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IntroductionRunners competing in races are looking to optimize their performance. In this paper, a runner's performance in a race, such as a marathon, is formulated as an optimal control problem where the controls are: the nutrition intake throughout the race and the propulsion force of the runner. As nutrition is an integral part of successfully running long distance races, it needs to be included in models of running strategies. MethodsWe formulate a system of ordinary differential equations to represent the velocity, fat energy, glycogen energy, and nutrition for a runner competing in a long-distance race. The energy compartments represent the energy sources available in the runner's body. We allocate the energy source from which the runner draws, based on how fast the runner is moving. The food consumed during the race is a source term for the nutrition differential equation. With our model, we are investigating strategies to manage the nutrition and propulsion force in order to minimize the running time in a fixed distance race. This requires the solution of a nontrivial singular control problem. ResultsAs the goal of an optimal control model is to determine the optimal strategy, comparing our results against real data presents a challenge; however, in comparing our results to the world record for the marathon, our results differed by 0.4%, 31 seconds. Per each additional gel consumed, the runner is able to run 0.5 to 0.7 kilometers further in the same amount of time, resulting in a 7.75% increase in taking five 100 calorie gels vs no nutrition. DiscussionOur results confirm the belief that the most effective way to run a race is to run approximately the same pace the entire race without letting one's energies hit zero, by consuming in-race nutrition. While this model does not take all factors into account, we consider it a building block for future models, considering our novel energy representation, and in-race nutrition.
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SAFE: A Comprehensive Data Visualization System
This paper describes Situational Awareness for Events (SAFE), a comprehensive data visualization system for mass-participation endurance events. Working in partnership with the Bank of America Chicago Marathon and the Chevron Houston Marathon, and their public safety partners, we developed SAFE to enhance logistics, medical preparedness, and response for mass-participation endurance events such as marathons. The system incorporates critical data into a user-friendly dashboard to serve as a centralized source of information during the events. SAFE uses historical and real-time data to provide pre-event and on-site analytics via descriptive, predictive, and prescriptive models. These models help race organizers and relevant stakeholders effectively manage and oversee all participants, monitor the dynamic location of race participants, and manage health and safety resources throughout the event. The system was deployed successfully at the Chicago Marathon (2014–2018), the Shamrock Shuffle (2014–2018), and the Houston Marathon (2016–2018.
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- Award ID(s):
- 1640736
- PAR ID:
- 10143753
- Date Published:
- Journal Name:
- INFORMS journal on applied analytics
- Volume:
- 49
- Issue:
- 4
- ISSN:
- 2644-0865
- Page Range / eLocation ID:
- 249-261
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/inte.2019.0989
