You can't get any better source than that!
Sure you can. When I wrote Finding Amelia, Bellart's log was the only contemporary written source we had from someone who was in the radio room. I was correct in siding against Commander Thompson's later claim that Earhart said "cloudy overcast" because there was no support for it. Finding Amelia was published in September 2006. We got out first clue to the possible existence of the Carey's notes and diary the very next month but it was February 2007 before we had them in hand. New documented information changed the picture.
Bellart's recollections many years later may or may not be correct but if he passed the headphones to Carey as I suspect, he may have been absolutely correct in saying he never heard Earhart say that - but Carey's contemporary written notes trump Bellarts memory.
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That's interesting. Not to quibble about this point, but reporting an overcast at the time of a radio broadcast doesn't tell us about the conditions during the rest of the hour. Obviously they were satisfied with the accuracy of the navigation or they could have turned around and returned to Lae at the time of that first report and could have made it back to Rabaul up to the time of the second report as I showed with the point of no return calculation.
But putting those two reports behind us, there is
no dispute about the
logged report of "partially cloudy" at 1623 Z, conditions that allowed Noonan to get a fix even if he had not been able to get one in the prior two hour period. Based on the normally accepted level of uncertainty for dead reckoning of 10% of the distance flown, from that point to 1912 Z it is very unlikely that their DR position would be more than 47 NM in error. You wrote in an earlier post that Earhart could DR to Gardner with only a 7% uncertainty, which is better than the standard, so would improve the accuracy of the DR position. So using
your number, any error in the DR at 1912 Z is very unlikely to exceed 36 NM so they were not going to be far south of Howland, in fact, they would not have ended up south of Baker even with your maximum error, which is unlikely, since you are normally closer to the DR position than near the edge of the possible error band.
These types of navigational errors have been extensively analyzed statistically. The most complete treatment of the statistics of navigational errors is in the
American Practical Navigator, commonly known as "Bowditch," U.S. Navy Hydrographic Office Publication number 9 (H.O. 9) which is
the standard navigational authority in the United States and has been since the first edition in 1802. Appendix Q of the 1977 edition is a 33 page discussion of this topic. There is only one chance in twenty of being outside the 10% DR error band and the probabilities drop off very quickly after that. The chance of being at twice that distance away from the DR position (94 NM in this case) is only one chance in 15,800 and being three times as far away is only one chance in five hundred and six million, eight hundred thousand, 1/506,800,000!
So based on the
science of navigation Noonan would never have gotten so far south of Howland so that it would have made any sense to abandon their efforts to find Howland and instead to fly off to far away Gardner.
gl