From: John Eric Ivancich <ivancich@eecs.umich.edu>
Subject: (whorl) The Physics and Dimensions of the Whorl
Date: Tue, 07 Oct 1997 13:03:58 


[Posted from WHORL, the mailing list for Gene Wolfe's Book of the Long Sun]


Hi Everyone,

I'm going to try to pin down the radius and the circumference of the
Whorl with some physics calculations.  Now it's been more than a
decade since I've had a physics course, so I hope someone will check
my work.

Before I start, I would like to point out two things.  GW was a
mechanical engineer, so he could have done the same calculations, and
probably armed with nothing but a slide rule.  Second, GW, in his
answers to the WHORL, said he didn't know what the dimensions of the
Whorl were.

Assumption #1
-------------

Gravity in the Whorl is about the same as that on Earth/Urth.  Gravity
is measured by the acceleration rate towards the ground.  On Earth (at
sea level, at 45 degrees latitude) it is 9.80616 meters per second per
second.  Since most of us are probably more comfortable thinking in
terms of miles per hour, that would be 78986 miles per hour per hour.

Basic Relationships
-------------------

From the rate of acceleration we can determine the relationship
between the velocity at the inner surface of the Whorl and the radius
of the inner space of the Whorl.

        v*v
    r = ---   ;   "radius equals velocity-squared over acceleration"
         a

Since we know "a", all we need is a good estimate of "v", and then we
have "r".

Also recall the basic relationship between circumference and radius.

    c = 2 * pi * r

Assumption #2
-------------

We have some clues about the velocity of the inner surface of the
Whorl due to information we have about the floaters.

In Nightside, pp. 196-7 (mass paperback version used for all page
references) Silk, while returning to the city in Blood's floater
mentions the trip had taken hours on donkeys.  On p. 204, while in the
city, Silk says it had been less than a half an hour since he'd left
Blood's compound.

If a donkey travels at 5 mph (guess), and it took them 3 hours (guess)
to get to Blood's estate, then it's a distance of 15 miles.  When
returning in the floater it took them 30 minutes, so the floater was
traveling at 30 miles per hour.  If the donkey travels faster, or the
donkey-time were longer, or they spent some time in the city before
Silk mentioned the half an hour, then the floater traveled faster.  I
think it's safe to say, though, that the floater wasn't going any
faster than 60 mph.

Furthermore, that speed is safe, as there were no warnings of "vector
unacceptable".

Assumption #3
-------------

In Calde, pp. 303-6, they (Silk, Hyacinth, Oosik, Quetzal, Xiphias,
the surgeon, and a driver) try to speed away in the floater as the
pterotroopers are attacking.  They achieve an unacceptable vector, and
they, along with objects within the floater, start to float.  This can
only mean that they completely counter-acted the velocity of the
Whorl, negating its gravity effects.

If we can figure out how fast they were going (and assuming a strictly
southerly direction, p. 306) we know the velocity of the inner surface
of the Whorl.

They're in a city street filled with people.  That would seem to put
an upper-limit on their speed.  But the speed must also be
significantly greater than the typical speed the floater travels at,
since apparently they experience no significant altered-gravity
effects at the typical speed.

It thus seems to me, then, that the floater was traveling maybe in the
range of 150 to 200 mph, when they lost the effect of gravity.  Let's
assume the larger.

Calculation #1
--------------

OK folks, here we go.  Are you sitting down???

        200 * 200
    r = --------- = 0.5 miles ; diameter = 1 mile ; circumference = 3.14 miles
          78986

Seems we have a problem, huh?

What if the velocity is 400 mph -- which seems beyond reasonableness.

        400 * 400
    r = --------- = 2 miles ; diameter = 4 miles ; circumference = 12.5 miles
          78986

And we still have problems.

Calculation #2
--------------

Let's try it the other way.  Let's go from radius to velocity:

    v = sqrt(r * 78986)

On May 5, 1997, mantis posted to the WHORL estimating the radius of
the Whorl as being between 72 miles and 344 miles (I took the liberty
of converting from leagues to miles).

At 72 miles, the velocity at the inner surface would be 2400 mph.

At 344 miles, the velocity would be 5200 mph.

While these figures seem more reasonable for the dimensions of the
Whorl, the floater could never approach these speeds, particularly in
city streets, and thus they could never have significantly
counter-acted the gravity effect.

Conclusion
----------

GW took significant artistic license.  Although maybe he'd blame it on
Horn and Nettle...


Eric
(ivancich@eecs.umich.edu)