Landfall Procedure Navigation to Howland Island

Philip Van Horn Weems was a well respected authority on air celestial
. 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, (See: Weems, page 173) but other navigation
manuals, such as Air Force Manual AFM 51-40, use a 10% of the distance flown
accuracy standard as does Federal Aviation Regulations part 63 so I
will use the 10% accuracy standard for this explanation.

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 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 1723 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 49 minutes after civil
twilight at Howland and the Electra would have flown 236 nautical miles
in this time at 130 knots. Civil twilight occurred 17 minutes later 235
NM west of Howland so they could have obtained a fix using the stars and
the moon slightly later than 1723 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 accuracy 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  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.

(A more modern textbook "Air Navigation" published by the U. S. Navy
Hydrographic Office as PUB. No 216, (H.O. 216)1967 edition
page 184 and page 185 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 level of uncertainty, the accuracy would
still be 32 nautical miles plus the 10 mile original fix accuracy for an
uncertainty of 42 nautical miles at 1912 Z. Since Noonan was not inexperienced,
I will continue to use just the 10% accuracy standard.)

Looking at this uncertainty in the north-south direction and using the 10% level of uncertainty,
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 doubled this value up to an even 60 nautical miles for an extra safety margin. I will use this very conservative 60 NM value for illustrating
the landfall procedure.

There has been concern expressed that clouds could have prevented Noonan from taking star sights that late (1740 Z). Early in the flight they had reported flying at 10,000 feet so could have been at that altitude again later in the flight too, (or even higher since they were much lighter) which normally is above most clouds. Even if some clouds where higher than their altitude it is unlikely that they blocked the entire sky for hundreds of miles along the flight path.  Earhart reported at 1415 Z and again at 1515 Z "cloudy and overcast"  and 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, it is very probable that Noonan was able to take sights at about 1623 Z, only two hours and forty-nine minutes before the "must be on you" transmission at 1912 Z. At that point Noonan had a large selection of celestial bodies to shoot with his octant but, later on after sunrise, only two bodies would be available, the sun and the moon so it is possible that those objects might be blocked at least part of the time. Also, even though it is possible to take observation on the sun through a thin layer of clouds, even a thin layer prevents taking shots of the moon during daylight. Because or this, it is possible that Noonan was able to take sun shots to determine the the landfall LOP sun line through Howland but was prevented from taking observations of the moon to determine his distance north of Howland.. Almost directly in front of the plane (5° left of the nose) was the third brightest object in the sky, the planet Venus, and next to it (10° left of the nose) was the second brightest object in the sky, the Moon. Noonan didn't have to look for elusive stars darting between whatever clouds  existed at that point, it's hard not to see the moon! Because they were almost directly ahead, observations of these objects would have produced LOPs that ran approximately perpendicular to the course and so would have given them an accurate measure of the distance remaining to Howland. Off to the right, just 9° ahead of the right wingtip, was the 10th brightest star in the whole sky, Achernar. An observation of it would have produced an LOP approximately parallel to the course line and let them know if they were on course or how many miles they were off course, either to the right or to the left. In addition, there were five other, slightly dimmer, stars also positioned off to the right and left that would have also produced course line LOPs if Achernar happened to be hidden by a cloud at the moment. All of these objects were at heights that were convenient for observation. Crossing the LOP from the Moon (or Venus) with an LOP from one of the stars off to the side would have produced a fix with an uncertainty that should not have exceeded 10 NM. 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 only 36 NM.  We have to add to these estimates the original 10 NM uncertainty in a fix obtained at 1623 Z so the total is 46 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, 46 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. (I will use the very conservative 60 NM value of uncertainty for illustrating the landfall procedure.)

It is most likely that they had planned to use the radio as the primary, or preferred, method for finding Howland since it is easier to use and saves you the time and distance necessary for the landfall procedure. However, the celestial landfall procedure is accurate enough, by itself, to find Howland so was perfectly adequate as a backup, or secondary, method for completing the flight. When they failed to get the radio signals at the point that they had that expected to be able to receive them, they would have turned to commence the landfall procedure with the knowledge that if they did start receiving the radio signals they could abandon the landfall at that point and turn and follow the radio bearings directly to the island.
There is no other explanation for their report of being on the 157-337 line except that they were flying the landfall since that line has absolutely no relevance to any other approach. Using the landfall method of using a single sun line to find the island 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
(See:Single LOP Landfall procedure)

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
, 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
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, an easy task.

If he had aimed 60 NM northwest of Howland
then Baker provided an even larger safety margin, they would have to have been more
than 98 NM off course to the south at the point of intercepting the LOP
to actually pass south of Baker and so turn the wrong way, away from Howland.
In fact, with 20 NM visibility they would have had to pass 20 NM south of Baker
to miss it making the safety margin even greater since they would have had to have
been more than 118 NM off course to miss seeing Baker.

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

Weems pages 394 and 395

Weems pages 396 and 397

Noonan could be expected to have known this technique since he was a friend
Weems and contributed to Weems writings. This technique had well known since
Chichester had popularized it in 1931.

See also:

Navigator's Information File (1944)

Single LOP Landfall procedure

Precomputed altitude curves

Recent landfall approach evaluation of Noonan's method