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APPENDIX B

LIMITING CONDITIONS FOR VARIOUS 3-AXLE TRUCK LENGTHS ARE AS FOLLOWS:

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The degree of curvature that can be safely negotiated is reduced when there is less than standard cage or standard lateral freedom per axle.

Trains operating in draft around curves exert inward lateral forces on the track because a train tends to "string line" or assume a straight line when traversing the curve.

In normal operation the rail absorbs this lateral force and it is transferred to the roadbed. AVOID HEAVY FORCES TO START, DRAG OR ABRUPTLY INCREASE THE SPEED OF A TRAIN IN A CURVE, SINCE THE RESULTING "STRING LINE" EFFECT COULD SHIFT TRACK, TURN RAIL OVER OR OTHERWISE RESULT IN DERAILMENT.

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AVOID HEAVY BRAKING FORCES WAEN TRAINS ARE BEING SLOWED OR STOPPED ON CURVES SINCE THE TRACK MUST ABSORB ALL FORCES CREATED BY THE BRAKING ACTION. The lateral forces in such action are often increased by sluggish truck or coupler action cocking the truck and/or car (jackknifing) at other than normal position relative to the curve.

Trains traveling around curves are also affected by centrifugal force which acts away from the center of the curve and tends to overturn the cars as illustrated in Figure 5. This tendency directs the weight of the train toward the outside rail.

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Figure 5. Effects of Centrifugal Force

Centrifugal force increases as the square of the speed and increases in direct proportion to the degree of curvature.

The dynamic forces of train operation are additive to the ordinary forces of curve negotiation.

APPENDIX B

4.1.1.1. A

SUPERELEVATION

Superelevation is the raising of the outer rail on
a curve to permit using the weight (gravitational force)
to counteract the effect of centrifugal force. Raising
the outer rail moves the effect of the weight force
toward the inside rail. Combining the effects of the
centrifugal force and weight produces a resultant force
as illustrated in Figure 6.

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When the direction of the resultant force coincides with the centerline of the equipment and track the curve is described as being balanced and equilibrium speed has been reached. In this condition the vertical forces on each rail are equal and minimal frictional forces are occurring between the wheels and the rail. This permits maximum utilization of tractive effort and minimum wear on wheels and rail. However, trains may operate at all speeds from the maximum allowable to a complete stop on a curve. Also, the consist may have many different types of cars with varying centers of gravity. Therefore, the design of superelevation of a curve and the speeds allowed must be carefully chosen. Insufficient superelevation may allow a car to climb the rail or overturn. However, railway equipment will generally "climb" over the rail due to lateral flange pressure and friction before the car

APPENDIX B

will overturn. On the other hand, excessive superelevation may cause the wheels on the high rail to unload due to reduced vertical force and cause wheel lift.

Trains can operate around curves at speeds in excess of equilibrium with safety until reaching this point that wheel climb impends. The height of center of gravity becomes a major consideration when there is unbalance between speed, curvature and superelevation.

This is illustrated in Figure 7 which shows the approximate position of the dynamic resultant force of freight cars on curved track when traveling at speeds above 20 mph. As the center of avity increases, less underbalance ca be permitted.

It is recommended that the maximum speed permitted on a curve should not result in unbalanced superelevation beyond the limits where wheel climb impends.

When a train travels at less than the equilibrium speed around a superelevated curve there is an unbalance with the resultant force directed toward the inside or low rail. As more of the weight is carried by the low rail, there is an unloading of the outer or high rail. The extreme condition is for the low rail to carry the entire vertical force and the high rail to be completely unloaded. This is an unstable operating condition which can result in wheels lifting off the rail. Figure 8 illustrates the approximate position of the dynamic resultant force with overbalance to the low rail for a speed of 15 mph.

Figure 8 is based on lateral roll amplitudes running over track with normal irregularities. Equipment with 98 inch high center of gravity will not unload the high rail of well maintained track until the overbalance is slightly in excess of 6 inches. However, the "string line" effect of starting or pulling a drag train combined with overbalance effect may cause unloading of the high rail with less than 6 inches superelevation in the track.

When determining the superelevation of a curve, very
slow operation and stopped condition must not be ignored.
WHERE PRACTICAL SUPERELEVATION SHALL BE PROVIDED FOR EQUI-
LIBRIUM SPEED. OTHERWISE, IT IS RECOMMENDED THAT THE MAXI-
MUM SPEED OF THE 98" HIGH CENTER OF GRAVITY CARS (MAXIMUM
HEIGHT CENTER OF GRAVITY ALLOWED IN FREE INTERCHANGE) BE
RESTRICTED TO PROVIDE NO MORE THAN 2" UNBALANCE ELEVATION.
A CURVE MUST NOT BE ELEVATED SO MUCH THAT UNLOADING OF THE
HIGH RAIL MIGHT OCCUR AT VERY LOW SPEEDS OR WHEN STARTING.

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