gas giant refueling...

Hans:

>>Less than 24 ships per system.  For the Spinward Marches, that comes
>>to less than 6528 ships.
>
>As you pointed out elsewhere, you could need a 1000 ships to guard a
>gas giant. That would help, right? Not to mention the trip from the gas
>giant to the mainworld. Especially if there is an asteroid belt between
>them.

You probably won't bother to defend the gas giant...

If you don't like mathematical analyses of role-playing events, skip
this message.  --Steve

I asserted without proof last year that it is more profitable to buy
fuel at the starport than to do wilderness refueling at a gas giant.
Here is the proof:

Assumptions:

1)  The main world is not orbiting the gas giant.
2)  The gas giants are in the outer system.
3)  For the sake of discussion, the solar system is typical of solar
systems in general (I am not going to locate every gas giant in the
Imperium to prove the point.  I am going to use the solar system's gas
giant's to demonstrate the point)
4)  I will use a free trader, and a fat trader as example ships, because
I am too lazy to dredge up figures for every merchant type written up,
and those two are convenient.
5)  Mean time in Jumpspace = seven days.
6)  Mean time in port = seven days.

Average time to make a single trip (one way) is 14 days.
A ship can make 25 trips per year.
Unrefined fuel bought at a starport costs Cr4389 per trip (free trader)
or Cr7497 per trip (fat trader).

Time required for a one way transit to (or from) Jupiter: 155+ hours.

Assume a ship arrives at Jupiter, refuels, and transits to Terra (based
on a mean time to skim a gas giant from SOM).  The time required to do
so is about 162 hours, with a slight risk of loss of ship (5/1944).

Therefore, a ship which uses wilderness refueling adds about 1 week to
the cycle time for a single one way trip.

A three week trip cycle means the ship will only make 17 jumps per year
(if the crew feels safe about skimping on maintenance, 16 if not).

So, the ship saves immediate out of pocket expenses of Cr109,725 (free
trader) or Cr187425 (fat trader).
A ship will lose, by not jumping, a minimum of the income from a cargo
hold full of consignment freight.  Therefore a free trader will lose
Cr655,344 by making only 17 jumps per year (MINIMUM).  A fat trader will
lose MCr1.5984 under the same conditions.

Since the loss of revenue exceeds the cost of unrefined fuel at the
starport by a factor of 6 for a free trader, and 8+ for a fat trader,
using wilderness refueling at a gas giant is an idea whose time passed
the first time a merchant got hold af a calculator, which was probably
11,000 years ago (the Vilani LOVE profit/loss examinations).

Therefore gas giant refueling is irrelevant to a merchant, and defending
the gas giant superfluous (except from enemy fleets).

Objections to the proof:

Some main worlds orbit gas giants.  True.  If you don't mind the risk of
losing your ship, refueling at a gas giant is useful (in that specific
case).  Chance of losing a ship during gas giant refueling, over the
lifetime of the mortgage: greater than 82%.  How many banks are going to
finance a deal THAT risky.  That chance of loss assumes 17 trips per
year, all refueled at a gas giant.  Over the (80 year) lifetime of the
ship, chance of loss exceeds 96%, assuming the same.  Mean time to lose
your ship id gas giant refueling is SOP : 15.8 years.  Good luck, you'll
need it.  You'll also need to pay for your ship in 15 years if you even
HOPE to break even.  Good luck on that, too.

Some gas giants are closer than Jupiter.  Also true.  Some are farther
away.  A gas giant as close as Mars would add about 90 hours to your
turnaround time.  This reduces flights per year from 25 to 20 (or less).
This reduces lost income from the listed figures to Cr409,590
(Cr999,000).  This is still considerably higher than the cost of the
fuel.  Notice that the revenue from a full hold is higher than the cost
of a year's supply of fuel for a fat trader:  a fat trader should never
do wilderness refueling where the time required is great enough to cost
even ONE jump per year.  That condition applies if the gas giant is more
than 2.0736 Million Km away.  Therefore, by MT rules, a fat trader
should use gas giant refueling only in the case of a main world orbiting
the gas giant, or a gas giant in a captured orbit no more than 0.014AU
distant from the main world.  A free trader loses if it cannot make two
jumps, so the gas giant can be farther away, and still be remotely
useful.  The breakpoint for a free trader is 17.465 million Km
(0.117AU).

So effectively, no gas giant the main world is not orbiting is useful
for wilderness refueling, unless the ship captain doesn't mind losing
money.

BTW, it can be shown that the transit from jump arrival point to a gas
giant is long enough that a free trader/fat trader loses money by going
to a main world that orbits a gas giant.  Transit from Jupiter's jump-in
point to any of it's major satellites is about 20 hours, and Jupiter is
a SMALL gas giant by Traveller standards.  That would add two days to
your turnaround, and knock two jumps off your year's schedule, with
appropriate loss of revenue.

SO, defending the gas giant is largely unnecessary, and wasteful of
ships unless in a war situation (Navies don't care from money).

So, you only need a dozen ships per system to deal with pirates, and
twelve ships as small as a Sloan are NOT hard to come by.  Twelve ships
as small as an SEH aren't hard to come by either.  By TCS rules, a world
with population over about 38 million could support the latter, and
perhaps 10 million for the former.  Trin could buy enough for the whole
Spinward Marches.

It's still a LONNNG way to making piracy safe in the Marches.

Later...

- -- Via DLG Pro v0.985b

[email removed]

I have learned to use the word "impossible" with the greatest caution.
                                    --W. von Braun