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...