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Re: Compact H.O. 211 (Ageton-Bayless) question
From: Stan K
Date: 2016 Jul 16, 11:38 -0400
Paul,

I agree that extracting A and B values to tenths for either the original or compact Ageton, rather than rounding to units, really doesn't make a significant difference, but I have decided that in the next revision of Celestial Tools I will stick with the "rules" defined by the examples, that is to use the tenths in the original Ageton (H.O. 211) but round to integers in Ageton-Bayless.  Interestingly, the example of the Sadler technique in the Ageton-Bayless book retains the tenths, so Celestial Tools will also retain them for the Sadler technique.

FYI, I have been looking at some old Power Squadrons sight reduction forms that someone sent me, dating from long before I became involved with the Power Squadrons.  Apparently H.O. 211 was taught in the early '70s, with the rule to discard a sight if K is between 85º and 95º.  Some time later, but before the '90s, they switched to Ageton-Bayless, and the rule was changed to discard a sight if K is between 82º and 98º, as is stated in the Ageton-Bayless book. but also suggests the use of the Sadler technique if K falls in that range.

In Celestial Tools I made some compromises.  For both the original and compact versions of Ageton, If K is between 82º and 98º the program interpolates to get the value of B derived from the value of a that was derived from the addition of the value of A from the meridian angle and the value of B from the declination, and a note appears to indicate this ("If K is between 82º and 98º this B is interpolated.).  I originally simply said "An error of several miles can occur if K is between 82 and 98 degrees", but I found this unsatisfactory, as the sight should/could have been discarded.  Using the values of the example of the Sadler technique in the updated Ageton-Bayless, interpolation gives a value of 9611 for this B  (from an A of 22328).  Without interpolation it would have been 9614 (from the closest A of 22323 in Ageton-Bayless) or 9609 (from the closest A of 22332 in the original Ageton).

For the example of the Sadler technique in the updated Ageton-Bayless (t 89º06'W, Dec 53º16'S, L 33º19'S, Ho 26º35'), I get the following results for intercept:
Original, no interpolation 11.0 A
Original, with interpolation 2.5 A
Compact, no interpolation 28 T (K ended up being exactly 90º)
Compact, with interpolation 2 A
Law of Cosines 2.1 A

(Keep in mind that the compact edition rounds everything to whole arc-minutes, so the intercept will only be shown to integer miles.)
Unless I did something wrong, it can be seen, comparing the results to that of the Law of Cosines, that this example gave terrible results unless interpolation or the Sadler technique was used.  Looking at the results using the original Ageton, IMHO it is not worth using the Sadler technique, which is only marginally better than interpolation.

Stan

-----Original Message-----
To: slk1000 <slk1000@aol.com>
Sent: Fri, Jul 15, 2016 8:10 pm
Subject: [NavList] Re: Compact H.O. 211 (Ageton-Bayless) question

```On 2016-07-10 10:13, Stan K wrote:
> In looking at the "Example of the Complete Reduction of a Sight" in the "Compact Sight Reduction Table" (Modified H.O. 211, Ageton's Table) book, I noticed that the value of B for the dec of 3º30'S is 81, but the table value is 81.1.  In fact, all table values less than 166 are shown to tenths.  Why bother showing the tenths if they are just going to be rounded out in the calculation anyway?

A few weeks ago I said, "In my opinion, extracting A and B
values to tenths of a unit from the standard Ageton table is not worth
the extra work." That's also true of the Bayless table. In my Monte
Carlo simulations (which retain tenths, if they're present in the table)
the improvement is not easy to distinguish from the statistical noise.

If altitude is restricted to 5° - 80° and observer latitude to 0° - 70°,
my Monte Carlo test with the Bayless table had a root mean square
altitude error of 2.03'. About 43% were worse than 0.5'.

Significant improvement occurs if A(R) is interpolated from B(R) when t
is within 5° of 90° (about 4.5% of sights), RMS altitude error improves
to 0.82'. There's a small but definite degradation to 0.86' if the table
gives whole numbers only.

By the way, my promised evaluation of the Sadler technique has not been
forgotten. The code is written but I still have to run the simulations
and write up the results.

```
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