NavList:

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...@pacbell.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
    

--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to NavList@fer3.com
To , send email to NavList-@fer3.com
-~----------~----~----~----~------~----~------~--~---