How to compute your own travel time equation values

 What is a travel time equation and what can you do with it?

A travel time equation is a formula that computes how many minutes it will take you to travel to a place when you know how far away that place is. 

The equation looks like this:
t = mx + b

t  is time in minutes
m is minutes per mile, a coefficient you calculate. It is like speed inverted.
x is miles, the distance between the start and end points as measured on a map
b is minutes, a constant you calculate. It is minutes added to every trip.
Further data about a specific travel time measurement project are:
  • x(average miles), b(average minutes)
  •  R2 (standard deviation measuring goodness of fit of time values computed)
You can think of average miles and average minutes as an indicator of how urban and compact is the travel environment that was measured.
R-squared or the standard deviation is a goodness of fit measure.  For travel time equation projects, R-squared is a rather large number which means the relationship between distance and time is pretty sloppy.

When you compute a travel time equation for a specific mode of transportation, like driving  your car or  riding the public bus, you are finding a succinct numerical measure of the performance of that mode of transportation for you in your specific home location and in your specific commute and employment situation.

Travel time coefficient values are affected by the rules of data collection,  the circumstances affecting the traveller and the decision to exclude data points made during analysis and calculation.
  •  Result values are affected by the data collection rule followed during the trials: A rule stipulating one specific mode of travel for all trips will result in a different data set from data collection using selected modes of travel for specific trips.
  • A base of trips containing many similar trips like a specific daily commute drive will tend to reflect the time and distance of the specific commute.
  • In particular, commute trips tend to reflect the extended optimization that can be performed on a commute trip to find the fastest and shortest route to work and the shortest and most productive route back home.
  • If specific trip records are excluded because of events like traffic or road problems or vehicle trouble, these exclusions

Uses of the travel time equation:
  • Compare the travel time required for different modes of transportation.
  • Evaluate the benefits of changes in bus routes, times and schedules.
  • Do microeconomic analysis of the time, cost, energy use and environmental impact of different transportation schemes.
 Collect travel time records, manual method

You need to make a record of your daily travel which I will call a trip. 
  • The travel time records you make are a scientific log. 
  • You will need at least a pad of paper, a pen and a wrist watch.
  • For bus travel, it is helpful to have a backpack for your logbook.
  • I have used a Garmin GPS 60 global positioning device to make time and location records. Even with a gps device, you still need pen and paper notes to document the GPS data points  recorded.
  • Save your original data. I have travel time records that are ~40 years old. The paper records are still usable.  Other data on 30 year old magnetic cards are now unreadable because the card reader does not work.
Trip record format:

Start. House number and street of starting point.
The time you left the starting point, recorded to the nearest minute.
Count time from when "fingers leave the doorknob" to get a consistently measured start time. Use the same rule for measuring trips on different modes of transportation.

End. House number and street of ending point or destination of your trip.
The time. Use "when fingers touch doorknob" or other rule to get a consistently measured end time.
Make your record show clearly the mode of transportation you used. If you start out making a bus travel record and a friend gives you a ride, note the changes.

Or, collect trip records with a global positioning system

A global positioning system (GPS) is a hand held device that receives satellite transmissions and computes the longitude, latitude and altitude of where the GPS device is located.  The GPS usually has a feature called Mark that creates a time, date and location record in the GPS memory.

For finding a travel time equation, we need only the times and locations measured at the start and end of each trip. A lot more data is available from a GPS device.

GPS data, has the appearance of great accuracy. You must surround GPS data with written notes. You need to be able to read your notes and identify what a specific block of GPS data refers to. Note the mode of travel, names of some trip destinations, and other factors about these trip records. 

An example of GPS data.
 Latitude Longitude Date and time

37.5463 −122.53 7-Dec-2010 7:51:19
37.6701 −122.48 7-Dec-2010 8:29:11
37.6701 −122.48 7-Dec-2010 15:27:54
37.5464 −122.53 7-Dec-2010 16:01:56

Excel compatible spreadsheet with sample data, calculations and comments

Gnumeric compatible spreadsheet with data, calculations and comments

Find the travel distance and compute the trip duration from your trip records

You can measure a map:

Or you can access and type in the start address and end address and read the distance between the points.
Make a scatterplot graph to give you a visual image of your trip data

Scatterplot of auto trips made Dec 7 to 9, 2010 from El Granada, California

Using the simple linear regression method, calculate a travel time equation from your trip data.

No comments: