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Hi Thomas

Attached, please find my preliminary study on scale lengths for the Bygrave.

Best Regards
Brad


-----Original Message-----
From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Thomas Kleemann
Sent: Wednesday, July 08, 2009 5:21 PM
To: NavList@fer3.com
Subject: [NavList 9033] Re: Manufacture new Bygraves?


Brad Morris schrieb:
> This is the method used by the Germans.  They wrapped the scale around aluminium tubes.

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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