Seeking Comments on New Date Line Theory

[Ric Gillespie]

Proof by Noonan giving o.b. sunset coordinates for precomputed time point , by mathematics inviolably connected.

When did Noonan give sunset coordinates for a precomputed time point?

[Walter Runck]

R.Jones . Angle for observation of sunset. A/c heading 079 T , sunset line 023-203 . Sight angle 079-23 = 56 degrees w.r.t. A/c´s axis , large enough for observarion through l.h. cabin door , magn.variation included ; window installed with special flat glass, no disturbance by vertical rudder. Proof by Noonan giving o.b. sunset coordinates for precomputed time point , by mathematics inviolably connected.

I thought the sun set in the west, more or less. So if the terminator ran 023-203, the azimuth of the sun as it set would be halfway in between at 293T.  They were heading easterly at 079T, so her six oclock was at 259T and the sun was at an angle of 34 degrees to the tail, or 144 degrees off the bow of the aircraft, not 56.  This was about her seven oclock.  Tough spot to shoot the sun if aircraft remains on course.

I'm going to wait for a more clear presentation of this hypothesis before investing further effort.

[Walter Runck]

Since comments were solicited on this theory, I'd like to add that evening twilight observations on the East Coast very often occur around midnight Greenwich time, so a difference of a few minutes during a busy time of day for a navigator in an Eastern ( GMT-5 or 4) ZD can force you to a different day in the almanac.  It's a pain, but a well understood pain and since FN worked up and down the east coast of North and South America, it's hard to imagine (although impossible to disprove) him getting tripped up on what was a very normal part of his existence.

I liked the thoughtfulness and presentation of the concept.  Thank you for the input.

[h.a.c. van asten]

Reply 32 W.R. The 56 deg mentioned is tha angle between A/c´s heading and the sun line (Az 67 deg @ sundown) to port. Your 34 deg from tail side is correct , imho no first line problem since A/c could , if necessary , steered more northwards for a while without risk since Nukumanu was nearby. Occam´s razor works in all directions.

[h.a.c. van asten]

Stays aloft that " local midnight" and "date line time" do not exist when navigating on GMT schedule , the latter as long as GMT2400 is not surpassed. July 02 Almanac page(s) was/were the only on stage for Noonan.

[Bob Brandenburg]

According to your paper, Noonan preset the bubble sextant to +53', including 37' for refraction.  How did he know the value to use for refraction correction?

[h.a.c. van asten]

53´ was an error (later corrected for sunset , for sunrise valid). The sun is affected by refraction , as a result we see the 32`diam. disc a number of arcminutes higher than it is actually w.r.t. the horizon. A bubble sextant registers on the sun´s centre which is also the reference for sun´s altitude in nav tables. At sunrise and sunset the refraction generally is 37 arcminutes and we see the sun this " distance" above the horizon. By presetting the bubble sextant negatively with 37´ on its scale , the true sun is in the horizon at collimation of the apparent sun and the horizontal crosshair which is the artificial horizon of this intstrument. For using the mariner´s sextant at sunrise/sunset we must apply additional correction for sun´s semi diameter of 16 arcmin , giving a total scale correction of 37´+ 16´ = (-) 53´. With this latter figure (sometimes taken 50´.0) sunrise-set tables in almanacs have been set up , giving LMT for upper limb (U.L.) in the horizon. By presetting a ship´s sextant for 53´ we see the apparent sun´s U.L. come up whereas the true sun´s centre is 53 armin below the local horizon.Above altitude 1,000 - 1,500 meters (av. 3,000 ft) the local horizon is not visible (optical path through haze too long) around the world and a bubble sextant must be used for any astro ; since the mariner´s sextant has considerably better accuracy it can effectively be used if the horizon is clearly visible. With low sun the lower limb of the sun is due to distortion unservicable for relably astronav.

[h.a.c. van asten]

reliable astronav. (typo)

[Bob Brandenburg]

The question is:  How did Noonan know how much refraction correction to apply?  Where did he get that information?

[h.a.c. van asten]

Refraction & Parallax (this latter for the sun negligible) are listed in Nautical Almanacs and p.e. in HO.no.208 "Corrections to Observed Altitude of Sun , Stars , and Moon" , the tables being derived from physical / astronomical formulas. It is known that Noonan always used H.O.208 "Navigation Tables for Mariners and Aviators" by J.Y.Dreisonstok , USN. Listings also appear in H.O.no.9 "Useful Tables".

[h.a.c. van asten]

R.Brandenburg. For navigators , H.O.no.117 "Azimuths of the Sun" was in the era available. For precision I used the underlying formula from spherics :  {cos Az =  +/- sin d - (sin h . sin L)} / (cos h . cos L). Shorter formulas , giving  sin Az , exist but the outcomes are ambiguous. For sunrise/sunset at June , December , 21st : Az = sin d / cos L . Results always for centre of sun . Az = azimuth from South , d = declination , h = elevation , L = latitude , all in degrees , arcminutes & -seconds.

[Bob Brandenburg]

The lowest sun altitude for which H.O. 108 gives a refraction correction is 6 degrees (correction -8').   The lower limit in the 1937 Nautical Almanac is 6.5 degrees (correction -7.8').

So the question remains:  how did Noonan know that he needed the refraction correction you claim he used?   

Are you suggesting Noonan had a copy of H.O. 117?  If so, what is your evidence?

Are you suggesting Noonan used -- or even was aware of -- the algorithm you used?  What is your evidence?

[h.a.c. van asten]

The 37 arcmin refraction of sun near the horizon is a by navigators universally known figure , besides that it is computed from spherics and appears in all textbooks & handbooks on navigation. Having H.O.no.17 (Azimuths of Sun) [I do not have my copy at hand here and do not readily remember the issue number , 117 , or 17] on board was for Noonan not needed : with the declination of sun near its maximum , the azimuth of the sun at sunrise/sunset in the equatorial region is always (90 - 23) = 67 deg .The formula is : cos Z = sin d / cos L =  0.39073 for which is found (now calculator , then log cos table) 67 degrees from North in the northern hemisphere , for d=23 and L= 0.

[Ric Gillespie]

The 37 arcmin refraction of sun near the horizon is a by navigators universally known figure ...

As usual, you have no evidence - just your own suppositions which you regard as facts. 

[h.a.c. van asten]

Proof by Noonan giving o.b. sunset coordinates for precomputed time point , by mathematics inviolably connected.

When did Noonan give sunset coordinates for a precomputed time point?

The position at 0730 GMT was given 159-07´-E / 04-33.5-E . Sunset at this coordinates pair was at 071930 GMT (071545 GAT) , the position has been recomputed step by step (EJN ,April 2011) via H.O.208 and by direct spherics , for the same point of time. It is therefore reasonable assumption that Noonan precomputed a running sunset fix , made the observation and informed Amelia to communicate the results at 0720 GMT (time gap 1/2 minute).