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    Re: Refraction
    From: Gary LaPook
    Date: 2007 Nov 21, 13:05 -0800
    Gary writes:

    I am attaching a message that I posted to an Amelia Aerhart list which goes into many aspects of refraction :

    "Gary wrote:

    Ric has always pushed the idea that Noonan observed sunrise and drew
    an LOP based on that observation which he advanced to Howland. Then
    Noonan dead reckoned from the first LOP to the advanced LOP and then
    started looking for the island. In this scenario Noonan might as well
    have dropped his sextant out of the door after sunrise since,
    according to Ric, he wouldn't use it again. Ric seems to have jumped
    to this conclusion on the basis that the azimuth of the sun at sunrise
    was 067º leading to the 157º-337º LOP. He ignores the fact that the
    azimuth remained at 067º until 1854 Z, more than an hour after
    sunrise. This means that any sight taken during this period would
    produce the same 157º-337º LOP.

    Evidence against Noonan observing the sun at sunrise has to do with
    refraction. When a navigator talks about refraction he is talking
    about the way the light from the sun and other celestial bodies is
    bent as it passes through the atmosphere. Because of the density
    range of the air all light rays are bent down toward the ground making
    objects appear higher in the sky than they actually are. The amount of
    this bending depends on how much of the atmosphere the light must
    traverse. An object directly over head will have its light bent not at
    all and there is no reason to worry about refraction for an altitude
    of 90º. As the measured altitude gets lower and lower the effect of
    refraction gets greater. The navigation computation tables used by
    Noonan (Hydrographic Office (H.O.) 208, Dreisonstok) provided a table
    of corrections for the navigator to use to correct for the refraction.
    The corrections are given in minutes of arc, 1/60th of a degree. An
    error of one minute of arc will cause the resulting LOP to be in error
    by one nautical mile. These corrections are always subtracted from the
    sextant altitude because the sextant always reads too high. This table
    says to use no correction above 70º; 1' between 70º and 36º; 2' down
    to 22º; 3' down to 15º; 4' down to 13º; 5' down to 10º; 6' down to 8º;
    7' for 7º and 8' for 6º. That is as low as the table goes. The
    equivalent table was also found in the 1937 Nautical Almanac. The
    reason these tables go no lower is because at lower altitudes the
    refraction becomes much larger and unpredictable so navigators are
    trained to not use such low altitudes and the omission of lower
    altitudes in the refraction correction tables was meant to discourage
    anyone from attempting to use such a low sight. In fact H.O.218, a
    more modern set of tables, only allows you to do your computations for
    altitudes above 10º. So Noonan couldn't use his correction tables for
    any sight below 6º.

    But what if Noonan was such a great navigator that he thought he could
    use lower altitudes? Could he just extrapolate from the table that he
    had to estimate the correction for sunrise? Well, no. The correction
    increases very non-linearly from 8' at 6º to 36' at zero degrees.
    However there was a table in The American Practical Navigator (also
    referred to as "Bowditch"), H.O. 9., that showed corrections all the
    way down to zero so Noonan could have ripped that page out and carried
    it with him but there is no proof that he did.

    But that still wouldn't have solved his problem. Since they were
    flying at 10,000 feet the visible horizon is actually 1º 37' below
    horizontal because he was actually looking down towards it. ( The dip
    of the horizon is calculated in minutes of arc as .97 times the square
    root of the height in feet. The square root of 10,000 is 100 times .97
    equals 97' or 1º 37'.) This means that at sunrise the actual altitude
    measured would also be minus 1º 37' and the refraction table in H.O. 9
    only goes down to zero. Well what if Noonan just used the maximum
    correction tabulated for a zero altitude which was 36'? Well the
    refraction table found in the modern Air Almanac for sights taken at
    10,000 feet shows the refraction correction for minus 1º 37' is 50',
    14' more than the correction for zero altitude. Noonan couldn't have
    known this but he would have known that it was greater than 36' but he
    couldn't know how much more. If he applied the 36' correction instead
    of the correct 50' correction he would have plotted his LOP 14 NM too
    close to Howland. If he took no more sights and just relied on dead
    reckoning from there he would have turned 14 NM too soon and could
    have missed Howland by being too far to the southwest.

    The bottom line is that Noonan was too smart a navigator to be
    ignorant of these problems with refraction. He had plenty of time to
    take sights on the sun after it had risen above 6º at about 1815 Z at
    Howland.

    BTW, if you watch the sun set over the sea with a clear horizon you
    will notice that the shape of the sun changes from round to a
    flattened or squished look. This is caused by the rapid changes in
    refraction as the sun nears the horizon. The sun is 32' in diameter so
    when the bottom is on the horizon the top is 32' higher. The modern
    refraction correction table shows the correction for zero is 34.5'
    while for 33' it is 28.2'. This means that he bottom of the sun is
    refracted up 6.3' more than the top edge is. This makes the sun look
    squished since it is still 32' across but only 26' from top to bottom.
    Sometimes the sun will take on a lumpy appearance or appear to have
    shoulders and this is caused by the erratic changes of refraction that
    can take place at low altitudes. When there is a very greatly
    increased refraction you can see mirages, objects that you could not
    usually see because they are hidden by the horizon. But with extreme
    refraction the light is bent so much coming from those objects that it
    comes over the horizon and is bent enough to stay near the ground
    where you can see it.

    These are the types of problems with low altitude shots, Noonan would
    have known about them and would not have attempted low altitude sights."

    gl


    Isonomia wrote:
    Gary,
    
    thanks for the pages on refraction. My comments on refraction on the
    horizon were just muddled thinking - of course the sky itself is a
    long way away and is therefore refracted, but the sea which determines
    the line of the horizon is only a few miles away and therefore doesn't
    have as far to suffer.
    
    However, as I've often seen a distortion of the sun as it goes beneath
    the horizon I think this is evidence for some kind of affect that
    distorts light at the horizon, which because it happens near the
    horizon must be due to some kind of affect that bends light close to
    the ground and surely this "heat haze" must have a significant impact
    on the position of the horizon?
    
    Perhaps a warm sea/cold air is an unlikely observation event (its
    called fog), but a cold sea with warm dry air coming over it must have
    some kind of affect which will alter the observed position of the
    horizon - or does it?
    
    Mike
    
    On Nov 20, 7:04 pm, Gary LaPook <glap...---.net> wrote:
      
    Gary LaPook writes:
    
    Attached is an excerpt from Dutton, explaining refraction, and the
    sextant correction table from the 1999 Nautical Almanac to assist Mike
    Lenzie. The sun correction table includes refraction and semi diameter
    for upper and lower limb observations. The included dip table is for
    correction of height of eye above sea level and can be computed from the
    formula:  dip (in minutes of arc) = .97 times the squaare root of the
    height of eye (in feet.)
    
     Dutton 1934 refraction.pdf
    97KDownload
    
     refraction, N.A. 1999.pdf
    53KDownload
        
    
    
      


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