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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Manufacture new Bygraves?
From: Gary LaPook
Date: 2009 Jul 8, 20:19 -0700

```You're close to the original Bygave which has a cotan scale 8.8 meters
long. But you would have to adjust your spacing slightly because there
can only be 44 turns between 20' and 89�40' since each turn must equal
a change in log cotan of .1. The log cotan of 89� 40' is about  -2.2
and the log cotan of 20' is about 2.2, a range of 4.4 making  44
changes of .1 which is the reason for the 44 turns on the original
Bygrave. Its tube is 2.5 inches in diameter times Pi makes the
circumfance of 7.85 inches times 44 turns equals 345.58 inches or 8.77
meters. If you adjust the spacing but keep the pitch unchanged and
make 56 turns it would cover a range of 1'30 to 89� 40' and so
eliminate the problem of sun sights near the equinoxes.

gl

On Jul 8, 2:21�pm, Thomas Kleemann  wrote:
>
> > This is the method used by the Germans. �They wrapped the scale around aluminium tub
>
> Here my 2 cents (we are EUR):
>
> I thought about some dimensions of an imaginary BSR (Bygrave slide rule):
>
> To see what is practical and achieveable, I rummaged for my school time
> slide rule. Its scales are 250mm long (about 10in).
>
> In the area where the graduation is smallest, the tick marks are 0.4mm
> apart (10 marks per 4mm). I can read that easily without magnifiers, but
> some hyperopic may have difficulties.
>
> Inspecting the functions that form the scales of the BSR one can clearly
> see, that the closest ticks appear at 45� at the cotangent scale and at
> the smallest value of the cosine scale.
>
> By allowing 0.5mm spacing in the 45� area one can mark every single
> minute of arc on the cotangent scale. Using the original scale markings
> running from 0�20' to 89�40' it gets an overal length of 8847mm
> or 8.85m! Impressive, isn't it?
>
> Wrapping it around a tube of 50mm diameter (2in) with 8mm pitch (1/3in)
> one gets 56 turns distributed over 450mm length (18in).
> Why 8mm pitch? A dimension of my slide rule again. A pitch of 7mm gives
> 400mm in length (16in).
>
> On my slide rule the scales are paired with the upper one having the
> readings above (like Gary's) and the lower one having the readings below
> the ticks. This way one can adjust the marks of both scales without the
> numbers overlapping each other. Only the tube material for the cosine
> scale has to be transparent.
>
> 68�
> .|....|...
> '''|''''|'
> � �35�
> � � 62�
> ....|....|
> ''|''''|''
> � 29�
>
> With this configuration there is no real need for a 'Cursor tube'.
> nor interpolations. One can directly read the cotangent scale to the
> nearest minute of arc against the other scale.
>
> The cosine scale is another story:
> Using the same spacing as for the cotangent scale one can tick off
> every min of arc from � 89� and 60�
> every � �2nd � � � � � �60� to 45�
> � � � � �5th � � � � � �45� to 20�
> � � � � 10th � � � � � �20� to 10�
> � � � � 20th � � � � � �10� to �5�
> � � � � 30th � � � � � � 5� to �3�
> and then every degree.
>
> Interpolation between the ticks is clearly needed here.
>
> So far it looks feasible and 50 x 450mm (2 by 18in) is not too
> cumbersome.
>
> /Thomas.
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