Swimming performance and mathematics
Swimming performance can be enhanced and analyzed through mathematical modeling and statistical techniques. Fluid dynamics, a branch of mechanics, plays a crucial role in understanding the interactions between swimmers and the water, especially concerning the complexities of human movement. Researchers have tackled challenges such as modeling how swimmers, who are partially submerged, interact with the surface of the water using advanced methods like smoothed particle hydrodynamics. Statistical analyses have also been conducted to forecast world record swim times and assess the impact of aging on swimmers’ performance, indicating a noticeable decline in speed as age increases. Additionally, the fairness of triathlon formats has been scrutinized, revealing significant discrepancies in the event lengths relative to the typical performance times of swimmers compared to runners and cyclists. As the sport evolves, advancements in swimming technology and mental health strategies have become integral, shaping the dynamics of competition. Trends are closely monitored leading up to events like the Olympics, as younger athletes continue to emerge while seasoned competitors maintain their edge.
Swimming performance and mathematics
SUMMARY: Swimming performance can be modeled and improved mathematically.
Mathematical modeling and statistical analysis have been applied to swimming in a variety of ways. Modeling the properties of fluids in motion is the subject of fluid dynamics, a sub-branch of mechanics. Placing objects in the fluid complicates the physics enormously. The interaction of the fluid and object at the point where the object meets the fluid (called the “boundary”) is of particular interest. Problems studied in this way include why flags “flap” in a breeze and how fish swim. Statistical analysis has been applied to a number of questions about swimming performance, including the prediction of future world record times, the modeling of deterioration in swimming performance as a function of age, and the evaluation of whether triathlons are fair to swimmers.
Improving Human Performance in Swimming
Modeling human swimming presented serious challenges for researchers. The use of arms and legs to propel the swimmer through the water added complexity to the fluid dynamics models. Because the human swimmer was not completely immersed in the water but kept part of the body above the surface, the interaction between the swimmer and the surface was particularly difficult to model. Researchers applied smoothed particle hydrodynamics to the study of human swimming performance which, unlike traditional fluid dynamics, treated fluid flow as the motion of individual particles. This hydrodynamics method enabled researchers to more accurately model and simulate the interactions of the swimmer at the surface. The goal of this research was to help individual swimmers improve their performance in competition.
Predicting World Record Swim Times
Statistical analysis of human swimming performance encompassed a number of different approaches and methods. An analysis of world records in swimming from 1960 to 2010 showed a nearly steady decrease in times, resulting in between 15 percent to slightly more than 25 percent improvement, depending on the event. The question remained how long times could continue to decrease, how much is because of increased participation in swimmingespecially women’s swimmingand how much is because of advances in technique and conditioning.
Predicting the Swimming Performance of Aging Swimmers
On a different tack, Ray Fair modeled the performance of elite swimmers of different age groups and modeled the performance at various swimming distances by age. For example, he predicted that a 60-year-old will swim a time about 10 percent slower than the swimmer had done at age 35, while a 70-year-old will be 25 percent slower.
Are Triathlons Fair to Swimmers?
Richard De Veaux and H. Wainer investigated the relative disadvantage of swimmers to runners and cyclists in a triathlon. Because the times taken for the three events are so different, they argued that the standard triathlon proportions (including the Iron Man and Olympic triathlons) are grossly unfair to swimmers. The best marathon runners in the world take about two hours, seven minutes to run the 26.2-mile marathon, with variation due to course and weather. An elite cyclist can cover about 60 miles in the same time, and an elite swimmer can travel 7.5 miles. Thus, to be fair in terms of average time taken, a triathlon based on a marathon should also contain a 60-mile bike leg and a 7.5 mile swim. In reality, the Iron Man is a 26.2-mile run, a 112-mile bike leg, and only a 2.4-mile swim, and thus disadvantages swimmers enormously.
Trends and Advancements
Prior to the start of the 2024 Olympics in Paris, researchers forecasted trends that would impact the games. As younger swimmers were making rapid advancements, several of these were projected beforehand to highlight the competition. This did prove accurate with the successes of French swimmer Leon Marchand. Australia's Kaylee McKeown and Ariarne Titmus fueled this trend, as did Canada's eighteen-year-old swimmer Summer McIntosh. Veteran Olympic swimmers, nonetheless, also achieved great success such as Katie Ledecky, the most accomplished female swimmer in Olympic history. In Paris, Ledecky won her ninth Olympic gold medal.
Performance attire enhancements continued and aided in a ten percent drop in swim times between 2000 and 2024. World records also continued to be challenged and overcome at record pace during this time period. An underconsidered aspect that became part of the sport's culture was its emphasis on incorporating mental health strategies to deal with the high-pressure environment of competitive swimming. Data and analytics were now offering important new insights into the effects of the trend in swimming and other sports.
Bibliography
Cohen, R. C. Z., et al. “Simulations of Human Swimming Using Smoothed Particle Hydrodynamics.” IFMBE Proceedings, vol. 31, 2010. doi.org/10.1007/978-3-642-14515-5‗45. Accessed 7 Oct. 2024.
Fair, Ray C. “How Fast Do Old Men Slow Down?” Review of Economics and Statistics, vol. 76, no. 1, 1994.
Goodman, Eric. "Olympic Swimming at Paris 2024: Biggest Stories, Replays, Medal Results, Top Athletes, New Records." NBC Olympics, 10 Aug. 2024, www.nbcolympics.com/news/2024-olympic-swimming-marchand-and-ledecky-re-write-history-books-usa-tops-australia. Accessed 7 Oct. 2024.
Hill, David. "“Riding the Waves of Change: Predictions for the 2024 Olympics in Swimming.” Medium, 25 Dec. 2023, medium.com/@kcswimcoach/riding-the-waves-of-change-predictions-for-the-2024-olympics-in-swimming-ccaec708f391. Accessed 7 Oct. 2024.
“Making Triathlons Fair: The Ultimate Triathlon.” Swim Magazine, vol. 10, no. 6, 1994.
Wainer, H., and R. D. De Veaux. “Resizing Triathlons for Fairness.” Chance, vol. 7, 1994.