Operating at High Cant Deficiency
Cant deficiency has a significant effect on curving performance of vehicles in both passenger and freight service. The forces due to centrifugal acceleration through a curve must ultimately be reacted at the wheel/rail interface. Curve lateral acceleration and the compensating effect of track superelevation can be expressed mathematically as shown in Figure 1.
At a specific speed, termed the balance speed, the compensation due to superelevation balances the acceleration due to curving. Relative to the track plane, the perceived lateral acceleration is then zero. At speeds under the balance speed, the lateral acceleration term is less than the superelevation term. This is termed cant excess, meaning the track has excessive cant for the present speed. At speeds over the balance speed, the lateral acceleration term is greater than the superelevation term. This is termed cant deficiency, meaning the track has insufficient cant for the present speed. With cant deficiency, perceived accelerations are to the outside of the curve; with cant excess, perceived accelerations are to the inside of the curve.
Cant deficiency or excess is often expressed as an amount of insufficient or excess superelevation—inches of cant deficiency. They can also be expressed as uncompensated acceleration—in ft/sec². As a conversion, 1 inch of cant deficiency corresponds to just over 1/2 ft/sec² of uncompensated lateral acceleration.
The left side of Figure 1 shows a rail vehicle on a superelevated curve. The vehicle body is actively tilted toward the inside of the curve, giving passengers a perception of greater superelevation and thus lower perceived lateral accelerations. Without a tilt system, the vehicle body would generally roll towards the outside of the curve with cant deficiency and towards the inside of the curve with cant excess. From the view of passenger comfort, these rotations are in the wrong direction and cause the passenger to perceive even greater lateral accelerations. If the center of rotation of the suspension system can be placed above the body center of gravity, the body will roll inward under cant deficiency. This creates a passive tilt system. The Talgo trains operating in the Pacific Northwest are an example of this design.
What are typical limits on cant deficiency or excess? For cant excess, the worst case is a stationary train. The cant excess limit is equivalent to the maximum allowable superelevation. The cant deficiency limit is typically dictated by maximum uncompensated lateral acceleration, rather than derailment safety. Safe operation is possible at much higher cant deficiency levels than trains usually encounter. Tilting trains prove this by operating at cant deficiencies two to four times those of conventional trains. Operation is safe, as evidenced by non-tilting power cars or locomotives.
Figure 2 shows representative cant limits for operations in three countries, France, Germany and Japan, which have well-established high-speed rail systems. France and Germany have maximum superelevation levels equal to the FRA limit of 7 inches. Japan is marginally higher at 8 inches. For cant deficiency, all three countries allow higher values than the 3 inches accepted in the U.S. (in the absence of an FRA waiver). On conventional lines, France and Germany allow operation with up to 6 inches cant deficiency. On TGV high-speed lines in France, the limit is 4 inches, in part because of the very large curve radii on such lines. Thus there is no requirement to go to higher cant deficiency.