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### AuthorTopic: Navigating the LOP with the offset method.  (Read 264597 times)

#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #195 on: June 13, 2011, 07:07:31 AM »

... 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

Nonsense , if you preset 31´ and you are not @ 1,000 feet the local horizon line does not match the instrument´s horizon mirror line , and you must ascend / descend .
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#### Martin X. Moleski, SJ

• Administrator
• Posts: 3006
##### Re: Navigating the LOP with the offset method.
« Reply #196 on: June 13, 2011, 07:45:22 AM »

“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. “

I believe that the 1912 GMT transmission gives their altitude as 1000 feet.  No motive is given in the transmission for the descent.

The splendid article, "Log Jam," records this as 07:42 a.m. Itasca time.

Previous altitude reports were all from early in the flight: 7000, 10000, 8000.
LTM,

Marty
TIGHAR #2359A

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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #197 on: June 13, 2011, 11:32:11 AM »

Nonsense , if you preset 31´ and you are not @ 1,000 feet the local horizon line does not match the instrument´s horizon mirror line , and you must ascend / descend .

Except that there is no such thing as the "instrument´s horizon mirror line" so you have nothing to compare with the local horizon (the visible sea horizon.) Mr. van Asten, have you never looked through a marine sextant?

That is the purpose of the bubble in the bubble sextant, to provide a level reference independent of the sea horizon and marine sextants do not have such a reference. Find someone who has a marine sextant and take a look through it.

gl
« Last Edit: June 13, 2011, 12:16:50 PM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #198 on: June 13, 2011, 11:45:46 AM »

@ 1,000 ft , 305 m altitude the horiron dips 00-31´ whereas the sun rises @ 13´.8 per time minute . Sun will appear 31´/13´.8 = 2m15s earlier (yours 1m50s) @ 1,000 ft than @ zero ft. Subtract from 175453 GMT and find 175238 GMTthe instant mr.Noonan saw sunrise . By addition of 2m15s he knew to be 150 mls off Howland . Sea navigators were much more familiar with calculation of angles etc. since they had not from the beginning of their career the "short methods" to their disposal . You p.e. have mentioned that the paragraph on sunrise fix for aircraft has been deleted from ´Dutton´ since 1934 . For that year Noonan was 41 with a 20 years seaman´s career behind . Within that era , sea liners captains ordered
two , sometimes three navigators on deck to separately shoot sun , moon or stars , after which , below deck , they computed for 20 minutes to establish position of ship . It is in short , reasonable that mr. Noonan exactly knew what he was doing.
I consequently jump to your critics on the 0720 GMT announced position near Nukumanu . Your statement about the time point having been 0718 GMT (before GMT sunrise 071930) does not hold . The figure is from a citation of the "Chater´s report" document and concerns tranmissions Lae to Earhart for weather updates @ 18 minutes past the hour. The figure is repeated (0418 , 0519 , 0718) through the report . The figure , not from radio logbook (there was none) , does not at all represent an agreement with the Earhart crew themselves.

Third : there have been comments stating that the departure time from Lae , 0000 GMT , concerned an @ random decision etc. etc. It was not : @ 6 a.m. 7/1 Earhart to Black radiogram reads in part "PLAN LEAVE BY TEN THIS MORNING NEW GUINEA TIME" . Later @ 7/01 followed , in part : "BLACK ITASCA DUE LOCAL CONDITIONS TAKE OFF DELAYED UNTIL 2130 GMT JULY SECOND" . Eventually , 7/2 : "URGENT BLACK ITASCA AMELIA EARHART LEFT LAE TEN AM LOCAL TIME JULY 2ND DUE HOWLAND ISLAND 18 HOURS TIME" . it is at least a reasonable supposition that the crew tuned departure time to mr.Noonan´s precomputed flight data .

1. There never was a "sunrise" paragraph in any edition of Dutton, you only cited to a sentence within one paragraph that you found in the 1928 edition that recommended using a marine sextant, nothing about a "sunrise" fix and this sentence was removed from the 1934 and subsequent editions.

2. Read the Chater report again. It says the position report was received at 5:18 p.m. (0718 GMT). Nor can you claim that Chater was merely writing down the scheduled times for communications with Earhart of 18 minutes after each hour because Chater recorded the prior report from Earhart as being received at 3:19 p.m. (0319 GMT.) So contrary to your claim, the figure was NOT repeated. Nor was there any report at 0418, there are only three transmissions from Earhart recorded, 2:18 p.m., 3:19 p.m. and 5:18 p.m. (0218, 0319 and 0518 GMT.)

3. They did not take off at the time that they had planned as stated in her radiograms.

gl
« Last Edit: June 13, 2011, 02:31:03 PM by Gary LaPook »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #199 on: June 13, 2011, 12:03:50 PM »

You may safely assume that in the course of 23 years I have consulted all representative flght manuals . When commencing the 055 T offset @ 1815 for the correct longitude sun´s altitude  was 04-26 , at the end @ 1859 it was 21-00 . On the erroneous offset the respective elevations were 04-21 and 16-00 , all figures rounded to arcmin. I already mentioned by comment that the 16-00 / 21-00 difference may be a weakness of determination , also since textbooks prescriptions ask for repeated observation like you say . Because for the article I had to do the work alone (no old style navigators available , no readers) , and against deadlines , combined with the menace of  making the treatise unreadable due to too many details , I decided for the text & diagrams as published . I have worked for 20 years in the sciences during my professional career , there is not any reason for which I would venture  to " wiggle out" (as you call it) from a problem . There is namely , a possibility (not yet computed) that the offset entire track was longer than 132 mls because instead of having made good 348 mls @ 175453 GMT , only 337 mls had been made good , this has influence on the ETA time-position groups .

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

If there really was a difference between the 16 degree altitude of the sun at the erroneous interception that you claim compared to the 21 degree altitude that you calculate for the correct LOP then the difference between them, 5 degrees, would produce an error of 300 NM, pretty hard for Noonan to be that wrong! AS I posted before, the correct altitude at the turn off point onto the correct LOP was 16° 04.5' at 1859 GMT.

There is something wrong with your computations of these altitudes.

Here is link to the U.S. Naval Observatory site that will do the computations for you so you won't get the wrong answers.

http://aa.usno.navy.mil/data/docs/celnavtable.php

Readers of these posts can go to that site themselves and check Mr. van Asten's computations themselves. Just put in the date, time, and the coordinates for Howland (0° 48' N, 176° 38' W) to calculate the sun's altitude at Howland and any place along the correct LOP through Howland. Look at the column marked "Hc" which is the standard abbreviation for "computed altitude." "Zn" = azimuth and "GHA is Greenwich Hour Angle. While you are at it you can check out Mr. van Asten's calculation of GHA of the sun for 175453 GMT, just enter in that time and look at the GHA column. Mr. van Asten said in his prior posts that the GHA of the sun at that time was 88° 43.2', did he get it right? I said the GHA at 175453 GMT was  87° 45.7', did I get it right?

And no, I do not assume that you have  consulted all representative flght manuals since you have failed to cite to any of them in your posts or in our other correspondence.

gl
« Last Edit: June 13, 2011, 10:50:48 PM by Gary LaPook »
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#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #200 on: June 13, 2011, 01:25:31 PM »

Never produced a thing ?  Read EJN-2011 for mr.Noonan´s own sunset fix with same fashion as for sunrise.

Well, since we do not have Mr. Noonan"s work papers, we have only your theoretical computations of them, how about producing at least one other example of anybody other than Noonan using your "sunrise/sunset" methodology or a cite to a navigation text describing your method?

gl

I will in due time find such back in my handbooks/textbooks .
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#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #201 on: June 13, 2011, 01:37:14 PM »

And no, I do not assume that you have  consulted all representative flght manual[/b][/i]s since you have failed to cite to any of them in your posts or in our other correspondence.

No , I just do not remember where I found the fashion , like I told you I am not at home now and must postpone consulting the books. I will recompute the altitudes , the coordinates are : correct turn-off point 176-53-W ; 01-13-N . Erroneous turn-off point 177-01-W ; 01-10-N .
« Last Edit: June 14, 2011, 09:41:58 AM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #202 on: June 13, 2011, 01:51:45 PM »

Never produced a thing ?  Read EJN-2011 for mr.Noonan´s own sunset fix with same fashion as for sunrise.

Well, since we do not have Mr. Noonan"s work papers, we have only your theoretical computations of them, how about producing at least one other example of anybody other than Noonan using your "sunrise/sunset" methodology or a cite to a navigation text describing your method?

gl
« Last Edit: June 14, 2011, 09:42:31 AM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #203 on: June 13, 2011, 02:47:02 PM »

No , I just do not remember where I found the fashion , like I told you I am not at home now and must postpone consulting the books. I will recompute the altitudes , the coordinates are : correct turn-off point 176-53-W ; 01-13-N . Erroneous turn-off point 177-01-W ; 01-10-N .

Mr. van Asten,

Using your coordinates for what you believe was the correct turn off point at 1859 GMT produces an altitude for the sun of 16° 00.8' so it was not the correct turn off point because the altitude is not equal to the altitude at Howland for the same time which was 16° 04.5'. and this is the essential requirement for the  LOP. However, I see that the altitude at the erroneous coordinates used by Williams, 0° 49' N, 176° 43' W produces an altitude of 16° 00.3' so your turn off coordinates are within half a mile of the LOP through the Williams coordinates so this is accurate enough. The difference between the altitudes at the Williams coordinates and the correct coordinates for Howland would have caused the LOP through the Williams coordinates to be parallel to the correct LOP and offset by 4.2 nautical miles, not enough to cause them to miss the island. Notice, none of these altitudes are anywhere near the 21 degrees that you claimed.

The altitude of the sun at 1859 at the point you identify as the erroneous turn off point  was 15° 52.2' a difference of 8.1 nautical miles from your correct turn off point onto the Williams LOP and 12.3 NM short of the actual LOP through Howland.

I can't believe that you didn't notice your error in claiming that the altitudes were 16 and 21 degrees, a difference of 5 degrees, since THE BASIC PREMISE behind all celestial navigation is that a difference of 1 degree produces an error, or difference, of 60 nautical miles. Your calculated altitudes produced an error of 300 NM!

Tsk, tsk.

Such an obvious error calls into question all of your other calculations.

gl
« Last Edit: June 14, 2011, 09:43:04 AM by Martin X. Moleski, SJ »
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#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #204 on: June 13, 2011, 03:04:07 PM »

Such an obvious error calls into question all of your other calculations.

Yes I made some arithmatic error somewhere here , but not in the other calculations . See corrections posted (diff. error vs correct  -28´)
« Last Edit: June 14, 2011, 09:43:42 AM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #205 on: June 13, 2011, 03:07:08 PM »

Mr. Long´s reply was not to me , he replied to mr. Jourdan , who later said to me that it was mr.Long´s getting on in years , that kept him from studying the 2008 article .

Mr. van Asten,

It seems likely that Mr. Jurdan was just trying to spare your feelings.

gl
« Last Edit: June 14, 2011, 09:44:09 AM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #206 on: June 13, 2011, 07:21:40 PM »

Mr.Lapook ,

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.

_________________________________
Mr. van Asten,

Your diagram in your article shows that they reached the turnoff point at 1859 GMT at which point the sun's altitude was 16° 04.5' (not the 21 ° that you stated) for an observer at Howland and anywhere else on the correct LOP through Howland. This was plenty high enough for accurate sextant sights.

Anytime after 1815 GMT the sun's altitude was above the six degree minimum needed by Noonan's refraction correction table so he would have been taking sights of the sun for 44 minutes prior to the interception and would not have relied on dead reckoning for 102 miles which would have introduced an uncertainty of 10 miles in the turn off point onto the LOP.  You apparently do not understand the basic idea behind the landfall procedure, that you take sights as you approach the LOP so that it is an accurate interception and then you take additional sights to ensure staying on the LOP to the destination. You do not DR for a long leg to the interception. If you were going to DR for 102 miles then there would be no reason to do the landfall procedure.

Try reading the flight manuals that explain this procedure that I have posted here:

https://sites.google.com/site/fredienoonan/topics/landfall-procedure

gl

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

You wrote in your 2011 published paper:

"Usually the Offset
Track was fiown by OR, especially with low sun giving
less reliable position outcomes due to difficult
assess of refraction."

You correctly point out that at the point that you believe that they turned to 55° T at 1815 GMT to intercept the LOP, 102 statute miles short of your "erroneous turn off point", that the altitude of the sun was only 4° 21' which was below the minimum 6° in Noonan's refraction table so he could not take a normal sun sight at this point. You then claim that because of this that the sun continued to be too low to allow additional sights as he approached the LOP and this is, obviously, incorrect since we know the sun was 16° high at the point of interception so its altitude had to rise above 6° at some place along this leg. Even at the initial point where the turn was made to 55° T the sun rose above 6° at 1823 GMT so allowed at least 36 minutes for Noonan to take additional sights. In this period Noonan should have been able to take 5 or 6 additional sights. See: http://www.fer3.com/arc/m2.aspx?i=116311

Your theory is that due to Noonan using a marine sextant instead of the bubble sextant to determine the 175453 GMT fix that he introduced an error that caused them to be 11 NM west of where they thought they were. Your theory goes on to claim that they then dead reckoned the rest of the way to where they believed Howland was located which maintained that 11 NM error in all subsequent DR positions. This shows that you do not understand that the whole purpose of the landfall procedure is to cure any existing errors in the DR by taking additional sights while nearing the LOP and then taking additional sights while flying on the LOP to ensure staying on the LOP. Even just one sight taken after 175453 GMT  would have cured the problem that you complain about since Noonan would then have a correct reading and a correct fix. Your entire DR leg, 102 SM to the turn off point plus 30 SM along the LOP is a total of 132 SM, would cause an uncertainty, due to the these DR segments, of plus and minus 13.2 SM. In addition to this uncertainty you must add the uncertainty in the original 175453 fix which is, according to all flight navigation texts and the Federal Aviation Regulations, considered to be 10 NM, 11.5 SM, making the total uncertainty, when in the vicinity of Howland, of plus and minus 24.7 SM. Nobody, in his right mind, would ever try to find this island with this level of uncertainty which is why you must take additional sights when flying the landfall procedure.

You don't have to take my word for this, you can read the standard flight navigation manuals that describe the landfall procedure here:

https://sites.google.com/site/fredienoonan/topics/landfall-procedure

gl
« Last Edit: June 13, 2011, 10:55:38 PM by Gary LaPook »
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#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #207 on: June 14, 2011, 12:45:11 AM »

You don't have to take my word for this, you can read the standard flight navigation manuals that describe the landfall procedure here:

https://sites.google.com/site/fredienoonan/topics/landfall-procedure

Yes , I certainly take your word , it is however , not so that I said that the entire offset lane would have a too low sun ; I estimated it , without specific computation , to about halfway , with the bubble sextant for observation . I do not think that using the marine sextant would for this event give other results w.r.t. the elevation differences @ the two turn off coordinates pairs , I will check nevertheless . I did not take the elevation of sun for Howland , but for the T.O.P.`s themselves (as by F.Chichester) . The entire OLA tracking 132 mls , mr.Noonan may have ventured DR only  , you reckon 10% deviation , 13 mls , but @ nearly still air his abberation  would certainly have been less , say 5% or 7 mls . In 1996 I have sent the pre-article  to the chairman of Royal Institute of Navigation , Great Britain . In a letter he admitted that basically , accumulation of errors I described , probably was cause of the incident . He btw added that I should best contact The Institute of Navigation (USA) since Amelia Earhart was a typical American pioneer.  In 2007 I so did , but received answer to appoint 3 referees myself : they did not find a referee for the of the era science of navigation . The answer came with a remark : "Why not distances measured in nautical miles as usual" (the manuscript was read through by a retired sea navigator) .
« Last Edit: June 14, 2011, 09:44:50 AM by Martin X. Moleski, SJ »
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#### Gary LaPook

• T5
• Posts: 1624
##### Re: Navigating the LOP with the offset method.
« Reply #208 on: June 14, 2011, 02:18:22 AM »

Yes , I certainly take your word , it is however , not so that I said that the entire offset lane would have a too low sun ; I estimated it , without specific computation , to about halfway , with the bubble sextant for observation . I do not think that using the marine sextant would for this event give other results w.r.t. the elevation differences @ the two turn off coordinates pairs , I will check nevertheless . I did not take the elevation of sun for Howland , but for the T.O.P.`s themselves (as by F.Chichester) . The entire OLA tracking 132 mls , mr.Noonan may have ventured DR only  , you reckon 10% deviation , 13 mls , but @ nearly still air his abberation  would certainly have been less , say 5% or 7 mls . In 1996 I have sent the pre-article  to the chairman of Royal Institute of Navigation , Great Britain . In a letter he admitted that basically , accumulation of errors I described , probably was cause of the incident . He btw added that I should best contact The Institute of Navigation (USA) since Amelia Earhart was a typical American pioneer.  In 2007 I so did , but received answer to appoint 3 referees myself : they did not find a referee for the of the era science of navigation . The answer came with a remark : "Why not distances measured in nautical miles as usual" (the manuscript was read through by a retired sea navigator) .

Mr. van Asten,

When doing a landfall the navigator uses the destination as the assumed position for the calculation of the Hc for the LOP. He calculates a series of sun altitudes at 20 minute intervals and plots the altitudes on a graph against time. The altitude at the destination determines the LOP through the destination so the altitude must be exactly the same at the turn off point as at the destination. The navigator does not care about the exact latitude and longitude of the turn off point, he doesn't even determine it. He just flies toward the LOP and takes altitudes and compares them to the graph of plotted altitudes until his measured altitude is the same as it would be at the destination for the time of observation which tells him that he has arrived at the LOP so he then turns to follow it.

See: Air Navigation, Weems; the Navigator's Information File; and Celestial Air Navigation, TM 1-206 available here:

https://sites.google.com/site/fredienoonan/topics/landfall-procedure

The air was not still but had strong winds out of the eastern quarter. Sometimes you might get lucky and have your DR error be only 5% but most times it is not that good. If you were in Noonan's position would you assume that this is the day that your will have really good DR accuracy, since you are betting your life on it. A prudent navigator assumes a maximum possible error when working out a landfall procedure to ensure that he arrives at the island. For normal flight he might expect a 10% uncertainty but for such a critical flight he would have allowed for an even larger possible error. No flight navigator would DR for 132 SM in this situation.

You needed a flight navigator, not a sea navigator, to review your papers. Flight navigation is much different than surface navigation because the wind speed and its variations are such a large proportion of the the speed of the aircraft. A 30 knot wind is almost one-quarter the speed of Earhart's plane and a variation in speed of 10 knots is normal and 20 knots is not unusual as is the change of direction by 20  or 30 degrees. In the open ocean it is very unusual to find a current of even one knot which is only one-twentieth the speed of most ships and ocean currents are very constant, it is hard to get all that water to change direction. So DR in the air has a much greater uncertainty than sea navigation. I have copies of Mr. Noonan's charts for the Natal to Dakar flight and for the California to Hawaii flight. On the flight to Dakar the plane was off course by 125 nautical miles at one point. On the flight to Hawaii there were fixes 35, 65, 85 and 125 nautical miles off course. You have not appreciated in your papers and posts this fact of life for flight navigators.

gl
« Last Edit: June 14, 2011, 09:45:33 AM by Martin X. Moleski, SJ »
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#### h.a.c. van asten

• T4
• Posts: 322
##### Re: Navigating the LOP with the offset method.
« Reply #209 on: June 14, 2011, 06:29:30 AM »

The air was not still but had strong winds out of the eastern quarter. Sometimes you might get lucky and have your DR error be only 5% but most times it is not that good. If you were in Noonan's position would you assume that this is the day that your will have really good DR accuracy, since you are betting your life on it. A prudent navigator assumes a maximum possible error when working out a landfall procedure to ensure that he arrives at the island. For normal flight he might expect a 10% uncertainty but for such a critical flight he would have allowed for an even larger possible error. No flight navigator would DR for 132 SM in this situation.

You needed a flight navigator, not a sea navigator, to review your papers. Flight navigation is much different than surface navigation because the wind speed and its variations are such a large proportion of the the speed of the aircraft. A 30 knot wind is almost one-quarter the speed of Earhart's plane and a variation in speed of 10 knots is normal and 20 knots is not unusual as is the change of direction by 20  or 30 degrees. In the open ocean it is very unusual to find a current of even one knot which is only one-twentieth the speed of most ships and ocean currents are very constant, it is hard to get all that water to change direction. So DR in the air has a much greater uncertainty than sea navigation. I have copies of Mr. Noonan's charts for the Natal to Dakar flight and for the California to Hawaii flight. On the flight to Dakar the plane was off course by 125 nautical miles at one point. On the flight to Hawaii there were fixes 35, 65, 85 and 125 nautical miles off course. You have not appreciated in your papers and posts this fact of life for flight navigators.

gl

Yes , I agree on the necessity of continuous celnav check of your DR , also @ relatively short distances off destination . For the OLA , according to prescriptions by Weems et al ,   the over destination sun´s elevation is taken as the reference hc for turning off if compliance with your sextant reading is acquired . Now proceed as follows : take the sun´s elevation @ the erroneous TOP for ETA 1859 GMT, this being hc(e) = 16-00 @ 177-01-W ; 01-10-N .  Then , compute sun´s elevation for Howland @ 176-43-W ; 00-49-N (the C.Williams in mr.Noonan´s chart specified coordinates) . You will find hc(c) = 16-00 . Thence mr. Noonan , coming from the erroneous offset lane initial point (181453 GMT , 178-14-W ; 00-13-N) , will have found ho = hc @ 1859 GMT [with any sextant type] , upon which he ordered the A/c to steer 157 T on the erroneous position line , having Howland (176-38-W ; 00-48-N) @ 16 mls on the port beam , instead of below the APL , at 1912 GMT : everything with exactness to the second for arc & time according to text & diagrams of article EJN-2008 .
« Last Edit: June 14, 2011, 09:46:33 AM by Martin X. Moleski, SJ »
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