Monday, February 21, 2011

My BIG Idea

It was nothing new. Just the same sinking feeling on last weekend's rides up King Ridge and Sweetwater with Wink spinning right by me. I've had the same feeling when all the other ABS (Avian Bone Syndrome)-types spryly dancing on their pedals when we hit the steep pitches on Cantelow. What makes it even worse is when those ABS check out their fancy Powertap-thingymajigs and brag about averaging this much or that much power. Like on the Jesse Moore ride - "better be ready to ride > 215W for 3 hours." Really? Put me on the flats and I could do that all day. In the hills? I'd probably have to be above threshold while the ABS are still pulling 220W. So with a long weekend, I began to think, "Why are we FABs (Fat-Ass Boys) always doomed in the race to the summit?"

I'm sure all the ABS are saying, "Yeah, you have more mass, so you should be able to produce proportionally more power." And looking at their skinny, knobbly legs you would think this would be true.

Looking at the graph above, the ABS would seem to be right. Say we are going out on one of JM's ride and the ABS (75 kg) pulls a constant 220W. On the flats this will get him going 32.8 km/h. To keep up with him, a FAB (95 kg) has to generate 229W. However, relative to mass this is only 2.41 W/kg for the FAB compared to the 2.93 W/kg the ABS is doing. If the ABS keeps his power constant as the grade increases, the FAB has to increase his power to equal the ABS' speed but relative to his weight, the FAB never reaches the ABS relative power even on a 9% grade!

So us FABs must be really weak, eh? Not quite. It's nice to think that power increases linearly with mass but it doesn't. Assuming that increases in mass are proportional in terms of muscle, bone, lungs, fat, etc., the increase in mass is a function of the 3rd power (i.e. cubed, not Watts), but unfortunately power (i.e. Watts) only increases as a function of the 2nd power (i.e. squared). This is because power is dependent mainly upon the surface area of vessels, capillaries, aveoli, etc. So rather than being linear, the relationship looks more like this....

Using a 50 kg "Uber-ABS" rider as the baseline, a 75 kg rider would have 50% greater power if there was a linear relationship between power and mass (red line). However, the increase in power should only be expected to increase by 31% (blue line). For the 100 kg "Uber-FAB" rider, the increase in power is only 59%, rather than the 100% expected.

Back on JM's ride with the ABS holding the 220W, this is what the true power/"relative" mass relationship is as the grade increases.

On the flats, the FAB only has to use a power/relative mass that is 89% of the ABS - big advantage. But this advantage is quickly evened out on a 2% grade and on a 6% grade, the ABS has a 5% advantage on the FAB.

Does all this rationalization make us FABs feel any better? I'll let you know the next time I get dropped on the WW ride.

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