-Z- (Z@Gundam.Com)
Mon, 11 Oct 1999 20:18:37 -0700


At 19:08 10/10/1999 -0700, you wrote:
>Shouldn't how much fuel you are willing to burn be taken into consideration.
>I mean, if you are truly in a hurry, and put your ship into constant burn
>for 40% of fuel starting from L4 to L5 and blow out the rest of the fuel
>near L5 for fast deceleration that should cut down on the transit time.
>(Not the most comfortable or healthy way of traveling, but should be
>faster).

Just so -- a constant-boost ship with an acceleration of one gravity
(9.80665 m/sē = 35.3039 km/h-s = 32.174 ft/sē) could go from Earth orbit to
lunar orbit (about 380,000 km) in 3.5 hours with a total delta-V of 122
km/s. At one gravity, you rack up 35 km/s in an hour while covering a
distance of 63,500 km. Your trajectory is still an arc, but now it's a
very flat arc.

We never see a constant-boost ship in Gundam. They most cruise in a
"Lazy-S" doubly-tangent Hohmann minimum-energy transfer orbit, conserving
fuel (whichis to say "mass") expenditure at the expense of travel time.
The closest we see is the pursuit of the Delaz Fleet by the Federation in
Gundam 0083, where the Feds blow off all of the propellant trying to catch
up with the colony falling toward the Moon. This little jaunt illustrates
the fact the Gundam ships simply don't carry that much propellant mass in
relation to their overall mass. In other words, they don't have a very
high mass-ratio.

To be economical, the mass-ratio should be no worse than 3:1, meaning that
if you start out with a metric ton (1,000 kg = 2,204.62 pounds = 1.10231
short tons) you arrive with a third of a metric ton (333.3 kg = 734.801
pound = 0.3674 short tons) and probably can't get much better than 1.1:1,
meaning that if you start out with a metric ton, you arrive with 90% of a
metric ton (900 kg = 1,984.16 pounds = 0.99208 short tons). The Gundam
ships seem to have a mass-ratio of about 1.5:1 -- very economical, but not
much mass to throw overboard.

Here's the kicker: the exhaust velocity required to obtain a delta-V of 122
km/s with a mass-ratio as uneconomical as 3:1 and an acceleration of one
gravity is on the order of 2,000 km/s, which corresponds to a temperature
on the order of 50 million degrees Kelvin.

OK, you don't need to boost at a full gee. How about a tenth of a gee?
Well, that drops your total delta-V from around 200 km/s down to about 65
km/s, but triples your travel time from 3.5 hours to 10.5 hours -- and
still requires a ship that's three times as much propellant as payload. By
the time you whittle your mass-ratio down to 1.5:1, you've quadrupled your
travel time to 42 hours or about one-third of the time it would've taken
you to coast there on a Lazy-S. You've also expended a megaton of highly
energetic plasma in a continuous stream both fore and aft across your
entire trajectory.

I'd say that this sort of thing would be OK on a flight out to Jupiter,
once you'd cleared the Earth Sphere and its busy intercolonial space
traffic, but that it'd only be used for the most serious emergencies within
the Earth Sphere.

-Z-

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