In the present analysis, the computations of Blair et al. are generalized by allowing the masses of the Moon-LL1 tanker and the LL1-LE0 tanker to vary widely as parameters. Using the Av estimates of Table 5.12, the efficiency of transfer of water mined on the Moon to LE0 is estimated as a function of the tanker masses. The quantities that define each step are given in Table 5.13.

Electrolysis of water produces 8 kg of 02 for every kg of H2. Since the optimum mixture ratio for 02/H2 propulsion is assumed to be 6.5, 1.5 kg of excess 02 will be produced per kg of H2 that is produced. This 02 would likely be vented, although 02 in LE0 might be useful for human life support. This indicates that, per kg of water electrolyzed, only 7.5/9 = 0.833 kg of useful propellants are produced.

C |
D |
E |
F |
G |
H |
I |
J |
K |
L | |

Total |
Inert |
Propellant |
Water |
Excess |
Water |
Water mined |
Rocket equation | |||

mass |
mass |
mass |
electrolyzed |
o2 |
transferred |
on the moon |
factors | |||

3 |
m, |
mi |
mp |
md |
mâ€ž 02 |
mw |
m (mined) |
r |
r- 1 | |

4 |
= H5/(1-L5-(K5/J5)) |
â€” L5*C5 |
= C5-D5-H5 |
â€” 1.2*E5 |
= F5-E5 |
= H5 + F5 |
= J5-1 | |||

5 |
53.50 |
5.35 |
23.15 |
27.78 |
4.63 |
25.00 |
52.78 |
1.763 |
0.763 |
0.10 |

6 |
58.51 |
8.19 |
25.32 |
30.38 |
5.06 |
25.00 |
55.38 |
1.763 |
0.763 |
0.14 |

7 |
64.55 |
11.62 |
27.93 |
33.52 |
5.59 |
25.00 |
58.52 |
1.763 |
0.763 |
0.18 |

8 |
71.99 |
15.84 |
31.15 |
37.38 |
6.23 |
25.00 |
62.38 |
1.763 |
0.763 |
0.22 |

9 |
81.36 |
21.15 |
35.20 |
42.25 |
7.04 |
25.00 |
67.25 |
1.763 |
0.763 |
0.26 |

10 |
93.53 |
28.06 |
40.47 |
48.57 |
8.09 |
25.00 |
73.57 |
1.763 |
0.763 |
0.30 |

11 |
109.99 |
37.40 |
47.60 |
57.12 |
9.52 |
25.00 |
82.12 |
1.763 |
0.763 |
0.34 |

12 |
133.49 |
50.72 |
57.76 |
69.31 |
11.55 |
25.00 |
94.31 |
1.763 |
0.763 |
0.38 |

13 |
169.74 |
71.29 |
73.45 |
88.14 |
14.69 |
25.00 |
113.14 |
1.763 |
0.763 |
0.42 |

The mass of either vehicle (LLT or LWT) is represented as a sum of three masses: Mp = propellant mass

Mi = inert mass (including the structure, an aeroshell for the vehicle that goes to LEO, a landing system for the vehicle that goes to the lunar surface, the water tank, the propulsion stage, and the avionics) Mw = water mass carried by the vehicle to the next destination Mt = total mass = Mp + Mi + Mw

The inert masses of the LWT and LLT tankers are of critical importance in this scheme. We shall assume that the inert mass is some fraction of the total mass. For each vehicle, we set

where K is an adjustable parameter, and we define K1 for the LWT and K2 for the LLT independently.

We begin the calculation by assuming that we will extract enough water on the Moon to send 25 mT of water to LL1. We will then work backwards to estimate how much water would have to be extracted on the Moon in order to provide propellants to send 25 mT of water to LL1. The results can be scaled to any arbitrary amount of water transferred to LL1.

The rocket equation provides that

For transfer from the lunar surface to LL1, we have

R = exp(Au/(9.8 * ISP) = exp(2,500/(9.8 x 450)) = 1.763

The total mass on the lunar surface is

Since we have specified Mw = 25 mT, Mt can be calculated. From this, all the other quantities can immediately be calculated. Table 5.13 shows the calculations for the transfer from the Moon to LL1.

The next step is returning the empty LLT from LL1 to the Moon using some of the 25 mT of water at LL1 to produce propellants. The spreadsheet for doing this is shown in Table 5.14. Negative values in Column H for water remaining at LL1 indicate that for sufficiently high values of Kj, no water can be transferred.

C |
D |
E |
F |
G |
H |
J |
K |
L | |

Total |
Inert |
Propellant |
Water |
Excess |
Water |
Rocket equation | |||

mass |
mass |
mass |
electrolyzed |
o2 |
remaining |
factors | |||

m, |
mi |
mp |
Mel |
mxs 02 |
mw |
r |
r- 1 |
ki | |

= D17 + E17 |
= D5 |
= D17* K17 |
= 1.2* E17 |
= F17-E17 |
= 25-F17 |
= J17-1 | |||

17 |
9.20 |
5.35 |
3.85 |
4.62 |
0.77 |
20.38 |
1.719 |
0.719 |
0.10 |

18 |
14.08 |
8.19 |
5.89 |
7.07 |
1.18 |
17.93 |
1.719 |
0.719 |
0.14 |

19 |
19.98 |
11.62 |
8.36 |
10.03 |
1.67 |
14.97 |
1.719 |
0.719 |
0.18 |

20 |
27.23 |
15.84 |
11.39 |
13.67 |
2.28 |
11.33 |
1.719 |
0.719 |
0.22 |

21 |
36.37 |
21.15 |
15.22 |
18.26 |
3.04 |
6.74 |
1.719 |
0.719 |
0.26 |

22 |
48.25 |
28.06 |
20.19 |
24.22 |
4.04 |
0.78 |
1.719 |
0.719 |
0.30 |

23 |
64.30 |
37.40 |
26.90 |
32.28 |
5.38 |
-7.28 |
1.719 |
0.719 |
0.34 |

24 |
87.21 |
50.72 |
36.49 |
43.79 |
7.30 |
-18.79 |
1.719 |
0.719 |
0.38 |

25 |
122.57 |
71.29 |
51.28 |
61.54 |
10.26 |
-36.54 |
1.719 |
0.719 |
0.42 |

The next step is transfer of the remaining water from LL1 to LE0. Here, a trial-and-error procedure is used. We guess how much water can be transferred and the propellant requirements are calculated for this load, assuming some value of K2. The amount of water that must be electrolyzed at LL1 is subtracted from the water remaining at LL1 (after sending the LLT back to the Moon) and the net amount of water is compared with the guessed value. The guessed value is varied until it agrees with the calculated value. A typical spreadsheet is shown in Table 5.15 for an assumed value of K2. Each row corresponds to the Kx values from Table 5.14. This process can be repeated for various values of K2.

Finally, we estimate the requirements for sending the empty LWT back to LL1 from LE0 as shown in Table 5.16.

The results of these calculations are summarized in Tables 5.17 and 5.18.

The crux of this calculation then comes down to estimates for Kx for the LLT and K2 for the LWT. For the LLT, the inert mass includes the landing structure, the spacecraft structure, the water tank, and the propulsion stage. The propulsion stage for H2-02 propulsion is typically taken as roughly 12% of the propellant mass,110 and since the propellant mass is likely to be about 42% of the total mass leaving the lunar surface (from calculations), the propulsion stage is perhaps 5% of the total mass leaving the lunar surface. The water mass is likely to be about 40% of the total mass leaving the lunar surface, and if the water tanks weighs, say, 10% of the water mass the tank mass would be about 4% of the total mass. The spacecraft and landing structures are difficult to estimate. A wild guess is 12% of the total mass. Thus, we crudely estimate the value of Kx for the lunar tanker as 0.05 + 0.04 + 0.12 ~ 0.21.

The LE0 tanker does not require the landing system of the lunar tanker, so the spacecraft mass is estimated as 7% of the total mass of this vehicle. The water transported by the LLT is about 55% of the total mass, so the water tank is estimated as 5.5% of the total mass. In addition, an aeroshell is needed that is estimated at 30% of the mass injected into LE0, which is likely to be about 90% of the mass that departs from LL1 toward LE0, so this is roughly 27% of the total mass leaving LL1. Thus, K2 for the LE0 tanker is roughly estimated as 0.33. These are only rough "guesstimates".

If Kj ~ 0.21 and K2 ~ 0.33, only about 5% of the water extracted on the Moon is transferred to LE0. However, approximately 12% of the water lifted from the Moon is transferred to LE0.

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