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

Back in July 2009 I did a series of first-order calculations on the effect of various parameters on riding speed. Calculating speed from power is difficult to do explicitly, but to first order the calculations become straightforward. First-order analysis is where much of the intuition is, anyway. One of these calculations was the effect of wind resistance on riding speed . Then in November 2009 I extended that analysis to the effect of wind speed on riding speed . To my dismay, I found an error in that result. I'd even rationalized the wrong result with incorrect arguments. I had to track the consequences of that error through the following two blog posts. I think I fixed everything. The corrected result was: d s / d s w = 2f / [ 2f + 1 ‒ s w / s ] where s is the rider speed, s w is the tailwind speed, and f is the initial fraction of retarding force due to wind resistance. There appears to be a singularity issue for strong tail-winds (see the denominator) but then

For the Terrible Two , I used data from Adam Bickett , who finished first ( PDF results ). A fast rider is good for model validation because he paced himself well and minimized rest time. The model doesn't include consideration of rest or recovery. Rather than do any formal fitting, I fit "by eye". To do this I examined VAM (rare of vertical ascent), speed, and time relative to schedule, all versus distance. The resulting parameters were the following. I won't attempt to assign error bars: v max : 17 m/s v 0 : 9.5 m/s VAM max : 0.52 m/s r fatigue : 2%/hr I didn't try to fit the cornering penalty, which I kept at 40 meters / radian, and which seemed to work fairly well. Note the VAM number is comparable to Contador on Spanish beef, but this is climbing in the infinite-sine-angle limit (mathematically impossible) and actual VAMs produced by the model are substantially less. First I plot how the time to a given point on the course compares between th

Recently I've been playing with a heuristic power-speed formula for cyclists on mixed terrain. I originally developed this for time-domain smoothing of hill profiles for rating the climbs: converting from altitude and distance to time requires a model for speed versus grade. It was designed based on two philosophies: that on descents a rider approaches a maximum safe speed, going no faster, and on climbs the rider approaches a maximum sustainable rate of climbing. Between these extremes I wanted it to be analytic (continuous in all derivatives). Here was the formula: v = v max / [ 1 + ln | 1 + exp( 50 g ) ] | . Here g is the sine of the road inclination angle and v max is the maximum safe descending speed. It worked great for this purpose. However, my interest in the model deepened when I wanted to apply it to predictions for riding times on the Portola Valley Hills course of the 2013 Low-Key Hillclimbs to establish checkpoint cut-off times. So for that I added

Until last fall, I would ride my bike to the Caltrain station, take the train to Mountain View, and ride from there to work. Since then, however, I've been leaving the bike at home. This is because in August I started training for early December's California International Marathon, then after that redirected my focus to the Napa Marathon. Napa is looking extremely grim due to extended training lost from post-holiday-travel sickness, but I prefer to not dwell on that. I've continued to go by foot to the train. It's interesting to compare the relative times, using the 314 train which departs San Francisco @ 7:14 am. Another day on the Caltrain bike car ( StreetsBlog ) Train: Leave home at 7:02 with bike. Ride to 4th and King station. 22nd Street station is closer (0.8 miles versus 1.3 miles), but if I go there I risk the bike spaces filling up before I arrive. It takes me around 7 minutes to ride to the 4th and King. However, if I leave any later than 7:02, I

Previous post I applied a heuristic power-speed model to a simple distribution of road grades. Instead of assuming grades are normally distributed, I assumed they are distributed proportional to cosine-squared. The cosine-squared distribution goes truly to zero. Since the normal distribution is characteristic of random processes, per the central limit theorem, it's widely applicable, but roads are designed and not random, so it's reasonable to expect a deviation from normal. With this distribution, each set of similar roads is described by a parameter, g max , which is the maximum grade encountered. I decided to apply this to Terrible Two to see what I get. I use 2011 Strava data from Adam Beckett , who road a blazing fast T2 with minimal rest stops. Data from fast riders is best, because they are least likely to have traversed on steep climbs, and that would reduce the apparent grade. They additional are least likely to have spent time in rest stops, and moving back an

I've long been frustrated at the lack of bars in my preferred size, 40 cm o-o or 38 cm c-c. My shoulders are relatively narrow, and when I go to wider bars, I feel like I'm in a less stable position, with arms spread out. If I'm holding the plank position, I want my hands directly under my shoulders, and on the bike it's the same. This is the position of greatest mechanical strength. On top of this, narrower bars are more aerodynamic and have less of a cross-section for contact with adjacent riders. It's win-win. Yet for some reason wide bars have been popular. People feel they can get more leverage on wide bars. But power on the bike comes from the legs, not the arms (tests have confirmed this). To maximize this, you want to have as smooth and fluid a pedal stroke as possible. That implies staying balanced on the bike, not wildly thrashing about. So I think any benefits of wide bars except in violent sprints are over-rated. But what about violent sprint

Recently I described a heuristic bike-speed formula which I thought came close to describing the behavior of a typical cyclist riding on hilly terrain. On climbs the rider tends to go relatively hard, approaching a constant rate of vertical ascent (VAM) until the road becomes too steep for gearing and balance, then the VAM drops. On descents, the rider's speed increases until it reaches a perceived safe limit, with additional delays for curves. It's interesting to take this model and predict how hills affect average speed. To first order, in other words for hills of near-zero grade, a rider goes a bit faster uphill, a bit slower downhill, and on average the speed is the same. But for any significant grades this is no longer the case. First, I'll run the model in terms of a "modified grade", which is the climbing per unit distance of travel, the sine of the angle, rather than conventional grade, which is the climbing per horizontal distance, the tangent of t

Lance I just finished the Kindle preview chapters of Racing Weight by Matt Fitzgerald and I already have some critiques. The book also has a website . I'm sure more comments come later if I buy the book. Note this is the first edition of the book, published 2009. The second edition, published in December 2012, appears to be not yet available on Kindle. First, an obvious. He uses as an example of the advantage of weight loss on performance the now infamous case of Lance Armstrong. Lance lost weight from cancer and went from getting passed in time trials to dominating them. We now know there's a lot more to that than losing his "linebacker's build" from cancer. Of course the full story came out after the book was published in 2009 but this was after David Walsh's book, so there was certainly plenty of evidence out there that Armstrong had "confounding factors", and I'd expect he could have used a more scientifically sound example. The

I spent a lot of time recently working on the web pages for the 2013 Low-Key Hillclimbs . Every year this series takes an enormous amount of time and every year I wonder if I want to scale it back or maybe even not do it again but the enthusiasm of participants always keeps me going, and every year I tweak things a bit to keep it fresh. For example, in 2012 I blew out my previous constraints on scoring code complexity, but the result was a much fairer balancing of scores week-to-week. Additionally 2012 was the first year using GPS timing, which worked extremely well for week 7 up Montara Mountain . This year brought two big changes: "coordinator's choice" where coordinators could pick their own climbs (rather than attempting to pick a balanced selection myself). This yielded an excellent schedule. But the big one is week 4: Portola Valley Hills , a GPS timing week much more complex than last year's dirt climb. The way of thinking about how the timing is working

Recently I wanted to estimate how long a "typical" cyclist would take to ride a certain course. You could assume the rider would ride at a constant power, but that's not realistic: we tend to ride at higher power uphill, a bit less on the flats, and low, zero, or even negative power on descents. And on the uphill, there's an optimal grade for power output: if the road gets too steep for a rider's gears or balance, power tends to drop. So rather than a physically based model, I chose a heuristic one: one which has the correct behavior under the different conditions, and connects them analytically. I've described the following model here before , where I used it in a formula for rating climbs: v = v max / [1 + ln | 1 + exp(50 g) |], where g is a modified road grade (the sine, rather than the tangent, of the road angle) and v max is the maximum speed the rider is willing to go on descents. For example, for a brisk rider, I chose v max = 15 meters/second

Previously I described data I'd come across on the saddle positions of various pro cyclists. I plotted those results, showing lateral position of the saddle versus saddle height, each relative to the bottom bracket center, as follows: The fit corresponded to a 66.4 degree seat angle with an intercept 93.5 mm ahead of the bottom bracket. So if the saddle was aligned with the sitting position aligned with a zero-setback post, then a slack, forwardly displaced seat tube would do the best job of fitting this diverse set of positions. It was pointed out to me on the WeightWeenies forum that such a bike had been sold. Here it is: the Aegis: I can superpost the data on the bike. First, I need to flip the axes, then I need to convert saddle height to vertical position above the bottom bracket. Here's the result: The match is remarable to the numbers I derived previously. Evidently the bike didn't sell. The issue is that it isn't needed: you don't need a sin

CyclingNews published a gallery of photos of the Astana team getting tested for bike position by Specialized. Of particular interest was the position changes given to Viscenzo Nibali, their new star for stage races, who rode for the Cannondale-sponsored team last year. Presumibly the superior fit provided by the Specialized crew led by Andy Pruitt would improve Nibali's time trialing. I was curious in how the position change, so I superposed the before and after photos in the article. To align the photos, I rotated and scaled them to align the arm pads. According to the article, "Nibali's bars were raised so he could try to relax his shoulders and drop his head". However, to me if anything his "before" shot looks more relaxed, with a lower head and a more aerodynamic position. If on top of this you shift his "after" position up (the bars being higher) the advantage of the before shot appears even greater. Of course, there's alwa

Approaching the San Bruno Hillclimb this year, two riders I know decided they needed to reach race weight. They weighed themselves daily, publishing the results via Twitter. I found the data interesting, so decided to do some analysis. Here's a plot of their recorded mass in kg versus the day, where I've designated "race day", 01 Jan 2013, as "zero". Rider C began his calorie restriction earlier then Rider B, who began soon after Thanksgiving holiday. Here's the data: I did a linear regression of their progress for the final 35 days (-34 to 0, inclusive). This includes all of Rider B's data up to and including race day, but excludes the day following. It excludes an upward blip in mass Rider C experienced during the Thanksgiving holiday (likely glycogen & water, I suspect). You can see the data generally follow the linear trend: both riders were exemplary in sticking to their diets. Rider B lost mass at approximately 66 grams / day,