Here is a scatterplot matrix of elapsed times for the overall, swim, bike, and run legs of the 2009 Ironman Championship in Kona.
Obviously, while the correlation is imperfect, it is still relatively strong (r(swim, bike) and r(bike, run) are both around .75, while r(swim, run) ~ .5), so if you're a fast cyclist you tend to be a fast runner and a fast swimmer. Fast people are fast, no surprise. The thing that mostly determines bike time on the Ironman Kona course is power to aerodynamic drag (since the course is pretty flat and usually pretty windy). On the other hand, the thing that mostly determines run time is power to weight. The commonality is power: power while biking is related to power while running. Likewise, power while biking or running must be related to power while swimming. However, this is for a selected group of athletes: those who qualified for the Ironman Championships and finished all three legs in one day. I am more interested in "stand alone" events.
We have bicycle power meters that tell us power output while cycling, and a rule of thumb that tells us that on firm flat ground runners expend around 1 kcal/kg/km. Although there is a fair amount of variation in running economy, that latter rule of thumb combined with an estimated gross efficiency of .239 can give us a new rule of thumb that relates running speed to power: running speed in meters/sec is roughly equivalent to watts/kg.
My question is this: is there an equivalent rule of thumb that would give an estimate of power while swimming? I understand that there is much more room for variation in swimming economy than in running economy -- I'm just looking for a rule of thumb.
Update: McArdle, Katch, and Katch (2005, "Essentials of exercise physiology", 3rd ed.) claim that there is a fair amount of variation in energy expenditure among swimmers, and that it depends on skill level, sex, and type of stroke (breaststroke requires the most energy expenditure while the crawl requires the least). They claim that sex matters because females tend to be more buoyant than males and their mass distribution is different so they tend to swim "flatter" in the water and thus have less hydrodynamic drag. Even with all these caveats, they claim "it takes about four times more energy to swim than to run the same distance. In contrast to running, a swimmer must expend considerable energy to maintain buoyancy and overcome the various drag forces that impede movement."
In addition, Barbosa et al. (2006, "Evaluation of energy expenditure in competitive swimming strokes", Intl J Sports Med 27:894-899) show a couple of regressions that show the relationship between swimming speed and energy expenditure for a group of elite "international level" swimmers. I am looking for the relationship between power and swimming speed (or a similar metric) for not-quite-so-elite swimmers.