Now lets look at the second theory, that she was to stage her own disappearance to give the U.S. Navy a justification to search throughout the Japanese Mandated Islands. Let's see if this would have worked by looking at it from the flight navigation point of view. The distance from Lae to Howland is 2556 statute miles and the course is 078 degrees true (image 6.) ( I state all courses in relationship to true north instead of magnetic north, true directions, not magnetic directions and distances are in statute miles.) Images 12, 13 & 14 show the courses to Truk, Ponape and Jaluit. (I am not considering Palau since it is so far off course.) The course to Truk is 18 degrees meaning the plane would have to be 60 degrees off course to get to the vicinity of that island. The course to Ponape is 38 degrees, off course by 40 degrees. To Jaluit is 60 degrees, 18 degrees off course. image 6 image 12 image 13 image 14 Another way to look at this is to see how many miles off course they would be if they were in the vicinity of those islands. Image 15 shows the perpendicular distances from the course to Howland to the various islands. Truk is 910 miles off course, Ponape is 770 and Jaluit is 580. image 15 The commonly accepted level of uncertainty of in-flight dead reckoning is 10% of the distance flown. So even without a navigator on board and with Earhart doing her own dead reckoning navigation, just holding a heading based on correcting for the forecast winds, and with no fixes in flight, no celestial fixes and no visual fixes over an island, she should not have been off course more than 255.6 SM either to the north or to the south of Howland. Image 16 illustrates the area she might have been expected to overfly on her way to Howland if using just dead reckoning. It extends 255 miles north of Howland which is about 6 degrees off the course to Howland. (A like area would be south of course but that is not important to this discussion.) Even though the area of course uncertainty extends 6 degrees either side of course, you are more likely to be closer to the course line than to the edges of the area. The probability drops off gradually as you move further away from the course line. With a navigator on board obtaining celestial fixes fairly regularly the plane should be very close to the course line and it is unlikely that it was near the edge of the area of course uncertainty. image 16 Image 17 shows how far off course in excess of the area of course uncertainty it would be to go to the Mandated Islands. Since the course uncertainty is 6 degrees, these numbers are six degrees less than the previous numbers, 54 degrees to Truk, 34 to Ponape and 12 to Jaluit. image 17 The 10% area of uncertainty expands in the along course dimension too. Even though the airplane (using dead reckoning) may have flown through the course uncertainty area it is not going to be near the western end of it since they flew through that area many hours prior to the last transmission. The plane is not likely to be more than 255 miles short of Howland nor likely to be more than 255 miles past Howland. Image 18 shows the final area of uncertainty (with the area south of the course line omitted. It would be the same size as the area north of the course line.) Like the uncertainty in the course, the plane is more likely to be near the center than near any of the edges. Again, with a navigator on board, the uncertainty would be much less. The depicted area of uncertainty is based on dead reckoning all the way from Lae to Howland without any landmarks or celestial navigation fixes. Any such fixes along the way would reduce the size of the area of uncertainty to 10% of the distance flown since the last fix. image 18 Image 19 shows the line from Jaluit to the nearest corner of the final area of uncertainty. This distance is 670 miles. It is slightly less to Mili, 530 miles. It is 1460 to Ponape and 1880 to Truk. image 19 The Japanese also understood navigation. It would be very difficult to convince them of a legitimate need to search near Truk, 1880 miles from the outer limits of her likely position or even to search near Mili, fully 530 miles away. To put this into perspective, images 20 and 21 show an analogous situation projected onto the U.S. The 10% uncertainty area south of the course line is the square centered on Washington, similar to the previous diagrams. If I were to disappear while flying my plane from Los Angeles to New York, a distance of 2460 SM (only 100 SM less than the distance to Howland), my family would have a very hard time convincing the police chief of New Orleans of the necessity of making a search for my plane in the swamps nearby. New Orleans is 780 miles off course, about the same distance as Ponape is off the Lae to Howland course and 808 miles from the nearest corner of the 10% uncertainty area. They would also have a hard time convincing the police chief of Tallahassee Florida to conduct a search. Tallahassee is 530 SM from the nearest corner of the 10% uncertainty area, the same distance at to Mili. And keep in mind that the depicted area of uncertainty is based on dead reckoning all the way from Los Angeles to New York without any landmarks or radio or celestial navigation fixes. Any such fixes along the way would reduce the size of the area of uncertainty to 10% of the distance flown since the last fix. The Japanese knew that Earhart had a navigator with her so would have assessed the area of uncertainty to be much smaller. 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 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. image 20 Image 21 Since U.S. planners would have been fully aware that the Japanese would never be fooled by such a subterfuge, there is no reason to believe that they would have attempted this deception. And, as pointed out before, the U.S. Navy had the right, at all times, to sail their ships and to conduct flight operations as close as three nautical miles to the shore of every Mandated Island so did not need any excuse to conduct surveillance in this area. See: First spy theory |