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The simple geometry behind any road

57 pointsby azhenleylast Thursday at 3:09 AM8 commentsview on HN

Comments

jstanleytoday at 8:27 AM

You're missing one very important type of curve: a clothoid (or "Euler spiral") is a curve of continuously-varying radius, these are encountered on roads very frequently. And especially on race circuits.

A clothoid is used to connect two lines the same way your fillet is, except instead of just 1 radius it has a radius configured for each end and smoothly changes in between.

https://en.wikipedia.org/wiki/Euler_spiral

They are also used in railways, because on a railway you don't have the freedom of moving the car's position across the road, so a transition from a straight track to a constant radius would imply an instantaneous step change in centrifugal force, or infinite jerk. Using a clothoid to smooth the change between the straight track and the constant-radius turn means the lateral acceleration increases smoothly instead of instantaneously.

show 2 replies
kalmartoday at 1:14 PM

The care taken here to achieve aesthetically pleasing results reminds me of this post about creating nice transit maps in the Transit App: https://blog.transitapp.com/how-we-built-the-worlds-pretties...

red_admiraltoday at 8:41 AM

And then you have various types of hairpin bend where you actually vary the width of the lanes with the radius: https://www.google.com/maps/@46.8360535,9.6369913,68m

lencastretoday at 11:02 AM

vehicular speed is very important as a consideration in any road curvature, as well as “pitch and yaw” when changing slope and direction at speed, so… simple it is not, and if we are mostly “offsetting” straight lines and arcs, we are doing it wrong

21asdffdsa12today at 10:18 AM

Expected it to at least mention the slant imposed on any road surface so water does not pool. Disappointed to tears and thus salt-water-aquaplaning in all games build upon this.

dilberxtoday at 8:40 AM

many are yet to catchup