
How Much Do Skyscrapers Actually Move? - mhb
http://gizmodo.com/how-much-do-skyscrapers-actually-move-1707522178
======
matthewmcg
When the World Trade Center towers were being planned, the builders discovered
that nobody really knew how much sway occupants of tall buildings could
tolerate. Wind tunnel tests showed that the (relatively) light buildings would
sway more than expected and the builders feared that any publicity about this
would scuttle the project.

They began conducting two secret research programs. One investigated methods
of dissipating energy to reduce sway. The other determined how much a room
could move before occupants noticed it.

This second investigation was conducted under the pretense of "free vision
exams." Participants were led into a room that was (unbeknownst to them)
mounted on rails and moved by hydraulic rams. The amount of simulated sway was
increased until somebody spoke up.

The engineers eventually determined that the sway could be brought within
acceptable (though still detectable) levels by installing viscoelastic dampers
between the floor joists and the building's perimeter columns.

The whole story is told in the 2003 book _City in the Sky_ , which is a
fascinating read.

~~~
wldcordeiro
That's a really interesting way to go about it, I like that solution. I'll
have to check the book out.

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paulannesley
The answer to the title question seems to be:

> Inside the building, on those top floors, the oscillation is what unnerves
> us. A forty-story building may sway a foot to the left, a foot to the right.
> The span of that period might last around four seconds. A hundred-story
> building, by comparison, may move on the order of two-and-a-half to three
> feet to each side, cycling through a ten-second period. Typically, the
> taller the building, the longer the period of its cyclical motion.

And the implicit question of how much movement we feel:

> Acceleration is what causes the body forces that might tip us off our firmly
> planted feet, or nudge us back into the passenger seat of a car pulling away
> from a stoplight. Fighter pilots experience acceleration at many times the
> magnitude of gravity—“4 Gs” or more. The top of our hundred-story skyscraper
> accelerates through its period, as it sways from one side to the other, at a
> mere fraction of what a fighter pilot feels: maybe ten milli-g’s, or one
> hundredth of the force of gravity.

~~~
jameshart
Surely it's not actually _acceleration_ that you feel most of the time. A
constant acceleration is, after all, indistinguishable from constant gravity,
and so small acceleration vectors which, when added together with the local
gravity vector, are still just a little more or less than 1 g, aren't really
detectable - they just feel like gravity is pointing in a different direction.
Obviously larger accelerations are detectable as being 'not quite like normal
gravity'. When it takes different-to-normal effort to move your limbs, your
body gives you feedback about it.

What you _can_ feel is change in acceleration - a sudden change in the
direction your body perceives as 'down'. Braking in a car doesn't feel much
different to driving down a hill, but when the car's speed reaches zero and
suddenly _stops_ decelerating, the jerk as gravity snaps back to vertical is
definitely noticeable. It's the jerk, not the acceleration, that throws you
off your feet when you're standing on the subway and it pulls into or out of a
station.

~~~
vacri
It's unbalanced forces you feel, not unbalanced acceleration per se. If you
have a constant acceleration, it's because there's a consistent force on you.

It's why this part of the article is wrong: > _Humans are also terrible at
perceiving velocity at a constant speed. [not perceiving sway] is why, when
you’re traveling on a train at a steady fifty miles an hour, your body
believes you might as well be sitting perfectly still._

Humans in a train moving steadily are enclosed in an environment where
everything is moving at the same speed as them - seats, air, everything. There
are no unbalanced forces to feel in the first place. Just the same as we don't
perceive the earth's movement around the sun (well, in a moving-body sense) or
the sun's movement around the galaxy (which is blisteringly fast on a human
scale); because our frame of reference moves with us.

Of course, in the real world, trains do sway side-to-side and also up and down
a little where the rails meet up (click-click click-click...), and we all feel
that. But we're talking about a theory train here, and only looking at forward
velocity :)

Edit: Wikipedia says the sun orbits the galaxy at 220km/s. Monty Python's
"Galaxy Song" says 40,000mph, which works out to 18km/s. Either way, it's
pretty zippy for us humans.

Galaxy Song:
[https://www.youtube.com/watch?v=buqtdpuZxvk](https://www.youtube.com/watch?v=buqtdpuZxvk)

~~~
mapt
Right: We're only terrible at perceiving constant velocity without visual
reference because it's physically impossible to do so in a controlled
environment, according to Newton.

What we're terrible at is perceiving _constant acceleration_ in very fine
increments, like 10 milli-G while standing, or on up past 100 milli-G while
sitting or prone. This is _directly equivalent_ to sensing a certain
slope/grade in the terrain, if one is robbed of accurate horizontal (horizon)
and vertical (trees/buildings) reference. The mind is capable of tolerating
several degrees of tilt while being perfectly convinced everything is flat, so
long as the visual references point in that direction... and even at greater
extremes we really only notice topography when it's highly variable, cliffs
and abrupt hills and sharp changes in slope. I have an unconfirmed notion that
our ability to, for example, carry things on our back, or walk while pregnant,
would be sharply curtailed if our body didn't automatically adjust to the
different center of mass, and different perceived gravity vector from the
standpoint of our skeletal centerline.

Humans directly perceive jerks, and they perceive them with alarm, because if
the ground is jerking in a natural context it means you're about to fall off a
slope and die.

------
firethief
> Humans are also terrible at perceiving velocity at a constant speed.

This is not so much a quirk of our species as a physical impossibility

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dmlorenzetti
For a fascinating read on the intersection of buildings, wind dynamics, and a
litigious society, see "The Fifty-Nine Story Crisis" [0]. The article
describes the response of the architect/engineer of the Citicorp Tower, when
he realized that the building would topple like a domino in winds that could
be expected at least once every 16 years.

[0]
[http://people.duke.edu/~hpgavin/cee421/citicorp1.htm](http://people.duke.edu/~hpgavin/cee421/citicorp1.htm)

~~~
nsxwolf
The litigious society seems rather justified in this case.

~~~
jonah
But did you read to the end and see how everyone involved behaved in the
aftermath? The opposite of what you seem to be implying. And honorably so.

------
sosuke
This damper movement video was really incredible to see
[https://www.youtube.com/watch?v=NYSgd1XSZXc](https://www.youtube.com/watch?v=NYSgd1XSZXc)

The small scale demos just don't do it justice.

[https://www.wikiwand.com/en/Taipei_101](https://www.wikiwand.com/en/Taipei_101)

~~~
Gravityloss
Why did you link through Wikiwand? It's some annoying overlay on Wikipedia
that makes the window really small? Here's the direct Wikipedia link:
[https://en.wikipedia.org/wiki/Taipei_101](https://en.wikipedia.org/wiki/Taipei_101)

~~~
bglusman
It's actually a browser plugin to restyle^H^H^H^H^H um actually not restyle,
redirect from wikipedia to same page on wikiwand? I think it looks nice but
hadn't used it before... curious if sosuke has any connection to them, but it
seemed more interesting when I thought it was just restyling... the redirect
to their own domain is a bit weird...

~~~
sosuke
Ha, no it was just a mindless copy paste.

------
stox
I used to work on the 97th floor of the Sears Tower. On a really windy day, we
would get downright seasick.

------
mschuster91
How does the concrete not develop cracks when the building sways so much? Same
for the lifts - why don't they hop out of their rails?

~~~
msandford
A building is say 500 feet tall. The top moves say 2 feet.

In order for this to happen every 10 feet of the building doesn't shift
sideways a certain amount. Every 10 feet of the building bends a certain
amount. A VERY small amount. Tiny fractions of a degree.

So the bottom 10 feet of the building bends say 0.001 degrees. The bottom is
flat, the top is tilted 0.001 degrees.

The next 10 feet bends an additional 0.001 degrees, but its base was already
tilted 0.001 degrees so its top is tilted 0.002 degrees.

The next 10 feet bends an additional 0.001 degrees, but its base was already
tilted 0.002 degrees so its top is tilted 0.003 degrees.

Repeat this 50 times (for 500 total feet) and you've got 0.050 degrees of tilt
at the top which might be noticeable. Further, you have to add up
displacements the whole way from the bottom to the top as well.

If you took a picture of the building sideways it would look like this:
[http://www.codecogs.com/users/23287/Cantilever-
Beams-101.png](http://www.codecogs.com/users/23287/Cantilever-Beams-101.png)

~~~
mturmon
I like your reasoning, but I wonder about magnitudes. Since:

    
    
      10 feet/story * sin(0.001 degree) = .00017 feet/story
    

then:

    
    
      50 stories * .00017 feet/story = .0085 feet [building]
    

If things added up this way, your magnitudes would be way off.

In fact, since sin(x) is linear for small x, you'd need about 100x more angle
to get 100x more deflection. 100x more deflection would be about 0.85 feet one
way, or 1.70 feet peak-to-peak.

Two feet peak-to-peak for 50 stories matches some of the figures quoted in the
article for buildings of this scale ("A hundred-story building, by comparison,
may move on the order of two-and-a-half to three feet to each side...").

However, on reflection, I think the offsets cumulate quadratically. Because:

    
    
       *
        \
         \  [story 2]
          \
          |
          | [story 1]
          |
    

The first story has an angular offset, but the angular offset of the second
story adds to that of the first, etc. This must be common knowledge among
structural engineers.

In that case, since we can just add all the displacements, the appropriate
quadratic multiplier would be 50 __* 49 /2 = 1225, not just 50, and the total
displacement is:

    
    
      1225 * .00017 feet/story = 0.21 feet.
    

This would mean your original, very tiny, angles were only about 5x too low.
Nice work!

~~~
msandford
Yeah it was a total guess, not informed by doing any actual math. Thanks for
adding some real numbers to the discussion!

------
iaw
There's a really fascinating and relevant 99% Invisible [1] on a building with
insufficient sway damping leading to potential for collapse. If I recall, a
student discovers the issue while running calculations for a class and reached
out to the architecture firm. Worth a listen if you haven't heard.

[1] - [http://99percentinvisible.org/episode/structural-
integrity/](http://99percentinvisible.org/episode/structural-integrity/)

------
adam74
A lot:

[https://www.youtube.com/watch?v=HB2jgJJG2is](https://www.youtube.com/watch?v=HB2jgJJG2is)

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z3t4
I wonder if you get "land" dizziness after spending time in a tall building!?

