Friday, November 22, 2013

Getting to Mars With The Reusable Falcon 9

Isn't it a bit odd that the most promising reusable launch vehicle under development today is being build by a company with a proclaimed love for heavy-lift launch vehicles?

As the Falcon 9 Reusable approaches the cusp of operations, with a successful demonstration of first stage reuse expected sometime next year, SpaceX is already moving on to a methane engine - Raptor - four times as big, for a rocket - MCT - with a much larger core size.

This, we're told, is Elon Musk's strategy for going to Mars and it's so much warmed over Bob Zubrin - Mars Direct, Mike Griffin - Apollo On Steroids, cargo cult of the Saturn V, stuck-in-the-1960s thinking.

If you have an operational reusable launch vehicle, as SpaceX says it is their goal to have, then there's much more sensible ways to get to Mars. Come on boffins, get the lead out, let's do the math on this one.


According to the best public numbers I can find, the second stage of the Falcon 9 v1.1 has a dry mass of 4,900 kg and launches with a propellant load of 70,800 kg. This is a very impressive propellant mass fraction of 93.5% and with its single Merlin 1-D engine delivering a specific impulse of 340s it can throw 22 tons on a fast transit (just over 6 months) to Mars (a delta-v of 4.3 km/s).

This alone is probably sufficient to do a great Mars mission. The hitch, of course, is that the second stage gets to orbit empty (well, with some unknown ullage) and must be refueled before it can be sent off to Mars. Also the typical payload to low Earth orbit of the Falcon 9 v1.1 is only about 13 tons, leaving us 9 tons of Mars-bound payload short. As it turns out, this is about the mass I'd estimate for a minimal Dragon-based Earth return capsule, so we'll assume the crew come and dock with the 13 ton Mars transit vehicle later.

The expectation is that the Falcon 9 Reusable will have about 25% less payload to orbit capability as it does acting in expendable mode - that is, about 10 tons, so the crew launch vehicle will not have to be expended. This is what you'd expect, as SpaceX is designing the Falcon 9 Reusable to reduce the cost of ferrying crews to the space station.

Now, about that fuel. We'll need about 70 tons of it, and at 10 tons per Falcon 9 Reusable flight, that's seven flights. However, part of the fuel is cryogenic - the liquid oxygen - and some of it may boil off depending on the length of the launch campaign. So let's say eight Falcon 9 Reusable tanker flights total. Still not enough? Okay, let's say nine flights. What's that? You want more? Okay, let's say ten flights. It's a fully reusable system.

There's some challenges in transferring liquid oxygen in zero-g, but they're minor compared to.. say.. liquid hydrogen. Figure it out.

What if a 13 ton transfer vehicle and a 9 ton crew return vehicle - 22 tons total to Mars transfer orbit - isn't enough? That's okay, just stage together two Falcon 9 v1.1 second stages. Both require 70 tons of fuel, so you're only doubling the total number of Falcon 9 Reusable flights, plus whatever you need to get the massive new payload into low Earth orbit.

Suppose the first stage provides 1463 m/s of delta-v before separating and falling away. The second stage ignites and provides the remaining 2838 m/s of delta-v. How much actual payload is thrown to Mars transfer orbit?

Would you believe, 47,850 kg? Almost 48 tons, surely that's enough!

The Saturn V was an amazing machine, but it was the product of a by-gone era. Fully and rapidly reusable launch vehicles combined with on-orbit refueling will make big boosters obsolete. At least, I sure hope it will.

9 comments:

  1. About damned time we heard from you Trent. Great post as usual.

    Let's also assume mars landers waiting in mars orbit. How many crew are going at 48 tons?

    8kg/day for 210 days is 1680kg + suited crewperson so let's round up to 2000kg per crew (2m3 for consumables.)

    How much mass is the ship? 4900kg for the upper stage (which cost us nothing to keep and pointed toward the sun becomes a radiation shield or a counterweight for artificial gravity.) 4200kg for the Dragon and another 2000kg for the inflatable. 11200kg total. Giving us about 16 crew. So we need 4 landers in orbit. 7 prepositioned landers on mars and another 4 in orbit to follow each crewed lander to minimize travel time once on the surface to the nearest supplies.

    Each lander would have about 30 days of consumables with the crew.

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    1. 48 tons to TMI is about Zubrin's Mars Direct requirement. So yeah, Mars Direct without a heavy lifter would be possible. You could avoid any on-orbit assembly by using Falcon Heavy to throw the entire payload into LEO too.

      However, I think he prefers around 5 km/s from LEO for the crew leg nowadays. That'll take slightly more propellant.. maybe some drop tanks.

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    2. Mars Direct is four crew (bad idea.) A dozen crew would be about 100 tons and require 3 prepositioned landers.

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    3. Nah, a dozen crew is a bad idea for a first mission. Four crew with cross-training is an expedition force that will put robots to shame.

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    4. Well of course, but many hands make light work. They have to land in three landers, so it is four at first. The difference is they don't have to wait 26 months for the next crew to arrive. Two more landers are waiting in orbit.

      To colonize a world there is a huge difference between 8.67 man-years and 26.1 in getting industry started.

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  2. Not obsolete, but for special purposes.

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  3. The main takeaway from all this? We are going. Add Raptor and we may be going sooner. At some point, while Elon is figuring out how to get costs down, somebody else will say, let me use what you've got.

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  4. 3 Falcon Heavy's can supply all needed fuel for 2 F9 Upper stages and based on current pricing on the web site it will be cheaper

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    1. If the Falcon 9-R is fully (and rapidly) reusable and the Falcon Heavy isn't, then there's no question that using the Falcon 9-R would be cheaper. Of course, if the Falcon Heavy ends up being fully reusable, you'll be right.

      What's baffling is that Elon seems to consider either of these options too small and seem to wantsto build a monster rocket (at least 7m diameter core!) that goes to Mars and comes back to Earth in under 6 months!

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