Friday, May 16, 2014

Pounding the Pavement

Sent this in to Randall at xkcd for his What-If column (Randall - on the very long odds that you like my question _and_ end up hitting this obscure little auto-blog; no peeking!)

Which exerts more pressure on the roadway; 200-pound me on my 30-pound mountain bike, or the 6-million-pound crawler-transport (that used to be) used to take the space shuttle to launch?

On my way to work this morning, I distractedly rode my mountain bike across some reasonably-fresh asphalt.  I worried whether I might have left a mark.  This got me thinking about the relative pressure - in the real sense; per unit-area - exerted by me and my bike.  I may be light compared to, say, a car, but the contact patches of my tires are pretty miniscule.

Several sources suggest the pressure exerted on the ground by a tire should be exactly equal to the pressure in the tire, but fail to back this up with experimental evidence.  This refutes that and does site evidence, so I'll do it the hard way.

This was useful for contact patch sizes for mountain bikes:  Ends up about 4.19 in^2.  Those calculations are for ~32 PSI in the tires, which seems ludicrously low to me, but they're probably talking about dirt-track riding - I rarely get off the pavement anymore, and keep mine up around 60 PSI.  But, it also finds pretty tiny amounts of variation, so I'll hope that doesn't skew it too much (and in any case higher PSI would _decrease_ the size of my contact patches, and therefore _increase_ the pressure on the pavement.)  I weigh about 200 lbs, and my bike weighs about 30 lbs, so 230 lbs / 4.19 in^2 =~ 54.89 PSI.  (Which is actually pretty close to my tire pressure, but that's probably coincidence given the contact patch size was estimated using a different pressure.)

This give me the dimensions of a single tread on one of the tracks of the crawler: 90" x 25" x 18".  Height should be the shortest, so I'm going with 2250 in^2 of contact patch.  This says it has 4 tracks with 57 treads each, but the photo down the bottom shows 33 in the air, so 24 on the ground at a time per track.  24 x 4 x 2250 = 216,000 in^2 of contact patch.  It also lists the curb weight at 5,999,000 lbs (I do _not_ weigh 6 million pounds!  How dare you!) leaving us with 27.77 PSI.  Me and my bike are pushing nearly twice as hard.

(Of course, in an ideal mathematical model the contact patches of a tire would be infinitesimally small at the point of first contact - they're bigger because either the tire or the road surface deforms.  I'm pretty sure I know which deforms most easily in the cases of: a rubber air-filled tire, asphalt, and metal treads.)

I wonder how big the contact patches are on my rollerblades?