McKinsey
Medium
Estimate the number of elevators in a 50 floor building
This is a supply and demand problem. Not a building trivia question.
Clarify first. Office, residential or hotel. An office peaks hard at 9 am. Residential demand spreads through the day. Building type sets the entire calculation.
Assume a 50 floor office tower. State the assumption before you use it.
Size the population. Floor plate around 10,000 sq ft. At 150 sq ft per person that is roughly 80 people per floor. 50 floors gives about 4,000 occupants.
Find the peak. Elevators are sized for the morning rush, never the average. Around 12% of the population has to move in a five minute window. That is 480 people.
Now the supply side. A n elevator holds about 20 people. Real loading is closer to 16. Round trip time in a 50 floor building is roughly 150 seconds.
So one car moves 32 people in five minutes. Two trips, 16 people each.
Divide. 480 over 32 is 15 passenger elevators. Add one or two service cars. Call it 16 to 17.
The real answer is not the number. It is zoning. Nobody runs 15 elevator serving all 50 floors. You split into three banks of about 17 floors, five cars each. Zoning is what collapses round trip time.
Wait time is the binding constraint, not capacity. An office tolerates 45 to 60 seconds. Luxury residential expects under 30. Halve the acceptable wait and you nearly double the elevator count.
Sanity check. A real 50-floor office tower runs 16 to 24 elevators. The estimate lands in range.
Change the input, and the method holds. Residential peak load is 2 to 3%, and the answer drops to 5 or 6 elevators.
Community Answers (2)
I'll start first with the purpose of an elevator: The main purpose of a lift (elevator) in a building is to provide efficient, safe, and convenient vertical transportation for people and goods between different floors. First I need to know who the lift will be transporting - so I need to know who will be occupying the 50 floor building - what kind building is this (Mall, Residential Apartment, Office Complex, Parking Complex) ?? Where is it located and how is it utilised?? (all floors are utilised for same purpose or not) Once, I know these details, The questions I need answers to is - 1. How many people can fit in that lift (assumption - 15) 2. Time taken to travel between floors (~ 10 s) 3. Time take during a stop (~ 15-20 s) 4. So during the peak usage each lift can carry 15 people and take a min time of 500 s (~ 10 min) to travel to top and a max of (14*20 + 500) (each person stopping at their floor*wait time per each stop + sum of travel times for each floor) = (~15 min) So during peak capacity of the building - It takes 1 lift 15 min to transport 15 people. and again 10 min to return. So it takes 25 (~30 min) for each lift to move across the building. So what is the frequency of the people moving through the building vs capacity of the building - Do all of them enter at the same time (like in office) (from 9 - 9:30) or Only few (working professionals leaving between 9-9:30 in an residential apartment) So the formula I would use is - (#entities that would transport through the building during peak hour)*(peak hour window/time taken by life per trip)*(capacity of lift)
#Floors: 50, # Seats per floor: 100, Maximum occupancy in a given day 80%, hence we need to design the elevators for 4000 people. Now, the elevator will be designed for peak. Let's day during peak hours 3000 people will travel in one direction, and 1000 in another. The ones travelling in another direction doesn't need to be considered Lift can handle a max of 30 people and takes 10 mins to travel each floor. The peak lasts for 30 mins, hence the design needs to happen only for 1000 people. The total number of elevators needed will be around 30