On Sat, Dec 23, 2017 at 03:33:33PM +1100, Rob O'Connor wrote:
> Richard Aiken wrote:
> > To my original question of "Is 5% of volume enough fuel for four
> > round trips to the typical 100d limit?"
[...]
> With 5% fuel mass (water 5% of volume), as previously calculated,
> one round trip with 1G continuous acceleration requires an exhaust
> velocity of ~9460 km/sec.

I get a slightly lower figure, but that could be due to differing
assumptions.

Taking Earth's 100D limit as "typical", I get a midpoint speed of
113 km/s, and 226 km/s delta-V for a minimum-time one-way trip at
1 gee, finishing at relative rest on arrival.  A round trip thus
requires 452 km/s delta-V.

If the reaction mass is 5% of the ship's mass, the exhaust speed would
need to be 8800 km/s.

> If we assume highly efficient fusion drives with an exhaust velocity of 10%
> of the speed of light:
> delta-v = exhaust velocity x ln(initial mass/final mass)
> delta-v = 0.1 x c x 0.051, using a fuel mass fraction of 5%
> = 1530 km/sec

Yes, which is ample for 3 round trips.

It would be enough for four round trips under slightly more relaxed
assumptions.  E.g. not needing to finish at relative rest, or taking a
few percent longer to cross 100D by coasting for a bit.

> So our water rockets likely violate conservation of mass-energy. You
> can't get more energy out of something than mc^2 for a given mass.

I don't see how you get that.  Did you accidentally apply the
ln(1/0.95) factor twice?

- Tim