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Date: Tue, 19 Nov 1996 18:59:57 -0500

Subject: Scale of FT (longish and contains physics......)

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There is actually enough information in More Thrust to calculate a
time and a distance scale for Full Thrust. The results are somewhat
surprising.
On page 13 of More Thrust we have the rules for planetary orbits. If
we follow the sugestions there and take an Earth-type planet to have
a radius of 6" then we can get to work.
The radius of the Earth if 6,378 km. straight away we have our distance
scale 1" = 1063 km. We can round it down to 1000km, but won't for
reasons that will be explained later.
Time for a bit of physics. One outcome of Newton's Laws of motion and
gravity is that for a circular orbit T^2 = (4 * Pi^2 * r^3) / G * M
where T = the period of revolution
r = radius of the orbit
G = Gravitational constant
M = mass of object being orbited (ie the planet)
In this case r = 12" = 12,756,000 m and M = 6 x 10^24 kg
Hence, T = 14309 s
Now a ship in this orbit moves 6" a turn around the circumference of
a 12" radius circle.
circumference = 2 * pi * 12 = 75.398"
At 6" per turn 1 orbit = 12.566 turns.
12.566 turns = 14309 s
And so 1 turn = 1138.7 s = 18.98 minutes
So we have our time and distance scales. Now we can calculate some
derived quantities. How much acceleration does 1 point of thrust
represent? If we assume thrust is applied over the entire turn then
this formula applies-
acceleration = change in velocity / time
1 thrust = 1" / 1 turn squared
= 1,063,000 / 1138.7 ^2
= 0.8198 m/s^2
So what? This is nearly exactly one twelth of 1g!
If we had made 1" = 1000km then it would have thrown this neat
coincidence out. If we make the time 19 minutes (1140s) then it
makes it even closer.
There is a problem. Say a ship starts from rest and accelerates at
this velocity. After 1 turn it is moving at 1"/turn. By the rules
it should have moved 1". By physics it should have moved 1/2".
The only way the rules can be correct physically is if a _very_
large acceleration was maintained for a _very_ short period of time.
However, if we apply one of the golden rules of Full Thrust, "always
round things up" we can achieve a solution. A thrust of 8 must move
the ship by just over 7".
This comes out with an acceleration applied for 1/4 of a turn and 1
thrust now equals 1/3g.
A thrust 8 escort can put out a thrust of 8/3g which is fairly good
for what a human crew could stand for extended periods and still
function.
Summary of what we've got so far:
1" = 1063 km
1 Turn = 19 minutes
1 Thrust = 1/3g applied for 4.75 minutes
The 36" range of pasive sensors and A batteries is equivalent to 13%
of a light second, which when coupled with the length of the turn
rather spoils the thread about targetting. There's enough time to
perform over 2000 ping-analyse-shoot cycles in one turn. Is that
enough to give you a 50% chance of hitting?
To move at 1% of the speed of light a ship would need a velocity of
over 3000"/turn!
At this scale our sun would have a radius of 655"!
But wait, I hear you muttering, surely the rules in More Thrust are
optional, what about Jim Webster's idea of defining one table edge as
the planet's atmosphere?
Well, this makes all the ranges much smaller. If we assume that the
short edge of a table 4' = 48" is the diameter of a planet. Then a
new scale emerges 1" = 265 km or 1/4 of what we had before.
How we scale time and thrust in this case is trickier as we have no
data on orbits. But if we assume that this scale implies a rather low
level of technology then gravity control is unlikely and our vessels
will have to operate at thrusts that won't cripple the crew. So we keep
the thrust at 1/3g. This gives us 1 turn = 9.5 minutes or half of our
previous value. If the planet is wider than the table then the scale
is further reduced.
(NB For constant acceleration the time will scale as the square root
of the scaling on the distance.)
That's quite enough for now.
Steve
+---------------------------------+----------------------------------+
| Stephen Richard Pugh |
| ptolemy@meta.physics.ox.ac.uk steve.pugh@dial.pipex.com |
| http://meta.physics.ox.ac.uk/~ptolemy |
+---------------------------------+----------------------------------+
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