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    Re: Distance off with Chicago buildings
    From: Frank Reed CT
    Date: 2005 Oct 10, 02:31 EDT

    Bill you wrote:
    "Which brings me to the  question of height on charts of lighthouses etc.  Not
    much in the way of  tides on the Great Lakes, although lake level can
    fluctuate several feet over  time. When the a structure's height (lighthouse
    etc) is given on a chart,  what is the starting point?  Mean low water level
    for sea, base,  etc?  And is the height to the top of the structure or to the
    light?  "
    The base for lighthouse heights should be the chart datum. I don't know  what
    that is for Lake Michigan but it's always in the fine print on the chart
    itself. The height is generally to the light rather than the top of the
    From my building altitudes, you determined:
    "It looks like  you're walking the beach in Gary Indiana.  At a steel  mill
    perhaps?  Interesting choice for a beach stroll.  "
    Yep. It's very nice there! I took photos. The Chicago skyline  (through haze)
    is here: www.HistoricalAtlas.com/lunars/skyline.jpg and the  Michigan City
    cooling tower is here: www.HistoricalAtlas.com/lunars/cooling.jpg  . For those
    reading along who are unfamiliar with Lake Michigan, the view of the  city of
    Chicago from the Indiana shore is really something to see (the photo  doesn't
    do it justice). The buildings downtown float on the horizon like some  strange
    giant ship. In the skyline photo, the tall tower on the left is the  Sears
    Tower, the one on the right is the Hancock Tower, and the one near the  middle is
    currently known as Aon Center. This view is towards the northwest from  the
    beach in Gary. Looking east in the second photo, far in the distance is the
    "cooling tower" we've been discussing. It's a big "hyperbolic cooling tower"
    like the ones usually associated with nuclear power plants. In the photo, it's
    topped by a plume of white steam. These photos are at the same scale so by
    knowing that the angle between the Hancock and Sears was 3d 07' you can get a
    scale on the images (pixels per minute of arc) and confirm --more or less-- the
     altitude observations which I posted previously.
    And you wrote:
    "This  is where I become deeply confused.  Where does the 10.7' figure for
    361' cooling tower come from?  The above location is approx. 23 sm  from the
    Michigan City cooling tower. (Reference NOAA Chart 14905.)   Therefore the
    land base and shore would be below your horizon at 14 ft height  of eye."
    Yes. And so without further calculation, there's nothing much to  be done
    with that measurement.
    "If I use Bowditch table 15,  "vertical angle between top of object and sea
    horizon," you would be  nominally 13 nm/15 sm away from the cooling tower
    with an angle of  11'."
    I don't trust Table 15 --not yet at least. Ignoring refraction, the  distance
    to an object beyond the horizon should be
    D=sqrt[(tan(A))^2 +  2(H-h)/R]-tan(A)
    where A is the height corrected for dip, H-h is the linear  difference in
    heights of observer and distant object, and R is the diameter of  the Earth.
    Including refraction multiplies tan(A) by a factor, call it k1, and  (H-h) by
    another factor, k2. Both k1 and k2 are on the order of 1.2 but vary  considerably
    depending on atmospheric conditions. Note that tan(A) can be  replaced by A if
    A is less than about 5 degrees and also note that the result is  in "radians"
    and should be multiplied by 3438 to convert to minutes of arc and  hence
    nautical miles. But since k1 and k2 are variable depending on the  temperature
    profile of the atmosphere over the height range from 0 to H, I  wouldn't expect
    results for distances estimated this way to be more accurate  than +/-5% or
    10%. I think I'll experiment some more and see if there's any  simple pattern in
    terms of temperature inversions and all  that.
    "I have not checked out the separation angle yet, as I am  very iffy about my
    building lat/lon (derived from Street Atlas). What have I  missed?"
    I don't think you missed anything.
    FWIW, you can get  very good lat/lons using terraserver.com. Pull up a
    satellite photo or aerial  photo and just mouse over the building that interests
    you. Lat/lon are displayed  in a panel on the left (to the nearest ten-thousandth
    of an inch or so --a  little overkill on the in-significant digits). Small
    errors in the registration  of the photo corners probably lead to errors
    occasionally as large as 0.001  degrees but so far I have been happy with the
    positions I take from  there.
    42.0N 87.7W, or 41.4N  72.1W.

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