# Correcting the numbers on Build the Enterprise

Crowlspace corrects various errors with Build the enterprise

Build the Enterprise, hit the news because of the author’s rather quixotic call to build a real interplanetary version of that most famous fictional starship lineage

I was directly emailed about the site but held off on a posting.

1. I suspected there were some significant calculation problems
2. The idea of spending a trillion over twenty years for this is not something I endorse. I think the trillion dollar estimate is low and justifying because we wasted over a \$100 to 200 billion on each of the space station and on the space shuttle is not a good plan. I would rather put money into bootstrapping into space and focusing on lowering costs. Get a fully reusable Space or Blue Origin system and work on fuel depots and other systems for lowering costs. I would also put money into non-space goals like SENS life extension, molecular nanotechnology and various approaches to nuclear fusion, deep burn fission and LENR

Numbers in Build the Enterprise

Running the numbers, the figures are wrong, wrong, wrong.

Here’s a preliminary list.

(1) Wet mass is quoted as 84,822 tons. Propellant load is 12,474 tons. Yet elsewhere, in pounds, it’s 187 million/55 million. Inexplicably the propellant mass has been halved. To get to Mars in 90 days with the quoted mass-ratio, (187/(187-55))= 1.42, means a very high exhaust velocity is required. Exhaust velocity and jet-power are inextricably related by:

P = 1/2.T.v

where P is the jet-power, T the thrust and v the exhaust velocity. To get to Mars in 90 days requires a high delta-vee (dv) – enough to travel to Mars on a short trajectory, against the Sun’s gravity, then matching to Mars’ orbital velocity. With a VASIMR that low mass-ratio might get it to Mars in 90 days – with a dry tank. The 0.002 gee acceleration quoted however is IMPOSSIBLE. Thrust, T = M.a i.e. mass (84,822,000 kg) times 0.0196 m/s^2 = 1,662,511 newtons thrust. With a bit of algebra we find that with a 1.5 GW jet-power the exhaust velocity is an impossibly low 1,262 m/s. A reasonable exhaust velocity (high-thrust VASIMR mode) is 15,000 m/s – meaning a maximum acceleration of ~0.00024 gee or a jet-power of nearly 25 gigawatts.

However a lot more propellant will be needed if the vehicle thrusts all the way at that exhaust velocity, so on a typical trip to Mars a VASIMR steadily builds up the exhaust velocity to a maximum 300 km/s at the half-way point, then a steady decline as the vehicle slows down for Mars arrival.

Often people will say VASIMR can get to Mars in 39 days. They don’t often say what power and fuel that requires. To reach Mars in 39 days also required that particular VASIMR option to aerobrake into orbit around Mars – something not recommended for a large vehicle like “Enterprise”. The required propellant mass would be 230,000 tons, and the power source would mass 48,285 tons, while delivering 96.6 GW of electrical power to the engines. A 90 day mission is far less challenging in technological terms.

There is a major issue not addressed by the TV spaceship creators. Waste heat. Specifically for the Gen-1 “Enterprise” the VASIMR is essentially an externally powered fusion rocket – hydrogen plasma is heated and directed just like in an operating magnetic-mirror fusion reactor. The difference is that there’s no attempt at energising it all the way to fusion conditions. In theory, a VASIMR could be up-graded to be an actual fusion rocket. But without actually making its own fusion power, the VASIMR needs to get power from fission reactors, and they all put out excess heat. There’s only one way to get rid of excess heat in space when it’s not being thrown over-board in the rocket exhaust gases and that’s via radiators.

And the “Enterprise” – Gen1 or the fictional versions – don’t have them. A real “Enterprise” will need a set of “wings” – big radiators – to handle the heat or else the whole lot will cook.

The “Enterprise GEN-1″ 3 times bigger than the fictional version? The fictional upgraded “USS Enterprise” was just over 300 metres long, yet its proposed namesake is ~950 metres long. I suspect an imperial-to-metric conversion error.