And there is no way that they ended up in the Marshalls due to a navigational error because it was impossible to be that far off course. Let me say that again, it was
IMPOSSIBLE to be that far off course. I’m not saying that it was “unlikely” to be that far off
course and I am not saying that it was “highly unlikely” to be that far off course. I AM saying that
it was IMPOSSIBLE to be that far off course.
The generally accepted level of uncertainty for a position found by dead reckoning is 10% of the
distance flown since the last fix. This means that if Earhart and Noonan flew all the way from
Lae to Howland, 2556 SM, inside solid clouds without the opportunity to see any visual
landmarks or to take any celestial sights then it is highly unlikely that they were more than 255.6
SM away from Howland at 1912 Z. (Of course this is not a real scenario since Earhart wrote that
“Noonan must have star sights” so they would have turned around if they could not see the stars.)
Mili is 856 SM from Howland, more than three times the accepted level of uncertainty if they had DRed all the way.
But wait, we know that they had a fix at 0718 Z near Nikumanu Island and it is only 1700 SM
from there to Howland so the expected uncertainty would only be 170 SM so Mili was five times
further away than the accepted uncertainty. And then they saw the Ontario at 1030 Z which was
only 1270 SM from Howland making the uncertainty at 1912 Z only 127 SM so Mili was about
seven times further away than the accepted level of uncertainty. Then they passed Nauru at about
1130 Z and it is only 1143 SM from there to Howland, the uncertainty became 114 SM making
Mili 7.5 times further away. Then they flew over Tabituea which is only 613 SM from Howland
further reducing the dead reckoning uncertainty to only 61 SM. Since Mili is 856 SM from
Howand it is 14 times further away than any possible error in the dead reckoning.
You might say “but what if a strong wind came up and blew them far off course?” Well since it
would only take about five hours to fly from Tabituea to Howland, to be blown off course 856
SM in this time period would have required a wind out of the southeast blowing at 174 mph, you
would think that Itasca would have noticed such a strong wind.
I have attached two images showing the course line from Lae to Howland with turn offs toward
Mili at Ontario and at Tabituea. The course to Howland is 078̊. From Ontario to Mili is 800 SM
and the course is 036̊ meaning that Earhart would have had to make a left turn there of 42̊ in
order to head to Mili. From Tabituea to Mili is 550 SM and the course is 339̊ so Earhart would
have had to make a left turn there of 99̊ in order to head to Mili from there. Obviously they
never made any such turns.
But what if they arrived in the vicinity of Howland at 1912 Z, couldn’t find Howland so they
flew off to the northwest looking for an alternate landing site such as Mili? They didn’t have
enough gas on board to make it to make it to Mili, 856 SM away.
I have been a lawyer for a long time and almost all of my cases involved airplane crashes. Based
on my experience I have come to be distrustful of “eyewitness testimony.” Even if a witness is
trying to be truthful it doesn’t mean that they actually saw what they think they saw. I’ll give you
an example. A number of my cases involved airplane crashes involving fires with the wreckage
badly burned up. We would take the testimony of 3 or 4 and in one case 6 eyewitness who
testified under oath “I looked up and I saw the airplane on fire, fire was coming out of the front
of the plane!” According to those who like the capture theory such testimony from so many eye witnesses would
establish the fact that the plane was on fire while it was still up in the sky, case closed.
Well, not so fast. When a plane catches fire after it impacts the ground, the fire and smoke goes
upward, just like the fire in your fireplace. When a plane is on fire while in flight the smoke trails
back and deposits soot on the tail of the plane, no soot on the tail, no in-flight fire. All these
witnesses that testified
under oath that they saw a plane on fire up in the air were wrong. They
weren’t lying, they were just wrong. This is just a sample but when you take sworn testimony
many times you start to realize that eyewitness testimony is not all that reliable. And these
witnesses were testifying shortly after the accidents, not 60 years later.
If you produced a thousand eyewitnesses who testified under oath that a flying saucer landed,
little green men came out and forced Earhart and Noonan into the saucer and then they took off,
no jury would believe that story even with that many witnesses. Jurors weigh the testimony and
compare it to their common sense to decide if the testimony is correct and reject testimony that
doesn’t make sense. This is especially so when the testimony makes impossible claims, such as
Earhart landing in the Marshalls.
It is easy to reject the many conflicting statements about Earhart and Noonan’s capture and death
made many years after the events. There are so many conflicts in the statements that you must
reject a good portion of the statements, keeping only the statements that support your own
favorite theory. Well if so many statements can be rejected, then why can’t they all be rejected?
They were captured here, they were captured there. They were executed, they died of dysentery.
They were buried here, they were buried there, etc.
So no, I am not swayed by the witness statements that some are so fond of.
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_deviationGoing 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 1912 Z was 255 SM which is 2 S.D.s so one S.D was 128 SM.
To accidently arrive at the closest Japanese island, Mili, would mean the plane was 785 SM from its
D.R. position over Howland which is 6.1 Standard Deviations and this will happen in less than one
case out of 506,800,000! This means that the odds against this happening is more than 506,800,000
to one! And this is based on dead reckoning all the way from Lae without any fixes. Fixes determined
enroute would have made the resulting uncertainty at Howland smaller so the S.D. would have been smaller
making it even more unlikely than this 506 million to one that they ended up at Mili.
The most complete treatment of the statistics of navigational errors is in the American Practical Navigator, commonly known as "Bowditch," U.S. Navy Hydrographic Office Publication number 9 (H.O. 9) which is the standard navigational authority in the United States and has been since the first edition in 1802. The 1977 edition has "appendix Q" which is a 33 page discussion of this topic.
https://sites.google.com/site/fredienoonan/resources/american-practical-navigator-h-o-9/h09-1962-1.JPG?attredirects=0I was stating my "best case scenario" for those who believe in the MIli theory.
I only cited the odds up to 6 standard deviations, 506,800,000 to 1 since that covered the case of dead reckoning all the way from Lae ( which we know was not the case.) 10 % of the distance to Howland is 255 SM which is two standard deviations so one standard deviation is half of that, 128 SM. It is 856 SM from Howland to Mili which is six point seven (6.7) times the standard deviation for a complete dead reckoned flight from Lae to Howland.
We know they had a fix near Nukumano only 1700 SM from Howland making the standard deviation for the DR position over Howland 85 SM so it would be 10 S.D. to end up at Mili.
They had a fix over the Ontario leaving only a 1270 SM dead reckoning leg to Howland making the S.D. only 63 SM making Mili 13.5 standard deviations away.
Next they had a fix over or abeam Nauru leaving only a 1143 SM dead reckoning leg to Howland making the S.D. 57 SM making Mili 15 standard deviations away.
It was reported that they were heard flying over Tabituea which is only 613 SM from Howland making the S.D. 31 SM making Mili 28 standard deviations away.
Noonan would also have gotten a celestial fix at or after the radio report of "partially cloudy" at 4:53 Itasca time (1623 Z) leaving only 2 hours and 49 minutes (or less) until the 1912 Z report of "must be on you" over Howland. At 150 m.p.h. the plane would have flown 422 SM (or less) making the standard deviation only 21 SM and placing Mili 40 standard deviations (or more) away.
The highest odds I could find was for 7 standard deviations, see:
http://en.wikipedia.org/wiki/Standard_deviation(if you can find a table that shows the odds for more that 7 S.D. please point it out to me, I am quite interested.)
The probability of being seven standard deviations away is one chance in three hundred and ninety billion, seven hundred million (390,700,000,000) So based on any of these fixes, the probability of ending up at Mili would have been even much lower than this number. The likelihood of being forty standard deviations off course after the 1623 Z fix is astronomical. In fact, there is not any significant difference in the probability of Earhart ending up at Mili as her ending up on the Moon!
The probability of less than one chance in more than 390,700,000,000 meets the definition, in most peoples' minds, of "impossible."
gl