Two big problems:

1. Details on submarine nuclear reactors are classified, but five minutes' Googling shows that a reasonable guess for their total mass (including shielding) is 1,000 tons. Meanwhile, the entire payload to LEO of the largest rocket ever successfully launched, the Saturn V, is only 155 tons -- and that's for the entire top stage.

2. Submarine nuclear reactors use water for cooling. Water that is not available in space. Cooling would be a huge problem.

So, existing submarine designs are not practical. You'd need to design something from the ground up that is much lighter, and the cooling system would be entirely different and likely more massive, since you don't have all of that free water available to dump heat into. Instead you're talking massive radiators.

Good point re: the mass of the reactor, that's a hell of a lot more than I'd have guessed.

But any mission involving humans is likely to carry a large amount of water beyond the crew's personal needs, because it makes such a good radiation shield. So presumably the same water would be used for cooling the reactor.

I am not convinced, if you can fly a reactor : https://en.wikipedia.org/wiki/Convair_NB-36H then I feel it unlikely that it weighs 1000 tons.

It all depends on the size and design of the reactor, though. A reactor that you put on a plane just for the hell of it (which is what that was) is going to be a lot smaller and lighter than a nuclear reactor that needs to power an entire submarine. The point to my reply was that submarine nuclear reactors were in no way suitable for space use because they aren't optimized for weight at all. Reactors optimized for plane use would be a closer fit. The reactor in that plane could be lifted to orbit on a Saturn V, so we're making progress, but, and this is a huge but, it was air-cooled.

A 3 MW reactor puts out a hell of a lot of heat, and without the benefit of air-cooling in space, I'm not sure what exactly you would do with all of that waste heat. Consider how massive the space shuttle orbiter's radiators were (they are on the inside of the cargo bay here: http://i.stack.imgur.com/Flgzb.jpg ), and all of that is only capable of shedding waste heat in the amount of ~6 KW! We can put a much more capable reactor into space than we can possibly cool, so we haven't bothered. Cooling is the real problem. The total mass of the radiators and the structure required to support them ends up being way more than the reactor itself.

So for good long distance transportation in space, not only do we need a working, efficient emdrive, but we also need better power generation that is much more efficient from a waste heat perspective. These are really hard problems.

You don't have to set off the equivalent of 500,000kg of TNT at the business end of a submarine to put it into the water.