Since the leg from Lae to Howland is 2222 NM and the common estimate of DR accuracy is 10% of the distance flown then one could expect to fly the distance from Lae to Howland solely by dead reckoning and still be confident of coming within in 222 NM of Itasca and so be close enough to pick up the radio signal and track inbound to Howland. So if AE was willing to rely only on radio she didn't need Fred. But obviously they wouldn't just rely on radio.
Gary,
Thank you for the detailed information in the previous post. I have yet to read over both of your links but will check it out after work. I have a simple question about the maximum error of 10% of the distance traveled. In your above example 10% DR results in 222NM. Is this the 'total error' meaning you could be 5% North or South of your target or does this mean you could be 10% too far South or 10% too far North? For example, if you were about to start searching, are the end points to the error window 111NM to the North and 111NM to the South or is it 222NM to the North and 222NM miles to the South?
You're right, the 10% is the radius of the circle of uncertainty. Remember, you are much more likely to be near the center of the circle, near the DR position, than near the edge of the circle. The 222 radius would only apply if they DRed all the way from Lae which we know is not the case. We know they had a fix at Nukumanu island, 1,500 NM from Howland so the maximum circle radius would be 150 NM. They also had a fix over one of the ships or at Nauru which are closer, about 970 NM from Nauru, shrinking the circle further. "NOONAN MUST HAVE STAR SIGHTS" so if they couldn't get fixes then they would have turned around prior to the PNR, just short of the Gilberts, returned either to Lae or, more probably,Rabaul and try another day. We know she was mentally prepared to do this because that was part of the planning for the original leg fron Hawaii to Howland and she did turn around several times on previous legs.
(To avoid getting confused if making comparisons, keep in mind that I use nautical miles on my website but sometimes use statute miles on the TIGHAR Forum.)
Assuming that it is 111NM North and 111NM South, and you started searching in the Northerly direction, would you travel the entire 111NM or stop short of the visibility range and turn around to go South? I am guessing on the trip South you would make the offset short of 2 times the visibility range. Would the choice of choosing an Easterly offset or a Westerly offset be arbitrary on your first pass?
Thank you in advance.
I see your point, if you figured a maximum error or uncertainty in your DR is 60 NM and you had 20 NM visibility then you could aim to intercept the LOP only 40 NM out and look real hard out to the side as you approach the interception and you would then be able to see the whole 60 NM band. But, since it is much more important to be sure to find the island and not so important to save a couple of minutes (especially for Earhart as they had plenty of fuel left at that point, "Penny wise and pound foolish" comes to mind) the standard interception of the LOP is at the point of estimated maximum error and the visibility off to the side along the extended length of the LOP is taken as an additional safety margin. See
standard flight navigation texts here. The same when you fly to the other end of the LOP, you go the total distance of the maximum uncertainty for the same reason before turning around to start a search pattern.
Regarding which way to offset when starting the search pattern you would normally turn in the direction to take you to an area you haven't been through yet, if that is not the situation you normally offset into the wind, in this case to the east. But for Noonan, since they knew the wind was out of the east and they expected a smoke trail that would extend off to the west, it would be less likely that they missed to the west than that they missed to the east by overshooting the LOP because they would have had to have had a much larger error if they turned short of the LOP to miss the smoke, than if they had gone too far so they should offset to the west when returning to commence the modified square search pattern.
Gary,
After reading over your page I am fairly convinced that when you state "within" an amount of error, this describes a radius around the target. Using your 2222 NM and 222 NM error, this describes a circle around the target with a radius is 222 NM.
You seem pretty convinced that FN was able to get a fix at 17:42 GMT as they announced they were 200 miles out. Why is that? If FN was able to get a fix then the fact that they did not make it to Howland seems irreconcilable. I do not think we can entirely ignore the claim by Bellarts who supposedly heard AE state "cloudy and overcast" at 14:10 GMT. Perhaps we need to look at the Itasca weather log a bit closer.
Yup, whether they got the last fix at 1623 Z ("partly cloudy") or as late as 1740 Z, Noonan would have planned a sufficient offset to allow for the maximum likely DR error in the leg from that fix to the interception point. That is the whole point of the landfall procedure, to cure any inaccuracy in the DR. So yes, it makes no sense that they didn't find Howland.
As far as intercepting a LOP NW of Howland goes, it seems that they time stamps in the radio log do not allow for that. It appears that they came straight in expecting to find the Island. As Jeff pointed out, perhaps the plan really was a RDF approach but only when that did not pan out did FN take over to find Howland. AE spent quite a bit of the time on the radio either attempting to take a bearing or have Howland take bearings and she probably wasted a significant amount of time on that effort. Perhaps FN was working out a plan in the meantime but obviously whatever that plan was, it failed as well.
Keep in mind, those radioed distances were not exact. It makes sense that they headed directly towards Howland, expecting to home in on Itasca's radio signal when they came within range. But they would have recognized that there was some problem with this plan when they couldn't receive the radio signal at the point that they expected to, let's say about 200 NM out. At that point, or shortly after that, Noonan would start the backup plan to do the landfall procedure. The earlier you turn off the direct course to aim for the interception point, the fewer extra miles you have to fly so they would not have delayed this turn unnecessarily. There was little downside to doing this because, if on the way to the interception point, they then started to receive the radio signal, they could turn immediately to home on the station after adding very few extra miles to their flight path.
I am also a bit troubled as to why they would have stayed on the 157/337 line an hour after having arrived at where they thought Howland was. It makes sense that they would have started a expanding square search pattern as you suggest but this would not be the case if you were flying on the line N and S on the 157/337 LOP an hour after you had arrived. Perhaps there was not plan or knowledge of how to begin the search pattern since they were lost. Perhaps they did search and going back in the line was a last ditch effort as the fuel started to run very low.
The only way I can make sense out of this statement is that they were flying a modified search pattern with longer legs parallel to the LOP and shorter legs perpendicular to it. Earhart might say that she was flying north and south "on the LOP" when on one of these long parallel legs.
gl