I have found this thread. It can no longer hide from me.
That said, let the nitpickery commence.
"Fast" is in fact a bit of a slippery concept when it comes to spacecraft. Speed in space is all relative to begin with; the more useful measure for a spaceship is delta v, "change in velocity" - especially, how much you can change your velocity before you run out of gas. For any given propulsion technology, the way to get more delta v isn't a more powerful engine but a bigger fuel tank. What a powerful engine does give you is higher acceleration - so you can achieve any given delta v more quickly.
This is, of course, wrong.
The delta v of any given space ship is not as simple as the writer assumes. Calculating the movement of a variable-mass system like space ship filled to brim with propellant is
complex and annoying and time-consuming, so let's simplify the problem by looking at a short duration burn, where the mass of expended propellant is significantly less than the entire mass of the ship:
m << M
The mass of the propellant is given ejection velocity v
e, and the conservation of momentum assures that the ship gains equal but opposite momentum.
Now, the momentum given to the propellant mass is
p = mv
ewhile the momentum that ship gains is
p = Mv
And conservation of momentum means that
mv
e = Mv
and solving the equation for the end velocity of the ship, we get
v = mv
e / M
From here, you can see the following statements can be made:
1. Increasing propellant mass expelled during the burn while keeping ejection velocity and ship mass constant will increase the end velocity v.
2. Increasing the ejection velocity of propellant while keeping other variables constant will increase the end velocity.
3. Reducing ship's mass and keeping engine parametres constant will increase the end velocity.
By now you should see the flaw in the reasoning in the quoted paragraph. "More powerful engine" does not only mean that it can dump bigger propellant mass per
dt out into space, it can also mean that it can do it at higher ejection velocity, which is in fact the more important term for the efficiency of the engine.
Basically, the higher the ejection velocity, the less propellant you need for a given change of momentum (and velocity). Keeping your ship as light as possible will also help immensely, but as far as propulsion technology goes (as long as it's based on conservation of momentum), increasing the amount of propellant is much less efficient than increasing the ejection velocity.
EDIT: Of course, it could be that when the writer says "any given propulsion technology", he means to say that the ejection velocity is fixed or in the same order of magnitude; however I disagree with this sort of classification, because especially with electromagnetic engines you can increase the ejection velocity pretty much linearly, unlike with chemical rockets where you are limited by materials and the properties of the expanding gas and chemical energy available from reactions.