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    Re: Dip uncertainty
    From: George Huxtable
    Date: 2004 Dec 7, 22:37 +0000

    Yesterday I wrote-
    "I think Bruce has got it wrong, about anomalous dip affecting observations
    from small vessels rather than from large ones.
    On my small boat, the cockpit sole is no more than inches above sea-level:
    it's only just self-draining. So my height of eye is no more than 6 feet,
    which puts my visible horizon 2.8 miles away. Let's say there's a marker
    North of me, just 2.8 miles away, just there to mark my horizon, appearing
    to float right on it.
    When I see the horizon to the North, the light-ray marking that horizon has
    skimmed just over the sea-surface, at a tangent to it, close to that marker
    vessel. The dip that I see is the angle between that light ray as it passes
    my head, and the direction of my own local horizon.
    You can think of that dip as being made up of three parts. The major part,
    by far, being simply the curvature of the sea surface, the "geometrical"
    component of dip, which is easy to calculate precisely.
    As you ascend above sea-level, the air gets less dense, according to a
    well-known law for a "standard" atmosphere. This density-gradient refracts
    the light from the horizon into a predictably curved path. The curvature is
    in a downward direction, as is the curvature of the surface, and the dip,
    depending on the difference between the two, is reduced by about one part
    in 12 as a result. So far all is predictable, and given in the standard
    "dip tables".
    But the region of the atmosphere, within a few feet of the sea-surface,
    through which the light has been passing, is rather special, because of
    exchange of heat with the surface. Depending on some complex factors, such
    as wind (or lack of it), temperature difference, surface roughness, complex
    layers may exist at different levels. The light, in passing through those
    layers, is refracted in an unpredictable way. That unpredictable component
    is "anomalous dip"; it can add to or subtract from the predicted dip.
    Without a dipmeter, nobody knows of its existence.
    What happens to the light which has passed my head, from the horizon 2.8
    miles away? It still carries on rising, and may be seen from the bridge of
    a larger vessel, from 24ft high, which is 5.6 miles from that marker on his
    horizon (because the horizon distance increases with the square root of
    eye-height) and 2.8 miles to my South.
    And what dip affects observations from that vessel? The standard dip, from
    the almanac, is doubled. The anomalous part of the dip will be, initially,
    the same as affected me at 2.8 miles, but now the light goes on, still
    close (from 6 to 24 ft) to the sea surface, so there's extra curvature
    added as a result of that additional 2.8 miles of its path.
    What Bruce is arguing, it seems to me, is that in the latter part of its
    path, that light is  sufficiently far (6 to 24 ft) from the sea-surface,
    that no anomalies of temperature-gradient will occur to affect the dip.
    This seems to me an unlikely proposition, but even if it were true, the
    anomalous dip would be no less than it was for me at 6 ft height-of-eye. So
    I don't accept his argument that anomalous dip will be more of a problem to
    smaller vessels; it's the other way about, as I see it."
    Since then, there have been so many messages on this topic that I am left
    quite confused.
    Would one or more opponents of my view, expressed above, kindly summarise
    what's wrong with it, in simple terms that I can understand?
    I would hope that any explanation would deal with the influence of
    air-layers on the dip as seen by our two mariners, at heights of eye 6 ft
    and 24 ft. Comparing three situations, as follows-
    Normal atmosphere, right down to sea level.
    A layer with abnormal temperature gradient, confined to within 6 feet of
    sea level.
    A layer with similar abnormal temperature gradient, confined to within 24
    feet of sea level.
    If we discuss it in such terms, then we don't need to make the impossible
    study that Bruce proposes, to discover what those temperature gradients
    actually are.
    Bruce wrote-
    "I still think my simplistic logic is nearer the truth. Put normal refraction
    aside, as Alex does in his thought experiment, and suppose light should come
    straight from the horizon. Now put a bend in the light somewhere along its
    path. For simplicity, let's say the bend is caused by a prism planted on
    top of a
    five-foot tall buoy. Climb on the buoy and look at the horizon through the
    prism. The angle between the horizon and where you see it through the prism will
    be huge.
    Now go twenty miles away, and from a height where you can see both the prism
    and the true horizon, look (you'll need a powerful telescope) at the prism.
    The horizon you see through the   prism will be only slightly out of line with
    the true horizon.
    That's because, from twenty miles away, the angle between top of the buoy and
    the horizon is small."
    and later added-
    "I realized, too late, that instead of a prism I should have specified a plate
    of glass with just enough difference in parallelism of surfaces so that a ray
    coming from the horizon (say 2' below horizontal) would be bent down 2' in
    passing through it, and come out of the glass horizontal to the earth at that
    point. At the buoy, looking through the glass, you'd see the horizon 2' above
    its true place. Looking through the glass from 20 miles away you'd see the
    horizon very close to its true place."
    Well, that's a prism too, if a narrow one, that (within limits) bends all
    light through 2', no matter where it is in the light path.
    I've been trying, but failing, to draw out the picture that Bruce wishes me
    to visualise. I wonder if he would kindly help me a bit further to put that
    geometry together.
    And if simplifying assumptions will help to make the point that I seem to
    be missing, (e.g. flat-earth?, no-atmosphere?, bending in horizontal
    plane?) then simplify, do!
    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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