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.