Tim Chartier, co-author of Numerical Methods: Design, Analysis, and Computer Implementation of Algorithms with Anne Greenbaum, explains how to take home the gold using math.
|A free-surface simulation of the forces experienced when diving, provided by Speedo® in their press release for the Fastskin Racing System®
Math can help win gold in London! From air passing over an athlete’s body, whether that person be running or biking, to water streaming along a swimsuit or the hull of a boat, many events benefit from numerical analysis and its role, in particular, in computer simulation. For example, aerodynamic research can improve a swimmer’s suit and shave off time that would otherwise be taken with added friction. Such numerics can also inform a biker on a more efficient body position.
Such work involves computing numerical solutions of partial differential equations. Two important stages occur in such work. First, one must develop and utilize appropriate mathematical models. If the model is too simple, its solution will not accurately reflect the real-world phenomenon. In such a case, the swimmer could end up with a suit that isn’t minimizing friction with the water. The second stage is solving the numerical solution to the model, which is performed on a computer with finite precision. As such, numerical methods that can efficiently and accurately solve the mathematical model are needed.
From sports science to the laboratory, modeling and numerics often complement each other, giving modern science a power, not possible without such digital resources. As such, learning the strengths and limitations of numerical methods, often coming through mathematical analysis, enables one to appropriately utilize such tools and leverage them to explore today’s difficult and important problems.
So, as you watch the Olympics, keep in mind that the body mechanics and equipment we see were often informed by mathematics. Such tools play an important role in training and the innovations that contribute to the feats we will witness in the coming weeks.