AskPablo: Going up?

elevator.bmp This week’s question comes to us from Pete, who writes

“Okay – I’ll admit it, I’m lazy. I work in a second floor basement, and we make a couple trips a day to the street level to bring in furniture and supplies. There is an elevator that we can use. There are also stairs. I used to be really good about taking the stairs every time. But now, about 9 months after I started here, I find I’m choosing to use the elevator every time. Both going up and coming back down. I know, I know… See, I know that’s the wrong choice. But I was wondering if there was some way to quantify exactly how wrong of a choice it is. So to convince me to get back to taking the stairs, I think I just need a numerical push, and you might be able to help.”

Well, since Pete already knows that he is making the wrong choice I won’t need to try and convince him of that. All I have to do is spit out some numbers that confirm his feelings, and that shouldn’t be too hard…

I found a great write-up about elevator energy use at the Energy Ideas Clearinghouse. This site includes a discussion of various types of elevators, from hydraulic to electric, various heights, from 3 to 32 floors, and two different load ratings, 2,500 and 4,000 lbs. Pete didn’t mention how many floors his building has but he did tell me that his elevator is rated for 10 people, or probably somewhere around 2,500 lbs. Assuming his building is around ten floors tall (including the basement levels), the elevator uses between 39 and 76 kWh of electricity per day.
While this is interesting it doesn’t really help Pete out much since he doesn’t ride the elevator all day. In order to get a per-ride result we need to do some calculations. First we need to understand how elevators work. Smaller buildings often use hydraulic elevators which move the elevator car up and down on a piston. These systems do not recapture any energy on the way down and are not very fast. Most elevators use electric motors that can recapture some of the energy that went into lifting the elevator car as it descends. Since I don’t know the efficiency of this hybrid system I will leave the recaptured energy out of the equation. Hybrid cars that use regenerative braking only recapture a small percentage of energy, primarily because the batteries cannot receive that much energy in a short period of time, but since elevators are grid-tied the efficiency may be higher. In researching for this column I came across the following on Wikipedia and found it to be interesting:

“In areas with large populations of observant Jews, one may find a ” Sabbath elevator.” In this mode, an elevator will stop automatically at every floor, allowing people to step on and off without having to press any buttons. Regenerative braking is also disabled if it is normally used, shunting energy collected from downward travel, and thus the gravitational potential energy of passengers, into a resistor network. This prevents violation of the Sabbath prohibition against doing useful work.”

Empty elevators don’t require much energy at all. The weight of the elevator car is counter-balanced so that the only energy used to moved an empty car is in acceleration and to overcome friction in the cable and bearings. So an elevator that is lifting a person by a certain distance is only lifting that person’s weight and not the whole elevator car’s weight. We know that Pete is taking his elevator from the 2nd sub-floor to the ground level, or about 20 feet. Assuming that Pete and his belongings weigh around 200 lbs we can figure out the energy required to lift him to his destination and we will assume that the downward trip is “free.”
The energy required to lift an object can be defined by the equation: m x g x h (mass x gravity x height). To make things a bit easier I’ll be doing this in SI (metric) units. Here are the parameters:

  • 20 ft = 6 m
  • 200 lbs = 90.7 kg
  • gravity = 9.8 m/s^2

So, 90.7 kg x 9.8 m/s^2 x 6 m = 5,333.16 J. And 5,333.16 J = 0.0015 kWh. If you assume that the entire system is about 50% efficient you use about 0.003 kWh of electricity to go up two floors (or 0.0015 kWh per person per floor). The website mentioned earlier bases its calculations on an 8 hour day of use, probably at capacity. Let’s see if our numbers come close…
A ten-person elevator may cover 10 floors (up and back down) in about 1 minute. There are 480 minutes in an 8-hour day, so this represents 4800 elevator trips. At a capacity of 10 people this equals 4800 people. Ten floors x 4800 people gives us 48,000 people-floors traveled and at 0.0015 kWh per person-floor we have a total energy use of 72 kWh/day. This fits into the 39-76 kWh range given by the website so I am reasonably confident in our calculations.
So Pete, every time you take that elevator from sub-floor 2 to ground level you are using 0.003 kWh of energy. If you do it 4x per day, 250 days per year (2,000 times) that is 6 kWh. At $0.15/kWh this costs about $0.90 for the year. No, it’s not much… But think of the health benefits, you lazy bum!
But seriously, walking one flight of stairs burns 5 calories (Mayo Clinic Proceedings (77) 2002), so 2000 trips per year up two floors (4000 floors/year) would burn 20,0000 calories.