Sunday, January 31, 2010

Nordic Wattage Revisited

Two years ago we did a post looking at energy output by Andres Soedegren on the Mordarbacken in Falun. It was a fun one to write, and now that I've got all the formulas on hand it's not too hard to calculate wattage for any given climb.

It's kind of embarrassing that it took me a month between watching the Tour de Ski final climb and realizing that it would be interesting to run the numbers. The final climb is waaay longer than the Mordarbacken, so it's a whole different type of effort. Let's look at the data for the two winners, Lukas Bauer and Justyna Kowalczyk.

As usual, all these numbers are based on assumptions.

The "final climb" is the last 3.4k of the course, starting at the 6.6k checkpoint for men and 5.6k for women.
The "final climb" is 450 vertical meters.
There is no descending during the climb (some of the artificial switchbacks looked pretty flat, if not downhill, to me)
Both athletes are skiing flat out the whole time (clearly not true, as both had time to celebrate as they approached the line)

Our methodology will be the same as last time, so we won't spell it out as much.

Lukas Bauer: I just thrashed you guys so hard, I have time to pick up a flag.

Lukas Bauer (75kg with equipment):
3400m in 16:58 -- 3.34 m/s
450 vertical meters in 16:58 -- 1591 vertical meters per hour
Energy required for ascent: 330750 joules
Average Power for ascent: 325W

Ski normal force: 735N
Ski drag force at 0.025 friction: 18.375N
Power to overcome drag @ 3.34 m/s: 61W

Air drag: 1.5N
Power to overcome drag @ 3.34 m/s: 5W

Total Power Output: 391W (5.4w/kg) for 17 minutes

Justyna Kowalczyk: I just thrashed myself so hard, I might be dead.

Justyna Kowalczyk (62kg with equipment):
3400m in 20:58 -- 2.7 m/s
450 vertical meters in 20:58 -- 1287 vertical meters per hour
Energy required for ascent: 273420 joules
Average Power for ascent: 217W

Ski normal force: 608N
Ski drag force at 0.025 friction: 15.25N
Power to overcome drag @ 2.7 m/s: 41W

Air drag: 1.5N
Power to overcome drag @ 2.7 m/s: 3W

Total Power Output: 261W (4.42w/kg) for 21 minutes


Luke S said...

This means significantly less to us skiers who don't know what the hell all of that means than it does to any bikers out there who are glued to their power readings and shit and try to understand nordic skiing.

Christopher Tassava said...

Oh, c'mon! Isn't this all about learning new things? From what I can glean from a good post at the Science of Sport blog, Bauer's numbers are comparable - when adjusting for a lack of gearing on skis, among other considerations I'd imagine to matter - to some top-tier Tour riders. The post mentions LeMond climbing at 5.7W/kg, and, in later, darker days, Riis at 6.47 W/kg, Ullrich 6.33 W/kg, and Pantani at an insane (and dopeful) 6.63 W/kg in '98. There's a nice chart of estimated power outputs by Armstrong over a bunch of big climbs, too...

Anonymous said...

Good stuff.

I linked back to your previous post on the specifics of the calculations.

I think a better comparison of wattage output (sport vs sport) would be with swimmers rather than bikers, since both swimmers and xc skiers are actively using their arms and legs to propel themselves forward, whereas with biking the power is coming mostly from the legs and lower trunk.

So have you ever done the calculation or are there any similar calculations of wattage output for top flight swimmers?

Colin R said...

Yeah, there are massive discrepancies between cycling and skiing. If nothing else, cycling is a weight-supported sport, so all that energy that a skier spends maintaining his balance during the stride, a cyclist can convert into speed. Cycling wattage should definitely be higher.

You could argue that skiers use more muscle groups and thus should go faster, but total energy output is always going to be governed by oxygen uptake anyway, so I don't think that really makes sense.

Swimmers would be a very good comparison. The fluid dynamics for a swimming person, though, must be insanely complicated! Maybe I try some naive calculations and see what I come up with, but I would guess that measuring swimming power would be too hard.

If only people swam uphill!