The lever arm for the locomotive’s weight is halfway between the rails, or 28 inches (0.7 m). The torque from the locomotive’s weight that tries to resist the overturning torque from the centrifugal inertial loading equals 320,000 lbs × 28 inches—almost 9 million inch lbs of torque.
The torque trying to overturn the locomotive is slightly larger than the torque from the locomotive’s weight resisting the overturning torque. The locomotive is just starting to overturn at 60 mph (97 km/h).
The outside rail on a curve is usually higher than the inside rail. The elevation of the outside rail relative to the inside rail is called superelevation.
A raised outside rail rotates a locomotive counterclockwise and helps ﬁght off the clockwise rotation from the centrifugal inertial loading, at least a little bit. In fact, if the car is made top heavy and the right wheel is lifted enough (even at zero mph), eventually the car tips over counter-clockwise. The car tips over at zero mph when the weight load points outside the inner rail, as shown in Figure 7.3.
In 1947, the investigators concluded that the locomotive would over-turn on the curve (with outer rail raised or superelevated 3.5 inches [8.9 cm]) at 65 mph (105 km/h).
Amtrak’s 150-mph (241-km/h) Acela creates its own bank angle by tilting up to 4.2 degrees. If the Acela is operating on a curve whose out-side rail is raised 2 inches (5 cm), the Acela can speed as if it is on a curve that is raised an additional 7 inches (17.8 cm) higher—for a total super-elevation of 9 inches (22.9 cm).
Tilting trains are far more complicated and not the ﬁrst choice of rail-road companies. It is easier to operate on redesigned curves with larger radiuses. Of course, curves with larger radiuses take up more real estate—difﬁcult to do in older, built-up neighborhoods.
Too fast on a turnout
Far more common is moving too fast on a turnout. On a turn-out the track crosses over with sharp turns to merge onto a parallel track. The engineer must slow the train for the turnout or risk overturning. Just such an accident happened in 1951 in New Jersey, killing 84.
Construction of the New Jersey Turnpike required relocating the train tracks 60 feet (18 m) north for a few months. The temporary track was about 2,800 feet (853 m) long and contained a 57-foot (17.4-m) temporary wooden trestle anchored on both ends by massive concrete abutments. The trestle was also part of the turnout, a 121-foot (36.9-m)-long curve with a radius of about 1,100 feet (335 m).
The speed limit on the main track was 65 mph (105 km/h). The temporary track went into operation for the ﬁrst time at one o’clock p.m. on the day of the accident, February 6, 1951. The speed limit on the turnouts and temporary track was 25 mph (40 km/h).
The rush hour train with 11 cars was particularly crowded with about 1,000 passengers, many standing. The locomotive and ﬁrst seven cars derailed. The third and fourth cars were the most damaged. Those two cars struck the concrete abutment (knocking off a big hunk) and fell down the 25-foot (7.6-m) embankment. The third car crashed onto its side, its center sill broke, and the roof and both sides were badly damaged. The right side of the fourth car was torn open its entire length. The investigators concluded that the locomotive’s speed exceeded the calculated 76 mph (122 km/h) overturning speed.
Too fast on a curve is by no means an obsolete problem. In a nearly identical accident in Chicago on September 17, 2005, a commuter train went off the tracks at a turnout, killing two. The engineer missed the signal to slow from 70 to 10 mph (113 to 16 km/h).