HP41 Navigation Pac Perpetual Alminac

[Dan Pfeiffer]

New posting here. been browsing a while.

I recently discovered go41cx for android. Wow. Revived my interest in tinkering with the HP41 Nav pac. I have had the hardware version since the 80's. Wrote a handful of programs that use the nav pac. Wrote one that did a 3 body fix and solved it using the matrix functions in the advantage pac. Doubt I could recall much of how that all worked at this point.

Also wrote a program to do a meridian passage sight (noon sight for sun) and get L and Lo and I was wondering about almanac accuracy so far out from OEM. So I did some tabulating for comparison with an online almanac at www.celnav.de/longterm.htm to see what I would get. I thought some others here might be interested in the results. I have seen a little chatter on this in the past 2 yrs?

I did a series of calcs for the GP (geographic position - lat and long where body is directly overhead) of the sun and the moon on both the HP41 and the web almanac and compared the results. I ran 8 dates from 1980 to 2280 and the difference for the sun averaged 0.46 nautical miles or about 26 arc seconds for you astronomers. That's not bad from a navigation perspective. What was perhaps more interesting was that the difference was always to the ESE. I have attempted to link to an image of the plot below. Posted the data too in a pdf.

Anyway, I thought some here might find this interesting. I am looking forward to tinkering with the nav pac with the go41cx program.

Dan Pfeiffer

[link:http://dan.pfeiffer.net/boat/hp41nav vs almanac.pdf]hp41nav vs almanac.pdf[/link]

[Dave Shaffer (Arizona)]

Some questions: do the sizes (magnitudes) of the errors depend on epoch? i.e. are the biggest errors at the later dates you tried?

Do you know anything about the shape of the Earth that is assumed for each program? Are all your checks for a single location? It's more work, but it might be informative to perform similar checks for various places on the Earth, particularly at widely different longitudes and both northern and southern latitudes.

What about time scales? How do the programs know what UT (or UTC or UT1) to use? Especially so far out in time!

I have some alternative programs (that run in Basic and Fortran under DOS!) for Sun and Moon positions. The best uses a rather complex US Naval Observatory set of parameters for the Moon. I'm not sure what epochs it is best for. Getting the Sun to 10 arcsec or so over a 100 years is not a big deal. The biggest concern may well be variable Earth rotation.

[Dan Pfeiffer]

See the PDF with the data here:
dan.pfeiffer.net/boat/hp41nav vs almanac.pdf

The tests were all at the same location so I don't know about that variability. The difference did not change in any trend I could see. I tested for the sun and the moon figuring the moon was more likely to show error.

I am not sure that using different longitudes would make a difference in what I was testing? I was not finding altitude/azimuth from a given location. Just the GP of the body by the almanac vs by the nav pac. Now that I think about it I should look at SHA/dec for the celestial coordinates and that would take out the error from the aries difference. I think.

Not sure about shape of the earth but the almanac routines do correct for precession, nutation, aberration and proper motion according to the manual. And the reference "Low-Precision Formulas for Planetary Positions" by Van Flandern and Pulkkinen who I believe were at the USNO back in the 70's. I don't know what time corrections are applied. My understanding is that the nav rom was largely the work of Kenneth Newcomer and I have a book he wrote with Henry Shufeldt called "The Calculator Afloat" and perhaps there are some insights to methodology employed in the nav pac. It is from 1980, right about the time they would have had development in high gear?

In general for navigation purposes getting a celestial fix that is good to within a mile is a job well done. If you're that close to your destination you have switched over to mark I eyeball for fixes and if the conditions are unsuited for that you're not likely to be doing any sextant work either.