# The Physics of Disaster: An Exploration of Train Derailments [Excerpt]

Understanding the science behind trains can help identify the causes of accidents—and lead us to safer railways

Too fast on a curve should be prevented in the future by Positive Train Control (see Chapter 6).

Derailing on curves

Before reaching the overturning speed, a slow, heavy freight train is far more likely to derail on a curve by rail rollover, wide gage, or wheel climb (Figure 7.4).

The tracks are constantly moving around (and constantly being readjusted) because of settlement and train forces (Figure 7.5). The track spikes do not prevent the rails from overturning but do keep them from spreading. Rail overturning is thwarted by the downward wheel forces. If the wooden cross ties are rotted, inertial loading on curves may widen the rails.

Standards are established for maximum distance between rails (gage),

Figure 7.4 and 7.5

maximum dips in each rail (proﬁle), and maximum deviation from straightness (alignment). Higher classes of track require tighter requirements to operate safely at higher speeds. For example, freight trains are limited to 40 mph (64 km/h) on Class 3 track and 60 mph (97 km/h) on Class 4 track. (The track classes are reviewed in Chapter 11.)Although track geometry today is measured automatically with high-speed cars using laser sensors, the standards are based on low-tech methods of measuring the deviation from a 62-foot (18.8-m) string pulled tight. Every 62 feet (18.8 m) of Class 3 track can deviate up to 1.5 inches (3.8 cm) from straight and dip up to 2.25 inches (5.7 cm). The Acela operates at 150 mph (241 km/h) on Class 8 track. Every 31 feet (9.4 m) of Class 8 track can deviate up to 0.5 inch (1.27 cm) from straight and dip up to 1 inch (2.54 cm).

Class 8 track geometry is checked every 30 days. In fact, when Amtrak was preparing to operate Acela at 150 mph, Amtrak’s chief engineer of maintenance, the director of track geometry, and many others rode the geometry car every two weeks for months. They considered it a bonding experience.

The operators will also report any rough or shifted track as it occurs. For all trains operating above 125 mph (201 km/h), at least one train per day has sensors to measure, quantify, and record the location of any rough track.

Concrete, instead of wood, is used for ties on Class 8 track. The concrete is less susceptible to shifting and water damage. At least once annually Class 8 track gage stability is checked with a special car that loads the rail sideways with a force of 10,000 lbs (44.5 kN). Class 8 track is also inspected twice a year with ultrasonic sensors for internal fatigue cracks.

L/v ratios

The tendency to derail is often described by the L/V ratio, where L is the lateral force and V is the vertical force at the wheel-track interface, as shown in Figure 7.6. The higher the L/V ratio, the more likely the car is to derail.

There are rough guidelines for L/V limits. Wheel climb may occur if:

Figure 7.6

L/V greater than 1 for new freight cars with new wheels on new, straight track

L/V greater than 0.82 may be unstable on curves

L/V greater than 0.75 can be unstable for worn wheels and worn rail

L/V greater than 0.68 may overturn a poorly constrained rail

Rails spaced too close together can also encourage wheel climb.

The stated L/V ratios are merely rules of thumb, not rigid predictors. There are many other factors that interact, such as the condition of the trucks, rails, and wheels and whether or not the car body is bouncing on its suspension.

The L/V ratio can also vary greatly as the wheels and rail wear and as the contact location changes. A worn rail on the outside of a curve is

Figure 7.7

View
1. 1. phalaris 03:07 AM 8/4/13

Good background article for the technically interested (i.e. probably the majority of SciAm readers!). Many thanks.

Shame the site is being polluted by these spammers again.
I don't see it on other blogs: it seems odd that SciAm can't prevent it.

2. 2. plcsys 05:04 PM 8/8/13

Thank you for the really interesting and educational article. It goes a long way to understanding the modes of failure for rail cars. I wonder how many derailments are from rail misalignment rather than overspeed on a curve. I have often wondered if a slow moving long freight train can derail towards the inside of the curve because of the force transmitted through coupling tension.

3. 3. Satya Narayan Tiwary 07:16 PM 8/11/13

Speed may cause derailment on curve because centrifugal force depends on square of speed.
S. N. Tiwary
Director

4. 4. Satya Narayan Tiwary 07:17 PM 8/11/13

Speed may cause derailment on curve because centrifugal force depends on square of speed.
S. N. Tiwary
Director

5. 5. pbalant 10:39 AM 8/19/13

A good article on train dynamics. The trains mentioned in this article derailed due to overspeed. It mentioned Postive Train Control, also known as Automatic Train Control. These systems drive the trains by computer control that can perform these mundane tasks much more reliably and safely than human drivers. The systems also protect from collisions and other hazards. In fact, there are commuter railways that have been successfully run without drivers since 1986.

6. 6. Gord Davison in reply to plcsys 07:25 PM 12/1/13

I would expect that many derailments have been blamed on excessive speed which were probably caused by poor rail and locomotive maintenance. The rail system is a profit oriented organization and things like maintenance are a cost that is always trying to be reduced.

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