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    Re: A-10 Sextant Manual
    From: Gary LaPook
    Date: 2009 Jun 11, 09:12 -0700

     From looking at his chart and the Nautical Almanac it is clear that the
    highest altitude he measured on sun was about 51 degrees which would
    produce a three-tenths of a mile offset at 45 miles (Table 19) and maybe
    one NM two degrees along the LOP, nothing to worry about.
    
    For those curious about computing winds based on drift sights I have
    attached an excerpt from Air Force Manual 51-40.
    
    gl
    
    Gary LaPook wrote:
    > Chichester did use  Mercator charts, actually plotting sheets, for
    > this flight. I have attached his charts. The first two are
    > illustrations from his books. The third is figure 41 from Chichester's
    > own explanation of the navigation of this flight published in the
    > Observer's Book, which I have also attached. This chart is a
    > simplified copy of the following charts, the actual chart that he used
    > on his flight from Norfolk to Lord Howe. The last chart is his actual
    > chart used for flying to Norfolk from New Zealand. I have also
    > attached Hughes' explanation of the navigation.
    >
    > The actual charts may look confusing because of the arcs and the
    > radial lines which was Chichester's method of determining the wind
    > encountered in flight based on his observations of his angle of drift
    > on two different headings. More modern practice is to plot the drift
    > lines on an E-6B rather than on the chart itself to determine the
    > winds. If you are just interested in the celnav aspects, you can
    > ignore all of these lines as Chichester did in his simplified figure
    > 41 in the Observer's Book.
    >
    > Your concern over plotting a curved LOP as a straight line on a
    > Mercator chart is unwarranted. I have attached Table 19 from Bowditch
    > which shows how much the curved LOP departs from a straight line. You
    > can see that, except for very high altitudes, this factor can be
    > ignored especially given the lower level of precision available with
    > celnav in flight.
    >
    >
    > You can download the complete American Practical Navigator for free
    > from this website, choose in the "select" box.
    >
    > 
    http://www.nga.mil/portal/site/maritime/?epi_menuItemID=35ad5b8aabcefa1a0fc133443927a759&epi_menuID=e106a3b5e50edce1fec24fd73927a759&epi_baseMenuID=e106a3b5e50edce1fec24fd73927a759Christian
    > Scheele wrote:
    >
    > gl
    >> Hello Gary,
    >>
    >> I hear you and I largely agree with you but please bear with me for a
    >> moment while I try to work something out. If you're assuming that a
    >> navigator is plotting on a Mercator chart ( I think Chichester was),
    >> I wouldn't say that deliberate offset navigation is a modern
    >> implementation of latitude sailing. Latitude sailing, using the noon
    >> method, gives you a latitude line and this means a position line that
    >> can be plotted on a Mercator chart as a straight line without the
    >> need for any corrections. When you find a position line on the basis
    >> of a sun shot at any other time other than noon, your plotted
    >> position line, because it is plotted as an uncorrected straight line
    >> on a Mercator chart, will always be "a bit" assumed unless..... you
    >> are actually plotting a real great circle arc, i.e. a position line
    >> corrected for the map projection. Could the astrograph do this? I
    >> assume not, because the curves on its foils are rigid, unless it
    >> actually came with maps to fit the curves, rather than curves to fit
    >> the maps, but that would be impractical way to do something I would
    >> imagine the astrograph was supposed to make easy in the first place.
    >> I am assuming, therefore, that the astrograph was, from a precision
    >> point of view, not a "perfect" plotter. I know that in world war 2
    >> some navigators had an astrograph over their tables, but how many I
    >> don't know, I don't know much about the military stuff. In any event,
    >> Chichester didn't use an astrograph. I'm still assuming that
    >> Chichester used a Mercator projection. Chichester was using sun, not
    >> star shots. When using the stars, if you have a reasonably good idea
    >> of where you are, say you are sure that you must be within about 2
    >> degrees, depending on which region you are in, of a point on the the
    >> position line which, again, is a small arc of a great circle track,
    >> and assuming that the global position of the sun is far away enough,
    >> then the aforementioned problem should not exist as you can then plot
    >> your position more or less as a straight line - the great circle
    >> radius is so big - just like Weems did in his books plotting star
    >> altitude curves. I say 2 degrees because I am taking an extract of
    >> Weems pages showing a latitude and great circle radius for which this
    >> arc size to gradient of position line relationship holds. You can't
    >> plot the "sun curves" in the same way as you would star curves,
    >> because of the rapid change of declination. When I said Chichester
    >> had an assumed  position line rather than a position line, I was
    >> assuming that such a relationship which allows one to plot a great
    >> circle arc as a straight line may not have been available to
    >> Chichester, had his D.R. navigation not been so good, all the while
    >> still assuming Chichester was plotting position lines as
    >> "uncorrected" straight lines onto a Mercator map.... But I am not
    >> entirely sure, maybe I should have phrased it as a question...here's
    >> what I was thinking.......Let's say his D.R. had not been so good and
    >> he had been on the unfavourable side of the position line, that is
    >> away from the island, further than he had planned to be at the
    >> precomputed time. Let us assume that this error had brought him
    >> beyond 2 degrees (120 miles) or so of the predetermined point on the
    >> position line.   Assuming this scenario, how serious would it have
    >> been had he plotted his position line as a straight line on Mercator
    >> chart? Imagine: The straight now really becomes a curve if, only a
    >> very slight one. Could this produce a substantial error? Norfolk
    >> island is 35sqkm. Lord Howe is 56sqkm. For this last stage of the
    >> flight, D.R. is of course used again. Did he have the drift, wind
    >> speed indicators that should have been around by the time of world
    >> war 2? What about his compass? Did he have more than one? An
    >> induction compass like Lindbergh - who did not use astro on his epic
    >> flight - to check the magnetic one? Let's say some of these issues
    >> come in and another error, albeit a much smaller one, is added on to
    >> the existing one. Could a pilot miss the island due to the combined
    >> sum of such errors? Very important in this regard is: How high was
    >> Chichester flying, i.e. what what was the range of his visible
    >> horizon? Perhaps I'm wrong and it wasn't that serious and any error
    >> would have been "innocuous" due to the far visible horizon. In
    >> referring to Chichester's navigational method, I was implicitly
    >> including this speculation....
    >> Again, I largely agree with you  ....but there's just that shred of
    >> doubt.
    >> I'll take a thorough look at your website as soon as possible.
    >> Thanks, I appreciate the tip.
    >>
    >>
    >> Christian Scheele
    >>
    >> ----- Original Message ----- From: "glapook---.net"
    >> 
    >> To: "NavList" 
    >> Sent: Thursday, June 11, 2009 4:01 AM
    >> Subject: [NavList 8612] Re: A-10 Sextant Manual
    >>
    >>
    >>
    >> Well, I don't know that you can call it "reckless" since Chichester's
    >> deliberate offset navigation procedure became the standard navigation
    >> method for finding islands and was taught to thousands of navy and air
    >> corps navigators during the second world war. It was actually a just a
    >> modern implementation of the centuries old method of latitude sailing,
    >> approaching to one side of a destination, east or west, and then
    >> following the latitude LOP to the destination.
    >>
    >> See the texts I have posted on my website at :
    >>
    >> http://www.geocities.com/fredienoonan/
    >>
    >> Go to "List of topics" then to "Single LOP landfall procedure."
    >>
    >> gl
    >>
    >>
    >>
    >> >>
    >>
    >>
    >
    
    
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