Bifurcation and Marginal Gains

What do aircraft wings, the Tacoma Narrows bridge and Coronavirus modeling all have in common? As you may have guessed from the title, it's bifurcation — just about the least intuitive (or predictable) behavior known to humankind. In this episode, we talk about bifurcation and its relation to all of these — as well as how understanding bifurcation can affect real-world racing...and how the same effect that can tear the wings off a plane can also make for the terrifying speed wobble you may have experienced on a fast descent on your bike.

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• Ian Tubbs

Surprised no one has asked about this yet (maybe they have elsewhere or with a phone call), but given your relating it to wobble in moto GP bikes, would you care to relate it to Chloe Dygertâ€™s recent crash in the World Championship TT. At least what I saw that caused it was a momentary loss of, and subsequent regain of traction by her front wheel.

• Tony Geller

Thinking about the change from optimizing equipment for a course to optimizing for the bifurcation point where the critical move goes, I was wondering how you account for the cost of the critical move optimized equipment elsewhere. For example, a race that will end in a sprint (field or small group) but has climbing early. Critical point would say go for the most aero set up possible, but if that entails extra weight, then the rider might come to the sprint more fatigued for having to climb with that extra mass. How would the bifurcation approach address this situation?

• Neil M Winkelmann

My favourite cycling bifurcation is the situation of trying to close a gap in a peloton. Simplifying the situation for the though experiment, there are 2 outcomes, the gap’s closed, or you’re dropped and ride in alone, many minutes down. Success at closing the gap can depend on very small speed differences. If the group is going 45 km/hr, and you (at max power) can manage 46 km/hr in the wind, a 10m gap will close in about 3 seconds. If you can only do 45.5km/hr it takes 6 seconds. If you can only do 45.1 km/hr it takes 30 seconds. If you can only do 45.0 km/hr then it never closes. Obviously, the longer it takes, the greater than physiological cost of your effort as well. There is a massive non-linearity, even if you don’t factor that the power and speed you can sustain drops as the time increases (and in the case of repeated gaps). Accordingly, aero advantages can be disproportionately important when trying to close a gap, compared to solo efforts where the aero gains are more linear. I’d contend that aero tweaks can be MUCH more important in a peloton than in a TT.

• Ron

Hi Josh loved this topic and really interesting info. As R Chung says everything is about bicycles we just need time to see it. My next question is what about the the Super Secret Drip lube, why not use this on other parts that need lube like bearings? WS2 is a good bearing coating and well max makes them immune to dust? Just remove dust seal clean and drip wax? Does that sound reasonable? Could this be the next video marginal gain?

• Robert Chung

My dissertation (decades ago) was about stable and nonstable equilibria in dynamic systems in the neighborhood of bifurcation thresholds. Everything is about bicycles—it’s just that sometimes we don’t know it yet.