Solvers of the Live Reckoning puzzle have been called upon to address challenges faced by Fred Noonan, navigator for Amelia Earhart's round-the-world flight in 1937.  What would turn out to be the last segment of the trip departed Lae in New Guinea for Howland Island, 2,556 statute miles toward the east.  Navigation would be carried out in three phases... 
 

Solvers of the Simplexity Aloft puzzle studied two modes of RDF, Simplex and Duplex, then identified a long list of critical issues in Phase 3, which, acting together, revealed the utter failure of RDF -- both modes -- which doomed the flight.   In this puzzle we allow ourselves to consider that Amelia Earhart would not have known that radio direction finding was indeed failing in Phase 3 of the Lae-to-Howland segment.  Until it was too late.
 

Purdue University sponsored Amelia Earhart's flight around the world ostensibly as a "flying laboratory."  This photograph features the loop antenna that was mounted atop the Lockheed Electra 10E and configured with the Bendix RA-1 Manual Dirction Finder for evaluation.  The loop was controlled by Earhart with a wheel inside the cockpit.  After tuning in and identifying a station on the ground, the antenna was turned to detect a 'null', which indicated the 'bearing angle' to the station.

There were always two positions of the loop antenna that produced a null, one pointed toward the radio station, while the other pointed 180 degrees away from the radio station.  The two null points were potentially confusing.  Some historians are troubled by that simple limitation existing in RDF technologies vintage 1937, conjecturing that it might have become critical.  Indeed, for simplex RDF, it would be necessary for Amelia Earhart to resolve the ambiguity, and to do that, she must know the general direction of the transmitter. Ironically, selection of the appropriate bearing is made easy when the flight is known to be approaching the station from far enough away.  For homing, the pilot merely selects the bearing angle closer to the present heading and turns the aircraft so as to reduce the bearing angle to zero.

Incidently, duplex RDF suffers from the same ambiguity.  The loop antenna on Howland Island and the one on board Itasca would each have two nulls.  Accordingly, for resolution, radio operators would need to know the direction from which the aircraft is approaching. 

The diagram below depicts angular relationships that may arise during homing. It seems clear that from anywhere inside the gathering range the appropriate bearing angles (black arrows) can be readily chosen.  At locations where both bearing angles happen to be perpendicular to the heading (double red arrows), of course, there will be directional ambiguity; however, prior to reaching those locations -- again, inside the gathering range -- there would be opportunities to ascertain the general direction of the station and to select the appropriate bearing for homing.

Success in Phase 3 apparently requires functioning RDF equipment and trained people plus getting inside that gathering range. 

Solvers of the Landfall Navigationg puzzle would have advised Fred Noonan not to take the direct course to Howland, with all of its navigational uncertainties, but instead...

{a} offset the aircraft's heading to one side, 
{b} intercept the 157-337 sun line of position, and 
{c} turn confidently toward Howland Island and the Itasca. 

 

What could possibly go wrong?

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