# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: NavPac**

**From:**George Huxtable

**Date:**2005 Jan 7, 20:44 +0000

I can add a bit more to Peter Fogg's useful posting about the software CD package and booklet "Nav-Pac and Compact Data", the new issue being for years 2006-2010. List members may be aware that the annual Nautical Almanac for each year, both that issued in Britain by HM Nautical Almanac Office, and that issued in Washington by the US Naval Observatory, are based on information, computations and tables that were prepared almost entirely in Britain by HM NAO. This is the same outfit that provides the package that Peter Fogg refers to: they know what they are doing. For the previous issue, for 2001-2005 (which I have), similar information was published in similar form, with software on CD, in the US, by Willmann-Bell, except for a modified title, being "AstroNavPC and Compact Data 2001-2005". If those arrangements continue, that might make for an easier purchase (but perhaps not a cheaper one), of the new edition for US-based list members. As I don't run a PC, and the software doesn't run on my old Mac, then for me the useful component is the text in the 150-page booklet rather than in the CD. And I can say that it has lots of astro information in it that you might not find elsewhere. For example, a little while ago I wanted to calculate GHA Aries rather precisely. I knew that it corresponded to Greenwich Sidereal Time, but was that Greenwich Mean Sidereal Time, or Greenwich Apparent Sidereal Time (there's a small difference)? None of my texts on spherical astronomy helped, and (though I thought I knew which) I didn't want to guess. But on page 59 of the booklet I found - "Table 5 may be used to calculate GHA Aries which is equivalent to Greenwich mean sidereal time (GMST)." Just what I needed to know. Referring to the printed pages, Peter says- >'The main tables contain monthly polynomial coefficients ... daily >polynomial coefficients ... and monthly Chebyshev coefficients ... and five >yearly coefficients ...' If it's a similar arrangement to that of 2001 - 2005, then those printed tables won't commence until 2006, so anyone buying a new copy and looking to make predictions of positions on Sun, Moon, Planets, Stars, from that printed data, will be out of luck for 2005. >'Astronomers and navigators will also find the package useful because the >CD-ROM contains the compact astronomical data in ASCII format, so that they >will be able to read the data directly into a PC ...' To judge by its 2001 - 2005 predecessor, in which the CD provides the coefficients for years back to 1986, then I would expect those for the year 2005, absent from the printed version, to be available and printable from the 2006 - 2010 CD (perhaps Peter can confirm whether that is the case). In which case, now might indeed be a good time to acquire the new edition. As for the program, which runs on a PC. The user is required to provide some sort of initial position. and a number of observations of bodies, from 2 to 15. The program will, if asked, make all the relevant corrections, and then derive a new position. If only two observations were made, there are only two solutions to the points where the position circles cross, and the most reasonable of these is chosen. If there are more, the program uses the least-squares method to obtain the most likely position and to draw an error-ellipse around it. This assumes that all errors are random in nature. The algorithm used is explained in the booklet, being the same as that shown in the back pages of the Nautical Almanac under "Sight reduction procedures - methods and formulae for direct computation". However, the explanation is somewhat less complete in the booklet than it is in the almanac back-pages. The least-squares method is an iterative process, though not everyone realises it. The user having guessed at an assumed position, the method derives a better one from the observations. If the initial guess was very bad, then that results in large offsets, and an untrustworthy result. If the initial position differed by more than 20 miles from the resulting deduced position, then the program recommends that the latter is chosen as a new initial postion, and a reiteration done. This operation is described well in the Almanac, with an example, but rather less well in the 2001 - 2005 booklet, in which the (different) example chosen happens to come within that 20-mile limit on the first iteration, so that working of a reiteration is not well explained at all. Perhaps Peter can tell us whether that aspect has been improved. With three (or more) observations, the resulting "cocked hat", or intersection of multiple lines, is shown on the screen, and an error ellipse drawn around it. The default is to draw an ellipse within which you might expect 95% of all observations to lie, but if you wish you can select a different percentage. With only a small number of observations (three, say) and random errors, you have to be aware that chance can play a big part in the size of a particular "cocked hat" triangle, and therefore in the size of the ellipse. Sometimes, just by chance, the triangle might be tiny, and also the error ellipse, but that doesn't necessarily indicate that it happened to be a particularly precise observation. With more observations, in a round of sights, the error ellipse becomes more trustworthy. Longstanding Nav-L members may recall a long and sometimes heated corresondence which demonstrated that with three observations and completely random errors, the true position would lie within the cocked hat only one time in four (and therefore, three times in four, outside it). I don't really wish to reopen that argument, but the program within this package should be able to provide a nice demonstration, using three observations randomly scattered. If, instead of a 95% error ellipse, you ask it to draw a 25% level, so only one-quarter of the observations will lie inside it. then I predict that the area of the resulting ellipse should closely match the area of the corresponding "cocked hat" triangle, because both figures, though quite different shapes, embrace just 1 in 4 of the observations, on average. That's a test I haven't made, not having a PC to run the program on, though it's a confident prediction. In the 2001 - 2005 edition, there were, as I see it, minor errors in the text of paragraph 7.5, "Estimated position error". In the last paragraph is the sentence "The ideal situation is to produce a circular distribution of errors, with A = B and C = 0 ....", which according to me should read "with A = C and B = 0 ...". Also. near the start of section 7.5, is the phrase "The standard deviations sigma-L and sigma-B in longitude and latitude ..." should be replaced by "... in miles along the longitude (E-W) direction, and in latitude ...". I wonder if Peter can confirm whether these corrections have been made in the new issue. Allowing for those minor exceptions, it's a most professional product, with everything carefully explained in the printed text, and in such a way as to provide excellent tuition in Celestial Navigation (or as we call it in Britain, Astro-navigation), not just a short-cut to an answer. The text is commendably careful to specify maximum errors in the predictions. The Nautical Almanac Office is based only 12 miles from where I live. Catherine Hohenkerk, at the NAO, is responsible for the issues of this program and text, and for the calculations of the Nautical Almanac. I have a social acquaintance with Catherine, which I hope has not coloured this assessment. George. ========================== Peter Fogg wrote- >HM Nautical Almanac Office, who also publishes 'The Nautical Almanac' in the >UK, has a navigational software package known as 'Nav-Pac and Compact Data'. > >It comes out every 5 years; the 2006/2010 version contains data for 1986 - >2010. The interface presents a set of functions: > >CALCULATE RISE AND SET TIMES OF NAVIGATIONAL BODIES > Times of rise, set and meridian passage. Also civil, nautical and >astronomical twilight as zone or UT. > >FIND LOCATIONS OF NAVIGATIONAL BODIES > Tabulates and plots altitudes and azimuths of bodies selected for >given time, date and location. The plot looks like a star map with the >bodies and data alongside. > The set of 7 best bodies are indicated. Apparently this selection is >the same as would be chosen using HO 249. > >CALCULATE GREAT CIRCLE/RHUMB LINE ROUTE > Positions to courses and vice-versa, including dates, times and >speeds. One detail I especially like is that dates and times are displayed >both in UT and Zone Time, so you can use either, or swap between them, >hopefully avoiding any confusion. For great circles the legs can be as short >as 0.1nm, although only the first 99 legs are displayed. An alternative is >to nominate meridians of longitude for course changes. > >CALCULATE POSITION FROM SIGHTS > From time to time there are postings on this List that indicate a >desire to squeeze the utmost in accuracy and/or precision from sights made. >This product could be a boon for that endeavour. The calculated intercept is >displayed to 4 decimal places (eg, -2.5687 nm) and the azimuth to the >nearest tenth of a minute of arc (eg, 124d 52.9'). Temperature and pressure >can be entered (or left as default settings) and the parallax, refraction, >and semi-diameter factors are displayed. The almanac data used, to the >nearest tenth of a minute of arc, is also displayed. Thus the software can >also be useful as a check for manual methods. A maximum of 15 sights can be >entered for a fix. > This leads to a 'Position Line Plot Form' which can be zoomed in and >out, the default setting is a 20 nm square with the fix in the centre and >the DR off to one side. A 95% confidence ellipse is shown as a default >setting. Position lines are shown in different colours for different bodies >(stars, planets, etc). > > >CONSULT ALMANAC > The usual suspects, 57 stars plus Polaris and Octantis and Aries. > >The software encourages the keeping of an electronic log, with fixes being >saved and results used for subsequent calculations. > >In the book that accompanies the CD (included as a PDF file within the >software) all of this takes less than a third of the book to explain, >together with examples. The rest is data to enable those who like to roll >their own to program a calculator or computer - another subject that came up >here recently. > >'The main tables contain monthly polynomial coefficients ... daily >polynomial coefficients ... and monthly Chebyshev coefficients ... and five >yearly coefficients ...' > >'Astronomers and navigators will also find the package useful because the >CD-ROM contains the compact astronomical data in ASCII format, so that they >will be able to read the data directly into a PC ...' > >There are pages and pages of formulae, and whole chapters of, for example, >Chebyshev coefficients. > >Also: '... a chapter from "The Admiralty Manual of Navigation" on the >practical aspects of sight reduction ... is included...' (as a PDF file) > >(tell 'em the price, son!) >Navigation Pac retails for 40 British pounds through www.tso.co.uk/bookshop >and possibly elsewhere. ISBN 0 11 887331 8 ================================================================ contact George Huxtable by email at george@huxtable.u-net.com, by phone at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. ================================================================