> 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.
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)