OK, so here you are, Fred, flying east towards Howland. Let's just say you haven't been able to get a celestial sighting for quite some time due to an overcast, and you are eagerly awaiting the dawn to get a sun shot.
Up comes the sun, and bing, you get your first sunshot from which you have already computed the time difference calculations between sunrise at Howland, so presto, you know exactly how many miles from your position to the advanced LOP, plus or minus what - 10% of the distance plus the uncertainty of the sun shot which I thing has been estimated at 10nm for a celestial sighting if you are good - Gary help me out here.
So, at sunrise at Howland, when Earhart is calling saying "200 miles out" we might expect that the error in finding the exact LOP through Howland is going to be 20nm plus the 10mn uncertainty in the sun shot = 30nm? Seems like a lot for a 200 nm distance flight, am I getting this right?
But, as Gary points out, Noonan could have derived the same LOP through Howland for at least another hour after sunrise (I think someone else said 3 hours after sunrise), and if so, they would have been not 200 nm out, but another 130nm closer to the LOP, so lets assume another sun shot 70 nm out, so our error might shrink to 17 nm. Gary had it figured down to 14 nm, 7 nm on either side of the LOP, in a previous post #504 on this page
http://tighar.org/smf/index.php/topic,555.msg11163.html#msg11163,
And, given that 90 minutes go by between the 200 miles out, and the "we must be on you" message, the 200 miles out message, would seem to be fairly accurate.
So, then when you hit the LOP, you are likely within 8.5mn of the actual LOP, well within visual spotting distance of an island, at least in theory.
So, if I know I'm flying on a line and that Howland is within 17 and perhaps 8.5 or even 7 miles of my line, why fly 40 mn off the the east and west of that line looking for something that I know isn't there?
Assuming Noonan chose to be North of the target is just that, an assumption. Might make sense then, and in our minds now, but given that they were expecting DF assistance, and the fact that AE says they are flying "north and south" on the line 157 - 337, it does seem plausible that they did not employ the offset landfall method and were barreling straight in. Why on earth would she say she was flying "north and south" if they had used the offset method? Why are we going to take a "should have - would have statement" offered in hindsight over a primary contemporaneous statement from AE herself? As I said before, something they did had to be out of the norm, otherwise they "would have - should have" made it to Howland, and we'd not be discussing it here.
It is Gary who is suggesting the expanding square search pattern, not a "modified box pattern", and I'm looking forward to hearing his reasoning why that would be employed over simply searching the LOP 157 - 337, as indicated in the radio traffic since it seems to me that the margin of error for the LOP would be pretty reasonable to deal with.
They had to hit the LOP well away from their target - beyond search pattern coverage - otherwise they would have found Howland / Baker. The LaPook hypotheses has yet to suggest why they were so far off, what went wrong?
Andrew