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

I've looked at this matter before, but one factor which I've seen continually neglected in all of the climbing power analysis estimates is the effect of grade variability. Road grade on climbs is almost never constant: it varies about a mean in some fashion. Yet the estimates are almost always done assuming constant speed, constant power. Now these estimates end up remarkably accurate anyway. Why? Because the grade variability effect is negligible? Well, no. It's because you're canceling one mistake with another. For example, you neglect grade variability, which always increases power, but you also neglect drafting, which always decreases power. How does grade variability increase power? It's because grade variability typically results in speed variability and speed variability yields variability results in variability in wind resistance and wind resistance, by virtue of being superlinear, is increased more by increases in speed than it is decreased by d...

Yesterday at stage 1 of the Vuelta al Pais Vasco, Alberto Contador won , finishing 14 seconds over Alejandro Valverdi and 34 seconds over Michal Kwiatkowski. The route included 8 rated climbs, including two ascents of the steep Alto de Gaintza, which gains 290 meters in only 2.3 km (see stage preview ). Four riders have uploaded the stage to Strava, Here's Kenny Ellisonde's activity . He was 40th, @ 2:42 down on Alberto. Here's the report on Alberto's time up the last ascent of Alto de Gaintza, the final climb of the race: #Itzulia , Stage 1. Alto de Gaintza (last 1.69 km, 15.33 %, 259 m) Alberto Contador: 6 min 56 sec, 14.62 Kph — vetooo (@ammattipyoraily) April 7, 2014 If these numbers are good, that works out to a VAM of 2241 meters/hour. Assuming a CdA of 0.32 meters squared (recommended by Vetooo based on extensive comparison of VAM and rider-reported SRM data, and coincidentally measured by Tour magazine in a wind tunnel), an air density of 1.15 kg/m 3 ,...

Going into San Bruno Hillclimb this year I knew I was underprepared. I'd barely ramped up my climbing fitness during the Low-Key Hillclimbs, showing some signs of speed at Lomas Cantadas (week 7), then exposing my weakness on the dirt @ Montara (week 8), then the following Thursday, Thanksgiving, paying for a lack of endurance @ Mount Hamilton (week 9). It was all a bit sobering. That launched me into a December full of travel: San Francisco - Philadelphia - Albany NY - Philadelphia - New Jersey - Philadelphia - San Francisco in two weeks. In addition to the planes and trains, I squeezed in some decent-quality running. But running isn't the same as riding, especially since my running is adaptation-limited at the moment. On the positive side I felt some running speed returning at the end of that period. My return to San Francisco on the night of the 27th allowed for just a few days to prepare for San Bruno. Due to commitments of visiting family, I ran, then later hiked,...

Marin Ave isn't like most other climbs. With Marin, it becomes as much a matter of survival as of speed. Speed is desired as much because it ends the suffering sooner as because of the desire for any target time, placing, or Low-Key Hillclimb points. Yet in the case of Saturday's 7X challenge of course the placing and the points were still important. A nice thing about metrology data is they tell a rich story if examined closely enough. In this case I didn't have a power meter, my PowerTap too heavy for timed hillclimbs, so I have to rely on other ways to judge my effort. On a climb this steep, VAM is a nice proxy for power, so I use that to judge my pacing. VAM extracted by numerically differentiating measured altitude with respect to time is inherently noisy, especially on a Garmin Edge 500 where altitude is reported with 1-meter resolution. So to get meaningful numbers I convolved the result with a Gaussian of sigma 3 seconds. This smooths the VAM to something w...

One issue in using VAM to predict power is the effect of variation in grade. I looked at this back in November, 2009 . Grade variation leads to speed variation (at constant power) and speed variation results in an increase in energy dissipated to wind resistance. The analytic result I got was: Δ p / p 0 ≈ 3 f [ < Δ grade ² > / ( grade 0 + C RR )² ] × [ ( 1 - f ) / ( 1 + 2 f ) ]² where f is the fraction of power from wind resistance, <Δ grade ²> is the variance of grade with respect to time (this is to first order the variance with respect to position), and C RR is the coefficient of rolling resistance. Using iBike data from a ride up Old La Honda (iBike directly measures grade, rather than indirectly via altitude), I concluded at constant power up Old La Honda the grade variation would lead to a 0.44% increase in power. I can convert this to the effect on VAM by multiplying by the fractional effect of power on VAM : Δ VAM / VAM 0 ≈ 3 f [ < Δ grade ² ...

This Tour de France has experienced truly epic increases in people calculating how much power riders generate on climbs, typically towards assessing whether Chris Froome is practicing illicit performance enhancement. One of the more popular practioners of this assessment is VeloClinic, for example in his Haiku-esque Tumblr page . In previous years, there has been a good deal of discussion about VAM, Ferrari's statistic of rate of vertical ascent. Since climbing primarily involves mass overcoming gravity, VAM is related to power/mass, but but it's only a crude instrument, since the more gradual the climb, the greater the fraction of power going into wind resistance and rolling resistance. Additionally, it is possible to sustain higher VAM for shorter climbs compared to longer ones: on shorter climbs you can use your anaerobic energy reserves more rapidly, increasing the energy per unit time, which is power. Furthermore, at higher altitude oxygen concentrations in the atmos...

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...

A followup to my run report... a look at VAM. VAM on running is a very different beast than on cycling. With cycling, once overcoming gravity becomes the dominanant task, wind resistance and rolling resis\ tance playing substantially minority roles, a relatively constant VAM can be maintained as long as there's an available gear to support a cadence in the target ra\ nge, at least until holding the front wheel on the road becomes a challenge. With running, the analog of rolling resistance is much larger, so there is no point \ where it can be trivially ignored, and by that point running becomes impractical and movement is more by walking or even scrambling. So VAM without the context o\ f road grade is meaningless. I repeat the analysys I did for Soda Springs Road, which is to plot VAM and road grade, each smoothed by a 30-second Gaussian convolution, on the same plot. H\ ere's the result: What I see is, on these axes, VAM and road grade track nicely until towards the ...

Last post I described my perception of the Low-Key Hillclimb up Soda Springs Road. I did the climb without obvious metrology: I relied only upon perceived exertion and the timer on my Garmin. It's interesting to see how data match perception. My PowerTap wheel it far too heavy to haul up the hill, but a good surrogate for post-ride power analysis is VAM (vertical ascent rate). This works especially well with a hill like Soda Springs road which sustains a relatively constant steep grade the entire way. I took my Garmin Edge 500 reported altitude as a function of time and differentiated it. That creates a highly noisy signal, so I convolved that with a Gaussian of sigma 30 seconds. I considered points only from the point I started riding, so points at the beginning and end wouldn't get smoothed with points from before the start or after the finish, which would cause sag in my VAM rate early and late in the ride. I then did a similar thing with road grade, which I extracte...

I was a bit shocked to see Valverde (Valv-Piti) and his seeming best friend Rodriguez out-climb both Contador and Froome in stage 8 of the Vuelta. Was it that Valverde has raised his game to become a world class sustained climber, but only when racing in the safe confines of Spain? Or was it more that Froome and Contador weren't up to their best, allowing Valverde and Rodriguez to keep up? The obvious check is the VAM: the rate at which they were able to gain altitude. It's roughly correlated to power/mass ratio. In the Armstrong era, it was typical during the Tour for Lance to be significantly over 1700 meters/hour for beyond-category climbs gaining over 1000 vertical meters. On short, punchy climbs riders were over 1800, even 1900. For profile data, all I really used was the official route data from the organizers. These show the climb gains 580 meters in 7.2 km, an average grade of 8.1%. That's fairly steep and fairly short by Tour de France standards, well-sui...

I had a good year at the Low-Key Hillclimbs this year. Often by the time October rolls around fatigue from the year is starting to kick it. Last year I came into the series fairly fresh and fit, but then started a new job and my fitness went straight downhill from week 3 (my first) onward. I finally started exercising at a reasonable rate again in April this year, a mixture of running and some cycling (mostly long commutes to work), and surprised myself with a sub-1:31 half marathon in August: I considered that good given my lack of formal running background. So I knew I had some fitness but wasn't sure about how I'd do on the bike. I did a few climbs of Diablo before the series, just to get some climbing legs, and was surprised my times weren't so bad. But for the Low-Keys, you've got to be better than "not so bad". Everyone seems to raise their game for the series. But despite my worries I did pretty well. So as the series wound down, Tim Clark a...

A few posts ago I posted a plot of VAM numbers for Cobo in the Vuelta stage up the horrific Angliru climb. Of course, Cobo went on to win the race. VAMs are difficult to assess. More relevant is power: in particular, watts/kg. Making liberal assumptions, I tried to come up with a W/kg estimate of Cobo on the climb (or in the early bit, the leader of the group containing Cobo). Here's the result (power at the crank, not hub, assuming 2.5% drivetrain losses): Impressive for sure, but still generally below the Armstrong-era "6.7 W/kg" attributed by Coyle to Ferrari.

Fremont Peak last year versus this year were two very different races. Last year, it was a steady tempo on the lower slopes. I stayed with Carl Nielson as long as I could, until I felt myself going too far into the red, and had to back off. This year, a moderate pace leading up to the steeper climbing was shattered when Kieran Sherlock launched an attack at the front which strung out the group. Most riders responded to this acceleration, but I chose instead to settle back into what I felt was more sustainable. Kieran had done the same thing on Wednesday's Noon Ride up Old La Honda: a hard acceleration right from the beginning. He's faster than me, that's all there is too it. My PR up OLH is 16:49, and that's a mediocre time for him these days. What I'd hoped is I'd be able to pull back some of the other riders. And I did, a few, but not as many as I'd thought I would. I crested the top of the climb just behind a Dolce Vita rider, having passed a...

Arguably the most epic stage of this year's Vuelta was Sunday's race to the mighty Alta d'Angliru , arguably the toughest steep climbs in professional bike racing. Here's a profile of the climb, from Climb by Bike : In the stage, Geox's Juan José Cobo climbed away from the group of favorites, including Team Sky's 1-2 in overall GC, Bradley Wiggins and Chris Froome. Some argued that it was a sign Cobo was dipping into the special sauce, a result too good to be true. While I realize VAM is subject to many sources of variability and is hardly a valid test of doping, I can't resist running the numbers here. Fortunately I managed to take time splits for each of the final 10 km for Cabo or the group containing Cabo, although I had to guess a bit at 6 km to go, where Cabo was trailing Anton. I guessed that Cabo was around 5 seconds behind here, although I didn't see this explicitly on the Eurosport coverage which I was watching on the web. These time...

This year the Tour de France climbed L'Alpe d'Huez , the " Old La Honda " of the Tour. The "official" climbs is 13.8 km long according to Wikipedia , and gains 1099 meters according to Strava , an average grade of 7.96% (the GPS recorded distance depends on trajectory through the switchbacks, for example, and in any case GPS isn't that accurate on distance along curvy routes). It was climbed during the Tour de France stage 19 this year. The climb was complicated by riders arriving at the start in small groups. Timing thus needed to consider the finishing time, well documented by the race, but also the starting time. According to Wikipedia : Since 1999 photo-finish has been used from 14 km. Other times have been taken 13.8 km from the summit, which is the start of the climb. Others have been taken from the junction 700m from the start. The following times were posted as "official" by the Inner Ring on Twitter: I assume these are ...

A lot has been said and written about Voeckler's remarkable climb to Plateau de Beille in stage 14 of this year's Tour. Voeckler had an advantage of 1:49 over second-place Fränk Schleck, 2:06 over Cadel Evans, and 2:18 over Fränk's brother and teammate Andy Schleck. Due to time and fitness lost in a crash, race favorite Alberto Contador was 4 minutes down. Any of these riders were considered a threat to overtake Voeckler, although the consensus most likely scenario was Voeckler would limit his time losses and hold onto the yellow jersey by maybe 30 seconds. Strava KOM: around a half-hour slower than Voeckler's time. Yet it's safe to say it was a shock to almost everyone when Voeckler not only held on to his lead over all other contendors for the yellow, but was a primary activist in chasing down attacks. I'd have expected Voeckler, by any reasonable measure outmatched in that group, to take a very conservative approach to the climb, following the smooth...

Quick post today..... I estimated the power taken for Contador to do the climb to Nevegal, which took him 20:58 from the checkpoint at the base of the climb to the summit: 600 meters climbed in 7.30 km for an average grade of 8.2%. For direct comparison with Horner's Sierra Road climb I used the same numbers: 65 kg body mass, 6.8 kg bike, 1.5 kg of other stuff, 0.32 m² CdA. I reduced rolling resistance from 3% to 2.5% since Contador was on time trial tires. I still assumed 3% drivetrain loss. I used a power-speed model including inertia. I assumed he started the climb at 40 kph. The result: 6.24 W/kg. This is lower than the 6.56 W/kg I had for Horner on Sierra Rd. Horner's VAM was 1916 m/hr while Contador was 1750 m/hr. Of course it's not a fair comparison as Contador had finished two brutally tough stages immediately preceding the rest week the day before, and may not have fully recovered. It seems riders aren't having rest days as productive as the...

After much speculation and indirect guessing, I finally got a time for Chris Horner climbing Sierra Road during stage 4 of the 2011 Amgen Tour of California. Recovox News VeloNews posted Rory Sutherland's power data , with analysis, for the climb. Rory started the climb in Horner's group and finished 1:15 behind. According to the article, Sutherland's time was an impressive 18:02. However that puts Horner's time at an amazing 16:47. I'd put maybe 2-second error bars on that number. For example, if Sutherland hit the base of the climb one second after Horner, then Horner's time would be one second longer. But I'll stick with this estimate. Sierra Road climbs 536 meters according to my numbers. So plugging that into Chris Horner's 0.280 hour ride and you get a VAM of 1916. Generally in the Tour de France if you see a VAM in excess of 1700 that's extraordinary. 1916? But in addition to overcoming gravity when you climb (producing ...

Strava reports the VAM, or rate of vertical altitude gain, for riders on different climbs. VAM allows comparison of climb efforts on climbs gaining different altitudes. It's correlated relatively strongly with power-to-mass ratio, and is considered a decent gauge of fitness. For example, I may climb Old La Honda while someone in France may climb Col de la Madone . We obviously can't simply compare times, or even average speeds, but the rider with the better VAM is probably the better climber. However, one issue with VAM is that it is easier to produce a higher VAM on shorter climbs. It is well understood riders can produce a higher average power for shorter durations than for longer ones. So you certainly do not want to provide an unfair advantage to those riding shorter climbs. Well, whenever one brings up the subject of the time-dependence of power, the CP model is the first thing to pop into mind. The CP model says: maximum power = critical power + anaerobic w...

After I'd reached Madonna del Ghisallo and visited the absolutely incredible church and museum, I saw some riders emerging from another building. Ah, that must be the bar and cafe, I realized, which was soon confirmed. What a difference between the US and Italy, that in any local snack bar you can get something as sublime as a delicious panini made with fresh bread, formaggio, lattuga, pomodori, and with Gazzetta dello Sport as a side: Let's take a closer look at what Gazzetta highlighted in that article, on Mosquera's dramatic stage win at Bola Del Mundo in stage 19 of the Vuelta a España : Wow -- a VAM of 1800 meters/hour for the final 3 km of a brutal climb three weeks into a stage race. But the roundness of that number immediately rang suspicious... Consider first the quoted stats: 12% average for 3 km. That's 360 meters. So how long does it take to climb 360 meters at a VAM of 1800? Simple: 1/5 of an hour = 12 minutes. But it says it took 12:53...