{0} Explicit Assumption
        {1} The Clock Won't Wait
        {2} Here Comes the Sun
        {3} Landfall Navigating
        {4} Live Reckoning
        {5} Point of No Return 
        {6} Simplexity Aloft
        {7} Gathering Range
        {8} Shoot the Moon
        {9} Wages of Flight
      {10} Which way, Amelia?

Amelia Earhart (AE) and Fred Noonan (FN) depart Lae, New Guinea for Howland Island, 2556 miles to the east. 

The Lockheed Electra Model 10-E NR16020 is equipped with two Pratt & Whitney R-1340 Wasp S3H1 engines capable of developing a maximum of 650 hp at take-off, with a fuel consumption rate of 95.3 gph total. The plane is loaded with 1,100 gallons of fuel. 

FN's flight plan included a headwind estimate of 15 mph. The flight takes up a true heading of 083^o on a direct course to Nukumanu. 

Fuel consumed at take-off 8 gallons, 1,092 gallons remaining.  AE throttles back to a cruise-climb power setting that consumes 50 gph at an airspeed of 115 mph and a sustained rate-of-climb of 250 fpm.{9}

With the estimated headwind of 15 mph, the Electra would theoretically make good a groundspeed of 100 mph while climbing.

Flight reaches cruise altitude of 8,000 feet.  Distance from Lae 62 miles, with 2,494 miles to go on the 083^o course direct to Howland.

Total fuel consumed in climb 35 gallons, 1,065 gallons remaining.  AE levels off and increases airspeed to FN's planned 157 mph consuming 50 gph.{9}

With the estimated headwind of 15 mph, the Electra would theoretically make good a groundspeed of 142 mph in level flight.

AE maintains airspeed at FN's planned 157 mph, consuming 50 gph.

Flight overflies the island of Nukumanu at 8,000 feet.  Distance from Lae 850 miles, with 1,706 miles to go on the 083^o course direct to Howland.  Position report was logged late, at 0718 GCT.  Report included measured headwind of 26.5 mph. {1}

With the measured headwind of 26.5 mph, the Electra actually makes good a groundspeed of 130.5 mph in level flight.  Total fuel consumed at Nukumanu 361 gallons, 739 gallons remaining.{9}
 

Overhead USS Ontario
1034 GCT -- Time Aloft 10.57 hr

Distance from Lae 1,300 miles, with 1,256 miles to go on the 083^o course direct to Howland.

AE repeated attempts to reach USS Ontario 200 miles ahead were all in vain.

FN becomes concerned about whether RDF was operative, calls for increase in airspeed to shorten dead reckoning from Last Celestial Fix.{0}

AE increases airspeed to 168.5 mph, consuming 59.3 gph. Total fuel consumed at this location 528 gallons, 572 gallons remaining.{9}

Total fuel consumed at this location 946 gallons, 154 gallons remaining.

FN takes Last Celestial Fix as flight approached beginning of Nautical Twilight.{2}

Distance from Lae 2,300 miles, with 256 miles to go on the 083^o course direct to Howland.  With the measured headwind of 26.5 mph, the Electra was making good a groundspeed of 142 mph in level flight.

AE reduces power for descent at 500 fpm, maintaining 168.5 mph and consuming 23 gph.{9}

FN calls for heading change from 083^o to 067^o offset of 16^o for shortest distance, direct course to 157-337 LOP (246 miles) and compensating for maximum dead reckoning errors of plus or minus 16^o of steering error from Last Celestial Fix.{3}

Total fuel consumed at this location following descent 951 gallons, 149 gallons remaining.{9}

With the headwind aloft of 26.5 mph, the Electra was making good a worst-case groundspeed of 142 mph with headwind slowing to 15 mph during the descent.{0}

AE sets up level flight at reduced power to extend endurance aloft, using 30 gph for 120 mph airspeed.{9}

Total fuel consumed on arrival overhead Howland, 1,024, landing with 76 gallons in reserve, 2:30 search time available.

Note: The flight would have already arrived at Howland before the Last Transmission by Amelia Earhart. Since the landing did not take place, Alternative #1 must be rejected.

The flight reaches the landfall turning point on 157-337 LOP at 1956 GCT, 71 miles north of Howland, requiring about 25 minutes of flying to reach visibility limit of 20 miles.

Total fuel consumed on arrival overhead Howland, 1,039, landing with 61 gallons in reserve, 2:02 search time available. The flight would have reached 157-337 LOP 17 minutes before the Last Transmission by Amelia Earhart.  The flight would have turned south and required only 8 minutes to reach visibility limit. 

Note: Since the arrival did not take place, Alternative #2 must be rejected.

The flight reaches the landfall turning point on 157-337 LOP at 2002 GCT, 142 miles north of Howland, requiring more than 1:13 flying to reach visibility limit of 20 miles. 

Note: Radio failures mean that no RDF gathering range is established.{7}

If the flight continues south, the total fuel consumed on arrival overhead Howland, would be 1,060, landing with 40 gallons in reserve, 1:20 search time available.

Alternative #3 The flight would have already flown 11 minutes toward the south at the time of the Last Transmission by Amelia Earhart, having reached a position 120 miles north of Howland on the 157-337 LOP.

Between 2013 GCT and 2113 GCT, AE decides that FN's offset to the north was in the wrong direction and reverses course.{0} 

Note: This is a reasonable assumption, which fits all the known conditions, including the profile of radio reception on board Itasca.{6} 

Most likely location of the ditching is between 234 and 334 miles north of Howland Island on a heading of 337 degrees true.

Simplexity Aloft described AE's 2013 GCT transmission as "An ambiguous -- indeed -- an impossible flight maneuver and altogether useless for guiding subsequent searches."

 

Based on the logic in the narrative set forth above, your immediate answer to the question, "Which way, Amelia?"  must  be "South."  An hour later, your answer must be "North."