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  George Huxtable writes:

 " Geoff, tantalisingly, adds-
 "
 " >.. only leaving the question of why there are two tides per day rather than
 " >one to be explained!
 "
 " Geoff's contribution sounds rather authoritative, and I wonder if he would
 " be prepared to respond to his own suggestion, in explaining the two tides.
 "
 Only 'authoritative' in the context of needing to display confidence
 (misplaced?) while teaching RYA Yachtmaster!  So, right or wrong, this is the
 way I explain two tides per day:

 * The Moon and Earth rotate around each other in the manner of a hammer-
   thrower before releasing the hammer
 * They both rotate about a point close to the surface of the Earth
 * The oceans are not rigidly connected to the Earth and are free to respond
   to the Moon's gravitational attraction by flowing towards the Moon
 * However if, with his second pair of hands, the hammer thrower was carrying
   a bowl of water as he rotated his eccentric motion would cause the water
   in the bowl to slosh outwards, away from the hammer
 * On the side of the Earth closest to the Moon the effect of Moon's gravity
   exceeds the sloshing effect and water levels are raised there - towards
   the Moon
 * On the side of the Earth remote from the Moon the sloshing effect exceeds
   the gravity effect and water levels are raised there also - away from the
   Moon
 * .. so there are two raised ocean levels opposite one another and as the
   Earth rotates beneath one experiences locally two tides per day

 I haven't done the calculations myself but have read (somewhere) that the
 two causes for ocean raising have slightly different magnitudes - which
 explains why plotting sequential tidal ranges from tide tables results in
 the 'odd' tides following a slightly different curve from that for the 'even'
 tides.

 " Geoff's reference to the Admiralty Manual of Tides reminds me of my
 " Liverpool University days of 50 years ago, during which I enjoyed a 1-year
 " course in Oceanography, when that Manual was the course-book for Prof.
 " Proudman's lectures on tides. It so happened that my wife took that same
 " course a few years later.

 A few years ago I bought the very last new copy of the Manual from the
 Hydrographic Office.  At the time I had just acquired a set of programmes
 written in Basic which calculated astronomical data for any date.
 I therefore had a means of obtaining all the parameters needed to
 calculate tide height for any location for which the tidal prediction
 coefficients were available, ie anywhere covered in the Admiralty Tide
 Tables.  The resulting programme will calculate tide heights to within one
 or two percent of published tide tables provided I have the coefficients
 for the port.

 I tested the programme for Liverpool and Portsmouth using coefficients
 published some 20 years ago.  Agreement was not as good as I had hoped.
 Using coefficients published in the Ad Tide Tables for last year agreement
 was within the above limits.  It hadn't occured to me before, but I see
 that updated coefficients are needed to reflect the effect of changes in
 channel dimensions, silting, dredging etc.

 " I understand that the Manual was produced at short notice in the early days
 " of the 1939-45 war to meet the sudden need to train up thousands of
 " officer-recruits for the Royal Navy. It's good to see it still being taken
 " as a reference.

 For this kind of project it is a wonderfully complete resource. However the
 mind boggles at the notion of 'thousands of officer-recruits' struggling
 with the chapters on the theory of harmonic analysis!

 The question often asked in Navigation-L: "where can I get a programme to
 calculate Nautical Almanak daily data?" set me off on another project to do
 just that using the same set of astronomical calculations.  The project has
 been on hold to allow for sailing this summer, but I can get some pretty
 reasonable agreement with the NA.  There are however some minor discrepancies
 of the magnitude of 0.2seconds in GHA for some bodies which I don't quite
 understand at the moment (although it may simply be due to the inevitable
 curtailment of some of the least significant terms in the Meeius algorithms
 on which the programmes are based - particularly for Moon and some planets)
 - and I would be prepared to accept a fix with that magnitude of error in
 circumstances when I would be relying on the sextant.

 Before anyone asks for copies I have to confess they are not bug-free and in
 no state to be used: they require a lot of work this winter even to have any
 kind of understandable user interface.

 I would be interested to know if anyone else has been doing the same thing.

 I found the following to be most thought provoking - as so often in this
 list: "Thanks, George"

 " The tidal force on Earth from a body turns out to be proportional to its
 " mass and inversely proportional to the cube of its distance; which has an
 " interesting consequence.
 "
 " By chance, the Moon and the Sun happen to subtend almost exactly the same
 " angle in the sky, seen from Earth. This implies that the ratio of the
 " volumes of Sun and Moon is almost equal to the cube of the ratio of their
 " distances. If Sun and Moon were made up of the same stuff (which they
 " aren't) so that their masses were in the same proportion, then the tidal
 " forces generated by Sun and Moon would be exactly the same. This would
 " imply that at neaps their effects would completely cancel, and neap tides
 " would be zero.
 "
 " The fact that we observe the Sun component of tide force to be about half
 " that from the Moon implies immediately that the mean density of the Sun is
 " about half the mean density of the Moon. It's a cosmological deduction,
 " that can be made simply by measuring the surface of the sea.

Geoff Butt

   

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