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Cant gradient is the amount by which cant is increased or decreased in a given length of track. The change in cant is required in order to connect a tangent track (no cant) to a curved track (with cant) through a transition curve. The rate of change of cant is used to determine the suitable cant gradient for a given design speed.
The cant of a railway track or camber of a road (also referred to as superelevation, cross slope or cross fall) is the rate of change in elevation (height) between the two rails or edges of the road.
Cant itself refers to the superelevation of the curve, that is, the difference between the elevations of the outside and inside rails. Cant deficiency is present when a rail vehicle's speed on the curve is greater than the speed at which the components of wheel to rail force are normal to the plane of the track.
Metros and pure commuter railways often also allow steeper gradients, over 4%, for the same reason. High-speed railways commonly allow 2.5% to 4% because the trains must be strong and have many wheels with power to reach very high speeds. For freight trains, gradients should be as gentle as possible, preferably below 1.5%.
The relationship between speed and tilt can be calculated mathematically. We start with the formula for a balancing centripetal force: θ is the angle by which the train is tilted due to the cant, r is the curve radius in meters, v is the speed in meters per second, and g is the standard gravity, approximately equal to 9.81 m/s²:
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The grade (US) or gradient ... If one looks at red numbers on the chart specifying grade, one can see the quirkiness of using the grade to specify slope; the numbers ...