Editing Jerk (physics) (section)

== In the geometric design of roads and tracks ==
[[File:Easement curve.svg|thumb|A [[track transition curve]] limits jerk. The transition is shown in red between the blue straight line and green arc.]]

Roads and tracks are designed to limit the jerk caused by changes in their curvature. Design standards for [[high-speed rail]] vary from 0.2&nbsp;m/s<sup>3</sup> to 0.6&nbsp;m/s<sup>3</sup>.<ref>{{cite report |date=August 2016 |title=High-Speed Rail Turnout Literature Review |url=https://railroads.dot.gov/sites/fra.dot.gov/files/fra_net/16631/HS%20Rail%20Turnout%20Lit%20Review_final_v2.pdf |publisher=U.S. Department of Transportation – Office of Research, Development, and Technology |page= |docket=DOT/FRA/ORD-16/34 |access-date=9 November 2023 |quote= |archive-date=8 November 2023 |archive-url=https://web.archive.org/web/20231108155231/https://railroads.dot.gov/sites/fra.dot.gov/files/fra_net/16631/HS%20Rail%20Turnout%20Lit%20Review_final_v2.pdf |url-status=live }}</ref> [[Track transition curves]] limit the jerk when transitioning from a straight line to a curve, or vice versa. Recall that in constant-speed motion along an arc, acceleration is zero in the tangential direction and nonzero in the inward normal direction. Transition curves gradually increase the curvature and, consequently, the centripetal acceleration.

An [[Euler spiral]], the theoretically optimum transition curve, linearly increases centripetal acceleration and results in constant jerk (see graphic). In real-world applications, the plane of the track is inclined ([[Cant (road/rail)|cant]]) along the curved sections. The incline causes vertical acceleration, which is a design consideration for wear on the track and embankment. The Wiener Kurve (Viennese Curve) is a patented curve designed to minimize this wear.<ref>https://depatisnet.dpma.de/DepatisNet/depatisnet?window=1&space=menu&content=treffer&action=pdf&docid=AT000000412975B {{Dead link|date=January 2022}}</ref><ref>{{cite web |url=http://www.mplusm.at/ifg/download/Presle-05.pdf |title=Archived copy |access-date=2014-08-17 |url-status=dead |archive-url=https://web.archive.org/web/20160313052948/http://mplusm.at/ifg/download/presle-05.pdf |archive-date=2016-03-13 }}</ref>

[[Rollercoaster]]s<ref name="thetartan2007">{{cite web |url=http://thetartan.org/2007/4/16/scitech/work |title=How Things Work: Roller Coasters - The Tartan Online |publisher=Thetartan.org |date=2007-04-16 |access-date=2013-09-15 |archive-date=2013-05-18 |archive-url=https://web.archive.org/web/20130518051700/http://thetartan.org/2007/4/16/scitech/work |url-status=live }}</ref> are also designed with track transitions to limit jerk. When entering a loop, acceleration values can reach around 4''g'' (40&nbsp;m/s<sup>2</sup>), and riding in this high acceleration environment is only possible with track transitions. S-shaped curves, such as figure eights, also use track transitions for smooth rides.