[Runequest] Fact check

Asher Royce Yaffee ashersensei at gmail.com
Wed Mar 27 13:11:02 EST 2013


Hi, All,
   With your permission, I will become dull, plodding and pedantic.

   First, the case of the fleas on the sling.  Imagine that 10,000 Greek
mercenaries wandering through the Persian empire have some slingers with
them.  One of these slingers is especially flea-bitten, so much so that
there are even fleas on his sling.
   As flea-bite swings his sling about, our first flea hangs onto the sling
at six inches radius (distance outward from center).  Circumference
(distance around edge) is 2 times pi times radius.  So, 1st flea travels 2
x 3.14 (or so) x 6 = 37.68 inches with each rotation of the sling.  Every
time flea-bite swings once around, 1st flea travels about a yard.
   Our second flea hangs on at 12 inches radius.  So, 2nd flea travels 2 x
3.14 x 12 = a little over two yards.  No surprise, right?
   But, in a single swing of the sling, that means 2nd flea travels twice
as far as 1st flea.  And that means 2nd flea travels twice as fast.

   Where am I going with all this?  The troll on the rim is like the 1st
flea -- closer to the center.  Only this time, the center is a star instead
of a slinger's hand.  The floor of the ring is like the 2nd flea.  The
floor is farther out from the sun.  Therefore, the floor is spinning faster
than the rim.

   When the troll makes his jump, he has the rotational velocity (motion
spin ward) of the rim.  When the troll reaches the ring floor, he will
encounter a landscape with greater rotational velocity.  So, if he lands in
a forest, the trees will come at him as if he drove a car into them.

   How much faster is the floor than the rim?  I have to look up the
formula and plug in the numbers.  First chance I get.  In the meantime, ...

   Maybe the troll doesn't need a parachute for his drop.  His top speed of
descent will be about 9.8 meter/second, or 32 feet/second -- the equivalent
of me jumping from 16 feet.  (A 16-foot drop is very bad for me, but maybe
the troll can make it.)  Maybe he needs the parachute instead to speed up,
to help him "catch up" with the ground speed when he gets within a few
hundred meters of the floor.  Deploy it sideways in order to match the
local windspeed (which people on the floor would perceive as the still air
and normal breezes of the day).
   Does that make sense?
   Sincerely,
Asher
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