{"id":294,"date":"2026-09-15T13:20:37","date_gmt":"2026-09-15T13:20:37","guid":{"rendered":"https:\/\/www.p-way.it\/?p=294"},"modified":"2026-09-15T13:23:21","modified_gmt":"2026-09-15T13:23:21","slug":"sopraelevazione-ferroviaria","status":"publish","type":"post","link":"https:\/\/www.p-way.it\/en\/sopraelevazione-ferroviaria\/","title":{"rendered":"Cant: Why the outer rail is higher (and by how much)"},"content":{"rendered":"

There railway superelevation<\/strong> This is the reason why, on curves, the outer rail is higher than the inner one. It's not an aesthetic detail: it's the way the track "leans" the train to counteract centrifugal force, like a cyclist leaning into a curve. The problem is that you can't compensate for everything for all trains: from this compromise arise two quantities that govern the geometry of the track\u2014the equilibrium superelevation<\/em> and the\u2019insufficient superelevation<\/em>.<\/p>\n

\"Sopraelevazione
Indicative image: on a curve the external rail is raised with respect to the internal one by a quantity called cant.<\/figcaption><\/figure>\n

The equilibrium superelevation<\/h2>\n

Imagine a train traveling around a curve at constant speed. It is acted upon by its weight (vertical) and centrifugal force (horizontal, outward). By raising the outer rail by a certain amount, E<\/em>, the track plane tilts and the resultant of the two forces can become perpendicular to the plane: in that condition the passenger does not feel lateral thrusts and the two rails are loaded equally. It is the equilibrium superelevation<\/strong>, and for standard gauge (1435 mm) the following applies:<\/p>\n

E = 11.82 \u00b7 V\u00b2 \/ R \u00a0\u00a0(E in mm, V in km\/h, R in meters)<\/span><\/p><\/blockquote>\n

The constant 11,82<\/strong> It is not arbitrary: it includes the gravitational acceleration (g = 9.81 m\/s\u00b2), the distance between the rail axles (about 1500 mm), and the conversion of units from m\/s to km\/h. The message of the formula is clear: equilibrium depends on the square<\/em> of speed and the inverse of the radius. Tight curves and high speeds require enormous superelevation\u2014often impossible.<\/p>\n

\"Rotaia
Indicative image: the track follows the curve; the superelevation develops gradually along the junction.<\/figcaption><\/figure>\n

Because you can't compensate for everything<\/h2>\n

The superelevation has a practical ceiling: if a slow (or stationary) train is on a very steep curve, the load shifts entirely onto the inside rail and the passengers "fall" towards the centre. For this reason the regulations set a maximum superelevation<\/strong> around the 150\u2013160 mm<\/strong> on ordinary and high-speed lines. But a curve is traveled by different trains at different speeds: a freight train at 90 km\/h and an intercity train at 160 km\/h cannot both be in equilibrium. The actual superelevation is therefore a compromise<\/em>, set to an intermediate speed.<\/p>\n

Whoever goes faster than the equilibrium "feels" a share of uncompensated centrifugal force: it is the\u201cinsufficient superelevation<\/strong> (D<\/em>, cant deficiency). The fundamental relationship holds E_eq = E + D<\/strong>, where E_eq is the equilibrium superelevation, E is the one actually achieved and D is the missing part, which the traveler perceives as transverse acceleration. Those who go slower have a excess cant<\/strong> (D negative): typical of freight trains on mixed lines.<\/p>\n

A deficiency of approximately 153 mm<\/strong> corresponds to an uncompensated transverse acceleration of approximately 1.0 m\/s\u00b2<\/strong>: it is the limit of comfort and safety around which the rules revolve.<\/p><\/blockquote>\n

The limits of the EN 13803 standard<\/h2>\n

There EN 13803<\/strong> \u2014 the European standard for the geometric design of tracks \u2014 establishes the permissible values. The applied superelevation typically remains within 160 mm<\/strong> (with lower values in the presence of switches or particular constraints). The cant deficiency has recommended limits around 130 mm<\/strong>, with exceptional values up to approximately 150\u2013153 mm<\/strong> for ordinary material; tilting trains (pendolinos), which tilt the body, can go much further. The excess cant is normally kept within approximately 110 mm<\/strong> so as not to penalize slow trains.<\/p>\n

A numerical example<\/h3>\n

Radius curve R = 1000 m<\/strong> traveled to V = 160 km\/h<\/strong>. The equilibrium superelevation is E_eq = 11.82 \u00b7 160\u00b2 \/ 1000 = 11.82 \u00b7 25,600 \/ 1000 \u2248 303 mm<\/strong>: unachievable, well beyond the 160 mm ceiling. Realizing the maximum elevation E = 160 mm, the insufficiency is D = 303 \u2212 160 = 143 mm<\/strong>, within the exceptional limit. If the radius were to rise to 2000 m<\/strong>, the equilibrium would drop to approximately 236 mm<\/strong> and the insufficiency alone 76 mm<\/strong>: this is why fast lines require large radii.<\/p>\n

\"Tracciato
Indicative image: radius, superelevation and development of the path are quantities that must be measured precisely.<\/figcaption><\/figure>\n

A fact to be recorded precisely<\/h2>\n

Superelevation, radius, and speed are linked by an equation that allows no approximations: a few millimeters of superelevation outside of tolerance, or an incorrectly measured radius, affect the perceived acceleration and the permitted speed limits. For this reason, the geometry of the curve\u2014superelevation, direction of the connection, development of the clothoid\u2014is among the quantities that track surveys must render with the greatest accuracy.<\/p>\n

 <\/p>\n

\n

Sources:<\/strong>
\nGareth Dennis \u2014 The cans and cants of railway curves<\/a>;
\nRailway Track Blog \u2014 Where the 11.82 comes from<\/a>;
\nEN 13803 \u2014 Cant and cant deficiency\/excess limits (table)<\/a>;
\nCant deficiency \u2014 technical summary note<\/a>.<\/p>","protected":false},"excerpt":{"rendered":"

In curva la rotaia esterna \u00e8 rialzata rispetto all’interna per compensare la forza centrifuga. Ma non si pu\u00f2 compensare tutto: da qui nascono la sopraelevazione di equilibrio e l’insufficienza di sopraelevazione. La formula, i limiti EN 13803 e un esempio numerico.<\/p>","protected":false},"author":1,"featured_media":315,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[96,94,92,93,91,90,95],"class_list":["post-294","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tecnica","tag-accelerazione-trasversale","tag-curve","tag-en-13803","tag-geometria-del-binario","tag-insufficienza-di-sopraelevazione","tag-sopraelevazione","tag-tracciato"],"yoast_head":"\nSopraelevazione ferroviaria: formula e limiti<\/title>\n<meta name=\"description\" content=\"Sopraelevazione ferroviaria: la sopraelevazione , la formula E=11,82\u00b7V\u00b2\/R, l'insufficienza di sopraelevazione e i limiti EN 13803.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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