This underwater image shows Brazil’s Cesar Cielo Filho competing for the men’s 50m freestyle semi-final on July 31, 2009 at the FINA World Swimming Championships in Rome. Photo: Francois Xavier Marit/AFP/Getty Images
It’s hard to be a champion, and harder still to set a record. Let me look at one event in particular, the 50 meter freestyle.
In this event, swimmers make one length of the pool. They simply dive in and swim. There are no turns. Well, unless they’re swimming a 50-meter short course, which uses a 25-meter pool. The cool thing about this difference is the men’s record for the long course is 20.91 seconds and the record for the short course is 20.30 seconds. Clearly swimmers get a pretty good boost pushing off the wall in a flip-turn.
Using the world record time on men’s long course, set by Cesar Cielo of Brazil in 2009, I can get an average speed for the race:
Perhaps you prefer different units. If so, this is about 5.3 mph. Of course, this includes the higher starting speed that comes with diving off the block. So it wouldn’t be unreasonable to say an Olympic freestyle 50-meter swimmer could have a speed of 2.2 m/s in the water.
But everyone wants to go faster. What does that take? Let’s look at the forces on a swimmer.
Illustration: Simon Lutrin/Wired
In this model, the swimmer is moving at constant speed. This means the net force must be zero (technically, the zero vector). The forces in the vertical direction aren’t important in this discussion, but let me say that the “up” force is a combination of buoyancy force and “lift” due to the motion of the swimmer.
For the other forces, the drag force is due to the collision of the swimmer with the water. This is why a swimmer does not continue accelerating throughout the race. It has some dependence on speed, but for now let’s say it is in the opposite direction of the swimmer’s motion. Thrust force is a result of the swimmer using his arms and legs to to propel him through the water.
The important thing is thrust is a result of the swimmers’ exertion, or using energy to move through the water. This is all about power. One way to think about power is to consider how much work is done in how much time. In this case, the work is the force exerted (the thrust) multiplied by the distance traveled. Yes, work is a little more complicated than that, but this definition will do fine here. (I was going to say this definition will work – get it?)
Putting this definition of power and work together, I can write:
Here the distance is just some distance and the time is just the time needed to cover it. Oh, hey — isn’t that just like the average speed? Yes. This makes the power needed to swim independent of the distance.
Also, since the swimmer is moving at a constant speed, the magnitude of the thrust force must be the same magnitude as the drag force. The drag force must, in some way, depend on the velocity of the swimmer. But how would you model this speed-dependent drag force? The best way would be to create some experimental method of measuring this force. For this post, let me assume the drag force is linearly proportional to speed. This means I can write the thrust required to move at a constant speed as:
Where b is just a constant that depends upon the size and shape of the swimmer (and the type of swimwear being worn). This means power from the swimmer is proportional to the square of the velocity.
So how about some values? First, what kind of power can a human produce in short bursts? This is a difficult question since it depends on how the person is moving. Also, power isn’t such an easy thing to measure. The paper Laboratory Measurement of Human Power Output During Maximum Intensity Exercise suggests a maximum power of around 1,200 watts for short periods. If I use this and Cielo’s world-record speed, I get a value for this drag coefficient (b).
Now suppose you want to break Cielo’s record and swim with an average speed of 2.21 m/s instead of 2.2 m/s. How much power would you need?
Increasing the speed from 2.2 m/s to 2.21 m/s is a 0.5 percent increase in speed. This requires increasing power by 0.8 percent. That may seem small from the comfort of your couch, but in the water, when you’re pushing the limits of human performance, it is big.
