Calculate the number of elevators required in a 100-floor building with an occupancy of 100 per floor.

Assuming we are talking about a Tier-1 city, where the family size is roughly 4

No. of floors - 100

No. of flats per floor - 100

Average family size - 4

So total no. of residents - 4*100*100 = 40000 (max)

Let each floor has 10 wings, with one security person for each wing, so toal security persons - 10*100 = 1000 (max)

Household professionals - Assuming 1 for 5 households, it totals upto - 100/5*100 = 2000 (max)

Guests - Assuming guests also have an average family size of 4 people. Also, for every 5 houses, guests will come at one house

So number of guests at a time - 100/5*4*100 = 8000 (max)

So, total number of people = ~50000

Capacity of each lift = 20 people

Let's say a lift takes 5 secs to cross 1 floor, so for 100 floors = 500secs *2 = 1000 secs (round trip) + 5 second halt in every 2nd floor = 1000 + 5*50*2 = 1200 seconds = ~ 20 mins

Peak hours - 7 am - 12 pm + 5 pm - 10 pm [80% of overall people] = Assume 20% people come within 5 min window = .2*.8*50000 = 800

So, in 20 mins window, 3200 people will come

So, for 3200 people, we would need to 160 lifts (3200/20)

So , we would need around 160 lifts for smooth passage without any wait time for the lift users.

Do we have any information on the elevator type as in it can carry 20 people at a time or 50 people at a time? → 20 people

Do we have any information whether elevators are divided among certain number of floors i.e., 1st floor to 25th floor, there are a few designated elevators, similarly for 26th to 50th floor and son? → assuming every elevator can traverse across all the 100 floors

What does occupancy of 100 mean - is it individuals, families? → individuals

Do we have any information on what kind of building it is - residential or office complex or for some recreational purpose (the number of people to be transported within a specific duration of time will vary) → assuming it to be an office space

I am assuming the occupancy starts from the floor above the ground floor. So, there are totally 100+1 (ground) = 101 floors

Assuming bulk of the employees come in the time frame of 8am-11am and leave in the time frame of 7pm-10pm.

So, the number of elevators required should be sufficient to satisfy the need in that 3 hours window efficiently.

 

Now there are policies regarding return to office and hybrid work, I am assuming most of the employees would be attending office. Let’s assume that in each floor around 10% of the folks would be absent - either on leave or working from home.

I am assuming all the 90% of 100*100 = 9000 employees come within the 3hour window. Assuming uniform distribution of incoming employees across the 3 hour window, No. of employees coming in 1 hour = 9000/3 = 3000. Assuming there are no visitors.

Since, this is a high-rise building, the speed of the elevator can be ~ 10m/sec. Standard height between 2 floors in a building ~3m.

For the elevator to travel from ground floor to 100th floor and back to ground floor without stopping at any floor, time taken = (3m*100)*2/10 = 600/10 = 60 sec.

When employees are coming in, I am assuming the elevator stops at every 2nd floor when the elevator ascends and does not stop anywhere while descending and it takes around 10 seconds for elevator doors to open up, for people to go out and doors to close. So, time taken for the elevator to travel from ground floor to 100th floor by stopping at every 2nd floor and back to ground floor without stopping at any floor = 60 sec + (100/2)*10 sec = 60 sec + 500 = 560 sec ~ 9.3 min or 9.5 minutes or 10 minutes

 

If the capacity of the elevator is 20:
10 minutes to transport 20 people.
Therefore, in 60 minutes or 1 hour - 20*60/10 = 120 people can be transported

120 people transported in 1 hour by 1 elevator.
3000 people can be transported in 1 hour by - 3000/120 = 25.

 

If the capacity of the elevator is 50:
10 minutes to transport 50 people.
Therefore, in 60 minutes or 1 hour - 50*60/10 = 300 people can be transported

300 people transported in 1 hour by 1 elevator

3000 people can be transported in 1 hour by - 3000/300 = 10

1) Clarifying Questions :-
 a.What type of building is it ? e.g. Commercial / Residential / Hotel / Hospital
 b. What does occupancy of 100 mean ? is it 100 families / 100 individuals or anything else ?
c. Is it for usual commutors or also needs to include provision for wheelchair , ambulance bed etc >

2) Assuming its for residential building with 100 individuals living on each floor and has 100 floors .
  i. Lets assume lift to accomodate 16 people at a time
 ii . Lets assume all 100 people would commute on an average of 4 times during the day
iii. Assuming equal distribution of upward and downward travel via lift
iv. Assuming 10% additional due to maids/plumber / delivery personnel etc
v. Average floors travelled per person ~50

WIth these assumptions
1) 3(no of times used per person)*100(no of people per floor)*100(no of floors) *50 ( avg no of floors travelled)  * 110% ( additional service personel)  => No of people floor travel count = 16,50,000

2) Assuming Peak hours 7AM to 11AM and 7 PMto 11PM
 i. Lets assume 80% of demand is around these 8 hours and
ii. Lets assume it takes 0.25 min to travel across 1 floor and average of 0.5 min wait time it would take 0.75 mins per floor  then it would fulfil 0.75 * 100 * 16= 1200 people floor travel count with 1 lift travel from 1 to 100 which would be taking 75 mins
Hence in 6 Hrs it would complere 480/75 *1200 = 7680

Hence no of lifts required ~ 16,50,000/7680 ~ 215 Lifts