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Bygrave formula accuracy with a slide rule has been mentioned recently.
A few years ago, in a test with 10 simulated observations, the root of
my mean squared altitude error was 2.5 minutes with a 10 inch rule.

The "observations" were generated at random by a program which
distributes stars uniformly on the celestial sphere, and observer
positions uniformly on the Earth. ("Uniformly" means constant
probability per square degree, regardless of distance from the pole.).
It excludes altitudes greater than 80 or less than 5°, and latitudes
greater than 70.

The Bygrave formulas are the most suitable I have seen for slide rule
solution of the navigational triangle. Since the inverse trig functions
are arc tangents, they have good mathematical leverage at any angle. You
can even compute the separation and position angles of a double star
pair from their catalog coordinates with good accuracy.

However, undefined operations (divide by 0 or tan 90) can occur and must
be trapped in any automatic Bygrave implementation so your computer does
not overheat and fail in a shower of sparks as in the old Star Trek TV
show. (In reality, the machine will simply abort the operation with an
error message.) The escape, as I explained on November 30, is a trivial
change to the observer's position.

--
Paul Hirose
sofajpl.com

   

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