How Much Do Skyscrapers Actually Move?

How Much Do Skyscrapers Actually Move?

The night Hurricane Alicia struck Houston in 1983, shattering high-rise windows downtown and stacking sailboats in the marina, there were two engineers waiting on the top floor of the Allied Bank Plaza. The 71-storey emerald glass tower -- since renamed, and renamed again -- had just opened that year. In August, its top floor was still unfinished. Unconnected wires dangled from the ceiling.

The engineers had driven in the middle of the night through rising gales and past sandbagged garages. A maintenance worker inside the building, on lockdown for the storm, had to operate the elevator for them. It wobbled on the way to the sky lobby, where the floor was already swaying noticeably, and then to the top, where the maintenance worker had the good sense to promptly return to the ground floor.

Robert Halvorson and Michael Fletcher made the trip to switch on equipment they had rented that would measure how the wind would play with the building, batting it back and forth along both axes and twisting it around its core. Then, they stayed for several hours -- past the point when they could no longer walk upright, well beyond the moment when they realised they could see flickering lights in the distance coming in and out of view as the tower contorted.

I had been told about this building, in this storm, by several people preoccupied with the study of skyscrapers in wind. In their world, where such live experiments are rare, and where human reaction in the midst of motion is variable and tricky to measure, the Allied Bank Plaza in 1983 stands out as a singular event: structural engineers were actually present, bearing accelerometers and their own senses.

I asked Halvorson what the motion on the seventy-first floor felt like in the middle of a storm that ended up devastating the city. "The only thing that was on your mind," he recalled, "was moving around. There was no other thing that was of interest, no other thing you could do."

The floor seemed to shift beneath him and Fletcher unpredictably. The wind pushed and pulled on the windowpanes, turning the glass into funhouse mirrors reflecting distorted images of the men inside.

Even at the height of the hurricane, the Allied Bank Plaza was never in structural danger, a reality the engineers were confident of in the back of their minds. What buildings can tolerate, however, is very different from what their humans can. We get motion sickness. We lose concentration. We are overcome by fear.

Engineers and architects could create perfectly stable, structurally sound skyscrapers that safely sway more than we even allow them to. But the human body responds violently to rhythmic motion. And, even at much subtler levels, our minds don't handle it well, either. As sure as Halvorson was that the Allied Bank Plaza would not tip over, most of us harbour an opposing notion: buildings are not supposed to move.

It is this conviction, as much as any law of physics, that constrains and shapes the design of skyscrapers we're now pursuing even higher into the wind.

Good Vibrations

In fact, all buildings move. This truth, which physics must tell us because human perception cannot, renders clear two humbling points: much of the world is not as solid as we think, and humans are awfully poor receptors.

The Pentagon moves. Madison Square Garden moves. Even the Pyramids move. Perhaps only on a minuscule scale and during the most severe windstorms, but every material and structural system must deform under its load. Nothing, according to physics, can be infinitely rigid. But as we have succeeded in building taller, narrower, and lighter, the acceleration of movement at the top of a building -- under just the right circumstances swinging to one side, then to the center, to the other side, and back again -- has eclipsed the threshold of conscious human perception.

Architects and engineers knew this in the 1930s. The engineer David Cushman Coyle was dragging a device of his own invention then to the tops of New York's skyscrapers, measuring the motion that was giving people "sky sickness." In a 1938 issue of Popular Science Monthly, Coyle appears bending over his suitcase-sized contraption under a lyric headline: "New machine proves skyscrapers shiver in wind." In the thirties, Coyle warned that the frames of tall buildings had to be stiff enough to keep the vibration caused by wind "within limits that inspire occupants with confidence in the strength of the structure."

In the earliest days of the Chrysler and the Empire State buildings, engineers understood that it wasn't enough to design for structural integrity; they had to design for the even narrower parameters of human confidence. What they did not know then -- and what they are still learning now -- is exactly where those bounds lie.

The physics of motion are the simple part, dictated by equations (force equals mass times acceleration) and measured in known quantities (thousandths of gravity). The worst problems arise not from wind striking the face of a building, but from wind travelling along it. Picture how water moves past a rowboat, creating swirling eddies in the boat's wake. Wind does something very similar as it courses around the edge of a tower, shedding spinning vortices as it goes.

These vortices, invisible little tornadoes, peel off along one side of the building, then the other, in alternating patterns that during strong winds can set an entire skyscraper vibrating. Here, another analogy is in order: buildings are also a bit like tuning forks. Strike a tuning fork, and it vibrates at its natural frequency, producing an audible pitch. Buildings have natural frequencies as well, although their vibrations occur at much slower speeds than a tuning fork. Your ear cannot hear them.

Skyscrapers really start to rock when the vibrations caused by vortex shedding bring the building's motion into harmony with its natural frequency. One last analogy, which is popular among structural engineers when they're forced to explain all of this to laymen: imagine a small child on a swing set. She's kicking her feet -- not a very impressive display of power. But if she does this with just the right rhythm, the swing rises higher and higher. It may take some time to get the thing going, but once she does, it takes little effort to maintain the motion. This is how the seemingly outmatched force of moving air along a planar surface, gusting over a sustained period of time, can get a 500,000-ton steel-and-concrete skyscraper rocking back and forth.

Inside the building, on those top floors, the oscillation is what unnerves us. A 40-storey building may sway a foot to the left, a foot to the right. The span of that period might last around four seconds. A 100-storey 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.

Sitting in a penthouse living room, the displacement of two or three feet would be imperceptible to you. "You would be like a fly on an elephant," says Nick Isyumov, a retired professor of civil and environmental engineering at the University of Western Ontario. "The elephant would be moving, and the fly wouldn't care." Humans are also terrible at perceiving velocity at a constant speed. This is why, when you're travelling on a train at a steady fifty miles an hour, your body believes you might as well be sitting perfectly still. What we can feel, however, is acceleration -- a train, or a building, gaining speed as it moves.

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 100-storey 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.

At that acceleration, most people would be able to perceive some sense of motion. Recognising this, engineering standards for buildings in North America for the last thirty years have recommended that the top occupied floor of residential towers not accelerate beyond fifteen-to-eighteen milli-g's during the kind of storm that is likely to occur once every ten years. The criteria are more lax for commercial buildings -- twenty-to-twenty-five milli-g's -- on the grounds that it's easier to evacuate an office than an apartment during an extraordinary storm like Alicia. It is also arguably less alarming when such motion occurs while you're seated at a desk than when you're leaning over your kitchen stove, trying to spoon marinara to your mouth.

That night in the Allied Bank Plaza in 1983 -- when, as planned, all of the commercial buildings downtown were evacuated -- Halvorson and Fletcher recorded a peak acceleration of forty-three milli-g's.

"Now," says Bill Baker, the chief structural engineer at Skidmore, Owings & Merrill, who, along with Isyumov, patiently clarified much of this for me, "having said that, a lot of the perception of motion is not related to this thing that we can calculate."

The Perception of Motion

Buildings are much easier to assess than humans beings. Where they are measurable and predictable, we are variable and illogical. One person may perceive the faintest tremors of an earthquake, while another may never know that one passed. The rise and fall of a sailboat that makes one man seasick may feel unremarkable to his co-captain. Even more confounding: in "moving room" experiments, conducted by Melissa Burton as part of her Ph.D. studies at the Hong Kong University of Science and Technology, nearly one in five people who were never subjected to motion at all believed that they had been when the question was later asked of them.

Our perception of motion sits at the messy confluence of physiology and psychology. Much of the understanding of it originally came from fields far outside of architecture, from the study of people aboard ships or piloting aeroplanes. In the early 1960s, a British engineer named E. G. Walsh first confirmed that our ability to sense motion derives from the vestibular apparatus in our inner ear. In experiments conducted at a school for deaf children, he asked subjects to lie down on a swinging stretcher suspended between four wires, which he gradually rocked back and forth. Compared to other subjects, children with a damaged vestibular apparatus perceived only the more dramatic motion.

Today, researchers believe that the most sensitive people, about ten per cent of the population, begin to perceive motion around three or four milli-g's. Discomfort starts to sets in between ten and twenty milli-g's. When we feel this kind of back-and-forth movement at periods of between three and six seconds, we become particularly susceptible to nausea. Then, as acceleration continues to rise, we have trouble manipulating utensils, and managing hand- and foot-to-eye coordination. At around forty milli-g's, walking becomes difficult, and above that, we struggle to maintain our balance. Somewhere around forty-five milli-g's -- roughly the level Halvorson and Fletcher experienced -- debilitating fear kicks in for most of us.

These numbers, though, represent shades of perception, not the hard maths of engineering. And beyond the onset of nausea, or the difficulty maintaining balance -- both physiological reactions -- so much of motion perception has little to do with the actual workings of the inner ear. In an apartment at the top of a skyscraper, we are also susceptible to cues outside of our bodies: to the sight of a chandelier swinging or water sloshing in a toilet bowl, to the sound of elevator cables clanging or the creaking of a building's structural frame. "You may perceive that a whole lot earlier than your inner ear feels the motion," Baker says. And these other cues may be just as disturbing.

How Much Do Skyscrapers Actually Move?

Testing a model in RWDI's wind tunnel, photo via RWDI

Even in sophisticated moving-room studies, where a room-sized box is placed atop hydraulics capable of simulating the precise motion of building sway, it's impossible to recreate the fear we bring with us to the top of skyscrapers, or the shock we experience when movement interrupts our domestic routines. It's impossible to simulate the cognitive dissonance of standing in a moving building that you believe is not supposed to move.

All of this context is essential to understanding why small motions that would not have much impact in other settings deeply trouble us at a 100 storeys. "Ultimately, it is the uncertainty that is really the principle," Isyumov tells me. We don't know if the building might tip over, or if it's supposed to behave this way, or when such motion might strike again. "We have this built-in mentality that some things move -- like cars and elevators and aeroplanes," Isyumov says. "And other things do not, such as buildings."

Americans are particularly wedded to this conviction. Our litigiousness, Burton says, makes us less tolerant of building motion than people she has studied in other parts of the world, suggesting that there is also a cultural component to how we perceive movement. Other research suggests that personality matters, too. People who are more neurotic tend to complain about motion at levels that don't bother the rest of us.

In theory, some of the fear associated with motion might ease with repeated exposure and education. Air traffic controllers, for instance, learn to concentrate while experiencing the sway of their traffic control towers. Likewise, tall building occupants might learn to shrug off minor motion if they could appreciate that some movement is inevitable, even natural, in any built system. But habituation solves only the psychological elements of motion perception, not the physiological ones. Those we cannot accustom ourselves to. "Motion sickness is like this evil sickness that humans suffer from," Burton says, "and we're stuck with it."

Fundamentally, though, the distinction between the physiological and the psychological is unimportant. Did you really feel a building move? Or do you believe you felt it move because you saw the chandelier sway? "Ultimately, it doesn't matter to us as the engineer or the designer," Burton says. "Ultimately, what matters is if it's being perceived at all."

"Solving for People"

In North America, the rules for acceptable building motion are based on a cruder product of these interrelated psychological and physiological variables: at what point are people inside a moving building likely to complain about it? The fifteen to eighteen milli-g standard is derived from that deeply pragmatic threshold, the point at which past experience suggests the most sensitive two per cent of residents in the top third of a building will complain about the motion experienced during a typical ten-year storm.

The small size of that hypersensitive population, during a rare, hypothetical event, might appear insignificant, particularly given its outsize influence on the design and engineering of an entire skyscraper. But given the high stakes of building high -- for property managers, owners, engineers, and architects -- the complaints of a few may be enough to seed broader fears that a building is unsound.

This is where skyscrapers pile one final, absurd demand on engineers. The less a building moves -- thanks to more robust structural systems -- the more expensive it is to build. And so the engineer's task is to guide a building's blueprint into that narrow space between what is cost-prohibitive on a balance sheet and what is minutely perceptible to the human body. "OK, now I've solved for gravity, I've solved for basic strength and wind," says Chuck Besjak, the director of structural engineering at SOM. Now the engineer must solve for people.

There are blunt ways to do this, with dampers or massive building-top tanks in which hundreds of gallons of water slosh around, counteracting the sway of a tower in high winds. Or, as engineers poetically put it, they can design buildings, like the Burj Khalifa, where the form of the towers themselves contribute to "confusing the wind."

How Much Do Skyscrapers Actually Move?

The Burj Khalifa, under construction in 2008, photo by Aheilner

The 2,700-foot tower in Dubai grows more slender as it rises in an inverted Y-shape, with three wings buttressing its core -- a shape that took form in a wind tunnel. Bill Baker and his colleagues kept tweaking and testing the geometry. They turned the building 120 degrees to account for Dubai's prevailing winds. They altered the direction of its signature setbacks, which now wrap around the tower as they ascend clockwise.

The final result may look like the product of an architect's ego, an elaborate minaret rising from the Arabian desert, but it is also a bulwark built to mock the wind. In the coming ten- or twenty-year storms, it will be exceptionally difficult for the kind of vortices to form off the Burj Khalifa that would cause the tower to vibrate forcefully.

Now, as the world's ever-taller supertalls aim to top the Burj, the tools available to simulate movement in wind, and shape towers to withstand it, are growing more sophisticated, more precise. They are a far cry from the homemade machine David Cushman Coyle used to prove that skyscrapers "shiver" in the wind. RWDI, a Canadian wind engineering consultant, can rapid-prototype building models with a 3D printer, then monitor the dynamic response of those models a thousand ways in a wind tunnel. RWDI has even begun to work with a ship simulator at Memorial University in Newfoundland. The Centre for Marine Simulation there has more than a dozen simulators built to train seamen to manage a ship in violent seas. The top floor of the Chicago Spire was also simulated there, as was the penthouse of a 1,400 foot-tall residential tower at 432 Park Avenue in Manhattan.

In each case, the equipment in a simulator meant to model a ship's bridge was replaced -- a couch was brought in, a table set for dinner, a chandelier. A skyscraper's view of the city replaced the simulator's views of the sea, all to give engineers and architects a sense of what the maths in a wind tunnel might mean in the real world.

As skyscrapers grow taller, evolving with the tools that make such heights realistic, it's possible that we'll change, too. "We fly in aeroplanes, we have people going off to the moon," Isyumov says. "It makes absolutely no sense why we cannot educate the public that movement of buildings is in fact one of their characteristics, as long as that movement doesn't make you ill." Maybe when more of us live in skyscrapers, when 2,700 feet becomes an unremarkable height, ten milli-g's during a dinner party won't mean much to us anymore.

By then, engineers will know even more about how to confuse the wind, if not about the remaining mysteries of human perception. Their record, even in 1983, was impressive. Isyumov did the original wind tunnel testing on the Allied Bank Plaza.

"The one really startling, wonderful conclusion that came out of that," Halvorson says of his live experiment, "was that what we measured in the field was, give or take, exactly the same thing that had been predicted by the wind tunnel. Here's this little teeny building in this little teeny city, in a modest-size wind tunnel with some little gauges on it. And from playing around with that, they are able to predict more or less exactly how this building would behave."

And that was thirty years ago, before 3D printers and marine simulators, before wind tunnel sensors capable of taking measurements 500 times a second. "That's remarkable," Halvorson continues, "given all the variables of nature and construction, and the limits of our computer analysis."

If engineers can be so accurate with the modelling of buildings in motion, perhaps they can also come to discover what remains mysterious about their human occupants: the limits of fear and culture, perception and personality, body and mind.

This essay appears in the new book The Future of the Skyscraper: SOM Thinkers Series and is published here with permission.

Emily Badger is a staff writer at The Washington Post, where she covers national urban policy for the paper's Wonkblog. She writes frequently about urban planning, housing, transportation, poverty and inequality -- and why each is intimately connected to the others.

Picture: Roy Luck

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