## Sunday, April 30, 2017

### Alternate ITS missions part 1

The Interplanetary Transport System is a spacecraft concept developed by SpaceX and designed to colonize Mars. While it is designed for that specific goal, it could feasibly be adapted to other missions. This post, part 1, talks about the performance of the ITS, and the second part will talk about what missions it is capable of.

The ITS has two configurations, the ship, and the tanker. The ship is designed to carry 450t or 100 people to Mars, while the tanker is designed to refuel the ship in Earth orbit.

Let's take a closer look at the performance.

First of all, the maximum delta-v.
Using the Tsiolkovsky rocket equation (DV = Ve*ln(minitial/mfinal)) like so:

DV =  3,747.42*ln(2100/150) = 9889 m/s

This is an impressively high delta-v, however it assumes no payload, with the standard ITS configuration (not the tanker).

With the tanker configuration:

DV = 3,747.42*ln(2590/90)  = 12589 m/s

You can calculate how much delta-v you need for transfers between planets with a porkchop plot, or you could just use a handy delta-v map of the solar system that assumes reasonably efficient transfers.

(Chart from Atomic Rockets)

We can reverse the rocket equation to find out how much payload we can carry, given a specific required delta-v. Wolfram|alpha can do this for us easily, and the answer is mfinal = minitial*-DV/VE
= Euler's constant, or ~2.71.

Payload equals mfinal - empty mass
Empty mass differs between the tanker and the standard ITS configuration by 60t. It's hard to tell what of that is necessary for a much smaller crew, as might be used on these missions. A safe bet is probably around 120t, halfway between the two numbers.

Propellant mass also differs, with 1950t for the ship and 2500t for the tanker. In this case, to keep costs low, the ship value of 1950t would be used, as there is no space for crew in the tanker, and changing the size and shape of the composite tanks is expensive.

Note that while SpaceX uses a value of 6km/s from low earth orbit (LEO) to trans-Mars injection (TMI), more efficient (but slower) transfers use on the order of 3-4km/s. Presumably, this is done to minimize life support costs; both consumables and radiation shielding. However, if you're sending 5 people instead of 100, consumable costs per day only scale 1/20 as fast per unit time, so almost any other missions would sacrifice travel speed for payload.

The ITS has 3 sea level Raptor engines, and 6 vacuum Raptors. Basically, in a vacuum you could use the sea level engines in addition to the vacuum engines, but it would just hurt our delta-v. In an atmosphere, you can't use the vacuum engines due to flow separation, which happens when your engine is overexpanded. (flow separation is an extreme example of what causes the space shuttle main engines to wobble as they start up, as they have to be efficient throughout the entire atmosphere: https://www.youtube.com/watch?v=hDCCBgppG4s)

So the ITS has different thrust-to-weight ratios (TWR) for different situations.

3*SL Raptor = 9150kn =  933 metric tons-force = empty TWR of 7.775