Fire Cloud...
An irregular marking on the exterior of Native American pottery: usually resulting from burning fuel coming in direct contact with the vessel during firing

Tuesday, 28 March 2017

Amelia Earhart - Death by Parallax?

Whatever happened to Amelia in 1937. I have my own unprovable theory. Parallax killed her and her navigator, Fred Noonan.

Amelia Earhart's disappearance on 2 July, 1937 has been the subject of much speculation over the years, with theories ranging from the plausible to the wildly fantastic. Here is a look at a reasonable explanation of why Earhart and navigator Fred Noonan failed to reach Howland Island on that fateful day(1).

Understanding Parallax-Human 'Depth Perception'

Parallax allows us to estimate the distance of objects that we can see. Hold up a finger approximately three inches in front of your nose and look at it closely. Then close first your left eye and then your right. Repeat this rapidly. Notice how your finger rapidly moves (or appears to move) from right to left, depending on which eye you use to observe the finger. Our brains deftly integrate information received from the parallax of our two eyes, and this allows us to estimate distances to objects. Parallax is therefore very useful in surviving on the motorway, picking fruit, playing games involving balls and in numerous other ways.

Stellar Parallax

Stellar parallax is another use of parallax and was an early method of estimating the distance of nearby stars. In this case, the angles for a nearby star are measured six months apart while the Earth is on opposite sides of its orbit. This parallax error defines a parsec (2), which is one second of arc and a little over three light years. This method of measuring stellar distances is useful for up to about 11 parsecs.

Photographic Parallax Errors

Here parallax begins to reveal its darker side. We find that what the observer views through the eyepiece may not exactly correspond to the size and dimension of the image that will end up traveling though the lens and falling upon the camera's film. This type of parallax error may be most noticeable on close-up photography when the viewfinder and lens of the cameras are on different lines of sight. Better cameras provide help with parallax correction features, which may be as simple as a visual box in the viewfinder indicating the size and shape of the eventual photographic image.

Geocentric Parallax Errors

Geocentric parallax can have fatal consequences for the unwary traveler. An adjustment is required to compensate for a false apparent angle between a celestial body and a human observer. The moon's observed altitude angle is usually misleading due to parallax because the moon is very close to the Earth. The sun and the stars do not require a correction because they are so far away that the parallax error approaches total insignificance. Failing to apply the parallax correction to celestial navigation observations can result in a really bad sun/moon fix or just a wildly incorrect speed-line or course-line(3) from the moon alone.

The amount of the celestial parallax error is at a minimum when the moon passes through the meridian and is also directly overhead (ie, on the same latitude as the observer). The amount of the parallax error can be as much as much as 60 minutes (4) (60 nautical miles or about 69.046767 English miles) when the moon is near the observer's horizon.

A 60-mile error on the moon observation can become a much greater error in determining your position on the Earth if the moon and a second body being observed have lines of position that cross at other than a 90-degree angle, which is almost always the case.

To get a picture of how it works, think of an observer on the equator, and the sun and the moon both circling about the equator on one of the equinox days. The moon rises exactly in the east and passes directly overhead to set in the west. The sun follows the same path. We will ignore the sun's insignificant parallax, due to its greater distance from the Earth. However, the moon can have an error in the observed altitude angle of approximately one degree (60 nautical miles) on the horizon. There is no geocentric parallax error at all when the moon is directly overhead and the observer is on a direct line between the moon and the Earth's centre.

The need for the parallax correction arises because navigation tables compute the altitude angle of the moon based on an angle between the celestial body and the exact centre of the Earth. The navigator/observer is hopefully somewhere else and on (or above) the surface of the Earth, so there will always be an 'error' in the observed angle of nearby bodies (ie, the moon) unless the body is conveniently passing exactly over the observer's head. The amount of the error can be computed from a table which is provided to all navigators who have not yet transitioned to the use of the infinitely more convenient and inexpensive handheld GPS devices.

My Own Experience with Geocentric Parallax

In 1966, as we prepared for a 4.00am local time take off from Wake Island, heading to Guam, the pre-flight revealed that our APN-9 LORAN(5) was broken. The APN-9 LORAN is perhaps good for 150 miles near an island under ideal conditions, but that can be critical if one is looking for an island from an 8,000 foot altitude. Islands usually pop into sight about 30 miles out. The LORAN is the somewhat inappropriately named 'Long range Over water Aid to Navigation'. In 1966 the 'Long' part of the name was certainly optimistic.
I told the pilot not to worry, since this would be an ideal day for celestial navigation without the APN-9 and both the sun and the moon would be up. My first sun/moon fix about three hours after takeoff placed us 75 nautical miles off track. I checked the drift meter and saw none of the whitecaps which might have indicated a strong but unanticipated crosswind. There was no evidence of a compass malfunction because both the autopilot's gyroscopic compass and whiskey compass agreed, so I concluded that there must be an error in my celestial LOPs from the sun and moon and we continued to 'dead reckon' and head in the original planned direction.

All of my measurements for the next four hours showed us being about 75 miles off course. I decided to ignore them. I was eventually glad to see the island, exactly dead ahead and about 20 miles out, rather than open ocean. I remembered much later that day after privately reviewing my manuals that the moon is so close to the Earth that it needs a special correction called the parallax correction. On this day, the parallax correction makes for a 75-mile mistake.

Amelia Earhart and Parallax

Amelia's navigator, Fred Noonan (6), should have been relying on sun/moon celestial 'fixes' during the last hours of the 2,556 statute mile flight to (or toward) Howland Island on 2 July, 1937.

Amelia and Fred had been flying though the night toward dawn (7). Fred should have had good celestial observations from stars and later the sun and moon (8).The sun rose near Howland 6.10am local time (Howland had an 11.5 hour time difference from GMT), about two hours before Amelia was due at (and still about 300 miles away from) Howland. The last quarter-moon rose at 12.18am. The moon transited overhead and about 20 degrees to the south at 7.01am and set at 12.43pm local time. Fred would certainly have used both the sun and moon (9). Both celestial bodies were available, it was an historic flight, the first of its type, and Fred would not have ignored the moon in the early daylight morning hours almost directly overhead (and to the south) or the sun rising in the east nearly dead ahead while making the final three-hour run into Howland. Fred probably got a several final fixes that morning using both bodies.

As Fred and Amelia approached Howland island after a gruelling 21-hour flight from Lae City in New Guinea, her last words indicated that she was at 1,000 feet (one explanation for flying that low would be to get under the scattered cumulus clouds while searching for a small island)(10) and running on a line (157-337) north and south. This researcher's theory is that Fred, clouds permitting, would have had a shot at the sun in the east and the moon in the south and would have been able to get a set of perfectly crossed lines of position any time after sunrise from those two bodies. However, Fred would have been relying on the moon for the course line and parallax error could have caused him to veer off course enough to miss the island by a fairly large margin. It is certain that, as Fred approached where he thought Howland should be, heading east, he failed to see the island appear where his sun/moon observation and dead reckoning indicated that it should be. Fred must have logically assumed that they had missed the island to the north or south. Amelia then began her run on a line 'north and south' hoping Howland would come into view.

The Electra used by Amelia had a speed of about 150 MPH and an endurance about 24 hours(11). The flight from Lae to Howland was 2,556 miles. In this researcher's view, it is totally improbable that Amelia would have agreed to add over six hours(12) to the flight by diverting to over-fly Truk to make clandestine photographs of Japanese military installations for the American military, as some conspiracy theory enthusiasts have suggested(13).

While she was alive, she was celebrated for what she accomplished and for what her example meant to women and aviation. Once she was presumed missing, Amelia Earhart the role model for women was increasingly replaced by Amelia Earhart the lost aviator, and attention was shifted away from her strongly articulated feminism to speculation about the circumstances of her fateful last flight.
- Susan Ware, Amelia Earhart and the Search for Modern Feminism, 1993, p206

Earhart's Electra had a new radio direction finder but Amelia was not trained on the use of the new RDF and failed to use it effectively. Her additional inability to receive voice messages may have been caused by damage on takeoff.Here is a link to a takeoff video, which may show the belly mounted voice antenna breaking off on takeoff. These critical problems, combined with the scattered cloud cover, low cloud bases, very small island, sun in the eyes, possibly inaccurate charts, lack of an alternate landing site, crew exhaustion, a possible hangover (14), an inadequate fuel reserve, no autopilot to maintain a consistent track. (15) and Fred's possible parallax correction error, certainly resulted in enough cumulative issues to kill the crew several times over.

Research Footnotes

1 The Executive Director of TIGHAR, which has expended great energy on this investigation, states: "That parallax was a causal, or at least contributing, factor in the Earhart disappearance is an interesting but, unfortunately, untestable hypothesis. The same could be said for any number of theories about observational or computational errors that Noonan could have made. The indisputable fact would seem to be that an error or errors of some kind were made."

2 A parsec is a unit of astronomical length based on the distance from Earth at which stellar parallax is one second of arc and equal to 3.258 light-years, 30,860,000,000,000 kilometres, or 19,180,000,000,000 miles. Assuming that a highly modified Pontiac is good for 100,000 miles of travel, it will require about 200 million Pontiacs to drive one parsec and the driver will still be a light year short of the nearest star.

3 American Captain Thomas H Sumner invented the concept of a celestial line of position, while bobbing about in intermittent fog and very rough seas in the St George channel between Ireland and Wales in 1837. The new concept conveniently occurred to him in a flash of genius and allowed him to head into port in terrible conditions. Some experts wonder why it took so long for humans to discover this simple trick and put it to work.

4 The nautical mile is a result of the size of the Earth. By convention, the Earth is divided into 180 degrees from pole to pole. Each degree is divided into 60 minutes and a minute is a nautical mile.

5 LORAN was invented by British boffins. The APN-9 was introduced into American B-29 bombers during the war. The APN-9 was still being used on some older USAF cargo aircraft in 1966 during the Vietnam conflict.

6 Mary S Lovell, the Sound of Wings (1989, p272) indicates that Fred was an almost pedantic navigator who planned the Lae takeoff at 00:00 GMT for ease of celestial calculations. However, some believe that the 00.00 GMT takeoff only a coincidence since it had been rescheduled several times due to an inability to get an accurate time check. Lovell states that Fred three chronometers on the flight. However, Lae maintenance records indicate that there might only have been one (three seconds slow upon time check).

7 The Lockheed Electra model 10E departed Lae at precisely 10.00am local on 2 July, 1937. It crossed the international dateline and made its last transmission two time zones and one day earlier at 8.42am, also on 2 July, 1937. If they had been heading East to West, 2 July would never have happened for them on many levels, in this researcher's opinion.
8 Reports from Howland Island indicate that there were fairly normal weather conditions. Scattered cumulus with bases at about 2,300 feet. The Itasca Commander wrote the following summary of radio log transmissions from Amelia at 2.45am local: '...cloudy and overcast.' Again at 3.45am: '..Earhart to Itasca, overcast.' However, the actual radio logs do not indicate the word overcast.

9 My own 1938 edition of Bowditch's American Practical Navigator states that 'Many times during daylight a position line with the moon makes an excellent cut with the sun' (p. 212). Page 384 contains the parallax correction tables. Did Fred refer to them?

10 The Itasca's Captain to concluded that Amelia would have seen Baker Island if she was off to the southeast so he began his search to the northwest of Howland.

11 The TIGHAR Executive Director states: 'Earhart flight-planned the airplane at 150 mph and its expected endurance with the 1,100 US gallon fuel load it had upon departure from Lae was a little over 24 hours (computed according to Lockheed Report No. 487 "Range Study of Lockheed Electra Bimotor Airplane" by C.L. Johnson and W.C. Nelson, dated June 4, 1936).'..

12 The total distance From Lae City to Truk to Howland island is 3,250 statute miles, compared with 2,556 statute miles when flying direct from Lae.

13 Randall Brink, Lost Star: The Search for Amelia Earhart, 1994, suggests that Amelia's Electra was heavily modified by Clarence L (Kelly) Johnson in the Lockheed 'skunkworks' to add speed, altitude and range. (The Lockheed 'skunkworks' is generally credited with producing numerous high-performance aircraft, including the U-2, the SR-71 'Blackbird' and F 117 stealth fighter.) He suggests that Amelia was captured by the Japanese and became one of the voices of Tokyo Rose, a rumour which circulated among Pacific theatre Gls in 1943. A disturbing picture in his book shows an emaciated woman who appears to be Amelia. Brink claims the photograph was taken by a Saipan native in 1937. He also quotes workmen at Lockheed who claim to have installed high-resolution military cameras on the Electra.

14 Mary S Lovell, The Sound of Wings, 1989, p270, describes a petulant drinking binge by Fred in Lae. However, the Executive Director of TIGHAR states that there is no historical evidence to support Fred drinking on Lae or elsewhere. He believes that Lovell's comments are based on a single interview decades later. My own experience was that pilots and navigators of my day often drank to excess.

15 Amelia was able to leave her seat during the long flight but sometimes passed notes to Fred using an improvised bamboo fishing rod when he was in the rear navigator's compartment. The Electra had an autopilot and Fred was also a pilot who spent much of his time in the copilots chair. They were both able to climb over interior fuel tanks to reach a rear lavatory, in case you were wondering.


  1. Gary LaPook writes:

    Some of the basic navigation is wrong. First it states that the moon passed 20º south of Howland at 7:01 am (1831Z) when, in fact the moon passed NORTH of Howland at 1837Z and its altitude was 76º 56' at that point since its declination was 13º52' North.

    The horizontal parallax of the moon at that time was 59.2' from the above almanac page. But that parallax is only if the altitude of the moon was horizontal or zero degrees. To find the correction that must be applied to the sextant altitude you must multiply the horizontal parallax by the cosine of the altitude. When you do this you find that the error in omitting the "parallax in altitude" correction only comes to 13.4' which is the same as 13.4 nautical miles. Also, if Noonan had omitted this correction then the plane would have been 13.4 NM north of where he thought it was so it would have been able to find Howland by following the sunline on a heading of 157 T.

    At the time of their last transmission at 1912 Z the altitude of the moon was 75º 41' so the P in A correction was still only 15.1' or 15.1 NM and the azimuth of the moon was 328º T so omitting the correction would still place them north of the island.

    However it is very unlikely that Noonan could have made this mistake since the navigation table he was using, HO 208, Dreisenstok, has the "MOON" correction table on the very first page, just inside the cover, and this table incorporates the parallax in altitude correction with the refraction correction. Adjacent to this table, and on the same page, is the table for "Sun or Star" which only has the refraction correction. These very same tables are also found in all the commonly available tables of the time including HO 211 and the Weems Line of Position Book going back at least as far as 1927. This table does not incorporate a correction for semi diameter since it is for use with a bubble sextant such as Noonan was using.

    BTW, the horizontal parallax is calculated by taking the arc sin of ( the radius of the earth, 3440 NM, divided by the distance to the moon.) Since this distance varies during the month from 196,164 NM to 218,954 NM the H.P. varies from 60' down to 54'.

  2. How did you manage to get a 75 NM error by not applying the P in A correction since the magnitude of HP maxes out at 60' and that for zero degree sights? Even with a bad cut I don't see how that ocurred.


  3. Here is link to the 1937 Nautical Almanac:

  4. Hi Gary,

    Thanks for the comments. I know that you have also discussed this theory on the TIGHAR site.

    Are you the same Gary J. Lapook who is also an attorney in California? How did you learn about celestial navigation? I suspect that you are more or less right in your facts.

    Let's stipulate that the Parallax error was only 13 miles. Have you plotted the sun/moon cut to see how far that might have put them off course? I think, even with otherwise zero error sun/moon LOPs (highly unlikely), the distance off track might be considerable.

    One would suspect that Fred would have aimed off to the North or South of Howland and then turned left or right to follow the sunline 157-337. An error putting them on the wrong side of the island would not have been good.

    Thanks for your comments. It's been 45 years since I've done any serious navigation. I'd be interested in how that plots out (my tools and maps are long gone).

    You might also throw in a nine NM error on each of the accurate LOPs and see what kind of possible circular error you get on what must have been Fred's last fix.


  5. Because the course approaching the island was not exactly at a right angle to the 157-337 sun line LOP and the fact that the sun's azimuth was rotating counterclockwise it makes sense that Noonan would have intercepted north of Howland. The importance of the moon line is that it would also place them north of Howland if the parallax correction had been omitted. Since they would have been following the sun line to the southeast the moon line would ensure that they did not continue to fly 350 NM to the southeast to Nikumoro expecting to find Howland.

    As to your other question, I just tell people that I play piano in a whorehouse : )

  6. From my previous TIGHAR post:

    The "cut" of the LOPs derived at Howland Island on July 2, 1937 for the sun and
    moon lines varied between 59 degrees at 1830 Z to 125 degrees at 2100 Z and
    back down to 69 degrees at 2400 Z which would provide acceptable "cuts" for
    accurate celestial fixes at anytime during that period. These cuts were not all
    the prefect 90 degrees but all are well above the minimum 15 degree cut stated
    in "Weems" 1938 edition on page 281.

    There has previously been a concern stated that the moon was too high in the
    sky to be measured with the sextant as it was above 75 degrees when they
    arrived in the vicinity of Howland. However, by 1945 Z its altitude was below
    70 degrees and got progressively lower as the day progressed while the altitude
    of the sun got higher. Both of their altitudes stayed below 70 degrees between
    1945 Z and 2400 Z (presumably the tanks dry point); both were below 65 degrees
    2015 Z through 2300 Z; below 60 Degrees 2030-2230 Z; and below 55 degrees
    2100-2200 Z.

    The only time of the day on July 2, 1937 in the vicinity of Howland that a moon
    shot would have produced a 157-337 LOP was between 1620 and 1626 Zulu or 0450 and

    0456 Itasca time well before the arrival of NR16020 in that vicinity. This makes

    it very unlikely that AE was referring to a moon LOP.

    It is not difficult to take an altitude of 70º through a flat plate
    especially with the type of sextant (A-7 or similar) that Noonan was
    supposed to be using because the index prism is way out in the front of
    the instrument. The center of the prism is only 1.5 inches back from
    the front of the instrument which can be placed up next to the window.
    Since the Tan of 70º is 2.8 the window only needs to be 2.8 times 1.5
    inches or 4.2 inches high to allow such a sight. Refraction is not a
    problem at any altitude with an optically flat window with both
    surfaces parallel.


    In addition, the sun shots he took on the Dakar leg had an altitude
    of about 74º so we know he could take such high altitude shots with the
    equipment he had and in the same aircraft.

  7. Gary, you state that: "Since they would have been following the sun line to the southeast the moon line would ensure that they did not continue to fly 350 NM to the southeast to Nikumoro expecting to find Howland."

    That makes a lot of sense. If the sun and moon were both available, and they were, certainly Fred would have used both. Why then WOULD he fly 350 miles past Howland to Nikumoro? Wouldn't it make more sense to look for Howland based on one or more sun/moon fixes? Interesting that you take that position considering the Tighar searches...

    My little slice of navigation in the 1965-1968 era didn't have any issues with high altitude observations. I was able to get a three-LOP fix off the sun one day between Wake Island and Oahu when the sun passed directly overhead on my latitude. It was a perfect triangle with observations at 11:56, 12:00 and 12:04 local time....obviously high altitude ...