Riding quality involves the changing rate of cant over time (proportional to cant× maximum train speed) and the changing rate of unbalanced centrifugal acceleration over time (proportional to cant deficiency x maximum train speed).
Ideally, the maximum value acquired from the above three conditions should be taken as transition curve length. If an adequate transition curve length cannot be secured, the speed should be restricted.
Transition curves are normally shaped as cubic parabolas. However, sine curves are also used in Japan for higher speeds. Changes of curvature are smoother with the sine curve.
(3) Cant
The maximum cant that can be applied to curves is determined in consideration of overturning of train on the inside of the curve due to wind pressure when stopping or running at low speeds. Normally the maximum cant is set at 1/10 of the gauge.
Cant balanced with speed (equilibrium cant) is given by:
C= GV2/gR
In this equation, C is the equilibrium (or balanced) cant, G is the gauge, V is the train speed, g is the gravitational acceleration and R is the curve radius.
The maximum speed is determined by the actual cant. When the balanced cant for maximum speed exceeds the actual cant, a cant deficiency 1/20 of the gauge is permitted.
Cant diminishing over transition curve can be classified into two types, namely linear diminishing by cubic parabolas and curve diminishing by sinusoidal curves.
3.4 Improvement of Turnouts
The properties of tangent sides and turnout sides differ significantly in the straight turnouts that are normally used. Turnouts easily produce large vibrations and lateral force due to their structure which is more complex than that of general tracks. Tangent sides have the following characteristics.
a As crossings have gaps, these areas become worn and produce strong vertical vibrations due to the impact of wheels.
b Wheel flanges impact strongly with crossing guard rails and wing rails, producing substantial lateral force.
