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    Re: Refraction
    From: Gary LaPook
    Date: 2007 Dec 11, 00:30 -0800

    Here is a link to a site that demonstrates refraction and formulas for
    calculation.
    
    http://www.jgiesen.de/refract/index.html
    
    gl
    
    On Nov 21, 1:05 pm, Gary LaPook  wrote:
    > 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 067� leading to the 157�-337� LOP. He ignores the fact that the
    > azimuth remained at 067� until 1854 Z, more than an hour after
    > sunrise. This means that any sight taken during this period would
    > produce the same 157�-337� 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 90�. 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 70�; 1' between 70� and 36�; 2' down
    > to 22�; 3' down to 15�; 4' down to 13�; 5' down to 10�; 6' down to 8�;
    > 7' for 7� and 8' for 6�. 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 10�. So Noonan couldn't use his correction tables for
    > any sight below 6�.
    >
    > 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 6� 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 1� 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 1� 37'.) This means that at sunrise the actual altitude
    > measured would also be minus 1� 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 1� 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 6� 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  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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