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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.
================================================================

   

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