The Physics of Swimming

By Clara Slight

I have swum all my life. Since we learned recently about drag force, I decided to calculate the drag force that is encountered while swimming. I decided to calculate this for two different aspects: for your hand while swimming freestyle and then for your entire body. When you take a stroke while swimming, your hand is moving faster than your entire body. I made some estimates, and used a velocity of 3 m/s, a cross-sectional area of .10 m, a viscosity of water of 8.9*10^-4, and a coefficient of drag of a half sphere or .42 (http://swimright23.webs.com/dragandresistance.htm). The drag force that a hand encounters while swimming freestyle is F_d = 1/2pC_dv²A = ½(8.9*10^-4)(.42)(3²)(.1) = 1.68*10^-4 N. For the entire body, the calculations change. I also made some estimates here, using a velocity of 1 m/s, a cross-sectional area of .4 m, the same viscosity of water, a coefficient of drag of a streamlined half body or .09. The drag force that a body encounters while swimming freestyle is F_d = 1/2pC_dv²A = ½(8.9*10^-4)(.09)(1²)(.4) = 1.60*10^-5. It is interesting to note that when a swimmer is completely submerged, the drag coefficient decreases to .04 and the subsequent drag force is less. The calculated value is F_d = 1/2pC_dv²A = ½(8.9*10^-4)(.04)(1²)(.4) = 7.12*10^-6. It is also interesting to observe that as the velocity increases, so does the drag force, which makes sense.