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1-092-DashItAll-ModelingSenario

Author(s): Kurt Bryan

Keywords: data running sprint Hill-Keller world record Olympics

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Abstract

Resource Image This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games.

This leads to a separable (in fact, autonomous) ordinary differential equation (ODE) for the velocity of the sprinter as a function of time. This velocity function can be integrated to predict the runner's position at any given time. The model includes one or more unknown parameters that must be estimated from comparison to the data. Students can then gauge the fidelity of the model to the data and validate the model by using it to predict how fast Bolt could run other distances, for which additional data is provided.

The project has two distinct parts---the first motivates the derivation of an ODE as a model for a physical process, as an introduction to the subject; the second part can be tackled after the students have seen separation of variables and/or phase portraits for autonomous ODEs. At this point they can fit parameters and make predictions, which requires the use of a computer algebra system; a Maple worksheet is supplied.

 

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Authors

Author(s): Kurt Bryan

Comments

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  1. 0 Like

    Brian Winkel @ on

    We are posting this on behalf of Michael Rogers,  Emory University, Atlanta GA USA who posted this in our original web community at www.simiode.org .

    Here's a nice Quanta article by Steven Strogatz about a couple of Usain Bolt's races, including the 2008 Olympic race.  It might make a nice follow-up reading, although it applies only first-year calculus.  It does raise questions about choices in modeling.

    https://www.quantamagazine.org/infinite-powers-usain-bolt-and-the-art-of-calculus-20190403/

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