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    Re: Navigating Around Hills and Dips in the Ocean
    From: George Huxtable
    Date: 2003 Aug 14, 10:10 +0100

    David Hoyte  wrote-
    
    >        The joint NASA-German GRACE project has released the most
    >accurate map yet of Earth's gravity field. It shows Gravity Anomaly,
    >(mGal), on a global map at the URL:
    >http://photojournal.jpl.nasa.gov/catalog/PIA04652
    >
    >        These gravity anomalies cause the geodic heigh of the ocean's
    >surface to vary around the world by up to 200 meters, 650 feet. Ref:
    >http://www.csr.utexas.edu/grace/publications/press/03-07-21-ggm01-nasa.html
    >
    >        In the Atlantic ocean, for example, there is a hill South of
    >Greenland of +200 feet, and a dip in the Caribbean of -250 feet, approx.
    
    ================
    
    This is interesting information. Then he went on-
    >
    >        I heard as far back as 1975, at the IBM Maritime Center in
    >Italy, that a large ship will use significantly more fuel if it passes
    >down into a gravitational dip and climbs the other side, rather than
    >following a longer path around the dip which will keep it more "on the
    >level".
    >
    >        Is there a published algorithm that relates the parameters
    >such as ship's tonnage, the size of the hill or dip, the path followed
    >and fuel savings?
    >
    >
    >        Is there perhaps a simple "rule of thumb" for the courses to
    >steer, for use at sea?
    
    =============
    
    Response from George Huxtable.
    
    I am a natural sceptic about most matters, and here's another to be
    sceptical about.
    
    What is being mapped, presumably, is a gravitational equipotential surface,
    with all its ups and downs with respect to the Earth's centre. If the Earth
    was spherical and non-rotating and of uniform density, then that surface
    would be a sphere. None of those applies, so it's not a sphere.
    
    What that surface maps out is an equal gravitational potential, so that
    moving from anywhere on its surface to anywhere else, there is no change of
    energy due to gravitational differences. It maps out the water surface,
    because it it didn't, any drop of water on the surface, being free to flow
    "downhill" to minimise its energy, would immediately do so, until the water
    surface conformed to the equipotential. (For the purists, I will mention
    that small "geostrophic" forces caused by ocean currents on a rotating
    Earth are here ignored, as are the oscillatory gravitational forces of the
    Moon and Sun that give rise to tides).
    
    What applies to that drop of surface water applies equally to any object
    floating in it, including a ship. It that were not so, such objects would
    congregate at certain locations, which would become floating graveyards of
    lost vessels!
    
    Gravitationally speaking, then, when a ship takes a path from A to B, both
    being on that equipotential we call the ocean surface, it matters not at
    all which path she follows, there's no loss or gain of gravitational
    energy, even though one path would take her nearer to the centre of the
    Earth than another. The fuel burned would depend mostly on the work done in
    displacing water to make way for her path, and so depends largely on the
    length of that path, but has to allow for likely winds and currents too.
    
    So where David Hoyte says-
    
    >I heard as far back as 1975, at the IBM Maritime Center in
    >Italy, that a large ship will use significantly more fuel if it passes
    >down into a gravitational dip and climbs the other side, rather than
    >following a longer path around the dip which will keep it more "on the
    >level
    
    I just don't believe it. On the ocean surface there are no gravitational
    dips. I suggest that the IBM Maritime Centre in Italy got it wrong, or else
    perhaps David has misremembered. Presumably someone was working on ship
    routeing algorithms at that time. If ship routeings have ever been adjusted
    to take account of the ocean's hills and valleys, then I suggest someone
    has got things badly wrong.
    
    Perhaps I should make it clear that my arguments are based on general
    physical principles, and I know little about the complex topic of
    ship-routeing. If anyone on this list can correct my conclusions, I hope
    that they will.
    
    George.
    
    
    ================================================================
    contact George Huxtable by email at george---.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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