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# A watts a pound and other conversions...

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# A watts a pound and other conversions...

01-12-11, 02:11 PM
#1
chuckb
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A watts a pound and other conversions...

So, like many here, I'm data driven, borderline data-obsessed. Here is a new way of looking at some of these numbers.

I'm 179 lbs (81.4 kg) and struggle to reach a 3:1 power/weight ratio, which is about 240 watts. The spreadsheet I use to calculate speed on climbs lets me change weight or change power to see how the time on a climb changes. Playing around with this spreadsheet, I noticed that dropping 1 lb on a 6% climb (which is a typical moderate long climb) gives the same time change as adding 1 watt. This is a bastard mixing of English and metric units, but it's how I think, power is in watts, but my weight is in pounds. I suspect most US cyclists look at it that way.

So, for typical climbs: Add a watt, lose a lb, it's all the same.

If you've gotten your bodyweight down near what you can reasonably achieve and have a reasonably light bike, one takehome message is that lowering weight will have pretty limited returns; you have to increase power and 10 watts improvement is better than all the dieting you can manage plus an expensive new bike.

What's also interesting is the derivative of heart rate with power, which can be directly translated into the derivative of heart rate with the weight you're carrying up the hill, since 1W is equivalent to 1 pound.

For me, a Conconni test has a slope of 2.7 watts/beat, so losing 2.7 lbs will lower my HR on climbs (at constant speed) by 1 BPM. Losing 10 lbs will mean about a 4 BPM lower HR. These are small changes, but since lactate threshold has a very sharp onset, this shows why lower weight is worth it.

I've never seen HR and power data used this way, so thought it might be of interest.
01-12-11, 05:50 PM
#2
grwoolf
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I'm pretty data driven as well and I get some of the points you're making, but your math is pretty simplistic I think. The watts to weight thing would not be linear, but I guess might be close enough assuming neither varies too far from your current levels. I'm actually suprised you wouldn't see more improvement from 10lbs vs. 10 watts on a 6% grade at your weight, so I'd question that spreadsheet (but have no hard data to do so).

Also, I'd argue that raising your FTP has just as much of a limit as reducing your body weight. In theory, you can always get it a little better, but there are trade offs and genetic limitations to consider (for both power and weight). Also, most find power/weight to be related once you get to a point (dropping weight will cause a decrease in power, so you have to find the right balance for the type of power you want). Finally, the extra wattage you might gain isn't always available (unlike weight loss). If you gain 10 watts in your FTP, did that take away from your anaerobic power? Weight loss is always there to take advantage of during a climb regardless of what type of effort you are making.

On the heartrate stuff, I would also question the accuracy of any calculation that said dropping x lbs would cause a drop of y beats per minute on a given climb at a given rate. The fact that threshold has a sharp onset highlights the lack of linear comparison between lbs and HR. On top of that, the relationship between power and HR is highly variable before you even try to translate the weight loss to a power increase.

I guess some attempt at a calculation is better than nothing, but it would be tough to get this one very close without accounting for an individual's power curve and adding a bunch of assumptions (never stopped the economists though).

It's interesting stuff, but
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