AlAA Space 2003 Conference and Exposition AIAA2003-6370 Long Beach,CA,Sept.23-25,2003. UNDERSTANDING THE ORBITAL TRANSFER VEHICLE TRADE SPACE Hugh L.McManus Metis Design,46 Second St.,Cambridge,MA 02140 and Todd E.Schuman Massachusetts Institute of Technology,Cambridge MA 02139 ABSTRACT INTRODUCTION This study uses new methods to explore the theoretical An orbital transfer vehicle,or"space tug,"is one performance of over a hundred possible orbital transfer instance of a broad class of vehicles that can perform a vehicle designs.The designs have varying propulsion variety of on-orbit servicing functions.The simplest types,fuel mass fractions,and grappling/observation function of such a vehicle would be to observe space equipment capabilities.Simple sizing rules are used to assets,hereafter referred to as targets,in situ.The calculate the performance of the designs and their targets may be cooperative (designed for servicing) utility to several types of users.Designs of interest are partially cooperative(e.g.maneuverable in ways further explored using Integrated Concurrent helpful to the tug),uncooperative (inert),or even Engineering techniques,resulting in complete hostile.The later case covers spinning or tumbling conceptual designs.The results give an understanding vehicles that would be hazardous to approach.A tug of the trade-space for such vehicles,including changes the orbits of these targets for operational sensitivities to both design variables and assumed user reasons(e.g.life extension),to retrieve the targets needs.This clarifies some of the challenges involved bringing them out of orbit or to other assets(e.g.Shuttle such as physical constraints and sensitivities to or ISS),or to eliminate debris.Similar vehicles may uncertain user preferences.Several potentially viable interact or service targets in a variety of other ways. designs are identified including an electric-propulsion The ability to interact with objects in space is a high delta-V vehicle dubbed the Electric Cruiser,and a desirable capability,but clearly the range of possible class of lower delta-V vehicles dubbed Tenders which approaches is large,and it has proven difficult to design are studied in a companion paper viable tug systems. NOMENCLATURE The concept of tug vehicles goes back to the early years of the space program.A literature review is included in C Cost ($ a companion paper.'Here,we will only note that Cd Dry mass cost coefficient($/kg) hypothetical tugs designed for a single mission rarely Cw Wet mass cost coefficient(S/kg) show an economic pay-off,although there is some Isp Specific impulse (sec) evidence that if an infrastructure for on-orbit service Acceleration due to gravity (9.8 m/sec could be created it would have positive value.The Bus mass(kg) concept in practice is made difficult by unfriendly mbf Bus mass fraction coefficient orbital dynamics (many desired maneuvers are M Mass of observation/manipulator system (kg) extremely energy-intensive),environments (the vehicle M Dry mass (kg) must be radiation hard,and/or hard against some level M Fuel mass (kg) of debris damage,to last useful lifetimes in many Mp Mass of propulsion system(kg) orbits).and economics (markets are uncertain,and mipo Propulsion system base mass(kg) payoff is difficult to prove).Some missions require Propulsion system mass fraction coefficient nuclear or other advanced propulsion systems,and most M Wet mass (kg) require advances in control systems and docking or Total utility grappling hardware. Single attribute utility for capability Single attribute utility for response time In this work,new space system architecture and Single attribute utility for delta-V conceptual design techniques have been applied to the Utility weighting for capability tug problem.A capability referred to as Multi-Attribute Utility weighting for response time Tradespace Exploration (MATE)with Concurrent W Utility weighting for delta-V Engineering(MATE-CON)was used.MATE is a Change in velocity (m/sec) method for examining many design concepts to Senior Special Projects Engineer,Associate Fellow AlAA Graduate Research Assistant.Department of Aeronautics and Astronautics Copyright 2003 by Hugh L McManus.Published by the American Institute of Aeronautics and Astronautics,Inc.with permission. American Institute of Aeronautics and Astronautics
AIAA Space 2003 Conference and Exposition Long Beach, CA, Sept. 23-25, 2003. AIAA 2003-6370 1 American Institute of Aeronautics and Astronautics UNDERSTANDING THE ORBITAL TRANSFER VEHICLE TRADE SPACE Hugh L. McManus* Metis Design, 46 Second St., Cambridge, MA 02140 and Todd E. Schuman† Massachusetts Institute of Technology, Cambridge MA 02139 * Senior Special Projects Engineer, Associate Fellow AIAA † Graduate Research Assistant, Department of Aeronautics and Astronautics Copyright © 2003 by Hugh L. McManus. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. ABSTRACT This study uses new methods to explore the theoretical performance of over a hundred possible orbital transfer vehicle designs. The designs have varying propulsion types, fuel mass fractions, and grappling/observation equipment capabilities. Simple sizing rules are used to calculate the performance of the designs and their utility to several types of users. Designs of interest are further explored using Integrated Concurrent Engineering techniques, resulting in complete conceptual designs. The results give an understanding of the trade-space for such vehicles, including sensitivities to both design variables and assumed user needs. This clarifies some of the challenges involved such as physical constraints and sensitivities to uncertain user preferences. Several potentially viable designs are identified including an electric-propulsion high delta-V vehicle dubbed the Electric Cruiser, and a class of lower delta-V vehicles dubbed Tenders which are studied in a companion paper. NOMENCLATURE C Cost ($) cd Dry mass cost coefficient ($/kg) cw Wet mass cost coefficient ($/kg) Isp Specific impulse (sec) g Acceleration due to gravity (9.8 m/sec2 ) Mb Bus mass (kg) mbf Bus mass fraction coefficient Mc Mass of observation/manipulator system (kg) Md Dry mass (kg) Mf Fuel mass (kg) Mp Mass of propulsion system (kg) mp0 Propulsion system base mass (kg) mpf Propulsion system mass fraction coefficient Mw Wet mass (kg) Utot Total utility Vc Single attribute utility for capability Vt Single attribute utility for response time Vv Single attribute utility for delta-V Wc Utility weighting for capability Wt Utility weighting for response time Wv Utility weighting for delta-V Dv Change in velocity (m/sec) INTRODUCTION An orbital transfer vehicle, or “space tug,” is one instance of a broad class of vehicles that can perform a variety of on-orbit servicing functions. The simplest function of such a vehicle would be to observe space assets, hereafter referred to as targets, in situ. The targets may be cooperative (designed for servicing), partially cooperative (e.g. maneuverable in ways helpful to the tug), uncooperative (inert), or even hostile. The later case covers spinning or tumbling vehicles that would be hazardous to approach. A tug changes the orbits of these targets for operational reasons (e.g. life extension), to retrieve the targets, bringing them out of orbit or to other assets (e.g. Shuttle or ISS), or to eliminate debris. Similar vehicles may interact or service targets in a variety of other ways. The ability to interact with objects in space is a desirable capability, but clearly the range of possible approaches is large, and it has proven difficult to design viable tug systems. The concept of tug vehicles goes back to the early years of the space program. A literature review is included in a companion paper.1 Here, we will only note that hypothetical tugs designed for a single mission rarely show an economic pay-off, although there is some evidence that if an infrastructure for on-orbit service could be created it would have positive value.2 The concept in practice is made difficult by unfriendly orbital dynamics (many desired maneuvers are extremely energy-intensive), environments (the vehicle must be radiation hard, and/or hard against some level of debris damage, to last useful lifetimes in many orbits), and economics (markets are uncertain, and payoff is difficult to prove). Some missions require nuclear or other advanced propulsion systems, and most require advances in control systems and docking or grappling hardware. In this work, new space system architecture and conceptual design techniques have been applied to the tug problem. A capability referred to as Multi-Attribute Tradespace Exploration (MATE) with Concurrent Engineering (MATE-CON) was used. MATE is a method for examining many design concepts to
understand the possibilities and problems of the space her need,and/or the designer's perception of the of possible solutions-the tradespace.3 It was appropriate design space,resulting in a need to repeat developed at MIT from earlier work on information the analysis.The semi-automated nature of the systems analysis applied to space systems.Integrated computations allows this valuable exploitation of Concurrent Engineering (the CON in MATE-CON,but emergent understanding with little cost or time penalty. usually referred to on its own as ICE)is a method for Eventually,a design or designs from the trade space are rapidly producing preliminary designs in a "design selected for further consideration. room"environment.The system used in this study descends from work at JPL and the Aerospace In this study.a somewhat simplified version of the Corporation,by way of Caltech.'The overall MATE- MATE method was used.The method was adapted in CON system,along with other front-end design tools, response to difficulties including the lack of an was developed by a consortium of MIT,Caltech,and immediate customer and a very open design space.The Stanford.8 customer utilities were handled parametrically to understand the sensitivities of the tradespace to ranges Using MATE,several hundred possible space tug of,and changes in,user needs.The analysis was done vehicles are evaluated for their ability to move mass in at a high level,using low-fidelity models,but covering orbit and interact with targets.The resulting tradespace a large range of possible designs. is examined to clarify some of the fundamental difficulties with the space tug concept,understand the Attributes and Utilities sensitivities of the tradespace to uncertainties in users The capabilities of a space tug vehicle determined to be needs,identify the Pareto front of"good designs,and useful to a potential user include:(1)total delta-V find some design points that are promising for multi- capability,which determines where the spacetug can go purpose tugs.ICE is then used to create ten conceptual and how far it can change the orbits of target vehicles: designs for a range of hypothetical mission scenarios (2)mass of observation and manipulation equipment The ICE designs lend credibility to the crude MATE (and possibly spare parts,etc.)carried,which models,further clarify design issues,and provide a determines at a high level what it can do to interact with starting point for further development of missions of targets,referred to here as its capability,and (3) interest. response time,or how fast it can get to a potential target and interact with it in the desired way.Note that the This paper covers the MATE and ICE models created design of observation and manipulation equipment and to do the analyses.the MATE tradespace and its its corresponding software is outside the scope of this interpretation,and the conceptual design of four tug study-the equipment is treated as a"black box"with vehicles for a mission involving the rescue of a mass and power requirements Geosynchronous Earth Orbit(GEO)satellite stranded in a transfer orbit by the failure of its apogee motor.A These attributes are translated into a single utility companion paper looks at a variety of specific missions, function.In the absence of real users from which to suggested originally by this tradespace analysis,that collect more sophisticated functions,"it was decided concentrate on servicing groups of satellites in similar that a simple function that could be explored orbits. parametrically was most appropriate.The three attributes are assigned single-attribute utilities.These MATE METHOD are dimensionless metrics of user satisfaction from zero (minimal user need satisfied)to one (fully satisfied In MATE.user needs are defined in terms of the user).The utilities are combined as a weighted sum system's attributes,or capabilities of the desired system,rather than the characteristics of the desired The delta-V utility is shown in Fig.1.Delta-V is a space vehicle.These needs are expressed and continuous attribute calculated for each system quantified in utility metrics,often through the use of considered.Utility is assumed to increase linearly with Multi-Attribute Utility Theory.Then a design vector is delta-V.with diminishing returns above the levels selected,consisting of a very large number (hundreds to necessary to do Low Earth Orbit(LEO)to GEO hundreds of thousands)of possible systems that could transfers.Variations on this utility are shown in Figs.2 be used to meet the user needs.Simulation models are and 3,which show respectively the utilities of a GEO- used to calculate the attributes of the proposed systems centric user(large steps in utility for achieving GEO The systems are then evaluated against the users and GEO round-trip capabilities)and a delta-V-hungry utilities to understand which systems best satisfy the user(continued linear utility for very high delta-V). users'needs.The results,collectively referred to as the The manipulator mass(capability)attribute has discrete tradespace,can then be explored.This process consists values,assumed to correspond to increasing utility as of the search for not only optimal solutions,but also fo shown in Table 1.The response time of a real system understanding of design sensitivities,key trade-offs. would be a complex function of many factors;at the dangerous uncertainties,and vulnerabilities to changes level of the current analysis it is reduced to a binary in the market or national policy.Often these attribute /valued at one for high impulse systems,and understandings will change a user's perception of his or zero for low impulse ones. 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2 American Institute of Aeronautics and Astronautics understand the possibilities and problems of the space of possible solutions – the tradespace.3 It was developed at MIT from earlier work on information systems analysis applied to space systems.4 Integrated Concurrent Engineering (the CON in MATE-CON, but usually referred to on its own as ICE) is a method for rapidly producing preliminary designs in a “design room” environment. The system used in this study descends from work at JPL5 and the Aerospace Corporation,6 by way of Caltech.7 The overall MATECON system, along with other front-end design tools, was developed by a consortium of MIT, Caltech, and Stanford.8 Using MATE, several hundred possible space tug vehicles are evaluated for their ability to move mass in orbit and interact with targets. The resulting tradespace is examined to clarify some of the fundamental difficulties with the space tug concept, understand the sensitivities of the tradespace to uncertainties in users needs, identify the Pareto front of “good” designs, and find some design points that are promising for multipurpose tugs. ICE is then used to create ten conceptual designs for a range of hypothetical mission scenarios. The ICE designs lend credibility to the crude MATE models, further clarify design issues, and provide a starting point for further development of missions of interest. This paper covers the MATE and ICE models created to do the analyses, the MATE tradespace and its interpretation, and the conceptual design of four tug vehicles for a mission involving the rescue of a Geosynchronous Earth Orbit (GEO) satellite stranded in a transfer orbit by the failure of its apogee motor. A companion paper looks at a variety of specific missions, suggested originally by this tradespace analysis, that concentrate on servicing groups of satellites in similar orbits. MATE METHOD In MATE, user needs are defined in terms of the system’s attributes, or capabilities of the desired system, rather than the characteristics of the desired space vehicle. These needs are expressed and quantified in utility metrics, often through the use of Multi-Attribute Utility Theory. Then a design vector is selected, consisting of a very large number (hundreds to hundreds of thousands) of possible systems that could be used to meet the user needs. Simulation models are used to calculate the attributes of the proposed systems. The systems are then evaluated against the users’ utilities to understand which systems best satisfy the users’ needs. The results, collectively referred to as the tradespace, can then be explored. This process consists of the search for not only optimal solutions, but also for understanding of design sensitivities, key trade-offs, dangerous uncertainties, and vulnerabilities to changes in the market or national policy. Often these understandings will change a user’s perception of his or her need, and/or the designer’s perception of the appropriate design space, resulting in a need to repeat the analysis. The semi-automated nature of the computations allows this valuable exploitation of emergent understanding with little cost or time penalty. Eventually, a design or designs from the trade space are selected for further consideration.9 In this study, a somewhat simplified version of the MATE method was used. The method was adapted in response to difficulties including the lack of an immediate customer and a very open design space. The customer utilities were handled parametrically to understand the sensitivities of the tradespace to ranges of, and changes in, user needs. The analysis was done at a high level, using low-fidelity models, but covering a large range of possible designs. Attributes and Utilities The capabilities of a space tug vehicle determined to be useful to a potential user include: (1) total delta-V capability, which determines where the spacetug can go and how far it can change the orbits of target vehicles; (2) mass of observation and manipulation equipment (and possibly spare parts, etc.) carried, which determines at a high level what it can do to interact with targets, referred to here as its capability; and (3) response time, or how fast it can get to a potential target and interact with it in the desired way. Note that the design of observation and manipulation equipment and its corresponding software is outside the scope of this study – the equipment is treated as a “black box” with mass and power requirements. These attributes are translated into a single utility function. In the absence of real users from which to collect more sophisticated functions,9 it was decided that a simple function that could be explored parametrically was most appropriate. The three attributes are assigned single-attribute utilities. These are dimensionless metrics of user satisfaction from zero (minimal user need satisfied) to one (fully satisfied user). The utilities are combined as a weighted sum. The delta-V utility is shown in Fig. 1. Delta-V is a continuous attribute calculated for each system considered. Utility is assumed to increase linearly with delta-V, with diminishing returns above the levels necessary to do Low Earth Orbit (LEO) to GEO transfers. Variations on this utility are shown in Figs. 2 and 3, which show respectively the utilities of a GEOcentric user (large steps in utility for achieving GEO and GEO round-trip capabilities) and a delta-V-hungry user (continued linear utility for very high delta-V). The manipulator mass (capability) attribute has discrete values, assumed to correspond to increasing utility as shown in Table 1. The response time of a real system would be a complex function of many factors; at the level of the current analysis it is reduced to a binary attribute Vt, valued at one for high impulse systems, and zero for low impulse ones
The combined utility is calculated as follows: necessarily twice as good as 0.4)or any physical meaning.The nominal weightings and two other cases Uio -W,V,+Weve +W,V (1) studied are shown in Table 2. The combined utility is a dimensionless ranking of the Design vector and calculation of attributes presumed usefulness of the system to a nominal user.It A set of design variables(in MATE parlance,a design needs to be interpreted with care,as it provides ranking vector)was selected to represent possible tug vehicles (0.8 is better than 0.4)but not scale(0.8 is not The following variables were selected:(1)observation and manipulator system mass;(2)propulsion type,and (3)mass of fuel carried. 1.00 0.90 Table 1 shows the relationship assumed between 080 manipulator mass,assumed capability,and utility value. a70 Leo-Geo RT No attempt was made to design or even specify the manipulator system,but for reference the 300 kg size is typical of small industrial robots,while the high 0.40 capability (3000 kg)is taken from a postulated system based on shuttle arm technology Leo-Geo 020 Table 3 shows the choices of propulsion system 010 considered,along with some assumed properties of the 0.00 propulsion systems.The total mass of the propulsion 2000 4000 6000 8000 10000 12000 system is taken to be Delta-V(m/sec) Fig.1.Nominal single attribute utility for delta-V Mp=mpo+mpyMj (2) The fuel mass M was set at 30,100,300,600,1200, 3000,10000,30000 or 50000 kg,obviously spanning a 1.00 large range of possible delta-Vs. 070 Leo-Geo RT Table 1.Manipulator capability attribute.with 0 corresponding utility and mass Capability Utility value Mass M. (dimensionless) (kg) Leo-Geo Low 0.3 300 Medium 0.6 1000 High 0.9 3000 Extreme 1.0 5000 0.00 0 2000 4000.6000 8000 10000 12000 Delta-V(m/sec) Table 2.Utility weightings Fig.2.Delta-V utility for GEO-centric user Attribute Nominal Capability Response Weights Stressed Time 1.00 Stressed 0.90 Delta-V 0.6 0.3 0.2 Capability 0.3 0.6 0.2 1 Response Time 0.1 0.1 0.6 050 0.40 -Geo RT Table 3.Propulsion system choices and characteristics 0.30 Propulsion Base Mass High System (sec) Mass Fract Impulse 020 mp0(kg） m时 0.10 Storable biprop 300 0 0.12 0.00 Cryo 450 0 0.13 0 500010000150002000025000300003500040000 Electric 3000 25 0.30 Delta-V(m/sec) Nuclear 1500 1000 0.20 Fig.3.Delta-V utility for delta-V hungry user 3 American Institute of Aeronautics and Astronautics
3 American Institute of Aeronautics and Astronautics The combined utility is calculated as follows: † Utot = WvVv +WcVc +Wt Vt (1) The combined utility is a dimensionless ranking of the presumed usefulness of the system to a nominal user. It needs to be interpreted with care, as it provides ranking (0.8 is better than 0.4) but not scale (0.8 is not 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 2000 4000 6000 8000 10000 12000 Delta-V (m/sec) Delta-V Utility Vv (dimensionless) Leo-Geo Leo-Geo RT Fig. 1. Nominal single attribute utility for delta-V 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 2000 4000 6000 8000 10000 12000 Delta-V (m/sec) Delta-V Utility Vv (dimensionless) Leo-Geo Leo-Geo RT Fig. 2. Delta-V utility for GEO-centric user 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 0 5000 10000 15000 20000 25000 30000 35000 40000 Delta-V (m/sec) Delta-V Utility Vv (dimensionless) Leo-Geo Leo-Geo RT Fig. 3. Delta-V utility for delta-V hungry user necessarily twice as good as 0.4) or any physical meaning. The nominal weightings and two other cases studied are shown in Table 2. Design vector and calculation of attributes A set of design variables (in MATE parlance, a design vector) was selected to represent possible tug vehicles. The following variables were selected: (1) observation and manipulator system mass; (2) propulsion type, and (3) mass of fuel carried. Table 1 shows the relationship assumed between manipulator mass, assumed capability, and utility value. No attempt was made to design or even specify the manipulator system, but for reference the 300 kg size is typical of small industrial robots, while the high capability (3000 kg) is taken from a postulated system based on shuttle arm technology.10 Table 3 shows the choices of propulsion system considered, along with some assumed properties of the propulsion systems. The total mass of the propulsion system is taken to be † M p = mp0 + mpf M f (2) The fuel mass Mf was set at 30, 100, 300, 600, 1200, 3000, 10000, 30000 or 50000 kg, obviously spanning a large range of possible delta-Vs. Table 1. Manipulator capability attribute, with corresponding utility and mass Capability Utility value Vc (dimensionless) Mass Mc (kg) Low 0.3 300 Medium 0.6 1000 High 0.9 3000 Extreme 1.0 5000 Table 2. Utility weightings Attribute Nominal Weights Capability Stressed Response Time Stressed Delta-V 0.6 0.3 0.2 Capability 0.3 0.6 0.2 Response Time 0.1 0.1 0.6 Table 3. Propulsion system choices and characteristics Propulsion System Isp (sec) Base Mass mp0 (kg) Mass Fract. mpf High Impulse Storable biprop 300 0 0.12 Y Cryo 450 0 0.13 Y Electric 3000 25 0.30 N Nuclear 1500 1000 0.20 Y
The design vector described above represents 144 3.6.and 7 are found in Tables 3 and 4.These values possible designs.A few of the more extreme of these comprise the constants vector in MATE parlance.The designs were omitted,more for clarity of the resulting calculations are set up so that these values can be easily graphics than for computational ease.A few designs altered.These values were varied +/-10%and no with intermediate values of fuel mass,corresponding to strong sensitivity was found to any of them.However. specific missions described in this and the companion it must be noted that some of them (e.g.the nuclear paper,were added;the final design vector contained propulsion properties)are quite speculative,and the 137 possible designs. trade space may look different if they were drastically altered. The attributes of each design were calculated as follows.The capability,and its utility,are determined Table 4.Misc.Coefficients directly from the manipulator system mass as shown in Table 1.The response time attribute is determined Constant Value (units) mb时 1(dimensionless) directly from the propulsion system choice.Those Cw 20k$/kg) capable of high impulse are given a response time 150(ks/kg) utility V of one;those not capable are given a /of zero.The delta-V attribute,and the cost,are calculated by some simple vehicle sizing rules and the rocket equation. MATE RESULTS The vehicle bus mass is calculated as Figure 4 shows the tradespace as a plot of utility vs. cost with each point representing an evaluated design. Mb=Mp+m时Mc (3) The Pareto front of desirable designs are down (low cost)and to the right (high performance).The Pareto The vehicle dry mass is calculated as front features an area of low-cost,lower utility designs (at the bottom of Fig.4).In this region,a large number Md=Mp+Mc (4 of designs are available,and additional utility can be had with moderate increase in cost.On the other hand. and the vehicle wet mass is very high levels of utility can only be purchased at great cost(right hand side of plot). M=Md+Mf (5 The propulsion system is highlighted in Fig.4,with The total delta-V attribute is then different symbols showing designs with different propulsion systems.The propulsion system is not a △v=g Isp In(Me/Md） (6) discriminator in the low-cost,low utility part of the Pareto front,except that nuclear power is excluded.At The delta-V utility is then calculated (by an the high end,on the other hand,the Pareto front is interpolation routine)from Fig.1,Fig.2,or Fig.3. populated by nuclear-powered designs.Electric Note that Eg.6 calculates the total delta-V that the propulsion occupies the "knee"region where high vehicle can effect on itself.Use of this value is utility may be obtained at moderate cost supported by the fact that most missions studied spend most of their fuel maneuvering the tug vehicle without Figure 5 shows the cost banding due to different an attached target.Alternately,this delta-V can be choices of manipulator mass,or capability.For the thought of as a commodity.If a target vehicle is lower-performance systems,increased capability attached to the tug,more of this commodity must be translates to large increases in cost with only modest expended.Mission specific true delta-V's for a variety increases in utility.High capabilities are only on the of missions are discussed in the companion paper Pareto front for high utility,very high cost systems. This indicates,for the nominal set of user utilities used. The individual utilities having been calculated,the total cost effective solutions would minimize the mass and utility is calculated using Eq.1.The first-unit delivered power of the observation and manipulation systems cost is estimated based on a simple rule-of-thumb carried.Using the utility weights for the "Capability formula. Stressed"user (Table 2)results in Fig.6.As expected, increasing capability systems now appear all along the C=Cw Mw+cdMd (7) Pareto front,although capability still comes at a fairly steep price. Equation 7 accounts for launch and first-unit hardware procurement costs.Technology development costs are not included.The values for the coefficients in Egs.2 American Institute of Aeronautics and Astronautics
4 American Institute of Aeronautics and Astronautics The design vector described above represents 144 possible designs. A few of the more extreme of these designs were omitted, more for clarity of the resulting graphics than for computational ease. A few designs with intermediate values of fuel mass, corresponding to specific missions described in this and the companion paper, were added; the final design vector contained 137 possible designs. The attributes of each design were calculated as follows. The capability, and its utility, are determined directly from the manipulator system mass as shown in Table 1. The response time attribute is determined directly from the propulsion system choice. Those capable of high impulse are given a response time utility Vt of one; those not capable are given a Vt of zero. The delta-V attribute, and the cost, are calculated by some simple vehicle sizing rules and the rocket equation. The vehicle bus mass is calculated as † M b = M p + mbf M c (3) The vehicle dry mass is calculated as † M d = M b + M c (4) and the vehicle wet mass is † M w = M d + M f (5) The total delta-V attribute is then † Dv = g Isp ln(M w M d ) (6) The delta-V utility is then calculated (by an interpolation routine) from Fig. 1, Fig. 2, or Fig. 3. Note that Eq. 6 calculates the total delta-V that the vehicle can effect on itself. Use of this value is supported by the fact that most missions studied spend most of their fuel maneuvering the tug vehicle without an attached target. Alternately, this delta-V can be thought of as a commodity. If a target vehicle is attached to the tug, more of this commodity must be expended. Mission specific true delta-V’s for a variety of missions are discussed in the companion paper. The individual utilities having been calculated, the total utility is calculated using Eq. 1. The first-unit delivered cost is estimated based on a simple rule-of-thumb formula. † C = cw M w + cd M d (7) Equation 7 accounts for launch and first-unit hardware procurement costs. Technology development costs are not included. The values for the coefficients in Eqs. 2, 3, 6, and 7 are found in Tables 3 and 4. These values comprise the constants vector in MATE parlance. The calculations are set up so that these values can be easily altered. These values were varied +/- 10% and no strong sensitivity was found to any of them. However, it must be noted that some of them (e.g. the nuclear propulsion properties) are quite speculative, and the trade space may look different if they were drastically altered. Table 4. Misc. Coefficients Constant Value (units) mbf 1 (dimensionless) cw 20 (k$/kg) cd 150 (k$/kg) MATE RESULTS Figure 4 shows the tradespace as a plot of utility vs. cost with each point representing an evaluated design. The Pareto front of desirable designs are down (low cost) and to the right (high performance). The Pareto front features an area of low-cost, lower utility designs (at the bottom of Fig. 4). In this region, a large number of designs are available, and additional utility can be had with moderate increase in cost. On the other hand, very high levels of utility can only be purchased at great cost (right hand side of plot). The propulsion system is highlighted in Fig. 4, with different symbols showing designs with different propulsion systems. The propulsion system is not a discriminator in the low-cost, low utility part of the Pareto front, except that nuclear power is excluded. At the high end, on the other hand, the Pareto front is populated by nuclear-powered designs. Electric propulsion occupies the “knee” region where high utility may be obtained at moderate cost Figure 5 shows the cost banding due to different choices of manipulator mass, or capability. For the lower-performance systems, increased capability translates to large increases in cost with only modest increases in utility. High capabilities are only on the Pareto front for high utility, very high cost systems. This indicates, for the nominal set of user utilities used, cost effective solutions would minimize the mass and power of the observation and manipulation systems carried. Using the utility weights for the “Capability Stressed” user (Table 2) results in Fig. 6. As expected, increasing capability systems now appear all along the Pareto front, although capability still comes at a fairly steep price
4000 + 3500 ◆Biprop 3000 +Cryo A Electric 2500 x Nuclear 留 2000 芭 AA 1500- XX X 1000 A△ 500. 0 0.0 0.2 0.4 0.6 0.8 1.0 Utility(dimensionless) Fig.4.Trade space for nominal user,with propulsion system indicated 4000 4000 3500 3500 +Low Capabaity Medium Capability Medium Capability 3000 △High Capablity 3000 △High Capablity x Extreme Capabality x Extreme Capabality 2500 2500 2000 2000 1500 1500 1000 44 1000 500 500 0 0 0.0 0.2 0.40.60.8 1.0 0.0 0.2 0.40.6 0.8 1.0 Utility(dimensionless) Utility(dimensionless) Fig.5.Trade space for nominal user,with capability Fig.6.Trade space for capability stressed user indicated American Institute of Aeronautics and Astronautics
5 American Institute of Aeronautics and Astronautics 0 500 1000 1500 2000 2500 3000 3500 4000 0.0 0.2 0.4 0.6 0.8 1.0 Utility (dimensionless) Cost (M$) Biprop Cryo Electric Nuclear 0 500 1000 1500 2000 2500 3000 3500 4000 0.0 0.2 0.4 0.6 0.8 1.0 Utility (dimensionless) Cost (M$) Biprop Cryo Electric Nuclear Fig. 4. Trade space for nominal user, with propulsion system indicated 0 500 1000 1500 2000 2500 3000 3500 4000 0.0 0.2 0.4 0.6 0.8 1.0 Utility (dimensionless) Cost (M$) Low Capability Medium Capability High Capablity Extreme Capability Fig. 5. Trade space for nominal user, with capability indicated 0 500 1000 1500 2000 2500 3000 3500 4000 0.0 0.2 0.4 0.6 0.8 1.0 Utility (dimensionless) Cost (M$) Low Capability Medium Capability High Capablity Extreme Capability Fig. 6. Trade space for capability stressed user