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    Re: Sextant accuracy with short distance to horizon
    From: Steven Wepster
    Date: 2001 Jun 22, 7:40 AM

    Dear Richard,
    I very much like your explanation why one should add the wave hight to the
    height of eye when observing from a wave top. Only for one 'but':
    your line of sight is tangent to the horizon, so for all practical purposes
    (wavelength assumed small w.r.t. curvature of earth) the horizon is formed by
    wave crests. There's no way of seeing a trough at the horizon because there is
    a crest relatively close in front of it. So both observer and horizon are
    raised by approximately the same distance (say, the significant wave height),
    and the dip should be calculated for the elevation of the observer above  this
    raised horizontal level.
    Sure, the difference is a bit academical, and I also agree to Rodney. The
    higher the waves, the less your own accuracy, generally. On the other hand dip
    is approx. a square root function of height-of-eye which makes it quite
    sensitive especially at the near-zero height where we enjoy ourselves. I guess
    that's also the reason why the issue isn't discussed in most text books
    (designed for merchant/navy use).
    > Steven Wepster writes:
    >  > Dear Dan and others,
    >  >
    >  > In my opinion you have hit a problem that is specific to astro on
    >  > yachts: the very small height of eye. The problem is not so much that
    >  > it makes the horizon nearby. The normal dip table should be sufficient
    >  > as long as it lists your height of eye. I don't know for shure what
    >  > Peter and  Russell meant by 'dip short' tables: my 1981 Bowditch
    >  > Vol.II has a different table 14, but it has a table 22 'Dip of the Sea
    >  > Short of the Horizon'. This table gives the dip of objects _in front
    >  > of_ the horizon, so it should not be used for a normal altitude above
    >  > the horizon.
    > That's an issue of different editions having different tables.  You
    > have the right table title, however.
    >  > More important: because your eyes are so low above the sea, it is most
    >  > of the time just plainly impossible to _see_ the horizon. The waves
    >  > get in between. When it is almost dead calm, there's no problem (but
    >  > it's not fun sailing then). You're lucky when the swell is running
    >  > high and regular, because then you can take a shot when you're at the
    >  > top.
    >  >
    >  > This raises another question: what is your height of eye at the top of
    >  > a wave? Do you have to add the wave height to your height above the
    >  > waterline of the vessel?
    >  >
    >  > In my opinion, the anser to that question is 'no'. I assume that waves
    >  > of appoximately the same height make up the horizon.
    > Strictly speaking, the answer is "yes", that is, one does add the wave
    > height to the height of eye.  The tables assumes a smooth surface and
    > an observer's eye on that surface.  The dip tables than adjust for
    > being off the surface.  Looking at the "Distance of the Horizon" table
    > shows that going from 10' above the water (standing height plus
    > freeboard on calm seas) to 20' (freeboard, standing but hanging on for
    > dear life [g], and 10' waves) now puts the horizon 5.2 miles out
    > instead of 3.7 miles out.  The dip table in the alamanc reflects this
    > change with a correction changing from -3.2 to -4.4.  Not a major
    > difference, I admit, but why add more "noise" to sights that will be
    > somewhat scattered (by boat motion)?
    > Now, your contention is that the 10' waves 5 miles away (that is, at
    > the boat's horizon) are higher than the horizon line and therefore
    > obscure the horizon.  Referring to (in '95 Bowditch) table 13,
    > "Geographic Range", a 10' wave is still visible at the horizon (and
    > remains so out to about 9 miles when height of eye is 20').
    > Nonetheless, by this point its height over the true horizon is reduced
    > to the point where the error from a raised horizon is more than
    > swallowed by the errors from sight motions induced by the boat's
    > motion.  Moreover, there is the very real possibility that at the
    > instant of a sight, the point where the object meets the horizon may
    > be at a wave trough or midway between trough and peak or at a peak.
    > In short, for practical purposes, the waves' effect at the horizon
    > should average out over a sight series.
    > Rick
    > S/V One With The Wind, Baba 35

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