To bike or to hike?

January 13, 2012

Today there was a seminar in a building maybe 8 minutes away on foot. Should I have biked or should I have walked?

Here are some simplifying assumptions (in SI units):
* My sole goal was to get there and back as quickly as possible.
* The same clothing suffices for biking and for walking. (The burden of putting on a helmet is negligible.)
* I can walk comfortably at a rate of 1.5 meters per second and can bike comfortably at 6 meters per second. There are no stairs or traffic stops to worry about.
* For each one-way trip, it takes me 15 extra seconds to walk to and from the bike racks (which take me away from the most direct route between my start and my destination) and 35 seconds to unlock and lock the bike. Thus a round trip (of any length) of biking will require 100 extra seconds in addition to the actual biking.

So what is the length of a “break-even” trip, at which biking and walking are equally fast, and above which it would be faster to bike?

tw = walking time (in seconds) needed to cover distance d (in meters).

Distance = speed*time.

If walking and biking are equally fast for an unknown distance d0, then
d0 = (1.5 m/s)*tw = (6 m/s)*(tw – 100).
1.5*tw = 6*tw – 600.
4.5*tw = 600.
tw = 600/4.5 = 133.3 seconds!
d0 = (133.3 s)*(1.5 m/s) = 200 meters!

In other words, if the round-trip distance to be covered is more than 200 meters, or takes more than 133.3 seconds to walk, it’s faster to bike.

This answer surprised me. I hadn’t realized that even a 4-minute walk could be replaced with a less-than-4-minute bike trip. I guess the “hassle” of locking and unlocking the bike makes biking seem less efficient than it really is.

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