I can be riding along the W&OD Trail on a weekday and not see anybody at all for two miles. I can do a whole ride–as I frequently do–when I pass few other cyclists and no cyclist passes me. And yet, often when I do overtake the slow cyclist, the walker, the dog walker with a chihuahua, the in-line skater novice learner (deadliest of all slow traffic, subject to sudden and uncontrolled lurches), as I am just about to pass them a traveller comes from the other direction. That traveller is moving just fast or slow enough, be it a cyclist or a mom/nanny with carriage, to require me to brake, often to a crawl, to let them pass before I can scoot around the low-speed obstacle in front of me.

This frustrating coincidence of being slowed down by a coordinated confluence of obstacles from each direction after miles of empty trail I call “convergence.” To my way of thinking this happens far more often than it should, statistically. After all, there’s almost nobody on the trail on weekday mornings, and yet so often when they do appear they appear in this convergence configuration, slowing me down.

So I would like to check it, but i have inadequate math skills to construct a formula. If we call N the number per hour of travelers that I pass going in my direction, and N’ the number per hour of travelers that I pass going the other way, and if R is the average speed of the N travelers, and R’ the speed of the N’ travelers, and at my rate of speed (about 15.5 mph) I need 40′ of clearance beyond the N travelers to pass them, how many “convergences” per hour should I expect? I could find or estimate the quantities for all those variables, but I cannot construct an equation that would give me the right answer.

Any help out there? It just feels in the “seat of my (specially padded spandex) pants” as though it shouldn’t happen as often as it does. I think, given the sparse population of the weekday trail, that it should almost never happen. But then I cannot deny a tendency to become easily frustrated.

©Arnold Bradford, 2010.

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I think this is a good question for Sean to help you with!

The mind tends to remember the exceptional and gloss over the ordinary. Also, consider the fact that your “convergences” involve slow-moving people which are therefore approaching/next to each other far longer than fast-moving people. Maybe the explanation lies somewhere between the two! I need to get up to the W&OD. I’ve heard nothing but good things about it.