# NavList:

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

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Re: Bygrave range of angles?
From: Hanno Ix
Date: 2015 Apr 21, 09:34 -0700
Gary,

thanks for the response..

I am asking myself about the angular range of the log-cot() scale.
What is the upper limit of angle it should go to?

Robin Stuart's magnificent scale I have in my hands goes up to
89deg 40min. But note: Given a certain physical length of the scale,
the closer you go to 90deg  - unreachable itself - the more
compressed the scale becomes around 45deg where the more frequently
used angles appear. Robin's scale takes about 25% of its length
for angles >= 89 deg - a big percentage for angles rarely used.
Or so I think.

Now, then again, what should this upper limit be trading off the various
needs of an active blue water sailor with a 40' boat operating up to
70deg latitude?

H

On Tue, Apr 21, 2015 at 5:11 AM, Gary LaPook wrote:
There is no limit on the latitudes that can be handled with the Flat Bygrave. There is a special case when the declination is less than one degree on the latitude is zero then you must use one degree for the assumed latitude but it still computes an accurate Hc and Z. From my website:
 Modern Bygrave Slide Rule - FredienoonanFlight navigation on Amelia Earhart's flight View on sites.google.com Preview by Yahoo
===================================================================================
When declination is less than one degree you can't begin the computation the normal way to find "W" because you have to start the process with declination on the cotangent scale and this scale doesn't extend below 1º. So in this case you just skip the computation of "W" and simply set "W" equal to declination. Using this method you arrive at an azimuth that is not exact but is a close approximation and in the worst case I have found the azimuth is still within 0.9º of the true azimuth but most are much closer. If the declination is less than one degree and the latitude is also less than one degree, follow this procedure and also assume a latitude equal to one degree. After you have computed the Az you then follow the same procedure discussed above for azimuths exceeding 85º by interchanging the latitude and declination and then computing Hc which will produce an exact value of Hc.

===========================================================================================
.

See the complete explanation on my websitegl

To: garylapook---.net
Sent: Monday, April 20, 2015 10:51 PM
Subject: [NavList] Re: Bygrave range of angles?

Hanno,
I don't know about the flat Bygrave, but with my cylindrical version (about the same size nearly as the original), I have done hundreds of reductions and rarely out more than 1-2' compared to calculator. the lat range seems to cover +/-nearly 90° as far as I can tell and for some reason i do not understand, why when you end up on the "compressed" side of the scales and are interpolating between fairly small scale marks, the accuracy stays the same. Maybe Gary knows why? (Interestingly, I have not found this with the Fuller, which is definitely more accurate in the "expanded" range of the scales. I get 4-7 places with the big Fuller depending on where you are in the scales)
Anyway, good luck. I'm sticking with cylindrical rules. I find them easier to make and use accurately using pre-manufactured, precision tubes, felt friction brakes, no pivot holes to drill etc. But each to their own I guess.
Best wof luck
Francis

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