# Stairs or Elevators? –Part 1: The Data.

By the end of summer school, I had lived at the Berkeleyan long enough to notice how darn slow the elevator was, and how much faster taking the stairs could be. So in response, I decided to quantify the time going up/down the elevator vs. going up/down the stairs. My analysis consisted of three Scenarios:

(1) going up/down +/- 1,2,3 and 4 floors on the STAIRS at a SLOW pace… slower than the average person would walk up or down for any given moment;

(2) going up/down +/- 1,2,3 and 4 floors on the STAIRS at a FAST, jogging/running pace… faster than the average person would go up or down the stairs in an average instance, but similar to how fast someone would go if they were rushing to class;

[Taking the middle ground between the two lines would probably approximate walking time of an average person who’s not rushing.]

(3) going up/down +/- 1,2,3, and 4 floors on the ELEVATOR.

For Scenarios (1) and (2), 3-4 “walks”/trials were timed on each of the +/- 1, 2, 3, and 4-floor intervals (8 sets of trials for each scenario, 4 for up and 4 for down). The averages of each set in each scenario were plotted and a linear regression was fit to the data.

For Scenario (3), 3-4 MOVING trials were timed from the beginning of elevator acceleration to the beginning of elevator deceleration on each of the +/- 1, 2, 3, and 4-floor intervals (8 sets of trials for each scenario, 4 for up and 4 for down). Additionally, 8 separate (“WAIT”) trials were conducted for each of elevator moving UP and elevator moving DOWN (16 total combined) to determine time from press button to the beginning of elevator acceleration, and from the beginning of elevator deceleration to elevator door opening. The averages of the “MOVING” trials for each set were summed with the corresponding average UP or DOWN “WAIT” to find the total time spent in the elevator, and plotted. And again a linear regression was performed on the data.

And the chart of time vs. number of floors:

The dashed best-fit lines indicate going DOWN; the solid best-fit lines indicate going UP.

They are not reported on the chart, but the best-fit equations and R2 values are:

Stair SLOW UP: $f(x) = 13.836x; R^2 = 0.9995$

Stair SLOW DOWN: $f(x) = 13.42x; R^2 = 0.9993$

Stair FAST UP: $f(x) = 6.574x; R^2 = 0.9978$

Stair FAST DOWN: $f(x) = 6.07x; R^2 = 0.9984$

Elevator UP: $f(x) = 4.091x + 14.54; R^2 = 0.998$

Elevator DOWN: $f(x) = 4.663x + 14.42; R^2 = 0.997$

In all cases, $f(x)$ represents the time and $x$ represents the number of floors up or down – not the same as the start or destination floor! The slope is the time it takes per floor, the y-intercept of the elevator graph is the wait time derived from the regression (slightly different from the one derived from experimental data).

Note that the +/- 3 floor SLOW walk trials were thrown out for inconsistencies with the data.

So, remarks. Note how the elevator is ALWAYS slower than running up the stairs, even though it technically travels faster (lower slope = less time to go up one floor). However, because of the ~14 sec wait time, the elevator seriously lags, and it doesn’t catch up if you go up four floors (i.e. L->5) or less. It CAN be nearly caught up to you if we extrapolate to five floors (L->R). That will be a good test to conduct for future studies. I predict that a person taking the elevator up to the roof will arrive almost at the same time as a person running up, given that the elevator is at the lobby at time zero.

For the slow walk, it can still be faster, but the elevator catches up rather quickly. Nevertheless, this graph does provide a strong incentive for walking up 1-2 floors, and as we’ll see, perhaps more…

Note that it is faster to go up the elevator than to go down, but it is slower to walk up the stairs vs. to go down. This suggests that it might be advantageous to go UP the elevator, but go DOWN the stairs.

More to come in Part 2…