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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Distance off with Chicago buildings
From: Frank Reed CT
Date: 2005 Oct 10, 02:31 EDT
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 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." 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