Over the last few days, we've all seen crazy estimated power numbers being thrown around for Vingegaard's ascent of Domancy during the Stage 16 TT. 7.6 W/kg is a popular number, but I've seen comments here and elsewhere claiming 8 W/kg as well.
The use of a TT bike, disc wheel, skin suit, aerobars, etc. make power estimation here much more difficult than on a long, sustained alpine climb where speeds are lower and aero matters commensurately less.
The trifurcation of the climb also makes power estimation tricky:
Segment 1, 1.45 km at 7.8%, was ridden by Jonas at 25kph. Here, aero drag makes up about 13% of total power demands.
Segment 2, 1.1km at 10.6%, was ridden by Jonas at ~20kph. Here, aero drag makes up about 6% of total power demands.
Segment 3, 3.5km at 5.2%, was ridden by Jonas at 32kph. Here, aero drag makes up about 25% of total power demands.
We can see, then, how small changes in assumptions on CdA, for example, might have large repercussions on our final numbers, especially over the shallower, high-speed Segment 3.
I thought it might be helpful to put pen to paper to show some of the raw calculations and how varying inputs affect W/kg estimates. To that end, I've put together the following presentation walking through my own process for modeling Jonas' estimated power for the Domancy climb.
The Course: climbing Domancy to Combloux
The course as-ridden is largely the same as shown on La Flamme Rouge and other sites; there was a small change in the location of T2 that reduced total elevation gain by ~11 meters, but this effect is small over the 6.05km course.
The components of power
Power demands are made up of three factors: air resistance, rolling resistance, and gravity. The rider must meet these demands to climb at a given speed, and there is some power lost through the drivetrain.
Components of air resistance & key assumptions
Air resistance, as we will see later, is more important on this climb than usual given the shallow back-half of the climb and the TT equipment used by most competitors. To estimate air density, I used local weather data from the time of the Stage 16 TT. FWIW, Neilson Powless' Strava has the temperature for the climb at 91F as well.
Components of rolling resistance & key assumptions
Rolling resistance is relatively straightforward.
Bicyclerollingresistance.com publishes Crr test data for most top tires; I've seen bike reviews for Jonas' S5 that mention his use of Vittoria Corsa Speeds, so I assumed he put the same tires on his P5. PCS provided Jonas' weight and Escape Collective, helpfully, provided an estimate for the weight of his P5 in an article written before the Stage 16 TT.
The course as ridden (T3 to finish: all aerobars, all the time
There is a significant aero difference (especially as speed increases) between climbing on aerobars and climbing on the bullhorns. I reviewed the GCN broadcast to estimate Jonas' position throughout the TT. The biggest question mark is between 5.2km and 4.6km. At some point off-camera, he transitions to bullhorns, but it is not clear when. I modeled Segment 1 with a CdA of 0.20, reflecting his use of aerobars, and Segment 2 with a CdA of 0.30, reflecting his use of bullhorns during the steep sections.
Putting it all together: base case CdA, as ridden
Crucially, after the T3 hairpin, Jonas is never again seen on the bullhorns. As his speed increases to ~32kph, he gets back into the aerobars and stays there. I modeled this whole Segment with a CdA of 0.20.