On Bicycles, and.... what else is there?

"I have a puzzle for you" my fellow passenger asked.... I was riding on the last northbound Caltrain baby bullet train out of Mountain View at 6:38 pm, the one I've been taking pretty much every day since starting my new job last October. If I leave any later, I start paying the price of riding trains which make more stops, get me home even later. This is the latest train I can take and have time to eat dinner, relax a bit, and get a solid night's sleep before catching the 6:11 am southbound the next morning. Long days, sure, but I'm having fun. "A jailer has too many prisoners in his prison and needs to get rid of 100. So he gathers 100 prisoners in a room. In an adjacent room he puts 100 hats, each hat containing one of the names of the prisoners, in random order. One by one, prisoners are brought into the room with the hats where they can pick from up to 50 hats (half) to find their name. If they find their name in those 50 picks, they leave thro

Earlier I reported on a Tour magazine windtunnel test of various "aero" mass-start road frames. Here was the plot from that magazine: Tour magazine windtunnel data Soon after, VeloNews , in its April edition, followed up with tests of its own on a set of its own "aero" bikes. You can read the article here , courtesy of Cervelo, which fared best in the VeloNews test. It is curious to compare the two, because the conclusion which are drawn from the two tests are substantially different: Tour used a dummy rider on each bike, using a hinged stem for handlebar placement, while VeloNews tested the bare bike Tour omitted cables, a potential source of variability due to uncertain cutting and/or placement, while VeloNews included cables. Tour omitted handlebar tape, while VeloNews used whatever tape was "stock" with the given bike. Neither test used any waterbottles VeloNews tested bikes with two sets of wheels: stock and Zipp 404s. Tour used a single

So much for my 6.74 degree estimate.... Theory: Experiment: Not that I'd want an aero frame in those conditions... like the guy on the Cervelo SLC who can barely keep his bike from going airborne.

This Saturday was Milan-San Remo, the "Prima Vera", a race considered by Italians to be their world championship. Like all of the "monuments" of cycling, it is an epic race, a grand journey which covers an enormous amount of terrain. And no professional race covers more: 298 km from Milan, to the Adriatic coast, then westward to San Remo. When I was at Lake Como last September I had two days before my flight to Milan. I'd been thinking of going north to the Dolomites: the Stelvio, the Gavia. But there was snow in the hills, and no sign of the temperature poking its nose above zero. I needed an alternate plan. On the bike car, toward Genoa So I decided to head southward. After some snafus at the train station, where I ended up buying two tickets by accident, then lost the relevant ticket and had to beg the stern conductor for forgiveness (funny: I take the train to work almost every day and have never forgotten my ticket there), I arrived in Genoa.

Today I checked out A Ruota Libera, a handbuilt bicycle show in San Francisco. Unlike the North American Handbuilt Bicycle Show, which was in Austin this year, which is held in a large convention center, the San Francisco show was a modest affair held in a medium-sized pizzeria. Indeed most of the room was taken up by the line for free pizza. Despite this, I managed to see some bikes. First up: a shout of "hi, Bruce!" had me look up to see a guy with a "Bruce Gordon" badge. Bruce Gordon, a legend of frame building, was standing next to his carbon fiber randonneur bike. Ti lugs, carbon tubes, carbon fenders, and a custom Ti front rack were topped off with SRAM Red components. The bike had been featured in the Autumn 2010 Bicycle Quarterly. The Ti lugs were masterful work: solid Ti had been machined down to thin lugs, with the Ti chips recycled. I'm not a big lug fan, but these were really impressive. Then across the pizza line from Bruce Gordo

I just got a copy of John Summerson's new book, the Guide to Climbing (by bike) in Colorado. It's not out yet, but I was very pleased John sent me an early copy. I really like what he's doing with this series ( web site here ): small, compact guides to various cycling-friendly regions in the United States. First he did his national book, and that was perfect for learning about regions (among those covered in the book) that I'd not ridden in, or perhaps (like Colorado) had ridden in but had failed to appreciate due to the restricted route options of a large organized tour. But obviously a modest single book cannot come close to doing justice the the climbs in the full United States, and if I am going to be traveling in a specific region, say Colorado, why should I want to carry around a heavy guide which includes climbs in Vermont, North Carolina, Hawaii, and the entire Pacific coast? These regional guides are perfect for that purpose. They're small, relative

The Cervelo R5-CA, Cervelo's $9000 carbon fiber frame for "experienced riders" who presumably want to ride with a lot of setback (I'm not sure if this is because of superior comfort on the bike or because of increased desire to "look pro") was designed with a 72 degree seat tube. The idea, claims Cervelo, is that the 72 degree seat tube run with a zero-setback post yields similar geometry as their canonical 73 degree seat tube run with a set-back post. Now I happen to like a zero-setback post even with my 74.5-degree seatpost. Obviously I'm not pro material. So those riding with a zero-setback post on Cervelo's 73 degree post seem to be left out of the priceless opportunity to buy this gem of a frame. Tragic: they're doomed to ride Old La Honda an extra 1.3 seconds slower than they could have by virtue of 100 extra grams. Cervelo R5-CA in the wild. This one checks in at 5.03 kg, 26% below the UCI limit. Or maybe this is overblown...

Here's my fourth post in my series where I try to derive a probability distribution for yaw angle. I ask myself why I spent so much time on it, but it became something of a silly obsession, and I suppose as far as temporary obsessions go it isn't so bad. I could have been doing Sudoko or doing crosswords, for example, or playing games on my new "smart" phone. Or worse, responding to work emails and studying manuals or reading literature. Anyway, here's the equation I derived: P(yaw) ∝ 2 cos yaw / sqrt [ γ² ‒ sin² yaw ] First I want to integrate this to derive an analytic normalization constant. For that I cheated and used the Wolfram Integrator : 2 arctan [ sin yaw / sqrt ( γ² ‒ sin² yaw ) ] which integrated across allowed values of yaw yields 2 π. In retrospect this is obvious, as this is the range of headings I'm considering, and I'm normalizing over all headings. So I can write the normalized result: P(yaw) = cos yaw / (π sqrt [ γ² ‒ s

Last time I began the problem of predicting the probability distribution of yaw angle if wind speed (|v|) is fixed but if the rider's heading relative to the wind (Φ) is unnbiasedly random. I calculated the derivative of yaw with respect to heading. Rider speed is s. The probability distribution of yaw is inversely proportional to the magnitude of the derivative at the given value of yaw. P(yaw) ∝ | ( (|v|² + s²) + 2 s |v| cos Φ ) / [ |v| ( |v| + s cos Φ ) ] | Special case: cos Φ = ‒1 P(yaw) ∝ | ( (|v|² + s²) ‒ 2 s |v|) / [ |v| ( |v| ‒ s ) ] | = | (|v| ‒ s)² / [ |v| ( |v| ‒ s ) ] | = | (|v| ‒ s) / |v| | = | 1 ‒ s/|v| | which goes to zero for s = |v|. But I'll look more at that case later. But in general, for this to be useful, cos Φ needs to be eliminated from the equation: tan yaw = |v| sin Φ / ( |v| cos Φ + s ) ( |v| cos Φ + s ) tan yaw = |v| sin Φ ( |v| cos Φ + s )² tan² yaw = |v|² ( 1 ‒ cos² Φ ) ( |v|² cos² Φ + 2 s |v| cos Φ + s² ) tan² yaw =

The last time I came up with a proposed distribution of wind speeds at the bike's level. This was based on an assumed relation between wind speed and height, which is for urbanized areas. It doesn't apply to open coastlines, but then it doesn't apply to dense forests, either: just an attempt to model truly "typical" conditions. But next I need to consider that the bike may be moving in any direction relative to the wind. I assume all headings relative to the wind are equally likely. Each contributes equally to the final net yaw probability distribution. I'll start by assuming the bike is moving at a constant speed and constant direction, and the wind is also at a constant speed and constant direction. I'll worry about probability functions later. To go from wind speed |v| to yaw, I add a parameter Φ, the relative angle between the rider's heading (at speed s) and the wind direction. Then I get two components of the relative wind, one parall

First Tour magazine , and now VeloNews have published wind tunnel data on "aerodynamic" mass‒start bikes. Each measured the bikes over yaw angles from 0 to 20 degrees, and each averaged over measured angles. Tour measured at 0, 5, 10, and 20 degrees, which implicitly gave uniform weight to the ‒12.5 to +12.5 degree yaw range, then a reduced weight to yaws out to at least ‒20 and +20 degrees. VeloNews tested at uniform intervals across the range from ‒20 to 20 degrees. Zipp reports, via NY Velocity , that the measured yaw distribution has peaks at around +/‒ 13 degrees, with peak extending (depending on conditions and rider speed) from 7 to 15 degrees, as measured at the head tube. So does this make sense? I thought so, but I wanted to do an analytic analysis of the problem. If wind is varying in speed, and the rider is varying in his heading, averaged over time what relative yaw angle is expected? Worth a quick calculation, I figured. Unfortunately my "quick

With the job I started back in late October, I've not been devoting much time or energy to training. Yesterday I got out for 50 miles on my bike, a ride cut short by a broken spoke on my Velomax wheel. Velomax wheels are designed with double-threaded spokes: one end threads into the nipple at the hub, the other end into a threaded hole in the hub flange (held there with Loctite). The idea is to avoid the stress-riser of a J-bend in the spoke at the flange side, supposedly improving spoke reliability. But this "theory" overlooks the fact a spoke can bend and rotate about a threadless flange hole, whereas with a threaded hole, the spoke end orientation is fixed, and any lateral pressure on the spoke will place a lot of strain on the spoke where it enters the hub, and since I take my bike onto the Caltrain bike car where bikes are stacked laterally, all it takes is someone's pedal in your wheel to supply lateral spoke force. Indeed, it is at the entry point of the f