Zoncolan power calculations revised

Basso climbing Zoncolan (CyclingNews)
Last post I proposed an estimate of the power used by Basso and Evans while climbing the mighty Zoncolan stage of the Giro d'Italia.

However, no sooner did I publish my estimates than CyclingNews published claimed numbers from Basso's SRM. That Basso had an SRM was surprising to me: this stage is one of the rare days in pro racing that riders use a 110 mm BCD "compact" crank. In the past, they've not made the investment (or their sponsors haven't made that investment) of a separate power-enabled 110 mm spider. But 110 mm BCD power meters are gaining increased acceptance as people realize that "compact" gears are suitable for racers, too, in addition to the substantial power meter market of performance-oriented cyclists who don't race. So they probably want to promote their compact option, and a epic stage like this one attains substantial visibility.

In any case, the numbers: Basso averaged 395 watts for the final 10.1 km, for a claimed 5.68 W/kg, implying a body mass of 69.5 kg. I'd calculated an average power of 6.08 W/kg. Ouch!

Let's check assumptions. I assumed a drivetrain efficiency of 0.97, which is considered typical for a derailleur system in good working condition. However, drivetrain efficiency is generally better at higher powers, and the pros ride at exceptionally high power, so I'll increase this to 0.98.

Another assumpption: I assumed a coefficient of rolling resistance of 0.5%. Assuming the road was in excellent condition (as is usual for grand tours) and the tubular tires used by the riders are relatively low rolling resistance, this is probably too high. I'm willing to reduce this to 0.3%.

What about bike mass? I assumed equipment + bike was 1/8 the total weight of the rider. Assuming Basso is near the 69.5 kg implied by that article, that's 8.4 kg. Well, silly UCI rules limit the bike mass to no less than 6.8 kg. So that leaves only 1.6 kg for helmet, clothes, contents of pockets, water bottle, etc. So there's no room to reduce this estimate.

Then there's wind resistance. I'd assumed CdA = 0.3 m² / 50 kg body mass. For Basso, this would yield 0.42 m². Evans was standing a lot during the climb, Basso less so. I'll reduce that 10%, to 0.3 m² / 55 kg, yielding 0.38 m² for Basso. Lower than this seems unreasonable. An excellent time trial position is around 0.23 m². When climbing steep hills riders tend to be relatively upright, far from an optimized time trial position, on bikes designed for handling rather than for aerodynamics.

Then there's drafting. Basso didn't pull the whole climb, certainly not at the bottom, and Evans even took a few pulls before he was dropped. I'll assume that Basso drafted half the distance, and while drafting, wind resistance power was reduced 30%. This reduces wind resistance power by 15%.

So I ran these numbers: the result was 5.76 W/kg, of which 0.24 W/kg was from wind resistance, 0.35 W/kg from rolling resistance, 4.52 W/kg from climbing. The disagreement is down to 0.08 W/kg, assuming zero wind, and neglecting the pushes Basso reportedly received from enthusiastic tifosi.

But what about that body mass? To resolve this difference I'd need to assume Basso weighed 68.6 kg, an error of 900 grams from his claimed weight. Dehydration during the stage could easily account for that.

So with these numbers, "theory" and "experiment" seem to agree rather well. Using the same assumptions, Evans averaged 5.56 W/kg for the stage. Barely good enough to win a Low-Key Hillclimb, let alone set a record up Old La Honda. But at the end of a gruelling stage, in the midst of a gruelling stage race, you'd expect some signs of fatigue to be showing.

In any case, it's clear that those who've accused Basso or Evans of doping in the Giro are unfounded. These power numbers don't come even close to some of the numbers we've seen in the past, including from Basso himself. See, for example, the Science of Sport blog post on the subject.