Live Reckoning
Copyright ©2010 by Paul Niquette. All rights reserved.
The expression 'dead reckoning' is commonly regarded by airplane pilots as an unclever contraction of 'deductive reckoning', preferring instead to use the term 'pilotage'. 

That etymology is not documented in any historical dictionary. According to the Oxford English Dictionary, 'dead reckoning' dates from Elizabethan times (1605-1615).   In antiquity, dead reckoning was navigation without celestial references. 

Whereas with stellar observation, you are, in some sense, live -- working with the stars and the movement of planets.  Conversely, using mere compasses and clocks but no sky, you are working dead.

It would be difficult to name a more qualified navigator for Amelia Earhart's round-the-world adventure than Frederick Joseph "Fred" Noonan, 44, an American sea captain and aviation pioneer who charted the first commercial airline routes across the Pacific Ocean during the 1930s.  Figure 1 below is based on contemporaneous information and depicts Noonan's plan for the ill-fated flight on July 2, 1937.  Taking off from  Lae in New Guinea, Earhart and Noonan would fly non-stop to Howland Island, a mere 450-acre speck, 2,556 statute miles away, over vast stretches of equatorial waters.  Notations in the sketch provide key parameters from the flight plan. 

In retrospect, we recognize three navigational phases: 

Phase 1  Dead Reckoning in daylight eastbound from Lae using island checkpoints for 900 miles, making a slight heading change overhead the island of Nukumanu. 
Phase 2  Live Reckoning (celestial navigating) following nautical twilight, flying in total darkness until reaching nautical twilight -- dawn -- 148 miles from Howland.
Phase 3  Radio Direction Finding homing on signals broadcast by USCG Itasca, loitering hard by Howland Island to support the Electra's arrival.
Things did not quite work out as planned.  The flight was already being delayed in Phase 1 by higher than expected headwinds.  Indeed, shortly after the flight left Lae, weather balloons launched in Hawaii were calling for changes in the winds aloft forecast from 15 mph to 26.5 mph.  That update was not acknowledged by Amelia Earhart, but about seven hours into the flight, she gave a position report as follows: 
That report curiously agreed exactly with the revised forecast by radiosonde (23 kts = 26.5 mph).  Earhart and Noonan were 'making good' only 130.3 mph instead of the planned 142.8 mph.  The Electra's groundspeed implied a total of more than 19.5 hours to reach Howland Island. 

For a long flight, fuel exhaustion would ordinarily be the main concern; however, the Electra took off with 22 hours of fuel on board for an 18-hour flight.   Solvers of Here Comes the Sun puzzle have addressed a different deadline:  Noonan's main concern was the time available for taking his Last Celestial Fix before 'nautical twilight'.  Dawn would mark the end of Phase 2 at some distance away from Howland, which inexorably increased with flight delay.  Figure 2a below depicts the estimated arrival situation for the planned flight.  Figure 2b shows the actual situation, as Fred Noonan was forced to complete his Last Celestial Fix more than 435 miles away from Howland Island-- hundreds of miles too far from Itasca for homing.  Cut off from Live Reckoning by the rising sun, he had no choice but to rely again on compass and clock.

Dead reckoning is notorious for accumulating navigation errors, dominated by imprecision in steering and unknowable variabilities in wind intensity and direction.  Radio Dirction Finding (RDF) has a vital feature: correcting out navigation errors -- a terrestrial form of Live Reckoning.  Thus, all trans-oceanic airline flights, which were already in service throughout the '30s, routinely relied on homing for reaching destinations.  An out-of-commission beacon at a destination aerodrome meant flying to an alternative destination, period.  As recognized by solvers of the Point of No Return puzzle, such an alternative was not available for Amelia Earhart and Fred Noonan on that fateful day in 1937.

Figure 3 below depicts a 'gathering range' for RDF as a circle reaching out a hundred miles or so in all directions from Itasca at Howland Island.  That estimate may not be especially conservative, given the limitations in wireless technologies back in the '30s.  A handful of available frequencies were crowded with maritime broadcasts.  Low power transmitters, confusing protocols, some in Morse code others by 'radiophone' -- all these realities resulted in uncoordinated transmissions and blocked signals for the Earhart Flight. Accordingly, as the sun began lighting up the sky obliterating celestial objects, Fred Noonan necessarily commenced a second interval of dead reckoning. Over a distance 300 miles or more from the Last Celestial Fix, there would be nothing to do but hold a magnetic heading in the windy sky and wait for an assigned time-slot on a negotiated frequency, trying repeatedly to establish RDF with Itasca -- the beginning of Phase 3

For RDF to be successful, equipment and people on the ground and on board the aircraft must work properly. Solvers of the Simplexity Aloft puzzle have studied the two RDF modes, Simplex and Duplex.  One day before the flight, Amelia Earhart took the Electra aloft for a brief test of the engines and instruments, which included exercising the on-board RDF equipment.  Using the Electra's loop antenna, she was unable to obtain a relative bearing from a ground station at Lae.  She speculated that the signal was simply too strong for a "null."  If her speculation was wrong, the on-board RDF equipment must have been defective and Simplex RDF would be unavailable throughout the flight to Howland. 

Figure 1 above shows the USS Ontario 1,200 miles into the flight, about half-way to Howland.  The U.S. Navy made the ocean-going tug available as an RDF fix in Phase 2.  If either mode of RDF succeeded, however, no evidence is recorded in the form of a position report by Amelia Earhart.  Moreover, according to the ship's logs, two-way communications were never established with the Electra, which ruled out Duplex RDF at Ontario and thereby put in doubt any expectations for Simplex RDF using a radio transmitter on Itasca as a  homing beacon.

With one exception, there are no records throughout Amelia Earhart's last flight that any radio transmissions  were received on board the Electra. In effect, she made her transmissions 'in the blind'.  Here is that exception...

...which depicts an admission by Amelia Earhart that Simplex RDF had failed and that she was changing to Duplex RDF.  Solvers of Which Way Amelia? will have some idea about the reasons why neither RDF mode could be made to work.  Given the failed two-way communications with Ontario, Earhart and Noonan must have concluded long before sunrise that Phase 3 was in serious jeopardy -- that for the approach to Howland there would be no Live Reckoning -- no homing by radio, that is (see Shoot the Moon)..
What would your advice have been for completing the flight successfully?