N.B. This post is from Gary LaPook. It seems to have been the one that was causing some problems with the thread.Quote from: Harry Howe, Jr. on September 09, 2011, 10:20:00 PM<blockquote>
Jeff
You mentioned an error being discussed. I don't have a link but I remember it being said that some charts of the area had the location of
Howland mislocated by 5 nm west of its "true" position. Hence the relative location of Gardner to Howland would have been incorrect and the course connecting them would be more like the line 158/338 rather than 157/337. Whether the additional error, 5 nm,would have affected the spotting of Gardner or not, who knows. Nor do we know whether FN had one of those charts or not. Maybe the charts he flew by are still on the plane.
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This question is always coming up, hopefully this will be the final answer to this question.
Clarence Williams was hired by Earhart to plan the flight legs for her. His planning was for a westbound circumnavigation but he also included information for an eastbound flight. As part of this navigation planning he drew "strip charts" covering the legs and extending a reasonable distance on each side of the planned course line. One of these strip charts covered the leg between Lae and Howland and Mr. Williams completed this chart on February 9, 1937. A copy of this chart is now in the archives of Purdue University. I am attaching a scan of this chart. You will notice near the northeast corner of the chart that the coordinates for Howland that he used for his planning which are 0° 49' north latitude, 176° 43' west longitude.
But this is not the end of the story. Sometime before Earhart departed on her second attempt, Itasca, on its normal resupply cruise, determined more accurate coordinates for Howland and Itasca did this by using the most accurate navigation system available, celestial navigation. The new coordinates for Howland are 0° 48' north latitude, 176° 38' west longitude. These coordinates were published in navigation manuals starting at least as early as 1938 and possibly in some earlier sources. These are still the coordinates published in official government manuals. Although there is no proof that these more accurate coordinates were communicated to Earhart, it is a reasonable assumption that they were based on the high government support for this flight; building an airport on the island for her use; sending several naval ships, in addition to the Itasca, on two cruises in support of the Earhart flight; Earhart's personal relationship with the White House (she gave flight lessons to Eleanor Roosevelt); and the obvious danger to Earhart if she was not provided with the most up to date coordinates would be apparent to everybody in possession of the new coordinates. The new coordinates are one nautical mile south and five nautical east of the old coordinates.
But if Earhart did not have the updated coordinates, would have made any difference?
Noonan was using the coordinates that he had for doing his celestial calculations. He calculated what the altitude (the height above horizontal) of the sun would be as viewed from
those coordinates. The sun's altitude changes constantly as the earth turns during the day so Noonan had to do these calculations for the times that he took observations with his sextant. Most likely he did these calculations in advance, either at Lae or early in the flight, to cover the period that he expected to be approaching Howland, say for the period from 1815 Z (the time that the sun would first be high enough for accurate observations) to 2400 Z. This sounds complicated, but using the tables that he was using, H.O. 208, it would have taken only about one hour for all the calculations to cover this five hour and forty-five minute period. (See:
https://sites.google.com/site/fredienoonan/resources/dreisonstock-h-o-208 and
https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves ) Then, when Noonan took observations of the sun, he simply compared his measured observation atitude with the calculated altitude for the same time at the coordinates for Howland, the difference instantly tells him if he is on the LOP (line of position) that runs through the coordinates or how many miles he must correct to get onto the LOP. One degree difference in the altitudes means a 60 NM space between him and the LOP. A one minute of arc difference (1/60th of a degree) means a one nautical mile difference. If he was using incorrect coordinates then his calculation would show his distance from the LOP running through those incorrect coordinates and not his distance from the correct LOP that actually runs through Howland. Noonan would follow the erroneous LOP to the incorrect coordinates and end up one nautical mile north and five nautical miles west of the corrected coordinates for Howland. So with twenty NM visibility they would have been able to see Howland from there.
But is gets a little more complicated. I have attached a map of Howland with the these two sets of coordinates plotted. You will notice that the newer, more accurate coordinates, are actually located 0.75 NM west of the west shore of Howland. Itasca's navigator had calculated the wrong coordinates (but these are still the published official coordinates) and this 0.75 NM error is most likely due to the Itasca's chronometer running three seconds slow. But is Google Earth more accurate than Itasca's navigator? Yes, I have checked the accuracy of Google Earth in this area, see my prior reply #72 on this thread. So even if Noonan was using the updated coordinates, the LOP that passes through those coordinates would have taken them 0.75 NM west of the island. This also means that the older coordinates are actually a little further from Howland, 6.6 NM straight west from the western shore of Howland. But the LOP did not run straight north and south but at an angle, 157°-337°. So plotting this LOP through to old coordinates shows that it passes just 5.0 NM from the nearest part of Howland and only 4.1 NM from the new coordinates.
So does it make a difference which set of coordinates that Noonan was using? No, they would have seen the island from five nautical miles away. Even allowing for the maximum likely error in a sextant observation of seven NM they would still have passed within 12 NM of the island and should have seen it with the visibility existing at the time. In addition, the smoke trail produced by Itasca blew further west than 12 NM so the plane should have passed directly over the smoke trail even if Nnonan's observation had the maximum likely error at the time.
gl