Watts Up, Doc?

[ornoth_cycling]

One of the most popular ways of measuring a cyclist's performance on flat terrain is functional threshold power, and Zwift provides riders with three different FTP tests. My FTP is generally around 210-230 watts.

But for those of us who aren’t afraid of hills, the best measure of climbing performance is one's time to climb the Alpe du Zwift, the virtual equivalent of France’s famous Alpe d’Huez. There’s even a highly sought-after “Liftoff” achievement badge for doing the 7.6-mile 3,400-foot climb in under an hour.

While I haven’t been able to break that barrier, I have done 30 ascents, which is enough data for me to draw some inferences. Since my average power on those attempts has varied from 162 to 234 watts, my times have also ranged from from 88 minutes to just under 63 minutes.

Now things start getting really geeky. You have been warned.

You would expect that if I plunked those numbers down on a scatter chart, there’d be a clear relationship between average power and time. And that’s exactly what I found. Then I added a statistical trendline, which matched my data points shockingly well (an r-square of 0.98 for the statisticians in the audience).

Now here’s where it starts getting interesting. Using that line, for any given average power, we can predict — with near-perfect precision — how long the climb would take me. Specifically, my (slightly simplified) equation is:

minutes = (watts - 400) / -2.76

So putting out 200W, I would finish in 73:13. At 220W, I would finish about seven minutes faster, at 65:58. And in fact we see clusters of past results right around those points.

Whether you use the equation or eyeball the trendline, that calculation also works in reverse, starting with a finish time and seeing what power you’d need to hold. So in order to earn the Liftoff badge by doing the ascent within 60 minutes, I would need to maintain an average power of 236.5 watts for an hour.

This does ignore the second variable that determines one’s ascending speed: weight. Conveniently, my weight doesn’t fluctuate much at all, so I can safely ignore it. But someone else with a different weight would have a somewhat different equation.

That’s why climbers focus on power over weight rather than raw power. Their preferred metric is watts per kilogram, or W/kg. If I re-did this chart using W/kg, it should be an even closer fit.

Among riders chasing the Liftoff badge there’s a common shared belief that you have to maintain 3.1 W/kg in order to climb the Alpe in less than an hour. Now we can put that idea to the mathematical test.

My equation says I would need to put out 236.5W. In order for that to equate to 3.1 W/kg, I would have to weigh 76.3kg. Lo and behold, that’s smack in the middle of my normal weight range, and within two pounds of my current weight. So that validates both my trendline equation as well as the common rumor.

To repeat: to climb the Alpe in an hour at my current weight, I’d have to produce 236W. However, my maximum sustainable power has stayed firmly in the 210-230W range. Alternately, rather than increasing my power output I could lose weight and still hit 3.1 W/kg. At 230W, I would have to get down to 164 pounds, which is pretty extreme for me.

After 30 attempts — and approaching 60 years of age — I won’t be disappointed if I never earn that Liftoff badge. But I enjoy analyzing my performances over time and finding the patterns of consistency that underlie them.

Comments

Badge Hunting - Lift Off Special

[(Anonymous)]

Hey there - I found your post looking for the Lift-Off badge image because the DIRT (Dads Inside Riding Trainers) Badge Hunt team are shooting for this badge as a team effort on Saturday to kick off Badge Hunting season with a bang. We've just launched the event but we hope that there'll be a good bunch around the yellow beacon to keep us all going and get the badge.

Here's the event link, hope you can join.

https://www.zwift.com/events/view/2329455