Frenet Equations in 2-d Which Result in the Cornu Spiral - Comment

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Discussion Overview

The discussion revolves around the Frenet equations in two dimensions and their relation to the Cornu spiral, exploring its applications in fields such as road and rail track construction, as well as roller coaster design. Participants reflect on the implications of the theory for real-world scenarios involving speed and acceleration.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant notes the historical use of the Cornu spiral in engineering, mentioning its application in road construction by Leopold Oerley and Hans Lorenz.
  • Another participant shares a personal anecdote about a previous calculation of the Cornu spiral that was included in a mathematics challenge, indicating interest in the mathematical aspects of the topic.
  • There is a mention of the practical implications of the Cornu spiral theory for Earth-bound moving objects, suggesting a connection between theory and application.

Areas of Agreement / Disagreement

Participants express appreciation for the insights shared, but there is no explicit consensus or disagreement noted in the discussion.

Contextual Notes

Some statements rely on historical context and personal experiences, which may not encompass all aspects of the Cornu spiral's applications or theoretical implications.

Who May Find This Useful

Readers interested in the applications of mathematical concepts in engineering, particularly in road and rail design, as well as those exploring the mathematical properties of curves like the Cornu spiral.

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Charles Link submitted a new PF Insights post

Frenet Equations in 2-d Which Result in the Cornu Spiral

cornuspiral.png


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Very nice! The German Wiki page says, that the Cornu spiral is widely used in road and rail track constructions and even for roller coasters.

"The Cornu spiral first has been used by Leopold Oerley in 1937 as geometric element of road construction. Since 1938 the engineer Hans Lorenz used it consequently in the planning for the autobahn Vienna - Brno - Wroclaw. 1954 the Cornu spiral has been made available to engineers in general in a comprehensive book with mathematical tables for track planning (Kasper, Schürba, Lorenz: Die Klotoide als Trassierungselement)."

I had to think about this as I read your considerations on speed and acceleration, which obviously has some very direct applications for Earth bound moving objects. All of a sudden the theory became alive.
 
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@fresh_42 You might find it of interest, I messaged this calculation of the Cornu Spiral to @micromass sometime around September 2016, and he included it as part of his October mathematics challenge (problem #1). @mfb solved it very quickly so I don't know how many others took the time to look it over. :) :)
 

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