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78.1 - Fall 2004

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By Qing Wang

Cheers and screams fill the Olympic Aquatic Center as swimmers approach the last fifteen meters. Head, spine, and legs aligned in a streamline position, Ian Thorpe throws his head under the water as he completes his final stroke and breaks yet another world record in the 200 meter free. So what is the secret of this current world record holder in the 200, 400, and 800 meter freestyle events? Those who admire the Thorpedo as a swimmer attribute his speed to technique and form. Those who are less enthusiastic fans are likely to give credit to his full-body shark skin suit instead. To understand the forces that shape a record-breaking swim, one must enter the intriguing yet baffling world of hydrodynamics.

The basic premise of swimming is this: move through water in a way that further propels motion. Simple, right? Four predominant forces act on Thorpe as he carves water: thrust, drag, weight, and buoyancy. The weight of a swimmer is offset by the buoyant force of water, which by Archimedes’ principle is equal to the weight of water displaced. Lift, which we normally associate with flight, plays a role in swimming as well.

When we swim, however, we are interested in not so much our vertical movement but our lateral. Therefore, the forces that we pay the most attention to are propulsion and drag. Both are forms of resistance and the very reason that water is such a difficult medium to move through. Nonetheless, resistance is also the force that drives our propulsion through water. In a pull, a swimmer pushes against a wall of water, inducing water to give a counter-push, or thrust, that propels the swimmer forward. Similarly, a swimmer can stay afloat by pushing downwards or, in other words, propel himself upwards. Newton’s third law: for every force, there is an equal and opposite force. This principle we know by intuition.

Just as thrust is a force that generates a swimmer’s velocity, drag acts as a countering force slowing the swimmer down. Drag can be broken down into three important components: skin friction drag, form drag, and wave drag. Skin friction drag, or viscous drag, is produced by the boundary layer —the layer of water closest to the swimmer’s skin. The amount of this frictional force is determined by the viscosity of the fluid.

CFD image of a swimmer

Form drag, also known as pressure drag, is caused by the momentum difference between the front and rear of a swimmer. When water flows over an object, such as a swimmer’s body, it diverges at the front and then converges again at the rear. If the swimmer is not streamlined, the flow cannot converge at the rear, thus creating a region with no water flow, just behind the object. This leads to a momentum deficit at the rear of the object that causes drag. The principle behind “streamlining bodies is to minimize this momentum deficit.

Streamline and Non-Streamline Shapes (Credit: Linnea Duvall)

Lastly, wave drag is the resistance created by turbulent waves that a swimmer himself makes. Both form and wave drag can be significantly reduced by correct swimming technique.

While the hydrodynamic forces acting on a swimmer or any moving object can be described conceptually, mathematical analysis is far more complex. The mathematical study of fluid dynamics originated during the 1800s. Many physicists such as Lord Kelvin and Heisenberg, now better remembered for their other contributions, had at some point worked on fluid dynamics. To describe the motion of fluids, French engineer Claude Navier wrote in 1821 a set of equations based on Leonhard Euler’s earlier work during the 1700s. Later revised and mathematically derived by English mathematician George Stokes in 1846, the Navier-Stokes equations remain the foundation of fluid mechanics.

However, as Percey F. Smith Professor of Mathematics Steven Orszag points out, these nonlinear partial differential equations are still too complex to solve even in today’s digital age. “Navier wrote them down by intuition, and Stokes later explained why they are mathematically valid. We think these equations are correct even today, but we still can’t solve them.”

With the advent of digital computers during World War II, scientists began to harness digital power to study fluid mechanics. During the early post-war era, most computational fluid dynamics (CFD) focused on weather analysis. In the late 1960s, this new capacity was also expanded to include aircraft design, material science, and combustion. Today, about half of all technical computing is used for solving fluid mechanical problems.

Having been presented with the new technology, scientists first attempted to directly apply computers to solve the Navier-Stokes equations. Usually, computers “solve” the problem by separating the fluid domain into a grid of small cells, after which it starts with an initial “guess” and uses iterative methods to find successive and increasingly accurate approximations to the equations of motion. Similarly, Orszag applied CFD to his work on turbulent flow. This type of analysis, though much more powerful than human computation, requires a grid with such a large number of single-byte cells that even the largest supercomputer cannot support it.

How can we overcome this problem? Do we just build more and more powerful computers? In an ingenious approach, scientists have now turned this problem around. Instead of using the Navier-Stokes equations as a given set of rules that the computer must use to calculate and model a flow field, one can derive the equations instead. “It is just like a computer game,” Orszag explains. “You set the rules of the game as the more basic laws of physics that the rules of fluid dynamics are based on and let the game run.”

From trial and error to CFD: Previously, designers may have spent months aerodynamically testing a new design in water tunnels or wind tunnels. Now the entire testing process can be completed within a few hours using CFD. (Credit: Steven Orszag and Hudong)

Take the design process of a new car model as an example — a process that is mostly based on trial and error. When a new design is suggested, it must be aerodynamically tested in a wind tunnel, taking up months of valuable time and accruing enormous costs. In the new CFD approach, a design is instead put into the computer “game” and analyzed for any violations of the rules set by the game. If it does, then the design “loses” and is consequently scrapped so that the next design can be tested. This approach shortens analysis time from months to hours — a huge advantage over competitors!

So how can CFD, such an integral part of weather forecasting and aerodynamic design, be applied to swimming? As Orszag suggests, these calculations can be used not only to test the apparatus used in swimming but also to modify and optimize stroke technique. Proper technique is the most crucial factor that distinguishes a novice swimmer from an Olympic-level swimmer. A good swimmer keeps his body streamline, minimizing form drag.

Interestingly, a common characteristic that experienced swimmers share is a symmetrical stroke. This can be observed in the symmetry in the vortex patterns they create in the water, which contrasts greatly to random and unorganized patterns of less experienced swimmers. As the well-known swimming coach Terry Laughlin puts it, “Any swimmer not tightly molded into a torpedo shape [loses] speed so dramatically that he or she [looks] exactly as if they’d run into wall.” Improper technique is what makes swimming such a hard workout for inexperienced swimmers.

Although a much smaller contributor to fast swimming, pool design can still make a significant impact since world records are often broken by mere milliseconds. A “fast” pool is designed to minimize wave formation and interaction. For example, the rows of spindles that make up a floating lane are used to diffuse waves and prevent them from expanding into adjacent lanes. Depth is also important in the design of a pool. Most fast pools are between one and two meters deep, the optimal depth that prevents waves from reflecting back onto the surface from the floor.

Currently, the world’s fastest swimming pool is in Sydney and was used during the 2000 Summer Olympics. It sports ten double-roped lanes of which only the middle eight are used. In addition to the two unused outer lanes, the pool’s gutter system is extra-wide and flush with the pool deck in order to minimize wave reflection and absorb turbulence.

Among the various attempts at improving swimming times, perhaps the most commercialized is swimsuit design. Speedo’s release of the Fastskin full-body swimsuit stirred up a wave of controversy about the extent to which technology should be allowed in competitive swimming. The evolution of the swimsuit had always followed the trend of less is better, exposing as much human skin as possible. After it became impossible to reduce coverage while staying within the confines of modesty, companies turned instead to replacing the human skin with a high-tech fabric that is “better.”

Swimsuit fabric has progressed from wool to cotton, silk, Nylon, and, finally, Lycra. In the latest development, the new Fastskin and rival products imitate sharkskin. Speedo claims that the fabric’s V-shaped grooves channel and control the flow of water, hydrodynamically reducing drag while at the same time gripping the water in the same way that the swimmer’s own skin would.

The benefits of this technology, however, are still unclear. In the swimming world, milliseconds can make a difference between gold and silver, so many are inclined to take faith in Speedo’s claims. Yet, no studies have truly confirmed that the swimsuit can actually improve times. Even if any difference is noted, it may not necessarily be caused by a difference in the fabric design. Fastskins are custom-made to fit the swimmer, and this in itself can have an impact on form drag and, consequently, swimming speed. In fact, some swimmers even dislike the swimsuit, because it confines movement and interferes with natural sensory perception of human skin. One needs to “feel the water.”

Fastskin may channel water, thus regulating its flow. But what about a fabric that can itself change in response to water flow? The idea of flexible skins, or compliant walls, is relatively new in the study of fluid dynamics and stems from the study of dolphin propulsion. As Orszag, who has done considerable work on this topic, explains, there are two types of compliant walls. Passive walls react to outside forces — they are merely pushed around. Active walls, on the other hand, actually change in response to these forces so that the walls can move in a certain way that optimizes propulsion. In dolphin skin, which some scientists believe is an active wall, the nervous system can regulate blood flow that in turn changes the shape of the skin. Can the concept of compliant walls be applied to swimming? Perhaps in the future.

Technology, of course, can only help swimmers so much. Birds fly and humans walk. Just as birds are built for flying, we are built for walking. For us to swim efficiently, learning correct technique can have a much greater influence than even the most advanced technology. Nonetheless, technology, such as CFD, can help us maximize our efficiency when we choose to use our secondary means of motion.

Why is the Thorpedo so fast? Well, he is just a really good swimmer.

QING WANG is a junior in Jonathan Edwards College and majors in molecular biophysics and biochemistry. She is delighted to learn that her longtime hobby of swimming is as scientific as her other activities.

The author thanks Professor Orszag for sharing expertise and beautiful graphics.

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