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From: Frank Reed (no email)
Date: Mon Oct 10 2005 - 02:31:21 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
structure.
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. <G>"
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
the
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.
And:
"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.
And:
"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.
-FER
42.0N 87.7W, or 41.4N 72.1W.
www.HistoricalAtlas.com/lunars
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