Here's the problem I had, maybe you can have fun with it.
First a couple of assumptions:
1) SFC propulsion is not Warp, but rather with Impulse engines that the Warp Core powers (which is represented by Warp boxes).
2) The Franz Joseph number for mass of the enterprise is correct: 190,000 metric tons
3) According to SFB: 1 hex is 10,000 km
4) IIRC SFB says: 1 turn is 1 minute
5) ships in SFB have an acceleration of 10 hexes per turn.
- meaning that the ship can increase its speed by 10 hexes per turn per turn.
6) An impulse drive is essentially an efficient Ion Engine
walk through the math with me here.
FCA can get up to top speed (30 hexes per turn; dropping the last 1 for ease of math for now; or 300,000 km/t or 5,000 km/s) in 3 turns, or 180 seconds.
Acceleration = ( desired Velocity - Initial velocity ) / time
Acceleration = 5,000 km/s / 180 seconds.
Acceleration = 27,778 m/s/s (or 27.8 km/s/s)
So...
Thrust = Mass * Acceleration
Thrust = 190,000,000 kg * 27,778 m/s/s
Thrust = 5,277,820,000,000 N (or 5,277,820 Meganewtons)
That's really damn high.
Let's put this into real-world terms.
A hypothetical fusion reactor puts out about 1000 MW (using theoretical numbers from ITER)
VASIMR, a real-world plasma drive, puts out 1N of thrust for every 100 kw it gets. I'll even assume that Impulse drives are 10 times as efficient as VASIMR and put out 1N for every 10 kw it gets.
Assuming that the Thrust to Input curve of the VASIMR (and by extension our theoretical Impulse drive) is linear, if we put it one Fusion Reactors worth of power, we get about 100 KN worth of thrust.
Since one "point" of power from an Impulse reactor is the same amount as one "point" from the warp reactor, we can assume that each Warp Box produces a similar amount of energy (the increased number of boxes represents both higher output and how resilient it is to damage).
So lets dump all 36 "points" of power the F-CA produces into the impulse engine - an amount coming out to about 36,000 Megawatts (30 warp boxes, 4 impulse boxes and 2 AWR boxes; this even ignores the SFB rule that only Warp power can be used for movement).
with all 36,000 MW thrown into our theoretical impulse drive we get a thrust of 3,600 MN - only about 0.0006821% of what we established as the required impulse engine output as.
and thats when I said "enough of trying to figure this out today" >.<
Perhaps Tus, who is an actual rocket surgeon, can come in and see if I've screwed the pooch in my math.
EDIT: Even if we technobabble handwave stuff by using some sort of sub-warp coil to reduce apparent mass in the impulse deck, I don't like the numbers that it would have to tweak the mass by, we're talking having to multiply the mass by 0.00001 or so for it to start to work