My projected average velocity for the year 2007: | 0.075 km/h, bearing 329° |

My projected average speed for the year 2007: | 6 km/h |

**Nuværende humør:**tired

Going around in circles - A Roguish Chrestomathy

the pultaceous wisdom of a word weevil

13 December 2007 @ 01:12

Going around in circles

My projected average velocity for the year 2007: | 0.075 km/h, bearing 329° |

My projected average speed for the year 2007: | 6 km/h |

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Assuming you started in Toronto, and that you gave a true bearing instead of a compass bearing, I'll guess you're somewhere in the vicinity of Chapleau, Ont.

If you know the radius of the circle, we could calculate your centripetal force, although the nonzero mean velocity suggests that the center of the circle has drifted around somewhat.

If you know the radius of the circle, we could calculate your centripetal force, although the nonzero mean velocity suggests that the center of the circle has drifted around somewhat.

I'm in Toronto now, but I wasn't in Toronto when the year began, and I won't be when it ends. So I should probably tell you that my average velocity for the year to date is about 0.06 km/h, bearing 34°. (Of course, all these figures are approximate, and I'm afraid I can't even guarantee that the number of significant digits I've provided is an accurate reflection of their precision. So don't be alarmed if your new calculations predict me to be underwater come year's end.) A potential minor complication is that I will be ending the year in a different time zone from the one in which I began it, but I was in essentially the same place for an hour before and after midnight at the beginning of the year, so we can safely take either time zone as definitive.

As for the circles of the title, they're not really circles at all; they're various long, skinny, non-concentric, highly irregular figures that are mostly topologically equivalent to circles. I plead poetic licence.

What is the acronym for your subway? D'oh, I know this. TART? TRAM?

Does this average the time you are motionless and the time you're zipping around under someone else's power?

And ... the hell? I'm confused.

Does this average the time you are motionless and the time you're zipping around under someone else's power?

And ... the hell? I'm confused.

TTC.

This averages everything for the whole year—definitely including time I've spent moving under someone else's power. If I were doing this under my own power, I would essentially have to spend the entire year moving around at a brisk walk, with no breaks at all, or else with breaks offset by bursts of running.

TTC is a *horrible* acronym! I much prefer TART; I'd lobby, but my non-resident status would lessen my influence. So, you do it, okay?

How did you come to these averages?

How did you come to these averages?

Your versions are much more fun. On the other hand, I assume TART would have to stand for something along the lines of Toronto Area Rapid Transit, which is both too broad and too narrow: there are other transit systems serving the GTA (GO, Mississauga Transit, Viva, etc.), and the TTC certainly includes some forms of transit that are not at all rapid.

Calculating the average velocity was easy; I just figured out the distance and direction between where I started the year and where I intend to end it (with some help from the Great Circle Mapper), and divided the distance by the number of hours in the year.

For the average speed, my estimate is a bit on the low side; I just added up the distances I've travelled on the various long trips I've made this year, and then added on a rough estimate of how far I've travelled back and forth to work, and again divided the total distance by the number of hours in the year. I've neglected to include small ad hoc trips that I have no good means of quantifying; for the mean velocity, these make no difference, but for the mean speed, omitting them understates the end result.

(April was a particularly busy back-and-forth month for me; my average velocity for the month was zero, but my average speed was probably over 42 km/h.)