### SpaceX ITS: Maximum Performance

The SpaceX Spaceship, with a full tank, has a mass of 2,100 tons, of which 150 tons is vehicle structure. Mass ratio is 2100/150 = 14. With an Isp of 382 seconds – call it 3,750 m/s – the MAXIMUM delta-vee is thus LN(14)*3,750 = 9,896 m/s.

The Tanker is a simpler vehicle, with 90 tons structure and 2500 tons propellant, thus a mass-ratio of 2590/90 = 28.78. Thus a maximum delta-vee of 12,598 m/s.

This assumes no payload. The maximum payload for the Spaceship is said to be 450 tons. Of course this could vary according to mission needs, as alluded in the previous post.

Let’s contemplate two full Tankers used as boosters for a Spaceship, also with a full tank. What’s the maximum delta-vee?

The mass-ratio of the first stage is thus (2100 + 2590 x 2)/(2100 + 180) = 3.193

Second stage is 14, and as stage mass-ratios multiply, overall it’s 44.702 i.e. a delta-vee of 3.8 x 3.75 = 14.25 km/s.

This assumes no payload. If it could all be added instantaneously at a point in Low Earth Orbit, with 7.75 km/s orbital velocity, then 19 km/s would be added to the vehicle’s solar orbital speed it shares with the Earth.

Let’s rework the figures for a fully loaded Spaceship:

Stage 1: (2550 + 2590 x 2)/(2550 + 180) = 2.83

Stage 2: 2550/600 = 4.25

Total mass-ratio = 12.034

Delta-vee: 9.329 km/s

As mentioned previously, the minimum delta-vee for a parabolic solar orbit is 8.75 km/s from LEO. Working out gravity losses from finite time boosts in LEO isn’t easy, but at a guess it’ll be roughly 0.1 km/s. That leaves about 0.4 km/s in the tank. We’ll need that aerobrake at Titan to land.

Getting to Callisto or Ganymede – Europa being in a radiation bath that’ll require a staging post to outfit the Spaceship properly – requires some more serious delta-vee. That’ll be the next post’s topic.