May 25, 2024: Elevators
Good afternoon. Elevators are as important for the upward growth of cities as cars are to their outward growth, but compared to other modes of transportation, elevators receive relatively little attention. And so today, we will take a look at the technology and economics behind elevators in tall buildings.
Elevators, in some sense, go back at least as far as Archimedes (236 BC), but the first modern, commercial elevator was installed by the Otis Elevator Company in 1857 at the Haughwout Building, founded a few years earlier by Elisha Otis. A safety brake, which Otis demonstrated in 1854 at the New York Crystal Palace with the encouragement of P.T. Barnum, was the key invention that made commercial elevators practical.
The first electric elevator was developed in 1880 by Werner von Siemens, and by the early 20th century, improvements in motor technology, thanks to the gearless traction electric elevator, enabled the skyscraper boom of that time.
The first commercial Otis elevator had a speed of 0.2 meters per second. In 2016, the Guangzhou CTF Financial Center opened with elevators from Hitachi with speeds up to 21 m/s, or 47 miles per hour, a 100X improvement in 160 years. Recent years have brought about substantial improvements in elevator technology, and the coming years could do the same.
Before we get into emerging elevator technology, let’s set context by reviewing some urban economics and the economics of tall buildings. The reason we have cities in the first place is economies of agglomeration, which means that, due to lower transportation costs of people, good, and information, it is more efficient for economic activity to be geographically clustered.
The Alonso-Muth-Mills model is the most standard model in urban economics. The AMM model holds that a city’s property values are highest at a central point, called the central business district. Property values fall as one moves farther from the CBD, compensating for increased transportation costs. The AMM model is simple and has serious limitations, but as a first approximation, it is a decent model and one that confirms our experiences of living in cities.
If agglomeration economies explain why most of us live in cities, rather than isolated houses dispersed evenly throughout the Earth, then agglomeration diseconomies explain why we don’t all live in one giant, 8 billion person city. The most pressing such diseconomy is congestion. I would contend that congestion, rather than overly strict zoning, is the most binding constraint on the growth of cities, and indeed congestion management motivates much zoning and opposition to new development.
A working definition of a city is a daily commutershed. In an American context, this definition better corresponds with a metropolitan area than with a city, as defined by political boundaries. The size of that commutershed is determined roughly by the distance traversable in a 30 minute commute, a value known as Marchetti’s constant, named for the Italian physicist Cesare Marchetti. Given two cities of different sizes but the same population density, the larger city tends to have more congestion because commuters will travel longer distances, thus occupying more road space throughout the day.
Because property values are highest at the central business district, there is a financial reason to maximize usable building space. That motivates, for instance, pedestrian skybridges in expensive cities, and it is also an argument for saving road space through drone delivery. This is why we see the tallest buildings at central business districts.
Developers are strongly motivated to maximize building space where property values are the highest, and elevator design is crucial in making that happen.
There are some rules of thumb for how many elevators a building needs.
For a residential highrise, one elevator for every 50-60 apartments.
For an office building, one elevator for every 50,000 square feet (~4600 square meters) of office space.
For a hotel, one elevator for every 75 rooms. Additional elevators are needed for meeting rooms and ballrooms. Also, one service elevator is needed for every two guest elevators.
For a hospital, one elevator for every 100 beds, plus an additional two elevators. Additional elevators are needed if medical waste is transported, as that should be separated from patients and their families.
There are some slightly different rules of thumb out there, but they all are roughly the same.
A typical elevator shaft has dimensions 1.7 meters X 2.1 meters, for 3.57 square meters, or ~38 square feet.
The key issue is this. Suppose that an office building (the same reasoning applies for other types of buildings) has n floors and s usable square feet per floor. There are ns square feet of space, and so the number of elevators needed is ns/50000. Since every elevator traverses n floors (this is not quite true, as we’ll see in a bit when we get to sky lobbies, but bear with me for now), the amount of space required by the elevator shafts is about n^2s/1300 square feet. The most important point is the n^2 term. As a building gets taller, the amount of usable space grows linearly in the height, while the elevator space required grows quadratically in height. Thus a greater fraction of the building must be dedicated to elevator space. We have a situation that is similar to traffic congestion: for very tall buildings, elevator space and congestion become serious problems and are major constraints in how tall a building can be while being economically functional.
A sky lobby is an intermediate destination for elevators in a skyscraper. If a person wishes to go to a floor above a sky lobby, they will first take an express elevator to the sky lobby, and then transfer to a local elevator to the desired floor. The system bears some similarity to the hub and spoke system in commercial aviation, whereby flights between two smaller airports usually entail a connecting flight through a major hub, such as (in the United States), Denver or Atlanta.
Completed in 1969, the 100 floor, 344 meter (1129 feet) John Hancock Center in Chicago was the first skyscraper to feature a sky lobby, which is at the 44th floor. A few years later, the 110 floor, 417/415 meter (1368/1362 feet) Twin Towers of the World Trade Center became the second and third buildings to feature sky lobbies, and the first two buildings with multiple sky lobbies at the 44th and 78th floors.
Opened in 2015, the 128 floor, 632 meter (2073 feet) Shanghai Tower holds the record for the most sky lobbies at the 22/23rd floor, 37/38th floor, 52/53rd floor, and 68/69th floor, and hotel access at the 101/102nd floor, for five total. Note that each sky lobby takes two floors; that is because the Shanghai Tower uses double decker elevators.
Sky lobbies save space and increase passenger throughput, but they don’t solve the basic problem that required elevator space grows quadratically with building height, since the average passenger still must travel half the height of the building. Likewise, double decker elevators and most other innovations discussed here help push the height boundary but do not overcome the scaling issue.
This paper by Kheir Al-Kodmany, though now a few years old, is a fascinating overview of emerging elevator technology, with case studies of then-recent and ongoing projects. These innovation save cost and space, which are essential to skyscraper economics. See also a more recent overview by the same author.
Some major innovations include AC motors, which are more efficient and only recently have the control systems necessary for smooth rides; gearless elevators; machine room-less designs, which save both energy and space by miniaturizing the control system; and regenerative breaking, similar to the feature in hybrid cars.
The rope is another important consideration in supertall and megatall buildings. Since the rope must suspend the car for as long as the base to the roof, in a 500 meter building, a steel rope can weigh more than 10 times as much as the car itself. This is a binding constraint on how tall an elevator shaft can be with a steel rope. To get around it, better materials have been developed, including the carbon fiber UltraRope by KONE. UltraRope was first used in the Marina Bay Sands hotel in Singapore, completed in 2010; then in the Burj Khalifa, also completed in 2010 and at 828 meters (2717 feet) as the tallest building in the world; and it is planned on the stalled Jeddah Tower in Saudi Arabia, which is intended to be the first skyscraper to exceed a kilometer in height. Aside from a better strength-to-weight ratio than steel, UltraRope promises longer maintenance cycles. However, due to the higher cost, Al-Kodmany estimates that a shaft must be at least 200 meters for UltraRope to be financially sensible. The tallest building in my city, Portland, Oregon, which is a second tier city, is the Wells Fargo Center at 166 meters.
ThyssenKrupp’s TWIN elevator system allows two cars to move independently in one shaft, allowing energy savings and operational simplicity compared to a double decker elevator. It is used at 50 Hudson Yards in New York City and various other projects.
Speed is important both to minimize passenger wait time and to increase the throughput on a shaft, thus minimizing space. At high speeds, vibrations from joints in the shaft and various imperfections cause major discomfort for passengers. To solve this problem, several recent elevators, such as at the new One World Trade Center, use computerized roller guides, which produce counterforces to the vibrations in the elevator car. Having once visited the observation deck at One WTC, to which one travels directly from the ground level, I can attest that it is a smooth ride. According to the Al-Kodmany paper, the original Twin Towers, lacking such roller guides, had janky elevator rides. I would be curious if anyone can attest to this from personal experience.
Air pressure differentials are a concern too, as anyone with experience in fast elevators at a highrise can attest, and managing these is an active area of research. As pressurizing an entire building is not practical, Al-Kodmany assesses that air pressure may be the most binding constraint on elevator speed.
On the software side, a destination dispatching system is a system that allows passengers to type in their destination at a keypad at the lobby, allowing elevators to group people with the same destination and improve efficiency. A DDS can be seen at the Bancorp Tower in Portland. Aside from efficiency, a DDS can be paired with an access keycard, adding a layer of security, a major concern around skyscrapers after September 11.
There are a few particularly novel technologies under development, but they may still be far from widespread use. A vertical subway is an elevator that operates on a rail, and this could greatly increase throughput and speed. But braking was, at the time of the Al-Kodmany paper, an unsolved problem. Here is an old promotional video from Vertrak, which was developing such a system. I haven’t been able to find anything recent.
A Circulating Multi-Car Elevator System is a revolving elevator system that sounds a bit like a Ferris wheel to me. It could possibly break the scaling problem described above, but there are all sorts of technical issues that would have to be solved.
Maybe the most interesting concept is ThyssenKrupp’s MULTI elevator (though it’s not ThyssenKrupp anymore). This system would move cars through magnetic levitation, breaking the scaling problem and height limitations. Furthermore, cars would not be confined to vertical movements, allowing for some novel building geometries, including motorized skybridge connection between buildings and integration of elevators and subways. MULTI would save 60% energy over a typical elevator. The system is undergoing testing at a tower in Rottweil, Germany. I haven’t been able to find good cost estimates, but given how much more expensive maglev trains are than other kinds of high speed rail, I have to imagine that this system would be expensive and only suitable for very tall buildings.
Finally, there is the space elevator. A space elevator is a cable suspended from a counterweight above Earth’s geosynchronous orbit, about 36,000 kilometers high. The rope would not hoist cargo as in a regular elevator, but rather it would allow easy climbing for space launch. Due to the extreme tension that a space elevator would experience, it requires a novel material such as carbon nanotubes, graphene, or hexagonal boron nitride. A spacefaring civilization would need infrastructure for easy access to space, such as a space elevator or some kind of mass driver, but this is a very long way off.
My guess is that the harshest constraint on elevator development in the coming years will be economic rather than technical. The technology has made significant advancements in the last few decades, and there are many significant advancements on the table. The economics of elevators are tied to the economics of tall buildings, which in turn are tied to the economics of cities at large. I see two major headwinds that may be permanent.
First, despite recent return-to-the-office trends as the worst of COVID-19 recedes into memory, the trend toward remote work for while collar workers looks strong. The United States continues to experience high office vacancy rates. Insofar as white collar workers remain in the office, trends in the United States heavily favor suburban office parks over central business districts. The bottom line is that, with telecommunication technology having improved so greatly over the last few decades and continuing to improve greatly, the agglomeration rationale of central business districts is fading, and with that, the economic rationale of spending such a premium on supertall and megatall skyscrapers.
The second headwind is that, outside of subsaharan Africa, most of the world is well past a peak in the rate of urbanization, both in terms of the portion of the population living in cities and the overall population. Most wealthy countries are already declining in population or having declines on the horizon. This must be a consideration for a real estate developer in thinking about a multi-billion skyscraper that could last for a century or more.
For these reasons, a golden age of urban development that we enjoyed in the 2000s and 2010s may now be mostly over. Maintenance, rather than construction, may soon emerge as the main preoccupation of urban economics. As for elevators, I suspect that we may be near the top floor for the foreseeable future.
Final Fantasy XV
Last year, I played and commented on Final Fantasy XIII, a good 13 years after the game came out. I recently played through Final Fantasy XV, which came out in 2016. I am now only eight years behind schedule. FF XV was first released for PlayStation 4 and XBox One; I played the PS4 version, though on a PlayStation 5, where there are some performance improvements.
Like other games in the series, FF XV excels in presentation, with a gorgeously designed world of Eos. If you have no interest in playing the game, some screenshots give a good feel of what it looks like, though they don’t come close to doing justice to the high resolution.
Compared to other games in the series, FF XV takes its storyline less seriously. After a brief opening, your car, the Regalia, breaks down, and your team pushes it to the Hammerhead gas station and car repair shop. After the car is repaired, you have great freedom to explore in the most open world of the series. Fans complained about how linear FF XIII was until near the end of the game; for FF XV, Square Enix apparently went to the opposite extreme. I spent so much time doing side quests and exploring the world that I rather forgot about the main story.
In the second half, the game suddenly takes such a linear term that it almost feels more like an interactive movie than a real game. There is an opportunity to do side quests again after beating the main game, including some quests that are only available after the end. The developers could have balanced this a lot better.
I won’t spoil the story, but I have to say that I found it to be one of the weaker stories in the series. There is a great main villain, though. Some of the story is advanced through DLC and a movie Kingsglaive, but the main game is self-contained enough, and I’ll stick with that. However FF XV does have one of the most charming casts of main characters. The early portion of the game has been described as a road trip.
As the series has progressed, there is a heavier reliance of minigames, and FF XV really went overboard on this. Fortunately, you don’t have to do all of them to play the game, though you have to do some to be appropriately leveled. Most of my play time went to fetch quests, and to make matters worse, they mostly did very little to advance the story. You meet various NPCs in the game who you initially think may be important characters, but all they do is send you on a chain of fetch quests.
FF XV’s battle system is, on paper, a very complex and sophisticated system. Unfortunately, if one does a sizable fraction of the side quests, the game is way too easy, to the point where to get killed in battle, you almost have to do it on purpose. Thus I found myself not using most of the depth. The progression system is rather busted too, with several superficial features rather than one well-developed feature, like the job system in III and V, espers in VI, materia in VII, and the sphere grid in X.
The soundtrack is composed by Yoko Shimomura, and FF XV is (so far) the only game in the series she has composed. The music is pretty good, though not as good as FF XIII in my opinion.
Overall, the game feels rushed. That is an odd thing to say because of the protracted development time. FF XV started as Final Fantasy Versus XIII, envisioned as part of the FF XIII series. That game was cancelled, and the game was moved from PS3 to PS4 and reappropriated as the next mainline entry of the series. Development started in 2006, a full 10 years before release, and it came out six years after the (first) release of the previous mainline entry. And yet, FF XV has some serious and what seem to have been easily fixable problems with the story, progression system, and imbalanced approach to linearity.
I did enjoy the game, but I can’t disguise my disappointment with several major aspects of it. Aside from the multiplayer games, Final Fantasy XVI is the last in the series that I have yet to play, and I’ll probably comment on that in a few months. I have a copy ready to go.
Quick Hits
There is a lawsuit alleging that the government of Saudi Arabia was more involved in the September 11 attacks than has generally been let on. There is an Atlantic article about it. The lawsuit still has to be tested in court, but depending of how it turns out, it could substantially revise our understanding of American policy in the War on Terror. The Saudi Arabia of today is very different from that of 2001, and so it is not clear that the lawsuit would much inform our approach to the kingdom today.