How Much Do Skyscrapers Actually Move? | Hacker News Reader

How Much Do Skyscrapers Actually Move?

gizmodo.com

107 pointsmhb39 comments

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.

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

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.

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.

There seems to be a colloquial usage of the word "acceleration" that only means "change in acceleration". It's not strictly correct, but it's pretty par for the accuracy on a Kinja property.

And the technical term for it is actually the jerk:

http://en.wikipedia.org/wiki/Jerk_(physics)

Yes - da/dt being called jerk is a great example of a technical term providing precision to something people have an intuitive understanding of. When we describe motion as 'jerky' it really is generally the case that it has high peak absolute 'jerk'.

What I wasn't aware of until I checked out that Wikipedia link, though, was that one school of thought for naming the next three derivatives of motion with respect to time is to call them 'snap', 'crackle' and 'pop', which I just love (much better than the more formal name for the next derivative, which is 'jounce').

One can certainly feel constant acceleration "in their bones" and more importantly, the inner ear [1]. I don't think that jerk or higher-order derivatives of position contribute significantly to these sensations. As you wrote, in cases where the overall deviation from the day-to-day experience of the Earth holding on to you via gravity is small, you probably don't feel anything even when there are significant "swings" in acceleration, just not in terms of magnitude.

  > Braking in a car doesn't feel much different to driving down a hill

This is why simulators can be bolted down and still give a close approximation of a moving vehicle by tilting the pilot instead.

[1] http://en.wikipedia.org/wiki/Vestibular_system

My initial reading of this comment caused me a bit of confusion. We really do feel acceleration in a literal sense, but I think the point is that as human beings, we're accustomed to the constant force of gravity, so any constant acceleration due to other forces feels like gravity. Just a nitpick: gravity doesn't change in any way when a car stops decelerating. The net force does change (causing the jerk, i.e., second derivative of velocity), but we feel it most because we become accustomed to the gravity-like forces (and their non-vertical direction) acting prior to stopping.

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

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.

So I think most people with a basic grasp of Newtonian dynamics get that if you're in a sealed box moving at a constant velocity, you can't actually tell if you're moving, or how fast. That's not too tricky (though you need Special Relativity to deal with why that's true even if you are moving very very fast, to explain why light inside your box still seems to go the same speed in all directions).

My issue with the article is that it agrees with that but then claims people are disturbed by small accelerations - and my contention is that you also can't detect small constant accelerations. As another poster wrote, a small constant linear acceleration is indistinguishable from the floor being slightly angled.

If you get back in your sealed train carriage and I accelerate it very gently forwards, you can't actually tell whether you are accelerating or simply at a slight angle. A small enough acceleration might not be noticed at all, just as a small angle of the floor would also go unnoticed. But if I change the acceleration - stop accelerating you or increase the acceleration - you will notice. It might be perceived as motion or the carriage rotating but it will be perceived.

Note that I'm not making the strong claim that you can't tell there is a net force acting on you. I'm only making the claim that you can't tell the difference between an accelerating force and being stationary in a gravitational field. And I'm claiming that when the net acceleration is close to 1g, your body can't tell at all that there is anything other than gravity acting on you. Higher g's are of course readily attributed to movement.

Obviously when a building sways, though, the acceleration is changing, switching between + and - a fraction of a g, not constant. And it's my contention that it is the changing acceleration - the presence of 'jerk' - that people detect and react to, precisely because the accelerations involved are too small to be perceived directly. You feel like you must be accelerating (or the floor must be tipping) because you perceive a change in the net acceleration you feel - a change in the direction you sense as down. You feel the jerk not the acceleration itself.

> 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

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

The litigious society seems rather justified in this case.

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.

This damper movement video was really incredible to see https://www.youtube.com/watch?v=NYSgd1XSZXc

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

https://www.wikiwand.com/en/Taipei_101

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

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...

Ha, no it was just a mindless copy paste.

Somewhat related. Not a skyscraper, but a container ship: https://youtu.be/NE_ri8PkihE

Impressive and unsettling.

On a smaller scale, you can see subway trains bend when going into a turn (where the outer rail will be a bit higher than the inner one)

Train bogies can rotate around their center and follow the curves, I'd be very suprised if the actual car bent.

They don't bend, they twist. In a leftward turn, the rail tilts a bit to the left. So, when entering a leftwards bend, the front right wheel moves up a bit before the back right wheel does. That causes slight torsion in the carriage.

Springs decrease the effect, but springs in railway carriages tend to be quite stiff, as the rail shouldn't have large bumps.

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

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?

Concrete isn't entirely inflexible either, and it's typically reinforced with steel. Lifts as well - the materials have some ability to flex, and the rails for lifts have some headroom for imperfection. That's all quite intentional because we expect the lift to be in a building that will flex.

For confirmation of this, stop a car sometime on a highway flyover bridge. These are mostly reinforced concrete. Even normal traffic makes it jump and rumble. A big truck going past makes them positively wobble.

Concrete can be quite bendy.

Not much of the exterior shells of these super tall buildings are concrete. Those are the areas that are experiencing large deflections, i.e. are bending in response to the wind. The floor slabs are concrete, but they are essentially rigid and do not see much bending that would cause cracking. The notion of a shear wall and/or shear core allows for the strength of reinforced concrete in shear to be taken advantage of, while not exposing the concrete to deflections that would induce cracking.

Not a "vertical transportation" guy, but elevators are often placed in the center of buildings, surrounded by shear walls precisely for the same reason that shear walls are. Less bending, less chance for displacements.

https://en.wikipedia.org/wiki/Shear_wall

Partly because the materials in question aren't infinitely rigid, and partly because the torsion is spread somewhat uniformly across the entire structure, and never concentrated at any one point.

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

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!

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

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/

A lot:

https://www.youtube.com/watch?v=HB2jgJJG2is

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

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