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    Re: Index corr., Octant as dipmeter
    From: George Huxtable
    Date: 2004 Nov 22, 00:23 +0000

    Apologies if I have recently posted a similar message on this topic,
    replying to Jared Sherman. I thought I had, but can find no trace in my
    email boxes. It seems to have vanished, so I'll try again.
    Jared Sherman has, I suggest, misunderstood anomalous dip.
    >At sea, well away from land and in theory surrounded by uniform water--at
    >least, surrounded by enough of it to reach the horizon--the dip correciton
    >is usually made by compensation for barometer and temperature, yes?
    NO NO NO!
    >And the inaccuracy in this is often from changes in temperature, i.e. from
    >being on land shooting a horizon over the water, where tempearatures in the
    >air will differ.
    From changes in temperature close above the water surface, largely. Being
    on land has little to do with it.
    >So let's look at what a dipmeter is measuring. It is *not* measuring the dip
    >in the direciton where you are taking your sight. Rather, it is measuring
    >that dip, and the dip behind you--which may or may not be the same--and then
    >averaging them.
    >If the dip behind you differs from that ahead of you, you've simply
    >compounded errors and wasted time doing so...
    Depends on how much it might differ,. It's almost certainly better to take
    that average than to make no correction.
    >... If the dip in both directions is
    >the same...I suggest the standard compensations for temperature and pressure
    >are close enough to be enough.
    >So then, here's my hypothesis for you:
    > Standard compenstaions under standard conditions (uniform air mass) are
    >significantly equal to the results obtained from a dip meter
    No, there's no connection AT ALL between correction for temperature and
    pressure, and anomalous dip.
    >AND a dip
    >meter may in fact introduce more errors while consuming the navigators time
    >and energy.
    It's most unlikely to increase any errors and takes little time and little
    energy from your exhausted navigator.
    > Therefore they were never popular and have no role in routine marine
    >navigation. And, they will add nothing significant to the precision of it
    True, they were never popular. True, they have no role in routine marine
    navigation. Untrue, that a dipmeter will not significantly enhance
    When we measure an altitude, it's an angle between the apparent position of
    the body in the sky,and the apparent horizon.
    1. The apparent position of the body is affected by refraction. The
    correction depends on the observed altitude and is the total bending of the
    light by the atmosphere from its path in space until it reaches the
    observer. That bending depends on the difference between the refractive
    index of space, which is 1.00000, and the refractive index of the air at
    the observer's eye, which is about 1.0003. So it all due to that difference
    of about 0.0003. And that difference depends on the density of the air at
    the observer, as you might expect. If the atmospheric pressure increases,
    so does the density, and so does the bending. If the temperature at the
    observer decreases, that also increases the air density and the bending.
    Humidity can play a part too, but a very small one.
    For the range of altitudes that concern us in navigation (say 5 or 10
    degrees to 90 degrees) it doesn't matter at all HOW the temperature and
    pressure vary along the light path down through the atmosphere. It's just
    the end-value that matters.
    We correct for that refraction, then by calculating the air-density at the
    observer, knowing the temperature and pressure.
    2. The apparent horizon is affected in two ways-
    2a. A purely geometrical effect due to the curvature of the Earth's surface
    and the height of the observer above it. This contributes most of the total
    dip and can be calculated with great accuracy, It presents no problem.
    2b. A contribution from refraction. This is the source of all the trouble.
    It works out to be about 7% of the dip under normal conditions, working in
    the opposite direction to the geometrical dip, to reduice it. This is how
    it comes about-
    Light from the most distant point you can see (i.e. your horizon, a few
    miles away) gets to your eye along a path that's always close to the sea
    surface, never being more than your height-of-eye above it. So it's damn
    nearly horizontal. All along its path there's a vertical gradient in air
    density (it gets less dense the higher you go). That causes a curvature of
    the light path, which reduces the dip (usually by about 7%). This is taken
    account of in the usual dip correction, which assumes the normal values for
    density gradient.
    But there's a complication. Within a few feet of the sea surface, there are
    likely to be large local changes of air temperature, due to the effect of
    the sea surface, which is usually (but not always) cooler than the air. So
    this can give rise to layers of air at different temperatures, which have
    an unexpected density gradient, and therefore cause a different curvature
    in the air path than the standard dip formula assumed. And that's what
    gives rise to anomalous dip. It's particularly likely where there's a hot
    wind from Sun-heated desert, blowing over a cooler sea, in places such as
    the Red Sea and Southern California. It's also prevalent over thin ice,
    particularly in still air.
    Attempts have been made to predict a value for anomalous dip, by measuring
    temperature on deck and also dangling a thermometer at a lower level, or by
    sampling the sea-water with a bucket to assess it's temperature. What's
    wanted is the way the air temperature varies with height above sea, not the
    temperature itself. They have not been very successful because there are
    too many other factors involved; wind strength, sea roughness, blown spume.
    The explanation above was intended to show that there are two different
    quantities that are affected by refraction: the bending of the light from
    the body to the observer, and the bending of the light from the horizon,
    and they are affected in quite different ways. Correcting for one does
    NOTHING to correct for the other.
    Jared complains that the dip in the direcion of the observed body may be
    different from that at the opposite azimuth. That may be the case, but
    remember, you're sampling a circle of, say, only 10 miles across, which is
    very small compared with the dimensions of any weather-system. If you could
    see a line-squall approaching from aft, that may provide a reason to
    distrust a dip measurement, which assumes that the dip is reasonably
    constant over your horizon circle. But it would take an immensely sharp
    variation of dip with position to make such an average value WORSE than not
    correcting for anomalous dip at all.
    So I don't accept Jared's statement "AND a dip meter may in fact introduce
    more errors..."
    Jared concludes- "Therefore they were never popular and have no role in
    routine marine navigation..."
    Fair enough (except for the "therefore"). Taking readings with a dipmeter
    is boring, in that most of the time, the dip is within a minute or so of
    the predicted value. It's only the occasional variations that get
    interesting. Who, in "routine marine navigation", is or ever was seriously
    concerned about an occasional error in position of three, or even rarely
    five, miles?
    Where dipmeters were used was in non-routine astro navigation, if
    paricularly exact results were required. I have already mentioned cable
    laying and grappling, in which John Blish was involved. Blish was a US Navy
    man, and perhaps I can suggest a dipmeter application that may have
    interested him. Long before the days of satnav and radar, big naval guns
    were, I think, capable of bombarding a shore target that was out of sight
    over the horizon. (I know little about naval gunnery, so someone correct me
    please if that's wrong). The shore target coordinates may have been
    obtained from maps, but to lay the guns, the ship's position was needed, as
    precisely as possible. Any tool, such as a dipmeter, which enhanced the
    precision of an astro position, would have been well worth its keep.
    "And, they will add nothing significant to the precision of it today"
    Does Jared dispute that anomalous dip remains the most important source of
    potential error in celestial positioning? Does he dispute that the error
    can be significantly reduced by measuring what the dip actually is? For
    those to whom precision was important, the dipmeter was a useful tool. As
    of "today", none of this is now relevant. If you need precision, today, you
    don't use astronavigation!
    Others who may take as interest in the dipmeter are the members of this
    list, who have frequently asked "what is the ultimate accuracy in position
    available from a celestial observation", and treat the elimination of
    errors as something of a challenge.
    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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