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Curvature and Maximum Permissible Speeds

Author(s): Adam Rumpf

Florida Polytechnic University

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Summary:
In this activity students will compute the curvature of a section of commuter rail and use it to determine a safe speed at which a train should can round the corner without tipping or derailing. The shape of the track is specified as a large table…

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In this activity students will compute the curvature of a section of commuter rail and use it to determine a safe speed at which a train should can round the corner without tipping or derailing. The shape of the track is specified as a large table of discrete coordinates rather than as a curve in closed form, which necessitates the use of a computer for numerically approximating the maximum curvature of the track.

Licensed under CC Attribution-ShareAlike 4.0 International according to these terms

Version 1.0 - published on 26 Dec 2022 doi:10.25334/0339-4S35 - cite this

Keywords

  1. data analysis
  2. calculus
  3. numerical approximation
  4. engineering
  5. calculus 3
  6. transportation

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  1. Resource Type
  2. Audience Level
  3. Open Science and Education Practices Ontology
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Description

This activity is meant for use in a typical multivariate calculus course, during the coverage of arc length and curvature. It is meant to demonstrate a practical, real-world application of the graphical concept of curvature to transportation engineering, as well as giving the students some experience in working numerically with a function defined as a data table rather than being able to analytically evaluate derivatives by hand like they would in class.

 

After this project, students should be able to:

  • Explain why the graphical concept of curvature is important in some engineering applications.

  • Numerically approximate basic calculus quantities (like derivatives) for a function consisting of a table of discrete values.

  • Use a programming language or spreadsheet software to organize and process a large data set.

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