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Peter Fogg wrote:

'Michael, can you expand this section a little ?'

> Furthermore, the horizontal sextant angle station
> pointer type method itself is notorious for a poor
> angle of cut built into its geometry, particularly >
if
> the 'middle' object sighted is further away than the
> two 'side' objects sighted.

Gladly Peter, ...

Given a known angle between two known objects viewed
from the boat,
it is possible to construct a circular LOP for the
boat through the two objects.
This is then repeated for another pair of objects to
get another circular LOP. Where these
circles cut is the boat's position. Because you save
the geometric effort of drawing the circles when using
a station pointer or similar, you get no indication of
the angle of cut between the two circles, hence the
potential danger.

To do the geometry, you draw a 'base line' between the
two known objects, take 90 deg minus the observed
angle = x, draw a line from each object at angle x to
the base line. Where these two lines meet is the
centre of the circle, which you can then draw with
your compasses. If your drawing is accurate, the
circle passes through the fixed objects. The boat lies
somewhere on the circle which I've called the circular
LOP. Repeat for another pair of objects and their
particular angular difference to construct the second
circular LOP. The circular LOPs usually cross, but
there's no certainty that they will...

In the extreme case, if all three fixed objects lie on
a position circle which also crosses the boat's
position, the 'plotted' position circles will lay over
each other, and the boat will get the same ambiguous
horizontal angles wherever it lies on the joint
position circle -  a major danger.

The general advice to avoid these dangers is to ensure
that the middle object used for the fixes is the one
nearest to the boat. In that case there is no way the
boat can be on a circular LOP which includes all three
objects. Even so, that set up does not ensure a decent
angle of cut.

I couldn't find a detailed reference to this in the
2002 Bowditch. The whole technique is counted, I
guess, more than a little past its sell by date. Older
navigation texts mention the technique and its
dangers: Admiralty Navigation Manual Vol 3 1938
edition page 176, M J Rantzen's 'Little Ship
Navigation' 1970 fifth impression page 142, and
Lecky's 'Wrinkles', 21st Edition, 1925, page 144 refer
to the dangers after describing the geometry.

Posibly other list members know web accessible
references to the same topic. If nothing crops up on
the list in the next few days, I'll crank up the
boss's scanner and send you some copied material by a
side email.

All the best

Michael Bradley







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