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

In the September 2010 VeloNews Magazine , which I just got in the mail today, there's a review by Zack Vestal of six aero wheel pairs Check out the magazine for all the numbers. The topic of this blog post is the rating system. That system is to rank each of the six wheels from 1 to 6 in the following categories, then to average those rankings to get a final score: Aerodynamic drag weight front wheel stiffness rear wheel stiffness rear wheel rotational inertia front wheel rotational inertia Rotational inertia describes how hard it is to change the rotation rate of an otherwise stationary wheel. For a given unit mass, its contribution to weight is obviously proportional to the mass, while the contribution to rotational inertia is proportional to the mass multiplied by the square of the distance of that mass from the axis of rotation. So mass at the rim contributes more to rotational inertia than mass at the hub. First, note that three of these rankings depend on mas

This morning, I was distressed to see this story in the SF Examiner : During a four-month period beginning in November, cyclists will be banned from the westside walkway — normally designated for bike riders — due to a construction project that entails the seismic retrofitting of the bridge cable’s main anchorage, which straddles both sidewalks on the northern part of the span. The first phase of the seismic work, which is scheduled to last four months, will shut down the western sidewalk. Cyclists will be added into the busy mix of walkers, tourists and sightseers during the weekends and weekday evenings. Normally, cyclists are allowed on the western sidewalk during weekdays before 3:30 p.m. There could be no clearer violation of City Charter 8A.115 : "Decisions regarding the use of limited public street and sidewalk space shall encourage the use of public rights of way by pedestrians, bicyclists, and public transit, and shall strive to reduce traffic and improve public he

Okay, for the record, here's a summary of the three candidate methods: The Fiets/Summerson formula: net climbing² / net distance (each reference uses a different normalization factor to make the result unitless). This is good because it can be applied to an broad ensemble of riders. Nobody may agree on what's steep, but everyone agrees to some extent steeper deserves to be rated higher. This formula has the advantage of being trivial to calculate in your head, especially if you are given average grade and are willing to make the approximation that climbing / distance = average grade. My simple formula: net climbing × (1 + [ 12.5 × net climbing / distance ]²). Note during this series of blog posts I've upped the coefficient on climbing due to feedback I've received on the tradeoff between steepness and altitude gained in perceived difficulty of the Low-Key Hillclimbs . This formula is also fairly easy to calculate in your head. The method I described in the pr

So to summarize, I developed a hillclimb rating algorithm using full profile data, which is the following, where I've made a few tweaks: Preferably interpolate initial profile data to a uniformly spaced mesh. This facilitates smoothing. I use a 10 meter mesh spacing. This step is optional. Smooth the initial profile, as needed, to reduce measurement noise (for example altimetric data from a Garmin Edge 500). I use convolution of a single period of a cosine-squared function with full-width-half-maximum of 50 meters. Calculate a "typical" time for each position point using a heuristic equation: d t /d s = (1 second/14 meters) ln [ 1 + exp(50 g ) ], where t is time, s is distance, and g is the derivative of altitude with respect to s . Smooth grade versus time with a smoothing function. I use convolution with a single period of a cosine-squared with full-width-half-maximum of 30 seconds, yielding a smoothed function g*. This operation, if done properly, shou

I encoded the previously described algorithm in a Perl script, and the results were interesting. Here's a comparison of a ranking of the climbs used in the 2008 through 2010 versions of the Low-Key Hillclimbs . All ratings are normalized to Old La Honda, something of a standard unit in any climb parameter. First the Fiets formula, sort of the prevailing standard for hill ratings (and also used by John Summerson): rating = net climbing² / distance rank climb Fiets/OLH 1 Mount Diablo (N) 2.22693 2 Alba Road 2.16942 3 Soda Springs Road 2.11797 4 Hicks - Mt Umunhum 1.92388 5 Kennedy Trail 1.90262 6 Bohlman-Norton-On Orbit-Bohlman 1.89235 7 Welch Creek Road 1.81027 8 Quimby Road 1.78158 9 Sierra Road 1.75709 10 Mt Hamilton Road

There's been two principal weaknesses with the methods I've described so far as ratings of difficulty: They neglect the difficulty associated with extended steep sections embedded withing a longer climb. In extreme cases, the optimal rating comes from rating a subset of the total climb, but this obviously neglects the additional difficulty presented by the additional, more gradual climbing. A climb with a short descent which then climbs steeply to make up the altitude lost in that descent rates the same as a climb which is flat for the distance taken up by that segment (the descent followed by the climb to restore the lost altitude). This really affects a climb like Mount Hamilton, which has two significant descents along its path. I wish to address this. To do so, however, really requires using full profile data. Some have suggested using "maximum gradient" in the formula to account for sections of steepness. But this obviously doesn't work well: a road l

The magazine Fiets has a formula for climb rating which is proportional to: rating = net climbing² / distance + (peak altitude - 1000 meters) / 100, where the altitude term is set to zero if the altitude is less than 1000 meters. I've already noted this altitude part is silly: it allows a flat road to have a positive rating. For the rest of this blog I'll neglect the altitude part. I already mentioned Summerson uses the same climbing and grade dependence as Fiets, although his altitude adjustment is superior.  The magazine actually normalizes this rating by 10 meters, so a climb averaging 10% for 1000 vertical meters, which my representation ranks as 100 meters, would be rated 10 (no units). Recall my formula is: rating = net climbing × ( 1 + [10 × net climbing / distance]² ) Now suppose one climb rates 1% higher in the Fiets rating than another. How would the climbs compare in my rating? Well, if they have the same grade and differ by distance, the answer is

My last post I showed how to apply a simple difficulty formula to a climb from the 2009 Low-Key Hillclimb series , Bohlman-Norton-Quickert-Kittridge-On Orbit-Bohlman . To summarize, the approach was to find the road segment which maximized the rating, and to use that to rate the net climb. Using the aggregate statistics from what we used for the Low-Key Hillclimb, 593 meters gained over 7.15 km, yielded a rating of 999 meters (the same rating as a very gradual climb gaining that altitude). However, by eliminating the first 160 meters (which are gradual) and the final 1100 meters (which gain only 20 meters altitude) the rating can be improved to 1083 meters, an 8.4% increase. Here's how the formula rates the climbs from the 2008, 2009, and 2010 Low-Key Hillclimbs. I added in the climb from Kennedy Road, for which we'd applied for a permit last year but were denied. On the x-axis is the altitude gained over the segment used for the rating (which is sometimes less than th

Here's some simple examples of running the proposed formula, which is: rating = net climbing × (1 + [ 10 × net climbing / distance ]²) Here's the profile for a climb which was used in the Low-Key Hillclimbs in 2009, Bohlman-Norton-Kittridge-Quickert-On Orbit-Bohlman (for brevity, I'll refer to this as "Bohlman-Norton" from here on): The obvious question on this route is: is it one climb or two? John Summerson ends the main "climb" at the top of On Orbit Lane, right before the short descent at near mile 2.5, with what follows after corresponding to a second "climb". For each possible segment length, I then found the segment which maximized the net climbing. This maximizes the rating. The top of On Orbit is often the optimal point to finish the "climb", until the segment length becomes so long that the subsequent descent must be included. It actually turns out to be more beneficial to start the climb at the beginning of

Last post I reviewed some existing ratings for climbs. All fell short. With this in mind, I propose my own rating here. First, a quick review of my rating philosophy: For simplicity, the rating should be based on net climbing and distance. For sufficiently gradual grades, the rider is assumed to be able to shift to remain in a comfort zone on the climb, and difficulty is then proportional to altitude gained. Beyond a certain grade, climbing becomes much more difficult. It may be possible to construct bicycles which can climb steep grades relatively easily, but the rating is designed for a "typical" fit rider on a typical racing bicycle. From the description, an obvious candidate for the rating is immediately self-evident for fans of polynomials: rating = net climbing × (1 + [ K × climbing / distance] N ) The only question is then: what value of K , and what value of N ? First, K : K is the distance / climbing at which a climb is twice as steep as it would

Fillmore Street in San Francisco: short and very, very steep.   Webcor Cycling The last time I wrote on this topic I described some of the issues with rating climbs. Here I'll describe some of the existing formulas. First a quick disclaimer. I tend to interchangably use grade and climbing/distance. By grade here I generally mean climbing/distance, even though grade is formally rise over run (not over the hypotenuse). net distance Let's start simple. One formula is distance. This seems absurd, but it's one you even hear today from commentators on bike racing. "Road xxx climbs for yyy km." Obviously distance provided difficulty, but we're interested here in the difficulty of climbing, and without considering road grade, distance is a very weak metric. net climbing Next is total climbing. As I noted climbing can be measured as net or gross climbing, but for simplicity I'll stick with net climbing. Then the total climbing is the initial a

I've been through this before: ride a hard double century, feel indestructable in the days following, fail to give my body the hard recovery it secretly craves. After Terrible Two three weeks ago, I didn't do anything overtly stupid; I even scaled back from my normal training. But despite this, after the following weekend, I was simply spent. I suspect allergies had a hand to play in this, as well, but then I think one becomes more sensitive to allergies when the adrenal system is overtaxed. And if double centuries are designed to do anything, it's overtax... At the start of the Livestrong San Jose, I was pleased with the generous support of donors to my ride. I think it helped I'm matching donations with one of my own to the Peninsula Open Space Trust, to whom I feel a huge debt for their work to preserve the lands which make the region between San Francisco and Santa Cruz such a cycling paradise. So the Lance Armstrong Foundation and Open Space were both

There's been a number of formulas proposed for rating the difficulty of cycling climbs. The Tour de France, as do essentially all stage races held anywhere roads go up and down, rates climbs. However, these ratings depend on many factors other than the intrinsic nature of the road itself, for example position in a stage, position of the stage within the overall race, and on the number and nature of other climbs both within the stage and in other stages. The goal of rating climbs isn't to reproduce the ratings used in the Tour de France or any other race. Rather it's to come up with an intrinsic rating which describes how challenging that climb might be, by virtue of its climbing, for a typical fit rider with typical road gears without stopping to rest. Obviously a 200 mile flat road in the heat is challenging, but it has a climb rating of zero, while a 100 meter road gaining 5 meters is substantially easier, but has a climb rating larger than zero. So we're t

I was watching VeloCenter where Scott and Todd were droning on and on about how long today's stage of the Tour was: 227.5 km (or, using their preferred units, 141 miles). Now I agree that's a long way to race, but anyone who's followed the Tour for any significant number of years knows 227.5 km is hardly extraordinary. Memories of LeMond racing in the 1980's where the long stage was 270, 280, or even 300 km... So I decided dig into some real statistics. For stage length, I relied on the excellent web site Memoire du Cyclisme . I found these pages easier to mine than Wikipedia. So I wrote a Perl script to download the relevant annual web pages from the site and sweep the HTML for stage lengths. First, I plot the data for each year using a log-normal plot. The x-axis describes stage length, while the y-axis describes the rank of the stage having that length. Each decade in the plot (only even decades to avoid too much clutter) is then represented by a cu

Last post, I feared the carnage and chaos which awaited stage 3 of the this year's Tour de France. The consensus among riders has been that the cobbled paths of Paris-Roubaix had no place in the Tour, it being inappropriate to introduce so much randomness and risk-taking into a single stage. On the other hand, the organizers position was riding on cobbles was an important part of the tradition of road racing, and the Tour was a test of the best all-around road racer, not simply the one with the best tried-and-true combination of climbing and time trialing which all too often seems to reduce the Tour to a predictable script. I've been in the former camp. I empathize with riders who invest their entire season on a good performance here, only to be stuck behind a crash in which they had no part. The pressure to stay ahead of these unavoidable crashes creates a dangerous game of musical chairs, creating still more crashes on the kilometers leading up to the cobbled pavé.

Well, within an hour of my previous post, stage 1 of the Tour ended in serial carnage. First Cavendish crashed with Freire and a few other riders, then a mass-pileup took out most of the remaining field, then a forward-moving domino effect eliminated Tyler Ferrar from green jersey competition. For him to make up the ground he lost on Thor Hoshovd would require Thor to suffer some mishap. The #1 rule of the green jersey is you must be in the points every day. This is because the difference between a winning sprint and a medicre sprint is a lot less than the difference between a mediocre sprint and no sprint at all. So Tyler was a big loser on stage 1. But then came stage 2, which was going to be an interlude between chaos. Instead, there were multiple riders down on the wet descents, including poor Christian Vandevelde who was taken out of GC contention, and may be out of the Tour completely (he went to the hospital after the stage, according to his tweet ). The field ne

The Tour started yesterday in Rotterdam, the start of 4 crazy days of bike racing. First, the prologue. This is amazingly the third consecutive Grand Tour (after the tours of Spain and Italy) to start in Holland, and for each, it's rained. A rainy prologue makes for changing conditions, and in this case riders like Christian Vandavelde, Dave Zabriskie, and Bradley Wiggins gambled with an early start time, hoping the weather would worsen for during the traditional start time for the favorites, prime-time at the end of the day. But while early-starter Tony Martin was able to squeak through with good conditions, these others were faced with rain and wet roads, while Armstrong, Contador, and Cancellara enjoyed some of the best conditions of the day starting in the final slots. Stage 1 is going as I write this. In the Dutch stages in the previous two grand tours, there's been carnage in the streets, as riders were faced with a seeming endless series of traffic circles. Today'

A bit more on the Western States 100 , held in California near Sacramento this past weekend... The race is considered to have been extremely tactical by ultramarathon standards. By Duncan Canyon at mile 23.8, a lead group formed of Anton Krupicka of Colorado, Geoff Roes of Alaska, and Kilian Jornet of Spain.  They mostly stayed together until near 45 Geoff fell off the record-shattering pace being set by the other two. Some thought this was a tactical decision but after the race Geoff admitted he simply couldn't keep up. Anton and Kilian continued to push each other hard, trading the lead, with Kilian going ahead on descents and Anton catching him on climbs. Kilian perhaps made the mistake of doing the race without carrying water, while Anton carried two bottles, and thus Anton was able to make faster transitions through aid stops. Since Kilian didn't want to let Anton get a gap on him, this caused Kilian to rush at rest stops and fall behind on hydration, a critica