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Back in mid-October, Joel asked-

>...what I would like to learn from you is whether contemporary sextant's
>mirror size and scopes are optimized. So you need not search >for the
>dimensions which are typical of most major brands they are:

>Scope 4 x 40
>Index mirror, 57 x 42mm
>Horizon Mirror, 57mm dia.

after I requested a bit more information about dimensions, he has recently
provided the following-
>
> Sextant A
>
> Scope 4 x 40
> Field of view 7.0 degrees
> Index mirror, 57 x 42mm
> Horizon Mirror, 57mm dia.
> Distance OL - HM,  12.3mm
> Distance IM - HM, 8mm
>
>
> Sextant B
>
> Scope 3.5 x 30
> Field of view 8.0 degrees
> Index mirror, 57 x 42mm
> Horizon Mirror, 57mm dia.
> Distance OL - HM, 10mm
> Distance IM - HM, 8mm
>
>
> Octant C
>
> Scope None - Peep sight
> Field of view, NA
> Index mirror, 50 x 31 mm
> Horizon Mirror, 24 x 20 mm
> Distance OL - HM, 9mm
> Distance IM - HM,  7mm

==================

I take it that the distances stated are actually in centimetres, so in mm
they should be 10x greater than shown.

Here are my comments about whether the geometries are optimised.

Sextant A. This has a field of view 7 degrees wide; that is, the view
extends to 3.5 degrees off the optic axis.

Take the horizon mirror first.  To allow full brightness at the centre of
the field of view (but tailing off toward the edges) 40mm diameter would
have been sufficient. However, at the distance of the horizon mirror from
the objective of 123mm, the mirror needs to have a diameter of 40mm + (2 *
123*tan3.5 degrees), or 55mm, to allow full brightness right out to the edge
of the field of view. As the horizon mirror is actually 57 mm., that's
perfectly adequate, and even allows for a bit of possible misalignment. The
outer millimeter of that mirror will never be able to reflect light that
will pass through the telescope to the eye, so could just as well be shaved
off. There would be no point at all in making it any bigger than its 57mm.

The horizon mirror needs to be able to pick out a dim horizon, with little
contrast, under twilight conditions, so the fact that the horizon mirror is
large enough to collect maximum light from the whole field of view is an
advantage.

Now for the index mirror. Again, as long as it was larger than 40mm, it
would allow full brighness for objects in the centre of the view. The
light-path to the objective, via the index mirror, is 123 + 80, or 203 mm,
so to achieve full brighness for objects at the edge of the view, it would
need to have a diameter of 40 + 2*203*tan3.5degrees, or nearly 65mm.
Clearly, it falls short of that, at 57 x 42. I presume that the larger
dimension is the "vertical height" one, to allow for apparent foreshortening
of the index mirror as it's turned to allow for larger altitudes, and 42mm
is its width. Let's presume we are measuring an altitude at which its
apparent height is foreshortened to 42 mm, so it's effectively a 42mm
square.  Then the brightness, at the edge of the field of view, would be
reduced to about 80% of what it was at the centre. But the field of view
itself would still be the field of view of the telescope, at 7 degrees wide.

Would that reduction of brightness in the index mirror, matter? Not a bit, I
suspect. The eye will hardly notice a reduction of brightness to 80%.  And
it only affects the edge of the view, which you need to get things lined-up,
but the actual measurement takes place at the centre, where you have full
brightness anyway. For the Sun and the Moon in the index mirror, their
brightness is only an embarrassment anyway, and  needs dimming with a shade:
also, observing those bodies, the eye-pupil closes down and limits the
effective aperture. So it's only the finding, not the measuring, of a faint
star that would be affected.by the restricted size of the index mirror, and
even that would be barely noticeable.

Conclusion for sextant A: both mirrors are rather well optimised. Enlarging
them would not increase the field of view at all, and enlarging the index
mirror would only make an insignificant change to the brightness at the edge
of the field of view.

Sextant B has exactly the same mirrors as does A, but its scope is
different, at 30mm dia, with a larger field of view of 8 degrees, and its
spacings are somewhat different. It needs a horizon mirror to be 44 mm dia,
so the mirror fitted, at 57 mm dia, is much bigger than necessary. You could
shave off 6.5 mm all round from its radius, and it would make no difference
at all. Light from that outer part can never reach the eye. Of course, if
that scope were exchanged for another, with larger aperture or field of
view, it would make more use of the outer edge of that horizon mirror.

For its index mirror, sextant B would call for a diameter of 55mm to ensure
that no brightness is lost at the edge of the field of view. With an
apparent index mirror of 42 x 42, only 6% of the light is lost toward that
edge, which would be quite imperceptible.

Conclusion for sextant B: The horizon mirror is quite unnecessarily large
for use with that scope, the index mirror is optimum.

C, the octant, is in quite a different category, with no telescope, just a
peep. There being no telescope to constrain the field of view, that becomes
much wider. In the horizon mirror one can see 15 deg x 12.7deg.,  and in the
index mirror 17.7 x 11 degrees (less in height as the altiitude increases),
with full brightness right to the edge. That makes it much easier to pick up
an object in the sky, just as an observer finds when he uses a sextant
without its telescope. Of course the penalty is that there's is no
magnification.

Conclusian for sextant C: With no telescope to restrict field of view, the
requirements for that octant are quite different. Maybe the aperture of the
index mirror could be enlarged a bit to correspond with that of the horizon
mirror, but it's quite well optimised. Such an octant would be easy to use,
if not very precise, with no telescope.

I wonder if those comments seem sensible, to Joel.

George.

contact George Huxtable at george@huxtable.u-net.com
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.

   

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