Geometric Design of Railway Track

By Vishwajeet Sinha|Updated : January 9th, 2017

Geometric Design of The Track

Different gauges


Safe speed on curves Based on Martins Formula

(a) For Transition curve

(i) For B, G & M.G

V=4.35√5-67 where, V is in kmph.

(ii) For N,G V = 3.65√R-6 For V is km/hr.

(b) For non-Transition curve

V=0.80 × speed calculated in (a)

(c) For high speed Trains V=4.58√R

Safe speed Based on Super Elevation

(a) For Transition curves


The above two formula based on the assumption that G = 1750 mm for B.G

G = 1057 mm for N.G

And image003 Where, e = super elevation.


Where, v= speed in km/hr

R = Radius of curve in ‘mm’

Ca = Actual cant in ‘mm’

Cd = Cant deficiency in ‘mm’

Speed from the Length of Transition Curve

(a) For speed upto 100 km/hr.

image005 (min. of two is adopted)

Where, L = Length of transition curve based on rate of change of cant as 38 mm/sec. for speed upto 100 km/hr & 55 mm/sec for speed upto 100 km/hr & 55 mm/sec for high speeds.

Ca = Actual cant in ‘mm’

Cd = Cant deficiency in ‘mm’

(b) For high speed trains (speed>100km/hr)

Either, image006

Minimum of the two is adopted.

Radius & Degree of curve

image007 if one chain length = 30 m.

image008 if one chain length = 20 m

Where, R = Radius

D = Degree of curve image009

Virsine of Curve (V)



Grade compensation

For B.G → 0.04% per degree of curve

M.G → 0.03% per degree of curve

M.G → 0.02% per degree of curve

Super Elevation (cant)(e)

image013 Where, Vav = Average speed or equilibrium speed.

Equilibrium speed or Average Speed (Vav)

(a) when maximum sanctioned speed>50km/hr.


(b) When sanctioned speed <50 km/hr


(c) Weighted Average Method

image016 Where, n1,n2,n3… etc. are number of trains running at speeds v1,v2,v3… etc.

Maximum value of Cant emax


Cant Deficiency (D)

Cant deficiency = x1-xA



xA = Actual cant provided as per average speed

x1 = Cant required for a higher speed train.

eth = eact+D


Where, eth = theoretical cant

eact = Actual cant

D = Cant deficiency.


Transition Curve (Cubic paraboa)

Equation of Transition curve:



(a) shift (s)

image023 Where, S = shift in ‘m’

L = Length of transition carve in ‘m’

R = Radius of circular curve in ‘m’

(b) Length of Transition Curve: According to Indian Railway.



L = Length of transition curve in ‘m’

Vmax = Maximum permissible speed in km/hr.

Cd = Cant deficiency in ‘cm’

Another Approach

L = maximum of (i), (ii), (iii) and (iv).

Where, (i) As per railway code, L = 4.4√R where L&R ‘m’

(ii) At the change of change of super elevation of 1 in 360.

(iii) Rate of change of cant deficiency. Say 2.5 cm is not exceeded.

(iv) Based on rate of change of radial acceleration with radial acceleration of 0.3048 m/s2.

image025 Where, V is in m/s.

Extra Leteral Clearance on curves

(a) over throw or extra clearance needed of centre = image026

(b) End throw or extra clearance needed at end




L = End to end length of bogie

C = Centre to centre distance of two bogie.

R = Radius of curve.

(c) Lean (L)


image030 Where, h = Height of vehical

E = Super elevation

G = Gauge.

(d) Total Extra Lateral Clearance Needed Outside in Curve


(e) Total Extra Lateral Clearance inside the Curve

E1 = Overthrow + Lean + Sway


Where, = Radius of curve in ‘mm’.

L = End to end length of bugie = 21340 mm for B.G = 19510 mm for M.G

H = height of bogie = 4025 mm for B.G

3350 mm for M.G

C = Bogie centres distance = 1475 mm for B.G

3355 mm for M.G

E = Super elevation in mm

G = 1.676 m for B.G = 1.0 m for m.G

Extra Clearance on Platforms

(a) For platforms situated inside of curve

= E­2-41 mm.

(b) For platforms situated outside the curve

= E1-25 mm.

Gauge Widening on Curves




B = Right wheel base in meters.

= 6m for B.G

= 4.88 m for M.G

R = Radius of curve in m.

L = Leap of flange in ‘m’.


h Depth of wheel flange below rails in cm.

D = Diameter of wheel in cm.

We = Gauge widening in cm.


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