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4 THE NAUTICAL ALMANAC (N.A.)
15. HISTORY AND MAKE-UP OF THE NAUTICAL ALMANAC (N.A.)
The word almanac comes from the Arabic al-manakh meaning the calendar. An almanac contains Astronomical data, and an N.A. provides the seaman with the Astronomical data he needs for ‘position-finding’ using the methods of nautical Astronomy. It is, therefore, a navigational instrument of the first importance, for, without the information it provides, the navigator’s sextant and chronometer would be of little use.
The earliest almanacs used for Astronomical navigation by the Portuguese and Spanish navigators during the early period of the Golden Age of Discovery contained little more than data necessary for finding Lat. It was not until the 18th century that satisfactory methods for finding Longitude at sea were available to the mariner, and it was during this time that the first British N.A. was published. This Almanac, first published in 1766 for the year 1767, contained Astronomical data useful not only for finding Lat. at sea, but also for finding Longitude
The essential problem in modern nautical Astronomy, as has been explained in Chapter 3, is concerned with the relationship between the position of a celestial body at any given instant of time, using the horizon and equinoctial systems of coordinates respectively. The data contained in the N.A. facilitates this problem.
The British N.A. is identical in content to the United States N.A. and is published jointly by HM N.A. Office and the U.S. N.A. Office, each year for the following year. The British and United States governments make available to any nation the data contained in the almanac in a form suitable for direct photographic reproduction. Up to 1974 the Brazilian, Danish and Norwegian almanacs were produced under this arrangement.
The principal part of the N.A. consists of Astronomical data by means of which the Dec. (Dec) and Greenwich Hour Angle (G.H.A.) of every celestial body used in Astro-navigation may be ascertained for any instant of G.M.T.
This takes the form of tables giving the predicted positions of the Sun, Moon, navigational planets, and the F.P. of Aries, using the equinoctial system of coordinates (Dec. and G.H.A.) against G.M.T., for every day of the year. Such an Astronomical table is called an ephemeris.
Tabulated values of G.H.A. and Dec. gave to an accuracy of 0.1′, are given for every integral hour of G.M.T. for the whole year, and special interpolation tables are provided so that the values for intermediate minutes and seconds of time can be found. In addition, a table giving the S.H.A. of each of the navigational stars is provided. By applying the S.H.A. of a star to the G.H.A. of Aries for any given instant, the G.H.A. of the star for the same instant may be found.
In addition to the ephemerides, the N.A. contains a great deal of other information of use to the navigator. Included in this information are: –
Calendar of religious and civil holidays – Times of twilight – Moonrise and Moonset
Star charts & altitude correction tables – Equation of time & Times of Sunrise and Sunset
Notes on planets & Pole Star Table – Concise Sight Reduction Tables
Times of Mer. Pass. of Sun & Moon – Table of Standard-Times throughout the world
Eclipse information – Adjustment to Tabular Altitude Tables
A pamphlet containing selected extracts from the N.A. is supplied with this ‘Ocean Navigation’ to familiarise students with the contents and use of the almanac and to enable them to work the examples and problems set during this ‘Ocean Navigation’. These extracts are for the hypothetical year 199X; for use at sea, of course, The N.A. for the current year would have to be used and copies of this are available throughout the preceding year from H. M. Stationary Office and all Admiralty Chart Agents.
Nautical ephemerides and other Astronomical data for mariners are also available in the supplements to commercial N.A.’s, notably Reeds and Browns in the United Kingdom, but for space reasons, this is necessarily somewhat condensed and in a slightly different form from the Admiralty Almanac. Although the data for Astro-navigation in these other almanacs is quite adequate and many may wish to use these almanacs after completion of this study in ‘Ocean Navigation’, for teaching purposes we prefer to use the official Almanac and all references to the N.A. in this study refer either to the official publication or to the extracts from this in the ASTRO-NAVIGATION PAMPHLET.
The principal part of the N.A. known as the daily pages (P.4-9 OF THE ASTRO-NAVIGATION PAMPHLET) contains the ephemeral data, arranged vertically, for these days Students should examine these pages in the pamphlet now.
On the left-hand daily page successive columns give G.H.A. Aries, and G.H.A. and Dec. of each of the four navigational planets Venus ♀Mars ♂ Jupiter♃ and Saturn ♄ followed by a table giving the name, S.H.A. and Dec. of each of fifty-seven selected stars.
At the bottom right-hand corner of this page the S.H.A.’s and G.M.T.’s of Mer. Pass. of the navigational planets over the meridian of Greenwich are given.
The right-hand daily page contains the Sun and Moon, Ephemeris. Twilight information, times of Sunset, Sunrise, Moonset and Moonrise, are also given on this page. At the bottom, right-hand corner of the right-hand daily page will be found the equation of time, the G.M.T. of the Sun’s Mer. Pass. at Greenwich and the G.M.T. of the Moon’s upper and lower transits at Greenwich, together with the age and phase of the moon.
The special interpolation tables for finding the increments to apply to the values for the whole hours given on the daily pages for minutes and seconds are placed at the end of the N.A. and on PAGES 16-19 OF THE ASTRO-NAVIGATION PAMPHLET. Great care is necessary when using the daily pages to ensure that the required data for the correct day is extracted. Since the data for three consecutive days is arranged vertically, it is a common blunder to extract the data from the wrong part of the page.
16. FINDING THE GREENWICH HOUR ANGLE (G.H.A.) FROM THE N.A.
To find the G.H.A. ♈︎, read off onto the appropriate daily pages, for the correct date, in the (G.H.A. column for the Sun. The G.H.A. figure for the whole hour of the G.M.T. required. Then turn to the Increments and Corrections interpolation table at the end of the Almanac and in the appropriate panel for the number of minutes in the time read down the second’s column (left-hand column) until the number of seconds in the time is encountered. Read off, alongside the second’s figure, the tabulated value of increment to G.H.A. in the column headed Sun/Planets. This increment added to the G.H.A. from the daily page gives the G.H.A. ♈︎ for the required G.M.T.
The G.H.A. of the F.P. of Aries is found in the same way except that the whole hour figure from the daily page is extracted from the Aries column on the left-hand page, and the Increment is extracted from the Aries column in the interpolation tables.
The G.H.A. for a planet is obtained in the same way as that for the Sun, except that the whole hour figure from the daily page is extracted from the column headed with the name of the planet and there is a small additional correction, termed the ‘v’ correction, to apply. Look out the whole hour value of G.H.A. for the planet on the daily page and, at the same time, copy down the ‘v’ value, which can be found at the bottom of the daily page under the G.H.A. column. Then turn to the appropriate minute panel of the Increments table and find the increment to G.H.A. for the minutes and seconds of G.M.T. under the heading Sun/Planets.
Finally, in the same interpolation panel, find the already copied ‘v’ value in the column headed ‘v or d’ and take out the correction alongside it from the companion column headed corrn.
These three figures (G.H.A. for the hour in question, G.H.A. increment for the minutes and seconds, and the correction for ‘v’) together give the required G.H.A. of the planet.
Normally the correction for ‘v’ is added, but if the ‘v’ value on the daily page is preceded by a minus sign, then the corresponding correction should be subtracted.
The G.H.A. for the Moon in derived in the same way as that for a planet, except that the whole hour value is taken from the right-hand daily page under ‘Moon’ together with a ‘v’ value which is tabulated in an adjacent column for every hour of G.M.T., and that the increment for minutes and seconds is taken from the column headed ‘Moon’ in the Increments table.
17. TO FIND THE G.H.A. OF A STAR.
Referring back to fig. 3-1 in Ch. 3 where PG is the celestial meridian of Greenwich, P is the meridian of the F.P. of Aries and PX the meridian of a celestial body such as a star; the G.H.A. of that star is the arc GX. But the arc GX is the sum of the arcs G ♈︎ + ♈︎ X, and G ♈︎ is the G.H.A. of Aries and ♈︎ X is the S.H.A.. of the star.
Therefore we can say: – G.H.A. Star = G.H.A. Aries + S.H.A. Star.
The same relationship is shown in fig. 4-1(a) drawn on the plane of the celestial equator (i.e., as if viewed from, a point directly above the celestial pole), where again: –
PG = meridian of Greenwich
P♈︎ = Meridian of Aries PX = meridian of Star
And it can be seen that: –
GX = G ♈︎ + ♈︎ X or: G.H.A. Star = G.H.A. ♈︎ + S.H.A. Star
The same holds good even when the F.P. of Aries does not lie between the celestial meridian of the star, because fig. 4-1(b) shows that:
GX = G ♈︎ + ♈︎ X = 360°
Since the subtraction of 360° does not affect the actual angular distance, then in all cases:
G.H.A. Star = G.H.A. Aries + S.H.A. Star
Herein lies the importance of G.H.A. ♈︎ Aries. Direct tabulation at short intervals of the Greenwich hour angles of all the stars likely to be observed by the navigator would occupy far too much space and result in an Almanac of unwieldy proportions, if space were reduced by increasing the intervals, elaborate interpolation tables would be necessary, and we have already said in the introduction in § 1. that seaman have never taken kindly to interpolation.
The whole problem is avoided by tabulating a quantity which is constant for reasonable periods of time for each star – its S.H.A. – which, added to the G.H.A. Aries for the G.M.T. in question, gives the G.H.A. of the star.
8. FINDING THE LOCAL HOUR ANGLE (L.H.A.) OF A CELESTIAL BODY.
As will be seen later in this ‘Ocean Navigation’, what the navigator really requires in order to obtain a calculated altitude to compare with his Obs. Alt. is the L.H.A. of the observed body. It was shown in Ch. 3. that the L.H.A. can be found quite simply by applying the observer’s Longitude to the G.H.A. of the body extracted from the N.A.; the formulae being: –
L.H.A. = G.H.A. + E. Long. : or L.H.A. = G.H.A. – W. Long.
A useful rhyme with which to remember whether to add or subtract the Longitude is: –
Long. W. Greenwich is best – Long. E. Greenwich is least
19. FINDING THE DEC. OF A CELESTIAL BODY FROM THE N.A.
The changing declinations of what we loosely termed the moving celestial bodies – the Sun, Moon, and the four navigational planets – are all tabulated for each hour of G.M.T. in the daily pages of the N.A. under the heading Dec. Thus, from pages 4-5 of the ‘OCEAN NAVIGATION’ PAMPHLET, it can be seen that on 02nd Jan 199X at 0400 hrs G.M.T. the Sun’s Dec. is 22° 56.4 S, the Moon’s Dec. is 28° 13.1 N and Jupiter’s Dec. is 0° 59.7 S.
To interpolate for intermediate minutes between the tabulated declinations for whole hours, a figure’ is given at the foot of each Dec. column in the daily pages of the Sun and the four planets, and a column headed’ is given alongside the Dec. column for the Moon. The quantity’ is simply the change of Dec. that occurs in one hour. (as Dec. does not change rapidly enough to justify such accuracy the seconds can be disregarded).
To find the Dec. of a body at any time extract from the daily page the Dec. for the whole hour of G.M.T. note the value given for ‘d’, turn to the Increment tables at the back of the Almanac to the panel headed with the number of minutes in the time, find the value for ‘d’ in the column headed ‘v’ or ‘d’ and read off the correction alongside it in the column headed correction. This correction should be added or subtracted to the Dec. for the whole hour extracted from the daily page according to whether the Dec. is increasing or decreasing – this being determined by noting whether the Dec. (on the daily page) for the next hour is larger or smaller than the one extracted.
It is even easier to find the Dec. of a star because, the stars being almost fixed in relation to the Earth, it is not necessary to tabulate their Declinations by the hour on the daily pages of the N.A.
To find the Dec. at any time, simply write it down from the Dec column of the list of 57 selected stars on the appropriate daily page.
The Dec. of a star changes so slowly that the value given in the list on any daily page opening may be used for any time in the three days covered by that opening. For example, the Dec. of the star Deneb for any sight taken on 01st – 03rd Jan 199X is 45° 16.8 N.
For explanatory purposes, we have described the extraction of G.H.A., L.H.A. and Dec. from the N.A. separately. In practice, however, these quantities would be extracted simultaneously, and to conclude this section we will show a few examples of the practical use of the daily pages. Students should study these and the preceding examples carefully until they are thoroughly familiar with the layout of the Almanac and the extraction of G.H.A. and Dec. for any instant of G.M.T. The facility at this is essential towards future ability to work out a sight. The N.A. is as much a tool of the navigator’s trade as is his sextant and both instruments must be thoroughly understood in order to practise Astro-navigation.
(in this example 360° had to be added to the G.H.A. in order to be able to subtract the westerly Longitude from it, the correction to Dec. was subtracted because Dec. of Venus ♀ is decreasing on the daily pages).
(in this example the excess 360° had to be discarded in order to obtain the L.H.A., but the correction to Dec. was added because the Dec. of the Moon is increasing in the daily page).
(since the L.H.A. of ✴︎ Altair is zero, the star must be on the same meridian as the observer)
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