Navigation to Dakar


                

This is an examination of  Amelia Earhart’s navigation from Natal to Dakar near the beginning of her
flight around the world. Although this leg took place well before the flight from Lae to Howland,
it has been seen as relevant in unraveling the final mystery as it may shine light on the
interaction between Earhart and Noonan. But just like the rest of this story, the information
concerning the flight across the Atlantic is confusing, contradictory, incomplete and difficult to
interpret.

I obtained a copy of  the actual chart that Noonan used on the flight from Natal to Dakar. The
original is kept in the archives of Purdue University and I had the archivist scan it for me.
(TIGHAR sells a copy of what it claims is this chart but it IS NOT an accurate copy of the actual
chart, markings have been erased and, even more inexplicably, it has added markings and
notations, so its provenance is suspect.)


Earhart and Noonan departed Natal, Brazil at 0615 Z (Greenwich Mean Time) on June 7, 1937
for Dakar and landed thirteen hours and twelve minutes later at 1927 Z in Africa but at Saint
Louis, about 100 SM north of their planned destination of Dakar. ( Earhart wrote in her book, and
others have copied, that it was 163 miles between Dakar and St. Louis but it just so happens to
be 163 kilometers so Earhart apparently was confused about what she had been told about this distance
by someone in St. Louis or Dakar.)


Amelia explained it this way:

“When we first sighted the African coast, thick haze prevailed and for some time no position
sight had been possible. My navigator indicated that we should turn south. Had we done so, a
half hour would have brought us to Dakar. But a "left turn" seemed to me in order and after
fifty miles of flying along the coast, we found ourselves at St. Louis, Senegal.” (Last Flight, page
119)

A careful examination of the actual chart work that Noonan did on this flight might further
explain what actually happened. (I have also examined Noonan’s chart for the flight from
California to Hawaii so I am familiar with his navigation methods.)

I have attached a copy of the southwestern portion of “North Atlantic Ocean, Southeastern Sheet,
(1930)”, the marine chart used by Noonan. I have also attached a black and white large scale
printout of this chart on which I have made annotations. (See chart 1 and chart 2  and image 3.) This
chart starts at the equator. The first thing you notice on the chart is the preplanned course line
marked at hourly intervals, every 150 statute miles (SM) since the planned ground speed was
150 mph. The last mark is at the 1800 SM point at 12 hours. From this last mark to Dakar is 71
SM for a total of 1871 SM, making the estimated flight time twelve hours and 28 minutes and
the estimated time of arrival (ETA) 1843 Z. (Earhart’s clock was set to Natal time which was
three hours slow on GMT and her notes are in Natal time. I have converted them to GMT (Z)
which is the time used by Noonan for his notations on the chart. I also use nautical miles (NM) as
these are the miles used by Noonan and all navigators. A nautical mile is 15% longer than a
statute mile so the distance from Natal to Dakar is 1627 NM. Since navigators use nautical miles
for distances they also use knots for speeds, one knot being one nautical mile per hour. The
planned ground speed was 150 mph which is the same as 130.4 K (knots).)


The true (T) course runs 41̊. Parallel to the course line you find the notation “241̊ M — 61̊ M”
and further along “60̊ M.” This shows the magnetic (M) course for use with reference to the
magnetic compass and is the true course adjusted for the magnetic variation of 20̊ west for the
first part of the flight and 19̊ west for the final portion.

Further to the west is another line running 31̊ T (true), 051̊ M. On my annotated chart I have
attached an extension at the bottom so that I could plot the departure airport at Natal at 5̊ 54'
south, 35̊ 15' west. Noonan did the same thing as we can see the two lines already mentioned
run across the neat line onto the border and converge on Natal. You can see Noonan’s notation
next to the leftmost line of “410" which is the distance in NM from Natal to the equator along
this line. I added a similar notation for the course line which crosses the equator 470 NM from
Natal. (See image 3.)

Earhart wrote that they crossed the equator at 0950 Z (6:50 a.m. Natal time) in her notebook.
This was based on dead reckoning (DR, moving the position based on the course flown and the
distance covered) and we can determine that they believed they were following the course line and not the
leftmost line by this notebook entry. From takeoff to crossing the equator took 3:35 which at 130.4 K
means they had traveled 467 NM which is consistent with the 470 NM distance along the course line to
the equator. Had they been following the leftmost line it would only have been 410 NM and it would have taken
26 minutes less so Earhart would have written "6:24 Natal time" for crossing the equator in her
notebook (0924 Z.)

At 1237 Z Noonan measured the sun’s altitude with his Bendix bubble octant (a kind of a
sextant) through the cockpit windshield as the sun was almost directly in front of them and the
measured altitude was 65̊ 34'. After doing the appropriate computations, Noonan
drew a line of position (LOP) across the course line running 130̊ T - 310̊ T which was at right
angles to the azimuth of the sun which, at that time, was 040̊ T. (See image 4.) Although Noonan didn’t write
the time of this sight down on the chart, we know it was 1237 Z as it was at that time that the
azimuth of the sun was 040̊ T at that point on the course line. Any earlier and the azimuth
would have been greater, any later and the azimuth would have been less. (Contrary to what is
observed in the U. S., from their location the sun moved counter-clockwise across the sky.) The
LOP represented their most probable location, they should be somewhere along this line. This
LOP is 809 NM from Natal and the elapsed time was 6:22 so the ground speed had been 127 K
(146 mph.)

Since there is some uncertainty in celestial observations, the LOP is actually a band 14 NM
thick extending 7 NM on each side of the LOP. It is very unlikely that a sextant reading will
produce an LOP that is more than 7 NM in error so this band should contain virtually all possible
locations of the plane and the plane is actually most likely to be nearer the center than the edges.
However, this one LOP couldn’t give Noonan his exact location as they could have been
anywhere along it but he could put some bounds on this uncertainty. (This is no more
mysterious than your saying that you are somewhere on Second Avenue.) A generally accepted
rule, used by flight navigators, is that the uncertainty of a dead reckoned position increases as
10% of the distance covered since the last fix. They had flown 809 NM from Natal so the
uncertainty extends 80.9 NM along the LOP in each direction from the course line making the
LOP 162 NM long and 14 NM thick. I have indicated the extent of the uncertainty band on the
hi-liter tape. (See image 5.)

At 1341 Z Noonan took another observation of the sun, this time from the left side cabin
window. He measured 74̊ 52' with his octant. After computation, he drew an LOP
running 90̊ T - 270̊ T meaning the azimuth to the sun was straight north, within a couple of
minutes of noon. At this point Noonan had reason to believe that he was west of the course line
at a longitude of 25̊ 35' west. We know this because at 1341 Z the Greenwich Hour Angle
(GHA) of the sun, the same as its longitude, was 25̊ 35' (west), Noonan would have found this in his
Nautical Almanac. Only if the airplane’s position was at the same longitude as the sun would the
sun’s azimuth be straight north producing an LOP running straight east and west. If they were still on
the course line then noon would have occurred earlier at 1335 Z at a longitude 24̊ 05' west, about 90 NM
further east. Noonan most likely  had determined that they were to the left of course by measuring the
plane’s drift with his Mk 2  driftmeter. Similarly to the first LOP, this LOP was also 14 NM thick but was
200 NM long as  they were now about 1000 NM from the last fix, the departure airport of Natal. Noonan drew this
LOP and labeled it “1341" and extended it so that it crossed the course line and also the leftmost
line running at 31̊ T. (See image 6.) Since this LOP runs straight east and west it defines a
latitude of 7̊ 37' north. This LOP crosses the course line 1070 NM from Natal and also crosses
the leftmost line only 943 NM from Natal. We can make an estimate of where along the LOP the
plane was. Earhart wrote in her notebook that they were flying at 6,000 feet, that the temperature
was 60 ̊ F, and the indicated airspeed was 140 mph thus making their true airspeed 155 mph (135 K),
5 mph faster than their planned speed.The plane had been flying for 7:26 so if they were on the
leftmost line then their average ground speed had been 127 K (146 mph.) If they were following
the course line then their ground speed would have been 144 K (165 mph). Either speed is
reasonable, as a 10 mph headwind or tailwind would account for these ground speeds and
such a wind would not have been unusual. Noonan sent Earhart a note saying that they had
averaged 147 mph but also saying that they now had a tailwind so that doesn’t us help much
in resolving the actual track of the plane. (I have attached a copy of this note which is kept at
Purdue, see note 1.)

The note also said that by crossing the 1341 Z observation with the first observation that he had
determined that they were north of course, to the left of course. Noonan was talking about a
standard navigational method of advancing the earlier LOP to the time of the second LOP and
taking the point that they cross as a “running fix.” A normal “fix” is at the intersection of two
LOPs taken at the same time which is no different than stating that you are at the intersection of
First Avenue and Main Street. A running fix is the same as your friend calling you on his cell
phone and saying “I have been driving east on Main Street and I passed First Avenue about a
mile back.” so you can figure he is at about Second Avenue now. A running fix has more
uncertainty than a normal fix since the navigator must estimate the movement of the airplane
between the two observations and advance the earlier LOP as though it had been attached to the
plane. Any error in this estimate will result in a similar error in the running fix. This is where the
skill of the navigator is critical and why navigation is also an art and not entirely a science.

Even though Noonan said that crossing the two LOPs showed them to be to the left of course and
that they now had a tailwind, he did not actually do the chart work to do this but apparently just
used his experience to estimate where the running fix would have been. On my chart I have done
the chart work and have advanced the 1237 Z LOP along the course line (maintaining its
alignment) 139 NM, the distance that would have been covered by the plane at the flight planned
130 K speed for the 1:04 period between the two sights. The first LOP was originally 14 NM
thick but the uncertainty increases at a rate of 10% of the distance the LOP is moved adding an
additional 13.9 NM (call it 14 NM) to each side of the original band of uncertainty making the
band or uncertainty 42 NM thick after it is advanced. (The length also increases by the same
ratio but this is not important at this point.) The intersection of the 1341 Z LOP with the 1237 Z
advanced LOP marks the running fix and the overlap of their bands of uncertainty contains the
actual position of the aircraft. This area is 14 NM thick north to south (the uncertainty of the
1341 Z LOP) and extends 60 NM east and west (since the lines cross at an angle), constrained by
the overlap of the 1237 Z advanced LOP. (See image 7.) In image 8 I have removed the excess
length of the two LOPs leaving only the overlap which is the total area of uncertainty of the
running fix. (See image 8 and image 9.) A navigator takes the actual intersection of the LOPs as the
running fix and does not draw in the uncertainty bands but he keeps them in mind and knows
that they grow bigger as time goes on.

The normal procedure is to mark the running fix on the chart and then lay off the new course
from that point to the destination but Noonan didn’t do this, why? He may have had some doubts
about the accuracy of the earlier sight and the rest of his chart work supports this theory. If we
look where the two LOPs intersect the course line we see that the distance between these two
intersections is 261 NM. For the plane to travel up the course line and cover the distance
between the two LOPs in 1:04 would require a ground speed of 245 K meaning a tailwind of 115
K which is impossible. So one of the LOPs is probably in error and Noonan apparently decided
that it was the 1237 Z LOP. Noonan advances the 1341 Z LOP three times to determine running
fixes and DR positions but never actually advances the 1237 Z LOP.

The next thing we see on the chart is a circle at the north end of the leftmost line labeled “1017
mi from Natal” and the time of “1115 AM, 1415” which gives the Natal time and the
Greenwich Mean Time. From this point a line was drawn to Dakar on a course of 76̊ M (56̊
T), the heading that Noonan’s note instructed Earhart to turn to. So what did this all mean? The
leftmost line runs 31̊ T, exactly ten degrees to the left of the course line. What Noonan
was doing here is that he knew that they were drifting to the left of the course line but he also
knew that he had not drifted more than the ten degrees delineated by this line. He then knew that
if he assumed the worst case, that he was ten degrees off course to the left, and then figured the
course from that point directly to Dakar and with the plane actually being anywhere to the east or
south of the 1415 Z point, turning to the new computed course, 76̊ M, would guarantee that they
would intercept the coastline south of Dakar. The further chart work shows that this worked as
intended.


They flew on the course of 76̊ M and then at 1625 Z Noonan took another sun observation and
drew the resulting LOP on the chart. We know the time of this observation by the azimuth of the
line and by the distance on course that the plane traveled between this line and the same line
advanced to 1700 Z. If you extend the course line back from the 1700 Z position until in
intersects the 1625 Z line you will measure 78 NM and based on their ground speed this
would take about 35 minutes placing this earlier sun line and sun observation at about
1625 Z. He did not label this LOP. He then advanced the 1341 Z LOP to
intersect the new LOP and formed the 1625 Z running fix, which is not labeled.(See image 10.)
As before, the new LOP is 14 NM thick and runs 21̊ T since the azimuth of the sun was 291̊ T.
Since the 1341 Z LOP had been advanced for 2:44, a distance of 356 NM, the advanced 1341 Z
LOP would have gotten about 71 NM thicker making it a total of 85 NM thick and this is in the
north- south direction since this LOP itself ran east and west. I have shown the resulting area of
uncertainty on the chart.(See image 11.)These two LOPs were then advanced twice to make the
1700 Z and the 1800 Z running fixes or DR positions. The 1625 Z LOP advanced to 1800 Z runs
to St. Louis and nowhere near Dakar. (Elgin Long wrote that Noonan actually took sun sights at
1700 Z and 1800 Z but the azimuths would have been different if he had done so. Also, it was
not Noonan’s practice to take sights on the hour as there were no such sights taken on the much
longer flight to Hawaii.) The areas of uncertainty expanded each time these LOPs were advanced
and I have illustrated these areas of uncertainty. (See image 12 and  image 13.) (This is not an
important disagreement with Long. If Long is right then the thickness of the uncertainty bands
along the 1700 Z and 1800 Z LOPs were 14 NM instead of getting wider as I have shown. My
illustration shows the worst case. If Long is correct then these positions are running fixes, if I am
correct then they are actually DR positions) If you draw a line through these last three positions
on a bearing of 256̊ M (the reciprocal of 76̊ M ) you will see that it takes you back to the 1341
Z running fix. This shows that the plane was within the uncertainty area of the 1341 Z running
fix when the course was changed to 76̊ M. The plane was never at the 1415 Z circled position,
Noonan only used that point as a worst case and used it to calculate the course to follow that
would assure him that they would intercept the coast south of Dakar. (See image 14.) If this isn’t
clear, what Noonan was doing was a way to deliberately aim off (like at Howland) to the south to
assure that he didn’t pass to the north of Dakar. Had he measured the course from the 1341 Z
running fix to Dakar he would have found 68̊ M but by measuring from an arbitrary point 60
NM further north he found a course of 76̊ M, eight degrees further to the south, which would
then cause the plane to end up well south of Dakar.

Up to this point all we have seen is perfectly normal flight navigation as practiced by tens of
thousands of flight navigators during WW 2 and by additional thousands of B-52 navigators up
to the end of the Cold War, only twenty years ago. But from this point Noonan’s navigation
becomes strange. Looking at map 1 you can see that there had been a line parallel to and between
the 1700 Z and 1800 Z LOPs that ran to Dakar but this line had been erased. We can also see that
the 1800 Z LOP runs to St. Louis, not to Dakar. The 1800 Z running fix (or DR) is 110 NM
south of the coast and even the extreme northern limit of the band of uncertainty is still 47 NM
south of the coast so there is no possibility that the plane could have hit the coast north of Dakar as Earhart claimed.
From this position it is 215 NM to St. Louis and from the northern edge of the band of
uncertainty it is 152 NM to St. Louis. If they turned towards St. Louis at 1800 Z to travel along
the LOP on a true course of 21̊, which is a magnetic course of 40̊, they would have crossed the
coastline 37 NM to the east of Dakar and even if they were at the extreme western edge of the
band of uncertainty, which is unlikely, they would still have hit the coast 10 NM east of Dakar.
(If Elgin Long is correct, that Noonan took an observation of the sun at 1800 Z, then the width of
the band of uncertainty would be greatly reduced, so even from its western edge, they would
have hit the coast 30 NM east of Dakar.) (See image 15.) The course to Dakar from the 1800 Z
position is 21̊ M (002̊ T) and the distance is 120 NM. Even from the nearest edge of the band
of uncertainty it is still 65 NM to Dakar. Flying along the 1800 Z line, when they hit the coast
they could easily have followed the coast to Dakar if they had wanted to go to Dakar rather than St.
Louis.

We can also look at the final stage of the flight by starting at the other end, at the landing, this is
a hard data point. The plane touched down in St. Louis at 1927 Z, 1:27 after the 1800 Z running
fix (or DR). Cruising at 130 K for 1:27 means the plane would have covered only 188 NM so we
know the plane had to be within a circle of that radius, centered on St. Louis, by 1800 Z. From
the 1800 Z running fix (or DR) it was 215 NM to St. Louis but only 152 NM from the northern
edge of the uncertainty band so the plane would have been somewhere in the northern portion of
the band of uncertainty at 1800 Z.

Now it gets even stranger. Earhart produced a note from Noonan that she received in flight
telling her to turn to 36̊ M at 1836 Z (3:36 p.m. Natal time). (See note 2.) This magnetic
heading would have caused the plane to fly north- northeast, parallel to the 1800 Z line, which
ran 40̊ M, with an allowance of a 4̊ wind correction angle for a light wind out of the west. But,
since this turn would not have occurred until 36 minutes later, the plane would have traveled 78
NM further to the northeast prior to making the turn. There is no notation on the chart indicating
this 1836 Z DR position. I plotted it on my chart and it falls almost directly over the town of
Bathurst (now called Banjul.) The band of uncertainty at the 1836 Z DR position is a bit larger
than the 1800 Z band and they overlap. (See image 16.) But we can eliminate from this band of
uncertainty that portion that is over land since they would have seen the coastline below them.
(See image 17.) A turn from the 1836 Z position to a heading of 36̊ M would have taken them
into “deepest, darkest, Africa” and nowhere near either Dakar or St. Louis. (See image 18.) From
the 1836 Z position above Bathurst to St. Louis is 160 NM but the time remaining to landing
would have been only 51 minutes so the plane would have had to fly at 188 K to make it, so we
know the plane was not at that position at that time. At its 130 K cruising speed the plane could
only cover 110 NM in 51 minutes. From the nearest edge of the band of uncertainty it was only
80 NM so the plane could have been in the northern section at 1836 Z. But Dakar was only 95
NM from the 1836 Z position so it would have been quicker and easier for them to just follow
the coastline there and it was even closer with the plane in the northern sector.

Just flying on a heading of 36̊ M was not likely to take them directly to St. Louis and might
have gotten them lost in the jungle. To avoid this possibility, and to ensure that they found St.
Louis, all they had to do was turn to a heading of about 345̊ T (004̊ M) as soon as they saw the
coast. This heading would have worked no matter where exactly they hit the coast, after turning
at 1800 Z or at 1836 Z. This heading would have taken them across the Cape Verde peninsula to
intercept the coastline between Dakar and St. Louis and would have guaranteed that they did not
overshoot St. Louis. Earhart said that they hit the coastline between Dakar and St. Louis and I
believe her, only they hit it coming from the land side, not coming in from over the ocean. Then,
like she said, they followed the shoreline to St. Louis, as planned. (See image 19.)


Of course the reason the Dakar story had relevance to the final disappearance is that it offered an
explanation for why they were unable to find Howland. It seemed possible, at the end, that
Earhart refused, as she said she had done on the approach to Dakar, to follow Noonan's advice on the
heading to follow that would have taken them the Howland.

I have attached a portion of aeronautical chart ONC K-0 depicting Dakar and St. Louis which I
think will be of interest. (See  chart 3.)

When I first heard the "I turned the wrong way when hitting the coast of Africa" story, I assumed
that the coast, at that point, ran in a straight line so that AE could reasonably question which side
of Dakar they were actually on. Now however, looking at this chart, it is impossible to believe
that story. The coast north of Dakar trends 040º T while south it trends 320º T, a difference of
80º, almost a right angle. All she had to do was point the plane along the shoreline and look at
her compass. If it said about 040º she was north of Dakar and if about 320º she was south.
No way to mistake this, there was no possible ambiguity. To make it even
simpler, the sun was setting in the west. If they had hit the coast north of Dakar then they should
have followed the coast to the southwest. If they had hit the coast south of Dakar then they
should have followed the coast to the northwest. Either way, if the sun was not in their eyes then
they were going the wrong way, didn’t even need a compass.

I think, for whatever reason (maybe better service available from the Air France facility,
personal contacts, etc.), they made a conscious decision to go to St. Louis and crossed the
coastline southeast of Dakar and proceeded overland to intercept the coast north of Dakar and
followed it to St. Louis. AE writes in "Last Flight"(page 119.)

"At St. Louis are the headquarters of Air France for the trans-Atlantic service, and I was grateful
for the field's excellent facilities, which were placed at my disposal."

Elgin Long thinks that they aimed directly for Dakar and that they passed west of Dakar and then
turned east and hit the coast north of there as Earhart said but there is a problem with his theory,
namely the 1800 Z LOP which showed that they had already passed the point where turning to
the heading Noonan had recommenced would have taken them to Dakar, and Noonan wanted her
to proceed even further to the northeast for another 36 minutes, 78 NM, prior to making the
turn. Most significantly, to the question of whether they accidentally missed Dakar, you can see
on Noonan’s chart that there had been a sun line that ran to Dakar on an a 21º T course but this
line was erased (but still visible) and the sun line was advanced to 1800 Z to run to Saint Louis.
This confirms that they deliberately hit the coast south east of Dakar and then deliberately flew to
Saint Louis. It's no coincidence that the 1800 Z sun line runs directly to Saint Louis. and that the
parallel line to Dakar had been erased. Long also recognized that Earhart's story could not be
believed due the the shape of the coast line and  stated that even though they knew
they were flying the wrong way, that Earhart knew that there were other airports every 150 SM
along the coast that she could go to. Even if this were true, they also had to know, based on their
navigation, that the nearest airport to them should be Dakar, it might be only ten miles to the
southwest while St. Louis could have been 90 miles northeast. Long also incorrectly claims that there
were no airports south of Dakar that they could have landed at if, by turning to the south, they were
actually going the wrong way. In 1934 an airport had been built at Bathurst that was actually closer
to Dakar than St. Louis was and by 1937 was in use for scheduled trans-Atlantic airline flights to
Rio de Janeiro. The 1836 Z position put them directly over Bathurst (Banjul) or very nearby.
(See St. Louis to Bathurst.)

Ric Gillespie agrees with me that they struck the coast southeast of Dakar (but his chart work
is wrong) but he then comes up with an explanation that doesn't make sense for their failure to
simply follow the coastline northwest to Dakar. Gillespie claims that flying into the sun in hazy
conditions would have made it too difficult to follow the coastline. Gillespie is wrong because
the easiest thing to do in hazy conditions is to follow a coastline! Flying into the sun in hazy
conditions limits visibility and pilots don’t like to do it, not because it would be difficult to
follow the coastline but because of concern about bumping into another airplane. There were not
very many airplanes flying near Dakar in 1937!

Earhart’s explanation was a complete fairytale, it never happened, and it is possible that note 2
was just a fabrication to support the fairytale since it makes no navigational sense.

As further proof that any competent navigator would have planned to hit the coast to the southeast of
Dakar, the Air Force navigation manual, AFM 51-40, uses this exact flight from Natal to Dakar
as the example of how to plan such a flight. (I have attached an excerpt from this manual, see
AFM-51-40..)

We may never know the real reason that they chose to go to St. Louis but it was an obvious
decision that they had made to fly overland to St. Louis instead of following the coast to Dakar.

The bottom line is that the Dakar flight provides no help in explaining
the final disappearance.

A further analysis of Noonan’s navigation makes it even more certain that they planned to land at
Saint Louis and not Dakar. I showed the areas of uncertainty before around Noonan’s
fixes but I didn’t elaborate on what these represented. As a plane flies along its course, the
possibility of wandering further and further off course increases as the distance flown increases.
It is generally accepted that you are very unlikely to be off course more than 10% of the distance
flown and, even then, it is rare that you would be even that much off course and that you are
much more likely to be near where you think you are, your DR position, than near the edge of the
area of uncertainty.

What is important in the analysis of the Dakar story is just the deviation north of course. The
only information that Noonan had concerning his position north and south was the 1341 Z sun
line LOP. The initial band of uncertainty was 7 NM meaning that it was possible that he was
7 NM north (or south) of this LOP but he was more likely to be much closer to the LOP and
unlikely that he was even 7 NM away. As they flew on towards Africa the width of the band of
uncertainty increased at the rate of 13 knots (13 NM per hour,) 10% of the distance flown each hour. The
first running fix after this was at 1625 Z, 2:43 later. Cruising at 130 K (150 mph) the plane had
flown 354 NM in this period so the band of uncertainty grew by 10% of this distance, about 35
NM, which we add to the original uncertainty of 7 NM making the band extend 42 NM north and
south of the running fix at 1625 Z which is what I illustrated on my chart. Doing the same
computations, the band extended 50 NM at 1700 Z; 63 NM at 1800 Z; and 71 NM at 1836 Z, all
of which I have shown on my chart.

Amelia said:

“When we first sighted the African coast, thick haze prevailed and for some time no position
sight had been possible. My navigator indicated that we should turn south. Had we done so, a
half hour would have brought us to Dakar. But a "left turn" seemed to me in order and after
fifty miles of flying along the coast, we found ourselves at St. Louis, Senegal.” (Last Flight, page
119)

We know that she landed a 1927 Z and that they were cruising at 150 mph (130 K.) To cover the
fifty miles up the coast that Earhart claimed would have taken twenty minutes meaning that they
were at the coastline at least twenty minutes before landing, but probably about 25 minutes to
allow for flying the landing pattern, so they hit the coast at about 1902 Z, according to Earhart.
Doing the same computation as before, the band of uncertainty extended 77 NM north of
Noonan’s plotted position at 1902 Z.

Most of us have heard of standard deviation and this is the concept governing the uncertainty of
dead reckoning. We can consider that the band of uncertainty contains about 95% of the possible
actual positions of the aircraft so there is only a about a 5% chance that you would be outside the
band. In standard deviation terms, 95% equals 2 standard deviations meaning that one standard
deviation was only half of the band of uncertainty. As you exceed this distance the probability
that you are further away decreases very quickly. In 1 case out of a 21 you will be beyond 2
S.D.s; in 1 case out of 370 will you be more than 3 S.D.s ; in 1 case out of 15,787 will you be
further out than 4 S.D.s; in 1 case out of 1,744,278 will you be out 5 S.D.s; and in only 1 case
out of 506,800,000 will you be out more than 6 S.D.s.

See: http://en.wikipedia.org/wiki/Standard_deviation

Going the other way, 68% of the time you will be within half of the uncertainty band, at 1 S.D.,
of the DR position which means that only about 32% of the time will you be in the outer one-half
of the error band. The uncertainty at 1902 Z of 77 NM was 2 S.D.s so one S.D was 38.5 NM.

I have attached another image showing where Earhart claims that she hit the shoreline.(See image 20.) This is
about 210 SM (180 NM) north of where Noonan’s chart work showed them to be. The error of
180 NM divided by the S.D. of 38.5 NM means that the spot Earhart claimed was 4.7 standard
deviations from Noonan’s position. The probability of being this far off course is less than one
chance in a million!

But what if they had unusual winds or the plane flew at a different speed than planned or Earhart
didn’t stay on the correct heading? Well all those things were taken into account when figuring
the band of uncertainty so none of those things change the conclusion that there was less than one
chance in a million that they hit the coast like Earhart said they did based on a review of
Noonan’s chart work.


If the math isn’t convincing then lets look at it with just common sense. Noonan had just missed
his landfall on the continent of Africa by more than two hundred miles and now Earhart was
going to have him navigate her to a one mile long island in the middle of the Pacific. As my kid
would say, “I don’t think so!”


Č
Ċ
Gary LaPook,
Mar 8, 2011, 12:59 AM
ą
Chart1.jpg
(2886k)
Gary LaPook,
Mar 8, 2011, 12:58 AM
ą
Chart2.jpg
(680k)
Gary LaPook,
Mar 8, 2011, 12:59 AM
Ċ
Chart3.pdf
(1227k)
Gary LaPook,
Mar 8, 2011, 12:59 AM
ą
IMG_10.JPG
(288k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
IMG_11.JPG
(317k)
Gary LaPook,
Mar 8, 2011, 1:04 AM
ą
IMG_12.JPG
(344k)
Gary LaPook,
Mar 8, 2011, 1:04 AM
ą
IMG_13.JPG
(294k)
Gary LaPook,
Mar 8, 2011, 1:04 AM
ą
IMG_14.JPG
(268k)
Gary LaPook,
Mar 8, 2011, 1:04 AM
ą
IMG_15.JPG
(336k)
Gary LaPook,
Mar 8, 2011, 1:52 AM
ą
IMG_16.JPG
(268k)
Gary LaPook,
Mar 8, 2011, 1:05 AM
ą
IMG_17.JPG
(367k)
Gary LaPook,
Mar 8, 2011, 1:05 AM
ą
IMG_18.JPG
(368k)
Gary LaPook,
Mar 8, 2011, 1:05 AM
ą
IMG_19.JPG
(355k)
Gary LaPook,
Mar 8, 2011, 1:05 AM
ą
IMG_20.JPG
(319k)
Gary LaPook,
Mar 8, 2011, 1:06 AM
ą
IMG_3.JPG
(197k)
Gary LaPook,
Mar 8, 2011, 1:02 AM
ą
IMG_4.JPG
(232k)
Gary LaPook,
Mar 8, 2011, 1:02 AM
ą
IMG_5.JPG
(265k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
IMG_6.JPG
(238k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
IMG_7.JPG
(292k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
IMG_8.JPG
(293k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
IMG_9.JPG
(271k)
Gary LaPook,
Mar 8, 2011, 1:03 AM
ą
Note1.jpg
(38k)
Gary LaPook,
Mar 8, 2011, 1:00 AM
ą
Note2.jpg
(29k)
Gary LaPook,
Mar 8, 2011, 1:01 AM
ą
Gary LaPook,
Mar 8, 2011, 1:00 AM
Comments