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Originally Posted by jmurrell
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If you have to bring your fuel up to speed with your engine to convert it, then your ship speed will stagnate at the engine's effective exhaust speed.
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Isn't this true for any engine though?
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No, you can do somewhat better if you carry a tank of fuel with you rather than scooping it up just as you need it. Using the internal fuel supply, the maximum speed you can achieve is:
Vmax = (exhaust speed)*natural log[ 1 + (mass of fuel)/(mass of rest of ship) ]
Since the mass of the stored fuel can be much larger than the mass of the rest of the ship, the final speed can be larger than the exhaust speed by some (not very large) factor.
Actually the best thing to do is to run off your collectors until you stagnate at (exhaust speed), then turn off the collectors and switch to your tanks. This adds an extra (exhaust speed) to Vmax, above.
As Anthony points out, having the Universe uniformly filled with fuel free for the taking, and convertible at arbitrarily high rates, leads to some interesting consequences. Which is part of the fun of SF.
TeV