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    Santa Barbara sights
    From: Peter Hakel
    Date: 2011 Jul 24, 17:57 -0700

    My recent to trip to Santa Barbara on the California Pacific coast presented me with an all too infrequent opportunity to practice using my sextant with a natural horizon. I hope this list will find the reported results interesting. The first three linked pictures were taken on Saturday July 16 from my observation site; #3 show the landmass over which the Sun has moved Saturday afternoon when I (almost) lost the natural horizon for observations.

    Google Earth ("GPS coordinates"): Santa Barbara Sailing Club beach (see two additional linked JPGs)
    N 34d 24.18' i.e. 34.403
    W 119 41.64' i.e. -119.694
    These coordinates were used as AP in the subsequent calculations.

    Sun SD = 15.7' during the two days of observations: 16-17 July 2011.

    Sextant: Davis Mark 15

    Chronometer: radio controlled Oregon Scientific RM323A. Convincing myself that the reflected Sun disk is indeed sitting on the horizon took a few seconds, which is why UT is rounded to the nearest 5 or 10 seconds - this is one of the areas in sight-taking that I need to practice more.

    Temperature and pressure were measured with a "Tech4o" digital gadget. I am not sure how accurate those values are considering the direct sunlight and the proximity of sand and my black leather sextant-transporting bag but the altitude corrections didn't seem to be terribly sensitive to these values anyway and there were other, bigger, sources of error (see below).

    The weather conditions were great and the ocean was calm.

    For each of the three data sets given below I made rough Sun azimuth estimates with a "Brunton Eclipse" magnetic compass (complete with a magnetic declination setting), which were found to be consistent with the later computed azimuths using the St. Hilaire method.

    The height of eye ("Heye") was estimated by Mark 1 eyeball... :-) Some observations had land behind the horizon but these land masses were sufficiently distant so no dip-short considerations were necessary. Indeed, the natural horizon looked unbroken when it "moved" in front of the land mass, as seen through the sextant's telescope.

    The main difficulty I had was establishing the index error of the instrument. The index mirror held perpendicular to the frame very well but I spent a lot of time tinkering with the horizon mirror. I repeatedly measured and adjusted the index error by looking at the horizon, overlapping the two sun disks, and also using the "Solar IC procedure" from David Burch's book on plastic sextants. The IE tended to gravitate toward 8' to 9' off the arc but I would have to attach an "error bar" of a few arcminutes to that value from what I saw. Using this Solar IC method to recover the Sun's semidiameter also showed differences of the order of 1'. Between sights I turned my back to the Sun and shielded the sextant from direct sunlight.

    On Saturday my goal was to test sight averaging and direct LOP-circles' crossing calculations. I made two sets of measurements separated by a few hours. In the morning I took four sights for averaging and/or slope-fitting purposes. Unfortunately in the afternoon I spent too much time fiddling with the sextant, adjusting the mirrors and practicing swinging the arc. By the time I was ready to take an actual sight, the Sun has just moved over a nearby land (sb3.jpg) and I was only able to take a single sight using the natural horizon. I also quickly "zeroed out" the index error before taking that sight by adjusting the horizon mirror the best I could.

    On Sunday I arrived at the beach not long before LAN with the intent of getting data for a noon curve. External time constraints (scheduled lunch with my wife) precluded me from observing the LAN itself; but I accumulated enough data to construct a parabolic extrapolation to the data. I have not familiarized myself with the ex-meridian method yet, so if anyone else wishes to use the data in that manner, I'll be curious to hear what they get. Before I began this sequence, I eliminated the side error as much as I could and measured the index error both with the horizon and with the Solar IC method, finding agreement of IE=-9' or so. After I finished the nine observations, I attempted to use the Solar IC method again, only to discover that a noticeable side error has developed in the meantime. Looking at the horizon again I observed IE=-8'.


    ==========================================================
    Data set 1:
    SATURDAY MORNING: T=25 C, P=1011 mb, IC=+8.0' Heye=6 ft
    16 July 2011
    UT Hs Ho GHA Declination Intercept Azimuth
    17:42:30 55d 48.2' 56d 08.9' 84d 06.4' N 21d 19.9' 0.4A 103.3
    17:45:20 56d 23.4' 56d 44.1' 84d 48.9' N 21d 19.8' 0.8T 103.9
    17:47:50 56d 51.6' 57d 12.3' 85d 26.4' N 21d 19.8' 1.0A 104.4
    17:50:30 57d 22.4' 57d 43.1' 86d 06.4' N 21d 19.8' 2.1A 105.0
    ------------------------------------------------------------------------
    Simply averaged UT and Ho: (not included in the Sum and Stddev calculations below)
    UT Hs Ho GHA Declination Intercept Azimuth
    17:46:32 ---- 56d 57.1' 85d 06.9' N 21d 19.8' 0.6A 104.1


    ==========================================================
    Data set 2:
    SATURDAY AFTERNOON: T=26 C, P=1010 mb, IC=0.0' Heye=6 ft
    16 July 2011
    UT Hs Ho GHA Declination Intercept Azimuth
    21:18:20 69d 00.6' 69d 13.6' 138d 03.7' N 21d 18.4' 1.6T 235.8


    ==========================================================
    Data set 3:
    SUNDAY MORNING (just before LAN): T=28 C, P=1018 mb IC=+8.0' Heye=10 ft
    17 July 2011
    UT Hs Ho GHA Declination Intercept Azimuth
    19:33:30 74d 38.4' 74d 58.8' 111d 50.0' N 21d 09.0' 4.0A 150.4
    19:35:30 74d 55.4 75d 15.8' 112d 20.0' N 21d 09.0' 1.1T 152.0
    19:37:55 75d 09.4' 75d 29.8' 112d 56.2' N 21d 09.0' 1.5T 154.1
    19:40:30 75d 16.2' 75d 36.6' 113d 35.0' N 21d 09.0' 5.1A 156.3
    19:43:00 75d 34.0' 75d 54.4' 114d 12.5' N 21d 08.9' 0.9T 158.5
    19:46:00 75d 45.0' 76d 05.4' 114d 57.5' N 21d 08.9' 0.8A 161.3
    19:49:50 75d 58.6' 76d 19.0' 115d 55.0' N 21d 08.9' 1.0A 164.9
    19:53:30 76d 08.0' 76d 28.4' 116d 50.0' N 21d 08.9' 2.1A 168.5
    19:57:30 76d 14.8' 76d 35.2' 117d 50.0' N 21d 08.8' 3.4A 172.5


    ==========================================================
    SATURDAY calculations:

    Direct two-body fix based on Saturday morning averaged and the single Saturday afternoon data:
    N 34d 22.8'
    W 119d 42.8'
    (see linked two_body_fix_sb.png)

    Distance and bearing of this celestial fix from the GPS coordinates: 1.7nm and 215, respectively.
    (see linked sailings_sb.png and error_of_fix.png)

    Overall I think I can be reasonably happy with this results and the intercepts I got. Considering the difficulties I had with the index error determination I was in fact a bit worried before I started the calculations. The error of fix and the standard deviation of intercepts are interestingly similar at about 2nm. Using this value as the "Scatter" parameter in the weighted least-squares fitting procedure (fitted, not precomputed slope), all weights came out equal, so this procedure also defaulted to making a simple average of UT's and Ho's (see linked average2_sb.png).


    ==========================================================
    SUNDAY calculations:
    The estimated height of eye is different from Saturday because on Sunday I encountered a beachgoer who had placed her chair right next to "my" rock on which I had sat taking sight the day before. :-) I moved a few feet away and took sights standing on a slightly elevated sand bank. Given my earlier attempts on NavList to extrapolate a noon curve, I was again a bit worried. The latitude is indeed a bit off, but the results turned out to be rather decently good, I think, considering that the data are extrapolated by the constructed curve:
    N 34d 29.1'
    W -119d 24.5'
    (see linked noon_motion_sb.png and sun_sb.png)
    In the linked image noon_curve_sb.png you can indeed see a rather convincing arc that would peak shortly after 20h UT. Sight #4 is slightly off for some reason. This plot has the Ho's on the y-axis; in the actual calculation before fitting these Ho's are adjusted to account for the Sun's hourly declination change of -0.4'. From previous experience I believe that the results might come out better (also contingent upon a good stable IE value!) if data on both sides of LAN were available for fitting.


    Peter Hakel

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