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Power vs. efficiency

posted May 30, 2012, 10:05 AM by Pat Windschitl   [ updated May 30, 2012, 10:05 AM ]
Power vs. efficiency: by Emmet Hines and Ken Forster

Recently there has been an exchange carried on within the pages of  that has intrigued us. Coach Terry Laughlin wrote an article for Swim Magazine's 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. 

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. 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 to increase 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!

Recap
  • An increase in speed of 10% through applied power only (i.e decreasing time for 100 yd free from 1:20 to 1:12) a swimmer must increase the amount of power applied by 33%!
  • There are two other techniques to increase speed. 
    • 1st: Decrease "drag factor" by streamlining
    • 2nd: Increase "mechanical efficiency" of stroke. 
      • An increase in efficiency by 10% means a swimmer can get the same time with only 90% of the original power!
      • If you maintain the same original power, and improve the efficiency of your stroke by 10%, your velocity (or speed) during the race can improve by 11%! 
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