Extra clearances are provided on horizontal curves keeping the following considerations in mind.
Effect of curvature
When a vehicle negotiates a horizontal curve, its frame does not follow the path of the curve, since, being a rigid structure, it is unable to bend. The vehicle, therefore, projects towards the inside of the curve at its central point and toward the outside of the curve near its ends. The distance by which the longitudinal axis of the body of vehicle moves out from the central line of the track is the extra clearance required (Fig. 13.16).
Fig. 13.16 Effect of curvature on long vehicle
(i) The extra clearance required at the centre of the vehicle, which projects towards the inside of the curve, is called overthrow and is given by the equation
EF = - (13.22)
(ii) The extra clearance required at the ends of the vehicle, which project towards the outside of the curve, is called end-throw and is given by the equation
L2 - C2
AP or BQ =- (13.23)
where L is the length of the vehicle, C is the centre-to-centre distance between the bogies and R is the radius of the curve.
Effect of leaning due to superelevation
On account of the superelevation provided on a curve, the vehicle leans towards the inside of the curve, thereby requiring extra clearance as shown in Fig. 13.17. The extra clearance required for leaning is as follows:
Lean = he/G
where h is the height of the vehicle, e is the superelevation, and G is the gauge.
In case the superelevation is not known, it is suggested that its value be assumed to be 70 mm up to a 1° curve and 115 mm for curves above 1°. No extra clearance, however, is required for leaning on the outside of the curve.
Fig. 13.17 Effect of lean due to superelevation
Effect of sway of vehicles
On account of unbalanced centrifugal forces caused due to cant deficiency or cant excess, the vehicles tend of experience an additional sway. The extra clearance required on the inside of the curve due to the sway is taken as one-fourth of the clearance necessary due to leaning.
On summarizing, the total extra clearance (in mm) required on curves is as follows:
(i) Extra clearance inside the curve = overthrow + lean + sway
where Cis the centre-to-centre distance between bogies, which is 14,785 mm for BG routes and 13,715 mm for MG routes, R is the radius of the curve in mm, L is the length of a bogie, which is 21,340 mm for BG routes and 19,510 mm for MG routes, e is the superelevation in mm, h is the height of the vehicle, which is 3350 mm for BG tracks and 3200 mm for MG tracks, and G is the gauge, which is 1676 mm for BG tracks and 1000 mm for MG tracks.
The empirical formulae normally adopted in the field for determining the extra clearance due to the curvature effect are as follows:
Extra Clearance Required in Various Situations
This section discusses the extra clearances required in different situations with regard to the track and the platform.
Between adjacent and curved tracks
In this case, the lean will not be taken into consideration, as both the tracks will have almost the same superelevation. The extra clearance required in this case will be the sum of the clearances required on the inside and the outside of the curve as follows:
where e is the superelevation in mm, h is the height of the vehicle (3.35 m for BG and 3.2 m for MG), and G is the gauge.
For adjacent tracks with structures in between
When there is a structure between two adjacent tracks, each track is treated independently and extra clearances are provided by considering each track with respect to the structure.
In the case of platforms, it has been observed that the provision of extra clearance on curves as discussed may lead to excessive gap between the footboard and the platform. It is, therefore, stipulated that next to platforms this extra clearance be reduced by 51 mm (2 in.) on the inside of the curve and 25 mm (1 in.) on the outside of the curve.
Example 13.7 Two high-level platforms are to be provided on the inside as well as the outside of a 2° curve on a BG track with a superelevation of 100 mm. What should the required extra clearances for these platforms, both on the inside and the outside of the curve, be? (Length of bogie = 21,340 mm, c/c bogie distance = 14,785 mm, height of platform = 840 mm.)
Therefore, an extra clearance of 45 mm should be provided for the outside platform on the inner side of the curve and of 10 mm for the inside platform on the outer side of the curve.