# Power Versus Efficiency

#### Which is more important?

Recently there has been an exchange carried on within the pages of Swim Magazine that has intrigued us. Coach Terry Laughlin wrote an article for the July/August issue in which he uses some numerical examples to lend credence to his claims that improvements in stroke efficiency are the best way to effect a swimming speed increase. In the November/December issue reader Mark Anderson of Wilmet Illinois takes him to task for a rather flagrant violation of the laws of physics, using some equations to prove his point. This resulted in some confusion over terminology, general principles of physics that apply, and the appropriate equations to describe the physical situation.

Coach Laughlin states that to produce a 10% increase in speed a swimmer must increase their power by 100% to compensate for the increased resistance. Mr. Anderson then pointed out in his letter that there was an error in this calculation. Mr. Anderson states that the "force equals one half mass times velocity squared (F=1/2 m v^2)." In fact, it is kinetic energy that equals one half mass times the velocity squared, KE=1/2 m v^2.

Forgive us but we must approach the chalkboard and get technical for a moment. Also, we would state here that Coach Laughlin's assertion that improvements in technique are the most effective way to improve a swimmer's speed, is correct.

Now, down to physics. If a body is moving through a medium such as water, then we can write that the resistive force acting on theis body (a swimmer's body perhaps) is equal to Dv^2 where D is an effective average drag factor for this particular body. This is a resistive force that slows the swimmer down. In order to keep moving at a constant speed the swimmer must supply an equal but opposite force to the resistnce, i.e. the swimmer supplies a force Dv^2 in the direction of motion.

The energy output per second is called power. In physics when a body is moving at a constant speed Power = F v (this works as a great approximation if there are small variations in speed). This is the power the swimmer supplies to keep moving with the same speed v. So the power P=Fv, and since F = D v^2, we finally get that P = D v^3. So the power required increases as the cube of the speed.

So if a swimmer increases his speed 10% through increases in applied power only (i.e decreasing his time for 100 yd free from 1:20 to 1:12) he would need toincrease power by 33%.. Here is where we get that figure from: Call the power that the swimmer puts out for the 1:20 swim Pslow, at speed v and and the power for the 1:12 swim Pfast at speed 1.1v (10% faster than the slower swim).

## Pslow = D v^3

## Pfast = D(1.1v)^3 = 1.33 D v^3 = 1.33 Pslow

Fortunately, as Coach Laughlin points out, there are other ways to improve your speed. There are two distinct technique mechanisms for increasing the swimmer's speed. The first is to decrease the "drag factor" via streamlining; the second is to increase the mechanical efficiency of the swimmer's stroke. These two mechanisms are often lumped together for swimming discussion under the general heading of "increasing efficiency." An increase in efficiency of 10% means that the force exerted by the swimmer against the water resistance is increased by 10% for the same effort.

While mathematically these are quite independent, physically they are connected. Typically, as the swimmer improves technique the drag factor is reduced and the mechanical efficiency of the stroke is enhanced.

If, by improving technique, a swimmer improves his efficiency by 10%, the swimmer will then swim at 90% of the original power to achieve the same speed. Or if the power level remains the same then the velocity will increase by 11%! So, by improving a swimmer's technique, increases in speed are attained more readily than with straight increases in power!

*Coach Emmett Hines is the head coach of H2Ouston Swims. He has coached competitive Masters swimming in Houston since 1982 and was selected as United States Masters Swimming's Coach of the Year in 1993. Currently he coaches workouts at the University of Texas Health Science Center, the University of Houston and The Houstonian Club. He can be reached for questions or comments at 713-748-SWIM or through the Internet at emmett@usms.org. Ken Forster holds a PhD in physics and is a researcher at the University of Michigan as well as an accomplished Masters swimmer. Ken's Internet address is forster@howell.ro.med.umich.edu.*