| Cargos to the Moon
Dave Dietzler 2008 Introduction What follows is a cursory analysis of cargo transport to the Moon. We will discuss the use of the planned Ares V rocket capable of placing 286,000 pounds in LEO. It is important to realize that transit to the Moon by chemical rockets takes about three days and that it is not practical to store LH2 and LOX in space for that length of time. While LH2/LOX propulsion can be used for trans-lunar injection, a matter of hours after reaching LEO, braking into LLO (low lunar orbit) and landing on the lunar surface must be done with space storable propellants like MMH (mono-methyl hydrazine) and N2O4 (dinitrogen tetroxide). Essential parameters for this discussion: LEO velocity 7.8 kps Vesc 11 kps Braking into LLO and landing 3 kps dV for escape from LEO is 3.2 kps lunar escape V is only 2.4 kps but the vehicle will have some left over velocity when approaching the Moon and it will be accelerated by the Moon’s gravity during rocket burns so I am using the rough figure of 3 kps for braking into LLO and landing LH2/LOX 455 seconds in the vacuum 4.46 kps exhaust velocity (0.0098*Isp) MMH/N2O4 316 seconds in the vacuum 3.1 kps exhaust velocity Mass ratio = (mass initial/ mass final) = e^(v/c) v = rocket velocity c = exhaust velocity Mass initial denoted Mi is of course the mass of the rocket plus propellant before the burn and mass final denoted Mf is the mass of the rocket plus propellant at the end of the burn. Or the mass of the rocket alone when all propellants have been burned up. Calculations 1 For the TLI burn to Vesc with LH2/LOX engines: e^(3.2/4.46) = 2.05 286,000 lbs./(Mf) = 2.05 Mf = 139,512 pounds Moonward 286,000 lbs. – 139,512 lbs. = 146,488 lbs. of LH2/LOX burned By rule of thumb, tankage and motors is 20% of propellant mass That’s 29,297 lbs in this case. If we discard the LH2/LOX stage we will have less dead weight to brake into LLO and land on the Moon, but is this rocket stage really dead weight? Its tanks and plumbing will consist of materials like kevlar, carbon composites, and aluminum. Its motors and turbopumps will consist of alloy steel. This is stuff worth cannibalizing on the Moon. So let’s look at landing all this on the Moon. Using MMH/N2O4 rockets: e^(3/3.1) = 2.63 139,512/(Mf) = 2.63 Mf = 53,046 lbs. 139,512 – 53,046 = 86,466 lbs. propellant 20% of that is 17,293 lbs.. the mass of the MMH/N2O4 powered braking/lander rocket So 53,046 lbs. landed on the Moon minus 29,297 lbs. LH2 stage minus 17,293 lbs. MMH lander = 6456 lbs of functional cargo plus the mass of the cargo module that we will also cannibalize for its plastics and composites. That isn’t much functional cargo. If we jettison the LH2/LOX stage we have: 139,512 lbs into TLI – 29,297 lbs mass of LH2/LOX stage = 110,215 lbs towards the Moon Since we have a MR of 2.63 for braking and landing, we have 41,906 lbs landed on the Moon. 110,215/(Mf) = 2.63 Mf = 41,906 lbs. 110,215 – 41,906 = 68,309 lbs propellant MMH/N2O4 20% of 68,309 = 13,662 lbs for the braking/lander rocket 41,906 – 13,662 = 28,244 lbs functional cargo So it seems jettisoning the LH2/LOX stage is worth it to get about 14 tons of functional cargo to the Moon and almost 7 tons of hardware to cannibalize. If we don’t jettison the LH2/LOX stage we get a little more than 3 tons functional cargo and a little more than 23 tons of junk to cannibalize. This could be a matter of choice, since that 23 tons of junk will consist of kevlar and carbon composites that contain carbon, hydrogen, nitrogen and there will also be aluminum and steel. Strangely enough, if we don’t jettison the LH2 stage we get 26 tons total on the Moon and if we jettison it we get 21 tons on the Moon, and I have checked and rechecked my figures. Fortunately, there is a better way to do things. Electric Drives Electric drives like VASIMR, Hall thrusters, electrostatic ion drives, etc. are being developed. None existing now are big enough to propel large payloads to the Moon, but we can expect the development of these devices in the future if we are ever to industrialize the Moon. At this point we have to do some guesswork. Let’s say that we only need 10% of the mass in LEO, 286,000 lbs, for propellant to move the vehicle into space near the Moon. That’s 28,600 pounds electric drive propellant An electric drive and powerplant, possibly nuclear, might amass 10,000 lbs. So we have 257,400 lbs. Moonward and 10,000 lbs of it is electric drive module. We don’t want to jettison the electric drive module into space or let it crash on the Moon. It is too valuable and could be reused. So now things get tricky. We must brake 247,400 lbs. + 10,000 lbs into LLO with MMH/N2O4 rockets. e^(1/3.1) = 1.38 257,400/(Mf) = 1.38 Mf = 186,522 lbs. 257,400 – 186,522 = 70,878 lbs. braking propellant 14,175 lbs. is braking motors and tankage. I say we keep them and cannibalize them for their carbon, hydrogen, nitrogen, aluminum and steel. Now we can separate from the electric drive module in LLO. Since this module is now freed from the massive payload transferred to LLO and it only has to reach about 1 kps to leave LLO and aerobrake into LEO let’s just say that the propellant to do this is contained in the 10,000 pounds mass of the module. Yes, this is guesswork. So now we have 176,522 lbs. in LLO. 14,175 lbs of it is empty braking motor module. We need to make a 2 kps burn to land. e^(2/3.1) = 1.9 176,522/(Mf) = 1.9 Mf = 92,906 lbs landed on the Moon Since 176,522 – 92,906 = 83,616 lbs of MMH/N2O4 16,723 lbs is the mass of the lander tankage and motors. So out of 92,906 lbs landed on the Moon, 30,898 lbs. (14,175+16,723 lbs,) is empty braking and lander modules and 62,008 lbs is functional cargo. That’s about 31 tons of functional cargo and 15 tons of hardware to cannibalize. That beats 14 tons cargo and 7 tons junk. It beats 3 tons cargo and 23 tons junk also. We are talking 46 tons versus 21 or 26 tons. Conclusion Since it is projected that an Ares V launch will cost $1 billion, the cost of a pound to the lunar surface is $10,763 using electric drives based on our guesses for electric drive unit mass and propellant mass.. $10,763/ lb. Not bad if everything really works out this way. Remember, we were just guestimating the propellant mass for the electric drive and guessing at the mass of the drive module itself. If we launch ten Ares V rockets for $10 billion and use electric drives we can put 310 tons of cargo in the form of robots and other machinery like lasers, grinders, a small solar furnace, reflectors, solar panels, a small magma electrolysis unit, etc. And have another 150 tons of dead rocket modules to cannibalize for carbon, hydrogen, nitrogen, aluminum, steel, etc. Robots will use lasers to cut up the braking rocket modules and lander modules. Plastic and carbon composite materials will be ground up and roasted in a solar furnace until they decompose. Hydrogen and nitrogen will be collected and carbon will remain. The carbon will be used for making steel from iron fines scavenged on the Moon and iron from magma electrolysis. Robots will also deploy inflatable habitat modules and pressurize them with oxygen hauled to the Moon or oxygen from magma electrolysis or from the electrolysis of water ice from shadowed polar craters. They will cover the inflatables with regolith for thermal, radiation and micrometeoroid protection. Launch 100 Ares Vs for $100 billion and we have 3100 tons of cargo and 1500 tons of junk to cannibalize. Out of 1500 tons there should be a several hundred tons of carbon. Mass Breakdown For all chemical propulsion and without jettisoning the LH2 stage: 286,000 lbs in LEO 139,512 lbs. to Vesc 53,046 lbs. landed on the Moon $18,851 per pound @ $1 billion per launch 29,297 lbs. for LH2/LOX stage 17, 293 lbs. for MMH/N2O4 braking and landing stage Only 6456 lbs. functional cargo For all chemical propulsion and jettisoning of the LH2 stage: 286,000 lbs. in LEO 139,512 lbs. to Vesc 110,215 after jettisoning the LH2 stage 41,906 landed on the Moon $23,062 per pound 13,662 lbs. braking/landing rocket module 28,244 lbs. functional cargo For electric propulsion: 286,000 lbs. in LEO 257,400 lbs. to Vesc or “Moonward” 186,522 lbs. braked into LLO 176,522 lbs. after separating from electric drive module 92,906 lbs. landed on the Moon $10,763 per pound 14,175 lbs. is empty braking rocket module 16,723 lbs is empty landing rocket module 62,008 lbs. functional cargo |
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| MMH/N2O4 or H2O2 powered lander (316 sec. Isp) brakes into LLO unless ion drive can maneuver into polar LLO, and lands cargo on lunar surface. Estimated 31 tons actual cargo and 15 tons for lander that will be cannibalized on the Moon. About 14.3 english tons est. xenon propellant, 35.44 tons MMH/N2O4 for braking into LLO and 41.8 tons for touchdown on lunar surface. TOTAL: 275,000 lbs. Ares V to LEO 286,000 lbs. Ion drive mass 10,000 to 11,000 lbs. If electric drive can brake the spacecraft into LLO functional cargo mass will increase significantly when one considers that the braking rocket itself amasses 7 tons and uses about 35 tons of propellant to brake into LLO. Even greater payload masses could be obtained if rockets that I like to call Moon Shuttles fueled on the Moon with fuel produced on the Moon flew up to LLO, docked with the cargo and electric drive and landed them on the Moon. In this case we could also make use of the electric drive's solar panels and cannibalize it for raw materials. The lander module amasses about 8 tons and uses about 41.5 tons of propellant. How much more functional cargo could we land on the Moon by braking into LLO with the electric drives and using a Moon Shuttle fuel with LUNOX and silane perhaps? The braking rocket plus lander amass 15 tons together and they us a combined 76.5 tons of propellant. We could double or triple our functional cargo mass. |