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Author Topic: Navigating the LOP with the offset method.  (Read 175856 times)

Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #120 on: June 05, 2011, 06:05:00 PM »

Mr.Campbell ,

By the sunset fix you can see that Noonan precompted for checking position by celnav which was normal operating practice. For sunrise , due the on first leg delay , Noonan had to recompute en route since sunrise o/b would originally have occurred at the Turn Off Point before going inbound for Howland. If having gone astray , Itasca would have been long before 1912 GMT be warned by radio , but on the contrary : before 1912 GMT there was not any sign of distress. That holds Noonan precisely knowing where he was when commencing the approach procedure. Do we have any indication about this statement in terms of air navigation ? Yes we have : without exact initial calibration of latitude , the sunrise point of time having been precomputed , we know that the precise LHA of sun was 90-03-50 , computed by H.O.208 , Tab. II by navigator himself. @ 175453 GMT sunrise time the GHA of sun was  [(175453) x 15] - 180 deg = 88-43-15. Thence, @ observed sunrise the longitude was :  88-43-15-W + 90-03-50-W = 178-47-05-W. The latitude was already contained in the precomputation by homework. Whatever pre-sunrise track was flown , great circle , rhumb line , any other initial point , From sunrise Noonan knew exactly where he was , given some decline from observation error. I do btw not comment for "make point" , if a computation is good you can safely follow I.Newton : Non fingo hypothesis.

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

This is for you guys that may have been following this discussion and scratching your heads about what is going on. This post by Mr. van Austen provides the opportunity to show that his methodology is wrong by demonstrating a basic error that anybody should be able to understand.

Basic to all computations for celestial navigation is knowing the position of the body being observed, in this case the sun. Celestial positions are specified like locations on earth. On earth the position north and south of the equator is called latitude and the location east and west of the Greenwich Meridian is called longitude. For celestial bodies, the position north and south of the equator is called declination and the position west of the Greenwich Meridian is called Greenwich Hour Angle (GHA.) Since the earth turns, the GHA of the sun increases at the rate of fifteen degrees every hour, one degree every four minutes and one minute of GHA every four seconds. This is why accurate time is so important because if your chronometer is wrong by just four seconds you will take out a value for GHA from the Nautical Almanac that is wrong by one minute of longitude which will make the derived position in error by one nautical mile.

In his post, Mr. van Asten states that at 17:54:53 GMT the GHA of the sun was  88-43-15 (88 degrees 43 minutes and 15 seconds. This is the same as 88° 43.2', rounded to the nearest 0.1'.) We don't have to take his word for it since it is easy for us to figure it out for ourselves by using the nautical almanac.

Look at the 1937 Nautical Almanac for July 2nd, available here: https://sites.google.com/site/fredienoonan/resources/air-almanac-2009/sun-s-gha

Take out the value of the Sun's GHA for 1800 GMT (the closest tabulated value to Mr. van Asten's time of 17:54:53) which is 89° 02.5'. Since this is the location of the Sun 5 minutes and 7 seconds after Mr. van Asten's time, we must make a correction for this difference. To do this we go to the Interpolation for the GHA of the Sun table available at the same site. Enter this table for the time difference of 5 minutes and 7 seconds and take out the amount the Sun moved in that time period which is 1° 16.8' of GHA. Since we are interested in finding the Sun's GHA for an earlier period, we must subtract this correction from the 1800 GMT tabulated value and find the GHA of the Sun, as tabulated in the 1937 Nautical Almanac (the almanac carried by Noonan), for 17:54:53 GMT was 87° 45.7'. Comparing this to Mr. van Asten's value of 88° 43.2'  shows his in in error by 0° 57.5' equivalent to a 57.5 nautical mile error.

Check the math yourself:

GHA sun @  1800 GMT =     89° 02.5'

Adjustment for 5:07      = -  1° 16.8'

GHA at 175453 GMT =        87° 45.7'

then:

van Asten's  GHA =              88° 43.2'

Minus the correct GHA sun  - 87° 45.7'

Deference              =            0° 57.5'   

This would also produce an error in the time of sunrise of 3 minutes and 50 seconds which we can also see by using the interpolation table to find the time interval that would produce the difference in GHA of 0° 57.5' .

Is that simple enough?

gl
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #121 on: June 05, 2011, 07:54:44 PM »

Mr.Campbell ,

By the sunset fix you can see that Noonan precompted for checking position by celnav which was normal operating practice. For sunrise , due the on first leg delay , Noonan had to recompute en route since sunrise o/b would originally have occurred at the Turn Off Point before going inbound for Howland. If having gone astray , Itasca would have been long before 1912 GMT be warned by radio , but on the contrary : before 1912 GMT there was not any sign of distress. That holds Noonan precisely knowing where he was when commencing the approach procedure. Do we have any indication about this statement in terms of air navigation ? Yes we have : without exact initial calibration of latitude , the sunrise point of time having been precomputed , we know that the precise LHA of sun was 90-03-50 , computed by H.O.208 , Tab. II by navigator himself. @ 175453 GMT sunrise time the GHA of sun was  [(175453) x 15] - 180 deg = 88-43-15. Thence, @ observed sunrise the longitude was :  88-43-15-W + 90-03-50-W = 178-47-05-W. The latitude was already contained in the precomputation by homework. Whatever pre-sunrise track was flown , great circle , rhumb line , any other initial point , From sunrise Noonan knew exactly where he was , given some decline from observation error. I do btw not comment for "make point" , if a computation is good you can safely follow I.Newton : Non fingo hypothesis.

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

This is for you guys that may have been following this discussion and scratching your heads about what is going on. This post by Mr. van Austen provides the opportunity to show that his methodology is wrong by demonstrating a basic error that anybody should be able to understand.

Basic to all computations for celestial navigation is knowing the position of the body being observed, in this case the sun. Celestial positions are specified like locations on earth. On earth the position north and south of the equator is called latitude and the location east and west of the Greenwich Meridian is called longitude. For celestial bodies, the position north and south of the equator is called declination and the position west of the Greenwich Meridian is called Greenwich Hour Angle (GHA.) Since the earth turns, the GHA of the sun increases at the rate of fifteen degrees every hour, one degree every four minutes and one minute of GHA every four seconds. This is why accurate time is so important because if your chronometer is wrong by just four seconds you will take out a value for GHA from the Nautical Almanac that is wrong by one minute of longitude which will make the derived position in error by one nautical mile.

In his post, Mr. van Asten states that at 17:54:53 GMT the GHA of the sun was  88-43-15 (88 degrees 43 minutes and 15 seconds. This is the same as 88° 43.2', rounded to the nearest 0.1'.) We don't have to take his word for it since it is easy for us to figure it out for ourselves by using the nautical almanac.

Look at the 1937 Nautical Almanac for July 2nd, available here: https://sites.google.com/site/fredienoonan/resources/air-almanac-2009/sun-s-gha

Take out the value of the Sun's GHA for 1800 GMT (the closest tabulated value to Mr. van Asten's time of 17:54:53) which is 89° 02.5'. Since this is the location of the Sun 5 minutes and 7 seconds after Mr. van Asten's time, we must make a correction for this difference. To do this we go to the Interpolation for the GHA of the Sun table available at the same site. Enter this table for the time difference of 5 minutes and 7 seconds and take out the amount the Sun moved in that time period which is 1° 16.8' of GHA. Since we are interested in finding the Sun's GHA for an earlier period, we must subtract this correction from the 1800 GMT tabulated value and find the GHA of the Sun, as tabulated in the 1937 Nautical Almanac (the almanac carried by Noonan), for 17:54:53 GMT was 87° 45.7'. Comparing this to Mr. van Asten's value of 88° 43.2'  shows his in in error by 0° 57.5' equivalent to a 57.5 nautical mile error.

Check the math yourself:

GHA sun @  1800 GMT =     89° 02.5'

Adjustment for 5:07      = -  1° 16.8'

GHA at 175453 GMT =        87° 45.7'

then:

van Asten's  GHA =              88° 43.2'

Minus the correct GHA sun  - 87° 45.7'

Deference              =            0° 57.5'   

This would also produce an error in the time of sunrise of 3 minutes and 50 seconds which we can also see by using the interpolation table to find the time interval that would produce the difference in GHA of 0° 57.5' .

Is that simple enough?

gl

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

GHA sun @  1800 GMT =     89° 02.5'

Adjustment for 5:07      = -  1° 16.8'

GHA at 175453 GMT =        87° 45.7'


BTW, this is exactly the way that Noonan would calculate the GHA of the Sun for his celestial navigation so you can see there is nothing mysterious or complicated about it, it ain't rocket science.

gl
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #122 on: June 05, 2011, 11:37:29 PM »

G.Lpk  No , this is not simple enough , on July 2 , 1937 , between 1700-1800 GMT two phenomena had equal values : the equation of time and the sun´s rising velocity per minute of time ,both amounting to 3m50s , or 00-57´-30" difference of LHA . If figures are not used in the correct sequence (first 3m50s rising sun , from 53´/13´.8 , then 3m50s equation) , the result is the 57´30" difference you notify . Start again with diagram 3 , p.27 of EJN-2008.
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #123 on: June 06, 2011, 12:01:46 AM »

G.Lpk . 57´30" . The error you make is that  @   sunset the LHA is for the true sun´s centre in the horizon (bubble) , the sunrise LHA is for sun´s U.L. in the horizon (marine).
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #124 on: June 06, 2011, 01:36:29 AM »

G.Lpk  No , this is not simple enough , on July 2 , 1937 , between 1700-1800 GMT two phenomena had equal values : the equation of time and the sun´s rising velocity per minute of time ,both amounting to 3m50s , or 00-57´-30" difference of LHA . If figures are not used in the correct sequence (first 3m50s rising sun , from 53´/13´.8 , then 3m50s equation) , the result is the 57´30" difference you notify . Start again with diagram 3 , p.27 of EJN-2008.

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

Mr van Asten, it appears that you are you claiming that the GHA data for the Sun listed in the 1937 Nautical Almanac is wrong so you must be smarter than the people at the U.S. Naval Observatory!
gl
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #125 on: June 06, 2011, 01:46:15 AM »

G.Lpk  No , this is not simple enough , on July 2 , 1937 , between 1700-1800 GMT two phenomena had equal values : the equation of time and the sun´s rising velocity per minute of time ,both amounting to 3m50s , or 00-57´-30" difference of LHA . If figures are not used in the correct sequence (first 3m50s rising sun , from 53´/13´.8 , then 3m50s equation) , the result is the 57´30" difference you notify . Start again with diagram 3 , p.27 of EJN-2008.

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

Mr van Asten, it appears that you are you claiming that the GHA data for the Sun listed in the 1937 Nautical Almanac is wrong so you must be smarter than the people at the U.S. Naval Observatory!
gl

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

You wrote:
"175453 GMT sunrise time the GHA of sun was  [(175453) x 15] - 180 deg = 88-43-15. " (88° 43.2')

The GHA from the Nautical Almanac for the same time is 87° 45.7. These are two different numbers, they can't both be right. You claim you are right so you are claiming that the Nautical Almanac is wrong.

gl
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #126 on: June 06, 2011, 05:53:42 AM »

G.Lpk. 88-43-15 vs 87-45-40 LHA . The 88-43-15 LHA is for 175453 GMT centre of true sun in the horizon as seen by bubble sextant ; at this same point of time , U.L.of visible sun is in the horizon , with centre altitude minus 53´ . At 175453 GMT , observing by marine sextant , you actually look at the sun for 175103 GMT , centre 53´below. When sun´s centre comes in the horizon consequently , the mean sun has traveled to 175453 GMT + 3m50s = 175843 GMT . So , if you observe by marine instead of bubble you see the sun come up 175853 - 175453 = 3m50s too early , and you go 3m50s too early on the offset course. That is (in one session) the mechanism of the probable observation error commited.

The typical (air) navigator´s short method to obtain sunrise time after having fixed position @ sunset Is : (round arcseconds)

178-47  -  159-07  df lon     due E      22-06
LHA             @   sunset  /  centre      88-03
LHA             @   visible sun    U.L.     90-04
                                                    _____

                                                  200-13
subract from                                 360-00

                                                  ______

Travel of true sun @ flight               157-47

Divide by 15 deg / hr                   10h39m08s

Add to                                      07h15m45s
                                               _________


GMT of sunrise U.L. 150 off Hwl     17h54m53s

                                               ========

Thereof : A/c´s speed was  1326´ =  1,528.7  mls  @  10h39m08s  = 143.5 mph due eastward between sunset / sunrise coordinates. If A/c´s great circle due east speed declines from this figure , other tracking than via great circle was taken.





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Chris Owens

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Re: Navigating the LOP with the offset method.
« Reply #127 on: June 06, 2011, 10:27:05 AM »

H. A. C. van Asten, I'm having an awfully hard time following the thread here. Could you give a summary of the position that you are trying to support (or to refute,)  and what the evidence is that you are bringing forth in support of (or in refutation of) that position?   I'm completely lost in the weeds here.
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Irvine John Donald

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Re: Navigating the LOP with the offset method.
« Reply #128 on: June 06, 2011, 10:47:24 AM »

To Chris

The one absolutely clear thing I'm reading in this threataos that if you really are in the weeds Chris then you need a weed whacker before you can get that sextant to work! :D
Respectfully Submitted;

Irv
 
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #129 on: June 06, 2011, 10:58:04 AM »

G.Lpk. 88-43-15 vs 87-45-40 LHA . The 88-43-15 LHA is for 175453 GMT centre of true[/i] sun in the horizon as seen by bubble sextant ; at this same point of time , U.L.of visible sun is in the horizon , with centre altitude minus 53´ . At 175453 GMT , observing by marine sextant , you actually look at the sun for 175103 GMT , centre 53´below. When sun´s centre comes in the horizon consequently , the mean sun has traveled to 175453 GMT + 3m50s = 175843 GMT . So , if you observe by marine instead of bubble you see the sun come up 175853 - 175453 = 3m50s too early , and you go 3m50s too early on the offset course. That is (in one session) the mechanism of the probable observation error commited.

The typical (air) navigator´s short method to obtain sunrise time after having fixed position @ sunset Is : (round arcseconds)

178-47  -  159-07  df lon     due E      22-06
LHA             @   sunset  /  centre      88-03
LHA             @   visible sun    U.L.     90-04
                                                    _____

                                                  200-13
subract from                                 360-00

                                                  ______

Travel of true sun @ flight               157-47

Divide by 15 deg / hr                   10h39m08s

Add to                                      07h15m45s
                                               _________


GMT of sunrise U.L. 150 off Hwl     17h54m53s

                                               ========

Thereof : A/c´s speed was  1326´ =  1,528.7  mls  @  10h39m08s  = 143.5 mph due eastward between sunset / sunrise coordinates. If A/c´s great circle due east speed declines from this figure , other tracking than via great circle was taken.







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

Mr. van Asten, you wrote:

"G.Lpk. 88-43-15 vs 87-45-40 LHA . The 88-43-15 LHA is for 175453 GMT "

Are you are now claiming that the GHAs (Greenwich Hour Angles) that don't agree are actually LHAs (Local Hour Angles) which is an entirely different thing and, again, your computation of what the LHAs were is obviously in error.

gl

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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #130 on: June 06, 2011, 11:13:01 AM »

G.Lpk. 88-43-15 vs 87-45-40 LHA . The 88-43-15 LHA is for 175453 GMT centre of true sun in the horizon as seen by bubble sextant ; at this same point of time , U.L.of visible sun is in the horizon , with centre altitude minus 53´ . At 175453 GMT , observing by marine sextant , you actually look at the sun for 175103 GMT , centre 53´below. When sun´s centre comes in the horizon consequently , the mean sun has traveled to 175453 GMT + 3m50s = 175843 GMT . So , if you observe by marine instead of bubble you see the sun come up 175853 - 175453 = 3m50s too early , and you go 3m50s too early on the offset course. That is (in one session) the mechanism of the probable observation error commited.

The typical (air) navigator´s short method to obtain sunrise time after having fixed position @ sunset Is : (round arcseconds)

178-47  -  159-07  df lon     due E      22-06
LHA             @   sunset  /  centre      88-03
LHA             @   visible sun    U.L.     90-04
                                                    _____

                                                  200-13
subract from                                 360-00

                                                  ______

Travel of true sun @ flight               157-47

Divide by 15 deg / hr                   10h39m08s

Add to                                      07h15m45s
                                               _________


GMT of sunrise U.L. 150 off Hwl     17h54m53s

                                               ========

Thereof : A/c´s speed was  1326´ =  1,528.7  mls  @  10h39m08s  = 143.5 mph due eastward between sunset / sunrise coordinates. If A/c´s great circle due east speed declines from this figure , other tracking than via great circle was taken.







----------------------------------
Mr. van Asten,

You now show us an entirely new method (this must be the third or fourth) that you have invented for computing the time of sunrise that is different than the last method you showed to us. You now claim that this is " The typical (air) navigator´s short method (it doesn't look that short to me) to obtain sunrise time" but your original posts, and your two published articles, stated with certainty that Noonan used a much shorter method than this one to compute the time of sunrise, that of a simple interpolation in the Nautical Almanac sunrise table. So which one of all of the methods were most "typical"?  Do you have any evidence that Noonan had ever heard of any of your "typical" methods?

gl
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Monty Fowler

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Re: Navigating the LOP with the offset method.
« Reply #131 on: June 06, 2011, 11:20:06 AM »

"There are three kinds of lies - lies, damned lies, and statistics."    Benjamin Disraeli

Maybe we should amend that and add, "fun with numbers."? Just a thought.
Ex-TIGHAR member No. 2189 E C R SP, 1998-2016
 
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #132 on: June 06, 2011, 11:33:49 AM »

G.Lpk. 88-43-15 vs 87-45-40 LHA . The 88-43-15 LHA is for 175453 GMT centre of true sun in the horizon as seen by bubble sextant ; at this same point of time , U.L.of visible sun is in the horizon , with centre altitude minus 53´ . At 175453 GMT , observing by marine sextant , you actually look at the sun for 175103 GMT , centre 53´below. When sun´s centre comes in the horizon consequently , the mean sun has traveled to 175453 GMT + 3m50s = 175843 GMT . So , if you observe by marine instead of bubble you see the sun come up 175853 - 175453 = 3m50s too early , and you go 3m50s too early on the offset course. That is (in one session) the mechanism of the probable observation error commited.

The typical (air) navigator´s short method to obtain sunrise time after having fixed position @ sunset Is : (round arcsecond...



----------------------------------
Mr. van Asten,

You now show us an entirely new method (this must be the third or fourth) that you have invented for computing the time of sunrise that is different than the last method you showed to us. You now claim that this is " The typical (air) navigator´s short method (it doesn't look that short to me) to obtain sunrise time" but your original posts, and your two published articles, stated with certainty that Noonan used a much shorter method than this one to compute the time of sunrise, that of a simple interpolation in the Nautical Almanac sunrise table. So which one of all of the methods were most "typical"?  Do you have any evidence that Noonan had ever heard of any of your "typical" methods?

gl

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

Mr. van Asten,

Something I still remember from the logic course that I took way back in college is that "a contradiction is necessarily false." You stated:

"175453 GMT centre of true sun in the horizon as seen by bubble sextant ; at this same point of time , U.L.of visible sun is in the horizon..."

If the U.L (upper limb, the very top of the sun) is just appearing above the horizon, which you can see with the marine sextant (or with just the unaided eye), how can you, "at this same point of time", see the center of the sun by use of a bubble sextant? Even Superman with his x-ray vision looking through a bubble sextant could not see the center of the sun "at this same point of time" because it is below the horizon and the planet earth is in the way. This is an obvious contradiction so it must necessarily be false.

gl
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h.a.c. van asten

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Re: Navigating the LOP with the offset method.
« Reply #133 on: June 06, 2011, 01:02:16 PM »

Mr. Lapook ,

There is no contradiction at all : the time of optical sunrise U.L. is 3m50s earlier than the time of sunrise true sun central  . As a result , the observation being by marine sextant , at 175453 GCT , navigator looks at the sun for 175453 - 3m50s = 175103 apparent time , that is , the visible sun´s U.L. flashes the horizon. By the last posted calculation of sunrise from the sunset fix I demonstrated that Noonan had at his disposal a variety of simple methods to precompute phenomena he needed. Which method he actually made use of is of zero importance for consistency , it may very well have been a listing like in the N.A. , but with always identical outcomes as shown. If navigator , for the sunrise fix , had used the bubble sextant , the crew would , technically , with certainty have found the island without any other aid than celnav. The 3m50s time lag (not equation) existed for the entire 1700-1815 period  , that renders the navigation error independend of the precise position of A/c within the limits of reasonable air/groundspeed.   
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Gary LaPook

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Re: Navigating the LOP with the offset method.
« Reply #134 on: June 06, 2011, 01:38:34 PM »

Mr. Lapook ,

There is no contradiction at all : the time of optical sunrise U.L. is 3m50s earlier than the time of sunrise true sun central  . As a result , the observation being by marine sextant , at 175453 GCT , navigator looks at the sun for 175453 - 3m50s = 175103 apparent time , that is , the visible sun´s U.L. flashes the horizon. By the last posted calculation of sunrise from the sunset fix I demonstrated that Noonan had at his disposal a variety of simple methods to precompute phenomena he needed. Which method he actually made use of is of zero importance for consistency , it may very well have been a listing like in the N.A. , but with always identical outcomes as shown. If navigator , for the sunrise fix , had used the bubble sextant , the crew would , technically , with certainty have found the island without any other aid than celnav. The 3m50s time lag (not equation) existed for the entire 1700-1815 period  , that renders the navigation error independend of the precise position of A/c within the limits of reasonable air/groundspeed.   

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

You did not explain how a navigator, using a bubble sextant, can look through the earth to see the center of the sun when only the upper limb is actually above the horizon and you said these two observations are made "at this same point of time ."

gl
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