The simple geometry behind any road

by azhenley on 4/16/2026, 3:09:50 AM

https://sandboxspirit.com/blog/simple-geometry-of-roads/

Comments

by: jstanley

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.<p>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.<p><a href="https://en.wikipedia.org/wiki/Euler_spiral" rel="nofollow">https://en.wikipedia.org/wiki/Euler_spiral</a><p>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.

4/18/2026, 8:27:04 AM

by: red_admiral

And then you have various types of hairpin bend where you actually vary the width of the lanes with the radius: <a href="https://www.google.com/maps/@46.8360535,9.6369913,68m" rel="nofollow">https://www.google.com/maps/@46.8360535,9.6369913,68m</a>

4/18/2026, 8:41:33 AM

by: 21asdffdsa12

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.

4/18/2026, 10:18:22 AM

by: dilberx

many are yet to catchup

4/18/2026, 8:40:00 AM