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.
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.
"... 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
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.
Practically all very tall buildings have some sort of damper system. There have been some passive dampers, like a massive stone slab sliding on a film of viscous oil. Everything from the Empire State building, the old World Trade towers, the Sears building, etc. have to have such a system to counteract any wind loading that might hit the building's natural frequency. They are pretty effective, apparently.
Well, just reversing the servo would ram it into the stop. But, if you get it rocking at the building's natural frequency, the whole building will come down. There's Civil Engineer at Washington University (where I work) with the somewhat bizarre name of Shirley Dyke, who has built machines to shake buildings. It takes a remarkably small weight, maybe 25 Lbs. to deliver enough shaking to demolish even a mid-sized building. They let her test a couple buildings slated for demolition up to the point that the concrete columns started to crack.
Maybe this is what the guy wanting to maneuver 500 tons of something about was referring to. Let's see... we have a 500 ton counterbalance on top of a 1000 foot building and we just need to nudge it a bit off kilter....
I would say that buildings where this comes into play need to be tolerant of all of this $#!+. Something as tall as a WTC tower and twice as wide needing to be 1/2 inch wider at the top than the bottom - it better not be so touchy as to easily topple if it ain't!
Just consider wind problems! NYC can expect to get hit by a hurricane badly enough to get peak gusts around 90-100 MPH at "treetop level" at least once per century. Expect that to translate to about 110 MPH on the top half of a building that tall - even though hurricanes have their worst winds in lower parts of the atmosphere! 110 MPH of 74 F air at barometric pressure 28 inches works out to 27.9 pounds per square foot of wind-hit side area assuming drag coefficient 1 if I calculated right! The building's base would have stress a few times that of tension on the upwind side and similar compression stress on the downwind side! In terms of force per building footprint area, multiplied by reciprocal of fraction of the building footprint that has structural members that withstand this force.
Hurricanes ain't the only problem! Consider the Nor'easters of March
1932, March 1962, March 1984, October 1991, December 1992 and March 1993! Boston might also complain about a February 1978 storm and one in early 2005! Along with Nor'easters being worse 1,000 feet up than tropical storms with same treetop level winds are! As for Midwest - how about Ohio-Indiana around January 25 1978?
Also consider the downburst, microburst, gustnado and (less common but often worse) tornado wind effects that severe thunderstorms (some of which have deceptively little lightning and thunder, especially in off-season) have!
LA is a minor improvement, being in a minor tornado hotspot of "western USA" bad enough to be only a minor improvement over the USA east of the Rockies! Worse still - irregularity of tornadoes and other severe thunderstorm wind effects (often there with minor uptick from the unimpressive low lightning/thunder incidence that is normal there) - mostly during an El Nini winter rainy season! Along with bad windstorms other than tornadoes heavily occurring during El Nino winters, and with high incidence of bad winds worse-than-average being worse near/above
1,000 feet than at treetop level!
If a big building is so touchy that 1/2 inch off out of 400 feet is a big structural problem, then the building design has a big structural problem on the drawing board!
this all makes several invalid assumptions, one being that the earth is nearly spherical, the other that gravity is uniform - see WGS-84 for example for datums for earth parametrics
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.
Well, see this page for backup on my calculations :
formatting link
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.
He he! Now that I've got the formula figured out, a 6 mile span has a divergence from a straight line of roughly 24 feet. Of couse if you consider both ends "level" then the rise in the middle appears to be 12', I think.
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