From Train Wreck, The Forensics of Rail Disasters, by George Bibel. Copyright © The Johns Hopkins University Press, 2012.
Believe it or not, it’s possible to derail a train by going too slow—more about that later.
Too fast on a curve
In 1947, a Pennsylvania Railroad passenger train with 2 steam locomotives and 14 cars left Pittsburgh at 1:05 a.m. bound for New York City. The train had just descended a steep 1.73% grade when it over-turned on a sharp 8.5-degree curve (675-foot [205-m] radius) at 3:20 a.m. The speed limit downhill was 35 mph (56 km/h) and 30 mph (48 km/h) on the curve. Instructions required the train crew to test their brakes 2 miles (3.2 km) before the curve.
The 2 locomotives plunged down a 92-foot (28-m) embankment with 5 cars attached. Ten of the 14 cars derailed. Twenty-four people were killed. The investigators concluded that excess speed caused the train to overturn on the curve. The overturning speed was calculated to be 65 mph (105 km/h). Elsewhere in the news on the same day as the accident, the Pennsylvania Railroad, the largest railroad in America, reported operating losses for the year 1946—their ﬁrst ever. Speeding trains overturning on a curve also occurred in California in 1956 (killing 30) and in Virginia in 1978 (killing 6).
Everyone knows, or thinks they know, what centrifugal force is. It’s the phenomenon that ﬂings passengers against the car door on a curve, the force that keeps the water in the bucket when swung fast enough overhead, and the force that derails trains on a curve. But centrifugal force can be a source of much confusion because it’s not a force in the traditional sense. Centrifugal force is an inertial effect that occurs when a body in motion changes direction, as in each of the examples above.
Per Isaac Newton, a body in motion tends to stay in motion. If somehow we could eliminate gravity and air resistance, a ball thrown straight up would continue straight up forever. It takes additional force to change the straight-line motion of the ball and to move a train around a curve.
Inertia, the property of matter that resists changes in motion, is most easily explained by accelerating in an elevator. If a 100-lb (0.44-kN) person is standing on a scale in an elevator accelerating up, the scale reads something higher than 100 lbs. If the elevator is accelerating down, the scale reads something less than 100 lbs. If the elevator is accelerating up at 16 ft/sec2, or one-half the normal acceleration of gravity, the scale will read 150 lbs (0.66 kN). The extra 50 lbs (0.22 kN) is from the person’s body resisting acceleration.
When a body accelerates, or changes velocity, that acceleration is accompanied by a force. According to Newton’s Second Law, f m × a. The body’s inertia (m × a) is not a force even though it acts on the scale like a force. The additional 50-lb reading on the scale is the 100-lb person’s resistance to accelerating up 16 ft/sec2 (4.9 m/s2)—the person’s inertia.
Inertia always acts in the opposite direction of the acceleration. In the case of the elevator, the person is accelerating up and the inertial response is acting down and is being recorded by the scale. A similar thing happens in circular motion. Circular motion at constant speed creates an acceleration that points toward the center of rotation.
We tend to think of acceleration as being a change in speed (see Chapter 4). Velocity is actually a vector with both direction and magnitude. (The velocity vector’s magnitude is also known as speed.) Any change in