Funny you should bring this up. Bob Brandenburg and I have been spending a great deal of time doing exactly what you're talking about.
There are three ways to gauge where the airplane was on the LOP when the last in-flight transmission was received by Itasca. That time, btw, was not 08:43 or 08:44 Itasca time as is commonly supposed. As explained in the
Research Bulletin, "Last Words," the best estimate is 08:55 - or, as we prefer, 2025Z.
1. The last transmission was heard loud and clear - logged by the radio operator aboard Itasca as "Strength 5" (the maximum). Where on the LOP was the aircraft most likely to be at 2025Z for Itasca to hear a Strength 5 signal?
2. During the morning hours of July 2nd, the tide at Gardner Island was rising. Where on the LOP would the airplane need to be at 2025Z in order for it to reach Gardner in time to land on the reef before the water level at the apparent landing site reached 6 inches - the estimated maximum height permissible for a safe landing?
3. The credible post-loss radio signals could only have been sent if the airplane landed with enough fuel to run the generator-equipped engine long enough to provide the necessary electrical power. Where on the LOP would the airplane need to be at 2025Z in order for it to reach Gardner and land with enough remaining fuel to meet that requirement?
As you can see, the three methods approach the question from completely different directions. If the answers to all three questions overlap to some degree there is a high probability that the correct answer is within that area.
We have almost all the information we need to answer the three questions and I fully expect to be able to lay it all out in the TIGHAR Journal 2011 paper entitled "The Last Week of NR16020."
The last pieces of information we need are the reasonable variables for her speed and fuel consumption during the run down the LOP. On the final run-in toward Howland, Earhart reported she was flying at 1,000 feet (probably to stay under the bases of the scattered cumulus clouds). She was down there for at least an hour prior to the last radio message heard by Itasca. We're assuming that she stayed low while running on the line. We, of course, don't know what power settings and airspeed she was maintaining during that portion of the flight or how much fuel she was burning. We need to define the reasonable possibilities.
In "Last Flight" she writes that at the end of the Oakland/Honolulu flight, to kill some time and let the sun come up, she backed off to 120 mph burning only 20 gallons per hour - but that was at 10,000 feet.
Let's say she's down at 1,000 feet and decides to maintain her cruising TAS of 150 mph. How much power does she need to carry to do that and what does that do to her fuel consumption in gph? (answer: nothing good)
What happens if she backs off to, say, 140 mph? 130 mph? 120 mph? Or even 110 mph? We don't think she'd go slower than that.
Any help will be appreciated but it needs to be based on hard data, not seat-of-the-pants hunches.