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    Re: Amelia Earhart's aerial navigation
    From: Gary LaPook
    Date: 2009 Nov 17, 04:07 -0800
    Frank asked:
    I remember a discussion a few years ago of a proposed theory claiming that Noonan didn't understand the correction for the Moon's parallax... that theory struck me as pretty light-weight at the time. Can we dismiss it? 
    
    Yes, we con put a stake through its heart.
    
    
    The question of the Moon has relevance since it would have been available during the day as they approached Howland island and would have provided a good cut to the sun line allowing for a fix. TIGHAR's theory is that Noonan knew he was on the 157º-337º sun line LOP (from Earhart's last transmission) but didn't know where he was located north or south along this line so just blithely followed it to the south to finally arrive, after 350 NM, at Nikumaroro( then Gardner) island. The availability of the Moon line shoots down this contention which puts a nail in TIGHAR's coffin. 
    
    The "Death By Parallax" web page

    http://www.bbc.co.uk/dna/h2g2/A3694854

    has the basic navigation wrong.  First it states
    that the moon passed 20º south of Howland at 7:01 am (1831Z) when, in
    fact the moon passed NORTH of Howland at 1837Z and its altitude was 76º
    56' at that point since its declination was 13º52' North ( see Nautical Almanac for 1937, attached) and the latitude of Howland is 0º 48' North.

    The "horizontal parallax" of the moon at that time was 59.2' from the
    above almanac page. But that amount of parallax exists only if the altitude of the
    moon was horizontal or zero degrees. To find the correction that must be
    applied to the sextant altitude you must multiply the horizontal
    parallax by the cosine of the altitude. When you do this you find that
    the error in omitting the "parallax in altitude" correction only comes
    to 13.4' which is the same as 13.4 nautical miles because of the Moon's high altitude of
    76º 56' at that point.

    If Noonan had omitted the "P in A" correction then the plane would have been 13.4 NM north of
    where he thought it was so he would have been north of Howland and he would have stumbled onto  Howland while
    following the sun line on the heading of 157º T. If they had not seen Howland then they would have seen Baker island which is also on the 157º-337º sun line LOP 42 NM south east of Howland. In order to miss both of these islands with the 20 NM visibility reported by Itasca the plane would have had to have passed more than 62 NM south of Howland and no likely error in the moon line could have produced an error that large.

    At the time of their last transmission at 1912 Z the altitude of the
    moon was still high at 75º 41' so the "P in A" correction was still only 15.1' or 15.1
    NM and the azimuth of the moon was 328º T so omitting the correction
    would still place them north of the island.

    However it is very unlikely that Noonan could have made this mistake
    since the navigation table he was using, HO 208, Dreisenstok, has the
    "MOON" correction table on the very first page, just inside the cover,
    and this table incorporates the "parallax in altitude" correction with the
    refraction correction. Adjacent to this table, and on the same page, is
    the table for "Sun or Star" which only has the refraction correction.
    These very same tables are also found in all the commonly available
    tables of the time including HO 211 and the Weems Line of Position Book
    going back at least as far as 1927. This table does not incorporate a
    correction for semi diameter since it is for use with a bubble sextant
    such as Noonan was using.

    BTW, the horizontal parallax is calculated by taking the arc sin of (
    the radius of the earth, 3440 NM, divided by the distance to the moon.)
    Since this distance varies during the month  from 196,164 NM to 218,954
    NM  the H.P. varies from 60' down to 54'.

    gl



    Gary LaPook wrote:
    1. Most likely he was using a Pioneer octant similar to the A-5 but 
    there is no record showing for sure what kind of octant he was using. 
    See: http://www.fer3.com/arc/imgx/A-5-Manual.pdf
    
    2. TIGHAR claims that he was also carrying a marine sextant. They base 
    this claim on a letter written by Noonan to Weems in which he describes 
    the equipment carried on the much larger Pan Am Clippers including a 
    marine sextant as a "preventer." There is no reason to believe that he 
    carried one in the much smaller Electra, no records, no testimony, and 
    not on the Luke Field inventory (after the takeoff accident.)
    
    3. Mary S. Lovell's 1987 book, "The Sound Of Wings" discusses the
    different coordinates for the island.  Lovell writes that Williams had 
    used the coordinates
    listed in "Lippencott's Geographical Dictionary of the World" and also
    used by the Navy;s Hydrographic Office, as 0º 49' 00" north and 176º
    43' 09" west. She also states that Itasca had corrected the coordinates
    of Howland on the 1936 cruise but that those had not been published by
    the time Williams had consulted the Hydrographer's office.
    
    
    That position published in the 1938 edition of Bowditch was 0 ° 48' N, 
    176 ° 38' W. The previous position had been given about 5 NM further to 
    the west but Noonan may have had the correct position to work with.  
    Assuming that he computed his LOP to hit that spot five miles to the 
    westward and assuming normal accuracy of a celestial LOP shot from a 
    plane is 7 NM ( I will not explain why this is so) then if that error 
    placed them to the west of that LOP they would still pass only 12 NM 
    west of Howland so should have been able to see it given the 20 NM 
    visibility reported by Itasca. If the error was less or if it put them 
    to the east of the LOP they could have passed much closer and, possibly, 
    right over Howland.
    
    
    The position of Howland from Google Earth shows the southern tip at 0º 
    47.7' N, 176º 36.9' W. The northern tip is 0º 49.2' N. 176º 37.4'W. The 
    farthest west shore is at 176º 37.5' W and the eastern shore is 176º 
    36.7' W. The average of these is about 0º 48.5'N, 176º 37.0' W about a 
    mile east of the position given in Bowditch.
    
    I decided to do some more checking on the accuracy of Google Earth 
    coordinates to make sure they were accurate in the Pacific. I found the 
    published coordinates of Mili airport, 6º 05' N, 171º 44'E;  Mujuro 
    airport, 7º  03' 44'' N, 171º 16' 19" E; and Kosrae airport, 5º 21' 25" 
    N, 162º 53' 30"E since these were the closest to Howland. Then going to 
    them with Google Earth I found that the Google Earth coordinates were 
    exactly right, correct to the accuracy of the positions given in the 
    airport database. Mili was only given to the nearest minute but the 
    others were to the second. ( A second is only 100 feet!) You can check 
    for yourself, just go to Google Earth with those coordinates which you 
    will see fall on the runways.
    
    
    
    The only coordinates that have any relevance are those for where Howland 
    is actually located, which we now know to a high level of accuracy, and 
    the coordinates known to Noonan that he was aiming for. The difference, 
    if any, would be the size of any built in error in following the LOP to 
    the island. If Noonan was using the 176º 43' W value then he was aiming 
    about five or five and a half NM west of the western shoreline of 
    Howland. If he was using the 176º 38'W value he was aiming within one 
    half mile of the shoreline. Either way they should have been able to see 
    the island.
    
     In looking at the location of Howland and how possibly wrong 
    coordinates for the island may have contributed to Noonan missing the 
    island we have all forgotten an important fact, Itasca was making smoke. 
    Smoke from ships can extend for great distances and be seen for many 
    miles. It was these smoke trails on the horizon that U-boats searched 
    for  when trying to find a ship to attack. Smoke is made on purpose by 
    spraying unburned fuel oil into the exhaust stack much like smoke is 
    made on air show aircraft.
    
    All of the descriptions and the photos of the smoke screen being made by 
    Itasca say that instead of rising high up in the air that the smoke was 
    blown downwind. The wind was out of the east. This means that the smoke 
    would have been blown many miles downwind, to the WEST, probably more 
    than ten  miles (Safford) and beyond the erroneous coordinates given for 
    Howland and probably much farther. This means that even if Noonan had 
    been  aiming for the erroneous coordinates  he would certainly have seen 
    the smoke and followed it to Howland. Water don't burn. If they saw the 
    smoke they would have known that there was something at the end of the 
    smoke trail, a ship or an island, either of which wold have been a 
    better than splashing down in the ocean. And it wouldn't take them very 
    long to follow it to the end to see what was making the smoke even if 
    they went the wrong way at first. Since they had been fighting a 
    headwind all the way  they knew that the wind was out of the east so if 
    they saw the smoke they would have known to follow it to its source, to 
    the east.
    
    4. The equipment carried on the abortive westbound attempt was 
    inventoried after the takeoff accident at Luke Field. No known list of 
    equipment carried on subsequent attempt.
    
    5. They would have taken the sights at cruising altitude, about ten 
    thousand feet using the bubble octant. One of many reasons to not use a 
    marine sextant is the very large dip correction from high altitude which 
    has a great uncertainty due to the uncertainty in the altimeter. Also, 
    at ten thousand feet, the horizon is 130 NM away and it is very unlikely 
    that you would be able to see all the way to the natural horizon due to 
    limited visibility. Using a marine sextant Chichester had to descend 
    down almost to the sea so that he could calibrate his altimeter and then 
    climbed to one thousand feet to take the observation.
    
    6. The story about the moon's parallax was all hooey. Noonan used 
    Dreisenstock. On the first page are the sextant correction tables, one 
    for sun and stars and one for the moon. The moon correction table 
    combines the P in A correction with the refraction correction so there 
    is was no way for Noonan to correct a moon observation without allowing 
    for P in A. See attached.
    
    gl
    
    
    
    frankreed{at}HistoricalAtlas.com wrote:
      
    I thought it might be interesting to get a conversation going about Amelia Earhart's navigation --really Fred Noonan's navigation-- on their ill-fated circum-navigation back in 1937. There's a movie opening this week, "Amelia", produced by and starring Hilary Swank as Earhart. It's getting beat up pretty bad in the early reviews (currently at a dismal 22% fresh on RottenTomatoes.com: http://www.rottentomatoes.com/m/amelia_2009/), but I'm sure many of us will see it eventually.
    
    So... I know next to nothing about their navigation. Gary Lapook knows lots, and I expect I'm setting you up for some typing, Gary. :-)
    
    I'll just start off with some basic questions: what kind of sextant did they carry on that flight? Did they have multiple instruments? Were their different instruments during various legs of the flight? At what altitude would sights have been taken (or did it matter)? I remember a discussion a few years ago of a proposed theory claiming that Noonan didn't understand the correction for the Moon's parallax... that theory struck me as pretty light-weight at the time. Can we dismiss it? Did Earhart herself know any celestial navigation?
    
    Thanks in advance to any and all who can fill me in on this.
    
    -FER
    PS: Hey, Gary: when you visited Mystic back in 2008, did you get a chance to drive by the house where Amelia married George Putnam in Noank?
    
    
    
        
      
        
    
    
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