I would like to know if there is some formula / graph which would provide / show the efficiency of a certain type of propeller in space. Specifically, I'm interested in the acceleration attainable at certain speeds.
I'm writing a science fiction book and I'm trying to make it as correct as possible, fact wise. The propeller I'm talking about is the ion drive
Now, my book takes place in a world where fusion power is finally ours.
So, please, let us assume that we have unlimited energy so you could power a dozen huge ion drives non stop. OK, there's the question of argon/xenon fuel, let's assume we have 1 year of that.
So... the question is... what speed could you reach?
If a continuous acceleration of $10\frac{\mathrm{m}}{\mathrm{s}}$ is applied (I put that number because it would also constitute an advantage for my crew - living in Earth's gravity), that would mean that a ship would reach the speed of light in just 347 DAYS
But I know that's impossible because the EFFICIENCY of the ion drive would DECREASE as the ship's speed would approach the exhaust speed of the drive's "nozzle" (well, it doesn't have a nozzle per-se, as you can see in Wiki, but anyway...)
Please do not fear to elaborate on top of my question. Let's suppose for example that maybe the ion drives of the future have a much higher thrust/efficiency/nozzle exhaust speed.
This isn't only about currently POSSIBLE facts but also about THEORETICAL limitations which might be overcome in the future (such as fusion energy).