[Note that this article is a transcript of the video embedded above.]

There’s a new trend in high-rise building design. Maybe you’ve seen this in your city. The best lots are all taken, so developers are stretching the limits to make use of space that isn’t always ideal for skyscrapers. They’re not necessarily taller than buildings of the past, but they are a lot more slender. “Pencil tower” is the term generally used to describe buildings that have a slenderness ratio of more than around 10 to 1, height to width. A lot of popular discussion around skyscrapers is about how tall we can build them. Eventually, you can get so tall that there are no materials strong enough to support the weight. But, pencil towers are the perfect case study in why strength isn’t the only design criterion used in structural engineering.

Of course, we don’t want our buildings to fall down, but there’s other stuff we don’t want them to do, too, including flex and sway in the wind. In engineering, this concept is called the serviceability limit state, and it’s an entirely separate consideration from strength. Even if moderate loads don’t cause a structure to fail, the movement they cause can lead to windows breaking, tiles cracking, accelerated fatigue of the structure, and, of course, people on the top floors losing their lunch from disorientation and discomfort. So, limiting wind-induced motions is a major part of high-rise design and, in fact, can be such a driving factor in the engineering of the building that strength is a secondary consideration.

Making a building stiffer is the obvious solution. But adding stiffness requires larger columns and beams, and those subtract valuable space within the building itself. Another option is to augment a building’s aerodynamic performance, reducing the loads that winds impose. But that too can compromise the expensive floorspace within. So many engineers are relying on another creative way to limit the vibrations of tall buildings. And of course, I built a model in the garage to show you how this works. I’m Grady, and this is Practical Engineering.

One of the very first topics I ever covered on this channel was tuned mass dampers. These are mechanisms that use a large, solid mass to counteract motion in all kinds of structures, dissipating the energy through friction or hydraulics, like the shock absorbers in vehicles. Probably the most famous of these is in the Taipei 101 building. At the top of the tower is a massive steel pendulum, and instead of hiding it away in a mechanical floor, they opened it to visitors, even giving the damper its own mascot. But, mass dampers have a major limitation because of those mechanical parts. The complex springs, dampers, and bearings need regular maintenance, and they are custom-built. That gets pretty expensive. So, what if we could simplify the device?

This is my garage-built high-rise. It’s not going to hold many conference room meetings, but it does do a good job swaying from side to side, just like an actual skyscraper. And I built a little tank to go on top here. The technical name for this tank is a tuned liquid column damper, and I can show you how it works. Let’s try it with no water first. Using my digitally calibrated finger, I push the tower over by a prescribed distance, and you can see this would not be a very fun ride. There is some natural damping, but the oscillation goes on for quite a while before the motion stops. Now, let’s put some water in the tank. With the power of movie magic, I can put these side by side so you can really get a sense of the difference.

By the way, nearly all of the parts for this demonstration were provided by my friends at Send-Cut-Send. I don’t have a milling machine or laser cutter, so this is a really nice option for getting customized parts made from basically any material - aluminum, steel, acrylic - that are ready to assemble.

Instead of complex mechanical devices, liquid column dampers dissipate energy through the movement of water. The liquid in the tank is both the mass and the damper. This works like a pendulum where the fluid oscillates between two columns. Normally, there’s an orifice between the two columns that creates the damping through friction loss as water flows from one side to the other. To make this demo a little simpler, I just put lids on the columns with small holes. I actually bought a fancy air valve to make this adjustable, but it didn’t allow quite enough airflow. So instead, I simplified with a piece of tape. Very technical. Energy transferred to the water through the building is dissipated by the friction of the air as it moves in and out of the columns. And you can even hear this as it happens.

Any supplemental damping system starts with a design criterion. This varies around the world, but in the US, this is probability-based. We generally require that peak accelerations with a 1-in-10 chance of being exceeded in a given year be limited to 15-18 milli-gs in residential buildings and 20-25 milli-gs in offices. For reference, the lateral acceleration for highway curve design is usually capped at 100 milli-gs, so the design criteria for buildings is between a fourth and a sixth of that. I think that makes intuitive sense. You don’t want to feel like you’re navigating a highway curve while you sit at your desk at work.

It’s helpful to think of these systems in a simplified way. This is the most basic representation: a spring, a damper, and mass on a cart. We know the mass of the building. We can estimate its stiffness. And the building itself has some intrinsic damping, but usually not much. If we add the damping system onto the cart, it’s basically just the same thing at a smaller scale, and the design process is really just choosing the mass and damping systems for the remaining pieces of this puzzle to achieve the design goal. The mass of liquid dampers is usually somewhere between half a percent to two percent of the building’s total weight. The damping is related to the water’s ability to dissipate energy. And the spring needs to be tuned to the building.

All buildings vibrate at a natural frequency related to their height and stiffness. Think of it like a big tuning fork full of offices or condos. I can estimate my model’s natural frequency by timing the number of oscillations in a given time interval. It’s about 1.3 hertz or cycles per second. In an ideal tuned damper, the oscillation of the damping system matches that of the building. So tuning the frequency of the damper is an important piece of the puzzle. For a tuned liquid column damper, the tuning mostly comes from the length of the liquid flow path. A longer path results in a lower frequency. The compression of the air above the column in my demo affects this too, and some types of dampers actually take advantage of that phenomenon. I got the best tuning when the liquid level was about halfway up the columns. The orifice has less of an effect on frequency and is used mostly to balance the amount of damping versus the volume of liquid that flows through each cycle. In my model, with one of the holes completely closed off, you can see the water doesn’t move, and you get minimal damping. With the tape mostly covering the hole, you get the most frictional loss, but not all the fluid flows from one side to the other each cycle. When I covered about half of one hole, I got the full fluid flow and the best damping performance.

The benefit of a tuned column damper is that it doesn’t take up a lot of space. And because the fluid movement is confined, they’re fairly predictable in behavior. So, these are used in quite a few skyscrapers, including the Random House Tower in Manhattan, One Wall Center in Vancouver (which actually has many walls), and Comcast Center in Philadelphia. But, tuned column liquid dampers have a few downsides. One is that they really only work for flexible structures, like my demo. Just like in a pendulum, the longer the flow path in a column damper, the lower the frequency of the oscillation. For stiffer buildings with higher natural frequencies, tuning requires a very short liquid column, which limits the mass and damping capability to a point where you don’t get much benefit. The other thing is that this is still kind of a complex device with intricate shapes and a custom orifice between the two columns. So, we can get even simpler.

This is my model tuned sloshing damper, and it’s about as simple as a damper can get. I put a weight inside the empty tank to make a fair comparison, and we can put it side by side with water in the tank to see how it works. As you can see, sloshing dampers dissipate energy by… sloshing. Again, the water is both the mass and the damper. If you tune it just right, the sloshing happens perfectly out of phase of the motion of the building, reducing the magnitude of the movement and acceleration. And you can see why this might be a little cheaper to build - it’s basically just a swimming pool - four concrete walls, a floor, and some water. There’s just not that much to it. But the simplicity of construction hides the complexity of design.

Like a column damper, the frequency of a sloshing damper can be tuned, first by the length of the tank. Just like fretting a guitar string further down the neck makes the note lower, a tank works the same way. As the tank gets longer, its sloshing frequency goes down. That makes sense - it takes longer for the wave to get from one side to the other. But you can also adjust the depth. Waves move slower in shallower water and faster in deeper water. Watch what happens when I overfill the tank.

The initial wave starts on the left as the building goes right. It reaches the right side just as the building starts moving left. That’s what we want; it’s counteracting the motion. But then it makes it back to the left before the building starts moving right. It’s actually kind of amplifying the motion, like pushing a kid on a swing. Pretty soon after that, the wave and the building start moving in phase, so there’s pretty much no damping at all. Compare it to the more properly tuned example where most of the wave motion is counteracting the building motion as it sways back and forth.

You can see in my demo that a lot of the energy dissipation comes from the breaking waves as they crash against the sides of the tank. That is a pretty complicated phenomenon to predict, and it’s highly dependent on how big the waves are. And even with the level pretty well tuned to the frequency of the building, you can see there’s a lot of complexity in the motion with multiple modes of waves, and not all of them acting against the motion of the building. So, instead of relying on breaking waves, most sloshing dampers use flow obstructions like screens, columns, or baffles. I got a few different options cut out of acrylic so we can try this out. These baffles add drag, increasing the energy dissipation with the water, usually without changing the sloshing frequency.

Here’s a side-by-side comparison of the performance without a baffle and with one. You can see that the improvement is pretty dramatic. The motion is more controlled and the behavior is more linear, making this much simpler to predict during the design phase. It’s kind of the best of both worlds since you get damping from the sloshing and the drag of the water passing through the screen. Almost all the motion is stopped in this demo after only three oscillations. I was pretty impressed with this. Here’s all three of the baffle runs side by side. Actually, the one with the smallest holes worked the best in my demo, but deciding the configuration of these baffles is a big challenge in the engineering of these systems because you can’t really just test out a bunch of options at full scale.

Devices like this are in service in quite a few high-rise buildings, including Princess Tower in Dubai, and the Museum Tower in Dallas. With no moving parts and very little maintenance except occasionally topping it off to keep the water at the correct level, you can see how it would be easy to choose a sloshing damper for a new high-rise project. But there are some disadvantages. One is volumetric efficiency. You can see that not all the water in the tank is mobilized, especially for smaller movements, which means not all the water is contributing to the damping. The other is non-linearity. The amount of damping changes depending on the magnitude of the movement since drag is related to velocity squared. And even the frequency of the damper isn’t constant; it can change with the wave amplitude as well because of the breaking waves. So you might get good performance at the design level, but not so much for slower winds.

Dampers aren’t just used in buildings. Bridges also take advantage of these clever devices, especially on the decks of pedestrian bridges and the towers of long-span bridges. This also happens at a grand scale between the Earth and moon. Tidal bulges in the oceans created by the moon’s tug on Earth dissipate energy through friction and turbulence, which is a big part of why our planet’s rotation is slowing over time. Days used to be a lot shorter when the Earth was young, but we have a planet-scale liquid damper constantly dissipating our rotational energy.

But whether it’s bridges or buildings, these dampers usually don’t work perfectly right at the start. Vibrations are complicated. They’re very hard to predict, even with modern tools like simulation software and scale physical models. So, all dampers have to go through a commissioning process. Usually this involves installing accelerometers once construction is nearing completion to measure the structure’s actual natural frequency. The tuning of tuned dampers doesn’t just happen during the design phase; you want some adjustability after construction to make sure they match the structure’s natural frequency exactly so you get the most damping possible. For liquid dampers, that means adjusting the levels in the tanks. And in many cases, buildings might use multiple dampers tuned to slightly different frequencies to improve the performance over a range of conditions. Even in these two basic categories, there is a huge amount of variability and a lot of ongoing research to minimize the tradeoffs these systems come with.

The truth is that, relatively speaking, there aren’t that many of these systems in use around the world. Each one is highly customized, and even putting them into categories can get a little tricky. There are even actively controlled liquid dampers. My tuning for the column damper works best for a single magnitude of motion, but you can see that once the swaying gets smaller, the damper isn’t doing a lot to curb it. You can imagine if I constantly adjusted the size of the orifice, I could get better performance over a broader range of unwanted motion. You can do this electronically by having sensors feed into a control system that adjusts a valve position in real-time. Active systems and just the flexibility to tune a damper in general also help deal with changes over time. If a building’s use changes, if new skyscrapers nearby change the wind conditions, or if it gets retrofits that change its natural frequency, the damping system can easily accommodate those changes.

In the end, a lot of engineering decisions come down to economics. In most cases, damping is less about safety and more about comfort, which is often harder to pin down. Engineers and building owners face a balancing act between the cost of supplemental damping and the value of the space those systems take up. Tuned mass dampers are kind of household names when it comes to damping. A few buildings like Shanghai Center and Taipei 101 have made them famous. They’re usually the most space-efficient (since steel and concrete are more dense than water). But they’re often more costly to install and maintain. Liquid dampers are the unsung heroes. They take up more space, but they’re simple and cost-effective, especially if the fire codes already require you to have a big tank of water at the top of your building anyway. Maybe someday, an architect will build one out of glass or acrylic, add some blue dye and mica powder, and put it on display as a public showcase. Until then, we’ll just have to know it’s there by feel.