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I recently gave a half hour talk at 39C3 in Hamburg covering the basics of sextant operations and the meridian passage: https://media.ccc.de/v/39c3-celestial-navigation-with-very-little-math . The text and slides are also on my website https://trmm.net/sunwheel/  . Please let me know if there are any glaring errors; I'm very much an amateur at this.

In the talk I also introduce my own circular slide rule for performing the index error, dip, atc, and upper/lower limb corrections so that you don't need to use the tables or do the arithmetic.  It also helps with adjusting the declination based on the time of observation, again to avoid the need for the increment tables.  This has saved me quite a bit of time on my sights, although not as much time as it has taken to develop and refine, but hopefully will help speed up other people's fixes, too.  The source code to generate them is on the second link; I've been arranging them on an A3 sheet that the local print shop can also laminate to make a fairly water proof tool.

The back of the slide rule has another time saver -- a stereographic projection that allows computation of the Zn bearing to the Sun within a degree given the declination, local hour angle and assumed latitude, and without any special rules for Northern / Southern hemisphere or Same Name / Contrary Name.  The usage is a little different -- there's a pointer that selects the declination and LHA, and then the entire face rotates by 90-Latitude to result in a bearing and height. It's an accidental reinvention of the universal astrolabe and gives results much faster (for me) than consulting Pub 249 when plotting lines of position for the intercept method.  This technique also provides an estimate of Hc, but that is also only within a degree so a more accurate method is required.

Which I didn't have ready in time for the event...  But the paper prototypes are working well for another slide rule that computes Hc given the declination, LHA and Latitude inputs: Hav(90-Hc) = Hav(LHA)*cos(Dec)*cos(Lat) + Hav(Lat-Dec).  One side has a logarithmic haversine plus logarithmic cosine, and the other a linear haversine.  Since the logarithms turn addition into multiplication, the first side makes it easy to compute log(Hav(LHA)) + log(cos(Dec)) + log(cos(Lat)) which results in log(Hav(LHA)*cos(Dec)*cos(Lat)).  This intermediate result is then transfered to the linear side which adds it to Hav(Lat-Dec).  There's a complementary scale that allows direct reading of Hc within 0.05 degrees or better.  And again, since this doesn't require the interpolation tables I find it is much faster than going to 249 and the only arithmetic step required is Lat - Dec, which is fairly easy.  A draft writeup on it is https://trmm.net/navwheel/ along with the source code for generating the slide rules.

Together these slide rules eliminated my need for Pub 249 vol 2 and 3, and for sun sights I also have a script to produce single page almanac for an entire year of meridian declination and equation of time, which sufficient for fixes within a few nm. Hopefully they are of interest to other folks here!

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