plane of the track due to the circular motion. Referring to the figure above, it can be seen that the components of gravitational and centripetal acceleration in the plane of the track will be equal when the following balance equation is satisfied, where is the bank angle. For a given curve radius and bank angle (i.e., superelevation) the speed that satisfies the balance equation is called the balancing speed and is given by For reasons that will be mentioned below, passenger vehicles usually traverse a curve at a speed higher than the balance speed. The amount by which the actual speed exceeds the balance speed is conveniently expressed via the so-called cant deficiency, i.e., by the amount by which the superelevation would need to be increased to raise the balance speed to the speed at which the vehicles actually travel. Letting denote the rail gauge from low rail gauge side corner to high rail field side corner, letting denote the actual superelevation, and letting denote the actual speed, it follows from the definition that the cant deficiency, , is given by the formula Example Taking an example, a curve with curvature 1.0 degree per 100 ft chord (radius 1,746.40 m = 5,729.65 ft), GE = 1511.3 mm (59.5 inches), and SE = 152.4 mm (6.0 inches) will have If a vehicle traverses that curve at a speed of 55.880 m/s (= 201.17 km/h = 125 mph), then the cant deficiency will be On routes that carry freight traffic in cars with the maximum allowed axle loads it will be desirable to set superelevations so that the balancing speed of each curve is close to the speed at which most such traffic runs. This is to lessen the tendency of heavy wheel loads to crush the head of either rail. Limit values Allowed CD is set below the value that would be allowed based on safety in order to reduce wheel and rail wear and to reduce the rate of degradation of geometry of ballasted track. Choice of design CD will be less constrained by passenger comfort in the case of vehicles that have tilting capability. One historical approach to determining safe cant deficiency was the requirement that the projection to the plane of the track of the resultant of the inertial and gravitational forces acting on a vehicle fall within the middle third of the track gauge. Contemporary engineering studies