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On Wed, 20 Jan 2010 01:57:16 -0700,  wrote:

>
> The 'problem' is not parallax as the eye can look perpendicularly onto
> the scales  on the tubes quite accurately; it is the difference in scale
> lengths with different diameters of tube which I would consider a
> potential problem.

I believe the sheet of paper wrapped around the innermost cylinder may be
scaled smaller in one direction.  That way, the cut edge will meet the
proper spiral exactly along a longitudinal butt joint (actually, I
overlapped the join onto a quarter inch of blank space) while having the
length untouched so as to match the outer scale.

> Theoretically they should be exactly the same scale factors and hence
> same length wrapped around helically.

Yes, that would be true if the paper and tubes were infinitely thin.

> Different diameters necessarily means there will be slightly different
> scale lengths if printed with the same scale factor.

Yes, and so the scale factor in one direction will be changed to match the
diameter of each tube.  The scale factor in the other direction should be
the same on both tubes.

> I have not worked out the errors introduced with a real Bygrave SR, (I'm
> not sure of the exact diameters involved and the scale lengths
> themselves)  but assume it cannot be too great or it would be noticeable
> and would have been reported by now.

I think a little bit of trial and error in printing will give acceptable
results.  If the spiral segment ends match up on each cylinder to within
0.01 inches, I doubt any of the calculation results would differ.  Since
the real Bygrave has outside diameters of the tubes that differ by perhaps
ten times that amount (say a tenth of an inch), the paper scale must have
been reduced or enlarged in one direction accordingly; otherwise there
would have been an overlap or gap of the printed part by about a third of
an inch.

--
Richard . . .


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