Dry Launch 2: LH2 vs Kerosene

I had been expecting that LOX-LH2 would be less expensive than LOX-kerosene for a LEO-out boost.

At some goading by "anonymous", I reran the numbers assuming a different mission profile. (I really appreciate good criticism, by the way. Thanks.)

This time, lets assume SpaceX sends up Falcons whose top stages have been stretched to carry just extra LOX. The first mission leaves the top stage in orbit, later missions lift extra LOX to it, and we end up with a big LOX tank in orbit.

The LEO-out booster is launched from an EELV, e.g. Atlas. The idea is to use something that uses the dual-engine Centaur upper stage. You might want to consider a Falcon-Centaur, but then you have to deal with paying for all that integration and LH2 infrastucture when Boeing and Lockheed have already done it for you. My guess is that until there looks like a solid market for LEO-out boost, SpaceX will have nothing to do with Centaur.

Here are the numbers: An Atlas 551 can put 20,050 kg into LEO. If we assume an incremental tankage ratio of 25 (like the Space Shuttle external tank), we get a modified Centaur with enormously stretched tanks, 5.9x for the hydrogen tank, 4.9x for the oxygen tank. The Centaur launches with a full hydrogen tank and a nearly empty oxygen tank. After achieving LEO, the oxygen tank is empty and the hydrogen tank still has 83% of it's initial load. The Centaur picks up 86,240 kg of LOX from the Falcon tanker. This Falcon would have loaded LOX from 9 other Falcon flights. The stretched Centaur would then be able to add 4000 m/s delta-V to a 58680 kg payload. Burn time: 73 minutes.

That's a bit more than a third of the max payload of my earlier LOX-kerosene all-SpaceX proposal. Cost would be $270 M (SpaceX), perhaps $200 M (Atlas). Interestingly, the cost per kg ($8000/kg) isn't different from the all-SpaceX proposal ($8035/kg).

This didn't come out like I thought it would. First, note that the LEO-out booster performance is not terribly sensitive to the controversial tankage ratio, because the empty booster doesn't weigh all that much compared to it's payload, even if the tankage ratio gets cut in half. That's because 4000 m/s is not an amazing amount of delta-V if you have all day to burn your propellants. Maximum payload is affected, of course, and that has a big impact on the LOX-LH2 cost.

The fully fuelled LOX-kerosene LEO-out booster is heavier than the LOX-LH2 booster, but this big disadvantage is neatly balanced by the high cost of ground-to-LEO launch of the hydrogen.

The LOX-kerosene proposal assumes transfer of both LOX and kerosene, where the LOX-LH2 proposal requires the transfer of just one. My assumption is that the extra bother of kerosene transfer is not a deal breaker.

Here is a deal-breaker though: SpaceX uses an ablatively cooled combustion chamber and throat. Regenerative cooling is probably a requirement for this application, due to the ridiculously long burn times. I'm sure that regenerative cooling would be a major development headache for SpaceX. This makes a LOX-kerosene LEO-out booster unlikely unless SpaceX wants to develop long-burn engines for some other reason.  [Update: SpaceX has switched to using regeneratively cooled Merlins, so no deal-breaker any more.]

A LOX-LH2 LEO-out heavy booster would probably be better if a high-volume operator (like SpaceX hopes to be) were to pursue it. Assuming just a few uses, the choice is trickier. The LOX-LH2 option has less technical risk, as it requires no engine development and transfers just one propellant.