If Noonan used the correct date in his calculations, this coordinate would have been where Howland Island actually was, or rather, where Howland Island was mapped as being in 1937. This “Mapped Howland” was roughly 6 nautical miles west of Howland Island's actual location. (Mapped Howland is the destination coordinate used by Elgen Long in his work(1) as a starting point for drawing a search area.)
However, if Noonan used the wrong date in his calculations (July 3rd), the coordinate he was aiming for would have been one degree westward in longitude from Mapped Howland. Noonan would not have drawn it this way on his charts, of course. He would have perceived this date error as moving their own position on their flight path one degree eastward, putting them roughly 60 nautical miles closer to Mapped Howland than they actually were at the time of that celestial reading. If Noonan thought they were 60 nautical miles farther eastward toward Mapped Howland than they actually were, then relatively speaking, the point he was aiming for on the map was 60 nautical miles closer westward from Mapped Howland. We can refer to this coordinate as Fred’s Howland.
Fred’s Howland is the actual position Noonan would have been directing Earhart to fly towards – where he would have thought the island was located based on the incorrect date in his calculations. This coordinate is also the location where Earhart would have reported on the radio that she was “on you, but cannot see you.” This point is roughly 65.9 nautical miles at a bearing of 269.5 degrees from Actual Howland Island. It is outside of Elgen Long’s defined search area, but just on the edge of his 65 nautical mile radio circle – within the practical reaches of Long’s analysis of radio signals and strengths.(1)
If we take this coordinate to be the point Noonan was aiming towards, then we can use the same rationale Elgen Long used to draw his search box around Mapped Howland.(1) Noonan and Earhart would have arrived on site, and once they couldn’t find the island on the first pass, they would have began a search pattern, flying along their advanced line of position. In Long's estimation, it is most likely that Noonan would have kept them flying close to this original point, so as not to stray farther from their calculated destination. It is suggested by Long and others that the last set of radio calls from Earhart is indicative of a flight path running North and South along the 157-337 line of position while Noonan and Earhart looked for the island. They would have exhausted their fuel supply near their calculated destination and crashed into the Pacific Ocean.
In keeping with Long's research (and trying to stick purely to Celestial Navigation-derived notions for the Date Line Theory), we can draw a similar box around Fred’s Howland according to Long’s flight estimations and celestial navigation error calculations. This search box is derived assuming that Noonan and Earhart flew North and South along the 157-337 line of position, searching the area where they believed Howland Island to be for roughly an hour after they arrived on site. The LOP is drawn, in this case, through the coordinates for Fred's Howland Island, and expanded from there based roughly on Long's flight time calculations(1). The size of this search area is about 3200 square-nautical-miles, but it seems most probable that the Electra would be in a smaller area closer to the coordinates for Fred's Howland.
A Quick Note on “Error”
Elgen Long’s original search box includes calculations of measurement error – that is, small differences in measurements due to the built-in limits of the measuring tools and methods of celestial navigation. Fred Noonan knew that he could navigate to Howland Island within a certain measurement error that was acceptable for the flight. This measurement error is not to be confused with human error, or a mistake, in the calculations, such as using the incorrect date when using navigation tables. The search area above is defined by taking the result of a possible human error (the date) to set the center point, and then working backwards to expand the search area based on measurement errors that require inclusion.
NEXT: Some final thoughts...
1. Long, Elgen M. and Marie K. Amelia Earhart: The Mystery Solved. New York: Simon & Schuster, 1999.