I published this originally as a submission to BBC's quirky site "Hitchiker's Guide to the Galaxy". I'm transferring it here to my blog which permits a little more latitude in adding pictures, links and new research.
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 was broken-note 5. The APN-9 LORAN was 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. After the first electric shock of confused panic subsided, I checked the drift meter and saw none of the whitecaps which might have indicated a strong but unanticipated typhoon force crosswind. There was no evidence of a compass malfunction because both the autopilot's gyroscopic compass and whiskey compass still agreed, so I concluded that there must be a gross error in my celestial LOPs from the sun and moon.
We continued to 'dead reckon' and head in the original planned direction.
All of my frantically rechecked measurements and caculations for the next four hours showed us being about 75 miles off course. I decided to ignore them. Eventually we saw 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 made for a 75 nautical mile mistake. Am I the only one who ever made this stupid blunder?
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 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, which is one second of arc and a little over three light years-note 2. 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 travelling 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 traveller. 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 from the moon alone-note 3.
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
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.
Amelia Earhart and Parallax
Amelia's navigator, Fred Noonan
Amelia and Fred had been flying though the night toward dawn -note 7. Fred should have had good celestial observations from stars and later the sun and moon -note 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 -note 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) -note 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 -note 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
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, p206Earhart'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 -note 14, an inadequate fuel reserve, and Fred's possible parallax correction error, certainly resulted in enough cumulative issues to kill the crew several times over.
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 This Researcher's 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.
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.