Nuclear thermal or pulse, fission or fusion, aren't enough for interstellar relativistic speeds. They have way too low specific impulse. They don't even have enough for constant acceleration inside the solar system unless the acceleration is really low or the fuel ratio is huge.

> unless the acceleration is really low or the fuel ratio is huge

You’d need kilotons of nuclear fuel and a 10^3 fuel ratio. But that’s plausible.

The economically-plausible answer is antimatter, where the ratio stays in the single digits and starts permitting deceleration. But I wouldn’t call that technologically plausible at this time.

For practical values, nuclear pulse propulsion would only get you up to a few percent of the speed of light.

The best nuclear thermal, gas core, would give you 7000 seconds[0]. A "dusty plasma" rocket (suspend the nuclear fuel in dust form in a magnetic field) might get 100,000 seconds, or just over a day of accelerating at 1g.

[0] for the benefit of non-space nerds: the unit of measure is "lb-force seconds per lb-mass of fuel", which is kinda like "seconds at 1g" if the fuel is a very small fraction of the total mass, which it really won't be in a practical rocket.

g-seconds then? That seems like a very handy unit

> which is kinda like "seconds at 1g" if the fuel is a very small fraction of the total mass, which it really won't be in a practical rocket.

I think you mean “a very large fraction of the total mass”… generally the best efficiency comes if your fuel mass fraction is high, as it means there is little overhead of things in your spacecraft of things that are not fuel (the mass of the engine, etc)

No, I mean small, because I'm talking about the quality of the approximation not the way to maximise delta-v.

If you have 1 gram of fuel and a 1 ton payload and that fuel has 1e6 seconds of Isp, you can accelerate the ship for 1 second at 9.8m/s/s.

If you have 1 ton of fuel and a 1 gram payload and the same fuel and burn at 1 gram/second, the first second is mostly spent accelerating the fuel, which means you're no longer able to just approximate the Isp as "seconds at 1g" in a nice linear fashion — it starts off at 1 gee in this example, but ends up at 10^6 gee in the last moment, a million seconds later.

Makes sense, I misunderstood your initial post. Thanks for clarifying!