Mr. Lapook ,
According to your replies I would not have explained "looking at the same time by two sextant types" , etc. The key to overcome the misunderstanding is the following : the N.A. or any other source gives GMT of sunrise U.L. @ 175453 GMT . It here concerns the visible (also named ´apparent´-) sun , for which the true sun must be 53´below the horizon . Hence , if you go to look to sunrise U.L. with the marine sextant , you actually see the sun for @ GMT 175453 - 3m50s = 175103 Greenwich Apparent Time . The sun rises with 13´8 / time minute , so 53´/ 13´.8 = 3m50s after 175103 GAT , sun´s centre is in the horizon , elevation zero . Now you have 2 alternatives : I . @ 175453 GMT you observe with the marine sextant . You now see the sun with a LHA which is 57´.5 larger than it would be @ 175453 GAT. It will last 3m50s (53´/ 13´.
before the true sun (centre) is in the horizon , the LHA having diminished with 57´.5 . II . @ 175453 GAT you observe with the bubble sextant , the LHA has the correct opening since you view the true sun . During the time lag 175103 GAT to 175453 GAT however , the MEAN sun traveled from 175453 GAT to 175843 GMT by the time equation , equally being 3m50s . Balance : since you fly on GMT schedule , given that you observe by marine sextant , whereas you used the bubble sextant @ sunset last evening , you will seemingly arrive at precomptud Zulu time at your next initial point . However , actually , you will be there 3m50s early. If the initial point is at the "alter to offset course" place , you will consequently arrive 3m50s short of the precomputed Turn-Off-Point on the from sunrise advanced LOP .
I from experience know that this reasoning about time lags is a dreadful blackbox , inscrutable and demanding for many hours of study , but that´s just how it is.
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Imagine...you have taken your wife, .....
Enough for now.
gl
Mr.Lapook ,
I see , by many words , that you try to undermine the theory in question , which is good since any theory needs a testbench before it can be generally accepted . However , you continuously bring into discussion the relevancy rate of it , all your comments have , so far , no influence on the internal consistency . P.e. you write about the "van Asten sunset", whereas it is clear and explained that only a "Frederick Noonan sunset" is on record , communicated @ 0720 GMT for 159-07-E ; 04-33-30-S coordinates . You also bring into discussion bubble sextants , not marine sextants , given to WW-II air navigators because of the assumed amelioration of the instrument , whereas it is trivial that in war time , aircraft fly necessarily at high altitudes with sky and local horizon blended so that marine sextants failed their reference line. In all your comments stating "mr.van Asten is wrong again" and "You don´t know what you are talking about" , not one sentence concerning supposed inconsistency finds a good argument . It is , other example , not new to me that precomputation took place during flight : since the turn-off point after sunrise would have been originally reached at sunrise , Noonan had to recompute in flight for ephemeris of another coordinates pair. The exact algorithms used for his calculations indeed remain unknown , but that is no argument for the statement that mine would be too long , too intricate , upside down , etc. , it is for e.g. sunset clear that Noonan acquired the same outcomes , and that is unconditionall , one step and more forward in the field of quantitative research for the incident.
On hilltop no.3 , 1,000 ft above sea near sunset , sits a mr. L with a Gibson Girl , kite in the air , to contact his airline company at sunset time for checking the company´s new sunset tables. At precomputed sunset time , he looks to .. a disc and sees it largely and complete above the horizon through his marine sextant telescope . He calls the company , shouting : "your tables are wrong , with my calibrated sextant I still see the sun after sunrise , your Greenwich Hour Angle notation is adverse , I am sure I corrected for dip !"
shouts the company executive back : "You are fired , Sir , you should have turned up your horizon 53 additional arcminutes .. the knob at the underside" .
------------------------------------------------------------------------------
(Continuing on with our romantic vignette.)
...
“Noticing the confused look on her face he goes on ‘we are about a thousand feet above sea level
so when we are looking at the sea horizon we are actually looking downward, below the level
horizontal plane. The sun, even though we can still see the entire disk, is actually below the
horizontal level so it has already set. Now get up, we’re leaving.’”
“But wait, I wanted to see a romantic sunset, this sucks. How do you even know that the sun is
below the true horizontal?” she asks.
“Because
I figured out a way to determine it without help from anybody else, and I am pretty
proud of myself, I looked in lots of navigation manuals and this method is not in any of them! I
did find in these manuals that navigators have to allow for the fact that the visible horizon is
actually below the true horizontal when taking sights with their marine sextants. Since it is below
zero and it is used as the reference for the measurements, all altitudes measured with a marine
sextant are too large so navigators must subtract the amount that the visible horizon is below the
true horizontal from all of their sextant readings. They call this the “dip” correction and it varies
according to the height the observer’s eye is above sea level. They find this correction tabulated
in the “dip correction table” in the Nautical Almanac. I looked in the dip table and found that for
our height above the sea, one thousand feet, the dip correction is a little more than half a degree,
thirty-one minutes of arc, actually. So, I just set the index arm on my marine sextant to thirty-one
minutes, looked at the horizon through the horizon mirror on the sextant and waited until the
upper limb of the sun, that I was viewing in the index mirror, sank down until it appeared to be
lined up with the visible horizon reference in the sextant mirror so I then knew that the upper
limb was at the true horizontal and so the sun had set.”
She says “OK, that’s great. So that’s what you were doing over there by yourself, I thought... oh
never mind.”
“You’re
RIGHT, it is great,
I FIGURED IT OUT, nobody else had ever discovered this method
for finding the true horizontal!” he replied.
“O.K. but can we please wait a little while longer so I can actually see the sun disappear behind
the horizon, I’d like to see the green flash” she begs.
“No!, I know when the true sunset is, so we are leaving now.”
(We will now leave this couple to work our their “issues.”)
In fact, this method would work if anybody needed to find the point of “van Asten
sunset/sunrise” which no navigator has yet to discover the need to do.
I communicated with Mr. van Asten about this and asked him how Noonan would have known
his height above the sea so that he could look in the dip table to determine the correct value of
dip to place on his sextant. He responded that Earhart said that she was at a thousand feet and
that she knew that from her altimeter.
On May 16th I wrote to Mr. van Asten:
“To have an accurate altitude from a barometric altimeter you need to have a local altimeter
setting (QNH) for a reporting station within 50 nm of your location and Earhart had set her
altimeter on the ground in Lae, 2222 nm away and had not received any altimeter setting since
then. Over such a great distance it is possible for an altimeter to be off by a 1000 feet since the
change in atmospheric pressure for the different locations will cause the altimeter to read
incorrectly.
Just to give you an example, I just checked the weather at Minneapolis, Minnesota and at
Billings, Montana, two airports separated by only 644 nm. At 0600 Z the altimeter setting at
Minneapolis is 31.18 inches of hg and at Billings the altimeter setting is only 29.72 inches of hg.
With this difference in altimeter settings, a pilot taking off from Minneapolis and flying only 644
nm to Billings without getting the local Billings altimeter setting (QNH) would end up 460 feet
lower than what his altimeter is indicating, and this in only 644 nm. A pilot flying in the opposite
direction would find himself 460 feet too high. Noonan would not have used a mariner's sextant
because he would know of the uncertainty in the altitude and the resulting uncertainty in the
correct dip correction to use. Since Noonan did not have a current altimeter setting then his
height could easily have been off by plus or minus 500 feet so the dip might be anywhere
between 22' and 38' giving the marine sextant altitude 16' of uncertainty But using the
methodology that you laid out of setting the marine sextant to 31' (the dip at 1000 feet) and then
waiting for the upper limb of the sun to come up into alignment with the visible horizon seen in
the marine sextant then causes you to see the upper limb of the sun aligned with the true
horizontal . Then you said to subtract 53' (37' refraction and 16' of semi-diameter) from this zero
altitude to arrive at the true altitude of the center of the sun of minus 53'.
But if they were only at 500 feet instead of 1000 feet then the dip correction is only 22' so setting
the sextant as you said would not cause it to define the true horizontal but would actually set the
reference at 9' above the true horizontal so the observation would be in error by the same 9'
meaning that the true altitude of the center of the sun would be minus 44' not the minus 53' of
your computation, resulting in a 9 nm error in the line of position which would eventually place
them 9 nm east of Howland.
If, instead, they were actually at 1500 feet then the dip correction would have been 38' instead of
the 31' that you have set your marine sextant to which would then result in a 7' error, placing
them 7 nm west of Howland. There is 16' of uncertainty from this possible altimetery error
causing 16' of uncertainty in the correct dip correction to use. This results in a 16 nm uncertainty
in the derived position of the aircraft. Noonan would have gotten a more accurate LOP using the
bubble sextant which doesn't require a correction for dip. This would also cause the “van Asten
sunrise” to occur up to 36 seconds early or late compared to your computations.”
(You can see the dip correction table at:
https://sites.google.com/site/fredienoonan/resources/nautical-almanac-1937/almanac-1937-277.JPG?attredirects=0
You can also read about the dip and refraction corrections in the American Practical Navigator,
1888 and 1914 editions here:
https://sites.google.com/site/fredienoonan/resources/american-practical-navigator-1888and
https://sites.google.com/site/fredienoonan/resources/american-practical-naigator-h-o-9-1914These excerpts also contain the complete sections on the methods of determining longitude and
you can review them and you will find no mention of the “van Asten’s sunrise” method.)
Mr. van Asten’s response actually made me laugh out loud. He said Noonan could just use his
bubble sextant to measure the dip of the visible horizon to place on his marine sextant and then
look in the dip table for that amount of dip and so determine the altitude of the plane.
I responded:
“You come up with an interesting use for the dip table. But if they used the bubble sextant to
measure the dip then there would have been no need to determine dip at all since they would just
use the bubble sextant for taking the observations.”
Mr. van Asten has a bubble sextant and plays with it while standing on the ground so he doesn’t
understand the use of a bubble sextant in the air. Due to the constant accelerations a plane feels,
the bubble is in constant motion even if the air feels smooth to the occupants. In turbulence it
really moves around. So when taking an observation you are constantly turning the altitude knob
on the sextant to chase the bubble with the image of the sun. The extreme readings might actually
differ from the true reading by more than a full degree (60'). You must take many sights over a
short period and average the readings to get any kind of accuracy at all and you must accept an
uncertainty of plus and minus 7'. This would also apply to a measurement of the dip of the visible
horizon, so this uncertainty would then be transmitted to the marine sextant and would carry
through to the horizontal established by the “van Asten method..” The uncertainty introduced this
way is just about the same as that introduced by lack of a current altimeter setting.
Mr. van Asten also doesn’t allow for the uncertainty in the readings from a marine sextant.
Various statistical studies have been made using data from thousands of observations by
hundreds of observers and the standard deviation is about 1.6' so the uncertainty is twice this,
3.2'. This would be added to the uncertainty in determining the dip setting to be used so the total
uncertainty, if Noonan wanted to use a marine sextant to determine “van Asten sunrise”, would
be 10' or 11' which is worse than just using the bubble sextant alone.
I also pointed out to Mr. van Asten:
“She did not report being at 1000 feet until 1912 Z, 78 minutes after you believed that they were
observing sunrise at 1000 feet as part of their “must be on you” transmission when they believed
that they were already at Howland. They would have traveled approximately 170 nm in that time
interval. There is no reason to assume that they descended from their cruising altitude as soon as
you believe. Flying higher provided better fuel economy and better opportunities for celestial
observations. Clouds are often in layers at different altitudes. So, for example, if there was a
scattered layer at 15,000 feet and a broken layer at 8,000 feet then flying at 10,000 feet would
provide very good observation conditions with only a small part of the heavens obstructed.
Flying below 8,000 feet would produce possibly complete obstructions to observations as the two
layers (each having large openings) could overlap.”
Mr. van Asten wrote back:
“2. Besides mentions in biographies , why would Noonan have the plane going down to 1,000 ft ,
an unfavorable altitude for seeing a small island , if it was not necessary to have the horizon
sharply within visual range ?”
-To which I responded:
“Most people believe that they were down at 1000 feet when they thought they were near the
island and at that point (and not before) they had been compelled to descend below a low cloud
layer in order to search for Howland. “
(to be continued)
gl
