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.
@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. :) :)
We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling We Value Civility
• Positive and compassionate attitudes
• Patience while debating We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving