Power to Weight

(My Original Blog Post: http://ping.fm/ucC4f)
Dave Kalama is a pretty subtle guy. I think he doesn't like to give bad news, so maybe he cloaks it a little--sometimes so it sounds like a casual question. Unfortunately I'm a little slow on the uptake, so it takes awhile for me to get what he's talking about. I think he was recently telling me that I can be fat, or I can be fast, but I can't be both.

It started off with him telling me about a study he read on the effects of weight on canoe speed. He followed up by forwarding me an email from a friend on the Livestrong Canoe team:

I found a rowing study where they used a physics ratio of “the percentage loss of speed is one sixth the percentage increase in mass.” From that I compared Molokai Times between Livestrong and Shell and found an interesting correlation. Using a 95kg boat (paddler plus boat) they determined that for every 5kg of additional weight they added 31.68 seconds per hour to their time.

Assuming a race where the only difference between teams was the weight of the combined crew members: Livestrong a 532kg crew (6@195lbs) vs Shell Va'a a 477kg crew (6@175lbs) has a difference of 55kg. Adapting for the difference in weight ratio 55kg/5kg= 11 * 31.68seconds per hour= 348.48seconds per hour or 5.8mins/hour loss in time. So based on crew weight alone Livestrong would be losing 5.8mins/hr raced. Over a 4.66 hour race the heavier crew would have a slower time of: 5.8mins/hr * 4.66hours= 27.028mins

2009 Molokai Hoe result:
Shell vaa 4hr 40min (4.66hr)
Livestrong 5hr 8min (28mins behind)

Heres the link to the physics behind the study. http://ping.fm/v7UCm
Heres the link to the 95kg boat study. http://ping.fm/cE9RM

So I read the studies and thought I had found a flaw in the reasoning of Dave's buddy. The assumption in the example above is that both teams have identical strength. In reality the 195 pounds per crew member team should be stronger, and the formulas should include that in a full calculation. For a heavyweight like me comparing my potential to a lighter person that difference is vital. The study provides formulas for strength calculations. Since the constants used in the calculations are not known, the formulas are useful mainly for calculating relative effects. Anerobic strength (sprinting) is directly proportional to muscle mass, so two people of similar physique should have power equivalent to their weight. Aerobic strength (longer haul) is proportional to membranes passing oxygen. Aerobic power to weight ratio is inversely proportional to the cube root of weight. So a lighter athlete has a a power to weight advantage over longer distances.

Tuck all that back into the drag on hulls from weight calculation and you have a slight advantage for lighter paddlers in sprints, and a substantial advantage for lighter paddlers over longer distances. Most of our paddles are about ten miles. Game, Set, Match. See you later, chubster.

The last kicker is the "similar physique" assumption. Blubber is deadweight. The calculation is simple, multiply the fat percentage times weight for two paddlers. A paddler who weighs 180 pounds with a body fat percentage of 6 percent is carrying 11 pounds of deadweight. A 250 pound paddler with 18 percent body fat is carrying 45 pounds--a difference of 34 pounds. All that fat does is add to the hull drag penalty of 31.6 seconds per hour for every 5kg (11 pounds) of added weight, in this case about 1.5 minutes per hour in flatwater. Watching all the lighter, leaner paddlers disappear adds practical knowledge to the calculations. And here I thought I at least had momentum on my side.

Now add to all this the reality that the heavier SUP paddler needs a longer, wider board, that they have to put a lot more steam into catching bumps to accelerate their mass, and they are less likely to link runs since they slow so quickly, and you have an overwhelming advantage for fit over fat.

So okay, Dave, I get it. Shed the flab or get used to being last to the beach.

All is not lost though. Doing some napkin calculations and guesstimates I can see the great degree of improvement available to me. Each pound of fat I lose decreases both my weight and my fat percentage. At the 220 pound target weight I set for myself, assuming I lose only body fat I would be carrying 17 pounds of fat deadweight. A six pound difference from the 180 pound paddler. Better paddling technique, improvements in reading swells and wind, good equipment and general conditioning can overcome most of the remaining advantage.