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Re: Long term almanacs
From: Geoffrey Kolbe
Date: 2014 Jul 27, 07:03 +0100

As Hewitt says, there was a 1972 epoch LTA in Bowditch - but the problems with those tables is that:

a) There was no period of validity given for these tables. (Not that I could find anyway. Presumably, since they were to replace the 1956 tables, we can assume a validity period of less than 16 years. Which being the case, by analogy, the 1972 tables will now be long past their sell-by date!)

b) The quadrennial corrections did not seem to be valid for any period after 1972. Tests I did showed they were plain wrong and even the wrong sign for subsequent years after 1972.

c) The quadrennial corrections were certainly wrong for present day calculations.

So, I decided to create my own LTA based on the year 2000 as the epoch, (to make calculating which of the four tables to use (for the sun) easier.)

The quadrennial corrections are not fixed for each four year cycle. They do not even vary in a linear fashion. For this reason, I calculated average quadrennial corrections over 8 cycles from 2000-2003 to 2032-2035. Consequently, the calculated values of GHA and Declination in my LTA should be exactly correct for those years, will be pretty good for the years in between, and will become inaccurate progressively more quickly after 2035. By 2050 then, the stated expected errors in the tables of around 0.25 MOA will not longer be sustainable and so that limits the period of validity of my LTA tables.

If you want to create your own LTA with an epoch of 2012, then you will need to decide on what accuracy you are prepared to tolerate, what period of validity you need, and generate your own set of quadrennial corrections accordingly. Lifting quadrennial corrections from other LTA tables with different epochs will not work.

Geoffrey Kolbe

On Sat, Jul 26, 2014 at 6:26 AM, Francis Upchurch <NoReply_Upchurch@fer3.com> wrote:

A question for a couple of sages, probably Geoffrey Kolbe and Hewitt Schlereth please.
For years, I've been using the small "one page" long term almanac from Hewitt's book as part of my minimilist Crash bag kit. Reduced, it is also small enough to fit on the curser of my Fuller slide rule. Despite the base year being 1956, using the quadrennial corrections, I usually get GHA correct +/- 2-5' and declination usually better than that. I've got Geof Kolbe's excellent book which should take me out well past my own terminal declination at 2050! (if I'm still wealding my sextant at 99, I'll accept a few minutes inaccuracy).

My question is, Geoff says in his book that this quad correction routine only works for up to 50 years, then goes off rapidly. Any ideas how long before Hewitt's one pager will no longer be usable? Otherwise, I suppose we could update the 1956 GHA and DEC numbers to say 2012 almanac and start again? Would that work using the same quad correction routine as described in Hewitt's book?

If the answer is yes, with your permission Hewitt, I may volunteer to put a new one pager table together base year 2012.(probably not until the winter though) (unless you want to update your own wonderful book?)
the other way to go for minimalist kit is the EQ of time/ declination table which I do for each year and stick on my slide rule.
Am I correct in thinking that EQoT does not change year on year (except for dates), but only declination requires the quad correction?

Best wishes to all
Francis

Dr Geoffrey Kolbe, Riccarton Farm, Newcastleton, Scotland, TD9 0SN

Tel: 013873 76715

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