NavList:

On the TIGHAR site I was asked to explain how they would have navigated from the last

fix to the island.
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Philip Van Horn Weems was a well respected authority on air celestial
navigation. In "Air Navigation", 1938 edition he states regarding the
accuracy of dead reckoning on page 173:

"Reasonably efficient dead reckoning should produce an accuracy well
within 5 percent of the distance flown, or within 5 miles in 100, 10
miles in 200, 15 miles in 300."

So contrary to what we are constantly reading on the TIGHAR forum that they had
"no idea where they were north and south" we can expect that the error
would be limited to 5 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 but we will ignore that advantage and assume that the
latest time to obtain a stellar fix was 1715 Z to allow time for
shooting 3 stars. 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. In fact, this is probably the
reason that they departed Lae at 0000Z so as to arrive at Howland as
shortly after sunrise as possible so that the fix obtained at civil
twilight would be as fresh as possible.

From 1715 Z to 1912 Z NR16020 would have flown 260 nautical miles at 130
knots so the accuracy of their position would only have deteriorated 13
nautical miles based on 5% of the distance flown in that period. If you
add this 13 nautical miles to the accuracy of the original fix, say 10
nautical  miles (based on what Noonan himself reported to Weems in a
letter published at page 424 of the same book,) they should have known
their position  within 23 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.

A more modern textbook "Air Navigation" published by the U. S. Navy
Oceanographic Office as PUB. No 216, 1967 edition page 184 suggests that
an inexperienced  navigator should use a more conservative value for the
accuracy of  dead reckoning of  20 NM per hour plus 1 percent of the
distance covered. Even using this greater error level the accuracy would
still be 43 nautical miles plus the 10 mile original fix accuracy for an
uncertainty of 53 nautical miles at 1912 Z.

Assuming that the error was all in the north-south direction the worst
case is a 53 nautical mile north-south error. Noonan would have made the
same calculations based on his previous experience, maybe he even
rounded this value up to an even 60 nautical miles to be sure. (Or he
might have used a value closer to 23 miles since he was an experienced
navigator.) Either way they would not have flown hours southward still
expecting to find Howland.

It is almost certain that Noonan would have used the offset method
of using a single sun line to find the island as this allows you to turn
a "speed line" LOP into a "course line" LOP which you can then follow to
the landfall. As they approached the island the sun line would have
plotted at almost right angles to their course. The course from Lae to
Howland is 78 degrees and the sun line ran 157-337. Since it was not
exactly a right angle it would be slightly shorter flying  to alter
course to intercept the line north-north-west of Howland. If they were
going to intercept south-south-east of Howland they would be flying past
the island and then having to double back slightly. Another reason to intercept
the LOP to the northwest is that the the LOP through Howland rotated
counter-clockwise as the the day wore one. This means that if they
were running late that the LOP would have moved towards them shortening
the distance to be flown to find the island. If they planned to intercept
to the southeast the LOP would have been rotating away from them making
a longer flight to the island. After intercepting Noonan would have
continued to take sights to ensure tracking the LOP and would have
made heading changes as necessary. He would have a clear view of the
sun through the left window as the sun would be out by the left wingtip.

So why not just head directly for the island? here's why. Using the
previous assumptions, that they are right on course with 260 miles to go
to Howland, they fly these 260 miles in 2 hours taking sights on the sun
until they determine that have reached the sun line LOP that passes
through Howland and they don't have the island in sight so they have to
turn one way or the other to follow the LOP. Half of the time you guess
wrong. If they turn the wrong way they will proceed out along the LOP
for a distance equal to the maximum possible error in their dead
reckoning, say 60 miles and 28 minutes at 130 knots. Then they have to
make a 180 degree turn and come back the other way on the LOP, back to
their starting position where they made the first turn. This second 60 mile and
28 minute leg is a complete waste of time and fuel because they  have
already searched this part of the ocean and they know that the island is
not there.

They arrive back at the starting point 56 minutes and 120 miles after
having made the first turn onto the LOP which is 2 hours and 56 minutes
since the last fix and 380 flying miles. Only now, finally, do they
start searching along the LOP in the right direction and they find the
island after flying at most 60 miles further for (worst case) 28 more
minutes for a total since the last fix of 440 flying miles and 3 hours
and 24 minutes.

If at the time of the last fix, however, they had altered course 13
degrees to the left to 65 degrees they would have only had to fly 250
miles until intercepting the LOP 60 miles out from where they had in the
first example. (You can work this out on your E6B.) This takes only 1
hour and 55 minutes. They then turn right since they can be certain of
which way to turn. They fly inbound for 28 minutes, not seeing anything
and arrive at the point where the first turn onto the LOP was made in
the first example  after flying only 2 hours and 23 minutes and 310
flying miles for a saving of 33 minutes and 70 flying miles. Then, as in
the first example, they fly along the LOP and find the island after
flying, at most, another 28 minutes and 60 miles for a total since the
last fix of  2 hours and 51 minutes and 370 flying miles. Again the
saving is 33 minutes and 70 miles.

During this process you do not abandon your DR. By aiming off to one side
by the amount of the estimated maximum error in the DR at the point of
interception (60 NM in this example) you have converted  a 120 NM
uncertainty along the LOP, 60 NM left and 60 NM right, into a 120 NM
uncertainty extending 120 NM left and zero right. This ensures that you
do not end up to the right of the destination. This allows for the maximum
possible error but, in fact, you are more likely to be nearer to your DR
position than to the extreme edges of the maximum possible error. When
you intercept your aiming point 60 NM to the left you are not surprised
that you don't see the island since it is most likely to be about 60 NM
to your right. As you fly along the LOP your DR also moves along the LOP
getting closer to where the island should be and you expect to see it
as you approach that point. Even if you don't see it when you arrive there
you are not yet worried because it can still be ahead of you. But as you
continue further and further along the LOP after the DR put you over
the island you start getting worried. But you must still proceed out the
 whole 60 NM past where the island should be to be certain that you do
 not miss the island. At the end of that leg you would know that you have
 missed the island and would have to deal with that problem
most likely planning a standard expanding square search pattern centered
on the most likely point for the island.

However, due to the unique relationship of Howland and Baker, Noonan
might have decided to aim off to the northwest but using Baker as the
 reference island. Baker is 38 NM southeast of Howland and almost
exactly on the LOP. If Noonan was using a 60 NM offset he could aim 60 NM
northwest of Baker which would be aiming only 22 NM to the left of Howland
 and would then find Howland after flying a 38 NM shorter leg.
If he was actually towards the right side of the error band he would fly between
Howland and Baker and might see either one but if he saw no island prior to the
intercept he would still turn right and would shortly discover
Baker. He would know that it was Baker because there was no runway and
 no ship off shore so he would then know he had to fly only 38 NM
northwest to find Howland, and easy task.

See what Weems wrote about doing this landfall from his 1938 book :

http://www.fer3.com/arc/img/110778.weems-394-395.jpg

http://www.fer3.com/arc/img/110778.weems-396-397.jpg

Noonan could be expected to have known this technique since he knew
Weems and Chichester had popularized in 1931.

I will upload more reference works on this procedure.

gl