Comparison between Improvements to Curves and to Rolling Stock
(2) Transition Curves
The length of transition curves is determined by both safety with respect to derailment and riding quality.
Regarding safety, a large differential per unit length cant infers a large wheel load differential between wheels, increasing the possibility of derailment for wheels where the wheel load has decreased. Normally, the differential is set at between 600 to 1000 times the cant.
Riding quality involves the cant time differential (proportional to cant×maximum train speed) and the unbalanced centrifugal acceleration time differential (proportional to cant deficiency×maximum train speed2).
Ideally, the maximum value acquired from the above three conditions should be taken. If an adequate extension cannot be obtained, the speed is restricted.
Transition curves are normally shaped as cubic parabolas. However, sine curves are also used in Japan. Changes in curve ratio are smoother with the sine curve, but in reality, there is little difference.
(3) Cant
The maximum cant that can be applied to curves is determined in consideration of overturning the inside of the curve due to wind pressure when stopping, and derailment caused by reduction in wheel load of the wheels on the outside of tracks when traveling at low speeds. Normally the maximum cant is set at 1/10 of the gauge.
Cant balanced with speed (equilibrium cant) is:
C = GV2/gR
In this equation, C is the equilibrium cant, G is the gauge, V is the speed, g is the gravitational acceleration and R is the curve radius.
