NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Hanno Ix
Date: 2015 Jul 10, 10:31 -0700
Gary,
Here is my assessment of Bygrave vs sin-cos SR.
I assume a resolution of 1:10,00 for both in this comparison.
1. The Bygrave SR formula is superior to any other method I know that
uses logarithms. That includes Ageton, Dreisenstock, and S-tables.
There are sound mathematical reasons for that.
2. Bygrave SR is a logarithmic method and as such needs generally 1 digit more
than the sin-cos SR. IOW: you need in general 5 digits resolution for Bygrave to achieve
what sin-cos SR can do with 4 digits.
3. Bygrave needs consideration of special cases, whereas the sin-cos SR yields valid
results for all combinations of L, D, t.
The real great advantage of Bygrave when implemented as the classical tubular
slide rule is the execution by a mechanical apparatus which, in particular,
eliminates any and all multiplications and may reach frequently - not always! -
the accuracy of the sin-cos SR.
However, as a mechanical device, for a hobby engineer it is difficult to build with
the required precision and needs regular maintenance. Also, testing it thoroughly
after making it is a challenge. A design suitable for blue-water sailing is
really complicated. It is not commercially available.
The original sin-cos SR needs 3 multiplications for hc and 1 multiplication
plus 1 division for Z. That is a lot to ask and certainly not popular. And that
is why the Bygrave, the BN an others where created and their mechanical
complexity accepted, perhaps with a sigh.
The hav-Doniol is also user-friendly and mathematically entirely equivalent
to the sin-cos SR but requires only 1 multiplication for the calculation of hc.
The azimuth diagram eliminates any calculation of Z whatsoever anyway,
no matter the SR method used.
For a person who feels comfortable doing a single longhand multiplication
of two 4-digit integers the Bygrave calculator is not of advantage.
So, frankly, it may take longer to build / test a Bygrave than to re-learn
doing a very simple multiplication by hand.
I know this sounds like an advertisement but if you think it through you
might quite well decide I am right.
Regards
H
Thank you! I am having a ball with Bygrave equations. The next thing will be to sort out how to do them with my dad's old 10" K&E slide rule.
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Or you could make your own copy of a Bygrave sliderule, see:https://sites.google.com/site/fredienoonan/other-flight-navigation-information/modern-bygrave-slide-rule
