NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Douglas Denny
Date: 2010 Jan 22, 15:37 -0800
Original postings:-
------------
Thanks Gary.
This may lay to rest Douglas' concern regards the relative diameters over
which the scales lay. Or perhaps not!
Best Regards
Brad
------------
Yes I have compared and it is accurate as my other ones and the flat model.
gl
-------------------
Brad Morris wrote:
Hi Gary
Have you compared numerical output of the re-creation vs the flat
Bygrave? Is there any degradation in the solution?
Best Regards
Brad
=================================
I still have reservations, but am glad that Gary confirms the accuracy appears good despite the different diameters of the tubes.
Gary says in an earlier posting:
"Making the cosine scale presented a bit of a problem. Since the cosine
tube has an O.D of 1.750 and the cotangent scale was only 1.520 inches
in diameter it was necessary to print the cosine scale at a larger scale
than the cotangent scale which was not a problem using Acrobat. However
when I tried out the scales a problem presented itself. My printer made
the cosine scale wider but also taller so that the pitch of the scales
no longer matched. Although it worked this way it caused ambiguity since
the cursor would sometimes end up between spirals on the cotangent scale
and either answer (higher or lower than the end of the cursor) could
have been the correct one. I contacted Dave Walden (the original source
for the scales I have been using) and he was able to modify the vertical
and horizontal ratios of the cosine scale so that, when printed out wide
enough to fit around the tube, the vertical spiral pitch matched the
cotangent scale. (Thanks again Dave.)".
-----------
So the diameter difference does indeed noticeably affect pitch of the scales which had to be adjusted, but Gary says he adjusted the scale factor too:-
" it was necessary to print the cosine scale at a larger scale
than the cotangent scale "
Which leaves me wondering still ...?
I think the answer is the difference in scale length when adjusted like this when helically wound onto the tube is probably quite small compared to the full length of the scales if fully extended. (Imagine a single long straight slide rule). If you have a difference in the scale length of say an inch in a length of 20 feet that is only 0.4% error. It is probably not noticeable.
I should think for exactitude, the inner scale will have to be lengthened by a small factor for consideration of the smaller diameter if printed smaller(and the pitch adjusted accordingly too) to keep the extended lengths the same between the two scales, inner and outer.
--------
For the fun of it:
I counted 19 helical turns on the LogCosine scale of Gary's Bygrave SR and 37 turns on the LogCoTan scale in his pictures.
He quotes diameters of 1.5" for the LogCotan and 1.625" for the LogCosine.
This gives 176.9" (nearly 15 feet) total length for the LCoTan scale and 97" (8 feet) for the LCosine scale.
Now the LCosine scale is expected to be half the length of the LCoTan scale because of the maths of it, so there seems to be something wrong here in these figures. Perhaps I do not have the right number of helical turns. I would have felt more comfortable if they had worked out at 16 feet and 8 feet or very nearly so for the total lengths involved.
Over to you .......
Douglas Denny.
Chichester. England.
----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------