Watts vs. Watts^.67

HammerHead

Ric,

I've been staring at your web page for a while where you have general fitness categories based on W/kg^0.67. I'm used to seeing these types of comparisons based on W/kg. After staring at this for a while, it would appear that the W/kg^0.67 implies that weight (or lack of) has more of an impact that using W/kg. Is this the point? Vary power and you still have a linear relationship. Vary weight and, within most normal weight ranges, you essentially have a linear relationship. Couldn't you get the same categorization out of W/kg as long as you tweak your ranges a little? What's with the 0.67?

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frenchyge

W/kg is a fairly accurate indicator of climbing prowess, where the dominant mode of resistance is weight and gravity. On flat roads, where speed-induced wind is the dominant mode of resistance, he uses (W/kg)^.67 as a relative indicator of how much speed a rider should be able to produce.

(W/kg)^.67 is an approximation to account for the fact that a larger rider has a somewhat larger frontal area, but not linearly so since increases in thickness don't contribute to frontal area.

In other words, if your W/kg is twice what mine is, then you'll probably climb twice as fast. However, on the flats you'll only be about 2^.67, or 1.59 times faster.

robkit

i'm not sure where the metric first originated from but it concurs with the British Cycling fitness index...

http://www.britishcycling.org.uk/ph...itnessIndex.dwt


meaningful for the reasons frenchyge states.

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frenchyge

A guess at an explanation for where the .67 comes from would be the fact that an object's volume (and therefore mass) is a third-order function of its dimensions (ie, radius^3, for a sphere), but its surface area is a second-order function of its dimensions (ie, radius^2, for the same sphere).

Using mass^(2/3) therefore gives a rough approximation of an object's relative surface area as compared to other similarly shaped objects of equal density.

Or maybe they determined it empirically, and it just happened to come out to roughly 2/3....

ric_stern/RST

Yup, i 'pinched' the BC's metric for this, as when at uni i was under the tutelage of Peter Keen.

Whereas power to mass is better for strict hill climbs, power to mass^0.67 is a better predictor for all round performance. IMO (and others) if you're trying to compare performances between riders on road (or trails/tracks/etc) that aren't completely uphill and riders are different masses mass^0.67 is better.

ric

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frenchyge

Sorry... should be W/(kg^.67)

HammerHead

OK. So based onthis I think I might be better suited to climbing. I never really focus on weight loss as a goal, I tend to focus more on recover (eat ). Now I'm rethinking that. And maybe I should stop floundering in crits and cross races and do some hilly road races.....

__________________
I'm only truly happy when I'm anaerobic.

rouleur

Wait, is that notation correct?

^ usually means "to the power of", correct? i.e. x^2, x^3, x^y...

I'm seeing what I think should read:
W / (Kg * .67)
or
W / (Kg x .67)

i.e. Watts divided by 2/3rds of your weight... And I am understanding, from what I'm reading here, that this is more applicable for "rouleurs" than for climbers (who use W/Kg with no subequation to be run) as weight does not neccesarily equate to poor aerodynamics. This makes sense, to me...

Now, does this mean that we can/should use our mass * .67 when comparing ourselves to the Coggan power profiles?