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I had written :


"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.) "


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This contains an error stating that the cotangent scale was 1.520 inches
in diameter when it is actually 1.610 inches. The 1.520 diameter is the
size on my original Bygrave re-creation. Sorry for the confusion.

gl



douglas.denny@btopenworld.com wrote:
>
> 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.
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