Heat rises, yes? So “up” is away from the engines.
Coincidentally, that aligns with the direction of thrust.
So our local pseudogravity will agree- the engines are ‘down’, helm is ‘up’
No, heat expands. In interstellar space, there is no significant “up”, at least, no on the scale you would be talking about. Down might, for the payload, be aft-ward, but if something is not attached to the ship, there is no meaningful concept of up or down. If you have engines, you are pumping heat out the nozzle and to the aft in order to accelerate (or ply the local fluff), but you are leaving it behind, it is expanding to move you forward, which yields cooling (for the propellant). So even if your engine is mounted on a short pylon, if you design it efficiently, most of its heat will go into the tail stream. Ideally, anyway.
While the engines are running, aft is down for anything inside the ship.
Anything outside the ship is not in relevant to the discussion.
Yet, “down” aft is not relevant to “heat rises”. Heat on rises because “up” is an area of lesser density and the material is fluid. If you put a steel rod in a smith’s fire until its middle section is white hot, then plant the rod vertically in the ground, the heat will not tend to migrate upward (skyward) but will spread in both directions along the rod, possibly a little faster on the side that is colder. The only reason waste heat would migrate “helmward” is if it is cooler than aftward or there is a surface that gets hot from capturing EM off the engine.
Even if we launched tomorrow, we couldn’t be out of the solar system in 10 years. At least not with any current technology I’m aware of.
You don’t have to be out of the solar system in ten years according to the OP-just off the planet.
If we’re changing the parameters of the OP to something realistic, this is why I made my complaints about the closed life-support system. The closed life support system is ironically the most plausible part of the system. Lifting stuff from Earth, assembling it in space, and rocketing off to Tau Ceti are totally impossible, and this is why I wanted to make clear that a closed life support system that could support X number of people for Y years with food, air, and water is something that has never been done, and the sorts of experiments that have been done, like Biosphere 2, show that this is a really hard problem.
And that’s with free energy from the sun. Require that you power the plant life cycles with artificial light make it really really hard. I mean, yes, we know how to build nuclear power plants. And we could lay in enough Uranium or Plutonium to power it for 100 years, or 200, or whatever. But how many light bulbs are you going to need? How many virtual acres of hydroponic crops are you going to need per person? I realize you can stack racks on top of each other, but you’re going to need a lot of racks, and a lot of lightbulbs, and those lightbulbs are going to break and get dirty. You’re going to need an underground lightbulb factory.
You’re going to need factories that can manufacture all sorts of things that we just take for granted as part of the background noise of industrial civilization. And you can’t revert to a simpler lifestyle, because the survival of the people in the biosphere depends on them being able to fix, maintain, and rebuild every part of the infrastructure of the biosphere, from the nuclear power plant to the farms.
And not only that, they’re going to have to train their kids to do the same work. No one goes in, no one comes out. If you have a village of 100 specially chosen and trained nuclear engineers and hydroponics experts and fabrication specialists and psychologists, and they have 100 kids, how many of those kids will be trainable into top notch nuclear engineers? You can choose the cream of the crop from universities around the world for the initial crew, but the kids are guaranteed to show reversion to the mean, even with top notch educators packed into the tin can.