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 Astronautics4 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