The Tour today ended with a relatively steep, short climb on a stage on which riders had relatively fresh legs: a perfect opportunity for some truly impressive rates of climbing to be demonstrated. And sure enough, they didn't disappoint.
Various numbers have been tossed about for the stats on Verbier. Originally I used elevation data from MapMyRide's map of the stage: 630 meters climbed over 7.576 kilometers starting from the sharp left from Route de Verbier at km 199.1 in the stage, an average gradient of 8.32%. However, since then official data were posted in comments to The Science of Sport: 638 meters gained over 8.8 km, an average grade of 7.25%. They also reported reports that Contador did the climb in 20:36, a solid Old La Honda time for sure, but on a climb of this length an number as amazing as we've come to expect in the Tour.
Climbing rate is normally reported in a vertical rate of ascent, or "VAM", typically in meters/hour. The steeper the road the higher the number, assuming adequate gearing and traction: obviously on a dead flat road VAM will be zero, no matter how much power you produce. Using climbing times from The Science of Sport:
So who cares about the silly Tour, right? Old La Honda is the climb which really counts.
Lucas Pereira calculated Old La Honda gains 393 meters @ 7.3%. This is essentially equivalent to the grade of Verbier, sparing me the need to adjust for wind and rolling resistance. But Old La Honda is also shorter. Assuming Contador has an anaerobic work capacity to critical power ratio of 60 seconds, as a first iteration assuming climbing time is proportional to altitude gained, one can adjust for the distance using te critical power model: power ∝ 1 + AWC/CP / duration. This yields 2.9% higher power for Old La Honda Contador is dissipating around 69 watts in wind resistance (around 15% total), so added power doesn't all go into speed and therefore into VAM. Too lazy to do a formal calculation, I'll claim this is around 2.6% improvement in VAM, taking him to 1906 meters/hour up a well-paved Old La Honda (dream on!).
So then for a well-paved Old La Honda, Contador would have climbed it in.... drumroll... 12:22.5. Lance would have crawled up to the stop sign in a crippling 13:19.3, nevertheless winning the 35+ 1-2-3. The similar VAM numbers validate the assumption of time proportional to altitude gained. Comments on facebook suggest Eric Wohlberg has the record with 13:50, beating Greg Drake's best time, where Greg had cracked Eric Heiden's previous best of 14:15.
But what about that pavement? Old La Honda's in much better shape these days than it was in it's low-point in the early part of the millenium. A CRR = 0.6% might be about right. Let's say Verbier is around 0.2% lower. Then this yields a relative difference in mass-proportional power of 2.7%. Adjusting for wind resistance this would take Contador's time up to 12:35, with Lance at 13:32.
In any case, whatever fun we have with numbers, one thing is clear. These guys can ride.