Saturday, October 22, 2005

Dry Launch

Jon Goff has posted the idea of launching a LEO-to-wherever booster into LEO, and then fuelling it with subsequent flights. This makes me wonder how big a dry launch / on-orbit refuel booster can SpaceX put up, with just Falcon 9?

First, we need a bunch of assumptions.

  • Let's assume the complete but empty booster has to go up in one flight, so no seperate launch of fuel and oxidizer. Seperate tanks should almost double the resulting booster size and launch/fuelling cost. Using a Falcon 9S9 with the big strapons would nearly triple the booster size and launch/fuelling cost.


  • Assume insulated tanks are 2% of fuel mass. Payload size is highly sensitive to this number, which I just pulled out of a handy nearby orifice.


  • Assume that both the fuelling rockets and the LEO-out booster are just Falcon 9 upper stages outfitted with larger tanks and (in the booster's case) lots of insulation.


  • Assume that without the fairing and payload interface bits the Falcon 9 can boost 10,000 kg to LEO. Assume 300 kg for fuel transfer hardware.


  • The resulting super-stretched Falcon upper stage / LEO-out booster should hold 475,000 kg of propellant, making it about twice the size of the Falcon 9 lower stage. If built with the same tank diameter (3.6m), it would be about 56m long. At launch, the whole thing would be about 89m long, with an aspect ratio of 25, which is pretty skinny but probably doable.

    Such a booster could give 4,000 m/s delta-V to a vehicle with a empty mass of 168,000 kg. That's enough delta-V to get out of Earth orbit to L5, low moon orbit, and at least near Mars, see this handy cheat sheet. It's also just a bit more mass than the Saturn V rocket put into Low Earth Orbit -- not excessive for a manned excursion to anywhere dramatic.

    It would require 49 fuelling flights, with a total cost (just for the booster) of $1.35 billion dollars with SpaceX's published prices. SpaceX's prices are for single launches, assuming no hardware recovery/reuse. 50 total launches would get them a lot of experience with recovery, and change the whole cost dynamic. It would also take at least of year of fairly amazing launch activity.

    An equivalent booster, launched with the Shuttle-Derived Heavy lifter, would require about 3 launches, as it uses liquid hydrogen, which really helps this application. Shuttle launches are hard to account for, but probably around $500M each, and if the SDH is similar, it would cost $1.5B for this booster, not counting amortized development costs.

    I don't think anyone would start an Artic expedition that required 50 plane trips just to build a cache of dog food, so I don't think this version of the idea is going to fly. Perhaps liquid hydrogen is inevitable for this application. Alternatively, SpaceX's Merlin 2-based launcher may get launch prices down enough that Kerosene and LOX make sense even for a big out-of-LEO booster.

    [Note: the next post answers comments.]

    7 comments:

    1. Tanks 2% of fuel mass?! That sounds preposterous, a "tankage ratio" of 50.

      A centaur V1 has 22 t of full weight and 2.0 t of empty weight. When engines only weigh 0.15 t, the tankage ratio becomes (22-0.15)/(2.0-0.15) ~= 12.
      http://www.astronautix.com/stages/cenaurv1.htm

      Dense fuel stages have better, like the Zenit first stage which is about 18.
      http://www.astronautix.com/stages/zenit1.htm

      Remember that the whole thing has to fly to space complete and unharmed and also be thermally shielded. I would guess numbers close to 20 for hydrogen/oxygen tanks.

      ReplyDelete
    2. What you are doing here is not a comparison between dry launch and wet launch, but between dense fuels and hydrogen for space applications.

      For a fair comparison it would be better to use the same fuels.

      For example, have a LOX depot in low earth orbit that gets filled by Falcon 9 flights. Once it is filled, you launch a hydrogen stage with a similar mass ratio as the centaur on a falcon 9s9, but with just the LH2 tanks filled. Fill it up with LOX, and then dock the payload, which is also launched on a 9s9.

      The scaled up centaur will be able to get about 20t to the surface of the moon. That should be more than enough for a moon mission or even a base.

      ReplyDelete
    3. Meiza,

      I'm not so sure a tankage ratio of 50 is preposterous. Remember that this is the marginal tankage ratio: the engine, avionics, nosecone, thrust structure, and anything else are already paid for. All that's happening here is the Falcon 9 upper stage tanks are being stretched, and some insulation is being added.

      What do you think the marginal tankage ratio on Zenit is? Maybe 35?

      I looked at LOX-kero specifically because it requires only marginal tankage and has high density. LOX-LH2 requires another engine, avionics, etc, if you launch with a Falcon. I haven't done the numbers on all the possibilities, but my guess is that marginal tankage is a requirement for this application.

      I might run the numbers assuming Falcon 9 has a stretched Centaur upper stage and caches just LOX in orbit, as Anonymous suggests. But this scenario presumes SpaceX wants to deal with LH2. If I worked there, and most of my business was in Earth orbit, I wouldn't.

      ReplyDelete
    4. I ran some numbers myself. The centaur has a dry weight of 2026kg and a fueled weight of 22825kg. I could not get information about the mixture ratio, so I assumed 5.5. That gives a hydrogen weight of 3200kg and a total weight without oxygen of 5226kg.

      According to your very nice cheat sheet, it takes a deltav of 5500m/s to get to the lunar surface. A normal centaur has a deltav of 5500m/s with a payload of 4500kg. Scaling this up to the maximum LEO payload of the 9s9 gives a moon payload of 21312kg.

      This assumes a "lunar crasher stage" approach like in george william herberts "lunar millenium" proposal.

      ReplyDelete
    5. I'm curious if you'd looked at using tether assist for the beyond LEO component...

      Here's a paper that uses a preposterous aircraft but a buildable tether design...

      from

      http://www.niac.usra.edu/studies/studies.jsp

      click on Hypersonic Airplane Space Tether Orbital Launch

      ReplyDelete
    6. Mike,

      Funny thing, I've just been emailing a friend at LiftPort about the very same thing. I've read the Tethers Unlimited AIAA report, but not this one.

      It seems to me there is a tradeoff between tether length and airplane speed. I'm surprised that a Mach 12 aircraft is a good choice. I'd think it would be easier to do a mostly subsonic aircraft that does a rocket-boosted zoom into near-vacuum, maybe 1000 m/s at payload transfer, and use a much longer tether with a larger taper factor. Maybe this paper will go into how the taper factor varies with tether length and tip speed.

      Another thing I'd like to understand about tethers is whether you can "crack the whip" in order to get more tip velocity with only a local increase in required tether strength. It'd be pretty cool to store energy in the tether with a travelling wave that had all the benefits of rotating tip speed without the full-length strain of rotation.

      ReplyDelete
    7. Does not Falcon 9 Heavy with its payload of 53 tons rather change the picture? An entire Apollo spacecraft- CM+SM+LEM weighed 45 tons. This could probably be reduced , with modern alloys to nearer 40 tons. the remaining 10-12 tons could consist of a Merlin1e engine wt 1 tons ( thrust 138,000lbs in vacuo) , and stretched fuel tank 3-4 tons + fuel 6-7 tons of fuel in one go. Add to this a second Heavy Launch with c 50-51 tons of fuel. Dock in LEO transfer fuel and go for TLI.
      If the fuel for the third stage were LOX/LH2 there would be a considerable margin of excess. With RP-1 , improvements in the Apollo stack would not need to be too radical, and if the Isp of the third stage could be raised to 326( cf Kestrel) and even the use of jet fuel might be preserved?

      ReplyDelete