Ok---I'll ask the question of our navigator friends. IF the weather was cloudy during the nighttime part of the flight, Fred would NOT have been able to shoot a celestrial plot. So, when he was able to shoot the 157/337 sunline, how would he have known where along the sunline he was? He wouldnt have been able to guage their drift, so they actually "could" have been south of Gardner. AT 1000 feet, they may not have been able to see Howland, which "could" have been a few miles over the horizon from their position.
So--as they flew south along the sunline, they came across Gardner.
Does this make any sense to anyone??
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There is no reason to think that Noonan had not been able to get celestial fixes. Earhart wrote
that “Noonan must have star sights” so they would not have just changed their minds about this
requirement.
The “Point of No Return” is a standard calculation done by flight navigators, taking into account
air speed, wind speed and endurance, to determine the point along the planned course at which
the plane could reverse its course and return safely to the departure airport.
If Noonan thought he had a 24 hour endurance, using the 23 knot wind component that he measured in flight then he would have calculated the PNR as 1407 Z at 1511 NM from Lae, just five hours and 710 NM short of Howland.
Using a 15 knot wind component then he would have gotten 1323 Z at 1539 NM and with a 25
knot wind he would have gotten 1418 Z and 1502 NM.
It also turns out that there was an airport at Rabaul, 344 NM along the course line to Howland.
Noonan could have calculated a PNR for a departure from Lae with a return to Rabaul. Since
Rabaul was closer to Howland then this PNR would also be closer to Howland. Doing this
calculation we find the PNR occurs at 1526 Z, 1653 NM from Lae, only four hours and 570 NM
short of Howland. So if Noonan had not been able to get fixes they could have turned around and
returned safely to Lae or Rabaul and try again another day.
Air Force Manual 51-40 states the uncertainty of dead reckoning as 10% of the distance flown
from the prior fix.
So contrary to what many people believe, “that they had no idea where they were north and
south" when they intercepted the sunline LOP, we can expect that any error or uncertainty would
be limited to 10 miles for every 100 miles that they had flown since their last fix.
Sunrise at Howland was 1745 Z and civil twilight occurred 22 minutes
earlier at 1724 Z at which point the sky would have been too bright to
see the stars and to obtain a fix. Sunrise and civil twilight would have
occurred even later at their position west of Howland by an additional
one minute for each 15 miles that they were west of Howland. We can
assume that they had arrived close to Howland at 1912 Z when they
reported "must be on you." This is 1 hour and 48 minutes after civil
twilight at Howland and the Electra would have flown 235 nautical miles
in this time at 130 knots. Civil twilight occurred 16 minutes later 235
NM west of Howland so they could have obtained a fix slightly later than
1724 Z at 1740 Z. We can assume that Noonan was busy right up to the
time of civil twilight so that they would have the latest and most
accurate fix to use in locating Howland.
From 1740 Z to 1912 Z NR16020 would have flown 199 nautical miles at 130
knots so the accuracy of their position would only have deteriorated 20
nautical miles based on 10% of the distance flown in that period, If you add this 20 nautical miles
to the uncertainty of the original fix, 10 nautical miles according to
navigation textbooks, Federal Aviation Regulations, and also based on what
Noonan himself reported to Weems in a letter published at Weem, page 423 page 424 & 425, (see:
https://sites.google.com/site/fredienoonan/resources/weems/weems-422-423.JPG?attredirects=0 and
https://sites.google.com/site/fredienoonan/resources/weems/weems-424-425.JPG?attredirects=0 ) they should have known their position within 30 nautical miles. Although we do not know the time
of his last fix, Noonan did know and would have used that knowledge
in planning his approach and in figuring the possible uncertainty and
how far to aim off.
Looking at this uncertainty in the north-south direction you end up with a 30 nautical mile north-south uncertainty. Noonan would have made the same calculations based on his previous experience, maybe he even rounded this value up for extra safety.
There has been concern expressed that clouds could have prevented Noonan from taking star
sights that late (1940 Z). They had reported flying at 12,000 feet, which normally is above most
clouds. Even if some clouds where higher than 12,000 feet it is unlikely that they blocked the
entire sky for hundreds of miles along the flight path. It has been claimed that Earhart reported at
1415 Z and again at 1515 Z "cloudy and overcast" but these words are not found in either radio
log so there is no support for the claim that Noonan had been prevented from shooting stars. But
what is actually recorded in the radio log, more than an hour after this 1515 Z possible report of
"overcast" conditions, is at 1623 Z Earhart reported "partly cloudy." There are no reports after
this "partly cloudy" report so it is the most current report, in both time and location, so there is no
actual evidence that the weather deteriorated later so as to prevent celestial observations. Earhart
did not report descending to 1,000 feet until almost two hours later at 1818 Z.
Based on this last report of in-flight weather conditions, we can be almost certain that Noonan was able
to take sights at 1623 Z, only two hours and forty-nine minutes before the "must be on you"
transmission at 1912 Z. So looking at this as the worst case scenario, we can do the same
computations as before about the uncertainty of the D.R. position at 1912 Z. In two hours and
forty-nine minutes the plane would have covered 366 NM at 130 knots so the uncertainty caused
by dead reckoning for 366 NM is 37 NM for the 10% estimate of DR accuracy. We have to add
to these estimates the original 10 NM uncertainty in a fix obtained at 1623 Z so the totals is 47
NM of uncertainty at 1912 Z. Noonan knew the time that he obtained his last celestial fix and
would have used the right amount of offset to allow for the possible uncertainty.
So these two cases mark the bounds of the possible uncertainty in the north and south direction, 47 NM if the last fix was obtained at 1623 Z and 30 NM if the last fix was obtained as late as possible (clouds permitting) at 1740 Z. Either way they would not have flown for hours southward still expecting to find Howland.
Also see:
https://sites.google.com/site/fredienoonan/topics/landfall-procedurehttps://sites.google.com/site/fredienoonan/topics/accuracy-of-dead-reckoninghttps://sites.google.com/site/fredienoonan/topics/accuracy-of-celestial-fixeshttps://sites.google.com/site/fredienoonan/discussions/navigation-to-howland-islandgl