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    Re: Longitude from Local Apparent Noon Altitudes
    From: Peter Hakel
    Date: 2012 Aug 19, 17:44 -0700
    Hello Bruce,

    Thank you for your data set, it was a good exercise.  :-)

    I processed your numbers with the following Excel spreadsheets described on my site:

    time.xls: watch corrections and time-zone conversions
    alt_corr.xls: Hs to Ho conversions
    sun.xls: almanac data
    noon_motion.xls: the actual calculation (parabolic least-squares fit to data adjusted for vessel motion and declination change), of which I attach a screenshot.

    I get:
    Latitude:      N 42d 02.4'    (42.040)
    Longitude:  W 70d 04.7'    (-70.078)

    I don't calculate the associated errors but, in any case, this location agrees very well with the already posted results.

    In the attached map, the calculated location is indicated by the red/green pins.  There is a distance scale on the bottom left.  As expected, latitude is quite accurate; longitude agrees a little less, but it is still good.

    Peter Hakel

    From: Bruce J. Pennino <bpennino.ce@charter.net>
    To: NavList@fer3.com
    Sent: Sunday, August 19, 2012 7:41 AM
    Subject: [NavList] Longitude from Local Apparent Noon Altitudes

    I'm still working to improve CN skill and my data has improved (especially since I finally learned to keep object centered when I "swing the arc").
    I took the altitudes below and tried to determine longitude by "folding the curve" and taking mid point between rising and falling limbs. Decided to post data because it is useful for discussion and teaching students. Further, I'm curious that there must be a way to do a "best fit" regression analysis to determine high point Hs and line of symmetry (essentially longitude). Would love to hear others' conclusions about latitude and longitude.
    I'll eventually post exactly where I was , but for now the data was taken from the northern tip of Cape Cod very near the Pilgrim Monument in Provincetown,MA.
    The raw altitudes Hs are shown below. Index correction is zero. Eye height 14 ft. Date August 17, 2012. All times are eastern DAYLIGHT time. Watch is 26 seconds SLOW. Time on watch hour:min:sec altitude xx deg yy.y minutes
    Altitudes (measured with Astra iii B)
    12:21:39 60d 28.0 m ; 12:22:52 60d 34.8 m ; 12:24:26 60d 36.8 m;
    12:26:05 60d 38.6 m ; 12:26:59 60d 40.8 m ; 12:28:23 60d 41.8 m;
    12:29:35 60d 44.8 m ; 12:30:39 60d 44.6 m ; 12:31:50 60d 46.8 m;
    12:33:07 60d 47.8 m ; 12:35:13 60d 51.5 m ; 12:36:13 60d 51.5 m;
    12:37:03 60d 50.8 m ; 12:38:23 60d 53.6 m ; 12:39:36 60d 52.4 m;
    12:40:36 60d 52.2 m ; 12:41:44 60d 54.0 m ; 12:42:45 60d 52.8 m;
    12:43:52 60d 55.0 m ; 12:44:55 60d 54.2 m ; 12:45:52 60d 53.8 m;
    12:47:48 60d 53.0 m ; 12:49:27 60d 52.0 m ; 12:50:16 60d 51.0 m;
    12:51:04 60d 49.6 m ; 12:52:31 60d 50.2 m ; 12:53:43 60d 48.6 m;
    12:55:53 60d 47.2 m ; 12:58:14 60d 44.0 m ; 1:00:29 60d 40.0 m;
    1:01:55 60d 37.8 m ; 1:03 30 60d 34.4 m
    Again,,,,watch is 26 seconds SLOW. Please calculate latitude and longitude.Hope you enjoy interesting data.

    Best regards and thanks,
    Bruce Pennino
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