NavList:

Roger, thanks for that note on the date. Incidentally, I had no idea that Burch's "Hawaii by Sextant" (hope that's the right title) was "set" in 1982! I have never seen a copy, but I was under the impression its examples were much more recent. Could you describe why you're using that? Is it just because it gives some example scenarios to work? That period, 1982, now forty-four years ago, was, of course, the heyday of "disco navigation"! :)

I told you I would look at your calculations, but I have gotten very busy prepping for Advanced Lunars, which begins a bit more than 48 hours from now as I write this. I will have much more time starting Monday (two+ weeks off before the "Pacific" workshop schedule starts up).

A couple of quick notes. I think I saw that you used the equation -0.97'/tan(h) for refraction for a case with an altitude a bit less than 15°. That's not deadly if "a bit" (below 15°) is small, but really that should be the limit. For lower altitudes use refraction tables or one of those formulas that are "fitted" to the refraction tables. That's a minor thing in this case but critically important at lower altitudes.

The bigger issue that you're investigating: does the calculation of the line of position by the intercept method (the calculation by "PQR" in your work) match the two-point line of position (the "ABC" method of my workshops)? [spoiler: yes] To bypass plotting issues and focus on that as the primary question, I suggest you get your two points from the ABC method, as you have, and then use one of those two points as the AP for the intercept method calculation.

Quickly reading through your analysis, I noticed that you chose an AP in your work (maybe to align with the work in Burch's 'Hawaii' book??) with whole number latitude (nearest degree) and with longitude set to cancel minutes yielding whole number (integer) LHA of Aries. This highly constrained and restrictive selection of AP is only required by the lookup tables, e.g. Pub.249 and Pub.229 (or H.O. 249/229 or equivalents in other catalogs). The general properties of the intercept method allow you complete freedom to use any AP you want. In this case, if you set the AP for the intercept method to be one of the points by the two-point calculation of the same sight, the value of the intercept distance or 'a' (=Hc-Ho) should come out to be very close to zero, and the azimuth you calculate should "point" from there to the second point of the ABC calculation.

Finally for now (while I'm thinking of it), a major point and benefit of the two-point solution for celestial LOPs (the "ABC" method) is that you can do the plotting on common graph paper. All the plotting issues of "universal" plotting sheets are then irrelevant. No such luck withe the intercept method!

That's all for now. I'll take a closer look at your calculations on Monday...

Frank Reed

PS: For anyone who missed it, here's Roger's original post on this.