# Widening of Gauge on Curves

A vehicle normally assumes the central position on a straight track and the flanges of the wheels stay clear of the rails. The situation, however, changes on a curved track. As soon as the vehicle moves onto a curve, the flange of the outside wheel of the leading axle continues to travel in a straight line till it rubs against the rail. Due to the coning of wheels, the outside wheel travels a longer distance compared to the inner wheel. This, however, becomes impossible for the vehicle as a whole since the rigidity of the wheel base causes the trailing axle to occupy a different position. In an effort to make up for the difference in the distance travelled by the outer wheel and the inner wheel, the inside wheels slip backward and the outer wheels skid forward. A close study of the running of vehicles on curves indicates that the wear of flanges eases the passage of the vehicle round curves, as it has the effect of increasing the gauge. The widening of the gauge on a curve has, in fact, the same effect and tends to decrease the wear and tear on both the wheel and the track.

The stipulations laid down with regard to the gauge on straight tracks and curves on Indian Railways are given in Table 13.7.

The widening of the gauge on curves can be calculated using the formula

13( B + L)2

Extra width on curves (w) =--- (13.27)

R

where B is the wheel base of the vehicle in metres, R is the radius of the curve in metres, L = 0.02 (h2 + Dh)m is the lap of the flange in metres, h is the depth of flange below top of the rail, and D is the diameter of the wheel of the vehicle.

Table 13.7 Gauge standard for curves

 Type of track Gauge tolerances for BG Gauge tolerances for MG and NG Straight track including curves of 350 m for BG, 290 m for MG, and 400 m and more for NG -5 mm to + 3 mm MG: - 2 mm to + 3 mm NG: - 3 mm to + 3 mm For curves of radius less than 350 m for BG, 290 m for MG, and 400 m to 100 m for NG Up to + 10 mm Up to +10 mm For curves with radius less Than 100 m for NG - up to + 15 mm

* The gauge on a track with wooden sleepers need not be disturbed if it is likely to cause spike killing of sleepers.

Example 13.8 The wheel base of a vehicle moving on a BG track is 6 m. The diameter of the wheels is 1524 mm and the flanges project 32 mm below the top of the rail. Determine the extra width of the gauge required if the radius of the curve is 168 m. Also indicate the extra width of gauge actually provided as per Indian Railways standards.

Solution

(i) Lap of flange L = 0.02^h2 + Dh

where h = 3.2 cm is the depth of the flange below the top of the rail and D = 152.4 cm is the diameter of the wheel. Therefore,

L = 0.02^/ h2 + Dh

= 0.02^3.22 + (152.4 x 3.2) = 0.446m

.... ^ ... . . . 13(5 + L)2

(ii) Extra width of gauge (w) = -

R

13(6 + 0.446)2

=-= 3.21cm = 32.1 mm

168

(iii) As per Indian Railways standards, an extra width of 5 mm is provided for curves with a radius less than 400 m in actual practice.