This makes me wonder about how they would have established and used any LOP procedure - was it a 'last minute / last ditch' effort to establish how far east they had come after belatedly realizing that the RDF apparently was not working?
Drawing Lines of Position on charts is how navigators nagivate.
The intersection of two LOPS taken at practically the same time gives you your most probable location. It is fuzzy due to the limits of the instruments and observers.
If you can get three LOPs at about the same time, that gives you a triangle as the center of your most probable location.
We don't know how many celestial sightings FN got during the night.
Therefore, we don't know how many LOPs he drew on his charts.
We speculate that he was able to make the dawn sighting because the charts tell us that from the region west of Howland and close to the equator, the dawn observation would yield a LOP of 337-157--the same as was announced in the last transmission.
If so, could FN have made rapid readings on the fly ...
Could have. Maybe would have. They still wouldn't give him a fix all by themselves, but they would give him new LOPs to work with to refine his dead reckoning. But you have to give the sun time to change position significantly so that your new LOP has information not contained in your old LOP.
... that were enough off the mark to leave the aviators woefully further short of the progress across the pacific than they had thought?
I don't think that's likely. If FN got a good LOP at dawn, he would have a good sense of the distance between that LOP and a parallel LOP drawn through Howland. It seems that he
must have had the dawn sighting in hand; otherwise, it would make no sense for AE to announce that they were searching "the LOP" (i.e., "the advanced line of position that Fred drew through Howland parallel to the LOP he drew on the map shortly after our dawn, west of Howland") north and south.
They thought they were close--really, really close.
Could the sun have been well up by the time it fell to FN to determine a LOP?
FN didn't start drawing on his charts when they realized that they were not going to get help with direction finding.
Drawing lines on his charts was his job. That was the basis of the newscasts that AE made during the night about where they were.
Could cloud cover have made star shots in the preceding night difficult or impossible?
Yes, of course.
Could the early reports of how far out they were have come then from dead-reckoning alone when those calls were made, and not a sunrise LOP / offset reading?
I think this is
a list of all of the transmissions heard from the aircraft during the flight.
It seems to me that the "200 mile" message couldn't have been from a dawn sighting; it was logged at Howland 3 minutes before the sun rose there. AE and FN's local dawn would have to be at least a few minutes later than Howland's.
The "100 mile" message might be after FN had done some chart work with the dawn LOP.
Might then FN have resorted to a belated sun-shot to establish a LOP in haste - realizing he could not know how far south or north he was (and having to rely on dead-reckoning to believe he was "close")?
I think not. Drawing lines on his chart on the basis of celestial observations was not an emergency measure; it was Fred's job.
If so, how much error might be caused by a later-morning sun-shot under their flying circumstances?
You may assign as large an error bar as you like. Just make assumptions about visibility, troubles with instruments, exhaustion, hangovers, and ordinary human lapses in judgment. How big do you want the error bar to be?
None of that can really blow a hole in the logic we have seen put together to-date, but if we find ourselves having to 'rethink' things at some point then maybe some of these wandering wonderings will apply. Still, I am beginning to believe that AE and FN realized all too late how very lost they may have been after a night of assuming that all would be well with the RDF approach for too long into the flight.
They were assuming that the RDF would work from the time they left Oakland. If they had thought more about the technical difficulties, we wouldn't be here today talking about them.