I didn't think this through all the way, but something seems fishy about that article:
... if the exhaust velocity can be made to vary so that at each instant it is equal and opposite to the vehicle velocity then the absolute minimum energy usage is achieved. When this is achieved, the exhaust stops in space [1] and has no kinetic energy; and the propulsive efficiency is 100%
This argument is not Galilean invariant, which makes it seem highly dubious to me. There is no "stopping in space"; what absolute inertial frame defines what "stopped" means?
You always want to have an exhaust velocity as high as possible. The energy you have to impart to the exhaust is 1/2 mv^2, but you get m*v momentum. So small exhaust mass at very high speed will give you the same momentum, and cost you much less energy than bigger mass and less speed.
Sorry, this I'm completely wron... I mean: I was testing if you read the comments before upvoting.
The 1/2mv^2 vs mv points to an exhaust speed as low as possible, to get as much momentum as possible from as little energy expenditure as possible.
Now, if your exhaust comes from the outside world then that makes perfect sense. And this is why you have turboprop and turbofan engines: you slow down the exhaust of the turbine, speed up outside air, and do a favorable energy/momentum trade.
But in space you have to carry the mass you will exhaust. You don't have much choice: all the energy you get from burning fuel will be transfer to kinetic energy of your exhaust (in the reference frame of the rocket).
Yeah, you're right. A bit of algebra reveals that your delta-V per MASS of fuel (which is a frame-independent quantity) goes as the (propellant specific chemical energy)^.5.
However, it is also true that if you calculate the delta-V per unit propellant ENERGY used, it decreases with the propellant specific energy.
Since you don't really care about how much energy you carry but only about how much fuel you need to use per delta-V, it's always better to have higher exhaust energy. (As long as you are using a chemical propellant, i.e. the mass carrying the energy and the reaction mass are the same.)
The statement in the article about "propulsive efficiency" is total bogus. First: the relative kinetic energy of the rocket and the exhaust IS a frame-dependent quantity, so it's meaningless. Second, any reasonable measure of efficiency, like the delta-V per fuel energy, reveals that the "optimal" value is an exhaust velocity of zero. (Optimal in the sense that it's more energy efficient, but only because the delta-V goes to zero slower than the energy. It's still a useless optimum, because it results in no delta-V at all...)
Pretty sure the implied inertial frame is the one relative to the spaceship, and not any other encapsulating frames.
But I linked that mainly for the table just down the page a little comparing various efficiency measures of different propulsion systems. I'm pretty sure that chemical rockets are the least efficient we've ever implemented or imagined, barely sufficient for travel within the solar system, and certainly not efficient enough for any trips, round or one-way, beyond our solar system.
I think you're right. You get acceleration in one direction by accelerating and ejecting mass in the opposite direction. The degree to which it's efficient depends on how much of your energy source was converted into kinetic energy of the ejected mass, and how directional that ejection mass was. The relative velocity ("stopped" versus moving relative to some external frame of reference) only determines how much propulsion you're getting with respect to that frame of reference, nothing to do with efficiency at all.
On the other hand, this doesn't make blowing stuff up efficient. An explosion, unless it's lensed properly, will push mass equally in all directions.
http://en.wikipedia.org/wiki/Spacecraft_propulsion#Power_use...