Published on <a href="https://blog.prototypr.io/vertical-train-scalable-vertical-transportation-for-really-really-tall-buildings-part-1-ba9bf47649d0?source=rss----eb297ea1161a---4">| Prototyping: From UX to Front End &mdash; Medium</a> Mike L. <img alt="" src="https://cdn-images-1.medium.com/max/1024/1*s4IRF3KyYmsMYE4ROL3ChQ.png">
Elevators will not be the same in 100 years, they do not scale well for tall buildings. Find out why here.
This is part 1 of a 3 parts series that presents a solution to the “vertical scalability problem” of elevators. As buildings get taller, engineers find it increasingly costly and difficult to build elevator systems that sufficiently meet demand. This is because there is a fundamental problem for existing elevator systems, find out now:
<ol>
<li>What is the Problem?— part 1 (this page)</li>
<li><a href="https://medium.com/@mikebrianleung/vertical-train-scalable-vertical-transportation-for-really-really-tall-buildings-part-2-c7323d79e3c4">Insights on traditional solutions — part 2</a></li>
<li>A scalable solution — part 3</li>
</ol>
What’s the Problem?
As buildings get taller, cities run into a vertical scalability problem. The new <a href="https://en.wikipedia.org/wiki/One_World_Trade_Center">World Trade Center</a>, for example, has 73 elevators. These elevators take up a lot of floor space. To understand why tall buildings need so many elevators, let’s look at two numbers, # of occupants in a building and elevator capacity:
<img alt="" src="https://cdn-images-1.medium.com/max/1024/1*YX2hbXHPFs3nWdIvT7d1qQ.png">
For a normal building with a rectangular base and fixed floor height, doubling its height will double its volume, hence doubling its gross floor area and the number of people that can fit in it. What about elevator capacity? how does it scale?
<img alt="" src="https://cdn-images-1.medium.com/max/1024/1*gzPIHyB99bqKodYu8nbc9g.png">
Let’s spend some time to be careful about our terminologies:
<ul>
<li>Elevator Capacity is the number of passengers we can carry to their destinations in a given period of time.</li>
<li>Total Elevator Area is just how much floor area all the elevators have in total. More elevators and bigger elevators make this term bigger.</li>
<li>Avg. Operating Speed is how fast on average the elevators can progress through a trip. This is dependent on many things such as acceleration, deceleration, average stop duration, average stop number per trip, etc.</li>
</ul>
For this analysis, we focus on peak hours (morning) dynamics. In the morning, elevators pick up a full load and travel upward, until the last user gets off, then return to the ground floor to start over. With a normally full elevator with ~ 15 people, it is very likely that each elevator ride will travel most of the building’s max height (exactly how much of the building’s max height it travels can be derived with order statistics but it is not important here). The learning here is that as buildings get taller, each elevator ride becomes longer.
These all seem quite straight forward but the way these two quantities, elevator capacity and # of occupants in a building, scale with the buildings’ height creates trouble for architects. We can see this more easily if we look at Elevator Capacity per Tennant, which is just the former divided by the latter:
<img alt="" src="https://cdn-images-1.medium.com/max/351/1*JAaex1QAYvtHSENPfFV6lA.png">
<ul>
<li>Capacity = Elevator Capacity per Tennant</li>
<li>Area = Total Elevator Area</li>
<li>Speed = Avg. Operating Speed</li>
<li>Base = Area of the building site or cross-sectional area of building</li>
<li>Height = Building’s height</li>
</ul>
Let’s define a new term to assist our thinking. Let’s define Vertical Transportation Tax as Total Elevator Area divided by Building Base.
In plain language, Vertical Transportation Tax tracks how much of the building’s building area is used for elevators. It is a ratio between 0 and 1. It gets bigger when elevators take up more floor area and leave us less room for other purposes. The equation above becomes:
<img alt="" src="https://cdn-images-1.medium.com/max/287/1*Z-ZFTOFrsDC_O8-PxQb9rA.png">
<ul>
<li>Capacity = Elevator Capacity per Tennant</li>
<li>VerticalTax = Vertical Transportation Tax</li>
<li>Speed = Avg. Operating Speed</li>
<li>Height = Building’s height</li>
</ul>
The simplified implication of this is that if a building doubles in height, the elevators have to quadruple in speed to keep up with the demands (Elevator Capacity per Tennant). The speed has to increase quadratically (by a power of 2) as the building’s max height increases in order to keep the Vertical Transportation Tax from increasing if we don’t want people to wait longer for elevators.
In order to make up any shortfall of speed, tall buildings employing traditional elevator design will either:
<ul>
<li>Live with lower Elevator Capacity per Tennant, hence the long wait during rush hours in central business districts</li>
<li>Or, Increase the Total Elevator Area to Building Base ratio (Vertical Transportation Tax), or do both</li>
</ul>
<img alt="" src="https://cdn-images-1.medium.com/max/1024/1*zJXkJrt1m4ezqq0MDCrhEw.png">
What does increasing Vertical Transportation Tax look like? I will do my best:
<img alt="" src="https://cdn-images-1.medium.com/max/1024/1*kth-ELV-JerodNuFNJz23A.png"><img alt="" src="https://cdn-images-1.medium.com/max/1024/1*ugcA2HF5xb-1nTw255JGlQ.png">
They used to play dodgeball but now we can only play mini-golf. Oh! and where is my TV?
<img alt="" src="https://cdn-images-1.medium.com/max/1024/1*Y-___7Q53mmY97rIXdV6-A.png">
Annnnnd now even mini-golf is gone 🙁
At first sight, one might think that this is not going to happen because taller buildings will have bigger building sites so each floor will be bigger. You can see that this isn’t going to help because as we can see from the equations above, bigger building base means more people per floor and that leads to higher elevator demand.
So we have a real issue here, in the <a href="https://medium.com/@mikebrianleung/vertical-train-scalable-vertical-transportation-for-really-really-tall-buildings-part-2-c7323d79e3c4">next post</a>, I will go through some of the traditional solutions to this problem, discuss the interesting dynamics behind them, and propose a solution that is scalable.
<img src="https://medium.com/_/stat?event=post.clientViewed&amp;referrerSource=full_rss&amp;postId=ba9bf47649d0" width="1" height="1" alt="stat?event=post.clientViewed&amp;referrerSou">
<hr>
<a href="https://blog.prototypr.io/vertical-train-scalable-vertical-transportation-for-really-really-tall-buildings-part-1-ba9bf47649d0">Vertical Train (part 1) — scalable vertical transportation for really really tall buildings</a> was originally published in <a href="https://blog.prototypr.io">Prototypr</a> on Medium, where people are continuing the conversation by highlighting and responding to this story.

Vertical Train (part 1) — scalable vertical transportation for really really tall buildings

Top Stories