Monday, July 22, 2013

the lost summer continues

It's been 38 days since my crash, and things are progressing, but not as fast as I would like.

There was progress 1.5 weeks ago when I got a massage @ World Gym, which left me feeling good, then a productive acupuncture session last Wednesday, which also helped. This initiated a ramp-up of my physical activity. I did 10 minutes on the trainer on Thursday morning followed by a resistance training session in the evening where I was able to up the effort significantly from my previous one. While none of these exercises caused pain, I was left feeling quite fatigued, and waited for the bus rather than walk up Potrero Hill afterwards.

Friday and Saturday I was still tired. My walking was definitely off compared to how it had been on Thursday. Despite this, I wanted to stick to the trainer rides, so on Friday I did 20 minutes, then Saturday I did two rides, one of 10, the second of 20 minutes. I figured my fatigue had been from lifting, and the riding was good.

Unfortunately Sunday morning I was still feeling hobbled. Instead of continuing my upward trajectory in cycling, I took a rest day: heating pad, hot bath, self-leg-massage with The Stick. It all helped, and today I'm doing a lot better. But I want to check again with World Gym to see if I can get another massage appointment.

I've got a physical therapy appointment set up, but it's still not for a week. So until then I'm on my own.

On the positive side, my range of motion continues to improve. I even rode a bike a bit outside, just in a circle on Saturday while watching Luna Rosa sail a solo heat at the America's Cup trials. But I'm not especially close to feeling good taking a running stride or commiting to doing a ride of any significance outside. I think riding uphill would be quite a challenge. This would be an excellent application for Garmin Vector, as I'd like to see how much my right leg is slacking off on the trainer rides.

At this point, I'm still on track for a 6-8 week recovery typical of significant injuries. The doctor told me if I plateau out and am not "significantly improved" by next Tuesday I should get an MRI. Hopefully I make that deadline.

On the plus side, I've been reading more than usual. Currently on my Kindle: The Gods of Gotham. Excellent stuff: New York 1845. I find city life in the pre-car era to be intriguing, although the lack of bicycles is deeply disturbing. Certainly the level of poverty portrayed in the book is sobering. But my recommendation to mid-19th century New Yorkers: invest heavily in real estate in the northern, agricultural part of the island.

Wednesday, July 17, 2013

simulating effect of grade variations on climbing VAM

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:

Δp / p0
3 f [ <Δgrade²> / (grade0 + CRR)² ] × [ ( 1 - f ) / ( 1 + 2 f ) ]²

where f is the fraction of power from wind resistance, <Δgrade²> is the variance of grade with respect to time (this is to first order the variance with respect to position), and CRR 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:

3 f [ <Δgrade²> / (grade0 + CRR)² ] × ( 1 - f )2 / ( 1 + 2 f )3

This is a bit indirect so it's important to review the assumptions:

  1. A rider is riding at constant power up a climb. This yields a certain speed variation associated with a certain grade variation.
  2. The speed variation is going to yield a certain power increase due to wind resistance relative to riding at a steady, average speed.
  3. The rider is riding a constant power, so higher required power must be canceled with a reduction in average speed.
  4. Lower average speed reduces average VAM.

The reason this came up is the recent widespread interest in the use of power analysis to assess the likelihood of rider doping in the Tour de France. If you estimate power using certain assumptions, it's important to assess the error introduced by those assumptions.

So I decided to test this, which took only a few minutes with the script I wrote for the preceding analysis of pVAM. I wrote some simple code which picked a random grade and a random fractional grade variation for a 10 km climb which I divided into 100 equal-grade segments of constant grade. For each new segment, I picked a new random grade, but because grade is locally correlated, I did a weighted average of 3-parts previous segment grade to 1-part this newly selected grade. This created hill profiles which looked realistic to me. The average climb had a 7.5% grade with an 18.3% grade variation, although both the grade and the variation in grade varied substantially. I simulated 1000 climbs this way.

Here's some sample profiles. Of the 1000 iterations, I plot the profiles with the least and greatest fractional variation in grade. They pass the "looks real" test to me:

sample hill profiles

Here's the VAM versus average grade (points) plotted against the result for a constant grade (red line). I didn't use the critical power model here, but rather assumed a constant power of 6 W/kg (Powertap power).

VAM for randomized hills

The VAM numbers are close to those for a constant grade of the same average. To see that a bit better, I plot the % VAM reduction due to the grade nonuniformity here, using a fresh set of 1000 hills (these points don't correspond to those in the previous plot):

VAM reduction for randomized hills

The result is consistent with that analysis from 2009: the grade variations reduce the VAM by a fraction of a percent. The plot brings out an interesting aspect of the equation: very low grade, and wind resistance dominates, and grade doesn't affect speed as much, while very large grade, and wind resistance is less relevant, so speed fluctuations don't matter much. The effect, though small, isn't unbiased: the VAM is always reduced, never increased, by grade variations. But the error from neglecting grade fluctuations is small compared to other error sources, in particular the wind (as was recently pointed out by Alex Simmons).

I also checked the result of the detailed simulation against the analytic equation. As you can see in the plot, the analytic equation is generally good to within 10% of the detailed simulation result. The notable outlier contained a short descent and obviously exceeded the low-order analysis used. Note the plot is showing the fractional reduction in VAM due to the grade variation, not the fractional error in VAM. That would be much less, since the total reduction is typically on order 0.5%.

VAM reduction for randomized hills

Monday, July 15, 2013

pVAM and the Critical Power Model

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 atmosphere are less, so it becomes more difficult to produce a given threshold of power. For all of these reasons, comparing against a fixed VAM is misleading. On steep, short climbs at low altitude you get a big number and all of a sudden you become suspicious the rider is doping, while for an extended, less steep climb like Ventoux (climbed today in the Tour) you get a lower number and conclude everything is good.

To address this, VeloClinic describes a new variable, pVAM, which represents the VAM a top Grand Tour rider would have been able to attain on a given climb during the biological passport era, 2009-2013. The formula is:

pVAM = 2885.17 + 416.825 ln Gradient - 0.06197 VClimb - 0.08796 Altitude

There's a bunch of issues with this, for example it fails to consider where the climb falls within the race or within a stage. A short stage ending with a climb early in a stage race is going to produce a higher VAM than a climb which is part of an epic stage late in the stage race. Still, it's a step in the right direction, and nice work, as long as the limitations are recognized.

But my greater concern is the use of a linear fit. It's generally considered that power is the limiting factor on climbs, that on shallow climbs and steep climbs, riders can ride to a certain power, and the VAM differences are due to differences in the fraction of total power which goes into overcoming gravity. There's a standard model for this, which I have used often in this blog (it's being called the "CPL model" on Twitter, after the Cycling Power Lab website which allows you to calculate it).

Additionally, for the length of the climb, the more time it takes to climb a hill, the lower the power a rider can produce. This effect is treated in the pVAM formula with a linear dependence. But there's a simple model for this which has been vetted in the peer review literature, and that's the critical power model (CPL website page).

So rather than rely on a linear model, an alternate approach is to assume constant power, that power a function of climb duration using the critical power model. For that, I need parameters. So I'll assume a critical power of 6 W/kg (Powertap: equivalent to a slightly, for example 3%, higher power at the crank), and an anaerobic work capacity of 90 seconds times the critical power, which is 540 J/kg. These numbers might be exemplary of an exceptional Tour de France climber.

Note this becomes an implicit calculation: to calculate VAM I need power. To calculate power I need the duration of the climb. To calculate the duration of the climb I need VAM. So I need to iterate until the solution converges. That's handled easily enough with Perl scripts I wrote long ago.

Then there's the altitude effect. I neglect that in my calculations, but there's plenty of on-line references for how sustained power varies with altitude (for example, in the CPL site). I could easily add these to my scripts. It would reduce my VAMs somewhat but the shape of the curves would be very similar.

I compare two situations: one is a 7.3% grade climb of different net climbing. 7.3% is the mean grade of Old La Honda Road, and I consider it the canonical climbing grade. The next one is to fix the climbing at 1000 vertical meters and vary the grade. 1000 meters is typical of a hard climb in the Pyrennees or Alps.

First, the total climbing plot:

VAM vs altitude

The parameters I chose for the CP model are rather arbitrary, so I don't expect the two curves to line up, but I would expect the shape to be similar. But they don't: the pVAM curve has a substantially different shape than the one calculated using the CP model. The CP model is simplistic, for sure, so I don't claim it's a gold standard, but at least it's been validated against a range of experiments, so I trust it more than an arbitrary linear model.

VAM vs grade

Here again, under the assumption of grade varying, the linear model used in the pVAM calculation deviates substantially from the use of the bike speed-power equations and the CP model.

So what sort of differences does this represent? On short climbs and long climbs, the CP model predicts higher VAMS than pVAM. And on both gradual and steep climbs, the CP model predicts lower VAMs than the pVAM model.

The result is that one needs to be careful when using the pVAM model for climbs which deviate substantially from the "average" climb used in the fitting, assuming the assumptions used here are applicable: 1. that the CP model predicts how the power varies with duration of effort, and 2. that riders tend to produce the same power for different grades for a given duration of effort.

Since I tend to trust power calculations more than linear fits, what I would be looking at is the predicted critical power for riders based on efforts they can generate on a given climb. To get this, you need a number for anaerobic work capacity. Set this to some time multiplied by CP, for example 90 seconds, or treat it as a fitting parameter in analyzing historical data. By looking at CP (critical power) the duration of the climb is eliminated. Then if you want to add an altitude effect, make it CP at sea level (or some other reference altitude).

Sunday, July 14, 2013

riding the trainer; Chris Froome

Today I rode the trainer for the first time since my crash a month ago. I borrowed Cara's cyclocross frame because it's small and I can more easily get my leg over the top tube. Previously leg mobility was limiting on me being able to get on the bike, but today I tried and I could do it. Pedaling has also been a concern but I was able to turn the pedals without too much problem. The limiting factor is more muscular than aerobic: I did just a few minutes today. But that's a starting point. I've also been going to the gym, doing light weights, and I think that's helping, even if it leaves me tired. I see my general practitioner tomorrow, the first time since my crash, so maybe he can give me some advice on my progress.

In Tour news, it's been all Froome. I realized last year, his first year on Sky, that I'd seen him years before.

Froome (Telegraphe)
Triplets of Belleville

Friday, July 12, 2013

Time trial position: Anquetil versus Martin

L'Equipe recently posted a nice article on the history of time trialing, including the hour record. The posting included a wonderful photo of Jacques Anquetil, an unsurpassed time trialer in the history of professional bike racing. Jacques' peak was the late 1950's and early 1960's. He won the Tour 5 times, perhaps with the assistance of blood transfusions in the later years.

Anquetil was famous for his extreme toe-down pedal style. It's typically recommended the foot at the bottom of the pedal stroke be at a relatively shallow angle, for example 15 degrees. But Anquetil's foot was at a much steeper angle: closer to 45 degrees. It's hard to argue this approach slowed him down at all, but I've not seen it imitated by accomplished racers.

The dominant time trialist of today amomg the ProTour ranks is clearly Tony Martin. His most recent victory is the first individual time trial in the 2013 Tour de France, which is ongoing as I write this. Despite having suffered appalling road rash on his back in a crash in the Tour's opening stage in Corsica, he was able to beat yellow jersey Chris Froome in the time trial, Froome by far the fastest among the general classification contenders.

Riders today have access to sophisticated wind tunnel and field testing to optimize their positions on the bike. The position of aero bars is tuned to the millimeter, with subtle differences in hand and arm position assessed for their influence on drag. Racers such as Martin spend hundreds of hours on their time trial bikes each season, acclimating themselves to the position so they can reach the full potential of their cardiovascular systems in generating power while aerodynamically optimized.

Anquetil, on the other hand, had access to none of this. Until the mid 1980's, time trials were contested on a similar bike with a similar position used in mass-start road races. The equipment focus on the bike was on everything except wind resistance: minimizing the weight, using the lightest oil in the bearings, and using thin tires pumped to the highest pressures.

You might think the rider positions would be night and day between Anquetil and Martin, the latter having access to more than a half century of technological advances. To check this, I overlaid an image of Martin similar to the Anquetil image with Gimp. I scaled the Anquetil image to match the outside diameters of the front tires, since these are similar. I then superposed the front tires. I then rotated each image so the line tangent to the top of the two tires was horizontal.

This approach is good, but it's still subject to perspective distortion since the positions of the cameras relative to the two riders isn't perfectly matched. So it's not consistent with a high degree of precision. But the result is interesting:

The similarity of the positions might be surprising.

First, consider the bikes. Anquetil's wheelbase is longer, especially due to longer chainstays That was the style then: due to relatively rough roads, the chainstays were kept long to reduce vibrations. Additionally, the front fork was dramatically raked to act as a spring, reducing vibrations at the front as well.

An additional feature of the bike is a remarkable lack of handlebar drop by modern pro cyclist standards. This is because racers in Anquetil's day used the drops for a "racing" position, while today the hoods are more commonly used since that's where the shifters are now. Despite the lack of drop, he has no problem adopting a position with the top of his head below the peak of his back. He looks at least as aero as Martin.

Could Anquetil's position be tweaked with wind-tunnel analysis? No doubt. But despite the drastically different bicycles, it's more similar than different.

Thursday, July 11, 2013

Pen2SF bike commuting group

Since the mid-naughts SF2G has served as a catalyst for cyclists to commute from San Francisco to the Peninsula. The focus has been Google's Mountain View campus, but I've never worked for Google, and I've ridden with the group to Stanford Campus, my old office on California Ave in Palo Alto, and to my present work-place south of Google at the Mountain View - Sunnyvale border. There's no leader; instead riders call rides via the Google Group, then others affirm their intent to join with a Googlesque "+1".

But until now, despite the fact SF-to-Peninsula is considered a "reverse commute" (although with the flight back to cities from suburbia this is changing), there's been no comparable organization of cyclists who work in the city and live on the Peninsula (the "forward commute"). That changed today with the launch of a new group, "Pen2SF". They also have a web site (still under development as I write this).

I really hope it takes off, because the group can serve not only riders working in the city, but also riders who work in the northern peninsula, for example South San Francisco, Foster City, and San Mateo. And people making this "forward commute" have a big advantage: the wind tends to blow lightly from the south in the morning, and strongly from the north in the evening, so at least in the evening commute there's a substantial tailwind likely over at least a portion of the ride.

With the enormous popularity of cycling here, and the favorable weather, there's a huge latent demand. Success is just a matter of people finding out about it.

Wednesday, July 10, 2013

slowly recovering

Its tinjury+26 days, and I'm still hobbling around. Generally I'm hobbling better than the day before, but not always. I'm not working from home any more, instead braving my Caltrain commute with its close to 1 mile of walking each way (assuming I take the MUNI 10 bus and the VTA light rail in Mountain View). I can do this but it's tiring. I have more functional strength in my adductors on the right, injured leg. I can do push-ups.

Getting on and off a bicycle would still be an issue. I've not thought much about riding since last Thursday: I was in Martha's Vineyard and was able to straddle a small hybrid bike, but pushing off with the injured leg just seemed too hard. I'm overdue to try again, but since I live on a 17% slope, the barrier to entry is higher. No "quick spins around the block". Virtually every road in Potrero Hill of San Francisco is steep.

It's frustrating. I've gone to acupuncture 4 times, and while it's amazing at loosening up tight muscles, the muscles appear tight for a good reason: after acupuncture walking becomes painful. It seems the tight muscles are protecting the injured bits, whatever those are, from stress. Loose muscles and force to resist gravity extends to where I don't like it to be.

I mentioned this to a coworker from China, that I felt worse after acupuncture. "That's normal", he said, but he encouraged me to stick to it, that it was good for healing. I then expressed frustration over my rate of progress. "In China, we say 100 days... you're well less than that so no need to worry." 100 days is 13 weeks, so that's a generous allocation for wound healing. 6-8 weeks is what I've seen for muscle tears. Hopefully it's not much worse than that. Of course it could also be a hairline fracture which the early X-ray missed. But it doesn't really matter, does it? My body will heal when it heals, and all I can do is treat is as well as I know how to do, consistent with the requirements of employment.

I'm going to the doctor on Monday. Maybe then I can get a physical therapy referral. For now, I'm just doing exercises on my own. That was going fairly well until I started going back to work yesterday. Just going to and from work is tiring.

At least I don't need to nap any more. Indeed the one positive of this is this is the longest I've been without caffeine since I became interested in caffeine, which was in college. I don't think caffeine and healing go together. I don't want to run my adrenal system into the dirt with exogeneous stimulation. I want all the rest I can get.

The worst of it is the general fatigue. Part of that may be due to sleep disruption. I'm sleeping better, but not as well as when healthy. Mentally, I'm not sharp. At work, I can get by with experience, but work alone isn't enough.

A favorite pastime, analyzing cycling data, has been trending up as during the Tour there has been a lot said about Chris Froome's incredible domination. I have my feelings about that: look to Tenerife, not France, to explain how he's ridng. His watts aren't particular exciting, it's that he's so incresibly skinny. That's why he flies up hills, that's why he gets his wind resistance so low. How is he able to train hard and yet be so lean? Sky embracing nutrition science in a way which hasn't been done before at that level? Or supplements? Strangely, I find myself not caring much, not because I don't think the doping fight is important to cycling, but because professional cycling itself doesn't seem important.

Same deal with my fitness. A month off the bike just when my climbing was going really well. Basically my season is shot. Where to go next? Running? Cycling? A bit of both, perhaps, to start? Maybe that's the best approach right now. Mix it up. That's good for overall body fitness. I need to rebuild the foundation before I do anything else. Frustrating. Set my sites on next year, when I'll be another year slower. At least I got Devil Mountain Double in. This year wasn't a total loss.

Anyway, I'm off to the gym for the first time since the crash. Take it easy, focus on range of motion, light resistance. I'll see how it goes. I want to prepare for physical therapy, assuming the doctor gives me a referral for that.

Monday, July 1, 2013

minimalist pedals: weight vs price

There's now three minimalist pedal systems on the market, as I pointed out in a previous post:

  1. Aerolite: the original, from 1979, very early days for clipless pedals. Cleats are set up for 4-hole mounting, like Speedplay but with a different spacing, although they can also be mounted in 2-hole (mountain bike) shoes or 3-hole (using 2 of the 3 holes).
  2. Ultralite Sports: I became introduced to these at Interbike last year: very slick. They have a novel clip-in, clip-out mechanism.
  3. TriRig Mercury: still in limited release, closer to the Aerolite than the Ultralite Sports, but with 3-hole cleats rather than 4-holes.

Aerolite makes 3 models of pedal. The lightest is "time trial" version with holes drilled in the Turcite sleeve which surrounds the axle, and also the spindles have minimal length to keep the feed close to the bike, which was considered more aerodynamic back then. Then they have a "criterium" pedal, also with short spindles, in this case not for aerodynamics but to improve cornering clearance. Then finally they have a "road" version with a longer spindle. All are made of hollow titanium: I think there was at one point a steel version but that's no longer available. These pedals have had a truly amazing run.

The clip-in is amazingly simple: the nylon cleat contains a semicircular hole whose surface extends a bit more than 180 degrees. So the rider simply puts his foot in the correct position then applies pressure. That causes the nylon to sufficiently spread that it snaps over the pedal sleeve.

There's a discussion here on the WeightWeenies forum. Like most things which trade functionality for lightness, people seem attracted to them but then subsequently move on.

Ultralite Sports is a bit different, with a different clip-in mechanism. They have two versions: a more expensive Ti version and a heavier steel version. There's a good review on BikeRadar here. What I love about the review is they point out a critical deficiency: the pedals can't be used with street shoes. That's a big deal for me. Even for race-only pedals, sometimes you want to hop on your bike and go somewhere without changing into cycling shoes. At least with Aerolites and TriRig Mercuries you should be able to pedal in walking shoes. Caley Fretz at VeloNews also did a review of these pedals. There's some nice photos at that review.

One advantage of the Ultralites versus the other shoes is you can get cleats with a small amount (5 degrees) of float. While with proper cleat set-up float shouldn't be necessary, a little float just to shift the load to different muscles temporarily is something I find attractive. A possible specific disadvantage may be clip in and clip out, which is somewhat unique. The inventors claim it just takes a bit of practice. At least the pedal is always in the correct orientation, unlike a one-sided pedal.

TriRig Mercuries were next, and appeared to come rather close to copying the Aerolites. One added benefit they provide is pedal stance ("Q-factor") adjustment, by disassembling then reassembling the pedal in a different configuration. But I don't see this as a big advantage, since Aerolite comes in two different spindle lengths. But adjustability is always good.

I noted in that post that TriRig Mercury had switched from a hollow to a solid Ti spindle to increase strength, but in doing so they added 18 grams to the mass of a pair of pedals. I was interested in how this positioned them relative to the competition. Here's that plot:

If these pedals are your thing, if the TriRig Mercury would go back to the hollow spindle, losing 18 grams, it would be very competitive with the Aerolites and the Ti Ultralite Sports, and at a lower price. Even if the hollow spindle was more expensive, for example as an option, they have some breathing room below the price standard set by the competition.

But an issue with each of these pedals is walking in the shoes. For bike tours, etc, where there's going to be a lot of walking, of course mountain biking pedals are the best option. But some walking happens on every ride I do, and living in crowded San Francisco, I often encounter traffic lights, and at traffic lights I often need to support myself with my foot. Even for race day only pedals, there's going to be a bit of walking. If this is better with one system then another, that's worth something.

So while I find the light weight and mechanical elegance of these pedal systems attractive, I think I'll stick with my tried-and-true Speedplays. Those pedals do everything fairly well as long as they aren't worn out and become sloppy, which they're prone to do.