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    Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    From: Henry Halboth
    Date: 2009 Apr 16, 20:15 -0700

    Hi all,

     

    I previously raised the possibility of limitations or restrictions to the use of Equal Altitudes for the purpose of obtaining the Lat/Long at Noon, and have several times been quoted to this effect in subsequent Posts. I hasten to emphasize that these limitations and restrictions are essentially quotations from the noted sources, i.e., Bowditch (1909), Raper (1909) and Lecky; they do not originate with me and seem to primarily concern the slowness of high Latitude altitude change as well as a larger error introduced by an error of only 1 min (arc) in the observed altitude.  These limitations or restrictions do not necessarily negate use of the method to obtain an approximate position – it just depends on the degree of approximation the user may find acceptable, as well as perhaps the expertness of the observer.

     

    Bowditch (1909) states ...”the interval form the meridian being not greater than 10 min (time) and the altitude not less than 75 degrees.” ...and, “... if observations be taken when the body bears not less than 80 degrees from the meridian, the time of meridian passage may with accuracy be regarded as equal to  the mean of the times of observation, no matter what course may have been steered by the vessel in the interval.”

     

    Lecky (22nd Ed) states ... “even in moderately high Latitudes the change in altitude near noon is very slow. Inversely, an error of only 1’ in the altitude means a large error in the time of Longitude.”  Although Lecky obviously does not favor this method utilizing the Sun, he speaks in favor of its use with Stars, and provides a clear rendition of Raper’s approximate correction for change in Latitude between observations.

     

    My use of Equal Altitudes for determination of Lat/Long at noon and Chronometer Error, both at sea and ashore, has been primarily between Latitudes 40 N and S, as well as in the tropics, with no practical high Latitude experience. I have always found it to be reasonably accurate. even when corrected for a difference of Latitude between sights. Much depends, of course, on the quality of the sea horizon available and the observer’s reaction time in accurately calling the time of the descending limb contact – this being extremely important to the success of the method, no hesitation or uncertainty in recognizing and acting on this later contact is allowable.

     

    At my stage of the end game, I certainly have no objection or criticism regarding the reinvention of navigation, yet must state a degree of perplexity at the effort being expended in making what was an historically simple procedure into the complexity of analysis here seemingly evidenced and elevating it to an all encompassing system of Celestial Navigation.

     

    Regards,

     

    Henry

     

     

     

      
    --- On Thu, 4/16/09, Brad Morris <bmorris{at}tactronics.com> wrote:


    From: Brad Morris <bmorris{at}tactronics.com>
    Subject: [NavList 7977] Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    To: "NavList@fer3.com" <NavList@fer3.com>
    Date: Thursday, April 16, 2009, 1:37 PM


    Hi Marcel

    There is no doubt that the human eye can place a line pretty reasonably.
    I was merely pointing out the difference between a mathematically rigorous
    least squares fit (which is what the LINEST function provides in Excel), and the proposed methodology.
    That isn't subjective or an opinion, rather it is a factual observation.

    I eagerly await Jim and Frank's independent results.  At this point, I think
    we can all begin to see that the proposed methods will provide an estimation
    of longitude (latitude is nearly free!).  What remains is a debate regards
    how well it performs. There may be exclusionary limitations, as alluded to
    by Henry and others.

    Best Regards
    Brad





    -----Original Message-----
    From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of Marcel Tschudin
    Sent: Thursday, April 16, 2009 1:04 PM
    To: NavList@fer3.com
    Subject: [NavList 7974] Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT


    Brad, regarding your comment on the least square fit:
    "The navigator is urged to, in one case, fair a line thru a series of
    data points or in another, to visualize a parabola as we slide the
    paper.  That isn't a least squares fit by any stretch of the
    imagination."
    It's actually surprising how well we can estimate a linear regression
    line through data points with a reasonable correlation only by using a
    ruler. In this case it would only require to adjust the scale of the
    axis accordingly.

    Marcel

    On Thu, Apr 16, 2009 at 6:55 PM, Brad Morris <bmorris{at}tactronics.com> wrote:
    >
    > I agree with your result for a least squares fit of the parabola to the measured data. With the variation
    > limited, there is no doubt that the least squares fit will provide a reasonable parabola and therefore a
    > fairly good estimation of Lat and Lon.  If this is how the method is used in practice, you will find little
    > argument from me.
    >
    > However neither procedure, as I understand them to date, uses a least squares fit.  The
    > navigator is urged to, in one case, fair a line thru a series of data points or in another, to visualize
    > a parabola as we slide the paper.  That isn't a least squares fit by any stretch of the imagination.
    > As such, we may find that the deviation in longitude is somewhat greater than your value of 5.68nm.
    >
    > Best Regards
    > Brad
    >
    >
    >
    >
    > -----Original Message-----
    > From: NavList@fer3.com [mailto:NavList@fer3.com] On Behalf Of waldendand{at}YAHOO.COM
    > Sent: Thursday, April 16, 2009 11:23 AM
    > To: NavList@fer3.com
    > Subject: [NavList 7970] Re: Lat/Lon by "Noon Sun" & The Noon Fix PROVE IT
    >
    >
    > The .doc file works great. Thanks.
    >
    > I took George's spreadsheet and automated it with a macro.
    >
    > First, I used it to generate 1000 sets of 13 observations.  For each set, I let excel fit the parabola, and find the time and altitude of its peak.  I then find the difference between the resulting latitude and longitude thus calculated and the true values.  Thus for each set of 1000, I get a mean and standard deviation of the error.
    >
    > Using George's convenient "scatter switches", I tried various combinations.  He has four switches. In order, the first turns on/off the scatter in ship speed (if one always uses the nominal 10 knots in the calculation), the second changes the equation of time (as I understand it, changing the value to be calculated as opposed to introducing scatter into the result), the third changes the longitude (same comment), the fourth adds scatter to the observed altitude. In the table below, the switches are listed in order, 1=on, 0=off.
    >
    > As can be seen for everything on, the standard deviation of longitude error in nm is 5.68.  It can be seen the ship speed scatter seems to have a slightly greater effect than the altitude reading scatter.
    >
    > The 1 mile lat and 5 mile long estimates look pretty good to me. YMMV.
    >
    >
    >
    >
    > 1,1,1,1 min lat min long        nm long
    > mean    0.00    0.19    0.11
    > stdev   0.40    10.16   5.68
    > max     1.29    48.02   26.85
    > 0 1 1 1
    > mean    0.01    0.19    0.10
    > stdev   0.44    6.57    3.67
    > max     1.55    22.64   12.66
    > 0 0 1 1
    > mean    0.00    -1.00   -0.56
    > stdev   0.42    6.73    3.77
    > max     1.41    20.77   11.61
    > 0 0 0 1
    > mean    -0.01   -0.38   -0.21
    > stdev   0.44    6.72    3.76
    > max     1.14    20.50   11.46
    > 1 1 1 0
    > mean    0.00    -0.22   -0.12
    > stdev   0.05    7.48    4.18
    > max     0.25    24.18   13.52
    > 0 1 1 0
    > mean    -0.01   -0.38   -0.21
    > stdev   0.00    0.01    0.01
    > max     0.00    -0.34   -0.19
    > 1 0 0 1
    > mean    0.01    0.17    0.09
    > stdev   0.42    9.97    5.58
    > max     1.33    32.45   18.14
    > Linked File: http://www.fer3.com/arc/imgx/dwVERSION2.xls
    >
    >
    >
    >
    > "Confidentiality and Privilege Notice
    > The information transmitted by this electronic mail (and any attachments) is being sent by or on behalf of Tactronics; it is intended for the exclusive use of the addressee named above and may constitute information that is privileged or confidential or otherwise legally exempt from disclosure. If you are not the addressee or an employee or agent responsible for delivering this message to same, you are not authorized to retain, read, copy or disseminate this electronic mail (or any attachments) or any part thereof. If you have received this electronic mail (and any attachments) in error, please call us immediately and send written confirmation that same has been deleted from your system. Thank you."
    >
    > >
    >



    "Confidentiality and Privilege Notice
    The information transmitted by this electronic mail (and any attachments) is being sent by or on behalf of Tactronics; it is intended for the exclusive use of the addressee named above and may constitute information that is privileged or confidential or otherwise legally exempt from disclosure. If you are not the addressee or an employee or agent responsible for delivering this message to same, you are not authorized to retain, read, copy or disseminate this electronic mail (or any attachments) or any part thereof. If you have received this electronic mail (and any attachments) in error, please call us immediately and send written confirmation that same has been deleted from your system. Thank you."


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