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Author Topic: Navigating the LOP with the offset method.  (Read 202615 times)

h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #165 on: June 11, 2011, 10:16:56 AM »

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´.8) 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.

--------------------------------------

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.J
PG?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-1888

and

https://sites.google.com/site/fredienoonan/resources/american-practical-naigator-h-o-9-1914

These 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




Is any document available  on low cloud area westward of Howland ?
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #166 on: June 11, 2011, 10:24:26 AM »

The bubble sextant measures the angle between
  • A line between your eye and the observed object, and
  • The horizontal plane, as measured by what is essentially a very precise refinement of a carpenter's level.
In this case, ascending or descending doesn't change anything, so your altitude doesn't need to be taken into consideration, except for the special case when the observed object is very close to the horizon and subject to atmospheric refraction.

I'll take your word for this that this works.

The fact that the altitude of the observer makes no difference in the calculation of the LOP derived from an observation must be due to the inability of the instrument to detect the tiny difference in altitude compared to the vast distance from the celestial object.  It must be a difference that makes no difference.  If, instead of measuring the eye angle from the observer to a stars we were measuring the eye angle from the observers to a weather balloon, the difference in altitude between the observers would make a difference in the angles measured--wouldn't it?

To put it the other way around, looking at the situation from the standpoint of the star being observed, the two different observers are, for all practical purposes, at the same altitude (?).


The horizon for a bubble sextant is the celestial horizon which is parallel to the ´equator´of the observer since the extension of the equator and the celestial horizon point to infinity .
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #167 on: June 11, 2011, 02:21:31 PM »

... 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.  ...

Does the Pioneer bubble sextant obviate the need to know one's altitude when drawing a LOP based on an observation?

Or does the potential error introduced by not being able to calibrate their altimeter to a local barometric reference affect both kinds of instruments equally?

Altitude is of no importance for any artificial horizon sextant since the bubble is in line with the celestial horizon which is parallel with the observer´s "equator" , both pointing to infinity.

Altimeter and b-sextant have no interconnection in the given sense . If no QNH is available and the altimeter off scale , the possibility to assess low altitude remains by consulting the table for dip in H.O.208 , giving 00-31´ for 1,000 ft. If you turn up a mariner´s sextant to 31´ and you see the optical horizon in the reference line , you are @ 1,000 ft altitude.
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #168 on: June 11, 2011, 03:01:23 PM »

Mr. Lapook ,

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 forgot to say that the accuracy of marine sextant sights was determined for observations taken on shipboard where the height of eye above sea level was measured so there was no uncertainty in the dip correction to be use. There is no reason to believe that an in-flight marine sextant observation would be  more accurate than a shipboard observation and would probably be less accurate but there are no statistics on that BECAUSE NO ONE USES A MARINE SEXTANT IN FLIGHT!

gl

Chichester , and a variety of ocean pilots used marine sextants to establish A/c´s position w.r.t. lines of position in the One Line Approach operation , they all were succesful in finding their destiination this way , there is no record of any miscarriage by using the method. Hegenburger/Maitland (on a completely precomputed navigation plan to Hawaii) even carried a single telescope to be able observing objects of which elevation was of no importance , p.e. for sunset/sunrise not any instrument besides the unarmed eye and facultatively a green filter is needed , since only the point of time @ U.L. appearance is of importance , to match it with the running list figures for latitude/longitude. If p.e. mr. Noonan used the mariner´s sextant (for it´s green filter) or not , that has zero influence on the error he possibly/probably committed by not using the bubble sextant like @ sunset . The only second condition for observing sunrise from an A/c is : fly low to avoid seeing the sun earlier than @ sea level which is the lower reference for elevation of heavenly bodies. It is for these reasons of no use to bring yes or no marine sextants in the field of discussion , for any navtable or navformula if computed elevation is zero .
 .
 
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #169 on: June 11, 2011, 03:13:19 PM »

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´.8) 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.

--------------------------------------

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.J
PG?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-1888

and

https://sites.google.com/site/fredienoonan/resources/american-practical-naigator-h-o-9-1914

These 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



When mr. A Einstein heard a journalist comment : "Sir , hundreds of people can deliver proof that your theory is conflicting" , he replied : "If so , one would had been enough" .
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Chris Owens

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Re: Navigating the LOP with the offset method.
« Reply #170 on: June 11, 2011, 03:46:37 PM »


If, instead of measuring the eye angle from the observer to a stars we were measuring the eye angle from the observers to a weather balloon, the difference in altitude between the observers would make a difference in the angles measured--wouldn't it?

Yes... consider the extreme case where, to the observer on the ground, the weather balloon is directly overhead (altitude of 90 degrees); to an observer at the same altitude as the weather balloon, the balloon would be at an altitude of zero.

Quote
To put it the other way around, looking at the situation from the standpoint of the star being observed, the two different observers are, for all practical purposes, at the same altitude (?).

Yes.  the star is, for all practical purposes in celestial navigation,  infinitely far away.
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #171 on: June 11, 2011, 10:48:09 PM »

... he has his own idea
of what “sunset” is that doesn’t comport with anybody else’s understanding of that word! ...

Basically, this weird idea of what sunset or sunrise is, (which is different than everybody else’s
and is not found in any dictionary or navigation manual) leads to all of Mr. van Asten’s theories,
methods and conclusions.

I actually understand his theories and methodology and even his complex computations ...


Thanks for clarifying the nature of the argument.  Much appreciated!

Quote
We will start with his idea that Noonan measured the point of “van Asten sunrise” with a marine
sextant and not with his bubble sextant. This is critical to his theory since he blames Noonan for
using the wrong technique with the marine sextant and that the error (that he believes led to the
loss) would not have occurred if Noonan had used his bubble sextant tor the “van Asten sunrise”
observation.

Thanks for untangling that.

Quote
If there was no marine sextant on board
then no way to make this error.

Even if there was a marine sextant on board (with or without the bubble modification used on many Brandis instruments), there is no reason to think that Fred would have chosen to use it rather than the Pioneer instrument that was designed for use in aerial navigation.

Oh, reading further along, I see that we are already in agreement on that score:

Quote
... There is no reason to believe that Noonan would have used a marine
sextant (even if he had one available) for taking any observations from the Electra. Noonan said
himself, that even though a marine sextant had been carried in the Pan Am Clipper as a
“preventer” (a backup), that all observations had been made with the Pioneer bubble sextant.

Van Asten's bottom line appears in Figure 6 of "Where to Search for the Earhart Lockheed Electra."  Using his system, he calculates that the plane came down in an area roughly 85 miles NNW of Howland Island--the area immediately searched by the Itasca on 2 July 1937.  I'm not sure how close this is to Elgen Long's calculations or whether the two Nauticos searches have covered that area.

I do not know about Nauticos searches , Waitt discoveries searched along E.Long´s ´circles of uncertainty´ , southwards of 1 deg 49 - N . That the area would have been visited by Itasca confirms nothing : there have been numerous aircraft on sea accidents without trace.

On your remark abt. E.Long : remarkably and fully independent of each other , supposed that mr.Long could not have read my contribution on fuel supplies & management of 1996 in the magazine of R.Neth.A.F. museum , Soesterberg , we register the 1845 GMT fuel reserves @ 45 US . In his book published after 1996 , Long gives just the figure ,no calculation .
In the course of 2008 mr.D.Jourdan handed over to mr.Long a copy of my EJN-2008 article . On receiving it he replied that , after thirty years research on the subject , he could no more afford the time and energy for studying other vistas .
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #172 on: June 12, 2011, 06:35:42 AM »

Mr.Lapook ,

You write " We will start with his idea that Noonan measured the point of "van Asten sunrise" with a marine sextant .."  mr.Noonan´s  assumed observation error did not occur due to using the mariner´s sextant , but on the contrary : it occurred by not using the bubble sextant like @ sunset. At best the m-sextant delivered an easy means of establishing A/c´s exact altitude above ocean´s surface (via the dip table of H.O.no.208) , whereas also the dark green filter was a feature . Sunrise point of time could be established by observing with the unarmed eye (but : see filter) , with a telescope , binoculars , etc. since sunrise time is not a measurement , it is an observation only to match time with the preomputed running fix graph , or time-position group listing . Also the short period between  071930 GMT sunset & the 0720 position report delivers proof that a running fix table , or graph , had been precomputed.

The possibly only direct irrelevancy of the navigation model is that on the error-offset lane the sun´s altitude (16 deg) @ the erroneous turn-off-point differed considerably from the elevation (21 deg) @ the correct t-o-point , normally Noonan would have seen this . I can evade the complication (1) since when steering on the offset course the sun was below elevation (04--21) for reliable corrected sextant altitude , up to about halfway and (2) by estimating the 102 mls offset having been flown on D.R. , this last by preference . But it remains the more or less a flaw on the step of internal inconsistency . With the correct offset initial point the elevation difference was negligible (04-26 vs 04-21) for low sun given.

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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #173 on: June 12, 2011, 05:11:42 PM »

... 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.  ...

Does the Pioneer bubble sextant obviate the need to know one's altitude when drawing a LOP based on an observation?

Or does the potential error introduced by not being able to calibrate their altimeter to a local barometric reference affect both kinds of instruments equally?





Altitude is of no importance for any artificial horizon sextant since the bubble is in line with the celestial horizon which is parallel with the observer´s "equator" , both pointing to infinity.

Altimeter and b-sextant have no interconnection in the given sense . If no QNH is available and the altimeter off scale , the possibility to assess low altitude remains by consulting the table for dip in H.O.208 , giving 00-31´ for 1,000 ft. If you turn up a mariner´s sextant to 31´ and you see the optical horizon in the reference line , you are @ 1,000 ft altitude.
--------------------------------------------------

It only works if you already know your altitude accurately. If you set your marine sextant to 31' and you are not actually at 1,000 feet then the sextant will define a false horizontal and all of your reading will be wrong. You have come up with a circular argument. If you measured the angle between the visible horizon and the "optical horizon" (that's a new term that you just came up with, I take it you meant the true horizontal) and the measurement was 31' you're right, you would be at 1,000. The problem is there is no reference out in the air somewhere showing where the true horizontal is so there is no way to make this measurement.

See the dip table at: https://sites.google.com/site/fredienoonan/resources/air-almanc-1982/AirAlmanac1982%2Cdiptable.jpg?attredirects=0

and you will see that if your true altitude is just 33 feet different from 1,000 feet then your horizontal will be off by 1'. If off by 500 feet then your horizontal will be off by 8'.

gl

« Last Edit: June 12, 2011, 06:49:23 PM by Gary LaPook »
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #174 on: June 12, 2011, 05:33:21 PM »

Mr. Lapook ,

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 forgot to say that the accuracy of marine sextant sights was determined for observations taken on shipboard where the height of eye above sea level was measured so there was no uncertainty in the dip correction to be use. There is no reason to believe that an in-flight marine sextant observation would be  more accurate than a shipboard observation and would probably be less accurate but there are no statistics on that BECAUSE NO ONE USES A MARINE SEXTANT IN FLIGHT!

gl

Chichester , and a variety of ocean pilots used marine sextants to establish A/c´s position w.r.t. lines of position in the One Line Approach operation , they all were succesful in finding their destiination this way , there is no record of any miscarriage by using the method. Hegenburger/Maitland (on a completely precomputed navigation plan to Hawaii) even carried a single telescope to be able observing objects of which elevation was of no importance , p.e. for sunset/sunrise not any instrument besides the unarmed eye and facultatively a green filter is needed , since only the point of time @ U.L. appearance is of importance , to match it with the running list figures for latitude/longitude. If p.e. mr. Noonan used the mariner´s sextant (for it´s green filter) or not , that has zero influence on the error he possibly/probably committed by not using the bubble sextant like @ sunset . The only second condition for observing sunrise from an A/c is : fly low to avoid seeing the sun earlier than @ sea level which is the lower reference for elevation of heavenly bodies. It is for these reasons of no use to bring yes or no marine sextants in the field of discussion , for any navtable or navformula if computed elevation is zero .
 .
  


------------------------------------------------


Chichester, Coutinho and several other early pioneering aviators did use marine sextant but this was only because bubble sextants had not yet been perfected. During the 1910's and 1920' rapid progress was made in improving and perfecting bubble sextants, with many false paths until it all came together, the right lenses and, most importantly, the right curvature to the top of the bubble chamber.

You can read about these developments here: http://www.fer3.com/arc/imgx/Bubble-sextants-Precision-Astrolabe.pdf

By the early 1930's the bubble sextant had been perfected so no one used a marine sextant after that to take observations from airplanes.

I sent this to him before:

"It is interesting that you list some early aviators implying that they used your sunrise method, do
you have any sources for this claim? Ellsworth used a bubble sextant, Lindbergh used a Pioneer
bubble sextant (there is a photo of his navigation equipment in Weems, 1938). They all used the standard Line Of Position computation, not your "van Asten sunrise" method.  I have analyzed
Chichester’s navigation extensively and he used a marine sextant to take five sextant
observations on the New Zealand to Norfolk Island flight in 1931, all were in the range of 23° 12' to 50°
50'. On the next leg to Lord Howe Island he also took five observations, all in the range of 23° 48'
to 53° 42'.  So contrary to your claim, none of his observations were anywhere near a zero altitude
or a sunrise sight. "


Coutinho in 1922 took 40 observations with a mariner's sextant but the lowest altitude he measured was 16° 15', nowhere near the "van Asten horizon."

Mr van Asten also mentioned that these early aviators precomputed their sights and although that may be true what they precomputed were the normal "computed altitudes" used for the normal Line Of Position navigation method, not for the "van Austen sunset/sunrise" method. It appears that Mr. van Austen doesn't understand how these precomputations were done. Here is link to many flight navigation manuals that explain this procedure and he might get some value from reading them.

https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves

I have asked Mr. van Austen repeatedly to produce any proof that he might have that anybody ever used his method and he has never produced a thing.

gl
« Last Edit: June 12, 2011, 05:56:38 PM by Martin X. Moleski, SJ »
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #175 on: June 12, 2011, 05:39:18 PM »

Mr van Asten also mentioned that these early aviators precomputed their sights and although that may be true what they precomputed were the normal "computed altitudes" used for the normal Line Of Position navigation method, not for the "van Austen sunset/sunrise" method. It appears that Mr. van Austen doesn't understand how these precomputations were done. Here is link to many flight navigation manuals that explain this procedure and he might get some value from reading them.

https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves

--------------------------------------------------------------

Here is a link to a recent example of precomputation :

http://www.fer3.com/arc/m2.aspx?i=116311&y=201104

gl
« Last Edit: June 12, 2011, 06:52:01 PM by Gary LaPook »
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #176 on: June 12, 2011, 05:45:17 PM »

Chichester , and a variety of ocean pilots used marine sextants to establish A/c´s position w.r.t. lines of position in the One Line Approach operation , they all were succesful in finding their destiination this way , there is no record of any miscarriage by using the method. Hegenburger/Maitland (on a completely precomputed navigation plan to Hawaii) even carried a single telescope to be able observing objects of which elevation was of no importance , p.e. for sunset/sunrise not any instrument besides the unarmed eye and facultatively a green filter is needed , since only the point of time @ U.L. appearance is of importance , to match it with the running list figures for latitude/longitude. If p.e. mr. Noonan used the mariner´s sextant (for it´s green filter) or not , that has zero influence on the error he possibly/probably committed by not using the bubble sextant like @ sunset . The only second condition for observing sunrise from an A/c is : fly low to avoid seeing the sun earlier than @ sea level which is the lower reference for elevation of heavenly bodies. It is for these reasons of no use to bring yes or no marine sextants in the field of discussion , for any navtable or navformula if computed elevation is zero .

Mr. van Asten,

It would be an error to use the marine sextant only if he had computed data for use with a bubble sextant and then only if he were using the "van Asten sunset/sunrise" method which you have never produced any proof whatsoever that it was ever used by anybody, and this includes you, since you have never used it either.

gl
« Last Edit: June 12, 2011, 06:53:20 PM by Gary LaPook »
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #177 on: June 12, 2011, 06:24:15 PM »

Mr.Lapook ,

You write " We will start with his idea that Noonan measured the point of "van Asten sunrise" with a marine sextant .."  mr.Noonan´s  assumed observation error did not occur due to using the mariner´s sextant , but on the contrary : it occurred by not using the bubble sextant like @ sunset. At best the m-sextant delivered an easy means of establishing A/c´s exact altitude above ocean´s surface (via the dip table of H.O.no.208) , whereas also the dark green filter was a feature . Sunrise point of time could be established by observing with the unarmed eye (but : see filter) , with a telescope , binoculars , etc. since sunrise time is not a measurement , it is an observation only to match time with the preomputed running fix graph , or time-position group listing . Also the short period between  071930 GMT sunset & the 0720 position report delivers proof that a running fix table , or graph , had been precomputed.

The possibly only direct irrelevancy of the navigation model is that on the error-offset lane the sun´s altitude (16 deg) @ the erroneous turn-off-point differed considerably from the elevation (21 deg) @ the correct t-o-point , normally Noonan would have seen this . I can evade the complication (1) since when steering on the offset course the sun was below elevation (04--21) for reliable corrected sextant altitude , up to about halfway and (2) by estimating the 102 mls offset having been flown on D.R. , this last by preference . But it remains the more or less a flaw on the step of internal inconsistency . With the correct offset initial point the elevation difference was negligible (04-26 vs 04-21) for low sun given.



---------------------------------

Yep, that is a pretty amazing performance by Noonan and Earhart. Since he took the sextant reading (according to van Austen) at 07:19:30 GMT and the message was received at Lae at 07:20:00 GMT. This means that in only 30 seconds Noonan read the sextant, compared his reading with his precomputed table, wrote the position on a piece of paper, stuck that paper on the end of a fishing pole, slid the pole across the fuel tanks to the cockpit, Earhart removed the note from the fishing pole, read the message, picked up the microphone and sent that message! I wonder how many times they had to practice those maneuvers in order to get their time down to only 30 seconds. But wait, in keeping with Mr. van Austen's level of precision in his computations, we must allow for the time it took for the radio signals to travel all the way to Lae. From that position is was 1,384,820 meters to Lae and radio waves travel only at the speed of light, 299,792,458 meters per second so it took 0.00461962 seconds for the message to get to Lae, so Earhart must have started transmitting at 7:19:59.995380738 GMT. This means that all these action had to have been completed in less than 30 seconds, in only 29.995380738 seconds. I am really impressed now.

Of course, what makes this performance even more amazing is that the message was received in Lae at 0718 GMT, a minute and half before Noonan took the sextant reading (according to Mr. van Austens's theory) so the radio signals must have traveled faster than the speed of light and traveled back in time by one and a half minutes. See the Chatter report.

Basically, this proves that Mr. van Austen was wrong about his "sunset running fix" in his published paper and his theory relies on this "sunset running  fix" for proof that Noonan was attempting a "sunrise fix" the next morning. He also relies on the distance traveled from this earlier "sunset running fix" as a basis for the "sunrise fix". Neither of these fixes were precomputed or measured by Noonan.

gl
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #178 on: June 12, 2011, 06:29:07 PM »

... he has his own idea
of what “sunset” is that doesn’t comport with anybody else’s understanding of that word! ...

On your remark abt. E.Long : remarkably and fully independent of each other , supposed that mr.Long could not have read my contribution on fuel supplies & management of 1996 in the magazine of R.Neth.A.F. museum , Soesterberg , we register the 1845 GMT fuel reserves @ 45 US . In his book published after 1996 , Long gives just the figure ,no calculation .
In the course of 2008 mr.D.Jourdan handed over to mr.Long a copy of my EJN-2008 article . On receiving it he replied that , after thirty years research on the subject , he could no more afford the time and energy for studying other vistas .

I hate to admit that Elgin Long is smarter than I am but he was smart enough to ignore Mr. van Austen and his weird theories and did not waste a lot of his time, as I have, in responding to Mr. van Austen.

gl
« Last Edit: June 12, 2011, 06:43:59 PM by Martin X. Moleski, SJ »
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #179 on: June 12, 2011, 06:33:59 PM »

... The only second condition for observing sunrise from an A/c is : fly low to avoid seeing the sun earlier than @ sea level which is the lower reference for elevation of heavenly bodies.

The only way to fly low enough to "to avoid seeing the sun earlier than @ sea level" is to be in a submarine, since you would have to be below sea level.

gl
« Last Edit: June 12, 2011, 06:56:51 PM by Gary LaPook »
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