After reports that the Metro-North commuter train that derailed just outside of New York City was traveling at 82 mph along a 30 mph curve, there has been growing speculation about when the train's brakes were applied. Basic physics may help explain how the train’s seven cars flew off the track, with two flipping on their side near the Hudson River.
Four people died and 67 were injured in the crash, which happened early Sunday morning on a train bound for New York City’s Grand Central Station. The National Transportation Safety Board released its preliminary findings on the accident, which was largely recovered from the train’s data recorder.
Preliminary info from event recorders shows train was traveling at approx 82 mph as it entered the 30 mph curve.
— NTSB (@NTSB) December 2, 2013
Even before the NTSB’s statement, speculation about the cause of the crash centered on the train’s speed. Most images showed the seven cars and one rear engine mostly off the sharply curved track that runs beside the river. Approximately where the track curves most is where the Metro-North train appears to leave the tracks. What amount of speed and force did it take to do that?
With the NTSB’s numbers, Mashable asked physicist and author of How to Teach Physics to Your Dog Chad Orzel about the physics behind the disaster.
First of all, any time you have an object in motion on a curve, you have to apply what is called “centripetal force,” a sort of counterforce to keep the object from going in a straight line — as it prefers — instead of a curve, Orzel wrote in an email.
The amount of centripetal force you have to apply depends on both the speed and radius of your curve. “So the force required gets bigger for tighter curves, and gets bigger really fast as the speed increases — about seven and a half times bigger at 82 mph than at 30 mph,” Orzel said.
Orzel added that engineers building roads and railways take these forces into account when designing curves. “The force that a track can exert on the train is limited by the size of the track and the friction between the wheels and the track,” he explained.
Recommended speeds for these curves, like the 30 mph zone on the Metro-North track, are set based on these factors. While train tracks are invariably flat, you may notice that highways manage some centripetal force by banking the roadway, which helps apply gravity to the equation.
The other factor and one that helps explain why the train traveled so far after it left the tracks is how long it takes to stop an object in motion.
Monday's NTSB report indicates that the train's brakes were used, at least to some degree.
Approx 5 seconds before the engine came to a stop, pressure in the brake pipe dropped from 120 psi to 0 - which resulted in max braking.
— NTSB (@NTSB) December 2, 2013
However, the agency does not yet know “the initiating event for the throttle going to idle or the brake pressure dropping to 0 psi.”
What is clear, at least from a physics perspective, is that those brakes had their work cut out for them. “An object that starts out moving at 82 mph would need seven and a half times the distance to stop an object that started at 30 mph,” Orzel said.
Frictional force between the derailed cars and the ground help accident investigators determine initial speed (in this case 82 mph) in such crashes, he added.
Obviously, there remains much we don't know about the derailment. The NTSB is still interviewing crew members and searching for other clues:
The engineer's cell phone has been recovered and as part of our routine process, we will obtain the data from the forensic examination.
— NTSB (@NTSB) December 2, 2013
In the meantime, though, we can apply what we know about physics to understand a bit more about the tragic accident.
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Image: Getty