Gathering Range

Copyright ©2010 by Paul Niquette. All rights reserved.
The diagram below is schematic in nature, such that all distances are left unspecified.  It depicts a realistic case pertinent to the final phase of the Lae-to-Howland flight.   The heading was set by Fred Noonan to the left of course as a conventional strategy for mitigating navigation errors.  The offset angle was chosen to assure that the maximum navigatonal error to the right would bring the aircraft directly into the gathering range at Howland, wherein RDF would become functional. 

The most extreme navigation error to the left is shown missing the gathering range.  However, upon reaching the sun line-of-position, Amelia Earhart would be advised by Fred Noonan to turn with confidence to the right and onto a course of 157 degrees.   The expectation -- indeed, as it turned out, the hope -- would be that eventually the Electra would come within gathering range and successfully complete the flight using RDF.

Sophisticated solvers will observe that even with perfectly functional RDF equipment and people for both modes of RDF, Amelia Earhart and Fred Noonan would be deprived of all advanced knowledge of RDF's operability -- that outside the gathering range, whether RDF will ever become operable would not be knowable. 

Solvers of Wages of Flight will be keenly aware that while approaching Howland Island, the Electra was getting low on fuel.  The offset for landfall navigating would exacerbate the endurance issue.  The plane would be slowed to extend time aloft, but that also puts final maneuvers into slow motion and increases psychological pressures on the two aviators who have already been aloft for more than 20 hours and would now be earnestly gazing at the Pacific waters ahead looking for any sign of Howland or the Itasca.

For our solution, then, we offer the following answer to the question in the puzzle:.
 

"What could possibly go wrong?"
  1. Noonan called for an offset to the north, thence for a turn as indicated toward the south onto a heading of 157 degrees 
  2. By happenstance, cumulative navigation errors were near the extreme toward the left (green line), taking the flight outside the gathering range.
  3. After some -- substantial -- period of time Earhart concluded that the flight should be inside the gathering range, but gets no joy on the radio.
  4. Earhart is unaware that because of multiple RDF failures, no gathering range ever existed that day at Howland Island.
  5. She concluded that Noonan's landfall offset was to the wrong side -- that the gathering range and Howland lay to the north. 
  6. As pilot-in-command, Amelia Earhart reversed direction to 337 degrees and flew toward the north, away from Howland until fuel exhaustion.

Item 6 in our solution is the most controversial.  It is not unprecedented, however.  Exclamation point optional. 

Nearly a month earlier, on June 8, 1937, Amelia Earhart's round-the-world flight crossed the Atlantic, departing Natal at the eastern tip of Brazil with Dakar at the tip of the Cape Verde Peninsula as its destination.  The Bendix RDF was known not be working, so Fred Noonan had to rely on sun-shots and dead reckoning for navigation, using the drift meter for cross-course corrections. 

Upon arrival over the coast of Africa, landfall navigation called for a turn to the south. Amelia Earhart decided to turn north instead. Long described the result this way (p.143), "As it turned out, it was the wrong direction but the right decision."  In 20 minutes, they landed not at Dakar but at St. Louis in French West Africa, 120 miles north of Dakar.  No such outcome was possible on July 2, 1937.

Sophisticated solvers might take note that the puzzles in this series deliberately do not make use of information from flights prior to July 2, 1937.  This is the only excerption.


 
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