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

[Proctologically Violated©®]

Awl,

(See the original thread on alt.machines.cnc, where Elson dissed me and I thusly started the usual web-bristling, w/ the usual huff, puff, and attendant dance. But really, he shouldna dissed me, man, shouldna dissed me....)

But moving onwerd and forwerd:

Even tho I had it on good authority that no goddamm builder on earth uses the earth's curvature ceptin builders of long-assed bridges, the image of oh-so slowly diverging radii of the earth did bring this to mind:

For a tall building building to be "truly plumb", *each wall* would have to be plumb, ie, lie exactly along the *line of the earth's radius*, from the point where sed wall touches the ground.

*Necessarily*, then, the walls of a tall building must **diverge**, just as the earth's radii diverge, from the earth's center to the base of the building.

Rough calcs indicate that a 1500 ft tall building, w/ a 400' x 400' base, would have its top floor about 1/2" longer on an edge than the ground floor. (!!!) Iow, a "properly" constructed building will be a very long truncated pyramid, point-side down, base up.

If a skyscraper is constructed w/ strictly parallel walls, as far as gravity is concerned there is actually a tipping "moment", sorta like the Leaning Tower of Pizza. Not significant, of course, but hey, 1/2" is 1/2". Which gives the top floor an area of 160,400 sq ft, vs the ground floor's

160,000 sq ft. Which is, hey, but another lawyer's/stockbroker's office, which is, hey, but even mo' rent.

Or, inversely/conversely/obversely/reversely/obtusely, A tall building might have to be built pyramidally, *narrow end up*, to

*counteract* the slight tipping moment of one (or both) of the walls not lying strictly in line w/ the earth's radii. Uh oh, there goes the lawyer's office....

I can see Elson now, w/ his gadget at the Sears tower....

[Jeff R.]

"Proctologically Violated©®" wrote in message news:%EK7h.32$ [e-mail]...

1/2" on an Empire-State-sized building? I trust your calcs, but do you really think there are builders working at that scale to *that* accuracy? (Other than just interesting "measuring" exercises, that is)

Interesting concept, (I've often pondered it myself), but swallowed up entirely in the tolerance (or margin for error).

You could argue, f'r'instance, that any one "vertical" strut would indeed have the earth-centre-pointing vector contained entirely within itself, unless it was considerably less than 1/2" thick.

-- Jeff R. (pass me another beer)

[Proctologically Violated©®]

You're preaching to the choir here. :) Read the claims in the original thread. goodgawd....

1/2" is positively *gargantuan* compared to the other stuff. :)

[Nate Nagel]

I would ASSume that how they are actually constructed would be that the imaginary centerline of the building's core would be constructed plumb and the building would be squared to that. Therefore there would be no "tipping moment" as WRT the earth's gravity all outside walls would be leaning in equally. However, I haven't personally built anything bigger than a large shed, so I dunno.

IRL it seems that most tall buildings have terraces and therefore the upper floors are smaller in areas than the lower floors discussion above notwithstanding.

nate

[Charles Schuler]

Parallel lines averaged to the center plumb line should work fine.

Some folks think a plumb bob won't work next to mountain.

Much ado about nothing.

[Snag]

Ya know , there's something to this . I read once of a (oblong , and big !)tank/fountain/whatever , that was supposed to have an even volume of water falling over the edge all the way around . Kind of a water curtain effect . They forgot to include the curvature in their calcs , the thing was only overflowing in the middle ! Don't recall how they solved it , but I recall pics of it "after mods" . T'was wayyyy cool .

[Proctologically Violated©®]

Technically, they might be correct. Would have to calculate relative masses, tho. Main earth no doubt swamps the mountain. But....

[Proctologically Violated©®]

Coriolis force?

[Proctologically Violated©®]

You are correct. I guess ahm in my alarmist mode. :)

And you are correct about terraced buildings. This is actually required in some areas by the urban planners, as well as setbacks for these tall buildings. The reason can be plainly seen ( or not seen!) by parts of very lower Manhattan, where walking on the sidewalk is much like being in the bottom of a goddamm well--you see the sun only when it is directly overhead! Ergo, the terracing. Oh, and the area of the top floor would be 16,040, not 16,400: 400.05 x

400.05, approx.

[Jon Elson]

I don't know whether I don't know whether these buildings are actually designed this way, but I'll bet they are BUILT this way. The reason is, they use LEVELS when putting the walls up! So, the walls have to diverge by that tiny amount. You'd never be able to measure it on one floor, but if you were to carefully measure the walls over a few floors, I think they might show the divergence.

Ahh, I can't measure that one, because it is too far off the local vertical!

Jon

[Carl McIver]

"Proctologically Violated©®" wrote in message news:%EK7h.32$ [e-mail]...

The Boeing plant in Everett, WA is about .6 miles long according to my odometer. You can see the curvature of the earth in the ramp in the front of the building, and if you look just right at the building from an approaching highway you can see the curvature of the roof to match. Haven't been on the roof but once, and I wasn't looking for that when I was up there. Since the building is actually many separately constructed building joined together by semi-flexible joints and floor plates between buildings for earthquakes and natural ground movement, you can't see the curve inside the building unless you put your head to the floor and look from one end to the other in the main aisleway inside. It's .3 miles deep, and arranged so that there are two buildings front to back and six or so longways. I imagine that if you could somehow measure the centerline of the posts that hold up the walls and roof, you might be able to measure the difference in span between the floor and the roof structure.

[Gary Brady]

Properly constructed buildings are built with parallel lines, not truly "plumb" lines in the strictest sense. The alignment is done with optical instruments calibrated to set benchmarks which which ignore the divergence that you describe. If tall buildings were built with plumb bobs, perhaps the divergence would be more of a problem, but then, where would you hang the plumb bob from?. Large civil structures, such as bridges, are often subject to this divergence due to their large size. Bridge towers will indeed be further apart at the top than the bottom due to the earth's curvature.

Sorry, can't comment on tipping moments.

[Snag]

No , the water surface actually was curved to match that of the earth . The tank (for lack of a better word) lip was straight ... therefor it was only flowing over the edge in the middle .

[hhc314]

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=A9=AE wrote:

[Beachcomber]

The problem with the Sears Tower was its asymmetric construction. There were multiple rectangular structural elements all bolted together, but each section terminated at a different height. Thus, when they got to the highest center section, they found that the very top of the building was cockeyed (leaning in one particular direction).

A similar analogy would be a man coming home from work while each of his say 5 children jump on him and hang on at different levels. If the children weigh enough, the man is going to have difficulty standing straight.

I briefly worked in the Sears Tower earlier in my lifetime and up above the 100th floor was not a good place to be during the big storms that occasional hit Chicago with 40 - 50+ mph winds. The building swayed so much that hanging light fixtures would swing swing back and forth.

Beachcomber

[Lew Hartswick]

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...

[Jeff R.]

Holy Mother of God! They'd have to be pretty *wide* all right!

-- Jeff R.

[Ned Simmons]

Yes, pretty wide. The widest I can think of is the reflecting pool at=20 the Christian Science Center in Boston, which is 686 feet long. The=20 water spills over a granite curb that surrounds the entire pool. The=20 earth's curvature over 686 feet is only 1/32". Walking through the plaza=20 on a windy day it's obvious that on this scale the wind is a much=20 greater influence than the earth's curvature.

Ned Simmons

[Jeff Wisnia]

Cribbed from Wilkopedia's section on the Citibank tower in New York, built in 1977:

**********

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.

**********

Full article on the building here:

Jeff

[Jeff Wisnia]

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