With terrible consequences.

Patrick Di Justo has a succinct physics explainer over at The New Yorker analyzing how the high-speed train that crashed in Spain earlier this week may have careened off track, killing 78 people.

Turns out the train was riding on a hybrid rail line built both for stretches of high-speed travel as well as for slower trains. The tracks – as much as the trains themselves – present an engineering challenge, one highly attuned to the speed of travel and the physical forces associated with it. From Di Justo:

One of those forces is centrifugal (“to flee from the center”) force, the inertia that makes a body on a curved path want to continue outward in a straight line. It’s what keeps passengers in their seats on a looping roller coaster and throws unsecured kids off carousels. Centrifugal force is a function of the square of the train’s velocity divided by the radius of the curve; the smaller and tighter the curve, or the faster the train, the greater the centrifugal force. As it increases, more and more of the weight of the train is transferred to the wheels on the outermost edge of the track, something even the best-built trains have trouble coping with. That’s where the concepts of minimum curve radius and super-elevation, or banking, come in.

Banked curves, in which the outer edge of the track is higher than the inner edge, balance the load on the train’s suspension. Since gravity pulls a train downward and centrifugal force pulls it outward, a track banked at just the right angle can spread the forces more evenly between a train’s inner and outer wheels, and help to keep it on the track.

The culprit in the Spanish crash appears to be not the tracks themselves, but the speed the train was traveling. The train was reportedly going 120 miles per hour when it was rounding a curve meant to be taken at half that speed. Most of history's sharp curve-related terrible train accidents, Di Justo writes, have stemmed from the same problem of man-made calculation (or hubris?), not bad infrastructure.

In related news, the driver of the train, Francisco José Garzón Amo, has now been arrested by Spanish authorities. According to The New York Times, the guy had a galling reckless streak:

The train driver did little to hide his taste for speed. He posted a photograph of a locomotive speedometer needle stuck at 200 kilometers miles per hour, or about 125 miles m.p.h., on Facebook last year, boasting that the reading “has not been tampered with” and openly relishing the idea of racing past the authorities.

“Imagine what a rush it would be traveling alongside the Civil Guard, and passing them so that their speed traps go off,” he wrote, in all capitals. “Hehe, that would be quite a fine for Renfe, hehe,” referring to his employer, the Spanish rail company.

The black box just recovered from the train revealed the driver yelling: "I fucked up. I want to die."

Top image of a firefighter carrying a wounded victim from the wreckage of a train crash near Santiago de Compostela: Xoan A. Soler/Monica Ferreiros/La Voz de Galicia/Reuters

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