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Subject: Re: The pedant's rhumb-line.
From: Herbert Prinz (hprinz@XXX.XXX)
Date: Fri Oct 11 2002 - 12:25:09 EDT
Thanks to George Huxtable for giving us a new perspective on an old familiar.
David Weilacher is concerned that henceforth we will have to distinguish
carefully between the shortest rhumb line and others. George has already given
a hint how to resolve this potential source of confusion by a slip of his
finger (or by a stuck "b" on his keyboard). He is therefore given credit for
the following
Definition:
"The rhumb line is the shortest loxodrome between two points. A rhum line is
any loxodrome that is not a rhumb line. It is aptly so called, as only a sailor
who had his fair share of the beverage would chose to lay course on it."
I have heard rumors that NIMA is retracting their new edition of Pub 9
(Bowditch) in order to amend it with an enhanced version of the chapter on "The
Sailings". Here are a few of the worked examples to be included in the new
edition:
"The rhum line distance from the North Pole to the South Pole is exactly
100.000 km. What is the course?"
"Show that two vessels departing at the same time from port A and heading for
port B at equal speeds on different rhum line courses will never collide unless
A and B are on the same meridian."
Show that a navigator arriving at the pole will be swallowed up or
disintegrate. Outline of the proof:
The loxodrome comes arbitrarily close to one of the Poles, but never reaches
it. Thus, following the loxodrome, one can never get quite to the Pole. On the
other hand, the loxodrome is of finite length. (In close vicinity of the pole,
the loxodrome becomes a logarithmic spiral, the length of which is finite.) So,
assume that you are at a suitable point near a pole, such that you are, say, 6
nm away from the pole measured along a chosen loxodromix course. Now you start
going at 6 knots, following that loxodrome. Where are you after exactly 1 hour?
You must be on the pole!? But you cannot be on the pole!
This, by the way, is the sailor's version of Zeno's paradoxon.
Herbert Prinz
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