Any mechanical system comprised of springs, when excited, will vibrate or resonate at a given natural frequency known as its harmonic frequency. A good example of a simple harmonic system is a guitar string. Depending on the mass (weight/diameter) of the string, its tightness (spring constant), and location of striking, the string will resonate with a certain tone or frequency.

A freight car is also a harmonic system comprised of mass and springs with a critical frequency at which it tends to resonate. For a typical freight car, the resonate frequency is between roughly 12 and 24 MPH. The energy to excite car rocking comes from the track structure, principally the pattern of joint spacing. Joints tend to deflect vertically under the weight of the wheel, allowing the springs to compress in response to the joints. The energy stored in the compressed springs is then fed back into the car body between the joints, propelling it in the opposite direction. If the joints are staggered approximately one-half rail length apart, then the maximum energy is fed into the car body at just the precise frequency to violently rock the car back and forth side to side. In extreme conditions, wheel lift and derailment can occur. The forward speed of the car, in conjunction with the joint deflection and spacing, determines the exciting frequency. The spring characteristics, center of gravity height, and truck center distance determines the resonate frequency of the freight car. Therefore, operating at the resonate speed over jointed track has the potential to excite a car into its natural rocking mode. Figure 1 shows the harmonic response curve of a typical hopper car.

Track Factors

Rock and roll occurs primarily on track with staggered joints. A staggered joint as joints that alternate left and right that are spaced further than 10 feet apart. Many railroad's past practice was to stagger the joints exactly one-half rail length (19.5 ft.) apart. While this practice had merit in the early days of railroading, the advent of 100 ton hopper cars with nominally 39 - 40 foot truck center spacing, when operating over half staggered joints, caused severe harmonic rocking. To break this pattern up, many railroads changed their practices and began to stagger joints at one-quarter to one-third rail length apart. This corrective action had good success at eliminating rock and roll. Another corrective action used by some railroads was to install the longer 78 ft. jointed rail on one side of curves. This tended to break up the harmonic action by eliminating every other joint.

However, just operating a car over staggered joints does not automatically insure that it will rock and roll violently. There must be sufficient vertical deflection at the joint to introduce sufficient energy into the car body to excite the rocking motion. In general, a dynamic joint deflection of over 1" is required to even begin significant rocking motion. Therefore, joints that deflect due to poor tie, ballast, or pumping conditions are candidates to excite harmonic rocking. In addition, there must be a number of consecutive joints, generally five to six in a row to sustain the rocking motion.

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