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

I previously described a heuristic but fairly comprehensive bike power-speed model. This was based on trying to model speed directly from course features, rather than going through power, since riders typically don't ride at a constant power, although that represents a physiological constraint. The model assumes riders have a given cruising speed on flat roads (I assumed 30 kph), a theoretical maximum rate of vertical ascent (I assumed 1300 m/hr), and a safety-limited rate of descending (I assumed 14 m/sec = 50.4 kph based on conditions on these courses; perhaps this was slightly low). I assumed a rate of fatigue of 0.5%/hour, which affects climbing rate (directly) and speed on the flats (1/2 as much). The model further assumes riders lose distance versus time when they turn: 40 meters per radian of cornering at max descending speed, much less when cornering slower (proportional to speed squared). I have compared this model to actual rider data and it seems to match fairly wel...

Back in January I proposed that road grades tended to follow cosine-squared probability distributions with the maximum grade as a parameter. Different roads could then be characterized by their maximum design grade. The choice of cosine-squared over the Gaussian which would be suggested by the Central Limit Theorem was because roads aren't random, they're designed, and designers impose a maximum grade beyond which the probability is exactly zero. This was important because I had proposed a heuristic speed formula for how long it takes a cyclist to ride a given road, and even for the rapid attenuation of probabilities associated with a Gaussian distribution, the cycling time would have been dominated by pathologically steep grades. Using cosine-squared this issue went away. Anyway, I got curious as to how the Devil Mountain Double course compared with the Terrible Two course in that regard. Which is steeper, and do both tend to follow the superposition-of-cosine-squared p...

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...

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...

Today I'll take another look at the route data from the Death Ride , Climb to Kaiser , and the Terrible Two . Here for each climb I first map the data onto a 50 meter grid, then slightly smooth it using an estimated 15 second time constant (the same as when I calculate a climb rating), then I map it back to a 50 meter point separation (since smoothing disturbs this at the beginning and end of the ride) then I calculate the total climbing (with zero threshold) between each pair of points on the route. For each segment length (which is the number of contiguous points minus one multiplied by 50 meters) I find the segment which maximizes this total climbing. The only efficiency trick is if I have a given segment length, I don't need to calculate it fresh each time: if I start with the segment from points 1000 to 2000 (length 50 km), and I want to calculate the climbing from points 1001 to 2001, I take the previous sum, subtract the climbing from 1000 to 1001, and then add the ...

Last time I used grade histograms and total climbing versus climbing threshold to compare three really solid one-day riding challenges: the Death Ride , Climb to Kaiser , and the Terrible Two . What I left out is sort of the obvious: the route profiles. Every big ride shows its route profile, and they all tend to sort of look the same: up and down. So to compare the three, I plotted them on the same axes. I use km for distance and meters for altitude: That one's worth more than the measly 100 kpixels shown here, so if you click on the plot you should see a higher resolution version. Anyway, the Death Ride and Climb to Kaiser look sort of imposing here. The Terrible Two is almost lost under the giant altitudes of those other two rides. Climb to Kaiser is perhaps most striking of the three, starting down in the lowlands before rising to and beyond the lofty altitudes of the Death Ride. Indeed, Climb to Kaiser is a very special ride, one I often recommend to those who th...

First, a bit about the climbing algorithm. Just two paragraphs, I promise. Then on to good stuff. I just described an algorithm by which you can calculate total climbing from a route profile with a given "climbing threshold" designed to both eliminate small bumps which can be coasted over, but more importantly to get rid of the small altitude fluctuations which occur with "noise" in both barometric and GPS-based altimeters. I proposed that a 5 meter threshold worked well, but that there was no unique answer for what is the "true" climbing of a route. Well, that algorithm does work well for a relatively small climbing threshold, but when you crank the threshold up to the size of the largest hills on a ride, it can be fooled. For this post, I thus added an extra step to the process, in which peaks closer than the climbing threshold from the minimum altitude on the ride, and valleys closer than the threshold from the maximum altitude on the ride are b...

I don't use my PowerTap on hillclimbs because it's too heavy, and I don't use my PowerTap in mass-start races because sometimes you've just got to dig deeper than you think you can. But for Terrible Two, I decided within the last few days I wanted it. Sure, hauling that 1020 gram wheel up 16 thousand feet of climbing was going to add work, and work equals time. But a double century for me isn't about minimizing work, but rather in minimizing work done over threshold. And to keep my enthusiasm in check on the early climbs the power numbers would be useful. Additionally, as a diagnostic tool it would be really valuable. I wanted to compare the power I could sustain on later climbs to those I was able to hold on the earlier climbs. Now, I've already documented here my torque measurements suggest my Powertap reads low. The steeper the climb, the more low it reads. This error is on the order of 10 watts or so, so view numbers reported here with that sort o...

2010 profile from race-winner Bo Heberstrat My last report ended as I left the lunch stop, one of my quickest stops on the route. It's easy to lose a lot of time at lunch, although skipping it means you need to be especially careful to stay on top of calories and hydration while on the bike, especially if (like me) you haven't been doing the big-mile rides you would have preferred to have done before this event. Skaggs Springs I passed a sign which said Camp Gualala was in 25 miles, Stewarts Point in 35. I remembered Gualala marked the beginning of the steepest climb on the Terrible Two, the Rancheria climb. But I forgot what came in those 25 miles to Gualala. Of course I could have checked my route sheet. But it was jammed in a pocket of my vest, which was jammed in a pocket of my jersey. And what was the point? Whatever was there, I would ride. And what was there was tough. First, the nine miles to the first water stop after lunch was an 1800 foot climb in two segmen...

Chuck Bramwell data from slightly shorter 2003 route Pre-Ride The start of the Terrible Two is incredibly organized. How do you possibly open "reg" 20 minutes before it's mandatory for riders to be at the start line ready to go? Well, the answer is you lay out each rider's number in alphabetical order on tables so each can pick his up without waiting in a line. Then you have a separate table for pre-ride drinks, another for gel flasks from sponsor Hammer Nutrition , and a third table for bagels. And have a big box of pins. It all went well, and I felt like I had plenty of time in hand having ridden the 1.5 miles from my hotel to the start to arrive at 4:55 am. On the start line, I was slightly chilly but not too bad. I had on a mesh tank-top, a long-sleeve undershirt, arm warmers, a short-sleeve jersey, a vest, shorts, and knee warmers in addition to socks, shoes, and short-fingered gloves. This seems like overkill, but I really don't like the cold, ...

The Terrible Two this year was held for the 35th time. The Terrible Two was without much doubt the most difficult double century in the United States until Scott Halversen introduced us to the Devil Mountain Double . Now it's a continual debate which is the tougher of the two. Terrible Two wins on the steepness of the climbs and on the potential for hot near-solstice weather, while the Devil Mountain Double has more sustained climbing and less daylight. I first tried the Terrible Two in 1999, when I flew in from Austin for the pleasure. I'd participated in part of the Texas Hell Week that year, a March endurance training camp of eight days at close to 100 miles per day. I'd also been doing long weekend rides including Texas Randonneur Brevets. These long miles plus the near-daily exposure to Texas heat really gave me a lot of confidence I'd be able to handle what T2 had to offer. What I didn't expect it to offer, however, were flat tires. Two flats, p...