by Dave Dietzler
Constituent Mare Basalts Oxygen % Highland Anorthosite Oxygen %
Silicon 21.00% 24.00% 21.00% 24.00%
Aluminum 7.00% 6.20% 15.00% 13.33%
Total 28.00% 30.20% 36.00% 37.30%
If we use the proportions of elements that nature has given us with magma electrolysis of "de-ironed" moondust and burn a mixture of silicon and aluminum we can use about 58.2% of Mare basalts or much better 73.3 % of Highland anorthosite for monopropellant. Anorthosite is preferable for its high aluminum content as monopropellant.
We can use the Al/Si alloy directly from the magma process. We cannot use magnesium as it is shock sensitive and will detonate.
These will be ground up to ultrafine particles and mixed with LOX. Note that the metal fuel to oxygen ratio in both cases is about 50/50 by mass.
For every ton of Al there will be 0.888 tons LOX or 0.785 c.m.
For every ton of silicon there will be 1.143 tons LOX or 1.012 cubic meters.
Thus the mixture will contain 21 tons Si at 2.3 tons per c.m. or 9.13 c.m. silicon and 21.25 cubic meters LOX; 15 tons Al at 2.7 tons per cubic meter or 5.55 c.m. Al and 11.775 cubic meters LOX.
Metal Metal volume LOX volume Metal mass LOX mass
Silicon 9.13 21.25 21 tons 24 tons
Aluminum 5.55 11.78 15 13.33
Totals 14.68 33.03 36 37.33
This comes up to 47.71 cubic meters per 73.3 tons of monopropellant. The density of the monopropellant will be 1.54 that of water or 1.54 tons per cubic meter.
This will not be exceedingly dense or hard to pump. The ultrafine particles will be dispersed into the LOX with ultrasonic agitation that can even make water and gasoline mix to form a fine suspension. Magnetic stirrers or ultrasonic agitators in the ship's tanks will keep the supsension homogenous at all times.
Moon Shuttle Propellant Masses
Since the 21 meter wide ascent tank had 4846 cubic meters it holds 7463 tons of monopropellant. The 13m wide descent tank had 1150 cubic meters and holds 1771 tons monopropellant. The total monopropellant mass is thus 9234 tons.
If the dry mass of the rocket is 510 tons it has a lift-off mass of 9744 tons (round to 9745 tons) and a mass ratio of 19.1 to 1, therefore it can reach 7.23 kps at 250 seconds ISP and 8.24 kps at 285 seconds ISP. Plenty for a 12 hour ascent to L2 and a 12 hour descent. Estimates of the ship's dry mass have some overkill so reality will be much more pleasant.
With the ascent tank empty the rocket has a mass of 510+1771=2281 It will have a MR of 2281/510=4.4725 It will reach 3.67 kps at 250 seconds and 4.18 kps at 285 seconds. This is enough speed for descent from L2 in 12 hours.
If it has to fire explosive bolts and detach the upper stage (estimated 270 tons) and use the back-up motors it will reach 4.95 kps @ 250 seconds and 5.65 kps @ 285 seconds, so it has enough speed to save itself.
At lift-off the ship amasses 9745 tons and will burn 7463 tons of monopropellant so it will have a lift-off mass to burnout mass ratio of (9745)/(9745-7463)= 4.27 and this will allow 3.556 kps @ 250 seconds and 4 kps @ 285 seconds. So the rocket has enough speed to reach L2 in 12 hours.
Estimating Time of Flight
At 2.3 kps we can reach L2 on a minimum energy trajectory in 90 hours. I have estimated 3.2 to 3.4 kps to get there in twelve. At 2.4 kps we reach lunar escape velocity and upon reaching a distance of several hundred thousand kilometers the rocket has almost no velocity left over.
Since V2hyperbolic = V2burnout - V2escape we can determine that a rocket leaving the Moon at 2.5 kps has 0.7 kps leftover after reaching the limit of the Moon's "gravitational sphere of influence"; a distance at which it is just inching along slowly after rocketing away at escape velocity. So I am estimating that the rocket leaves LLO with 2.45 to 2.5 kps and has 0.7-0.9 kps left upon entering the L2 region.
Based on an average velocity of (2.5+0.7)/2=1.6 it travels the distance 70,000 km/1.6 kps =43,750 seconds or 12.15 hours. So the ship needs to reach 2.5 kps and retro brake about 0.7 to 0.9 kps upon arriving at L2. The total is 3.2 to 3.4 kps. The Moon Shuttle can do this.
However, the Earth's gravity will also be tugging on the rocket as it leaves LLO (low lunar orbit) and this will slow it down, perhaps enough so that it doesn't need to retro into L2, sort of like falling into a gravitational well. This might slow it down so much it takes more than 12 hours to get there. The actual determination will require real rocket engineers who know calculus, astrodynamics and how to do computer simulations with mathematical models. My mathematical analysis is admittedly naiive. Hopefully, others will find inspiration in this.
LH2 and Silane
If we look farther into the future, there will be a time when ample LH2 is available from Mars, Deimos, Phobos, asteroids and/of ice moons of Jupiter. It will be possible to make silane by combining hydrogen with plentiful lunar silicon.
Silane has a density of 0.68, burns in a 1:2 by mass ratio with oxygen, and yields up to 340 seconds. With 6000 cubic meters of tankage, we could run about 5540 tons of silane and LOX. In a 510 ton rocket we get a mass ratio of 11.9 and a delta V total of 8.25 kps compared to a total delta V of 7.23 kps @ 250 sec. and 8.24 kps @ 285 seconds on Al and LUNOX monopropellant.
