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[Roger London]

Lae, sighting Nauru, to Howland           [extensive formatting and images have not transferred into this: please see attachments]

The details below are to illustrate the principle of how a 5600ft high light could have thrown them way off course, and whilst intending to be reasonably representative are not definitive.

For simplicity I leave to others the accurate calculation and conventions of true/magnetic, sm/nm, altitude/speed/fuel, metric/imperial, dead-reckoning/celestial/lunar/solar, nautical/Google map subtleties, air/ground speed, etc.

Below are simple rounded figures, and a large chunk of what MyFred might have considered! I use MyFred in attempting to alleviate future Forum-searches using extracts out of context.

They illustrate how with the wrong height for the Nauru light the closer one flies to Nauru the less the subsequent navigational error. Directly over-flying the Nauru light only provides head- and not cross-wind figures.

For indication of winds and weather reports see: http://tighar.org/Projects/Earhart/Archives/Research/ResearchPapers/Worldflight/2ndattemptweather.html

The calculations below do not address whether the before Nauru, and after Nauru, winds are from different, or one, weather system. Here they are regarded as steady for each leg. See footnote: Winds

Nomenclature:
a) Figures for a heading change to counteract a wind I’ve called a course correction.
b) Figures to counteract flying parallel with their intended course I’ve called a course offset.



Course M  (sighting Nauru, ignoring Myrtlebank)
Direct flight to Howland on bearing circa 77degrees, with Nauru way-point course correction.
Aim is to arrive 70m north of Howland (range 2560miles) and pass 110m south of Nauru.
110miles is near the maximum distance the 560ft high Nauru light could be seen from the plane at 10,000ft.
Lae-Nauru:   Flight altitude 11,000ft.
      Range 1500miles at 150mph (air speed) plus 20minutes for the  initial climb and subsequent rain/squall avoidance, then mostly. Headwind 10mph, 1500miles/140mph(ground speed)=10.7hrs; 10.7+0.3hours=11hrs.
      S to N crosswind component 5mph. Course corrected to S by 11hrsx5mph=55miles over the 11hrs.

Nauru light bearing taken when tangential/opposite it:
Simply:
   Say light is circa 500ft asl, thus 11,000ft-500ft=10,500ft=circa 2miles below.
   They are on course, so, a fix on the light reads 89degrees, at 2mile high, thus they’d be in their correct position 110miles to its south.


See attachment: 20150106 Nauru lights 110miles.jpg

Believing light is at 5600ft:
   Calculation becomes the same angle reading of 89degrees BUT calculated at only 1 mile below, gives range of only 55miles.
   They are too far north indicating the southerly crosswind has increased pushing them 55 miles further north.
Two factors ensue:
   1: MyFred revises his original 5mph southerly crosswind course correction to 10mph; to bring them back south an additional 55miles (11hrsx10mph=110 miles total) over the Nauru-Howland leg.
   2: Believing they are offset 55miles north of intended position he offsets heading for the Nauru-Howland leg to bring them back south by 55miles. [Otherwise they’d continue and be flying parallel with their intended course & arrive 70+55=130miles north of Howland.]
   Their heading is now a potential 110+55=165miles to south.
   But they are not 55miles off position and after Nauru the southerly crosswind disappears as the wind becomes (veers?) northerly. Thus leaving them with a 165miles of unwanted course correction.
Nauru-Howland leg.:
   Range 1050miles, at 150mph air speed.
   Headwind component increases to 20mph, =130miles ground speed, flight duration 1050miles/130mph(ground speed)=8hours.
   The crosswind is now North to south at 10mph.
   Without course correction the crosswind will push them 10mphx8hrs=80miles to south.
   However at Nauru they are (as planned) 110miles south, and are on correct course to arrive 70miles north of Howland.
Result:
   Intending to be 70miles north of Howland, but now: less 110miles erroneous correction against non-existent southerly crosswind; less 55 miles Nauru-Howland course offset to south; less 80miles of unchecked northerly crosswind = 70-110-55-80=175miles south of Howland (circa 135miles S of Baker).


The GoogleEarth image below, modified in Photoshop, is only illustrative & it is not to scale:


See GoogleEarth attachment: 20150106 Howland nav diagram-02.jpg

What might the weather have been like 100+miles south (& west) of Howland?

A side observation:
   Its said* MyFred was an adherent of Sir F Chichester’s method of navigating to an isolated island by flying to a position 200miles N (or S) of the destination. Thus MyFred might well have targeted 200miles north of Howland On a 338degree bearing from Howland this intersects W177deg53’, thus forming a mathematical triangle with 200mile hypotenuse, a 185mile N-S side & a 90mile E-W side. With the same navigational errors and conditions in Course M above they could be 175 miles south but longitude W177deg53‘ thus 185-175=10miles north of Howland but Longitude W177deg53’ passes 90 miles west of Howland’s actual position.
   Thus if they then flew southerly along this 338-138 LOP (Line Of Position) they could be nearly 90miles west of Howland and pass more than 80 miles west of Baker. Too far to have spotted Howland especially if there were at a mere 1000ft and there was scattered cloud casting shadows on the sea.

   * Ref: M S Lovell in Sound of Wings pg357


Course N  (nearer Nauru)
Aim is to arrive 70m north of Howland (range 2560miles) and pass 40m south of Nauru, with intended course alteration after Nauru.
Lae-Nauru:   Lae-Nauru bearing 75degrees.
      Flight altitude 11,000ft.
      Range 1500miles at 150mph (air speed) plus 20minutes for the  initial climb and subsequent rain/squall avoidance, then mostly. Headwind 10mph, 1500miles/140mph(ground speed)=10.7hrs; 10.7+0.3hours=11hrs.
      S to N crosswind component 5mph. Course corrected to S by 11hrsx5mph=55miles over the 11hrs.

Nauru light bearing taken when tangential/opposite it:
   Nauru light fix of 87.1degrees at 2mile high puts them 40miles to south.


See attachment: 20150106 Nauru lights 40miles.jpg

      Believing light is at 5600ft: the reading is still 87.1degrees but calculated at only 1 mile below, puts them only 20miles to south of Nauru.
          They’ve apparently been pushed 20miles to north so MyFred perceives southerly crosswind has increased by 20/11= approx 2mph.
Two factors ensue:
   1) MyFred increases his original 5mph southerly-crosswind correction from 5 to 5+2=7mph, spread over the next 8hours for the Nauru-Howland leg, so as to correct them to the south by 7mph; viz 11hrsx7mph=circa 75miles to the south.
   2) Believing they are 20miles north of their intended position he offsets heading for the Nauru-Howland leg to bring them back south by 20miles.
   But for the next leg the crosswind has changed (veered?) from southerly to northerly and increased, and they are not 20miles off position.

Nauru-Howland leg:
   The now north to south crosswind component increases to 10mph, of which 0mph is corrected against.
   This northerly crosswind is now set to push them south by 11hrsx10mph=110miles.
   However at Nauru they are 40miles south, and are on correct course to arrive 70miles north of Howland.
Result:
   70miles north of Howland, less 75miles non-existent southerly wind correction; less 20 miles Nauru-Howland course offset, less effect of northerly wind pushing them 110miles south: 70 -75 -20 -110 =135miles S of Howland (circa 95miles south of Baker).

BUT they may also not be on the correct 338-158 LOP
   In the Nauru examples above they intend to arrive 70miles north of Howland, & need to obtain a sunrise and longitudinal reading to calculate the LOP.
   In 1935 Howland was shown as approx 6 miles west of its present-day position. MyFred may or may not have had the correct position.
   70miles north of 1935-Howland on bearing 338 is longitude circa 177-03’W
   But if they were actually well south and on longitude 177-03degreesW they could be:

Course M (Myrtlebank):    175 miles south and 30 miles west of Howland

Course N  (Nauru):       135 miles south and 30 miles west of Howland


Plus the Date Line: (see http://www.datelinetheory.com/p/effects-of-date-line.html)
   If MyFred used the wrong date in his celestial calculations after midnight on 2nd when they were still west of (ie before) the Date Line, the date onboard becomes the 3rd. Continuing to fly east and crossing the Date Line (IDL) it’d restore the date ‘back’ to the 2nd
   Using the wrong date after midnight and before crossing the Date Line, erroneously indicates to them that they are 60nm(69sm) being 1 degree longitude east of their actual position. The difference is due to the 4minutes daily change between sidereal day (23hrs 56minutes) and our 24hour day [http://en.wikipedia.org/wiki/Sidereal_time] Thus they’d be about 70m further west in both the examples above!

Course M (Myrtlebank):    175miles south of Howland and 30+70=100 miles west

Course N  (Nauru):       135miles south of Howland and 30+70=100 miles west
   … umm, a miss is as good as a mile! [and a mistress is even better . . . so the saying goes!]

Yet they made Niku!! So wherever they were might MyFred have decided, after aborting Howland, realise they must be too far south of Howland and thus their LOP was too far west, by at least 30miles, and thus, that they needed to fly east 30+miles, to obtain a fix on longitude 174deg30’W, then south . . . Perhaps 200 to 250miles, circa 2hrs flying and . . . Niku!?


Winds:
a) If the winds are from different weather systems then arguably one could use the average of the increase in wind speed for each leg.
   Namely:    Lae-Nauru 5mph, increasing to 10mph, being 7.5mph average.
         Nauru-Howland 10mph increasing to 20mph, being 15mph average.

b) If  it is one veered wind then the effect is mathematically more involved. Perhaps averaging from 5 to 20+mph over the whole route and steadily veering from southerly to northerly which continuously changes the cross- and head-wind component; and additionally the wind’s effect due to the plane bearing:
   Roughly:    1st leg: wind somewhat SE, aircraft bearing somewhat NE.
         2nd leg: wind somewhat NE, aircraft course-changed to somewhat SE.
    . . . a navigators’ paradise!

Noon Sight
Arguably a Noon Sight might have been the best to locate Howland but they‘d have been out of fuel before noon! Should they have left Lae later in the day?                  (20150108 RFW edit-save 35)

[Martin X. Moleski, SJ]

The details below are to illustrate the principle of how a 5600ft high light could have thrown them way off course, and whilst intending to be reasonably representative are not definitive.

The Warsaw Radio Mast was the second tallest structure ever built, they say.  It was 2,120 feet tall.

If there had been a mile-high radio tower on Nauru, I think we would know about it.  It would have been one of the wonders of the world!

The elevator took 30 minutes to travel from the bottom to the top of the tower.

The mast was equipped in 16 levels with air traffic warning lights with 200 watts power.

In 1988 the mast was repainted, but this could not be done to the desired extent, as there was not enough paint available.

Yes, if there had been a mile-high light, or if Fred thought it was a mile-high and it wasn't, and if they saw the light, or if they thought they saw the light, that would probably have thrown them off-course. 

I don't believe there was a mile-high tower.

I don't think Fred would have believed their was a mile-high tower.

I'm just expressing an opinion here about why I believe this is a red-herring, and therefore not likely to help determine where to look for the remains of the aircraft.

[Roger London]

Yes Martin, there are a multitude of ifs, that's life for all investigation. However as I've previously mentioned on TIGHAR there are hundreds of Peaks of Prominence throughout the world, and numerous websites about them, this URL is detailing islands:
http://en.wikipedia.org/wiki/List_of_islands_by_highest_point
Even the Galapagos in 'mid' Pacific. There are many in and around the Pacific.
MyFred must have encountered mountains on his various travels and at Lae being told in-print there was an island peaking at 5600ft need not have phased him. Indeed it would hardly be a radio mast that high, and I have not suggested that at all.

[Jerry Germann]

 In the case of the telegraph two wrongs don't make a right; Had Fred, been relying heavily on the information contained within, after studying it's content ,he may have questioned it's reliability. Note; The sender or reciever of the information has Nauru's location incorrect, as well* ( another typo ?) in addition to the blackened out center of the word ( bright)....if Fred had considered this light on Nauru of great importance, upon seeing these errors, it may have compelled him to question the telegraphs trustworthiness.

*  correct location 166.55 East
Note also ....wing? ......wind SE 3
 

[Roger London]

Indeed we are not to know what transpired, but something went wrong as they didn't locate Howland. Even if one discards Nauru entirely and focuses solely on Ontario's (two positions), or Myrtlebank a significant navigational error can occur. I have done detailed exercises (which I have not posted), one illustrates they might have ended up 85miles south of Howland. I believe these are pertinent navigational points and should be considered, and only where appropriate discarded.

[Martin X. Moleski, SJ]

As I've previously mentioned on TIGHAR there are hundreds of Peaks of Prominence throughout the world, and numerous websites about them ...

Here on this website is a post that shows that in 1921, Nauru was not that tall.

We'll just have to agree to disagree, I suppose.  You think Fred would have taken the telegram as gospel and based his calculations on it; I think he would not have.

[Andrew M McKenna]

What I find interesting about this is that we know something DID go wrong with Fred's navigation, otherwise they would have made it to Howland.

What exactly went wrong, we don't know, but exploring the options derived from clues I think is useful, especially when the results show that they may have ended up South and West of expected, which is where we've come to conclude that they must have been to miss Howland and end up at Nikumaroro going all the way back to Randy Jacobsen's Monte Carlo analysis and later work.

We may never know what exactly the error was, but there is nothing wrong with exploring the possibilities.

Andrew

[JNev]

That might be a stretch, Andrew: Fred, per his Pan Am memo (see last paragraph - last sentence quoted here) wrote "While the use of (radio) bearings will not insure extreme accuracy in navigation, they are nevertheless of inestimable value and will always serve as a dependable homing device."

The radio DF portion of the work was Earhart's.  It is tempting to believe that celestial - Fred's effort, might have gotten them home, but he in fact acknowledges the vagaries and limits of celestial for accurate tracking (read entire memo to get his full message).  By the above statement, Fred further acknowledges comfort, at the very least, in the notion of having a way 'home' via the radio. 

As such the flight could well have gotten within say, 15 miles of Howland - but with no radio DF of any effect, no landfall.   I picked that distance as one that might be reasonably demonstrated as outside of spottable range by the Itasca, and perhaps leaving Howland as not so distinguishable by Earhart and Noonan.

I realize the hard work and deep thought that went into Jacobson's Monte Carlo and how one can envision the Electra as being displaced from Howland by some distance to the south and perhaps west of Howland at the 'must be on you' point, by error and vagaries such as Fred mentions in his memo.  One must however also consider that those same vagaries could have led to outcomes not so supportive of our focus (a Gardner arrival), of course. 

In this case it may also be more difficult to find a red herring, as Marty reminds us to be alert for: it seems more difficult to predict an error at the end of a flight of this length with so many unknowns and unknowables thus than it would be to establish that the flight likely did not approach Nauru closely enough, much earlier in the flight, for the light to create a navigation error.

In any case, t'was apparently Earhart who should have been made to 'narful the garthok' for the end-of-flight miss, not Fred.  Fred may well have performed in a 'stellar' fashion and still missed the mark enough for the loss for want of a needed DF success.

[Frank Hajnal]

Since the subject of Nauru and Navigating has come up, something I noticed playing around with Google maps is that flying from Lae to Howland via an overflight of Nauru is very similar in mileage to flying Lae to Howland by a direct great circle route.  If AE's planned route had included an overflight of Nauru, that would have given AE and FN one more potential navigational reference point (looking for the lights of Nauru).  Also, Nauru had a radio station that had a broadcast frequency that was out of the range of the Electra's direction finding equipment, which might have offered one more opportunity to discover (either in flight or before) that there was a problem with the DF equipment before they were low on gas. 

I know, just a bunch of lots of ifs and might haves, but I find it kind of interesting nevertheless.

[Ric Gillespie]

Occam says keep it simple.  All it takes to put the flight significantly south of course is a stronger-than-forecast northeasterly wind during the overcast night. Reported winds-aloft at Howland the next day seem to bear that out.  That's what the Navy thought happened and why they sent Colorado to search along the LOP south of Howland. Later, as the post-loss radio signals became more and more credible and Lockheed said the plane had to be on land, they shifted the search to overflying the islands of the Phoenix Group. . 

[Bruce W Badgrow]

Everyone seems to be looking for the big navigational blunder that Fred Noonan made. In my opinion Fred didn't make any big mistakes, he didn't have to. There were enough inaccuracies in the documentation and the navigation methods in use in 1937 to make finding Howland Island visually a very iffy thing. One example is that it appears that the maps of the Pacific Ocean in use at that time showed Howland Island in the wrong place. In all the reports the US Navy wrote at the time of the Earhart search they say the island was 1 mile north and 5 miles west of where it actually is. The Clarence Williams strip chart also shows Howland Island at this incorrect location. Even if Noonan could locate his LOP and then navigate along it with GPS like precision, he still would have missed Howland Island by 5 miles. Back in 1937 navigation was not the exact science it is today.

Bruce W Badgrow

[Martin X. Moleski, SJ]

Everyone seems to be looking for the big navigational blunder that Fred Noonan made. In my opinion Fred didn't make any big mistakes, he didn't have to. There were enough inaccuracies in the documentation and the navigation methods in use in 1937 to make finding Howland Island visually a very iffy thing.

FWIW, I couldn't agree more.

Fred did his job.  He got them within radio range, with plenty of time and fuel to home in on Howland using RDF.  I don't think anyone expected him to get there unassisted.

I think Amelia is largely to blame for the loss of the flight.  "Proper Planning and Preparation Prevents [Pitifully] Poor Performance."

[Ric Gillespie]

There were enough inaccuracies in the documentation and the navigation methods in use in 1937 to make finding Howland Island visually a very iffy thing.

At the time Earhart disappeared PanAm was flying scheduled passenger service across the Northern Pacific hitting tiny islands (Midway and Wake) with precision week after week.  Finding Howland would not have been iffy at all had Earhart used the system pioneered, in part, by Fred Noonan.  Take off, use RDF to stay on course until you're out of range, stay more or less on course using dead Reckoning and Celestial until you're with range to use RDF to guide you to your destination.  PanAm Clippers had dedicated Radio Operators who communicated with ground stations in Morse code.  Dedicated navigators, like Noonan, did the DR and Celestial to keep the flight on course until it was within radio range.  The RDF bearings were taken by the ground stations on signals sent from the airplane.  The ground station then told the airborne radio operator what heading to fly. The radio operator passed that information to the pilot.  It was an entirely workable system and the basis for what Earhart intended to do.  Noonan did his job. She was not able to do hers because she failed to acquire the necessary knowledge and skills. 

One example is that it appears that the maps of the Pacific Ocean in use at that time showed Howland Island in the wrong place. In all the reports the US Navy wrote at the time of the Earhart search they say the island was 1 mile north and 5 miles west of where it actually is. The Clarence Williams strip chart also shows Howland Island at this incorrect location. Even if Noonan could locate his LOP and then navigate along it with GPS like precision, he still would have missed Howland Island by 5 miles.

Probably a myth.  Williams' strip charts were done sometime in late 1936 or early 1937 but by that time the correct location of Howland Island was known to the Coast Guard, the Bureau of Air Commerce and the Dept. of the Interior.  They were there building runways for Amelia.  It seems inconceivable that someone did not pass that information to Earhart.
The very fact that Williams' strip charts are now in the Purdue archive is a pretty good indication that Noonan didn't use them on the second world flight attempt.

[Martin X. Moleski, SJ]

The very fact that Williams' strip charts are now in the Purdue archive is a pretty good indication that Noonan didn't use them on the second world flight attempt.

Thanks, Ric.  That's the best laugh I've had this week!   

[Monty Fowler]

The very fact that Williams' strip charts are now in the Purdue archive is a pretty good indication that Noonan didn't use them on the second world flight attempt.

Now, now, we all know that paper, left to its own devices, will breed prodigiously. I've never actually seen it "in the wild," so to speak, but I know this must be true because the piles on my desk never seem to get any smaller. These Purdue strip charts are probably the demon spawn of some long forgotten cartographer.

LTM,
Monty Fowler, TIGHAR No. 2189 ECSP