giles@ucf-cs.UUCP (11/10/83)
One major problem with any non-equatorial launch loop will be
pseudo-forces created by the earth's rotation.
A good example of what I am talking about is the Foucault pendulum.
At the north (or south) pole, the "ground trace" of the pendulum bob
will rotate by 360 degrees in exactly 23h 56m ... as the earth rotates
underneath it. (Note: this is one rotation with respect to the *stars*,
not to the *sun*).
Meanwhile, here below the deep south (seriously, 50 km due west from KSC,
and at the same latitude as Cairo, Egypt) our Foucault pendulum at the
University makes one complete revolution every 48 hours. As I recall,
the period of rotation at any latitude L is given by 24/sin(L) hours.
This is important for any non-equatorial launch loop because it is
*impossible* to secure the track against these psuedo-forces. Sure, it
should be no problem to anchor the magnets for the *lower* portions of
the track, after all the force/unit length of track should be fairly
small, but the *upper* portions of the track cannot be anchored. After
it has been up for a few days, I suspect the track will begin to look
like this from above:
^north
(------ |
( ------ |
( ------ +----> east
(------------------------------------------)
ground portion ------ )
------ )
------ space portion
If the ends of the space-borne portion of the track are anchored as
shown in *Analog*, the curve of the track should be even more inter-
esting, but totally impossible to show on a text terminal.
Unfortunately, this is not the only pseudo-force involved with the
loop. Because of the high speed of the track, its phyical dimensions,
and its mass, it will have a *very* large angular momentum. As a result,
it will act as a giant gyroscope balanced on the earth's surface. The
coriolis effect described above, or any of a number of other ghastly
forces will then have very strange effects on the loop. For example,
if I did my cross product correctly the coriolis force will cause the
figure-eight pattern shown above, and then the properties of a gyroscope
will cause the *entire* loop to slide in a east-west direction. (I am not
sure which direction). However, in this case the forces exerted on the
ground anchors may be into the hundreds or thousands of tonnes of force.
Needless to say, trying to simultaneously (1) support that segment of
the loop, (2) deflect the loop either up or across, (3) keep the loop
from touching the magnets, and (4) stop the entire loop from sliding
along its length is a major task.
What other forces can be exterted on the loop?
(1): If the earth's magnetic field changes around the loop, a nice
hefty current will be generated in the loop. (well, it is a
conductor).
(2): If static charges are carried with the loop (or even "standing
waves" of current under correct conditions), the entire loop
will act as a giant generator.
In both cases, the loop will be coupled to the earth's magnetic field,
and thence to the sunspot cycle of the sun, and thence to ....
I have not had the time to calculate the exact numbers based on the data
given in the December issue of *Analog*, but I am fairly certain that
moving the loop away from the equator will greatly complicate the dynamics
of the loop, possibily to the point where the loop can no longer be
controlled.
Bruce Giles
---------------------
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