduc ed.by 30Vo,
then the propellant mass flow rate was also assumed to reduceby 30vo.
The aerodynamic properties of the booster were modelled as a table of lift and drag coefficients
for different Mach numbers and angles of attack (as shown in Appendix E). These values were
then interpolated using a 3-dimensional interpolation routine, to generate an aerodynamics
model. From this model, the total amount of lift and drag was determined for a specific flight
condition. The components of these aerodynamic forces were then determined by the bank
angle. For example, if the booster was at a non-zero bank angle then part of the aerodynamic
lift would be supporting the weight of the booster and the rest would be pushing it left or right in a plane horizontal to the Earth's surface.
4.4.1.2 Virtual environment
The virtual environment had a number of different models, which it could use to model the flight environment. A spheroidal Earth model was used to determine the radius of the Earth
(see Section 3.1.6) at a given latitude. A 4th order gravitational model was implemented to approximate the Earth's gravitational field. The atmospheric parameters were either calculated using the US Standard atmosphere (see Section 3.7.4.1) or the MSISE 93 atmosphere model
(see Section3.l.4.2). A wind model was also available to model atmospheric wind speed and direction at given altitudes, dates, flight times,latitude, and longitude (see Section 3.1.5). The virtual environment again had the capability to switch between a number of environmental models, depending on what type of flight environment was required.
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 4.4. Flyback guidance software 93
As was the case for the ascent guidance software, the virtual system had the capability to
introduce random variations in a number of parameters. The random numbers were used to
model random gusts, random wind reversals, errors in staging conditions and navigation errors.
4.4.2 Guidancecomputer
The simulation environment within the guidance computer employed a simplified 3DOF dy-
namics model with only seven states. At every guidance call, information about position and
velocity was given to the guidance system, which propagated the trajectory using a 4th order
Runge-Kutta integration technique. The stopping condition for the guidance simulation inte-
gration was an altitude (h) of l2O\Om. At this termination altitude, the guidance compurer was able to calculate the target constraint erïors, which were velocity, heading angle and flight path angle. A parameter update technique was then used to calculate the steering parameters
(in this case bank angle and angle of attack) required to achieve the correct cruise conditions.
As with the ascent guidance, two parameter update techniques were used. The first was a gra- dient projection optimisation routine (see Section3.2.7), which generated steering parameters to attain the correct target constraints, while at the same time minimising the distance to the launch site and limiting the maximum loading during flight. In a real application, this opti- misation routine would be used during an open loop flight phase, prior to staging, when no steering updates were required. Once the guidance computer began updating the bank angle and angle of attack steering parameters in real-time, a Newton-Raphson restoration technique was used. The restoration technique dropped the requirements to minimise flyback distance and vehicle loading and was only required to drive the target constraint violations to zero. As was discussed for the ascent guidance computer (Section 4.3) thesteering parameters remained as close as possible to the original values, which produced an optimal trajectory with respect to the complete cost function. The restoration thus still retained a notion of optimality in its command generation.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 94
The numerical guidance system was used to guide the virtual booster from staging to a flight path angle (y) of - 10.0o, a velocity (v) of 270mf s and a heading (X) of - 106.0' at an altitude (h) of 120OOm. After the numerical guidance phase, feedback controllers were used to pull
the virtual booster out of the shallow dive and maintain cruise conditions. The first was a
constant descent controller, which used angle of attack to keep the virtual booster at a constant
flight path angle of -5'. This would be required if the virtual environment model caused the virtual booster's flight path angle to shallow to -5", before guidance termination. The bank angle commands were still generated using the numerical approach, but the angle of attack
commands were modified by the controller, which had the form shown in Equation 4.77.
U -- dcurren¡ I kgamt (Trorrr, - y) - kto z (T) (4.17) where ksamt and kgamz àrê the controller gains, ucurrent the current angle of attack, y and i the current flight path angle and flight path angle rate respectively and y¡orrr¡ is the target flight path angle, which in this case is -5o.
Once the guidance altitude of I200Om had been reached, three controllers were activated to achieve and maintain cruise conditions. A proportional+derivative altitude controller was used to achieve the cruise altitude (h"ru¡r") of 10000m and maintain it for the duration of the return flight to the launch site. The controller had the form shown in Equation 4.18.
U: arurrent t ko¡¡1(hrruir, - h) - ko¡¡2vsiny (4.18)
where ko¡¡1 and ko¡¡2 are the controller gains, dcurrent is the current angle of attack, and y, v and h arethe current flight path angle, velocity and altitude respectively. It should be noted that the altitude controller and the constant descent controller were never active at the same time. The constant descent controller was only activated above 12000m altitude and the constant altitude controller was only activated at or below an altitude of 72000m.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 95
A constant velocity controller was implemented below an altitude of 73000m. The air-breathing
engines were throttled to maintain a velocity of 24Ùmf s. The controller was a simple propor-
tional controller and it had the form shown in Equation 4.19.
tr : kthrot (vrrr¡r" - v) (4.1e)
where /r is the throttle setting, k¡¡ro¡ is the controller gain and v and vcruíse are the current virtual
booster velocity and the target velocity respectively. This throttle value was limited between
the values of 0 and 1 and then multiplied by the maximum engine thrust and maximum fuel
flow rate.
After the numerical guidance system had attained a heading of -1060 and the altitude had dropped below l02km the heading controller was activated. This proportional-derivative con- troller used bank angle to maintain a heading that would make the flight path of the virtual booster intersect a heading alignment cylinder (HAC). The current and desired geographic position was used to determine the required bank angle, using Equation 4.20.
,,:kh".dl(-'"(*ffi) -;) -4 Ø20) where k¡ro¿ is the controller gain, õ and À are the current latitude and longitude respectively, with the subscript "tatget" indicating the position of the edge of the HAC, and^tris the current heading. The reason the heading controller was only activated close to level flight was to minimise the control effort while the virtual booster was attaining level flight.
The activation timing for the four flightphases discussed above (shown later in Figure 8.1) will now be explained. The first was a numerical guidance method, which used a parameterised steering model updated by either a Newton-Raphson restoration technique or a Gradient pro- jection optimisation algorithm. This phase operated from staging until an altitude of l2.4km.
Between 72.4km and 72.2km. the parameterised steering model was still used, but the parame-
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 4.4. Flyback guidance softwarc 96
ters were not updated. Instead, the same parameter set was used to calculate the angle of attack
and bank angle values for the entire phase. Between 72.2km and 77km, a constant descent con-
troller was used to keep the virtual booster in a shallow dive with a constant flight path angle
of -5o. Below llkm, a constant altitude controller was used, which pulled the virtual booster
out of the shallow dive and maintained an altitude of l\km. The program flow and switch
conditions for the four guidance phases are shown in Figure 4.7.
if numerical-guide.true and h > 11000m if h > I2200m ifh<13500mand ganma > -5 deg goto 100 endif if h > 72400m update steering parameters endif cal-cul-ate angle of attack values calcul-ate bank angJ_e values
else 100 activate const. descent contro.l_ endif
el-se
numeri cal-guide . f al_ se activate al-titude control activate heading control endif
if h < 13000m activate cruise velocity control endif
Figure 4.7: Flyback program structure
Below an altitude of l3km, the air-breathing propulsion system was activated to prevent the
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 97
velocity from dropping below the required cruise velocity. Finally, a switch was implemented
to prevent the virtual booster from flying with a shallow descent rate when close to the ter-
mination point. This was done by switching to a constant descent controller if the flight path
angle rose above -5" when the altitude was below l3.5km. The afore mentioned switches were all implemented to improve robustness.
4.4.2.1 Vehicle models
The same propulsion model was used in the guidance computer as was used in the virtual
booster (see Section3.l.2). The aerodynamic properties of the booster were modelled as a ta- ble of lift and drag coeffrcients for different Mach numbers. The aerodynamic model included
variations in both angle of attack and Mach number to calculate aerodynamic coefficients.
4.4.2.2 Environment models
The guidance flight environment was modelled using a spheroidal Earth model with a Newto- nian approximation for the gravitation fleld (see Section 3.1.7). The atmospheric parameters were calculated using the US Standard atmosphere (see Section 3.1.4.1). Wind effects were not considered in the guidance computer.
4.4.3 Steering model parameterisation
Both angle of attack and bank angle steering parameters were used during the flyback phase.
Both models were parameterised using a time grid model as explained in Section 4.2.4. These grid points were linearly interpolated to obtain the steering angle values between the grid points. The angle of attack profile consisted of 12 gnd points with corresponding values for angle of attack. Only the last two parameters were updated by the guidance computer. The remaining angle of attack parameters were fixed for the entire flight and so were not updated by
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 98
the guidance computer. The bank angle profile consisted of five grid points with corresponding
bank angle values. All of the active bank angle parameters were updated by the guidance
computer during the virtual flight. It should be noted, as for the ascent case (Section 4.3.3),
once the parameter no longer had an effect on the remaining trajectory it was ignored, with
only the remaining parameters being updated by the guidance system.
Typical steering parameter models for the flyback mission are shown in Figure 4.8. The angle
of attack parameters at each grid point, shown by the circles, were linearly interpolated to
obtain an angle of attack profile for the entire virtual flight. Again, it should be noted that
only the last two parameters were updated by the guidance computer. The first 10 parameters
remained the same throughout the virtual flight. The bank angle parameter model consisted
of five parameters, which were also linearly interpolated to obtain a bank angle profile for the
full flight time. From Figure 4.8 it can be seen that by changing the parameter values (small
circles), the angle of attack and bank angle profiles can be changed.
The guidance computer used the current set of steering parameters to propagate the trajectory and determine the expected end conditions. It then varied the parameters, thereby changing the entire bank angle profile, and the lattêr part of the angle of attack profile. The new parameter set was used to generate the commanded bank angle and angle of attack values, corresponding to the virtual booster's current flight time, until the next guidance update was called.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 4.4. Flyback guidance software 99
40 0
-10 30 ()ào -20 E ¡1o (! () Ë20 go (t -30 o c) ¡1 èo -40 A 10
-50
-60 150 200 250 300 350 400 100 150 200 250 300 350 400 Time [s] Time [s]
Figure 4.8: Typical steering model
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 5
Sensitivity Analysis
5.L Problem description
An analysis was performed using a simplif,ed planar ascent simulation environment, to deter- mine which parameters dominate the shaping of trajectories and what accuracies are required for both the integration technique and model parameterisation. Nominal vehicle and environ- mental models were used to determine the steering parameters required to produce an optimal trajectory. These vehicle and environmental models were then varied to determine their influ- ence on an open loop trajectory.
The nominal environment and vehicle models were used to produce optimised steering param- eters to deliver a payload to a low Earth transfer orbit (LTO) with an altitude of 200km, a flight path angle of 0' and a velocity of 9162.4m/s. The reason this transfer orbit was chosen, in- stead of a 94x466kmorbit, is that flight data was available for the given conditions (Lenorovitz,
7984), thereby allowing confirmation of the simulation results.
100 5.2. Nominal models 101
5.2 Nominal models
The vehicle model used in this study was that of an Ariane III expendable launch vehicle. The
vehicle consists of three core stages in series and two strap on solid boosters, which operate
during the first stage burn. The four first stage liquid rocket engines have a specific impulse
of 247.26s atsealeveland2ll.lsinavacuum,withapropellantmassflowrate of 275.8kgls
each. The two strap on boosters produce 296.8s of specific impulse and have a propellant mass
flow rate of 228.7kgf s each. The second stage consists of one engine with a vacuum specific
impulse of 293 .5s and a propellant mass flow rate of 27 5 .3kg I s. The third stage rocket engine
has a specific impulse of 444.5s in a vacuum and a propellant mass flow rate of l4.37kg/s.
The gross lifroff weight (GLOW) is239852k9.
A Standard atmosphere was used to produce a nominal atmospheric density profile and wind
effects were neglected. The Earth was modelled as a sphere of radius 6378.76km with a New-
tonian approximation of its gravitational field.
5.3 Results
Most of the results will be presented in the form of an altitude vs. time graph only. Although altitude is not the only state affected by modelling errors, it is one that is commonly used to illustrate such errors. Altitude is also a parameter with which most readers are familiar, and therefore will be able to appreciate the scale of the effors discussed.
5.3.L IntegrationVerification
A time increment of integration implies a resolution or degree of accuracy for the integration process. The upper bound for the integration step size is determined by the time step size at which the assumption of linear behaviour between two integration steps is violated. That is
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Resulfs 102
to say that if the integration step size is too large, then the behaviour of the dynamic model is
not linear between consecutive integration steps, leading to an inaccurate solution. The lower
bound is determined by the resolution of the computer. If the step size is too small then the
differences between consecutive integration steps cannot be accurately determined as it is close
to the working accuracy of a computer (i.e. a32bit word). Within these bounds it is generally
the case that the smaller the time increment, the higher the resolution and therefore the more
accurate the solution. The problem is that the smaller the time increment the more computation
time required. It was therefore considered important to determine the resolution required to
obtain a sufficiently accurate solution with as short a computational time as possible. For
this reason a comparison was performed using different simulation runs with different fixed
integration step sizes. The reason a fixed integration step size was used, was to simplify the
analysis. It should be noted that the data sets under examination were all from simulation runs
and no actual flight data was used in this comparison. The ls time increment was the most
accurate solution compared to the flight data, and so this was used as a reference for the other
data sets.
300
250
200 F tr J¿ €rso lsec - 2 sec 5 sec 100 I0 sec
50
200 400 600 800 1 000 Time [s]
Figure 5.1: Altitude vs Time for integration step comparison
Figure 5.1 shows a negligible difference between the altitude profiles of the data sets with
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Results 103
integration step sizes below 5s. The data set using a 10s step size is shown to prodtce a 2Vo
difference in maximum altitude compared to the ls step size data. This indicates that the
integration step size should be kept below 5s for sufficient accuracy of altitude data.
lsec - 2 sec 30 - - 5sec ---- 10 sec ão -\1 (.) lr ß20 H O d alo
20 40 60 80 100 120 140 160 Time [s]
Figure 5.2: Dynamic Pressure vs Time for integration step comparison
Figure 5.2 also suggests that integration step sizes below 5s produce accurate dynamic pres- sure simulations. The 10s step size is clearly not adequate for dynamic pressure data as there is not sufficient resolution to accurately represent the peak in the graph. The error in maxi- mum dynamic pressure, from Figure 5.2, is in excess of I27o.It should be noted that, although there are more accurate integration techniques available (Teukolsky et al., 1990), Runge-Kutta integration techniques are widely used in the literature. For this reason, this technique was deemed satisfactory for the present study, provided an integration step size of 5s and below is used. For comparison, Rao et al. (1997) used an integration step of 0.04s for the optimisation of Titan launch vehicle trajectories. This small integration step size would only be required if particularly high precision was necessary, such as when determining propellant slosh or bend- ing modes. For the purpose of trajectory propagation, ls is sufficiently accurate (Schoettle,
2002).
Commercial launch vehicle design and predictive guidance development Matthew R. TetIow 5.3. Results 104
5.3.2 Modelling error sensitivity
An investigation was performed to determine the effect of modelling errors on open loop tra-
jectories. The optimised steering parameters were fixed, while system or environmental pa-
rameters were varied, to determine their effect on the open loop trajectory. The investigation
was broken into two groups, the first being parameters that can be measured directly or can be
designed to be a certain value, for example, vehicle masses, engine specific impulse and mass
flow rate of fuel. The second group was parameters that cannot be accurately estimated, such
as atmospheric density.
600
Nominal 500 -''' 57o increase '-'- 27o increase ---' l%o increase - - IVo decrease ã400 J¿
€soo5
200
100
200 400 600 800 1 000 Time [s]
Figure 5.3: Sensitivity to specific impulse of first stage engine at sea level
The first parameter varied was that of specific impulse 1ro, which was varied by Ll%o, *2Vo and -l5Vo of the actual value. As seen from Figures 5.3 and 5.4, the lro of the first stage engines needs to be measured with high accuracy. An error of only l7o of its actual value produced a final altitude error of 70km or 357o of the required value. As seen from references such as Isakowitz (1995), it is possible to measure lro to an accuracy of 0.ls (0.03%o of value).
This fact indicates that although only a small error in lro estimation can be tolerated, it can be readily measured to sufficient accuracy.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Resulrs 105
500
Nominal - 5Vo ircrease 400 ---'2Vo increase lvo increase --- l7o decrease $oo (,) ! E 200
100
200 400 600 800 1 000 Time [s]
Figure 5.4: Sensitivity to specifrc impulse of first stage engine in vacuum
350
Nominal 300 - 27o increase ---' LVo increase ' 2Vo decrease 250 '-"- I7odecrease â E¿oo
ËÉ E 150
100
50
200 400 600 800 1 000 Time [s]
Figure 5.5: Sensitivity to specifrc impulse of second stage engine in vacuum
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Resulfs 106
Figure 5.5 shows how a variation in vacuum lro, for the second stage engine, affected the
altitude. This parameter is also seen to require an estimation accuracy of well within I7o,
however, its effect is less pronounced than the values for stage L. A IVo estimation effor was
found to produce a final altitude error of 25km or I2.57o of the required value. This was an
expected result, as stage I 1"o estimation errors would have longer to propagate and so \ryere
expected to have a greater effect on the trajectory.
1 000
900 Nominal - 5Vo increase 800 ---' 27o increase l%o increase 700 - - I7o decrease
Euoo €soo E {+oo 300
200
100
200 400 600 800 1 000 Time [s]
Figure 5.6: Sensitivity to mass flow rute of the frrst stage engine
The next parameter varied was that of mass propellant flow rate, ri4,through the main engines.
Figure 5.6 shows the altitude profiles for errors in the modelled rfu of the first stage engine.
This could occur if there was a malfunction in the throttling mechanism in the engine. The value of propellant flow rate was varied by tl%o, 2Vo and SVo. A -I7o error in modelled rn 1 would result in the vehicle crashing into the ground, while a tITo error would result in a
-f I50km altitude error.
Figure 5.7 shows sensitivity to mass flow rate, rit2, through the second stage engine. A 2Vo decrease in estimated fuz is seen to produce only a I\km enor in final altitude, as opposed to the L5Okm error produced by an error in rfu. The trajectory was thus considerably more sensitive to errors in estimated propellant mass flow rate in the first stage than in the second.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Results 107
350
300
250
Eeoo €(.) c Nominal 150 - 27o increase ---' l7o increase IVo deqease 100 -'- 2Vo decrease
50
0 0 200 400 600 800 1 000 Time [s]
Figure 5.7: Sensitivity to mass flow rate of the second stage engine
A reason for this may be that there was a nominal propellant mass flow rate of over I L00kgls
during the first stage burn and only 275kgls during the second stage burn, causing the total propellant mass effor to be larger for the first than for the second stage.
300
250
ã200 l¿ €l so = Nominal ----- 50kg decrease 100 - - 50kg increase . f00kg increase --- 100kg decrease 50
200 400 600 800 1 000 Time [s]
Figure 5.8: Sensitivity to gross lift otr weight
Vehicle masses are crucial parameters when designing a launch vehicle. The Ariane III launch vehicle weighs almost 24Ùtonnes, yet Figure 5.8 show that a mere 100frg (or 0.04L7o) error in
Commercial launch vehicle design and gedictive guidance development Matthew R. Tetlow 5.3. Results 108
GLOW would cause a 57o enor in target altitude.
700
T1= 10s (Nominal) 600 - T1 = lls ---' Tl = 9s 500 7 å¿oo q) E '8300E
200
100
200 400 600 800 1 000 Time [s]
Figure 5.9: Sensitivity to initiation time of frrst roll manoeuvre
700
T2 = 20s (Nominal) 600 ---'T2=2ls- -- T2= l9s 500
å¿oo (J EÉ 'E300
200
100
200 400 600 800 1 000 Time [s]
Figure 5.10: Sensitivity to frnal time of frrst roll manoeuvre
Control parameters are also a source of trajectory effors. The first parameter considered was that of initiation time of the initial pitch-over manoeuvre, as shown in Figure 4.1. From Figure
5.9, it can be seen that if the pitch manoeuvre was initiated ls early, the launch vehicle would crash into the ground. This suggests that pitch manoeuvres need to be executed with high
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Results 109
accuracy. Figure 5.10 shows the sensitivity to the execution time of the end of the pitch-over
manoeuvre. Again a 1s error would result in impact with the ground. This suggests that care
should be taken to ensure the control system executes any turns with high accuracy.
300
250
200 E J¿ o ! 150 ) Nominal -- - 2Vo increase --- 5Voincrease 100 lÙVo increase - - 2Vo decrease - -- 5Vo decrease 50
0 0 200 400 600 800 1 000 Time [s]
Figure 5.11: Sensitivity to aerodynamic lift and drag coeffrcients
Aerodynamic models can either be obtained experimentally or through computational mod- elling methods, both of which are susceptible to errors. This may cause an inaccurate predic- tion of the lift and drag forces on the body. Figure 5.11 shows that the aerodynamic properties can be varied significantly before the trajectory effor becomes large, indicating that a precise aerodynamic model is not essential for trajectory prediction. This can be explained by the fact that, as is the case with most launch vehicles, Ariane III flew a steep ballistic ascent trajectory.
Firstly, a steep ascent trajectory causes the vehicle to spend only a short time in the dense atmosphere. Most of the flight time is therefore in the low density upper atmosphere where atmospheric forces are low, and so have little influence on the trajectory. The second point is that being a ballistic vehicle, lift is negligibly small, so the only relevant aerodynamic model is the drag model. This causes aerodynamic lift model variations to have very little effect on the trajectory.
The parameters discussed so far were related to the physical properties of the launch vehi-
Commercial launch vehicle design and gedictive guidance development Matthew R. Tetlow 5.3. Results 110
cle, and can be controlled by careful design and manufacture. The next section deals with
parameters that the designer cannot control, such as atmospheric conditions. An atmospheric
parameter typically used for sensitivity analyses is atmospheric density.
Figure 5.12 shows the open loop trajectory errors that would occur if the atmospheric density
had a modelling error of up to 57o over the entire flight. Even a 2Vo er::or in the estimated
atmospheric density is seen to produce anlSkmerror in the open loop trajectory's final altitude.
Applying a step increase in atmospheric density of 607o over the nominal value, between
altitudes of 40km and 60km, is shown in Figure 5.13, to produce only a I7o enor in the open
loop trajectory. This result was expected as the atmospheric density is typically very low
at altitudes above 40km (see Appendix B). This low density would cause low aerodynamic
forces on the vehicle, thereby not influencing the trajectory to a large extent. If Ariane III
were to experience a step increase in density at lower altitudes, the results would be different.
Figure 5.14 shows that a 407o increase in atmospheric density, between altitudes of I5km and
40km, would cause a 2Ùkm error in final altitude. This investigation seems to indicate that
atmospheric density variations in the lower altitudes (below 40km) influence the trajectory
more than variations at higher altitudes.
300
250
,100 É ,y () ! É 150 Nominal '- 57o increase ---'2Vo increase 100 - - 2Vo decrease - - 5Vo decrease
50
200 400 600 800 1 000 Time [s]
Figure 5.12: Sensitivity to constant atmospheric variation at aII altitudes
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.3. Results 111
300
250
-200 J¿ q E á 150 Nominal - lÙVo increase ---' 40Vo increase 100 - - 607o increase
50
200 400 600 800 1 000 Time [s]
Figure 5.13: Sensitivity to an atmospheric density increase between 40km atd 60km
300
250
200
J o E 150 Nominal - ' lo%oincrease ? ---' 407o increase 100 - - I0Vo decrease - - 40Vo decrease
50
0 0 200 400 600 800 1 000
Time [s]
Figure 5.14: Sensitivity to an atmospheric density inqease between l5km and 40km
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 5.4" Sensitivity conclusion 112
5.4 Sensitivity conclusion
The sensitivity analysis indicated that the parameters that cause the largest deviation are those
which influence the vehicle in its early stages of flight. This may be because the errors have
a longer time in which to propagate and therefore, these parameters require higher modelling
accuracy.
The specific impulse and GLOV/ were seen to produce open loop trajectory errors in the re-
gion of 57o. Although this is an appreciable error, careful design of the vehicle would reduce
errors in these two parameters, thereby reducing their contribution to trajectory enor. propel-
lant mass flow rate needs to be estimated or measured to well within IVo ofits required value
during flight, as it affects both the thrustprofile and mass history of the flight. High altitude at- mospheric density variations were seen to produce negligible trajectory etrors, however, lower altitude variations of around 5vo caused trajectory errors of up to 2ovo.
Atmospheric density can only be modelled to an accuracy of l57o (Marcos et al., 1994), how- ever, a 20Vo enor in injection altitude can result from a 5Vo vanation in atmospheric density.
This indicates that some sort of closed loop guidance system is desirable for a payload delivery system. Further, using traditional trajectory control methods, such as that used on the Space
Shuttle, small differences between actual and modelled environmental parameters can cause significant trajectory variations. This may imply that even if predetermined trajectories are accurately followed, they may be sub-optimal, due to differences between the models used for pre-flight analysis and the actual flight environment.
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 6
Launch Vehicle Design fnvestigation
As was discussed in Section 1.1, new launch vehicles need to be developed that will sig- nificantly reduce launch costs while at the same time improving reliability and operational flexibility. For the investigation of future launch system designs, two fixed gross lift offweight
(GLOW), reusable launch vehicles were analysed, on a basis of payload capability, using dif- ferent flyback strategies for the booster stage. The first concept used air-breathing engines for a powered return flight to the launch site, while the second employed an unpowered aerody- namic glide to return to the launch site.
RTSOPT was used to optimise the trajectory for both vehicle concepts at three different staging conditions. By examining the payload capabilities at each staging condition it was possible to determine the near optimal staging conditions for each concept vehicle. The nea¡ optimal payload capabilities were then compared to determine which concept vehicle could deliver the heavier payload to orbit.
113 6.1. Design choices 114
6.1 Design choices
There are a number of suitable subsystems such as wings, different propulsion systems, dif-
ferent recovery systems etc. which can be used on a concept vehicle. The vehicle designer
needs to consider the advantages and disadvantages of each subsystem to produce a launch
vehicle that meets the design requirements. These decisions are based on performance as well
as reliability, safety and operational constraints, to mention a few.
The shape and configuration of the vehicle are influenced by a number of factors, including
level of reusability, mission profile, propulsion system, etc. The first choice to make is to
decide on the number of stages. In Section 2.3, the topic of Single Stage to Orbit (SSTO)
was discussed; although the literature indicates that SSTO is possible with today's technology, there are no operational SSTO vehicles. If the technology has not been extensively tested, then it is not well suited to a commercial launch company, as there are often unforeseen problems that only become apparent once the project starts (Gregory, 1989). For this reason, the more common approach of Two Stage to orbit (TSTO) was chosen for this study.
In order to minimise the time between flights, both stages were required to return to and land at the launch site for processing before the next launch. This would eliminate the costs and operational constraints imposed by a vehicle landing down range from the launch site. A recent example of both stages retuming to the launch site is the Kistler Kl launch vehicle, where both stages land close to the launch site (Mueller et al., 1998). This simplifies the operations by not having to transport the stages over long distances. However, in the case of the Kistler vehicle a recovery is still needed to retrieve the stages and bring them back to the launch facility for processing. To further minimise the time between flights, the present study will investi gate a horizontal landing at the launch site. This requirement implies the requirement for wings on both the booster and the orbiter. A winged orbiter would also provide greater flexibility for the re-entry mission as opposed to a ballistic re-entry vehicle. The orbiter would be able to return to the launch site from a number of different entry points, thereby avoiding the case
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.2. Mission analysis 115
of the orbiter having to do a number of orbits around the Earth to achieve the correct entry conditions
6.2 Mission analysis
The results of a study conducted by the FAA (Middleton, 1999) show that the Geosynchronous
Earth Orbit (GEO) satellite market is expected to have a shift towards heavier satellites. The number of satellites over 5443kg requiring launch is expected to grow over the next 10 years.
An example of one of these large satellites is the 20:20 model from Space Systems/Loral which will have a launch mass of 6500kg. The vehicle payload capability for this study was chosen to be able to address the expected future satellite market. The concept vehicle was thus required to deliver approxim ately 7OOÙkg of payload to a Geosynchronous Transfer Orbit
(GTO). This would allow the delivery of either one heavy (Stonnes) satellite or two medium sized (> 2000kÐ satellites to GTO. The large Low Earth Orbit (LEO) capability of such a vehicle would also enable it to service the International Space Station (ISS), at its maximum altitude of 466km (Messerschmid et a1.,1997).
A mission to GTO usually requires a kick motor, on the payload, to propel it from from LEO to
GTO. The reason this is done, instead of having the orbiter take the payload directly into GTO, is that a considerable payload loss would occur due to the extra fuel required to accelerate the whole orbiter to GTO velocity. The orbiter in this study was thus designed to fly to a 466km circular orbit. This orbit would allow either delivery of the payload to the ISS or provide a stable orbit from which to launch into GTO.
When launching from Earth into LEO, it is common to launch into an elliptical Low Earth
Transfer Orbit (LTO) and then to employ a second burn, after a coast phase, to achieve the required circular orbit. According to Schoettle (2002), it is advantageous to have a low perigee
LTO, in order to minimise Âv losses, however, the lower the perigee, the less stable the orbit. If
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 6.2. Mission analysis 116
the orbiter's propulsion system did not ignite when required to circularise the orbit, the orbiter
and payload may have to complete an orbit of the Earth before another attempt could be made.
At a higher perigee LTO, this would not present a problem, as a further orbit of the Earth
could be completed in the vacuum of space. If, however, a low perigee LTO was used, the
vehicle would have to pass through the upper atmosphere again, thereby possibly damaging
the exposed payload and even lowering the orbit in the case of multiple passes. A trade off
therefore has to be made between minimising the Âv losses and using a stable LTO. This orbit
insertion method is employed by the Space Shuttle, which shuts down its main engines at
LTO, with an altitude of 177 .5km and a velocity of 7823m/s (Isakowitz, 1995). Two Orbital
Manoeuvring System (OMS) burns are then used to attain the correct circular orbit. In the
conceptual study conducted by Edge and Powers (1976) a 90x780km LTO was used. The
same 90x180kmIJ|O was used by Freeman et al. (1995) for a conceptual design of a manned launch vehicle.
The reference orbit chosen was thus a466km circular orbit inclined at an angle of 31.5", after launching from Woomera in South Australia. The ascent trajectory was optimised for perigee insertion into a 94x466km transfer orbit, with an allowance made for the fuel required to circularise to a 466km circular orbit. The payload capability for GTO was based on a
466x35862km altitude elliptical orbit. In this case the payload for the 466kmcircular orbir was the initial mass of the GEO payload, with its own kickstage and enough fuel to change form the circular LEO to GTO.
ThefuelandstructureweightforthekickstagewascalculatedusingEquations 4.5and4.6.The velocity change required was calculated from the difference between the velocity for a 466km circular orbit and that for a 466x35862km GTO (Brown, 1998). The velocity change used was
2379.136m1s. The propellant mass fraction for the kickstage was taken from the Japanese H2 launch systems to be 0.85 (Isakowitz, 1995). The I* value for the propulsion system was taken from the Ariane 5 launch vehicle to be 324s (Isakowitz, 1995). It was also assumed that the payload would perform the inclination change from a 37.5o GTO to a 0' GEO. The mass and
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.3. Reference mission 117
propulsion system assumptions with regard to the kickstage are not intended to represent a real
system, but simply to obtain an estimate of the kickstage mass required for such a mission.
6.3 Reference mission
The trajectory was optimised to deliver the payload to a94x466kmlJ1O, at perigee. The ve-
hicle was conceived to perform a vertical lift-off with the two stages operating in parallel as
shown in Figure 6.1. After staging, the orbiter would fly to orbit while the booster executed
a retum to launch site flight. The powered flyback concept assumed an aerodynamic turning
glide flight until reaching sub-sonic cruise conditions. The remainder of the return flight (not
shown in Figure 6.1) was then performed at cruise conditions powered by air-breathing en-
gines. Cruise conditions were taken to be a velocity 270mf s, a flight path angle of 0" and an
altitude of 72.5km. The glide back concept booster employed only aerodynamic gliding forces
to achieve both the tum manoeuvre and the flyback mission. In both cases considered in this
study, the vehicle was assumed to reach approach for landing at a velocity of l20mf s. This was considered a good approach speed in order to achieve a landing speed of around 95mf s, which is similar to the 92mf s used by the Space Shuttle (Isakowitz, 1995). Final approach and landing was not considered in the simulation.
6.4 Design concept
The unmanned concept vehicles in this study had a gross lift off weight of l4\\tonn¿s. This value was chosen to enable the delivery of approximately 2\tonnes of payload to LEO, thereby allowing these vehicles to address the GEO market requirements discussed in Section 1.1.
The vehicles consisted of two winged stages that operated in parallel during launch and initial ascent (Figure 6.2). A cross-feed fuel system was employed to allow the orbiter to use pro- pellants stored in the booster, during mated flight. This enabled the orbiter mass to be kept
Commercial Iaunch vehicle design and predictive guidance development Matthew R. Tetlow 6.4. Design concept 118
orb¡ter 100
Staging 80
=60E Mated ! ascent Þ(¡) Ë40f
0 -31.s at -31 Boostèr. -30.5 Jlyback -30 i4B 150 i44 146 -29 5 142 140 -29 1g6 138 Latitude ldeg] (South) Longitude [deg]
Figure 6.1: Mission profrIe
Booster
Orbiter
Figure 6.2: Concept vehicle (Tetlow et aI., 2001)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.4. Design concept 119
to a minimum, which was found in the FESTIP study (FESTIP, 1993) to be optimum for a
two stage vehicle. The mated vehicle employed 11 liquid oxygen (LOXy kerosene rocket en-
gines for the ascent flight, providing a thrust to weight ratio of approximately 1.2 (Schoettle,
2002) at lifçoff. The number of rocket engines on each stage depended upon the stage sizes,
which were different for each of the six optimised vehicles. Clearly, the larger the orbiter, the
more engines required to propel it during the upper stage flight. While l1 rocket engines may
seem excessive and may pose reliability issues, it should be noted that one of the most reliable
launch vehicles, Soyuz, employs 20 engines at launch (Isakowitz, 1995). The powered return
vehicle concept employed two or three kerosene air-breathing engines for fly back, depending
on the size of the booster stage. The orbiter had the capability to land with its full launch pay- load, thereby enabling it to return a payload from orbit and also to avoid the payload having to be dumped in the event of an aborted launch.
6.4.1 Propulsion
As discussed in SectionZ.2, there are a number of different propulsion systems, each with ad- vantages and disadvantages. Although solid rocket propulsion systems are generally cheaper and less complicated than liquid fuelled systems, the fact that they cannot be shut down after ignition makes them "high risk". They also have a lower specific impulse than liquid pro- pellant systems (Isakowitz, 1995). They were therefore not considered for this design. The decision thus lay with what type of liquid propellants to use. Hypergolic propellants were also considered to be "dangerous", because of their explosive nature when mixed. This would lead to handling difficulties and a dangerous working environment for the launch personnel.
High energy cryogenic fuels such as liquid hydrogen produce the highest specific impulse
(up to 455.2s (Isakowitz, 1995)) and, although their fuel tanks add complexity to a design by requiring insulation and/or refrigeration, they are a popular propulsion system. This can be seen in examples such as the Space Shuttle, H2, Ariane 5 and Atlas II. Kerosene propul-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.4. Design concept 120
sion systems are also seen in many examples such as Delta 7925, Soyuz and the Kistler Kl.
Kerosene-fuelled engines generally have slightly lower performance (up to 33ls (Chakroborty
et a1., 1998)) than the high energy fuels, but the fact that the fuel is much easier to store makes
them an attractive option. Kerosene is about 11 times as dense as liquid Hydrogen, making
kerosene tanks smaller and lighter for the same volume of fuel. This makes kerosene fuelled
rockets more compact than liquid Hydrogen fuelled ones. It was therefore decided to use
kerosene and liquid Oxygen (LOX) as propellants for this study.
The propulsion systems chosen for this study included both rocket and air-breathing systems,
depending on the configuration being considered and the flight regime. The liquid rocket
engines used for the ascent were the Aerojet AJ26 series engines. These engines are modified
Russian NK33 and NK43 engines, as used on the Russian lunar program (Chakroborty et al.,
1998). The modifications made by Aerojet include updated electronics, igniters, electronic controller, actuated control valves and 6o gimballing.
The rocket engines used on the booster stages were the Aerojet AJ26-59 engines, which have an lro value of 331.3s in vacuum and 297 .2s at sea level. They produce l.68MN of thrust in vacuum and 7.57MN at sea level (Chakroborty et al.,l99S). These engines are suited to low altitude flight as they have an expansion ratio of 27. The Orbiter was equipped with AJ26-
60 engines, which have an 1"o value of 345.3s in vacuum and produce 1.75MN of thrust in vacuum. These engines are suited to high altitude flight as they have an expansion ratio of 80.
Previous concept vehicles such as Sänger (Rahn et al., 1999) used their air-breathing propul- sion system during ascent and descent-turn flights as well as cruise flight, thereby suggesting that an engine operating in the higher Mach number range of the flyback phase was optimal.
It was, however, discovered that the propulsion system should be throttled to produce only a fraction of its possible thrust during the supersonic descent phase (Rahn et al., lggg). Further,
Sänger used the air-breathing engines for ascent and so already had high speed engines for use during descent. From the results of this study, it was decided that high speed air-breathing engines were not required, therefore lighter sub-sonic air-breathing engines were employed
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.4. Design concept 121
during cruise conditions
The air-breathing propulsion system used for flyback was the M88-35 turbo jet engine. With-
out afterburners, this engine can produce 60frN of thrust with a fuel consumption of 80kg /kN .h.
The air-breathing engines were not used at all during the launch phase due to operational con-
straints. From an optimisation point of view, using the air-breathing engines during ascent would increase the payload capability, as it would increase the launch thrust. However, the
added complexity of advanced intake nozzles would make it an unrealistic proposal. For this reason, the air-breathing engines were only activated during sub-sonic cruise conditions in the flyback phase.
6.4.2 Aerodynamics
The aerodynamic data used for the present model was taken from an aerodynamic model devel- oped at the Space Systems Institute in Stuttgart (Rahn etal.,1999) and then scaled to represent the aerodynamics of the FSSC-I (FESTIP, 1998) concept vehicle in the hypersonic region.
This scaling resulted in a somewhat optimistic maximum lift to drag ratio of seven at a Mach number of 0.9.
6.4.3 Component masses
Vehicle component masses were estimated using the statistical mass modelling technique dis- cussed in Section 3.1.3. The following component masses were calculated using this mass modelling technique: wings, horizontal stabiliser, vertical stabiliser, fuselage, thrust frame, oxidiser tanks and feed systems, fuel tanks and feed system, TPS, landing gear, ACS system,
OMS system, avionics, separation system and power supply.
The masses of the rocket and turbojet engines were not calculated using statistical data as they were known. A mass of 750kg (FESTIP, 1998) was used for each M88-35 turbo jet, the mass
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.5. Staging condition ¡esu.lús 122
of each Aerojet AJ26-59 engine was taken tobe l459kg, while a mass of 1505ftg (Chakroborty
et al., 1998) was used for each Aerojet AJ26-60 engine. Vehicle sizing was calculated from
the amount of propellant required to be stored in the vehicle's tanks, including a 47o propellant
reserve, as used in Rahn (1998). In addition an 87o mass margin was included to allow for
modelling inaccuracies.
Assumptions had to be made regarding the mass of the non-structural kerosene tanks, due to the lack of available data. The tanks were assumed to have the same mass fraction as that of the oxygen tanks. Due to the fact that kerosene can be stored at lower pressures than oxygen, and that kerosene tanks can be manufactured from composite materials (NASA, 2002), this assumption was considered to be conservative but satisfactory. The vehicle form and layout was based on the FESTIP FSSC 16 concept vehicle (FESTIP, 199S).
6.5 Staging condition results
The staging conditions play a signif,cant role in the determination of an optimal trajectory for a given mission. Hence, it is important to perform staging at optimal conditions to maximise the payload. A number of optimisation runs were therefore performed on an orbiter stage using different staging flight path angles, velocities and altitudes. This was done to determine an initial estimate of the optimum staging conditions for the concept vehicle. A fixed start mass of 450tonn¿s was used with a thrust to weight ratio of 7.2.
Figure 6.3 shows that the ejected mass fraction increases with an increase in staging veloc- ity and altitude, where the ejected mass fraction is the vehicle mass at main-engine-cut-off
(MECO) divided by the initial mass (450r onnes). The staging velocity was shown to influence the ejected mass fraction more than the staging altitude. A 76.6Vo increase in staging velocity caused a 7.5Vo increase in ejected mass fraction, while an 78.8Vo increase in staging altitude only increased the ejected mass fraction by 0.257o. The staging flight path angle is shown to
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback resulfs 123
19 v=2000 m/s Þ75km E--Ð 65km
1 x--X 55km èa oÉ
(no q! v=1750 m/s Ø Ø 1 7 (n
(.) o o i¡ 1 6 v=
15 10 20 30 Staging flight path angle [deg]
Figure 6.3: Staging condition comparison have an optimal value of around 20o, with a shift to lower flight path angles with an increase
in staging velocity and altitude. It should be noted that this result is for staging velocities of between 7500mls and2000m/s. The results can be extended to include those in Schoettle
(1989), who used staging velocities between 2ÙOOmls and 35OOm/s. In Schoettle (1989) the optimal flight path angle is between 7.5" and 20o for staging velocities between 2000mf s and
3500m1s.
The main result from the current study and that in Schoettle (1989) is that there is a slight shift towards lower flight path angles for an increase in staging velocity and staging altitude.
6.6 Powered booster flyback results
The first concept considered was a two stage, winged vehicle in a parallel configuration em- ploying a powered booster return flight. The booster flyback was achieved using air-breathing propulsion, which allowed staging to occur far down range, thereby allowing high staging velocities. The trajectories for three different staging conditions were optimised and then
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback resulfs 124 compared to determine the design point for the configuration. The results from the optimi-
sations, shown in Table 6.1, indicate that the optimum staging condition for a vehicle of this conf,guration is at a velocity of approximately 3000mf s.
Mission using powered booster flyback Staging velocity 3o00mls 3500mls Staging flight path angle 150 loo 8o Staging altitude 59.8km 62.\km 1Ùkm Booster mass at launch lÙ64tonnes 7723tonnes 7782tonnes Booster mass at MECO S5tonnes S4tonnes S9tonnes Orbiter mass at launch 336tonnes 2'7'Ttonnes 2lStonnes Orbiter mass at MECO T0tonnes 6Stonnes 63tonnes Flyback distance 682km 847km lO64km Maximum load factor 3'5go 3'6go 3'6go No. of air-breathing engines 2 2 3 Payload to ISS 77943kg 27693kg 20822kg Payload to GTO 5793ks 7oo5kg 6723kg Table 6.1: Powered booster vehicle comparison
Previously it was shown that the higher the staging velocity, the higher the injected mass frac- tion, however, the higher the staging velocity, the higher the first stage mass, due to the need for larger propellant tanks. This higher mass would require a larger volume of propellant for the flyback manoeuvre. At cruise conditions, thrust - drag and lift : weight, therefore thrust to weight ratio equals lift to drag ratio. This implies that as the weight increases, the thrust must also increase to keep the vehicle at cruise conditions. Therefore, another factor con- tributing to the vehicle becoming heavier for higher staging velocities, is the greater number of air-breathing engines required to overcome aerodynamic drag during the retum flight. For the vehicle staging at 3OOÙmf s, only two engines were required for flyback, while the higher staging velocity o13500mls required three air-breathing engines.
The optimal staging velocity obtained in the present study was similar to the value of 3200mf s obtained by Rahn et aI. (7999) for the optimal staging velocity of the Ariane-X concept ve- hicle. The Ariane-X vehicle displayed a relatively small range of payload variation around the optimum staging velocity value. Table 6.1 also shows a relatively small difference be-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback ¡esu.lrs 125
tween the payload for a 3000m/s staging velocity and that for a 3500mf s staging velocity.
This may indicate that the payload is not highly sensitive to staging velocity in the region of
the optimum value. Therefore in this region, the design of a commercial launch vehicle may
be dominated by factors other than the payload capability. For example, it may be beneficial
from a cost point of view to have a slightly smaller payload capability but be able to use fewer
air-breathing engines.
The mass model in the present study used the landing mass of the vehicle to calculate the
required mass of the wings (see Figure 3.1). It considered a maximum load factor of 3.75gs
for a pull-up manoeuvre before landing. This value was chosen as it was between 3.5gs used
in Rahn et aI. (1999) and 4.2gs used by the Space Shuttle (Isakowitz, 1995). An investigation
was performed using the 3000m/s staging velocity, to determine if it would be beneficial
from a payload point of view to perform a tighter turn during the flyback and thereby have a
shorter flyback distance. The problem with performing a tighter turn is that this would increase
the wing loading and therefore require stronger, heavier wings. Essentially, the investigation
aimed to determine if the added wing mass, required to withstand a higher load turn during
flyback, would outweigh the increased payload.
The mission was first optimised to allow a 3.6gs turn during flight, yielding a payload of
21693kg (as shown in Table 6.1). A comparison mission was then optimised to allow a4.6gs turn, yielding a payload of 27827kg. Hence, the difference in payload was l34kg. The dif- ference in mass between a wing designed to withstand a3.75gs load during landing and one designed to withstand a 4.6gs turn during the return flight was calculated to be 62lkg. It is thus not optimal for this vehicle to perform high load turns during flyback, as the extra wing mass required to allow the higher loading would outweigh the payload advantage from such a turn. A further reason for not employing stronger wings is the fact that development cost is related to dry mass (Schoettle,2002). That is to say that, as well has having a lower payload capability, the heavy wing vehicle would also be more expensive to develop.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback resulfs 126
6.6.1 Design choice for powered flyback concept
The design point for this vehicle concept was a staging velocity of 3000m1s, flight path an-
gle of l0o and altitude of 62.8km. The vehicle consisted of a 1723tonne booster employing
nine AJ26-59 rocket engines and a 277tonne orbiter having two AJ26-60 rocket engines. The
vehicle operated in parallel during Phase 1, employing a cross-feed fuel system to enable the
orbiter to use propellants stored in the booster. This minimised the structural mass of the or-
biter, thereby reducing the mass that had to be accelerated to the final orbit conditions. A
return to launch site flight of 84lkm was required by the booster, during which it consumed
77Ù6kg of fuel. The booster required two M88-35 turbo-jet, air-breathing engines to overcome
drag during cruise flight.
100
80
É60 J¿ (.) €á ?40 " ' Mated ascent Booster flyback 20 - --- Orbiter ascent
0 0 100 200 300 400 500 600 Time [s] Figure 6.4: Altitude profrle
As Figure 6.4 shows, the vehicle flew in the mated configuration for 186s before separation.
The orbiter then switched to its own propellant tanks and continued the ascent to perigee of a 94x466km orbit. The booster performed an open loop coast phase while in the upper atmosphere with an angle of attack of 4Ooand a bank angle of -60". The reason for this was to perform as much of a turn and braking manoeuvre as possible while in the low den-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback resu,lfs 127
sity atmospheric region. After approximately 330s, the optimisation was activated and the
booster performed a controlled braking and turning manoeuvre to change its heading towards
the launch site and to achieve cruise conditions. Once cruise conditions had been reached, the
air-breathing engines were started, which propelled the booster back to the launch site (not
shown in Figures).
Figure 6.4 shows that the altitude profile for the booster flyback had 2 "hl4mps" during the
descent phase. Because the booster was flying a steep descent, the density was increasing
faster than the velocity was decreasing. This caused the lift to increase enough to shallow the
flight path angle and even allow a slightly upward flight. The shallow flight and high drag
caused the velocity to decrease again, thereby reducing the lift and allowing the booster to
continue its descent.
8
"' Mated ascent Booster flyback - 6 --- Orbiter ascent
¡¿ >ì 4 O (.)
2
0 0 100 200 300 400 500 600 Time [s]
Figure 6.5: Velocity profrIe
From Figure 6.5 it can be seen that the ascent phases of the mated vehicle and the orbiter had distinct exponential velocity increases. This was caused by the thrust increasing, due to improved engine specif,c impulse, and vehicle mass decreasing, due to propellant consump- tion, as the vehicle ascended. The ascent of the orbiter stage was throttled during the last 30s of flight to avoid exceeding the maximum load factor. This constant acceleration produced a
commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.6. Powered booster flyback ¡esu,lts 128
linear increase in velocity during the final 30s of flight time. Figure 6.5 shows the velocity
of the booster remained relatively constant, around a value of 3}00mls for the first 180s after
separation. This was due to the low atmospheric density during this flight time, producing
low aerodynamic forces on the booster. The velocity then began to decrease as the increas-
ing atmospheric density produced more drag. SmaLl "humps" can be seen during the booster
flyback, which correspond to the altitude "humps" seen in the altitude profile (Figure 6.4).
-29 Termination of Optimization '' Mated ascent Booster flyback - -30 .- - Cruise flight ()ào
Ëc)
rl 31
-32 t36 138 140 t42 144 t46 Longitude [deg]
Figure 6.6: Ground track
Figure 6.6 shows a significant heading change close to the termination of the optimisation. The reason for this is that there was a high lift force at this altitude (t20km), due to the relatively high atmospheric density (see Appendix B). It was also a suitable time to execute a turn as the booster's velocity was relatively low (sub-sonic), resulting in an acceptable load factor of
3.690 during the turn. It can be seen from Figure 6.6 that from staging to approximately l44o longitude, the booster followed the ascent plane instead of executing a turn. Although there was a high bank angle and angle of attack (as will be shown in Figure 6.8), low atmospheric density of the upper atmosphere produced little turning force.
From Figure 6.7 , itcan be seen that the booster climbed to an altitud e of Slkmbefore beginning
commercial launch vehicle design and predictive guidance deveropment Matthew R. Tetlow 6.6. Powered booster flyback resulús 129
100 J l0
80 0
èo 2 C) I Eeo I -l0g v I l¿ èo I o I cd 'o I I b E I <) 't I d {) -20 3 èo .. Velocity tri Altitude 20 - -30 --- Flight path angle
0 0 -40 100 200 300 400 500 600 Time [s]
Figure 6.7: Booster flyback mission (post-staging)
its descent. At this high altitude, the lift force was low, typically around 23kN, thereby making
steering less effective. This was evidenced by a relatively low sensitivity to steering parameters
in this flight regime.
The optimisation was performed with the constraint of achieving a cruise velocity of 270mf s
and a flight path angle of 0o at the termination of the simulation. A final altitude was not specified as an optimisation constraint to allow more freedom of optimisation. Provided the termination was above the specified cruise altitude, the solution was accepted. The booster was assumed to descend slowly at cruise conditions until it reached the required cruise altitude.
This accounted for the difference between the altitude at which the simulation terminated
(20km) and the required cruise altitude (l2.5km).
In Figure 6.8, it can be seen that the bank angle control parameter started at a value of -60' and the angle of attack started at 40". The reason for this was to perform as much of a head- ing change as possible during the early flight phase, thereby avoiding too much down range distance. Initially, an optimisation parameter was used in this early flight region, but it proved problematic to the optimiser due to low optimisation sensitivity of the parameter. It was thus
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7. Unpowered booster flyback ¡esulfs 130
40 0
Angle of attack 30 - Bank angle 20 oòo Ë ()Þo J¿o 6 c) Ëzo -40 90
o J¿ 0) òo ÉCd
0 -60
300 400 500 Time [s]
Figure 6.8: Flyback control parameters decided to use a constant value for the angle of attack and bank angle until the aerodynamic forces became significant enough to allow stable optimisation.
The bank angle is seen to decrease to about -28o as the optimisation parameters became active, before returning to high bank angles (close to -60') for the remainder of the flight. The angle of attack is seen to remain at around 40" until approximately 415s flight time. It then decreased dramatically to minimise the wing loading as the atmospheric density began to increase while the velocity was still relatively hígh (l.25kmls). The peak in the angle of attack at around 500s was required to create sufficient lift for the booster while it was at the maximum bank angle of -60'. This served to produce a large turning force, while at the same time preventing a steep descent.
6.7 Unpowered booster flyback results
The following concept used an aerodynamic glide to achieve the booster return flight. Al- though the booster had a limited flyback range due to the absence of a propulsion system, it had the advantage of being a cheaper and simpler system. As with the powered return concept,
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7. Unpowered booster flyback resulfs 131
the trajectories for three different staging conditions were optimised to determine an approxi-
mate value for the optimal staging conditions. The results for this concept vehicle are shown
ínTable 6.2.
Gliding booster flyback mission Staging velocity 7000mls 7100mls T2OOmls Staging flight path angle 270 270 270 Staging altitude 26.4km 30.6km 34.Okm Booster mass at launch 729tonnes 770tonnes 799tonnes Booster mass at MECO 6Ttonnes 62tonnes 62tonnes Orbiter mass at launch 6Tltonnes 630tonnes 60ltonnes Orbiter mass at MECO 83tonnes Sltonnes SOtonnes Flyback distance 69Skm 8O.9km 92Skm Maximum load factor 2.1go 2.6g0 3'4go No. of air-breathing engines 0 0 0 Payload to ISS 1347lkg 74079kg 14709kg Payload to GTO 4358kg 4546kg 4749kg Table 6.2: Unpowered booster vehicle comparison
The maximum distance that the vehicle could glide during flyback was determined using Equa-
tion4.4. As the booster mass did not change during flyback, the log term was eliminated. This implied a flyback distance based on the aerodynamic properties of the booster, the initial con- ditions and target conditions. As for the powered return flight concept vehicle, the stopping criteriafortheoptimisationwasavelocity of 270mf s andaflightpathangleof 0o. Thisveloc- ity was used as the initial velocity in Equation 4.4. The final velocity was taken tobe l20mf s, which agaínwas the assumed approach velocity.
From Table 6.2, it is clear that the maximum payload was achieved using the highest staging velocity possible. The limitation on the staging velocity was the ability of the vehicle to glide back to the launch site after staging. This maximum velocity from which a return to launch site glide was possible was found to be approximately 7200mf s, corresponding to a
Mach number of 3.9. When comparing this value to the one used in Powell et al. (1991), it was found to be considerably (307o) higher. Powell et al. (1991) chose a staging Mach number of 3.0 to allow a glide return flight to the launch site. This made an allowance for a
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7. Unpowered booster flyback resulús 132
safety factor with respect to the glide distance and was also low enough to limit aerodynamic
heating. Low aerodynamic heating eliminated the requirement for a thermal protection system
on the booster. The present study may have used different aerodynamic properties from Powell
et al. (1991), thereby allowing a greater flyback distance. The present study also included a
thermal protection system on the booster, thereby allowing higher heating loads and possibly
accounting for the higher staging Mach number.
6.7.1 Design choice for unpowered flyback concept
The design point for this concept was a l2oOmf s staging velocity. Again, the vehicle consisted
of a parallel configuration, propellant cross-fed, winged, two stage system, as used in the
powered flyback study. The booster employed six AJ26-59 rocket engines and had a lift off
mass of 769tonnes, while the orbiter had five AJ26-60 engines and a lift off mass of 637tonnes.
100
80 ' Mated ascent Booster flyback - 860 --- Orbiter ascent J¿ o j .E < Z+U
20
0 0 100 2w 300 400 500 Time [s]
Figure 6.9: Altitude profrle
As Figure 6.9 shows, staging occurred at an altitude of 34km. The booster and orbiter then separated and the orbiter continued along its ascent trajectory while the booster began its
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7- Unpowered booster flyback resulfs 133
unpowered return flight to the launch site. The altitude profile shows that the orbiter flew on
its own for almost TOVo of the ascent flight duration, causing the orbiter to be a much larger
vehicle than the orbiter used in the powered flyback concept. Again, a "hump" is evident in
the altitude proflle at around 310s flight time, caused by an increase in lift as the high velocity
booster encountered a dense atmosphere.
8
" " Mated ascent Booster flyback - 6 --- Orbiter ascent
J¿ >ì 4 () o C)
2
0 0 100 200 300 400 500 Time [s]
Figure 6.10: Velocity profrle
From Figure 6.10 it can be seen that the vehicle in the mated configuration produced only a small portion of the total velocity change required for the mission. The remaining velocity change necessary was performed by the orbiter alone. The engines on the orbiter were throttled for the final 95s of flight time to limit the acceleration of the vehicle to 3.5g¡. The velocity profile for the booster shows a deceleration phase straight after staging, followed by a slight acceleration phase caused by the booster beginning its descent flight. After another short high deceleration phase, the velocity levelled out and remained within 5Vo ofthe cruise velocity for the rest of the flyback.
From Figure 6.11 it can be seen that after separation, the booster completed a turn manoeuvre to obtain a heading towards the launch site. It then glided a further Skmbefore the optimisation was terminated at a velocity of 25Ùmf s. At this point, the vehicle was still 92.3km from the
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7. Unpowered booster flyback resulús 134
-30.8
' Mated ascent Booster flyback - -31 -.-. Final glide
obo Termination of ! optimization () -t .2 J
Fl
-31.4
Staging -31.6 136.5 137 137.5 138 138.5 Longitude [deg]
Figure 6.11: Ground track landing site. Using a lift-to-drag ratio of 7.3 from the termination of optimisation, it was
estimated that the booster could cover a flyback distance of l09km, thereby making a92.3km flyback distance achievable. It was assumed that the vehicle glide phase, after termination of the optimisation, was at an angle of attack that would maximise the return flight distance.
During the first 30s after separation, Figure 6.11 shows that a significantheading change oc- curred. This was due to the fact that staging occurred at an altitude with a relatively dense at- mosphere (see Appendix B). This allowed a turn manoeuvre to be executed before the booster coasted into the lower atmospheric density region. In this low density region a straight (ie no turn) flight was observed, as was the case for the powered booster flight.
Unlike the velocity profile for the powered booster concept, Figure 6.12 shows that the booster began decelerating immediately after separation. This was due to the fact that the atmospheric density was relatively high in this region, thereby producing high aerodynamic drag on the vehicle. The aerodynamic drag at the time of staging was approximately 764MN. Figure
6.12 also shows a sharp peak in the flight path angle between 130s and 220s flight time. This corresponds to the "hump" seen in the altitude plot at the same time.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.7. Unpowered booster flyback results 135
50 1.5 30
...... Velocity 20 - Altitude 40 --- Flightpathangle 106 1.0 d) _Ø ! È E c) l¿ J¿ 0ão €¡o >' ¿d 5 o ô -10 8. c) > èo 0.5 5 -20r\ 20
-30
10 0.0 -40 0 100 200 300 Time [s]
Figure 6.12: Booster flyback mission (from staging)
40 0
35 -10 ..-.' Bank angle 30 Angle of Eo - -2oa 9zs () J¿o G' {) Ëzo -30 E cÉ o l¿ *. rs € É -40 Êq 0 -50 5
s0 r00 150 200 250 300 Time [s]
Figure 6.13: Flyback control parameters
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.8. Comparison 136
As with the control model for the powered booster flyback, an initial bank angle of -60o and an angle of attack of 40" was used before the activation of the optimisation process. A small
step in the bank angle at 10s into the flight can be seen in Figure 6.13, which changed the bank
angle to around -50o. This was maintained until 80s flight time, after which the bank angle increased to its maximum value of -58'. The bank angle returned to 0o at 210s flight time.
The angle of attack is seen to have remained at about 40' until50s flight time, after which it
decreased dramatically. Again, this was to minimise the wing loading while the velocity was
still high (75Ùmls) and the atmospheric density was increasing. In the region of 145s, there
was a peak in the angle of attack, before it steadily reduced to a constant value of 4'. This
peak was produced to account for the loss of lift due to the high bank angle, which was at a
value of -58" in this flight region. The angle of attack at the termination of optimisation was
close to the cruise angle of attack of around 7", thereby requiring only a minor attitude change
for the flyback flight.
6.8 Comparison
After the two vehicle concepts had been optimised, they were compared on a performance and
operational basis to determine which vehicle would best suit commercial requirements.
The powered booster flyback concept vehicle was found to be capable of delivering nearly
7000kg (507o) more payload to the ISS orbit than the unpowered booster flyback concept vehicle. A powered booster would also have significantly more operational flexibility and would be able to land at a range of other landing sites in an emergency. This would lead to improved safety for the mission as well as reduced risk of losing the booster in the event of it not being able to land at the launch site. The initial cost of this concept vehicle would be higher than that for the unpowered booster flyback concept, due to the added hardware and complexity of air-breathing engines. The operational costs would also be higher due to
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.8. Comparison 137
servicing and maintaining the air-breathers. It is, however, believed that the higher income
due to the improved payload capability would outweigh the extra component and operational
costs.
The unpowered booster concept is likely to have lower vehicle costs as well as lower opera-
tional costs, due to the absence of air-breathing engines on the booster. There would, however,
be considerable logistical limitations. The full glide potential of the booster would not be
exploitable due to the safety implications. A considerable factor of safety would have to be
applied to the flyback distance in case the booster encountered unexpected weather conditions
or some other external influence. The booster would also be limited by the number of landing
sites it could fly to in the event of the launch site not being available for landing. The most
signif,cant disadvantage of this concept is its inability to exploit high staging velocities, which
support higher payload capabilities. This is due to the limited flyback capability of the booster.
When considering the two concepts discussed above, it was decided to choose the vehicle employing air-breathing propulsion for the return to launch site flight. Although this vehicle would be more complex and have higher operational costs, the payload advantage of 7000kg seems to be significant enough to make it the preferred design concept. For servicing GTO missions, it is recommended that a kick motor on the payload be used. Table 6.3 shows the mass distribution for the powered booster flyback concept vehicle. The booster has a propellant mass fraction of 0.92, which is within the bounds of current technology (Huzel and Huang,
1992). From Table 6.3 it can be seen that the orbiter has heavier wings than the booster even though the booster has a higher dry mass. The reason for this is that the orbiter is designed to land with its full launch payload, thereby making the design landing mass almost the same for the booster and the orbiter. The orbiter, however, has a smaller lift-producing fuselage, and therefore requires larger, heavier wings than the booster.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 6.9. Summary and discussion 138
Description Booster Orbiter Base structure and tanks [tonnes] 24.9 77.2 Aerodynamic surfaces [tonnes] 3.1 6.1 TPS [tonnes] 4.4 6.4 Propulsion system [tonnes] 73.1 5.1 Auxiliary systems [tonnes] 13.s 6.4 Uncertainties [tonnes] 4.8 3.5 Dry mass [tonnes] 65.0 39.3 Aditional propellants [tonnes] 19.0 7.r Propellants consumed at MECO [tonnes] 1039 209 Payload [tonnes] 277 21.6 Table 6.3: Mass breakdown for powered booster flyback concept vehicle
6.9 Summary and discussion
It can be concluded that the optimal staging velocity for a two stage reusable vehicle is approx-
imately 3000mls for a powered booster flyback concept vehicle and approximately l200mls
for an unpowered booster flyback concept vehicle. Further, the staging velocity for an unpow-
ered flyback concept should be as high as possible while still low enough to allow a safe return
glide flight to the launch site.
The investigation also indicated that for a staging velocity of 300om/s, it would not be advan-
tageous to employ stronger and heavier wings to allow a high load turn during flyback. The
added wing weight would outweigh the payload gains obtained by a high load turn. It is thus benef,cial to design the wings for loads encountered during landing flare, and limit the loading during the flyback accordingly.
The optimal design for a reusable launch vehicle was chosen to be a powered booster flyback concept rather than an unpowered one. There would be additional costs and complexity with the powered booster due to the inclusion of air-breathing engines, however, it is believed that these would be compensated for by the significantly improved payload capability. A further suggestion is the use of a kickstage to achieve GTO. This would limit the mass that needed to be accelerated to orbit, thereby increasing the GTO payload capability.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 7
Predictive Guidance for Ascent
7.1. Introduction
From the background research conducted in Section 2.4 it is clear that minor effors in orbit
insertion conditions cause large errors in final orbit. The sensitivity analysis in Section 5
showed that slight variations in vehicle and environment models caused significant variations in trajectory. These two points imply that an open-loop guidance (see Section2.6) strategy is not sufficient to guide a launch vehicle to orbit and some form of closed loop (see Section 2.6) guidance is required.
As was already mentioned by Calise et al. (1998), guided flight outside the atmosphere can be achieved using analytic methods, which have been successfully implemented in a number of launch vehicles, such as the Space Shuttle (McHenry et al., 1979) and Pegasus air-launched space vehicle (Rovner, l99l). Atmospheric flight guidance requires considerably more com- plex analytic methods, which are computationally intensive while still not having the accuracy of numerical methods (Feeley and Speyer, 1994). Numerical guidance methods have been proposed for the re-entry mission of the X-38 and found to be robust enough for real-time application (Wallner et al., 1999).
139 7.2. Problem description 140
The aim of this study was to apply a numerical guidance strategy to an upper stage ascent
mission. This numerical guidance system was developed for real-time application, using the
vehicle design concept developed in Section 6. Again a series of atmospheric variations were
introduced to test the robustness of the guidance system.
7.2 Problem description
The aim of this guidance system was to accurately guide a fully autonomous orbiter from stag-
ing to the required orbit. Because atmospheric flight is affected more heavily by wind and
atmospheric density variations than exo-atmospheric flight, it was considered more challeng-
ing for the guidance system to guide a vehicle during atmospheric flight. For this reason it
was decided to use the vehicle design concept from Section 6 that employed an unpowered booster flyback mission, as its orbiter flight started at a lower altitude than the design concept
employing a powered booster flyback.
Guidance was required from staging, at an altitude of 40km, a velocity of 120omls and a flight path angle of 26.8", to orbit insertion at an altitude of 94068m, a velocity of 7556mls and a flight path angle of 0o. Angle of attack was the only steering parameter generated by the guidance system, so orbit plane changes could not be commanded. As a result, the virtual orbiter remained at an orbit inclination of 31.5o, resulting from a due East launch from
Woomera, Australia.
The reason an altitude of 94068m was used instead of just 94km, was to have the same inser- tion point as that used for the vehicle design study. Because the vehicle design study used a spherical Earth model, while this investigation uses a spheroidal Earth model, there was a dif- ference in final altitude using the same distance from the centre of the Earth. For this reason, the altitude had to be adjusted slightly for this investigation.
Angle of attack was used as the steering parameter in either a grid or function type parame-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.3. Vehicle description 141
terisation model, as discussed in Section 4.3. The guidance computer used its own simulation
model to project the trajectory forward, using the current angle of attack model, to the velocity
stopping condition of 7556m1s. At the stopping velocity it was able to calculate the expected
flight path angle and altitude effors. It then used a Newton-Raphson restoration technique to
determine the required modifications to the steering model to attain the correct orbital insertion
conditions. These steering parameters were returned to the virtual orbiter, which continued its
virtual flight using the updated steering parameters, until the next guidance call.
7.3 Vehicle description
The vehicle model used was the orbiter of the two stage concept vehicle using a winged or-
biter and a winged unpowered booster, developed in Chapter 6 (see Figure 6.2). The ascent
propulsion was supplied by 5 LO)lKerosene Aerojet AJ-26-60 rocket engines. The AJ26-60
rocket engines have a specific impulse of 345.3s in a vacuum and can produce a vacuum thrust
of 395000/b. They have a propellant mass flow rate of 579.7kgf s, a mass of 1505frg and are
throttleable between 507o and 7l4Vo. The aerodynamic model from the orbiter of the Ariane-X
(Rahn and SchoettLe, 7996) was used to determine the aerodynamic coefficients. This model
was then scaled to represent the aerodynamic properties of the FESTIP FSSC-I concept vehi-
cle (FESTIP, 1998).
Owing to the inclusion of an attitude controller, the mass properties of this virtual orbiter were required. The values for radii of gyration of the dry launch orbiter were not determined during the concept vehicle design study and therefore had to be estimated for the present investigation.
It was decided to use values from a vehicle that was perceived to have a similar configuration to the orbiter. They were thus taken from the GD XF-91 (Roskam, 1999) as this is a delta winged aircraft with no engines on its wings.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.4. Mission profile 142
7.4 Mission profile
Figure 7.1 shows a typical orbiter ascent flight profile from staging at an altitude of 40km to the perigee of a94x466km transfer orbit. The x-axis of the plot shows the distance along the surface of the Earth, using the staging point as the beginning of the flight. Straight after staging a steep ascent flight can be seen, because of the 28.60 staging flight path angle. The ascent rate is then seen to shallow as the flight progressed, ending at the target flight path angle of 0o.
100
90
80 Eto?- () ) E60
50
40
200 400 600 800 1000 Down range [km]
Figure 7.1: Ascent mission profrIe
7.5 Developmentobservations
A number of general observations were made during the software development that were not speciflc to certain virtual environmental perturbations. They will be discussed prior to the results section as they were applicable to all of the test cases, instead of a specific set of flight conditions.
The guidance computer assessed the trajectory by calculating the altitude and flight path angle effors at the point where the orbital velocity was reached. This meant that the velocity was
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.5. Development observations 143
always accurately satisfied, while the steering parameters were varied to try and reduce the
altitude and flight path angle enors. If the velocity had a zero or near zero gradient at the
end of flight then the small parameter changes, introduced by the restoration step, could have
caused large variations in the final flight time. This extended flight time may have included
multiple sign changes in the flight path angle, leading to inaccurate gradient calculations or
even restoration instabilities. The velocity for the ascent phase was, however, found to have
a steep gradient at the terminal condition. In fact the velocity profile had a constant gradient
at the end of flight, as the load factor controller was active, thereby maintaining a constant
acceleration of 3.59. Velocity was thus found to be a good stopping condition due to its steep
gradient at the end of flight. The velocity profile also did not have any points of inflection,
which added to the stability of the guidance computer.
An important observation made was that the guidance updates could not be calculated right up
until the final flight time. Instead, the restoration algorithm became unstable from around 8s before the end of flight. As the final flight time was approached, large parameter changes were required to produce small trajectory modifications because of the short flight time remaining.
This caused unrealistically large parameter variations, of the order of 10o, to be commanded, resulting in the restoration algorithm becoming unstable. Guidance updates were therefore not performed for the final 8s of flight; instead, the final parameter set was used without modification until main engine cut off.
As was expected the optimisation algorithm required a "balanced" problem in order to function properly. If forced to attain high accuracy constraints in the final guidance phase or if the steering parameters did not affect the trajectory, the algorithm became unstable. It is therefore important to ensure that the optimisation problem is well "balanced" in order to attain a robust guidance algorithm.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 144
7.6 Ascent guidance results
The results section will show the performance of the guidance system, using various pertur-
bations in the virtual environment to model non-nominal environmental parameters. As was
discussed in Section 4.3, the guidance computer used a simulation model to predict the final
orbit of the virtual orbiter. In a real application, the flight environment would differ from the
guidance computer's simulation model as the actual flight environment cannot be accurately
estimated. According to Marcos et al. (7994) atmosphere models are prone to 15Vo errors
without even considering the enors arising from wind. The simulation within the guidance
computer cannot therefore be made to accurately model the flight environment, implying that
it would have to be able to operate using only a rough estimate of the current environmental
conditions. These differences between the guidance computer's simulation model and the ac-
tual atmospheric conditions would make the orbiter fly a slightly different trajectory to the one
that the guidance computer expected it to, resulting in the steering model requiring updates at
every guidance call.
In order to test whether the guidance computer can operate with a rough estimate of the flight
environment, perturbations were included in the virtual environment. These perturbations were
added one at a time, as shown in Figure 7.2, to see how the guidance system performed with
each additional perturbation. Note that in each case, the guidance computer simulation model
remained the same, while the virtual environment was made to differ more and more at each
point. The final block in Figure 7.2 shows a Monte Carlo simulation run was performed as a
final robustness and performance analysis.
The results will be displayed showing the "open loop" case and the "guided" case. The open
loop graphs show what errors would occur if the virtual orbiter were to fly without any guid-
ance updates during flight. The optimal steering commands, relative to the guidance simulation models, were given to the virtual orbiter at the staging conditions. These parameters were then used as open loop commands to steer the virtual orbiter from staging to the orbital velocity.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow c) S o 9\ Þ CD ø o ci o Virtual envi¡onment Guidance computer Virtualenvironment Guid¿nce computer Þ Virtual envi¡onment Guidance computer US Std. atmosphere US Std. atnoqphere 4û order graviøtion Newtonian gravitation 4ú order gravitation Newtonian gravitation Oc È) 4ù orde¡ gravitation Newtonian gravitation MSISE93 atnospherre US Std. atrnoçh;ere MSISE93 atmosphere US Std. atrnosphere a- g Wind o (D o (6 II ø o Oa o a. ai 6 o Ua \ oa t\) q o a. a lj G (d c) Þ. o g o ,+, Steerin parameter model Vi¡hnl envi¡onment Guidance computer Guidance call interval analysis o analysis 4ú order gravitation Newtonian gravitation environment Guidance computer 0e i{ Vi¡tual MSlSE93atmosphere US Std. aünosphere 4ù order gravitation Newtonian graviøtion Virt¡al environment Guidance conrouter 4ù order gravitation Newtonian gravitation (¡ Wind MSISE93 atrnoçhere US Std. atnosph;ere MSISE93 afinosphere US Std. atnosphere o Sensor erro¡s Wind o Wind ct oa_ (D o 'lJ
CD ñ*. o ø Vi¡tual envi¡onment Guidance cornouter Monte Carlo Analysis Virûral environment Guid¿nce computer 4ü order gravitation Newtonian gravitation Virtual envi¡onment Guidance computer 46 order gravitation Newtonian gravitation MSISE93 aûnosphere US Std. aünosphere 46 order graviøtion Nev¡lonian gravitation MSISE93 atnosphere US Std. alrnosphere Wind MSISE93 aünosph;ere US Std. atnosphere o$ Wind Sensor errors Wind { Sensor er¡ors Randomwind and Sensor erors Random wind and afnospheric densþ R¿ndom wind and * aûnospheric density Staging point enors atmospheric density ol Thnrst errors Stagingpoint errors o (àA 7.6. Ascent guidance results 146
The graphs labelled "guided" show the trajectory flown by the virtual orbiter when it received guidance updates throughout the flight.
In the steering model plots, there are steering profiles labelled "OL command", "Guided com- mand" and "Guided flight" . The "OL command" profile is the original set of steering pa- rameters given to the virtual orbiter, straight after staging. The "Guided command" profile shows how the parameters were varied by the guidance computer during the virtual flight, and therefore shows the commanded angle of attack at each second. The "Guided flight" profile shows the actual angle of attack attained by the virtual orbiter at each second. The difference between the "Guided command" and "Guided flight" profiles comes about because of the dy- namic response of the virtual orbiter. When the guidance computer commands a specific angle of attack, the attitude controller attempts to attain that commanded value as quickly as possi- ble, considering the dynamic response of the virtual orbiter. This response time is shown by the difference between the "Guided command" and "Guided flight " profiles. The inclusion of the attitude controller was a further robustness test, as the guidance computer was operating with a time lag between attitude command and attitude attained.
7.6.L Gravitation model perturbation
The first test was to determine whether the guidance computer could operate in a stable manner if its gravitation model differed from that used in the virtual environment. The difference between the two gravitation models would cause different gravitation forces to be generated in the virtual environment and guidance computer simulation. The virtual environment used a
4th order approximation of the Earth's gravitational field, while the guidance computer used a
Newtonian approximation. Both the virtual environment and guidance computer used the US
Standard atmosphere with no wind model. Guidance updates were performed every second, a four parameter grid type steering model was used and the attitude controller was activated.
Figure 7.3 shows that the flight path angle (fpa) histories for the open loop and guided cases
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 147
110 8 30
100 25
90 6 20s Ø Ë a80tr ---- Open loop c) J¿ J¿ ào ãro Guided alt 4b 15F á - o Guided vel o (d - () À Guided fpa 10.Ë - èo flr 2 50 5
40 0 30 0 0 50 100 150 200 250 Time [s]
Figure 7.3: Flight profrle for the gravity perturbed case are almost identical for the initial flight segment, with a slight deviation becoming evident at around 130s flight time. Although there is a slight difference of approximately I7o after 130s flight time, the curves remain close for the remainder of the flight, with the open loop case consistently having a slightly shallower flight path angle. The altitude histories show a similar pattern to the flight path angle histories, with the curves being similar until around 130s flight time. After this time, the open loop altitude profile begins to drop below the guided profile due to its slightly shallower flight path angle. Figure 7.3 shows that the open loop and guided terminal velocity errors were0mf s, with the two profiles differing by only 3 -4mf s during the flight. As was discussed in Section 4.3, velocity was used as a stopping condition so no enor
\vas expected. For completeness, the values of the orbit errors at the end of the virtual flight are shown in Table 7.1.
Constraint Targets OL error Guided error Flight path 00 -0.095' -0.045' Altitude 94O68m -I826m -0.3m Table 7.1: Constraint violations for the gravity perturbed case
The presence of the deviations in flight path angle and altitude could indicate that the Newto- nian approximation of the gravitation field produces slightly inaccurate gravity forces. These
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance ¡esulfs 148 differences are probably small, indicated by the fact that the deviation only became evident at l30s flight time, after the errors had had time to propagate. It may, however, be valuable to improve the gravity model in the guidance system to a higher order approximation (possibly
2'd order).
Figure 7.4 shows that only small changes in angle of attack were required by the guidance system to achieve the target conditions. The first parameter was increased by 3Vo whlle the third parameter was decreased by around the same amount. This indicates that there was less lift or more gravitational force in the initial flight phase. The decrease in the third parameter indicates that there was more lift or less gravitational force than was expected by the guidance computer at this flight time. The angle of attack was again increased at the final parameter to attain the target conditions.
A further result that can be seen in Figure 7.4 is that the "Guided command" profile and
"Guided flight " profile are very similar. This indicates that the attitude controller operated successfully by tracking the commanded angle of attack with a time delay of around ls. There was a slight steady state error in angle of attack of around 0.08' due to the controller design.
Although this error could be eliminated using a more advanced controller, it was considered unnecessary as the controller was only included to generate a steering command delay, caused by the dynamic behaviour of the launch vehicle. The slight steady state error also served as a further robustness test for the guidance computer.
7.6.2 Atmosphere model perturbation
The next variation was to implement different atmosphere models as well as gravitation mod- els in the virtual environment and guidance computer simulation. In effect, this investigation would determine if the guidance computer could operate in a slightly different flight environ- ment to the one it expects. The guidance computer used the US Standard atmosphere, and the
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulús 149
T2
''' '' OL command 10 ---- Guided command Guided flight - ò0 €() 8 &o d I fil 6 tff o c.) à0 4
2
50 100 150 200 250 300 Time [s]
Figure 7.4: Steering model for the gavity perturbed case
MSISE93 atmosphere model was used in the virtual environment. Again the four parameter grid type angle of attack model was used and guidance updates were performed every second.
110 8 30
100 25
90 6 20s Ë =80 ---- Open loop (.) J¿ àD J¿ 15F €io - Guided alt 4b ! O .E Guided vel o Cd - (.) È ?60 Guided fpa 1o= - èo fIr 2 50 5
40 0 0 50 100 150 200 250 Time [s]
Figure 7.5: Flight profrle for the atmospherc perturbed case.
Figure 7.5 shows the flight profile for the open loop and guided virtual flights. The flight path angle (fpa) is seen to be similar for the early part of the flight, however, again after about 130s the two flight path angle profiles begin to diverge slightly. The altitude profiles are also very
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulús 150 similar until around 130s flight time, after which they too begin diverging. Again, the velocity profiles are almost identical. l2
OL command 10 --- Guided command Guided flight -
Òo €(.) 8 J1 (no
GI 6 (N o () è0 É 4
2
50 100 150 200 250 300 Time [s]
Figure 7.6: Steering model for the atmosphere perturbed case
Figure 7.6 shows the steering commands for the open loop, guided and flight profiles. Again,
\rye see only minor modifications in steering parameters between the open loop and guided parameter sets. The biggest parameter variations occurred in the first and third parameters, and were around 0.7'. The final target errors for the guided and open loop cases are shown in
Table 7 .2. The open loop case shows unacceptable errors in injection orbit, while the guided case attains near perfect injection conditions.
Constraint Targets OL error Guided error Flight path angle 00 -0.101' -0.00047' Altitude 94068m -I924m -0.3Lm Table 7.2: Constraint violations for the atmosphere perturbed case
An interesting result is that the differences in the guided angle of attack profiles between
Figures 7 .4 (gravitation perturbed case) and 7 .6 (gravitation and atmosphere perturbed case) are of the order of 0.050. The minor changes in the steering parameters required suggests that the differences between the US Standard atmosphere and the MSISE93 atmosphere models do not have a significant effect on the trajectory. The reasons for this are firstly, that both
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance ¡esulfs 151 models are attempting to model nominal conditions around the Earth, and so are expected to produce similar atmospheric conditions; secondly, differences in atmospheric density have a smaller effect on upper stage ascent than they would for some other flight phases, due to the high altitude (above 40km) of upper stage ascent. At high altitudes, aerodynamic forces are typically small and so do not have a significant effect on the trajectory. Small variations in these already small aerodynamic forces cause little change to the trajectories. A more important test may thus be to introduce random variations in atmospheric properties in an attempt to model non-nominal conditions.
7.6.3 Wind model
The next variation was to introduce wind in the virtual environment. The absence of a wind model in the guidance computer would mean that the wind in the virtual environment would continually affect the virtual orbiter's relative velocity, thereby affecting its lift and drag forces.
The guidance computer would thus be required to modify the steering parameters in order to meet the required target conditions. The IIWM wind model was used, as described in Section
3.1.5, to introduced a South'Westerly wind in the virtual environment. The effect on the virtual vehicle was thus to have a tailwind blowing the vehicle North. It should be noted that only angle of attack was used as a steering parameter, so heading adjustments \ryere not possible.
As a result, any forces out of the ascent plane were ignored by the guidance computer.
Figure 7.7 shows the flight profile with wind in the virtual environment. Again, the velocity profiles are well matched as velocity was the stopping condition. The altitude profile for the open loop and guided graphs are similar until around 80s flight time, after which time they are seen to diverge. The open loop case is seen to produce alarge altitude error of 6.7km.
The flight path angle (fpa) profiles also diverge at around 80s flight time with the open loop trajectory consistently having a steeper flight path angle. This is the expected result as the tail- wind would have caused the virtual orbiter's velocity relative to air to be reduced by the value
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 152
ll0 8 30
100 25
90 6 20ff
F80 (.) tr ---- Open loop ßi J ,y ào Guided alt 15F E'á ro - 4à Guided vel () cl - ô È Guided fpa c) 1o.g èo trr 2 50 5
40 0 0 50 100 150 200 250 Time [s]
Figure 7.7: Flight profrle for the tailwind case of the wind speed. This reduction in air-relative velocity would have caused the lift to drag ratio to increase, thereby causing the steeper flight and higher altitude seen in the open loop case. Figure 7.8 shows the steering commands for the case with a S\¡/ wind in the virtual en-
t2
OL command 10 ---- Guided command Guided flight - è0 €4) 8 xo
c! 6 (+r o (.) òo 4
2
50 100 150 200 250 300 Time [s]
Figure 7.8: Steering model for the tailwind case
vironment. The guidance system is seen to reduce the first and second parameters by between
0.5o and 1o to account for the increased lift to drag ratio experienced by the virtual orbiter at
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance ¡esulfs 153 lower altitudes. The third and fourth parameters are increased slightly by the guidance system, compared to the open loop case. This angle of attack profile displays the opposite behaviour to the case with perturbed gravitation and atmospheric density models, shown in Figure 7.6.
Constraint Targets OL error Guided error Flight path angle 00 -0.44" -0.00039' Altitude 94068m 6107m -0.247m Table 7.3: Constraint violations for the tailwind case
Although the open loop steering commands produced significant errors in the target states, the guided terminal conditions were satisfied (see Table 7.3). This shows successful operation of the guidance system by varying the parameters appropriately to attain the required injection conditions, also shown in Table 7.3.
110 8 30
r00 25
90 6 208 ! ---- Open loop o v=80 tr bn J¿ lsF €70 - Guided alt 4b Guided vel (d - 8 È Guided fpa c) 1oË - èo tri 50 2 5
40 0 0 50 100 150 200 250 Time lsl
Figure 7.9: Flight profrIe for the headwind case
In order to properly test the guidance system's performance when wind is implemented in the virtual environment, the wind direction was reversed and the results analysed. Figure
7.9 shows the flight profile for the case when the virtual orbiter was experiencing a North
Easterly wind, which produced a headwind blowing the trajectory South. As for the tailwind case, the velocity profiles were found to be consistently similar, which was expected as the
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 154 wind velocities were two orders of magnitude smaller than the virtual orbiter's orbital velocity.
Contrary to the tailwind case, however, the open loop flight path angle shallowed earlier than the guided case. From about 65s flight time, the flight path angle (fpa) was shallower for the open loop case than for the guided case. This caused the open loop case to reach its maximum altitude at around 200s flight time, after which it began decreasing altitude until the terminal velocity was reached. The headwind caused the velocity, relative to the air, to increase. This caused a lower lift to drag ratio, resulting in the virtual orbiter finishing at a lower than required altitude while also descending at -0.58'flight path angle.
12
OL command 10 ---- Guided command Guided flight - bI) o 8 !Ë J¿o cú (! 6 (+i o C) Þ0 4
2
0 0 50 100 150 200 250 300 Time [s]
Figure 7.10: Steering model for the headwind case
The angle of attack profiles for the headwind case are shown in Figure 7.10. As expected it displays opposite behaviour to the tailwind case. The first angle of attack parameter (at 60s) was increased by about 10, as the virtual orbiter experienced less lift than expected in the lower altitudes. Table 7.4 again shows the successful operation of the guidance system by achieving accurate orbit insertion conditions.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulús 155
Constraint Targets OL error Guided error Flight path angle 00 -0.59' -0.00071" Altitude 94068m -9517m -0.496m Table 7.4: Constraint violations for the headwind case
7.6.4 Steering parameter models
In order to analyse the effect of trajectory parameterisation on guidance performance, a num-
ber of guided flight simulations were performed using different parameter models and numbers
of parameters. For this investigation, the virtual environment used a 4rh order approximation
for the gravitational field, the MSISE93 atmosphere and the IIWM wind model. Two differ-
ent parameter model types were used. The function type model used the parameters as the
coefficients of a time-dependent function describing the angle of attack profile. The grid type
model used the parameters to make up a time-referenced grid that was linearly interpolated to
generate an angle of attack vs time profile, remembering that the angle of attack parameters
were dropped once their grid times had been exceeded. The two types of parameter models
used were discussed in more detail in Section 4.3.
Up until this point a four parameter grid type steering model was used. The reason the analysis
of the steering parameter models was only performed at this point in the investigation, is that
it was thought to be more useful to perform the analysis using a perturbed virtual environment
rather than a nominal one.
Considering the two models that used three parameters, shown in Table 7 .5, the function type
model performed better than the grid type model, with respect to both injected mass and accu-
racy of final conditions. One reason for this is that the function type model had three steering
parameters active for the entire virtual flight duration. The grid model, on the other hand, had
only two parameters active for the final 38s of flight. When the flight time exceeded the sec-
ond grid point, the first parameter was dropped as it was no longer required to calculate cunent
or future steering commands. A second reason may be due to the function parameterisation being more optimal than the grid type model. The justification is that a similar function type
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 156
formulation was found to be optimal for minimal fuel ascent trajectories by Bryson and Ho
(1969). Although the problem formulation used in Bryson and Ho (1969) was more simplified
than the formulation used in the present study, it is comparable and may therefore retain a
notion of optimality. The problem with the function type model is that the parameters were
very small. The smallest coefficient was already of the order of 10-5. If another coefficient
was introduced, it would have needed to be smaller again (by two orders of magnitude) as it
would have been the coefficient of time-to-the-power-of three. This restricted the number of
coefficients that could be used. For this reason, higher parameter numbers were not examined.
Using a grid type parameter model, Table 7.5 shows a decrease in target orbit errors as the
number of grid points increases. The improving accuracy was expected as increasing the
number of parameters makes the parameterised steering model a better approximation of a
continuous model. The difference in performance between using five and six parameters was
shown to be small, suggesting that it may not be worth using more than five parameters. The
four parameter grid model was also shown to produce adequate accuracy and was therefore
used for the remaining robustness tests.
Parameter model type No. of parameters Altitude error FPA error Injected mass Function 3 O.4l9m 0.00051' 84003.9kg Grid 3 0.78m 0.00102' 83992.7kg Grid 4 -0.241m -0.00039" 83990.2kg crid 5 -0.12m -0.0002' 83998.9kg Grid 6 -0.778m -0.0002' 83999.7kg Table 7.5: Performance with different parameter models
Note: The injected masses shown in Table 7.5 would allow about 14700kg of payload to be
delivered to the ISS.
7.6.5 Guidance call intervals
The guidance interval refers to the time between successive steering parameter updates by the guidance computer. Theoretically, the more frequently the steering parameters are updated,
Commercial Iaunch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resuifs 157
the more accurately the target conditions will be satisfied. The reason for this is that the trajec-
tory errors will be given less time to propagate between guidance calls. As well as achieving
more accurate target conditions, more frequent guidance calls will also reduce the magnitude
of the steering forces, thereby reducing the effort required by the steering mechanism. The
computational loading is, however, increased with shorter guidance call intervals since more
computer time is required to update the steering parameters. It is thus important to deter-
mine the required guidance interval to allow stable performance while at the same time not
overloading the on-board computer. In order to investigate suitable guidance call intervals, a
number of virtual flights were performed using different guidance call intervals. The results
were obtained using the MSISE 93 atmosphere model, a4th order approximation of the Earth's
gravitational field and a IIWM wind model, which generated a South Westerly wind in the vir-
tual environment. Up until this point a guidance call interval of ls has been used. The reason
the analysis of the guidance call intervals was not performed at the beginning of the study is
that it was thought more useful to perform the analysis using a perturbed virtual environment
rather than a nominal one.
The results in Table 7.6 show that for guidance intervals of 10s and below the target constraints
were satisfied, with a slight decrease in performance as the interval increased. This was ex-
pected as the more often the guidance commands are updated, the better the target condition
accuracy. To maintain consistency, and because the computational power is available, a guid-
ance interval of 1s second will continue to be used for the following investigation. It should,
however, be noted that guidance calls of up to 10s are sufflcient to achieve a consistently
accurate solution.
An interesting observation is that all of the solutions show negative errors for both altitude and
flight path angle. The reason for this is that the wind conditions, atmospheric density variations
and gravitation field differences between the guidance computer and the virtual environment were consistent for all the flights. These variations tended to shallow the trajectories, thereby giving negative erors.
Commercial launch vehicle design and predictive guidance development Matthew R. TetIow 7.6. Ascent guidance resulfs 158
Interval Altitude error FPA error Injected mass 1s -0.247m -0.00039' 83990.2kg 10s -0.932m -0.0009' 83998.3kg 20s -5.27m -0.0035' 83989.1frs Table 7.6: Performance with different guidance call intervals
7.6.6 State errors (sensor errors)
In this section, sensor errors will be modelled in the virtual orbiter. Up to this point, it has been assumed that the guidance computer received accurate information about current position and velocity. In a real application, this may not be the case as navigation suites typically produce measurement errors. A sensor error model was thus introduced to model these random sensor errors. Random numbers between - 1 and 1 were multiplied by the maximum navigation error, shown in Table 7.7, and then added to the correct state information. An independent error was generated for each state at each guidance call, thereby producing near-random variations in the states required by the guidance computer.
State Targets Max. error Velocity 7556mls 0.l52mls Flight path angle 00 0.07' Altitude 94068m 9lm Table 7.7: Maximum senso¡ errors (source document is commercially sensitive)
The short segment of the altitude profile in Figure 7.11 shows the random effors given to the guidance system. The solid line is the altitude vs time profile, as flown by the virtual orbiter, while the dashed line is a plot of the altitude values given to the guidance computer. Note that the full altitude profile is shown in Figure 7.12.
Figure 7.12 shows the flight profile when sensor effors were modelled in the virtual orbiter.
Again, the virtual environment used the 4th order approximation of the Earth's gravitational fleld, the MSISE 93 atmosphere model and the HWM wind model, which generated a South 'Westerly wind. The sensor effors do not affect the open loop case as there are no guidance
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 159
93.5
93 ? tr l¿ q E á
92.5 Actual ---- Used
180 185 190 Time [s]
Figure 7.11: Altitude profrIe with sensor errors
110 8 30
100 25
90 6 20il Ë ã80 (l) Ê ---- Open loop tr .\1 & lsFäo Ë70 - Guided alt 4b Guided vel Cd - 8 È Guided fpa C) 1o.E - èo tIi 2 50 5
40 0 0 50 100 150 200 250 Time [s]
Figure 7.12: Flight profrIe with sensor errots
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance ¡esulfs 160 updates, which means that the measured state is not relevant. The open loop case is thus the same as the one shown in Figure 1.1. The guided flight also shows similar behaviour to that seen in Figure 7.7. This suggests that the sensor errors can easily be accounted for by the guidance system. As expected, the graph of the parameter models is similar to Figure 7.8, and so will be not be displayed.
7.6.7 Non-nominal atmosphere perturbations
The atmosphere and wind models used up until now have all been nominal models. That is, they were all derived from statistical data and they all modelled the nominal environmental conditions. Although some models could account for seasonal changes in weather patterns, none of them were able to model short term (below 10s), local variations from these nominal conditions. They were not able to model local wind gusts or local atmospheric density varia- tions. To more thoroughly test the guidance system against environmental variations, random perturbations in wind speed, wind direction and atmospheric density were introduced.
The wind was tested by multiplying the wind vectors (N-S and E-W) generated by the IIWM wind model by a random number between -1 and 1. This had the effect of producing a wind that varied in speed and direction every second during the virtual flight. The nominal wind 'Westerly direction used was a South wind, so if the random number was negative for that second, the wind direction would become North Easterly. The density was multiplied by a random number between the values of 0 and 2. This caused the atmospheric density to change from between twice the value generated by the MSISE93 atmosphere model and zero every second. These variations may have been slightly unrealistic as atmospheric conditions would probably only vary by this amount in a violent storm, which could be avoided by delaying the launch. It does, however, show that the guidance system is robust enough to handle severe environmental changes during flight.
From Figure 7 .13 it can be seen that random variations in wind speed, direction and atmo-
Commercial Iaunch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulús 161
Constraint Targets OL error Guided error Flight path angle 00 0.026" -0.0005' Altitude 94068m -II26m -0.346m Table 7.8: Constraint violations for the random atmospheric density and wind case spheric density did not produce significant variations in the virtual flight profile. The fact that the open loop virtual flight produced relatively good end conditions (see Table 7.8) suggests that the effect of random wind variation over the whole flight was small. This flight profile
@gure 7.13) shows similar behaviour to that seen in Figure 7.5, which used only different nominal atmosphere and gravitation models. This suggests that the trajectory that the virtual orbiter flew in this case was similar to when there was no wind in the virtual environment. The reason for this is that the continuous reversal in wind direction had the effect of minimising the average wind speed. The trajectory was shown to be sensitive to wind in a constant direction: the open loop cases are seen to have large target orbit errors (up to 9.5km altitude errors). The wind force in the random wind case was not constantly blowing the orbiter off-course in one direction, but instead was randomly changing direction.
110 8 30
100 25
90 6 20r ?80 € ---- Open loop {) v àD J¿ 15F €70 - Guided alt 4b Guided vel ôO - (l) È Guided fpa 1oE - bo =H< 50 2 5
40 0 0 50 100 150 200 250 Time [s]
Figure 7.13: Flight profrIe for the random atmospheric density and wind case
Although the random variations were found to have a reduced effect on the trajectory, they were more testing on the guidance system as the virtual orbiter's lift to drag ratio was con-
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 162 tinually changing from below to above the nominal value and visa-versa. This caused larger parameter variations to be required at each guidance call, as is shown in Figure 7.14. The pa- rameter variations were up to 2.5 times higher for the random varied case than for the constant wind case. Only a short segment of the control model is shown in Figure 7.I4, to enable the scale to be reduced, so that the parameter changes can be seen clearly.
5
Nominal wind ----' Random wind
4.5 bo (l) ! J¿() (!
cd 4 o (.) òo
3 .5
I 65 t70 r75 180 185 190 Time [s]
Figure 7.14: Partial steering profrIe for the random atmospheric density and wind case
7.6.8 Staging errors (staging point errors)
The next part of the analysis was to determine if the guidance computer could tolerate effors in the staging conditions, which could occur if the first stage ascent flight, which is often open loop guided (Bordano et al., 1991), flew an off-nominal trajectory. The virtual environment employed a 4th order approximation of the Earth's gravitational field, the MSISES3 atmo- sphere model, the FIWM wind model and random perturbations in states given to the guidance computer (sensor errors), as well as random variations in atmospheric density, and wind speed and direction. Although this aspect of the study was more a test for the initial optimisation rather than the on-line part of the guidance system, it was considered important to the overall robustness of the guidance system.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resu.hs 163
The staging point effors used were a staging altitude error of -7O0Om (1.067o), a flight path angle error of -2" (7 .46Vo) and a staging velocity error of -25Ùmf s (2O.8Vo). The guidance system operated successfully by reducing the error at the target conditions and achieving an altitude error of 3.4m and a flight path angle error of 0.0012". The problem was that the injection mass was only 76519È9, which is significantly lower (8.97o) than the values seen in
Table 7.5. This would have resulted in mission failure as the orbiter would not have been able to carry 7.Stonnes of extra fuel in case of large staging errors. The failure was not however, due to guidance system failure, but rather that the orbiter would have required more fuel to achieve orbit from its staging position than it would have required had it staged at the conect conditions. The important result is that the guidance computer was flexible enough to change the flight profile and achieve the required target conditions.
7.6.9 Thrust loss
It was shown in Section 5 that ascent trajectories are highly sensitive to thrust profiles. It was therefore considered useful to determine if the guidance system was capable of accounting for variations in thrust, caused by a propulsion system malfunction. Two scenarios were in- vestigated. The first was if the guidance system did not detect the thrust malfunction, and so continued to generate guidance commands assuming that the propulsion system was operat- ing properly. This means that in the guidance system's trajectory propagation, it continued to use the original thrust model. The second was the case where the guidance system detected the thrust malfunction and therefore began generating steering commands with the knowledge that the propulsion system was malfunctioning. That is to say that instead of using the origi- nal propulsion model to propagate the trajectory in the guidance computer, a modified thrust model was used that included the reduction in thrust experienced by the virtual vehicle.
The virtual system employed an MSISES3 atmosphere model and a 4th order approximation of the Earth's gravitational field. Wind was activated in the SW direction and sensor errors
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 164
were modelled. It was assumed that the launch vehicle staged at the nominal conditions i.e. an
altitude of 40km, a flight path angle (fpa) of 26.8o and a velocity of 72oomls. The results are
shown in Table 7.9.
Description - parameter model type Alt. error FPA error t flinht Inj. mass Undetected 757o redtction after 120s - grid -85.9m -0.06" 278s 837l2kg Undetected 757o reùrction after 50s - grid -219m -0.17" 297s 82978kg Undetected 75Vo reduction always - grid -605m -0.3" 30ls 82777kg Detected l57o reduction always - grid 486m 0.2" 301s 82242kg Detected 75Vo reduction always - function 73m 0.0015" 301s 82306ks Table 7.9: Guidance performance with thrust enors
For the case where the thrust error was not detected and a grid type parameter model was used,
it is clear that the solution decreased in accuracy the earlier the thrust error was introduced.
The reason for this is the fact that the grid points ended at 255s flight time, after which time
no parameter updates were performed. This means that the flight time after 255s was open
loop guided. Because the guidance system was not aware of the thrust error, the last guidance
update assumed nominal thrust behaviour. Therefore, the greater the flight time above 255s,
the greater the time for the errors to propagate.
In the case where the error was detected, the grid type parameter model still shows a consid-
erable orbit insertion error. The reason for this is again the length of flight time after the 255s
grid point. The function type model, however, shows near perfect orbital insertion conditions
due to the fact that guidance updates could be performed until the end of flight.
The injected mass is seen to vary from the nominal value of S4tonnes by no more than 2.7Vo.
This indicates that although the flight time is drastically increased, only a small amount of
extra propellant would be required to achieve the correct orbit. The cases where the orbit
conditions were not reached were not analysed, with regard to injected mass, as their effors
in orbit condition would have contributed considerably to the variation in injection mass. The
important result is, however, that the guidance system was able to guide the vehicle to the required orbit when there was a l57o decrease in thrust.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 165
7.6.10 Monte Carlo analysis
For completeness, 1000 missions were simulated with random variations in the staging condi- tions to ensure robust operation of the guidance computer. The virtual environment employed a 4th order approximation of the Earth's gravitation fleld, the MSISE93 atmosphere model, the
HWM wind model, random variations in the states given to the guidance computer (sensor er- rors) and random variation in atmospheric density, wind speed and wind direction. The random variations for the various parameters are shown in Table 7.10. The performance of the simula- tion runs with respect to each target constraint violation will now be analysed independently.
Parameter Upper error bound Lower error bound Staging flight path angle 2.0" -2.0" Staging altitude 1000m -1000m Staging velocity 25omls -250mls Altitude sensor error 97m -9lm Flight path angle sensor error 0.07' -0.07' Velocity sensor effor O.l52mls -0.752m1s Wind speed variation I00Vo -7OOVI Atmospheric density variation 2OO7o 0 Table 7.10: Eror bounds for random variation
Figure 7.15 shows the final altitude of the virtual orbiter for each simulation run. The target altitude of 94068m is seen to be satisfied with high accuracy. The maximum effor was below
6m, which is an error of approximately 0.006Vo, with more than 95Vo of all simulations being within 2m of the required orbit altitude. The mean value for the altitude was 94067.6Jm and the standard deviation was 0.91m.
Figure 7.16 shows the flight path angle for each staging condition error. The target flight path angle was 0o. The largest flight path angle error was 0.005o, with more than957o of the errors being below 0.002'. The mean value for the final flight path angle was -0.00053" with the standard deviation being 0.000758". Again, this shows the guidance system is capable of highly accurate insertion flight path angles.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.6. Ascent guidance resulfs 166
94072
94070 ã
ci) 94068 ۇ
94066
94064
200 400 600 800 1 000 Run number
Figure 7.15: Monte Carlo result for frnal altitude
0.004
Target fpa - 0.002
èot) ! C) èo^ .000 cú É ÞcË t .go -0 .oo2 lr
-0 004
o 2oo ooR.uo nu-o*Îoo 8oo 1 000 Figure 7.16: Monte CarIo result for flight path angle
Commercial launch vehicle design and pedictive guidance development Matthew R. Tetlow 7.7. Summary and discussion 167
7.7 Summary and discussion
In summary, the numerical guidance system developed in this study was found to be well suited to an upper stage ascent mission. It was shown to be robust to environmental factors, such as wind and atmospheric density variations. Both nominal and randomly perturbed environmental models were considered, with wind variations found to have a greater influence on trajectory shaping than atmospheric density. The guidance system was found to be capable of accounting for variations in staging conditions, as well as effors associated with position and velocity measurement (sensor errors).
The attitude controller was also found to perform well and was able to track the commanded attitude with a small time delay (below 1s). There was also a slight steady state error in angle of attack of around 0.08' due to the controller design. The steady state error and time delay both served as a further robustness test for the guidance computer.
The guidance system produced stable steering parameter updates until around 8s before the end of flight. It is therefore suggested that the guidance updates be used until 8s before the end of flight, followed by an open loop flight phase. Guidance update intervals during the virtual flight of 10s and below were found to produce accurate orbit insertion points, with a slight decrease in orbit accuracy with increased guidance call intervals.
A number of different parameter models were investigated, with a three parameter function type model producing a more accurate orbit insertion than the three parameter grid type model.
Due to parameter value limitations, only the grid model was tested using higher parameter numbers. Considering the grid type parameter models, the use of more than five parameters was shown not to improve the orbit insertion points significantly. Even a four parameter grid model was shown to produce sufficient orbit insertion accuracy. For the case when thrust errors were introduced, the function type model was found to produce a better guidance solution as the parameters could be updated up until the end of flight.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 7.7. Summary and discussion 168
By observing the effors in the open loop virtual flights, it can be seen which environmental parameters are the source of large target state errors. Considering the open loop virtual flights, the simplifled gravitation model used in the guidance system was found to cause a target alti- tude error of 7826m, or almost 2Vo, whencompared to the 4th order gravitation model used in the virtual environment. The difference between the US Standard and MSISE93 atmosphere models had only a minor effect (0.17o ) on the target altitude. The inclusion of wind in the virtual environment, was found to produce large target point errors (707o altitude error).
Although the guidance system was found to operate successfully in its current state, if excess computation power was available, two improvements could be implemented. Firstly, it would be worthwhile implementing a higher order gravitation model in the guidance computer as it would produce more accurate parameter updates. The second would be to implement a nomi- nal wind model, as the constant headwind and tailwind cases were shown to create large target point errors. The small differences observed between using the US Standard and MSISE93 at- mosphere models suggest that implementing the more advanced MSISE93 atmosphere model in the guidance computer would not improve the software significantly. The randomly varied wind was also shown to produce small trajectory errors, suggesting that short duration wind gusts do not require modelling in the guidance computer.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 8
Predictive Guidance for Flyback
S.L Introduction
To date there have been no operational flyback boosters. This means there are no operational guidance systems available to guide booster flyback missions. There are, however, various guidance systems for re-entry vehicles, which have some common attributes with flyback mis- sions. For example, they both have atmospheric deceleration flight phases. One requirement for a flyback mission that is not required in a re-entry mission is a turn-around flight. A re-entry vehicle usually deorbits flying in a direction towards a Heading Alignment Cylinder (HAC).
A booster, however, would generally be flying away from the HAC and would therefore need to turn through about 180' to attain the correct heading. This means that re-entry guidance systems such as those used on the Space Shuttle (see Section2.T) would not be directly appli- cable to booster flyback missions. Numerical guidance, such as that proposed for the re-entry mission of the X-38 (Wallner et aI., 1999), seems to be more applicable to flyback guidance.
The aim of this study was thus to apply a numerical guidance strategy to a booster flyback mission. This numerical guidance system was developed for real-time application, using the
169 8.2. Problem description 170 vehicle design concept developed in Chapter 6. A series of environmental and system varia- tions were also introduced to test the robustness of the guidance system.
8.2 Problemdescription
Considering the powered and unpowered boosters investigated in Chapter 6, the powered fly- back booster would require the more complicated guidance system. The reason for this is that it would have a longer flyback distance and would also be exposed to a larger altitude varia- tion, with a staging altitude 20km higher than that for the concept vehicle with an unpowered booster flyback. The powered booster would also require control of the propulsion system and would need to account for variations in mass as fuel was consumed. If the guidance system was capable of guiding the powered flyback booster, it would also be robust enough to guide the unpowered booster.
Because the powered booster was a more complicated system it was used as a test bed for the guidance system. The flyback guidance system was required to guide the powered booster from staging at an altitude of 62.8km, a velocity of 3OOOmls, a heading of 84.9" and a flight path angle of 10.0", to cruise conditions at an altitude of 70kmt, a velocity of 240mf s, a heading tangent to a HAC and a flight path angle of 0o. The cruise conditions were maintained by the guidance system, but approach and landing was not considered. It was assumed that standard aviation approach and landing techniques could be applied in a real application.
Both angle of attack and bank angle were used in a grid type parameter model (see Section 4.4) as steering parameters. The guidance computer used its own simulation model to project the trajectory forward to the stopping condition, which in this case was an altitude of 72km. At the stopping altitude it was able to calculate the expected flight path angle, heading and velocity effors using the current steering models. It then used a Newton-Raphson restoration technique
lThe reason l}kmwas chosen as a cruising altitude is that it is the approximate cruising altitude of commercial jets, which also use air-breathing propulsion systems.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.3. Vehicle description 171 to determine the required modifications to the steering models to attain the correct target con- ditions. These steering parameters were returned to the virtual vehicle, which continued its virtual flight using the updated steering parameters until the next guidance call.
8.3 Vehicle description
The vehicle model used was the flyback booster from the two stage, 7400tonne GLOW, parallel configuration vehicle developed in Chapter 6. The powered booster had a mass after staging of 82623kg, which included the flyback fuel. Flyback propulsion was supplied by two M88-
35 turbojet engines, producing 6OkN of thrust without afterburners. The engines consumed
80kg lkN .h of fuel and weighe d 7 5Dkg each. An aerodynamic model developed at the Space
Systems Institute, Stuttgart, Germany, by Rahn and Schoettle (1996) was used to determine the aerodynamic coefficients. This model was then scaled to represent the aerodynamic properties of the FESTIP FSSC-I concept vehicle (FESTIP, 1998).
8.4 Mission profile
As was discussed in Section 4.4 there were four different guidance phases covering this mis- sion, which are shown in Figure 8.1. From staging to an altitude of l2.4km, the steering commands were generated by a parameterised steering model, updated by a numerical restora- tion step. Between 72.4km and l2.2km, the parameterised steering model was still used, but the parameters were not updated by the restoration step. Between 72.2km and 77km a constant descent controller was used to command a shallow descent flight of -5" flight path angle. Below lTkm an altitude controller was used to achieve the cruising altitude of TOkm and to maintain it for the flight to the HAC. A more detailed description of these controllers and their operating ranges can be seen in Section 4.4.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 90 o È
(D a^ ci Ø o No parametei ll ct s 90 upt'ates : .. o Staging . . l=1'20s:, Guidance: CD activatiqn "'.: C) 80 (D ^/. oa- .A 70 oa tt Numerical guidance Þ . a. 860 flight Bhase : \J d a- å .Eso o J"o (D Ë E+o Oe a- {so ã'3 o v) o t=367s, Constant oa. Ë20 descênt control (ù o g 10 IJ õ" o 0 "Oiuise 31.5 conditions
31 145 144
Êo 30.5 143 142 o 141 { 30 F 140 FJ 139 (ìr 29.5 1sB o Latitude [deg] South \ € Longitude [deg] N) 8.5. Development observations 173
A typical mission profile is shown in Figure 8.1. Although the bank angle was f,xed at -600 for the first 120s after staging, the low atmospheric density in this flight regime allowed only a slight turn to be executed. The altitude axis shows that the virtual booster had a steep descent flight before shallowing the dive and executing a sharp turn late in the flight. After the turn and at an altitude of 12.2km, the constant descent controller was activated which attempted to acquire and maintain a flight path angle of -5". Below llkm the altitude controller was activated to achieve and maintain cruising altitude.
8.5 Development observations
A number of results and software requirements were observed during the investigation, which were either necessary for the operation or improved the robustness of the guidance system.
As they were not linked to any specific set of operating conditions, but were important to the operation of the software, they will be discussed prior to the results.
The first observation was that the trajectory was not able to be modified to a large extent. This will be shown in most of the results by the fact that the open loop and guided trajectories displayed only small differences (typically below 5Vo). One reason for the similarities is the scale of the graphs, but it is also because there was only a small amount of steering force available during flyback. That is to say that only minor modifications in the trajectory were possible due to the relatively small steering force. Consider that during the ascent mission, the steering force was provided by gimballing the main propulsion system, while the flyback mission was controlled by aerodynamic forces. It is difficult to draw a direct comparison between the steering forces in these two missions, as the virtual boosters' mass properties also influence the effectiveness of the steering force, however, a comparison can be drawn between the total force, which is up to eight times higher for ascent than for flyback.
Coupled with the small control forces is the fact that the steering parameters could only be changed by small increments. In order to maintain restoration stability, at each restoration
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.5. Development observations 174 step the trajectory was required to be similar to the one for the previous restoration step. This means that the parameters were only modified by small amounts (the maximum parameter variation being 0.0057') at each guidance call. In order to generate a large trajectory variation, the parameters would have to be changed by small amounts over a large number of restoration steps. The restoration steps, however, had to be limited to six per guidance call, to ensure that guidance updates could be performed in real-time.
The trajectory was found to be highly sensitive to the parameters that were active in the latter part of the flight, but relatively insensitive to those in the early part of the flight. This was an expected result as the low atmospheric density in the upper atmosphere would require large changes in control angles (i.e. bank angle and angle of attack), typically above 10o, to produce even small trajectory changes. In the dense lower altitudes, the opposite is the case. Very small changes in angle of attack, below 0.1", were shown to produce large changes in the trajectory.
From this result, an attempt was made to allow large changes in steering parameters in the high altitudes, but damp the changes in the lower altitudes. The damping was introduced using the cx,ft parameter discussed in Section 3.2.7, thereby making the parameter updates no longer
Newtonian. This, however, caused restoration instabilities at the points where the damping factor changed. For this reason, c[ft was set to one for this study, making the problem Newto- nian once again. The steering parameter modifications were adjusted to maintain restoration stability in the lower altitudes, allowing only a small amount of control in the upper atmo- sphere. This led to the fact that the initial parameters, i.e. the parameters that the guidance system first used to propagate the trajectory, were required to be relatively close to a solution.
If they were not, then a satisfactory solution was not obtainable within the allowed six restora- tion steps. This meant that for a number of guidance calls, the full six restoration steps were required before the target constraint tolerances were satisfied, after which time the restoration step number would reduce to one or two.
In the low density upper atmosphere, variations in control parameters were found to have little effect on the trajectory. The reason for this is that the low atmospheric density caused small
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.5. Development observations 175 aerodynamic forces, which were not sufficient to change the trajectory significantly. This led to restoration instability. The angle of attack parameters did not affect restoration stability as they followed an open loop profile during the first 350s of flight time. The bank angle, however, was controlled in this flight regime and was found to be the cause of these restoration instabilities. As a result, the bank angle was kept at -600 for the first 120s of flight. After this time, the steering parameters were found to allow stable restoration and the numerical guidance began controlling the bank angle.
Another observation is that one of the most important parameters, from a restoration stability point of view, is the integration stopping condition. The stopping condition was required to have a steep gradient close to the termination condition. The reason for this is that if there was a shallow gradient in the stopping condition then small variations in steering parameters could cause large variations in the flight time. Large variations in flight time, in the order of 10 - 100s, were found to cause instabilities in the restoration technique. For example, if altitude were used as a stopping condition, as was the case in the present study, a terminal flight path angle of 0o could not be used. The reason for this is that during a shallow descent the change in altitude with time is small. A small change in a steering parameter could be sufficient to make the virtual vehicle fly for an extra 20s before reaching the termination altitude. This caused large differences in terminal conditions for small changes in steering parameters. Large erratic terminal condition changes for successive restoration steps led to restoration instabilities. A better solution was to use a steep flight path angle i.e. -10o as a target condition, thereby allowing parameter changes without changing the flight time by more than 2s. This stopping condition requirement forced the use of a constant descent and an altitude controller to reach level flight at the cruising altitude.
The following flight profiles show that the open loop case usually achieved the correct cruise conditions. The reason for this is that the open loop guidance strategy still used the constant descent, altitude, velocity and heading controllers below 72.2km, as shown in Figure 8.1. This allowed the open loop case to generally achieve the correct cruise conditions.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resuJfs 176
8.6 Flyback guidance results
The results section will show the performance of the guidance system, using various pertur- bations in the virtual environment to model non-nominal environmental parameters. As was discussed in Section 4.4,the guidance computer uses a simulation model to predict the veloc- ity, heading and flight path angle at the terminal altitude of 72km. In a real application, the flight environment would differ from the guidance computer's simulation model as the actual flight environment cannot be accurately estimated. The simulation within the guidance com- puter cannot therefore be made to accurately model the flight environment, implying that it would have to be able to operate using only a rough estimate of the current environmental con- ditions. These differences between the guidance computer's simulation model and the actual atmospheric conditions would make the vehicle fly a slightly different trajectory to the one that the guidance computer expected it to, resulting in the steering model requiring updates at every guidance call.
In order to test whether the guidance computer could operate with a rough estimate of the flight environment, perturbations were included in the virtual environment, causing the virtual booster to fly a slightly different trajectory, between guidance calls, to the one predicted by the guidance computer. These perturbations were added one at a time, as shown in Figure
8.2, to see how the guidance system performed with each additional perturbation. Note that in each case, the guidance computer simulation model remained the same, while the virtual environment was made to differ more and more at each point. The final block in Figure 8.2 shows a Monte Carlo simulation run was performed as a final robustness and performance analysis.
The results in the following sections will be displayed showing the "open loop" case and the
"guided" case. The open loop graphs show what effors would occur if the virtual booster were to fly without any guidance updates during flight. The optimal steering commands, relative to the simplified guidance models, were given to the virtual system at the beginning of flight.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow ô 90 o 9\ tl CD q ã Virtu¿l e,nvironment Guidance comuter Vi¡t¡al environment Guidance cornouter Virtral envi¡onment Guidance computer Êo Èt 4ù orcler gravitation Newtonian gravitation o MSISE93 atmosphere US Std. alrnosphere 46 order graviation Newtonian gravitation F MSISE93 afrnosphere US Std. atnosphere Oe 4ù order gravitation Newtonian gravitation MSISE93 atnrosphere US Std. Atnosphere rùr'ind Wind o Se¡rsor errors o. o tD o Ìl Cd o Oc U) o a. ai 6 õvt oo Oa ì\) Ø o Ê. e È (ì at o Þ. o Vi¡tual envi¡onment Guidance computer Virh¡al environment Guidance cornputer Guidance call interval analysis o 4ú order gravitation Newtonian graviøtion 4ü order graviøtionNewtonian gravitation Virh¡al environment Guidance comouter (ù MSISE93 aûnosphere US St¿ alnrosphere I MSISE93 atnosphere US Std. afnosphere 4ù order gravitation Newtonian graviøtion 0q Wind Wind MSISE93 US Std. atnosphere Sensor emors atnosphìere Ê- Sensor errors Randomwind lvind Þ o Randomwind point Sensor er¡ors oc) Staging enors a. ci o
õ (D
C¡ ìt SD
14 Monte Carlo Analvsis Vi¡hral environment Guidance comouter 4Û Newtonian gravitation Ê)' order gravitation MSISE93 atnosphere US Std. afrnosph;erc (D Wind Sensor errors F R¿ndomwind Él Staging point errors (DJ o \ì € \ 8.6. Flyback guidance resuJfs 178
These parameters were then used as open loop commands to steer the virtual booster from staging to the cruise altitude. The graphs labelled "guided" show the trajectory flown by the virtual booster when it received regular (5s interval) guidance updates throughout the flight.
The reason 5s guidance intervals were used was to limit computational loading.
8.6.1 Gravitation and atmosphere model
The first test was to determine if the guidance system could operate in a stable manner for a case when the atmosphere and gravitation models used in the virtual environment were dif- ferent from those used in the guidance computer. The virtual environment used a 4th order approximation of the Earth's gravitational field and the MSISE93 atmosphere model. The guidance computer used a Newtonian approximation of the Earth's gravitational field and the
US Standard atmosphere model. Guidance updates were performed every f,ve seconds.
From Figure 8.3 it can be seen that the guidance computer was able to guide the virtual booster from staging to cruise conditions. The altitude profile is seen to behave in a similar manner to the mission profile shown in Figure 8.1, with an initial increase caused by the fact that the virtual booster had a staging flight path angle of 10.0'. After a peak of around 82km, a steep descent flight is shown. At approximately 200s and 300s, the altitude is seen to have a small "hump", which was caused by the fact that the atmospheric density was increasing faster than the velocity was decreasing. This caused the lift to become high enough to produce an increase in flight path angle (shown by the two peaks in the flight path angle plot of Figure
8.3). Using an optimisation routine, these "humps" can be avoided by introducing a flight path angle limitation in the cost function, however, during the real-time virtual flight they were found to be difficult to avoid.
The open loop and guided velocity profiles are shown by the velocity plot in Figure 8.3 to be very similar. Although they did differby up to20mf s, this is less than alTo difference, making it difficult to show on the plot. There is an initial deceleration corresponding to the
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 179
3
80 2.5
Open loop 60 27i l¡ Guided Þ x J¿ o 1.5;'õ .E ¿o s l> c)
20 0.5
0 0 0 100 200 300 400 500 0 100 200 300 400 500 10
50 0 Òo Ë0) Òo t) (J òo 0g Ê òo -to É ! ct Cd (! È c) Ér Þo -50 rL -20
-100
-30 0 100 200 300 400 500 0 100 200 300 400 500 Time [s] Time [s]
Figure 8.3: Flight profiIe for disturbed atmosphere and gavitation case
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulfs 180 positive flight path angle flight segment between staging and approximately 75s flight time.
After this there was a slight acceleration as the virtual booster began its descent, followed by a steep deceleration as it began entering the atmosphere. At an altitude of 73km, the engines were started, causing the velocity profile to level out to the required cruise velocity of 240mf s.
At about 325s, the velocity plot has a shallow trough, which occurs when the virtual booster was experiencing a slight gain in height, as shown in the altitude plot. The velocity increased
agun briefly, as the virtual booster descended the altitude "hump", before levelling out to the cruise velocity.
The flight path angle plot in Figure 8.3 is seen to decrease steadily until around 150s, at which time the frrst "hump" was experienced. The second "httmp" at around 300s is much steeper and has a much higher amplitude than the previous one, causing the flight to almost level out before continuing to descend. A slight discontinuity can be seen at around 400s, which was caused by the transition from the numerical guidance method to the constant altitude controller. The flight path angle increased to a value of 0o as the altitude controller pulled the virtual booster out of the shallow dive to attain level flight. At an altitude of 72km the atmosphere and gravitation perturbations caused the open loop controlled virtual booster to have a flight path angle of - 14o, compared to -72" for the guided booster. This shows a 117o improvement using the numerical guidance strategy. At the activation altitude for the altitude controller, the constant descent controller had only managed to reduce the descent rate down to
-7 .4" for the open loop guidance case. The guided case had a flight path angle of -6.5' when the altitude controller was activated. This means that the guided case required less control effort from the constant descent controller to reduce the flight path angle from -12o to -6.5o, compared to the reduction from -14o to -7.4" for the open-loop guided case. The altitude controller would also require less control effort to level out a -6.5o descent rate compared to a -7.4" descent rate.
The open loop heading angle is seen to lag the guided one by about 2" from around 300s. This lag slowly increased to produce an open loop heading error of 4.3" at an altitude of lZkm. The
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 181
guided virtual booster had a heading of -105.5" at an altitude of I2km, which is an error of only 0.5' with respect to the required value. Although the differences between the open loop
and guided heading plots look relatively small, they did amount to the open loop virtual booster being a further 2.5km away from the launch site, compared to the guided virtual booster. This was a further 2.77o awa! from the launch site compared to the 92.5km distance discussed in
Section 6.
The guided case was shown to produce better results with regard to both heading and flight path angle at numerical guidance termination, compared to the open loop case. The main advantage of this is that the guided virtual trajectory ended closer to the launch site than the open loop one. This was primarily due to the improved control of the heading. A second advantage of achieving desired flight parameters at the activation of the controllers is that if the control effort can be kept to a minimum, there is more margin in the system. That is, that the less of the controller's capability that is used, the more robust the system.
40 0
-10 30 Open loop oòo Guided ! -20 g J¿o cË !' ã20 òo -30 o F o J4 èo F É -40 Êq l0
-50
0 -60 0 100 200 300 400 0 100 2N 300 400 Time [s] Time [s]
Figure 8.4: Steering model for disturbed atmosphere and gravitation case
The steering parameters for angle of attack and bank angle are shown in Figure 8.4. The angle of attack profile shows the open loop and guided profiles were identical for the first 360s. The reason for this was discussed in Section 4.4. It is due to the fact that only the last two angle of attack parameters were updated by the guidance computer. The first 10 parameters were
Commercial launch vehicle desiga and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulfs 182 not changed during the virtual flight, hence the same profile is shown for both the open loop and guided virtual flights. For this reason, the subsequent angle of attack profiles will only be shown from 350s flight time onward. It should also be noted that the last two angle of attack parameters did not have a flxed operating time as the parameters were active between a flight time of 360s and one of two heuristic switches. The first switch was an altitude of less than
72.2km, and the second a flight path angle above -5o, while the altitude was below l3.5km. For either of these scenarios, the constant descent controller was activated. This varied the activation time for the last angle of attack parameter.
The open loop and guided bank angle profiles are seen to vary only slightly during the virtual flight, with a maximum difference of around 1.0o at around 178s. As can be seen, in Figure
8.4, that all of the bank angle parameters were updated by the guidance computer, as evidenced by the difference between the open loop and guided bank angle profiles for the entire numer- ical guidance flight phase. The guided bank angle profile shows slightly steeper bank angles for most of the flight, which is consistent with the fact that the open loop heading plot (see
Figure 8.3) lagged behind the guided one. Essentially, the guidance computer detected that the heading angle was below the required value, and therefore increased the bank angle to attain the correct heading at the termination of the numerical guidance phase.
8.6.2 Wind model
The next variation was to introduce wind in the virtual environment. The HWM wind model was used as described in Section 3.1.5 to introduce a South'Westerly wind. Note that the wind speed and direction varies as shown in Appendix D. It is referred to as a South Westerly wind as that is the direction from which the wind comes, at low altitudes. As before, the virtual environment used the MSISES3 atmosphere model and a 4th order approximation of the Earth's gravitation field. Guidance updates were performed every 5s.
The altitude plot shown in Figure 8.5 displays similar behaviour to the results shown in Figure
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 183
3
80 2.5
Open loop a 60 Lâ g Guided E v l¿ (¡ 1.5 à E o .E 40 q) 1>
20 0.5
0 0 0 100 200 300 400 500 0 100 200 300 400 500 l0
50 0 èo rt() òo (.) C) - è0 0g ðo -to I ¡d G' d È c) Ér èo -50 IJ- ' -20
100
-30 0 100 200 300 400 500 0 100 200 300 400 500 Time [s] Time [s]
Figure 8.5: Flight profrIe with South Westerþ wind
Commercial launch vehicle desiga and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 184
8.3, with two altitude "hltmps", one at around 200s and another between 300s and 350s. The velocity profile also shows similar behaviour to the previous result. The velocity plot shown in Figure 8.5 does have a shallower trough, at around 320s, than the one shown in Figure
8.3. The reason for this is that the virtual booster was experiencing a headwind in Figure 8.5
at the time of the velocity trough. This headwind caused more aerodynamic drag, thereby keeping the velocity lower than that for the no-wind case. The velocity actually dropped to a value of 222.5m/s at the base of the trough before climbing back up to the required value of
24Omf s. As the propulsion system was designed for cruise flight at 240mf s, the extra thrust required to maintain velocity during a slight ascent flight while experiencing a head wind was not available. Hence, the velocity dipped below the 240mf s value with the propulsion system running at maximum thrust.
The flight path angle plot in Figure 8.5 shows a clear difference between the open loop and guided profiles. The guided flight path angle profile shows a constant descent flight of -5' between 385s and 424s, which was controlled by the constant descent controller. Although the increased drag was tending to cause a steep descent flight, the numerical guidance system was able to increase the angle of attack. This increased angle of attack decreased the descent rate to an acceptable value for the constant descent controller. The open loop profile shows no constant descent phase. The reason for this is that the virtual booster arrived at an altitude of l2.4km with a steep flight path angle of -18'. The constant descent controller was then activated, which began to shallow the dive down to a -5" flight path angle. By the time the altitude controller was activated at 7lkm, the virtual booster still had a flight path angle of
-7o. The reason for this steep descent flight was the increased drag caused by the headwind. Although the headwind caused increased drag, it also caused increased lift. This is shown by the fact that the heading of -106' was almost achieved for the open loop case. The heading at an altitude of TZkmfor the open loop case was -105.5o, while that for the guided case was -107.3". The guided case has a slight error, caused by the increased angle of attack to compensate for the increased drag.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulús 185
This SW wind case shows how the numerical guidance strategy achieves a more balanced re-
sult than the open loop strategy. Although the open loop guidance strategy may have achieved
a satisfactory heading angle, caused by the increased lift, it suffered a steep descent caused by
the increased drag. The guided case, however, achieved both an acceptable descent rate and
heading angle.
4 0
-10 J Open loop à0 Guided CJ 6 € -20 3 å¿ O d .9 Þ òo fit 2 (+r -30 ã o c) È6 èo -40 Êa
1 -50
0 -60 350 360 370 380 390 400 410 0 100 200 300 400 Time [s] Time [s]
Figure 8.6: Steering model with SouthWesterly wind
The part of the angle of attack profile updated by the numerical guidance system is shown in
Figure 8.6. The guided angle of attack is seen to be higher between 350s and 370s, compared
to the open loop case. This was expected as the virtual booster was experiencing a steeper than
desired descent flight (see Figure 8.5). The guidance computer therefore responded correctly
by increasing the angle of attack. The undulations in the open loop angle of attack profile
between 390s and 400s were caused by overshoot during the altitude controller phase. The
guided profile shows a smooth line, indicating minimal controller effort. The guided and open
loop bank angle profiles do not show large differences, which is consistent with the fact that
both trajectories achieved a heading angle close to -106".
To properly test the guidance computer's petformance, the wind direction in the virtual envi-
ronment was reversed and the results analysed. The wind for the following section was thus in
a North Easterly direction. This wind direction refers only to the lower altitude wind.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 186
3
80 2.5
Open loop 60 2 ø E' Guided l¿ v tt; I .5 x a .E ¿o o C)
20 0.5
0 0 0 100 200 300 400 500 0 100 200 300 400 500 10
50 0 èo €() Òo (.) Þo 0g é èo -to É ! E ÈCd CÚt)
òo -50 tJ- -20
-100
-30 0 100 200 300 400 500 0 100 200 300 400 500 Time [s] Time [s]
Figure 8.7: Flight profrle withNoøh Easterly wind
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 187
The altitude profile in Figure 8.7 again shows similar behaviour for the open loop and guided trajectories. The altitude proflles were within 6Om of each other for most of the flight. Com- paring the velocity profile for the NE wind case (Figure 8.7) to that for the SW wind case
(Figure 8.5), it can be seen that the small trough in velocity around 300s was much shallower
for the NE wind case than for the S\ü/ wind case. The reason for this was that the NE wind resulted in a tailwind during this flight segment. The result was that the velocity remained relatively high as there was less drag. This also resulted in the velocity at the termination of
the numerical guidance being about 290mls for both the open loop and guided trajectories,
which is7.57o higher than desired.
The flight path angle profiles in Figure 8.7 show that in both the open loop and guided virtual
flights, no constant descent flight phase was experienced. This was due to the fact that both trajectories were steeper than the required - 10" flight path angle. The guided flight path angle was -14.1" at an altitude of 12km while the open loop flight path angle was -13.75'. The heading plot shows that although the open loop and guided trajectories had similar headings
for most of the flight, at about 325s the two diverged. The open loop heading was -98.2o at an altitude of l2km, while the guided trajectory had a heading of -104.2" at the same altitude. The guided case was closer to the required -106" heading.
This result shows that although the guided trajectory had a slightly steeper flight path angle at
an altitude of 12km, the heading was significantly better than that for the open loop trajectory.
Again, this shows that the open loop guidance strategy is capable of arriving close to the required conditions, but the numerical guidance method consistently achieves a better more balanced solution.
The angle of attack profiles in Figure 8.8 show similar profiles for the open loop and guided
virtual flights. This is consistent with the fact that they both ended with flight path angles of about -I4o. The guided bank angle plot shows an increase in bank angle, compared to the open loop case, between320s and 365s. This increased bank angle caused the virtual booster
to perform more of a turn manoeuvre, thereby attaining a significantly better heading result.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulfs 188
4 0
-10 3 Open loop òot) Guided = ! -tn 6) A( '"É ñO ão0 þal 2 +r -30 ã o J¿ (.) g G Òo -40 ca I -50
0 -60 350 360 370 380 390 400 4r0 0 100 200 300 400 Time [s] Time [s]
Figure 8.8: Steering model with North Easterly wind
8.6.3 State errors (sensor errors)
Up to this point, it has been assumed that the guidance computerreceived accurate information about current position and velocity. In a real application, this may not be the case as navigation suites typically produce measurement errors. To model these sensor etrors, random variations in the position and velocity states were added to the information given to the guidance com- puter. These errors were introduced using a random number between the values of -1 and
1. This number was multiplied by the maximum navigation error, shown in Table 8.1, and then added to the correct state information. An independent error was generated for each state at each guidance call, thereby producing near-random variations in the states required by the guidance computer.
State Targets Max. error Velocity 270mls 0.I52m s Flight path angle - 100 0.007' Altitude l2O0Om 9Im
Table 8.1: Maximum sensor enors (source document is commercially sensitive)
The flight path and control models were similar to those shown in Figure 8.5 and 8.6, indicating that the random sensor errors did not affect the virtual flight considerably. The conditions at
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resu.lús 189 the end of flight, given in Table 8.2, show that although the open loop heading angle was relatively good (0.5' error), the flight path angle was very steep (5.4' too steep). This resulted in the constant descent controller not being able to shallow the dive to -5" by an altitude of
I7km. The guided result, on the other hand, had a slightly larger heading error (1o), but was on the shallow side of the flight path angle target, thereby allowing a flight path angle of -5.35' at the activation of the constant altitude controller at ITkm altitude. The guidance computer was thus shown to be robust enough to handle simulated sensor effors.
State Targets Open loop Guided Flight path angle (12km) - 100 -r5.4" -5.4" Flight path angle (11km) -50 -7.6" -5.35" Heading - 106" -105.5' - 107' TabIe 8.2: Flight results for case with sensor errors
8.6.4 Guidance call intervals
The guidance interval refers to the time between successive guidance updates. Theoretically, the more frequently the guidance parameters are updated, the more accurate the end conditions will be. This is because the trajectory errors are given less time to propagate the smaller the guidance call intervals. As well as achieving more accurate end conditions, more frequent guidance calls will also reduce the magnitude of the steering forces, thereby reducing the re- quired steering effort. The computational loading is, however, increased with shorter guidance call intervals since more computer time is required to update the steering parameters. Thus, it is important to determine the required guidance interval to allow stable performance while at the same time not overloading the on-board computer.
In order to investigate suitable guidance call intervals, a number of virtual flights were per- formed using different guidance call intervals. The results were obtained using the MSISE 93 atmosphere and a IIWM wind model, which generated a South Westerly wind in the lower
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulús 190 altitudes of the virtual environment. Up until this point a guidance call interval of 5s has been used. Interval Heading error FPA error Velocity error ls -0.50 1.6" -lmls 2s -0.80 2.2" -lmls 5s - 1.00 4.7" -2mf s 7s -2.7" 6.6" -2mls Table 8.3: Performance with different guidance call intervals
All three target constraints are shown in Table 8.3 for completion, however, the only one that represents the numerical guidance system exclusively is the heading angle. The reason for this is that at an altitude of l2km, velocity and flight path angle controllers had already been activated. The constant descent controller had began shallowing the descent rate in an attempt to attain a -5" flight path angle, and the velocity controller had already been activated to maintain a cruise velocity of 240mf s. This means that the flight path angle and velocity are not directly relevant as they do not represent the numerical guidance system results alone, but instead include influences from the constant descent and velocity controllers. The heading results in Table 8.3 indicate that guidance intervals of 5s and below are sufficient to obtain an acceptable heading angle error of only 1o. As 5s is an acceptable guidance interval, it will continue to be used for the remainder of the study.
8.6.5 Random wind variations
Up until this point, all of the perturbations introduced into the virtual environment have been nominal models. That is to say that they modelled large scale, primary environmental param- eters such as wind and atmospheric density. This investigation will attempt to model short duration (1s) wind gusts. As was done for the ascent guidance system, random wind speed and direction variations were introduced into the virtual environment. The ascent guidance system operated at high altitudes where low atmospheric densities generated small aerody- namic forces. These forces were too small to cause significant trajectory modifications. In the
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 191 flyback case, however, the virtual booster operated at relatively low altitude, and was therefore expected to be more strongly affected by wind variations.
3
80 2.5
Open loop a 60 ? Guided Èl J¿ l¿ €() 1.5 à (.) .E ¿o o l> C)
20 0.5
0 0 100 200 300 400 500 0 100 200 300 400 l0
50 0 òo Ëc) òo c) () èo 0 Ë É èo I -to € cúÈ od i= ðo -50 t -2o
-100
-30 0 100 200 300 400 500 0 100 200 300 400 500 Time [s] Time [s]
Figure 8.9: Flight profile with rundom wind variation
The open loop flight profile shown in Figure 8.9 is similar to that for the no-wind case (Figure
8.3). There was a steep descent rate of -15.5o, with a heading angle of -101.2' at an altitude of I2km.In the guided flight profile, the flight path angle plot shows that there was no constant descent phase, which has been shown to be consistent with a steeper than required flight path angle at an altitude of l\km. The constant descent controller again only had time to shallow the dive before the altitude controller was activated. This is confirmed by the fact that the guided virtual booster had a flight path angle of -L2.2" before the constant descent controller
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulús 192 was activated, and a flight path angle of -6.4" when the constant altitude controller was acti- vated. At L2km altitude, the guided virtual booster had a heading of - 105.2', compared to the heading of -101.2' for the open loop case. 4 0
-10 3 Open loop aòo Guided 6 ! -20 € J¿() cË I !'ào ñt 2 çr -30 F J4 (,) F è¡) m -40
-50
-60 360 370 380 390 400 410 0 100 200 300 400 Time [s] Time [s]
Figure 8.10: Steering model with random wind variation
The steering model for the random wind case is shown in Figure 8.10. The bank angle profile is seen to be similar for the open loop and guided trajectories. The bank angle is set to zero at
367s flight time for the pull-up to level flight. The guided angle of attack is shown to be 0.25' higher than that for the open loop case, at 363s flight time. This was a result of the guidance computer commanding an increase in angle of attack as the descent flight was steeper than desired. The angle of attack profile was smooth until a flight time of 367 s, after which it began to undulate. The reason for this was that 367s was also the activation time for the constant descent controller.
The numerical guidance system used a forward propagation of the trajectory to determine the steering parameters. This means that the effects of the random wind were spread out over the whole of the remaining flight time. That is to say that when the guidance computer detected a target point error, it modified the parameters over the whole flight to achieve the desired cruise conditions. This "long" time frame over which the trajectory was modified had the effect of smoothing the trajectory out. The constant descent and altitude controller
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 193 flight phases, however, did not have a projection over the whole flight and therefore were required to command steering parameters, to account for the error in flight conditions, as soon as possible. This caused a scenario where a headwind caused the altitude to increase, the controller accounted for this by commanding a lower angle of attack. The next second, the virtual booster experienced a tailwind, causing it to descend, so the controller commanded a higher angle of attack. This resulted in the undulating command angle of attack as seen in
Figure 8.10.
The guided system is again seen to obtain a better result than the open loop case, showing the advantage of having a numerical guidance system. A further observation is that random wind effects seem to have less influence on the trajectory than constant wind effects. The steering parameter models, however, varied more between guidance calls as the wind was continually changing direction. During the controller flight phases, the control effort to maintain the de- sired flight conditions was considerably higher for the random wind case. This is shown by undulations in the angle of attack proflles during the constant descent and altitude controller flight phases.
8.6.6 Initial condition errors (staging point errors)
The robustness of the flyback guidance system was also tested against errors in the initial conditions. These initial condition errors modelled errors in the staging condition, which could occur if the vehicle flew off-course during the mated ascent phase (see Chapter 6). The virtual environment employed the FIWM wind model, the MSISES3 atmosphere model, a 4th order gravitation model and modelled sensor errors. Guidance updates were performed at 5s intervals. The starting point effors used were a staging altitude error of 300m, a flight path angle error of 1o and a staging velocity error of 65mls. Condition I represents all negative staging condition errors (low, slow and shallow ascent) while condition 2 represents all positive staging condition errors (high, fast and steep ascent) as shown in Table 8.4.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resuJfs 194
Staging condition Staging velocity Staging FPA Staging altitude Nominal 3000mls 100 62.8km
Condition 1 2935mls 90 62.5km Condition 2 3065mls 110 63.Ikm Table 8.4: Staging condition enors
Figure 8.11 shows the two different guided virtual flight profiles obtained from the two dif- ferent staging conditions. Condition 1 shows a maximum altitude 9kmbelow that obtained from staging condition 2. This caused significantly different trajectories to be flown from the two staging conditions. Because of the lower altitude attained from condition 1, a more dense virtual atmosphere was experienced by the virtual booster, causing more aerodynamic drag.
This is shown by the lag in velocity up until 230s flight time. The heading profiles show that the virtual booster that staged at condition 1 began a turn manoeuvre approximately 70s earlier than the one from condition 2. The flyback distance from condition 1 was750km while that from staging condition 2 was 876km. For comparison, the flyback distance from the nominal staging condition was 7 68km.
The low altitude and low velocity after staging allowed the optimiser to generate a trajectory with an earlier turning flight, while at the same time keeping the wing loading below the required value of 3.5g. This optimisation of the trajectory allowed the virtual booster to be
48km closer to the landing site than that for the nominal case. If an open loop guidance strategy (not shown) had been used, it would not have been able to take advantage of the situation by reducing its flyback distance. An open loop system would not have been able to account for the increased lift and would have ended up turning too far and heading more South than required. This would not only have resulted in increased fuel consumption during the flyback phase, but it may also have increased the wing loading and possibly caused mission failure. The numerical guidance computer was seen here to not only save fuel, by minimising the flyback distance, but may also have been necessary for mission success.
The steering parameters for the two staging condition effor cases are shown in Figure 8.12. As was shown in the flight profiles (Figure 8.11), from staging condition 1 the guidance computer
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 195
3
80 2.5
Condition I a 60 Condition 2 Ë E, J¿ Ë() 1.5 .b o .E ¿o o () 1>
20 0.5
0 0 0 100 200 300 400 500 0 100 200 300 400 500 10
50 0 oò0 ! èo o () 9p 0g èo ! -ro €É Cd o È 6) È òo -50 I! -20
100
-30 0 100 200 300 400 500 0 100 200 300 400 500 Time [s] Time [s]
Figure 8.11: Guided flight profrIe with initial condition errors
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulfs 196
4 0
-10 3 Condition I òo Condition 2 c) 6 ! -20 )1 € (!o !'èo (d 2 CH -30 F o J¿ o F òo É Ê -40
-50
0 -60 350 360 370 380 390 400 4rO 0 100 200 300 400 Time [s] Time [s] Figure 8.12: Steering model with initial condition enors commanded a steeper turn early in the flight. This is shown by a steeper bank angle command between 160s and 270s flight time. The angle of attack profiles are different for the numerical guidance phases, as shown by the different profile shape between 350s and 375s. This was caused by the different bank angle profiles and different trajectories flown up to that point. It is interesting to note, however, that the angle of attack commands meet at 375s and remain to- gether until flight termination. When considering the flight profiles (Figure 8.11), the velocity, altitude, heading and flight path angle are all almost equivalent at a flight time of 375s. This shows that although the trajectories flown were considerably different, they both arrived at the numerical guidance termination altitude with the required flight conditions.
8.6.7 Monte Carlo analysis
One thousand missions were simulated with random variations in the staging condition, to ensure robust operation of the guidance computer. The virtual environment employed the
MSISE93 atmosphere model and the HWM wind model as nominal models. The nominal wind direction was South'Westerly, but was randomly varied in both speed and direction. Ran- dom variations in the states given to the guidance computer were also introduced to simulate
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulús 197 navigation enors. The random variations were produced by multiplying a random number between -1 and 1 by the maximum allowable variations, which are shown in Table 8.5. The performance of the simulation runs with respect to each target constraint violation will now be analysed independently.
Parameter Upper error bound Lower error bound Staging flight path angle 1.00 - 1.00 Staging altitude 300m -3O0m Staging velocity 65mls -65mls Altitude sensor error 97m -9lm Flight path angle sensor error 0.07' -0.07" Velocity sensor effor 0.152m1s -O.752mls Wind speed variation TOOVo -I00Vo Table 8.5: Maximum vañation bounds for Monte Carlo analysis
Figure 8.13 shows the f,nal heading for the 1000 virtual missions with the afore mentioned random perturbations. The results show good performance by the guidance computer in every case. The target heading was -106o. The median achieved value was -105.43", with a standard deviation of 0.2875". The final flight path angles for the virtual flyback missions are shown in Figure 8.14. The target value was -10". The median achieved value was -11.49o and the standard deviation 0.679". Figure 8.15 shows the final velocity for the 1000 virtual missions. The target value was 270mfs. The median achieved value was 266.3m/s and the standard deviation I.283ml s.
For completion, another smaller Monte Carlo simulation was performed using a North East- erly wind as the nominal wind direction. This was done to ensure that the small differences between the achieved values and the required target values were not caused by the nominal wind direction. This analysis also further extended the robustness analysis. The median values were similar to those shown above, with a heading of - 105.667 , aflightpath angle of - 11.51' and a velocity of 265.78m1s. The standard deviations were 0.31667" for heading, 0.7055o for flight path angle and I .2825m f s for velocity. The graphs of the Monte Carlo simulations using a nominal North Easterly wind are shown in Appendix F by Figures F.I,F.2 and F.3.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance resulfs 198
-96 . Heading atl2.4kmaltitude . Heading at 12km altitude -98 Target heading - -100 Òo Ë(,) èo -r02 € o r{ -t04
-106
-108
1 2N 400 600 800 1000 Run number
Figure 8.13: Monte Carlo result for frnal heading
0
. Flight path angle at lz.4krn altitude -5 . Flight path angle at l2km altitude Target flight path angle - bo € -10 c) èo I -rs g(d
.90 -20 t¡{
-25
2oo ool.un nu-o"foo 8oo 1000 Figure 8.14: Monte Carlo result for flight path angle
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.6. Flyback guidance ¡esulfs 199
280
. Velocity at l2.4kmaltitude . Velocity at 12km altitude Target velocity 275 -
E .â zto o o o
265
200 400 600 800 1000 Run number
Figure 8.15: Monte Carlo result for velocity
An interesting observation can be made when looking at the flight path angle and velocity
Monte Carlo plots. The flight path angle and velocity data sets for both wind directions @g- ures 8.14, F.2, 8.15 and F.3) show that, in most cases, the flight path angle at I2km altitude is steeper than the target value, and the velocity at l2km altitude is slightly below the target value. The reason for this cannot be the nominal wind direction, as the two data sets have opposite nominal wind directions. It is due instead to the switch from the numerical guidance system to the constant descent controller, at an altitude of l2.4km.
As the constant descent controller was attempting to achieve a -5o flight path angle, while the numerical guidance system was aiming for a -10' flight path angle, the expected result was to have flight path angles that were shallower than - 10o, at l2km altitude. This is not the result shown by this analysis. Instead, the median flight path angle value at an altitude of I2km was -1I.49". This was caused by the low gains used in the constant descent controller. From Equation 4.17 it can be seen that during the constant descent phase the angle of attack was incrementally changed, based on the flight path angle and the rate of change of the flight path angle. By increasing the controller gains, the angle of attack would have been incremented by larger amounts at a time, thereby shallowing the descent flight faster; however, these high gains
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.7. Summary and discussion 200 were found to cause erratic behaviour for the case when the virtual vehicle was experiencing a constant South'Westerly wind (Figure 8.5).
If the numerical guidance computer had continued to provide angle of attack command, instead of switching to a constant descent controller, it would have commanded the angle of attack to increase faster than the current constant descent controller did, thereby shallowing the descent.
However, the use of the constant descent controller was necessary, as discussed in Section 4.4, to prevent the trajectory reaching a zero flight path angle above an altitude of 13.5km, which could occur under certain environmental conditions.
Although the median flight path angle was nearly 1 .5o steeper than the desired - 10o, this value is stillrelatively shallow when compared to the Space Shuttle, which activates its approach and landing guidance system with a flight path angle of between -19o and -77" at an altitude of 10000/r (NASA,2OO2).
The median velocity at72km altitude was shown to be 3.7mf s below the target value of
270mf s; this was caused by the differences between the MSISE93 and the US Standard at- mosphere models close to the termination altitude. Specif,cally, the atmospheric density was slightly higher (0.357o) in the virtual environment (MSISE93) than in the guidance computer
(US Standard atmosphere), resulting in more drag in the virtual environment. This caused the virtual vehicle's velocity to decrease faster than the guidance computer expected it to. A1- though there was a propulsion system available, it was only required to maintain a velocity of
24omf s, and so would not have been activated to achieve the exact target velocity of 270mf s at an altitude of 72km.
8.7 Summary and discussion
In summary, the numerical guidance computer was found to be well suited to a booster flyback phase. The guidance system in its current form can thus be considered adequate for use during
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8"7. Summary and discussion 201
a flyback mission. Using a 5s guidance call interval, it was shown to be robust to environmental factors, such as wind and different atmosphere models. The guidance computer was also found to be capable of accounting for variations in staging conditions as well as effors associated with position and velocity measurement.
Altitude was found to be a good stopping condition for the integration routine provided the descent rate was relatively steep. A flight path angle of -10' was found to allow stable op- timisation untiI2Û0m above the termination altitude of l2km. With regard to the stopping condition, the"humps" in the altitude profile were found to be problematic for the restoration technique when they occurred close to the termination altitude. The reason for this was that they caused the flight path angle to shallow well below the -10" value. To prevent this from occurring, a switch had to be implemented in the guidance computer to switch to the constant descent controller if one of these "humps" occurred close to (up to l0Û0m above) the termina- tion altitude. The initial parameter set from the optimisation routine was found to be capable of eliminating these "humps", however, during the real-time guidance phase, they were found to be difficult to avoid.
The constant descent and altitude controllers were found to be robust enough to attain the re- quired flight conditions even when the conditions at the termination of the numerical guidance were far from the nominal value. The controllers were even found to be capable of achieving cruise conditions from a flight path angle of - 18o, which is 807o below the target value. Flight path angles above the required -10" were easily accounted for by activation of the constant descent controller.
The use of a Newtonian gravitation model in the guidance computer was shown to be a source of errors in the trajectory prediction. If sufficient computation power were available in the guidance computer, it is recommended that a better approximation of the Earth's gravitation field be the first modification implemented to the present guidance system.
Wind in a constant direction, i.e. NE or SW, was found to influence the trajectory more than
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 8.7. Summary and discussion 202 randomly varied wind. This was shown by the fact that both NE and SW wind cases produced errors in the guided flight target conditions. The random wind effects, however, produced errors very close to the no-wind case. This indicates that it would be valuable to have infor- mation about the primary wind speed and direction when performing guidance computations.
In order to improve the target accuracy of the guidance system, it may be useful to provide the guidance computer with primary wind information.
The altitude and constant descent controllers were found to be able to achieve the required cruise conditions without any steering command undulations when experiencing a constant wind force. Random wind, however, was shown to cause undulations in the angle of attack prof,le as the controller tried to maintain level flight.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Chapter 9
Conclusions
9.1 Vehicle design
The development of a fully reusable vehicle delivering an economical, reliable service to space should be able to capture a large portion of the commercial payload market. The literature strongly suggests that the key to cost reduction in the space market is vehicle reusability. For a vehicle to be a viable venture for a commercial launch company, the development costs as well as the operational costs need to be kept to a minimum. The use of proven and available technology would thus be suggested. A two stage LOXlkerosene propelled vehicle therefore seems to be well suited to commercial application. For the vehicle to be fully reusable, all of the stages need to be recovered. Recovering both the orbiter and the booster at the launch site would also reduce the turn-around time.
Recovering the booster at the launch site can be achieved using either rocket propulsion, wings
and air-breathing propulsion or wings alone. The use of wings would firstly allow the vehicle to use aerodynamic forces to support its weight during atmospheric flight, and would also allow it to land horizontally at the launch site. An aerodynamic horizontal landing would remove the requirement for rocket propulsion during landing, which requires large amounts of propellant.
203 9.2. Guidance 204
The use of wings and air-breathing engines on the booster would allow an aerodynamic flyback and an aerodynamic horizontal landing, as well as allowing staging to be performed at high velocities (above Mach 10), which were shown to support higher payload capabilities (Rahn and Schoettle, 7996) and (Tetlow et al., 2000).
The aim of the vehicle design investigation was thereþre to compare the payload capabilities of two winged launchvehicle concepts, one using air-breathing engines to perform a powered booster returnto launch siteflight, and one employing only aerodynamic glideforces, thereþre returning unpowered. The two concept vehicles were TSTO, LOX/kerosene propelled, and had wings on both the boosters and orbiters.
The vehicle concept employing a powered booster return flight was found to be capable of delivering 5OVo (Ttonnes) more payload to LEO than the one employing an unpowered booster flyback. There would be additional costs and complexity with the powered booster due to the inclusion of air-breathing engines, however, it is believed that these would be compensated for by the significantly improved payload capability.
9.2 Guidance
Current launch vehicles use both open-loop and closed-loop guidance strategies during ascent and re-entry (McHenry et al., 1919). Both guidance strategies require considerable pre-flight analysis and atmospheric measurement prior to flight, at a cost of up to l27o of the launch cost
(Bordano et a1., 1991). Reducing the pre-flight trajectory analysis time, using an on-line, pre- dictive guidance strategy could therefore, reduce the launch costs signiflcantly. Most current closed-loop ascent guidance systems do not model aerodynamic forces, so are not suitable for an atmospheric flight phase. This simplification can also result in a sub-optimal solution to the guidance problem. Although numerical methods are perceived to be less robust than analytic methods, they do have the advantage of being able to include any number of environmental pa- rameters when determining steering commands. The gap in existing technology thus seemed
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 9.2. Guidance 205 to be that there was no closed-loop guidance system that did not require extensive pre-flight analysis. There was also no operational closed-loop guidance system capable of guiding a booster and an orbiter during their atmospheric flight phases.
The aim of this section was thus to develop a robust numerical guidance strategy that could be used during both atmospheric and exo-atmospheric flight phases. A robustness analysis was also perþrmed to ensure that the guidance system could operate under non-nominal environ' mental conditions.
9.2.1 Ascent guidance
The numerical guidance system developed in this study was found to be well suited to an upper stage ascent mission. During the atmospheric flight phase, the guidance system was shown to be robust to environmental factors, such as wind and atmospheric density variations. Both nominal and randomly perturbed environmental models were considered, with wind variations found to have agreater influence on trajectory shaping than atmospheric density. The guidance system was found to be capable of accounting for variations in staging conditions as well as effors associated with position and velocity measurement (modelled sensor errors).
The attitude controller conceived was found to perform acceptably and was able to track the commanded attitude with a small time delay (below 1s). There was a slight steady state effor in angle of attack of around 0.08o, due to the controller design. The steady state error and
time delay both served as a further robustness test for the guidance computer. Clearly, for
a real application, this controller would have to be refined to achieve acceptable operational performance.
The guidance system produced stable steering parameter updates until around 8s before the
target conditions. It is therefore suggested that the guidance updates be used until approxi-
mately 8s before the end of flight, followed by an open loop flight phase. Guidance update
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 9.2. Guidance 206 intervals during the virtual flight of 10s or less were found to produce accurate orbit insertion points, with a slight decrease in orbit accuracy with increased guidance call intervals. The use of more than five parameters in a grid type steering parameter model was shown not to improve the orbit insertion points signiflcantly.
9.2.2 Flyback guidance
The numerical guidance computer was found to be well suited to a booster flyback phase.
Using a 5s guidance call interval, it was shown to be robust to environmental factors, such as wind and atmospheric density variations. The guidance computer was also found to be capable of accounting for variations in staging conditions as well as errors associated with position and velocity measurement (modelled sensor errors).
Altitude was found to be a good stopping condition for the integration routine, provided the descent rate was relatively steep. A flight path angle of -10o was found to allow stable op- timisation until2O0m above the termination altitude of 72km. With respect to the stopping condition, the local minima (previously referred to as "humps" ) in the altitude profile were found to be problematic for the restoration technique, when they occurred close to the termina- tion altitude. To prevent instabilities, a switch had to be implemented in the guidance computer to switch to a constant descent controller if one of these local minima occurred close to (up to
IOOOw above) the termination altitude.
The constant descent and altitude controllers were found to be robust enough to attain the re- quired flight conditions, even when the conditions at the termination of the numerical guidance were far from the nominal value. The controllers were even found to be capable of achieving cruise conditions from a flight path angle of - 18', which is 807o below the target value. Flight path angles above the required - 10' were easily accounted for by early activation of the con- stant descent controller.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 9.3. Recommendations 207
9.3 Recommendations
The concept vehicle employing air-breathing engines on the booster was shown to perform
better than the concept vehicle employing an unpowered booster. It is therefore optimal to
employ air-breathing engines on the booster of a launch vehicle similar to the one discussed in
the present study.
Although the guidance system was found to operate successfully in its current state, if ex-
cess computational power were available, two improvements could be implemented. Firstly,
it would be worthwhile implementing a higher order gravitation model in the guidance com- puter, as it would produce a more accurate prediction of the expected final orbit conditions.
The second would be to implement a nominal wind model in the guidance computer, as the constant headwind and tailwind cases were shown to create large target point errors. Current computational power may not be adequate for these changes to be implemented on current systems, but with future improvements, they may become a possibility.
9.4 Closing Remarks
A useful comparison was performed between powered and unpowered flyback boosters, show- ing the relative performance of each flyback strategy. A robust guidance system was also devel- oped for both orbiter ascent and booster flyback missions. The objectives of this investigation were thus satisf,ed, providing conclusive results.
The development of this guidance system will continue at the IRS in Stuttgart, Germany, as it has been proposed for use on future reusable launch vehicles investigated in the German technology program Astra.
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix A
Woomera weather
The following data was compiledby Bruce Brooks at the Bureau of Meteorology in Adelaide.
The data shown is for the months January, April, July and October. These months were chosen
to show a brief trend in the wind speeds, and do not show either the best or worst case scenarios.
Different launch systems are affected differently by winds at different altitudes, as they fly
different trajectories. For this reason it was diffrcult to determine which was the worst or best
case scenaflo.
There are two plots shown on each graph. The solid line shows the average wind speeds in
mf s for data taken over the last 10 years. The dashed line shows the 90 percentile data. That
is to say that907o of the time, the wind is below the values shown in the plot.
208 209
20 20
January April 5 15
E Eli å o €ro 0 !5 â .E .E Avefage 5 ---- 90percentile 5
0 0 0 l0 20 30 40 50 0102030405060
20 20
July October l5 l5 E' ti l/ ,v l0€ ãtoã E E
5 5
0 20 40 60 80 0 l0 20 30 40 50 60 Wind speed [m/s] Wind speed [m/s]
Figure A. 1 : Wind data for Woomera (B OM- Adelaide, 2002)
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix B
US Standard atmosphere model
210 211
(ô cì
l.)= otr\:, bo
! >t .À 'óc) (-) 'F ¡() (t)À o t.)É
\ô cì O
o ra¡ \a¡oloo\a¡o \a¡ $t o cO cA C'ì C'ì Ê Ê [uq] epruptV
Figure 8.1: US Standard atmospheric density profrIe
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix C
MSISE93 atmosphere model
212 213
cìu-l
I vv , (rìocooo >\ 'i>r '-{>' âââcdcg((l I I I
lr¡= oEri' èo v! È. ct) Ëo) o 'tr ci¡
¡t)È o o<
(
lcñ cì o
\ôo\n \n o S=fca 3KR!3 lurìl epnlpv
Figure C..l: MSISES3 atmospheñc density prcfrIe
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix I)
HWM wind model
100
80
TE60 Ec) Þ '- - Day 180 '.= Day20 ----- Day 130
20
0 t8 -16 -r4 -r2 -10 -8 -6 -4 -2 0 246 Southerly wind speed [m/s]
Figure D.1: IIWM SoutherlY winds
214 215
100
80
Dayz0 E' eo Èl ---- Day 130 o) -.- Day 180 E 'Ë
20
-40 -20 0 20 40 60 Westerly wind sPeed [m/s]
Figure D.2: IIWM Westerly winds
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix E
Aerodynamic coefficient reference table
216 217
10 Nunìlcer of angl-e of attack velues 22 Number of Mach number val-ues 1 Number of bank angle values
Ma 0.00 beta : 0.0
AIId_ -20.00 Cl : -1 .361 cd: 0.438 Cs: 0.00000 Al-fa: -10.00 CI: -0.633 Cd: 0.097 Cs: 0.00000 Al-f a: -s.00 -0 .299 cd: 0.031 Cs: 0.00000 AIfa: 0.00 C1 : 0.000 Cd: 0.017 Cs: 0.00000 Al-f a: s.00 Cl = 0 .290 cd: 0.030 0.00000 AIId_ 10.00 CI: 0.597 cd: 0.087 Cs: 0.00000 AIfa: 20.00 c1 L.2I8 cd: 0.353 Cs: 0.00000 Al-fa: 30.00 c1 1.809 cd: 0.762 Cs: 0.00000 Affa: 40.00 cl 2.292 Cd: 1.331 Cs: 0.00000 Al-f a: s0.00 c1 2.58't cd: r.123 0.00000
Ma 0.30 beta : 0. 0
åfrd- -20.00 c1 -1 .37 B cd: 0.460 Cs 0.00000 Alfa: -10.00 CI -0 .642 Cd: 0.r02 0.00000 Alfa: -5.00 CI -0.304 cd: 0.032 0.00000 AIfa: 0.00 c1 0.000 cd: 0.017 Cs 0.00000 AIfa: s.00 c1 0 .295 Cd: 0.031 Cs 0.00000 Alfa: 10.00 CI 0.606 Cd: 0.092 Cs 0.00000 Alfa: 20.00 cl L.236 Cd: 0.373 Cs 0.00000 Alfa= 30.00 cl 1.834 cd: 0. 804 0.00000 Al-fa: 40.00 c1 2.325 cd: r.422 0.00000 Al-f a: 50.00 C1 2 .626 Cd: 1.861 Cs 0.00000
Ma 0.50 beta : 0. 0 Alfa: -20.00 CI: -r.4r2 cd: 0.489 0.00000 Alfa: -10.00 CI: -0.660 cd: 0.109 0.00000 Al-f a: -5.00 cl_ : -0.313 Cd: 0.033 Cs: 0.00000 Al-f a: 0.00 cl_ : 0.000 cd: 0.017 Cs: 0.00000 AIfa: s.00 cl: 0.304 cd: 0 .032 0.00000 AI!d_ 10.00 CI: 0 .623 Cd: 0.099 0.00000 ATId_ 20.00 CI: 7.21 0 Cd: 0.400 Cs: 0.00000 Al-f a: 30.00 ct: 1. BB4 cd: 0.860 0.00000 Al-fa: 40.00 cl : 2.390 Cd: 1.543 Cs: 0.00000 Alfa: 50.00 cl_ : 2 .103 cd: 2.008 Cs= 0.00000
Ma 0.60 beta : 0.0 Al-f a: -20.00 c1 : -r .439 cd: 0.511 Cs 0.00000 Alfa: -10.00 C]: -0.673 Cd: 0.114 0.00000 Ár!d- -5.00 CI: -0.319 Cd: 0.034 Cs 0.00000 Alfa: 0.00 cl : 0.000 cd: 0.017 Cs 0.00000 Alfa: s.00 cl_ : 0.310 0.033 0.00000 Al-fa: t-0.00 Cl : 0 .63'7 Cd: 0.103 0.00000 Al-f a: 20.00 Cl : r.29't Cd: 0 .420 Cs 0.00000 AIfa: 30.00 Cl : r.924 cd: 0.900 Cs 0.00000 Alfa: 40.00 CI: 2 .44r cd: I.627 0.00000 Alfa: s0.00 CI: 2 .163 cd: 2 .099 0.00000
Figure 8.1: Aerodynamic coeffrcient reference table
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow Appendix F
Flyback-Monte Carlo (NE nom. wind)
-100
-101 Target heading - -toz
-103
oào -104 ! 00 -105 Ë(! o -106 Éi -ro7
-108
-109
1 zffi 400 600 800 1000 Run number
Figure F.1: Monte Carlo result for heading
218 219
-6
Targetfpa -8 -
òo € -10 +: o I Òo É d -1, (Ë Ê s -14 t¡i
T6
1 200 400 600 800 1000 Run number
Figure F.2: Monte Carlo rcsult for flight path angle
280
278 Target velocity 276 - 274 272 270 È, 268 () t o 266 c) t 2& I I 262 260 258 256 0 200 400 600 800 1000 Run number
Figure F.3: Monte Carlo result for velocity
Commercial launch vehicle design and predictive guidance development Matthew R. Tetlow 220
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