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Hanno,

A while back I wrote some flat Bygrave scales in Postscript. It's
essentially a programming language to create graphics, so I made my
own rules regarding frequency of tick marks and labels. Essentially
for each level of graduation (tens of degrees, degrees, tens of
minutes, five minutes, minutes, etc) I defined a minimum size of
division in (1/72 inch) pixels for which this particular division is
either subdivided with tick marks. Same goes for label positions:

By playing with numbers in table below I was able to fine tune
frequency of tick marks and labels to my liking.

cos.ps:
...
/divsize      [ 1   9    2   5    6   10   ] def   % - Number of
divisions on this level
across                                             % in each division
of previous level
/divstep      [ 90  10   5   1    1/6 1/60 ] def   % - Size of each
division in degrees
/ticklen      [ 8   7    6.5 5    3   2    ] def   % - height of the
tick mark
/tickbottom   [-1.5 -1.5 -1  0    0   0    ] def   % - bottom of
tickmark
/tickweight   [ 1.5 1.5  0.5 0.25 0.25 0.1 ] def   % - width of the
tick mark
/subticklimit [ 15  10 	 10  20   20  25   ] def   % - minimum size of
division,
                                                   % which is still
subdivied on next level
/labellimit   [ 120 60 	 100 180  250 200  ] def   % - minimum size of
division,
						   % which still has tick labels drawn
						   % for subdivision

/minutesonly true def % If true degrees are dropped from minute labels
...

See following post for working adjustable scales.

http://groups.google.com/group/NavList/msg/6bfe198c49d1af7d

If you look in files you can also see variables for distance of labels
from tick marks, font size etc.

BTW These scales are produced for flat Bygrave, for cylindrical
version you need to cut them in half vertically.

Martin


On Jul 18, 11:36�am, Hanno Ix  wrote:
> Hello:
>
> One of the difficulties I presently face in making test samples of Bygraves 
is the creation of accurate and well readable scales. The topic sounds 
perhaps trivial but well designed scales contributes much to the quality of 
the end product.
>
> In non-linear scales,
> how do you choose the graduations, and what is the rule to change them when the
> labels become "too close" ?� Where do you
> put the numbers - on top or next to the corresponding mark? Also, there 
should be means to shift and stretch them for certain amounts so as to adapt 
them to the drums, paper thickness, etc. Are there any programs or algorithms 
specifically for rulers and scales?
>
> I know some of you have made scales. Please let me know how you did it 
before I get lost in re-inventing this wheel.
>
> Regards
>
> --- On Thu, 7/16/09, engin...@clear.net.nz  wrote:
>
> From: engin...@clear.net.nz 
> Subject: [NavList 9119] Re: Bygraves
> To: NavList@navlist.net
> Date: Thursday, July 16, 2009, 7:59 PM
>
> Frncis has made a great start. I think it is possible to get something 
looking even more like the original.
>
> Ronald van Riet gives the dimensions of the tubes in millimetres, but I 
think the original outside diameters would have been imperial sizes:
> 2 1/2 in; 2 5/16 in; and 2 1/8 in. Nowadays, the only stock imperial sizes 
that are near are 2 1/2 and 2 1/4 in.� There is a wide range of tube wall 
thicknesses, so it will be possible to get to the required dimensions by 
turning and/or boring.
>
> The hexagonal top and the fluted base will be easy to make if a suitable material can be sourced.
>
> I suggest we make a start with the simplest item, the Bygrave, and graduate 
to the more complex German instrument. I can obtain suitable aluminium tubing 
for only the two larger diameters - and only in 5 metre lengths. If someone 
out there can send me 10 inch lengths of tubing with the right inside and 
outside diameters to reach the required diameters, I would be happy to make a 
start and pass the results on to the "scale fitters". This could prove the 
concept as well as setting up a cooperative to supply those who don't own the 
necessary machine tools.
>
> Bill Morris
> Pukenui
> New Zealand
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