How Long Do the Subway Doors Stay Open?

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Abstract

The purpose of this observational study is to find out how long the subway doors in a NYC subway stay open, and then to test it against MTA's mandated time of 30 seconds (Source: Anonymous MTA Representative. Telephone Interview. 4 June 2006).

Introduction

Have you ever run up to a subway platform only to find the doors closing right in your face? Have you ever missed your stop because you weren't quick enough to make it out of the subway? We've been through both of these situations for a countless amount of times. One day we just started wondering how long you actually have to get on or off the subway.

Procedures

1. First, we selected the trains that we would investigate and the stops we would collect data for.
2. Then, we scheduled the day we were going to collect data.
3. Next, we began our observation study by boarding the subway.
4. For each stop we recorded the time of arrival (which we defined as when the doors opened), the time of departure (which we defined as when the doors closed), and the time the doors stayed open. we also recorded the elapsed time between the doors closing at one station and opening at the next.

Analysis

Once we gathered all of our data, which can be seen here in Excel format, we decided to set up a confidence interval (CI) for the amount of time the subway doors stayed open. Before we could begin we first had to find the sample mean () and standard deviation (s) for how long the subway doors stayed open:

n = 184 stops
 = 16.604 s
s = 31.453

Once we compiled these statistics, we decided to use a One Sample Z-interval with a 95% confidence level:

Let the population be all of the time intervals that the NYC subway doors stay open

Conditions

• normal condition- To show the normal condition, we constructed both a frequency histogram and a box plot of the time distribution. When first looking at the histogram you get the impression that the data is skewed. This misconception is cleared up when you look at the box plot of the time distribution, which shows that when you take outliers into account the time distribution is approximately normal.

• 10% condition- we assume that the population > 1840 stops
• SRS- we assumed that the sample we used is properly representative of the population.

Conclusions

We found that one can be 95% confident that the population mean for the amount of time the subway doors stay open is between 12.059 seconds and 21.149 seconds. When you compare MTA's mandated value of 30 seconds with the confidence interval you notice that MTA's value is outside of the interval. Thus there is evidence to reject MTA's claim that the subway door stay open for an average of 30 seconds.

Sources of Error

1. One of the major biases would be convenience sampling since we only sampled the trains we took daily and/or the trains closest to our neighborhoods.
2. We did not factor in the possibility of train delays due to traffic or trains that are withheld because of commands from the dispatcher. Also, the train doors may be left open for an extended period of time because of a train arriving on the other side of the platform for people who may need to transfer
3. The subway doors close at different times depending on which subway car you are riding in. Generally the doors closest to the front of the subway close later than those near the rear.

Sam Teruashvili with Andrew Chan -- 2006

Students Choice pages in The Physics Factbook™ for 2006

• Physics of the Body
  • Center of mass of a human
  • Fingertip reaction time
  • More acceleration perturbations of daily living
  • Size of a human: Body proportions
  • Speed of a human running: Is footwear a factor?
• Miscellaneous Topics
  • How long do the subway doors stay open?
  • Coefficient of restitution

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