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

[Charles Link]

Charles Link submitted a new PF Insights post

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

Continue reading the Original PF Insights Post.

 

[fresh_42]

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.

 

[Charles Link]

@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. :) :)

 

[Greg Bernhardt]

Great Insight Charles!