OT: curvature of the earth and buildings--was g-dElson right?

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Beachcomber wrote:
<snipped>

Cribbed from Wilkopedia's section on the Citibank tower in New York, built in 1977:
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To help stabilize the building, a tuned mass damper was placed in the mechanical space at its top. This substantial piece of stabilizing equipment weighs 400 tons and has a volume of 255 cubic feet (7 m³). Designed to counterbalance the effects of wind by making the building sway, it is a concrete block that slides on a thick layer of oil and converts the kinetic energy of the building into friction. This mass reduces the building's movement from wind deflection by 50%. Citigroup Center was the first skyscraper in the United States to feature a tuned mass damper.
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Full article on the building here:
http://en.wikipedia.org/wiki/Citigroup_Center
Jeff
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Jeffry Wisnia
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Actually, while the subject of your post is rather silly, there is only one application of which I am aware where the curvature of the earth plays any significant role in the alighnment of vertical structures. That unique situation is the ROTHR (Relocatable Over The Horizon Radar) antennas. It's kind of an interesting case to engineer. Then to, rememeber that the ROTHR system bounces RADAR signals off the ionospher to a sea surface that reflects them back though the same reflection and propagation path to the receiver, over round-trip distances in excess of 3,000 miles. The spatial orientation of the antenna array is therefore very critical, rivaling a micrometer in accuracy.
The deal here is that to phase the scanning beam correctly, the vertical transmission towers spaced over a distance measure in miles must be precisely parallel to each other. Not vertical, but precisely parallel.
Erecting a tower vetically is a trivial effort requiring only a plumb line or its modern, more precise instrumentation equivalent. Erecting an array of tower space over miles is a challenging engineering effort due to the curvature of the earth -- you cannot use a plumb line reference.
What is important to realize is that the ROTHR towers are located a considerable distance apart, and not in the 50-yard proximity of the footprint of a very large skyscraper. So, who cares if the four structural members of the building are not precisly parallel. They're certainly sufficiently parallel and vertical enough for both government work and civilian construction.
Harry C.
Proctologically Violated©® wrote:

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Harry C. sez:
"... there is only one application of which I am aware where the curvature of the earth plays any significant role in the alighnment of vertical structures. That unique situation is the ROTHR (Relocatable Over The Horizon Radar) antennas.. . ."
Fresnel Zone clearance for microwave radio paths.
Bob Swinney
Actually, while the subject of your post is rather silly, It's kind of an interesting case to engineer. Then to, rememeber that the ROTHR system bounces RADAR signals off the ionospher to a sea surface that reflects them back though the same reflection and propagation path to the receiver, over round-trip distances in excess of 3,000 miles. The spatial orientation of the antenna array is therefore very critical, rivaling a micrometer in accuracy.
The deal here is that to phase the scanning beam correctly, the vertical transmission towers spaced over a distance measure in miles must be precisely parallel to each other. Not vertical, but precisely parallel.
Erecting a tower vetically is a trivial effort requiring only a plumb line or its modern, more precise instrumentation equivalent. Erecting an array of tower space over miles is a challenging engineering effort due to the curvature of the earth -- you cannot use a plumb line reference.
What is important to realize is that the ROTHR towers are located a considerable distance apart, and not in the 50-yard proximity of the footprint of a very large skyscraper. So, who cares if the four structural members of the building are not precisly parallel. They're certainly sufficiently parallel and vertical enough for both government work and civilian construction.
Harry C.
Proctologically Violated©® wrote:

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Proctologically Violated©® wrote: (all the stuff cliped since everyone has already read it)
I understand that the builders of very wide water falls as in shoping centers etc, also have to take into account the curvature of the earth to make the water a uniform thickness over the falls. ...lew...
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Holy Mother of God! They'd have to be pretty *wide* all right!
-- Jeff R.
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snipped-for-privacy@this.ng says...

Yes, pretty wide. The widest I can think of is the reflecting pool at the Christian Science Center in Boston, which is 686 feet long. The water spills over a granite curb that surrounds the entire pool. The earth's curvature over 686 feet is only 1/32". Walking through the plaza on a windy day it's obvious that on this scale the wind is a much greater influence than the earth's curvature.
Ned Simmons
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Proctologically Violated©® wrote:

<snipped>
The only time I ever got involved in compensating for such an rch in something I was building was about a dozen years ago when I was making, testing and calibrating some of cesium atomic clock controlled oscillators which provide autonomous timing signals onboard each of the GPS satellites.
We had to adjust the frequency of those units in the lab "off" by a little less than one part in ten to the eleventh (IIRC) to account for the relativistic and gravitational time shifts which occur when they were whizzing around at orbital speeds and altitudes.
Further corrections are provide elsewhere in the GPS sytem to accomodate for the satellites's orbits being a bit elliptical, so the velocities aren't constant throughout each spacecraft's orbit.
AFAIK thats the only example of a consumer product, the GPS navigation systems in common use today, which relies on stuff having to be built and adjusted to those levels of accuracy.
Jeff
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Who cares?
Look closely and you'd probably be lucky to find a building that's within 4" of square.
1/2" at 1500 feet? I'd bet that each floor varies more than 1/2" from the one below/above.
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Clearly, you don't get it.
But, sadly, I made another mistake. It's far from 1/2", as pointed out by an amc'er. It's proly .05, just based on ratios. <sigh>
But still, whenever I see a really tall skinny building now, I think of a long truncated upside-down pyramid. So g-d Elson AIN'T right!! :)
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Proctologically Violated©® wrote:

Well, see this page for backup on my calculations : http://mathcentral.uregina.ca/qq/database/QQ.09.02/shirley3.html
Now, using their same equation ...
Ahh, this is too hysterical to do in miles, so I converted everything to feet.
So, A^2 = (3963 * 5280) ^2 + 100 ^2 (for a 100 foot length)
Then, you have to subtract the radius of the earth, in feet (3963 * 5280), and convert feet to inches ...
I get .0029" of curvature over 100 feet. If I haven't made a mistake here, then it does come up smaller than what I was computing before. This isn't the only way to compute this, and takes a couple of shortcuts.
Running the same computation for 1000' gives .287" 1500' gives .645"
Even at these incredibly small angles, the non-linearity of the function shows up clearly in the last 2 numbers.
Jon
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The Earth's curvature is 8' per mile from what I remember... But taking the diameter of the planet and using a CAD program, you could figure out the difference based on height I suppose...
I always argue with a friend of mine that a 1 mile long "flat" runway would actually rise well above ground level (4' on each end) unless it wasn't truly flat - If it was built to the Earth's curve, it would actually be flat to a level (which works on gravity) but not flat to a perfectionists rules.
...What's the point of this thread again? <G>
Regards, Joe Agro, Jr. (800) 871-5022 01.908.542.0244 Automatic / Pneumatic Drills: http://www.AutoDrill.com Multiple Spindle Drills: http://www.Multi-Drill.com
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says...

THe airplane doesn't care though (in more ways than one ;). It's lift vector will be perpendicular to gravity at each end.

Mental masturbation?
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Keith

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No more masturbatory than fuckin around in a shop, bruh. :)
PV: Look what I made!! Wife: You need a second job....
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