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

I looked at how grade variability affected average power when climbing a hill. Honestly I thought the result was going to be larger, but the reality was it was a relatively minor effect. When the hill is very gradual, for example 1%, variations in grade of a certain fraction have little effect on speed. When the hill is very steep variations in grade are more significant, but since they increase power only via wind resistance, and wind resistance is relatively unimportant (assuming still air), again variations in grade have little effect. It's only important in the middle ground where speeds are high enough that wind resistance is relatively important but where grade variations have a relatively large influence on speed. A virtually equivalent logic applies to rolling resistance variation. A variation in rolling resistance about an average value (averaged over distance) will have the same effect as a variation in grade by the same absolute amount. So the effect of variabilit

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

Watching the Astana supremacy in the final kilometers of today's stage at the Giro gave me an idea... The biopassport is based on the assertion that there is a statistical uncertainty in testing values. But the more data you have, the tighter the bounds which can be set under a given threshold of certainty. If you're examining data from 8 riders in a batch, while any one of them may exhibit variations consistent with normal variation, if they exhibit correlated variations then that becomes less consistent with random chance. So does it make sense to apply testing protocols to teams as a whole in addition to individual riders? If the team fails analysis while each individual on a team passes, do you eliminate the whole team from the race? It seems a promising idea. No two-year bans, of course:, that would be unfair to individual riders, but disqualification from a race, at least. The key is you're introducing an additional source of variation in addition to tempora

I had my misgivings about the Ohlone 50k on Sunday, for which I'd registered. I wasn't sure how I was going to get there. I'd tried going down the entry list for other runners who live in San Francisco, checking for them on Strava to see if they lived close, and none did. So I tried to send messages to those I could find on facebook to see if we could coordinate somehow a ride out. But I got only one response, in the negative. He was staying in Pleasanton the night before, relatively close to the "finish" in Del Valle where we were to meet for a shuttle ride to the start of the point-to-point run. Maybe I should try to get a hotel as well, I thought. Then I could ride to the finish on my bike. Or, more fun, I could try camping out in Del Valle. But that involved carrying a tent and sleeping bag and making reservations which probably weren't available still. It all became irrelvant when I checked the event website to see that the run had in fact been

I saw this on a favorite cycling forum, where I "redacted" some of the key details. Spoke to a friend and reliable source, employee of a large pro team. His sentiments about the tweet is that basically everyone agrees with it and openly think that has organized doping going on to some extent and/or still has back channels to Schumi. Also, the common belief is aligned with what Voigt and TSP said in that if the UCI didn't give the license they would have their pants sued off by entities with very deep pockets so they had little choice. A final rumor is that some riders are using new peptides similar to those that were recently banned like GW-501516 , a new type of growth hormone and IGF that aren't tested for yet, and various banned anabolics in suspension form during training camps so that the ultra short half-life times won't show up on test results. If the rider were to take the substance right after a ride the glow time would only be around 6-8hrs for a n

I heard at the Tour of California that the new Cannondale Evo is basically done, and I further read there's a new version of the CAAD10 which will be called the ... drumroll.... CAAD12. So what about the CAAD11? The answer is they're skipping the CAAD11 to make room for that to be used for the lower-level version of the new bike. If it's like the Evo and CAAD10 the two bikes will be very similar except for that the Evo bike is carbon and the CAAD is aluminum. I've ridden very few bikes (I always say I want to test bikes but it's surprisingly hard to make time to do this). The Evo is the 2nd to last bike I've test ridden (the latest was the Parlee ESX, the name supposedly short for "Essex". Yeah. Right). Anyway, Evo was a [i]very[/i] nice bike: the handling was spot-on, it felt good, there seemed to be no penalty for its stiffness, and it went against the fatty tube syndrome which had been in full fashion at the time it came out. Fatty tube is

Here's a finish line photo of the final stage of the 2015 Amgen Tour of California: I love photo finish images because the "x-axis" which is usually position in most photographs, is time instead. There's only one spatial dimension. The camera records a slit image of what is crossing the finish line at a given time. So if you measure the "width" of a bike crossing the line, that's how much time it takes for the bike to cross the line. If I assume all bikes are the same length, then speed is inversely proportional to the amount of time taken to cross the finish. Here's a typical bike geometry chart, in this case for Trek's racing bikes, which have "H1" and "H2" geometry. Note the wheelbases vary from 97.4 to 101.8 mm, a range of 4.5%. In contrast the Specialized Tarmac goes from 970 mm to 1013 mm, a very similar range. Cannondale: 962 mm to 1012 mm. In all, wheelbases seem to vary by around 5% among bikes across t

I couldn't figure out how the hummingbird feeder worked. Why didn't it overflow? Forces need to balance, of course. Neglecting surface tension, there liquid level is higher in the inner reservoir than in the feeding chamber, so there must be a corresponding pressure difference. Suppose the pressure in the inner chamber were zero. Then the column height difference would need to be atmospheric pressure / (density of liquid × gravity). But this is over 9 meters! Obviously the height difference is only approximately 1% of this. So the pressure difference inside versus outside is only approximately 1%. The inside is only slightly below atmosphere. So air is getting in. How? Does it diffuse through the liquid? If this were the dominant mechanism, it wouldn't take long for the pressure inside to go from 99% to 99.3%, for example, which should be plenty to push the column of liquid down in the inside chamber and thus push liquid out through the holes. It would over

Last time I described that the recursive algorithm I proposed for finding climbs in a profile was: identify all non-overlapping rateable climbs in a profile: If there's no rateable climbs of some minimum climb rating, then we're done. identify the highest-rated climb in a profile. identify all rateable climbs preceding this climb (recursive) identify all rateable climbs following this climb (recursive) I implemented this in Perl, which went a lot faster than it had taken to implement my previous, unsuccessful iterative approach. I tested this on randomly generated "profiles". I put "profiles" in quotes because they're not very realistic. I had to define a "minimal" climb, so this I decided was 5 meters gained in 0.1 km. This is a 5% (approximate) grade for only 100 meters. So to be identified as a "climb" the simulated road would need to be steeper and/or gain more altitude. Initially I used the conventional Fiets formula

Recently I became interested in Jobst Brandt's climbing-descending algorithm for the Avocet 50. Jobst died recently, and I think it's safe to say the man was absolutely brilliant. Among his many contributions to cycling is the Avocet 50 altimeter climbing-descending algorithm, which has been the "gold standard" for determining total climbing on routes. For many years it was the most reliable determination of what a cyclist would consider "climbing", filtering out small altitude fluctuations which could easily be due to "measurement noise". But to compare Jobst's algorithm to mine I needed hill profiles. So I wrote a little code to make random hill profiles. But it gave unrealistic results: rounded profiles, where the hills were more like sine waves than jagged peaks. This wasn't too surprising because the algorithm I used was simple: generate random-normal distributed altitude points then convolve the resulting profile with a well-be

The Tour of California men's race is underway and so it's time for me to post my picks. So without any excess discussion, here's my picks: Andrew Talansky, Garmin-Cannondale Phil Gaimon, Optum Joe Dumbrowski, Garmin-Cannondale Darkhorse picks for the top 10 are the Morton brothers on Team Jelly Belly . Talansky is an established stage racer, and his teammate Dumbrowski did a breakthrough race here in 2012 ( story on Dumbrowski here ). Phil Gaimon honed his form with Garmin in the World Tour last year, and is focused on this race. He won the Redlands Classic fairly conclusively and knows what it takes to do well in California. A lot of the pack is here just for training or stage wins. So the battle for GC is fairly limited. So these are my top 3. Really funny with Gaimon: Diamondback had a special cookie-themed bike built for him for the race but they did it in the wrong size. That's perhaps the difference between the pro tour and pro-continental. I'm

I had to do this problem for some C++ code I'm writing for work and so decided to put the result here. I have a scalar function defined over an irregular 2-dimensional mesh of triangular elements and I need to integrate the function over the surface, for example to find the average value. All I have are the coordinates of the elements. triangular mesh example, from University of Vermont Consider an element with points p 0 , p 1 , and p 2 . I can define side vectors r 0 ≡ p 1 - p 0 , and r 1 = p 2 - p 1 . Then I can determine the area of the triangle a = | r 0 × r 1 |. The integral of the function over the area is the multiplication of the average value of the function times the area. I have the area so I need the average value. This is of course ill-defined because I don't know how the function varies between the three points. But I can guess that it varies linearly. A linear function in two dimensions is defined by three degrees of freedom, for example an inte

Yesterday was the Wine Country Century, or more completely, the Wine Country 35 mile, 100 km, 100 mile, and 200 km rides. I was excited to go because Cara had wanted to do the metric century, and even though I thought with a bit of preparation she could do the 100 miler, I was glad she was ready to do events again, after a series of injuries. The official start time window for the 200 km course ended at 7:30 am, and at 7:20 am I saw Jeffrey at the start. "You're starting late!" he said. "No -- it shouldn't take much more than 8 hours to finish," I responded, my feelings slightly hurt. But I immediately realized I had no basis to make this claim. I'd hardly been riding at all. My "training" for the event consisted primarily of an easy ride with Cara the weekend before. and part of the SF2G First Friday Friendly Frolic on Friday, the day before the ride. That FFFF had been encouraging, though, as I managed to tie my PR up Cortland Road in