The Spatial Absorption Spectra of Bicycles

I spent three-ish weeks riding around Mexico’s Sierra Madre Occidental on roads worse than the fire roads in the San Gabriel Mountains with Bryan.  Las Barrancas del Cobre.  Para conocer el otro lado.  It was incredible.  It was also I think, somewhat beyond the original design specifications of our rigid frame bikes (a Surly LHT for me, and a Traveler’s Check for him).  The bikes performed heroically though, and we got through the whole trip with nothing more serious than a flat tire, a lost bolt (for which a replacement was had), a broken chain, and some worn out brake pads.  With some bone rattling descents taking half a day, and spanning 1400m vertically (not unlike the Mt. Wilson Toll Road, except steeper, and in much worse condition) I got very familiar with the different sizes of rocks and ruts and hills and other topographic obstacles, and what they would mean as far as the ride.  I also had a lot of time to think about why the hell Bryan was already up on top of the hill ventilating his nether regions by prancing around in flip-flops and a turquoise sarong, while I was still hurling obscenities at the inch thick layer of obstacle obscuring volcanic ash dust covering the road and often obligating me to push the bike up a 10% or steeper grade.

Ultimately, I figure it comes down to the absorption spectrum of the bicycle and rider in question.

Here’s what I mean: for any bike tour, you’re tracing out a one dimensional path or parametric curve through a two dimensional surface in three dimensional space.  Thus you can look at the topography of the path you’ve chosen as if it were a waveform.  Stretch it out with the x-axis representing distance (or time) along the path, and the y-axis being altitude.  The task of the bicycle and rider is to absorb that wave, which is composed of a superposition of many different waves having different frequencies in different proportions.  Different systems are engaged to deal with these different frequencies.

At the highest frequencies (the smallest elements of topography) the waveform can be absorbed purely by the spokes in the wheels and a rigid frame.  You can ride a bike with no tires on steel rails, because there is almost no mid-scale topography on railroads, just the tiny imperfections in the rails, and maybe the joints between them at one end, and the largest scale (mountain range) scale topography at the other end.  The timescale for these smallest responses is probably on the order of milliseconds.  The physical scale is millimeters or less.

Next you have small bumps and gravel and rocks and little sticks, on the order of a centimeter in size and hundredths of a second in time.  To deal with this kind of topography you need pneumatic tires.  Get a little bigger, a few to ~10 cm or so, and a tenth of a second, and at any appreciable speed or complexity, things get very difficult.  This is the scale that suspension systems on mountain bikes are generally made to deal with.  Washboard.  Rain ruts.  Baby-head rocks.  Good luck on a rigid loaded touring bike!  Beyond, from 10cm to a few meters, there’s a dead zone where with many waveforms, you can hike or climb, but the bicycle just isn’t the right technology.  If the amplitude is low enough, and the variations are taking place over on the order of a second, then you can effectively use your arms and legs as the shock absorbers, and from here on out the rider becomes more important than the bike.

You can climb a lot of very steep one to ten meter hills anaerobically, putting your quads into oxygen debt temporarily, for seconds or minutes.  You might even be able to do 100 vertical meters that way.  Once anyway.  But if you want to climb a kilometer, you can only do it with your heart and lungs, and it’s this distinction (anaerobic vs. aerobic) that I think ends up separating riders, especially couples, who are touring together.  On a flat road, someone with a lot of aerobic capacity can pedal harder, but they end up getting diminishing returns for this effort, because wind resistance also increases (and becomes a significant force around 20-30 km/hr… cube of the velocity, etc.).  Climbing a hill on the other hand, increased power output translates directly into increased ground covered.  On a dirt road this is even more true, because often on bad steep climbs, the speed that would correspond to a sustainable aerobic power output is actually too low for the bike to be effectively controlled, and once you’ve stalled out on a steep gravelly slope, it’s very hard to get started again.  So for a given climb, there will exist a threshold aerobic capacity below which one will often end up walking the hill, and above which one will generally end up riding.  Since riding is more efficient, this results in the slow person also ending up doing more work overall, and usually resting less.  This is very frustrating.  If you are the fast person, try to remember this.

But what if you don’t just want to climb 1000 meters one day?  What if you want to cross mountain ranges or continents over weeks or months or years?  Then you need to use other systems that let you deal with the longest wavelengths, systems largely composed of knowledge.  You need to be able to patch a tube, break a chain, replace your brake pads, identify a rim that’s been worn too far.  Maybe you need to know how to build a wheel.  You need to know to check and make sure no bolts have rattled loose.  Maybe you need to know some basic wilderness medicine.  You need to know to take your bike shorts off as much as you can during the day to dry yourself out.  You need to know how to pace yourself.  Riding 150 km once is totally doable.  Riding 150 km  every day indefinitely is much less so.  For a lot of people even 75 km a day on average may not be sustainable, depending on the topography, and depending on how much gear they’re carrying, and how good their knees are.  I don’t think I’ve ever done a tour that averaged 75 km a day.  They usually seem to end up around 60 km/day on average with one very mellow day in five or so.  You have to know how to keep enjoying yourself.  How not to end up lonely or frustrated.  Maybe you need a foreign language or three.  Maybe you need a friend.

Really it doesn’t seem so different from life itself.

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Zane Selvans

A former space explorer, now marooned on a beautiful, dying world.

One thought on “The Spatial Absorption Spectra of Bicycles”

  1. Thanks for this rather geeky (in a useful, very insightful way) rundown of some aspects of your trip – I was wondering how it went!
    I have a phobia about being left behind, so I’m not good at being the person bringing up the rear on a trip, which probably causes me to not undertake a lot of very worthy adventures. I hope to see photos.

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