From: Francis Upchurch
Date: 2016 Jan 7, 03:02 -0800
re.potential accuracy of 10' rule/ scale compression and improved Bygrave/BN.
May be a niave question (most are, i.e. I do not know the answer!).
If at least some of the inaccuracy of slide rules relates to the level of scale compression at a particular degree number (. e.g. tan scale for 45° on the Bygrave is very compressed.), is there a case for in some way "stretching" the scale for certain numbers to avoid this? Alternatively, what about using cosine formula for certain "low accuracy"Bygrave numbers? ( sine or cosine 45° is pretty stretched on the Fuller)
Also, although I have not done a statistically valid trial here, I get the strong impression of improved accuracy using "whole intergers" a la reduction tables with both Bygrave and even more so, the less accurate BN. OK, you loose the advantage of using exact EP rather than whole number AP, but acceptable if it provides greater accuarcy.
The simplest solution for me is to use Bygrave for Hc where 1-2' accuracy is acceptable and use Fuller2 for anything else (like Karl, cosine type lunars) requiring 4-7 decimal places, which gives "calculator" type results.) Frank says the "series" type lunar formula as described by Letcher, only requires 3 decimal places and therefore ok with the ordinary linear. (still not sure if I understand why this is so? Can anyone explain to a maths simpleton?)
I would be very interested to see how the nav slide rule project develops. the 3D plastic printing engineering sounds miraculous and beyond me. My simple, non precision craft skills seem adequate to produce consistently very accurate cylindrical slides rules, using ready made plastic tubes and ordinary ink jet printer. Not sure why anyone would prefer to build circular or linear slide rules with shorter scales and requiring more precision engineering for such things as central pivot bearing (circular) and slide grooves (linear).
I wait to be educated!