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 .

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Well, you almost have it right. At 1859 GMT Noonan takes an observation of the sun and measures 16° 00'. He then looks at his precomputed curve of the sun's altitude for 1859 GMT and sees that the precomputed altitude at the Williams coordinates at 1859 GMT is also 16° 00'. He then knows that he has intercepted the LOP through the Williams coordinates

because every point on that LOP will have the same altitude for the sun as at the Williams coordinates. Nonnan then turns to 157°. See graph of precomputed altitudes available here:

https://sites.google.com/site/fredienoonan/topics/precomputed-altitude-curves/Howlandprecomputation.jpg?attredirects=0(The red line is the line of precomputed altitudes for the incorrect Williams coordinates and the blue line is the curve for the correct coordinates for Howland. You will notice that the spacing between the two curves remains constant, 4', which is the same as the 4 NM distance between Howland and the Williams coordinates. Noonan did not have the correct coordinates for Howland so his graph would only have the red line. This is just a sample covering the period of 1858 to 1916 GMT. Noonan would have prepared a graph like this covering the period from 1815 to the estimated time of fuel exhaustion.)

If, at 1859 GMT Noonan had measured only 15° 52' he would see the difference between his measurement and the expected measurement of 16° 00' found on the red curve equals 8' so he would know that he had not yet reached his turn off point but that he still had an additional 8 nautical miles to go. Any altitude measurement that plots below the curve means that the plane has not yet reached the LOP and must continue toward the northeast. Any sextant altitude measurement that plots above the curve means that the plane has overshot the LOP so the plane must correct its heading back toward the southwest.

After he has turned to 157° he continues to take sextant readings. For example, if he takes a reading at 1907 GMT and finds an altitude of 17° 52' and he compares it to the red line for the same time and reads out 17° 50' he would see that the difference is 2' indicating that he is 2 NM to the left of course since his reading is greater than the correct altitude. He could then make a slight heading change to the right or just ignore it since a 2' difference is very small and well within the expected scatter of the sextant readings. This shows him tracking closely to the LOP that leads to the Williams coordinates. The LOP through the Williams coordinates runs parallel to the correct LOP through Howland, offset to the southwest by 4 NM.

Then at 1912 GMT he takes another sextant shot of the sun and measures 18° 58' and comparing it to the precomputed altitude on the red line for the same time and takes out the same number, 18° 58' which shows he is on the LOP through the Williams coordinates. Staying on this LOP will take the plane over the Williams coordinates.

Since the Williams coordinates are only 4 NM from Howland the plane will pass within 4 NM of Howland not the 16 miles that you stated. He will not have turned off too soon because his sextant reading has cured the error in the 175453 fix.

gl