Now let's look at the TIGHAR theory, that Noonan observed the sun as it rose, developed a line of position from this observation, advanced this LOP until it passed over Howland, measured the distance that needed to be flown by DR until intercepting that LOP, compute the time necessary to fly this distance based on their known ground speed, fly for the computed time, turn left and search NNW at the computed time of the intercept of the advanced LOP for a certain distance, make a 180° turn and search the other way along the LOP, and then continue to the SSE until finding Gardner. My question is "how far do you search to the NNW before turning around?"

I have attached illustrations of this theory. The first image shows the presumed fix at 1623 Z, the

10 NM circle of uncertainty around it. Based on the report at 1912 Z the plane would have flown 366 NM in this period after the fix. If no sun line LOP were obtained then, if navigating solely by DR, the uncertainty would grow by 37 NM making the uncertainty circle around Howland 47 NM in radius, 94 NM in diameter. The second illustration shows that the

uncertainty grows at 10% of the distance flown, starting from the circumference of the circle around the starting fix.

Sunrise at sea level at Howland was at 1745 Z and at 10,000 feet above Howland, ten minutes earlier at 1735 Z. By allowing for the rotation of the earth and the movement of the plane (I won't go into the details of this computation) we can calculate that at 10,000 feet they would have observed the sun peeking up from behind the horizon at 1749 Z. This is 1:26 minutes after the fix and the plane would have flown 147 NM in this time so the DR at the time of sunrise is plotted on illustration 3 along with the circle of uncertainty which has grown to a radius of 29 NM. There remains 179 NM to fly to Howland. Illustration 4 shows the sunrise LOP which runs 157° - 337° true and illustration 5 shows the plus and minus 7 NM uncertainty band. The aircraft would have to be located in this band and bounded on the north and south by the circle of uncertainty, somewhere along the 58 NM of the 14 NM wide band inside the circle. Illustration 6 shows this LOP advanced to 1912 Z and the uncertainty grows by 10% of the 179 NM covered, 18 NM, which is added to the original uncertainty of 7 NM making the uncertainty at 1912 Z of plus and minus 25 NM, a band 50 NM wide shown in illustration 7. The aircraft is within this 50 NM wide and 94 NM long band. With an uncertainty of 25 NM, the advanced sunrise LOP is

**not sufficiently accurate** to assure finding Howland since this exceeds the visibility and the scanning range.

(I have said for ten years that it was not possible to take a

"sunrise observation" for technical reasons and the current example shows yet another reason why it would be useless to take an observation when so far away from the destination which results in such a large DR uncertainty that the resulting LOP is of no use.)

Now, according to TIGHAR, they turn and fly NNW along the LOP, so how far must they go? They must go at least the 47 NM of the circle of uncertainty but after flying those 47 NM the uncertainty has grown by an additional 4.7 NM (call it 5 NM) so the plane must go at least 52 NM. At the same time the width of the band has also grown by the same 5 NM in each direction make the band 60 NM at the end of the NNW leg. Illustration 8 shows the area that must contain the airplane, 60 NM wide and now extends 52 NM NNW from the presumed location of Howland.

The plane now turns around and proceeds SSE, how far will it go in this direction? It must go 52 NM back to the starting position plus the 47 NM to the edge of the original circle plus 10 more NM to account for the increase in the DR uncertainty on this leg, a total of 109 NM placing the DR position at the end of the SSE leg 57 NM from Howland, 19 NM from Baker and 300 NM from Gardner. This leg also adds 11 NM on each side of the LOP making it now 82 NM wide, 41 NM on each side and absolutely useless for finding Howland. Illustration 8 shows this and the area that contains the plane at the end of the SSE leg. Noonan knows at this point that he must be SSE of Howland, most likely about 57 NM but with a range of zero to about 115 NM so he is certain the the closest land is Howland and Baker and the next nearest land in the Phoenix islands is at least 230 NM away and more likely about 300 NM away.

So what should they do at this point? Go back to the NNW until their DR shows them close to Howland and then do the expanding square search pattern. It makes no sense to continue further to the SSE where they would have to rely only on luck to stumble onto one of the

very scattered islands in the Phoenixs. Proceding in that direction would use all or most of their remaining fuel and they would not be able to do any search pattern in the vicinity of those islands for the simple fact they would have no way to determine that they had gone far enough. The uncertainty in their DR at this point

**where they had to make their decision** is fully 82 NM wide and 115 NM long and their DR accuracy will only get worse on the way to the Phoenixs which is why you can't dead reckon to a destination if you are not starting from an accurate fix. In fact, considering the 50 NM wide band of the LOP at 1912 Z which made the uncertainty similar along both axes, it would have made more sense to ignore the stale LOP all altogether and just start the search pattern at 1912 Z as I have shown in my prior posts and this would have save about 1:40 of fuel that could be used for the search.

gl