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fitting power-duration model to track & field world records

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Last time I described a running power model used by Péronnet and Thibault to apply a power-duration model to running world records. I pointed out some clear problems with their model. One was a clearly erronious estimate of wind resistance, substantially underestimating the metabolic cost of fighting wind resistance assuming reasonable parameters. Another was a strange presentation of acceleration work which looked suspiciously like two errors which essentially canceled each other. Here I'll follow a similar approach but with different parameters: P / M = K 1 η v + ½ [ C D A ρ / M + 1 / D ] v 3 where P is total power, M is total mass (runner + clothes), K 1 is a coeffient representing the metabolic cost of moving a unit mass a unit distance, η is a metabolic efficiency coefficient, C D is a coefficient of drag, A is the cross-sectional area of the runner in the direction of travel, and D is the distance traveled (amortizing the acceleration energy, where I assume a s...

running power vs speed in Péronnet and Thibault

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Yesterday I was reading Péronnet and Thibault, Mathematical analysis of running performance and world running records, Modeling Methodology Forum 1989 . This article describes a power-duration model applied to running world records. But running world records are recorded in distance and time, not power, so to apply their model they need a power-speed model for running. Their power-duration model has issues, in my view. For one it's not analytic (it contains a slope discontinuity). But for another, as written it contains an integral, trivially enough solved analytically, but presenting needless complexity as written. But this is a digression: the purpose of this pose is their power-speed model. They use the following, which they attribute to Di Prampero, Riv. Cult. Sportiva 3: 3-7, 1984. It's similar to the bicycle power-speed model: nothing exciting here. P v = BMR + 3.86 v+ 0.4 BSA v 3 /BM + 2 v 3 /D The first term, BMR, is basal metabolic rate. So it's immedia...

iPhone Strava app data loss

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Following a 7-day break from running following the Lake Chabois 30 km trail race, which went extremely well for me, it was back out there again today. I did a relatively short run, recorded by the Strava app at 12.8 km, but actually longer. I've had really poor luck since upgrading my phone from the venerable, battery-starved HTC Incredible to state-of-the-art iPhone 5S. The Incredible has extremely solid GPS tracking, so I expected at least as good from the iPhone. But I get these weird data drops with the iPhone. Here's my run today: Running on Howard I lost GPS, apparently semi-permanently, until I looked at my phone and brought up the app and saw the distance jump by 4 km within 2 seconds of bringing the app onto the screen. Here's another, a run from before the race: I lost signal on the way out, only getting recording again when I brought the phone out at the turnaround near Sutro Baths to check my distance. Another one: I lost signal when I was in a food...

comparing rides: power histogram and trend in L-R balance

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I've seen blogs where people just post their power numbers week after week. It gets quite dull. I'm risking making the same mistake here. But I started this blog as sort of a depository for whatever I find interesting, and this was sort of interesting. I took a break from running this week to give my legs a chance to recover from the Lake Chabot 30 km trail run. But I've been seriously craving cycling, especially riding to work in the morning (75 km), and this week gave me an opportunity to get a few SF2G rides in. I have gotten comments from 2 independent sources that 75 km commutes aren't "recovery". But riding at my commute pace, while fatiguing, is much less traumatic than running. And getting some endurance work in should keep my metabolism pointed in the right direction. It's a small gamble, but then I do miss riding, and need to get my little fix before starting another running ramp to the shining goal of the Woodside Ramble 50 km trail ru...

new bike part 8: Winter Allaban photo shoot

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After the bike was done being built (well, almost), Eric took it in for a photo shoot. Here's the gallery for my bike . Eric named the bike Allaban, a Scottish word for "wandering, wanderings, roaming" . It's a spectacular name for a randonneuring bike: surprising it hadn't already been snatched up by some litigious mainstream bike company. Keith Anderson's paint work was followed by SRAM Force shifters and derailleurs, Soma 26 mm compact handlebars, a Cane Creek headset, White Industries hubs, bottom bracket, and variable-bolt-circle crankset and rings, Paul Racer brakes, a Thomson Elite zero-setback seatpost, and a Crane brass bell expertly threaded into the stem by Eric. The Crane, in particular, has excellent sound. For the saddle, I decided to stick with an old Mythos saddle I had from my Fuji Team Al bike: I know it works well for me and didn't want to mess around. For the photos, Eric subbed in a Turbo. It fits. Eric also did something surp...

Garmin Vector: LR balance update after 3 rides

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Recently I've been experimenting with the Garmin Vector pedals, which measure L-R power balance. I've long been curious about L-R balance. How symmetric am I? How does the symmetry vary with different conditions? What I've not done yet is to validate the pedals against my Powertap. One reason for this is I'm out of 357 batteries. I ordered a pack of 20 via Amazon for $3. $3??? That's cheaper than a pair at Walgreens. I'm not sure what I'm going to do with twenty 357 batteries. Anyway, on the Vector, I've had a few issues. One was an anomolous 1-second right-foot-only power spike of 900 watts. I've not looked into whether this was a torque or cadence anomaly. The other was when I was carrying my bike off the train and accidentally slammed the pedal into a metal column. That wasn't a good thing, but it's neither the first or the last time I'll do such a thing. For that ride, the Edge 800 was reporting no left pedal data. Bu...

new bike part 7: color

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I knew early on as a nod to my Irish heritage I wanted the bike to be green. Here again was my early "sketch": There I used Kelly Green, which makes sense given the inspiration: But these are just cartoons, and it's a mistake to judge colors in a cartoon. So when it came time to discuss real color, I told Eric to base it based on this: a Lotus racing car: Charles @ PezCyclingNews has based bike designs on racing cars and motorcycles, for example: I didn't want anything so complex. The Lotus I showed is elegant in its simplicity. The green fades to black. The racing inspiration is there, but it doesn't dominate. Painting took awhile. But it was very, very worth it: Credit goes to Keith Anderson , who did the painting.