On July 2, 1937 at 0000 GCT, the Lockheed Electra Model 10E began its take-off role at Lae, New Guinea.  It was the beginning of a tragic flight and the biggest aviation mystery in history.   The over-water flight of 2,556 miles along the Equator to Howland Island would place extreme demands on all navigation resources and skills of that time.  The navigator for the round-the-world adventure was arguably the best in the world, Fred Noonan.  Nevertheless, the successful conclusion of the flight could be assured only by RDF -- Radio Direction Finding (see Live Reckoning) performed by the Pilot-in-Command, Amelia Earhart. 

Aviating, Navigating, Communicating

Piloting requires multitasking aloft. Each task has its own primacy; each is a sine qua non for the successful completion of every flight.  Contrary to the simplistic mandate cited above, priorities must change with the various phases of flight. 

Thus, during take-off and early stages of climb-out, the pilot will be focused most intensely on Aviating (see Pilot's Nightmare).  Same during the final stages of approach and landing (see Sloping in the Dark). 

In between, often for hours-on-end, Navigating takes first priority, as satirized in one definition, "Latitude is where we are lost, and Longitude is how long we have been lost there." 

So it would seem that Communicating should belong as the lowest priority. "Never drop the plane to fly the microphone," goes an old saying.

Receive-Only RDF ~~~ To establish a course directly toward Howland Island, Amelia Earhart would need to operate an RDF antenna, which is the loop being displayed on the right and visible as it was mounted atop the Electra in the photograph above. With an appropriately tuned radio receiver, she would be able to rotate the loop to "get a minimum" signal and thereby determine the direction from which a radio signal is being transmitted.  Using that bearing angle, the Electra would be turned to take up a heading directly toward the source.  In this mode, airborne RDF equipment operates "receive-only" -- simplex in radio parlance.  However... In 1937, no permanent radio beacon was installed on Howland.  Such a facility would be transmitting an identification signal continuously on a dedicated frequency identified by Morse Code.  Instead, the US Coast Guard cutter Itasca had been positioned at anchor offshore Howland to support RDF for the Earhart flight.  A qualified radio operator on board Itasca was supposed to broadcast an improvised homing signal in compliance with a time-of-day schedule on an assigned frequency, with station identification to be recognizable by Amelia Earhart -- all by protocols coordinated in advance of the inbound flight.  Duplex RDF ~~~ For guidance from the ground ('DF steer'), two-way communications had to be established with USCG Atasca, which is shown on the right.  Communications were to take place by voice or by Morse Code on assigned frequencies.  Amelia Earhart would then be requested over the radio to transmit a steady signal long enough for the Itasca radio operator to ascertain the direction of the source in the sky using a loop antenna on the ship.  Having obtained the bearing to the Electra relative to the ship's heading, the operator must compute the appropriate compass direction for the Electra to fly and transmit that information to Amelia Earhart as a heading by voice or Morse code.  All of that takes time, of course, and all the while, the Electra would be flying at over a hundred miles per hour on an uncorrected heading. In concept, Duplex RDF operates as a reciprocating, two-way, simplex system -- half-duplex in radio parlance.  By the way, wireless telephony, which we take for granted today, supports what is called full duplex communications, with transmitting and receiving going on in both directions simultaneously.  Full duplex is a feature still not found in radio equipment installed on even the most complex airliners of the Twenty-First Century.

As readily seen in the descriptions above, for RDF to be successful in either mode, equipment and people on the ground and in the sky must all be in good working order and coordinated. 

Last Words of Amelia Earhart

The figure below is based on transcriptions from the radio room aboard the USCG Itasca standing by Howland Island on July 2, 1937.  These are the last six radio messages received from Amelia Earhart over a period of two and a half hours on that fateful day. 

The pre-arranged 'radio schedule' comprises 'time-slots' during which Earhart was supposed to transmit simplex at quarter-to and quarter-passed each hour   In between, Itasca was supposed to transmit simplex on the hour and the half-hour. 

Historians have taken special notice of the potential for confusion resulting from two time-zones: Earhart and Noonan operated on Greenwich Civil Time (GCT) while the Itasca clocks were all set on local time at Howland ("IST" for 'Itasca Standard Time'), such that IST = GCT minus 11:30.  A source of confusion for sure, but if everybody stuck to the script, those time-slot assignments ought to have worked just fine in half-duplex. 

Sophisticated solvers will immediatly observe the following worrisome problems:

• Three different radio frequencies being called out by Amelia Earhart: 3105, 6210, and 7500 Kcps (thousands of cycles per second, "Hz" in today's terminology).
• Three different forms of modulation: "noise," "voice," "whistling" -- but not "code" (neither Amelia Earhart nor Fred Noonan understood Morse Code).

Complexity trumped simplicity for Amelia Earhart and Fred Noonan that day, hence the appropriation of "simplexity" in the title of this puzzle. As the Electra approached the end of its final flight, a lot could go wrong.  And apparently did.