Copyright 2012 Robert Clark
"Golden Spike Co" has released a paper describing their return to the Moon plans:
An Architecture for Lunar Return Using Existing Assets.
by James R. French et. al.
It gives several different architectures and types of missions. But on page 8 it gives the payload capability of the Falcon 9, presumably the new version Falcon 9 v1.1, as 16,700 kg. However, on the SpaceX site it's given as 13,100 kg:
Interestingly at the 16.7 mT number you can do a manned circumlunar mission on a single Falcon 9 + Dragon, even including a launch abort system(LAS), by using a half-size Centaur as the in-space stage. But at the 13.1 mt number it becomes more problematical .
Such a mission would be very important to accomplish. Recall the Apollo 8 mission was a manned lunar flyby that served as the prelude to the Apollo 11 mission. It is regarded then as being a part of the costly Apollo program, requiring the expensive Saturn V launcher.
The skepticism among many about the Golden Spike plan or other commercial lunar plans is the idea it would require large, highly expensive Saturn V class launchers. However, if the manned flyby could be done by a single launch by what is still just a medium size launcher in the Falcon 9 v1.1 it would show that by going small and following a low cost, commercial approach, that a low cost return to the Moon is feasible.
The Falcon 9 v1.1 will cost in the $60 million range, and we might estimate the half-size Centaur to be in the $15 million range. So the launch cost for such a mission might be in the $75 million range.
As I discussed before in regards to using the first test flights of the Falcon Heavy for unmanned BEO test flights, the test flights of the Falcon 9 v1.1 could serve for unmanned test flights for this lunar flyby. Since SpaceX needs to do such tests anyway most of the cost of the Falcon 9 and Dragon capsule would be borne by SpaceX. Then you could have Golden Spike only paying ca. $15 million for the half-size Centaur.
There would be some development cost of course beyond that for this half-size Centaur. For one thing you would have to make the cryogenic propulsion undergo less boiloff for 1 to 2 week missions. ULA has done studies on this so should be doable but still it has to be carried out in practice. An advantage of this would be that this half-size Centaur is about the size you need for the lander. So the lander could be derived from this, and the development cost for the two stages could be reduced.
The Golden Spike landing plan specifies using two Falcon Heavy's even though it uses a Dragon sized capsule. This is more than 100 mT to LEO. This is puzzling since the advantage of using a lightweight capsule is that it should require smaller amounts to be launched to orbit, known as IMLEO, initial mass to low Earth orbit. For instance the Early Lunar Access plan only requires 52 mT to orbit using a small two-man capsule. However, I believe the Golden Spike paper by French et. al. explains where the discrepancy arises.
On page 13 is given a table of some masses for different possible propulsive stages. The mass for the Dragon with trunk and crew and supplies is 8,853 kg, well above the given dry mass of the Dragon capsule at 4,200 kg. The trunk section is less than 1,000 kg and the propellant for the Dragon is at 1,290 mT. The mass for crew and supplies in the Golden Spike paper is given as 300 kg. Evidently then the extra mass to get to a 8,853 kg mass is coming from the launch abort system (LAS).
In any case a 8,853 kg mass would be at the mass of the Orion capsule and we would lose any advantage of a lightweight architecture. Then I suggest an alternative to the SpaceX LAS that has the LAS permanently integrated into the capsule.
We could use again a tower type LAS that would be jettisoned prior to reaching orbit. To estimate its mass we might make a comparison to the Orion LAS. The Orion LAS is at 6,000 kg. The Dragon is at half the mass of the Orion capsule. Then we can estimate the mass for a tower type LAS for the Dragon as 3,000 kg.
This is also a high additional mass. However, typically a tower LAS is jettisoned soon after first stage separation. So we can estimate how much this will subtract from the payload to orbit by making a comparison to how much the payload is reduced for an increased dry mass to the first stage. A rule of thumb is that every kilo of mass added to the first stage dry mass subtracts off 1/10 of a kilo from the payload. So we can estimate 300 kg being subtracted off the payload.
Now we'll estimate the size of a cryogenic stage needed to take the Dragon to a circumlunar mission. In the table on page 13 in the Golden Spike paper is given a cryogenic, LH2/LOX, stage at 1,196 kg dry mass and 7,534 kg propellant mass. This is a mass ratio of 7.3 to 1. Notably this is less than that of current Centaur upper stages at about 10 to 1. This is because mass ratio improves as you scale up your rocket stages.
This rocket stage would be sufficient to carry the Dragon's 4,200 kg dry mass plus the 300 kg for crew and supplies using RL-10 engines. The delta-v for trans lunar injection(TLI) is 3,150 m/s. Using a 451 s Isp for the RL-10 engines we get a delta-v of:
451*9.81ln(1 + 7534/(1196 + 4500)) = 3,700 m/s.
But because of the loss of payload capacity due to the LAS from SpaceX's cited payload to LEO of the Falcon 9 v1.1 of 13.1 mT, this would be slightly more mass than can be carried to LEO. So we'll use a slightly smaller stage. Let the propellant mass be 7,000 kg. Keeping the same 7.3 mass ratio, this corresponds to a dry mass of 1,100. Then the delta-v will be:
451*9.81ln(1 + 7000/(1100+ 4500)) = 3,600 m/s, still sufficient for the TLI.