Swim Stroke Efficiency
Apple began providing a measure of swim stroke efficiency - SWOLF - beginning with WatchOS 9. SWOLF - short for swimming golf - combines the number of strokes per 50 meters distance with the time in seconds per 50 meters distance. A value ranging from 90 to 100 is typical for a swimmer capable of a 1:40 cruise pace. Like golf, lower values of SWOLF are better indicating increased efficiency.
SWOLF is the product of time and strokes
The problem with SWOLF is that it does a poor job of estimating efficiency. In engineering and science, efficiency always measures the ratio of output to input. In swimming, the output is the swimmer’s speed through the water. The input is the number of strokes. Or more precisely, the output is the power required to maintain a given swim pace and the input is the amount of power the swimmer adds to the water per stroke. SWOLF multiples these values together, when they should be divided! SWOLF - since it is a product of strokes and time - actually measures a total energy quantity (the units are approximately J・s), and not efficiency.
Thermodynamic efficiency is the output energy divided by the input energy
Swim+ calculates swim efficiency by first estimating a value for the required power output for a given lap time. In fluid mechanics, the power required to move an object through a fluid scales with the cube of velocity. The energy produced during a given time period is the power output multiplied by the time. The input energy is the total number of strokes, which assumes that each swim stroke inputs the same amount of energy into the water. The benefit of the Swim+ swim efficiency score is that it can be used to estimate swim efficiency over any distance. SWOLF is only valid for comparing 50 meter distances.
Swim efficiency is the product of velocity cubed and time divided by strokes
Astute readers will recognize a problem with this approach - the required power output also depends on the drag coefficient of the swimmer and the swimmers frontal area. Both of these values will be impossible to determine using an app. Additionally, we don’t know how much energy is added by each stroke. Without this information, you are calculating an efficiency score, but not a true efficiency ratio of output energy to input energy. But, if you determine a theoretical maximum swim efficiency score, you can present an efficiency value that is a percentage of the maximum possible score.
Fluid power is the product of the water density (ρ), the drag coefficient (Cd), the frontal area of the swimmer (A), and velocity cubed
Swimming world records were studied to estimate a maximum possible swim efficiency score. Sun Yang set the world record for the 1500 meter freestyle at the 2012 Olympics in London with a time of 14:31.02. He averaged 28 strokes per 50 meters, which provided a swim efficiency score of 5.296. Cesar Cielo set the 50 meter freestyle world record at the 2009 Brazilian Open Championships with a time of 20.91 seconds while taking 33 strokes, for a swim efficiency score of 8.695. The speed in a 50 meter sprint requires 260% more power than a long distance, 1500 meter effort, so the efficiency score during this type of effort must be correspondingly greater, even though a swimmer takes more strokes per 50 meter while sprinting. Swim+ uses a time of 20 seconds for a 50 meter sprint, with only 30 strokes, as a theoretical maximum swim efficiency value. For typical recreational swimmers, the swim efficiency values range between 10% and 20% of this maximum possible value.
Swimming power output scales with the cube of velocity which makes small increases in speed challenging
As a swimmer improves their stroke efficiency through improved biomechanics, they will observe both an increase in pace along with an increase in the distance each stroke propels them through the water. The increased distance per stroke will decrease the number of strokes over a given distance.