geometric design of the track

GEOMETRIC DESIGN

OF THE TRACK

Necessity of Geometric Design:

Smooth & safe running of trains.

Maximum speed.

Carrying heavy axle loads.

Avoid accidents & derailments.

Less maintenance efforts.

Good aesthetic value.

There, if all the above elements are properly

designed, the possibility of derailments due to defects

in the track can be avoided.

GradientsThe amount of slope in longitudinal direction of railway track

is called gradient or grade.

Gradients are provided to negotiate the rise or fall in the level

of the railway track.

Rising gradient rises the track in the direction of movement,

whereas, falling gradient cause the track to go down in the

direction of movement.

A gradient is represented by the distance traveled for a rise or

fall of one unit.

It is written as; 1 in ‘X’ or 1 in ‘n’ or as percent

Gradients are provided on the track due to the

following reasons.

To provide a uniform rate of rise or fall as far as

possible.

To reach the various stations located at different

elevation.

To reduce the cost of earth work.

Gradients – Types

Ruling gradient

Momentum gradient

Pusher or Helper gradient

Gradients in Station Yards

A) Ruling gradient: This is the design gradient basically,

because it is determined on the basis of the performance

of the locomotive and at the same time, it tries to look at

the total amount of load which that locomotive can take

up along with it, while negotiating any gradient without

any loss or major loss in the speed of the movement.

Ruling gradient;

It is a maximum gradient (steepest gradient), which may

be permitted on the section of the track.

It is determined by maximum load that a locomotive can

haul with maximum permissible speed.

Extra pull required by locomotive on gradient with ‘ ’

inclination. P = W Sin = W * gradient

For Ex:-

Weight of train (W)=500 tonnes

Gradient = 1 in 100

Extra power (P) = 5 tonnes

Ruling gradient with one locomotive.

• In Plane area = 1 in 150 to 1 in 250

• In hilly area = 1 in 100 to 1in 150

Once a ruling gradient is specified for a section,

then all other gradients provided in that section

should be flatter than the ruling gradients (after

making due to compensation for curvature)

Gradients – Types ….b) Momentum gradient:

Momentum gradient steeper than ruling gradient that is

overcome by momentum gathered while having a run in

plane or on falling gradient in valleys.

Use additional kinetic energy received during run on a

section.

No obstruction like signals are provided on section with

these gradients.(means the train should not be stopped

at that territory)

For example, in valleys, a falling gradient is usually

followed by rising gradient acquires sufficient

momentum.

This momentum gives additional kinetic energy to

the moving train which would enable the train to

overcome a steeper rising gradient than the ruling

gradient for a certain length of the track.

This rising gradient is called momentum gradient

and this gradient is steeper than ruling gradient.

C) Pusher or Helper gradient:

Gradient steeper than ruling gradient requiring extra

locomotive.

• It reduces the length of a railway section.

• It also reduces the overall cost.

Examples : In Darjeeling Railways 1 in 37 Pusher gradient is

used on Western Ghats, B.G tracks & N.G tracks 1 in 25 is

provided.

d) Gradient at Station Yards:

As per as possible the track along the stations & yards

should be level or gradients should be sufficiently low.

• To prevent standing vehicle from rolling & moving

away from the yard due to combined effect of gravity &

strong winds.

• To reduce additional resistive forces required to start a

locomotive to the extent possible.

• Minimum gradient from drainage consideration.

• On Indian railways, maximum gradient permitted is 1 in

400 in station yards & minimum gradient permitted is 1 in

1000

Grade Compensation ( On Curves):-

If a curve is provided on a track with ruling

gradient, the resistance of the track will be increased on this

curve. In order to avoid resistance beyond the allowable

limits, the gradients are reduced on curves & this reduction in

gradient is known as grade compensation for curves.

In India, Compensation for curvature is given by.

o BG track: 0.04% per degree of curve

o MG track: 0.03 % per degree of curve

o NG track: 0.02 % per degree of curve

Grade Compensation ( On Curves);.Example :If the ruling gradient is 1 in 250 on a particular section

of B.G & at the same time a curve of 4 degree is situated on this

ruling gradient, what should be the allowable ruling gradient?

Solution:

As per Indian railway recommendation, the grade compensation

for of B.G track is 0.04% per degree of curve.

Therefore, Grade compensation for 4 degree curve

= 0.04 * 4 = 0.16%

Ruling gradients is 1 in 250

= 1/250 *100 = 0.4%

Therefore, Required ruling gradient or Actual gradient

= Ruling gradient – grade compensation

= 0.4- 0.16

= 0.24% or 1 in 417

Radius & Degree of a curve:- The main curved portion of a railway track is kept circular

i.e, the radius at every point of the curve is same.

The radius of a railway curve is sometimes represented by the

degree of the curve.

Degree of a railway curve:-

The angle subtended at the center of the curve by an arc of 30.0m

length is defined as a defined as a degree of the curve.

Relationship between the radius & degree of a curve.

Let, R=radius of the curve in meters, D = degree of the curve

Now, total circumference 2πR makes

360o at the center.

Therefore, for 30.0 m arc makes an angle.

D/30 = 360/2πR

D = 360*30/2πR

D = 1718.87/R

D = 1720/R

Safe speed on curves...

Safe speed for all practical purposes means a speed which

is safe from the danger of overturning & derailment with a

certain margin of safety. This speed, to negotiate curves

safely, depends upon the following factors.

• The gauge of track.

• The radius of the curve.

• Amount of super elevation provided.

In India, using safe speed V in kmph, formula.

B.G & M.G : V = 4.35 R- 67

N.G: V = 3.65 R- 6

Superelevation or Cant….

When a train moves round a curve, it is subjected to a centrifugal

force acting horizontally at the centre of gravity of each vehicle

radially away from the centre of the curve. This increases the

weight on the outer rails.

To counteract the effect of centrifugal forces, the level of

the outer rail is raised above the inner rail by a certain amount to

introduce the centripetal force. This raised elevation of outer rail

above the inner rail at a horizontal curve is called “Cant”.


It is the difference in elevation (or height) between the outer

rail and inner rail at a horizontal curve is called “Cant”.

Inner rail is taken as a reference rail & is maintained at its

original level.

Inner rail is also known

as ‘gradient rail’.

It is denoted by “e”.


Objectives of Superelevation.

To neutralize the effect of centrifugal force.

Equal distribution of wheel loads.

Providing smooth track, improving passenger comfort.

To reduce wear & tear of the rails & rolling stock.

Equilibrium Cant…. The cant or super elevation as given by equation e=(GV2/1.27R)

cm, the load carried by both the wheels will be the same, the

springs will be equally compressed & the passengers will not

tend to lean in either direction, such cant is known as the

“Equilibrium cant”.

Equilibrium Cant….

The cant is provided on the basis of average speed of the

trains.

The majority of Indian Railways provide super elevation for

equilibrium speed or average speed under condition of level

track.

Average speed or Weighted average speed

= n1V1+ n2V2+ n3V3 / n1+ n2+ n3

Where, n1, n2,n3 = Number of trains

V1, V2,V3 = Speed of trains in kmph

Cant Deficiency (Cd)…. The equilibrium cant is provided on the basis of equilibrium speed

(or Average speed) of different trains. But this equilibrium cant or

super elevation falls short of that required for the high speed trains.

This shortage of cant is called “ Cant Deficiency”.

In other words, it is the difference between the equilibrium cant

necessary for the maximum permissible speed on a curve and the

actual cant provided. Higher cant deficiency causes more

unbalanced centrifugal force and discomfort to the passengers.

Maximum value of cant deficiency prescribed for Indian Railways.

B.G = 7.6cm, M.G = 5.1cm, N.G = 3.8cm

Negative Superelevation….

When a branch line diverges from a main line on a curve of

contrary flexure, the super elevation necessary for the average

speed of trains running over the main line, cannot be

provided.

The speed of the trains over the diverging track and main line

track has to be reduced considerably.

The reason for the reduction of speed is that, on the branch

line track, the inner rail remains at higher level than the outer

rail.

Negative Superelevation….D

Outer rail

Inner railInner rail


Ref fig: AD which is the outer rail of the main line curve must be

higher than inner rail BC or in other words, the point A should be

higher than point B.

For the branch line, however, BE should be higher than AF or the

point B should be higher than point A.

These two contradictory conditions cannot be meet at the same

time within one layout . So, outer rail BE on branch line is kept

lower than the inner rail AF. In such case branch line curve has a

negative super elevation & therefore speeds on both tracks must be

restricted, particularly on branch line.


Calculation of restricted speed on the main line & branch line.

Super elevation for branch line can be calculated

Calculate equilibrium super elevation for branch line (eb).

Find super elevation, X = eb – Cd for branch line.

This is to be provided on main line.

To calculate the maximum permissible speed for main line,

Cant should be, em = X + Cd

Super elevation for main line can be calculated

Calculate equilibrium super elevation for main line (em).

Find super elevation, X = em – Cd for main line.

Provided cant on branch line as ( -X ).

To calculate the maximum permissible speed for branch line,

Cant should be, eb = (-X ) + Cd

Transitional Curves….

Transition curve is defined as a curve of parabolic nature

which is introduced between a straight and a circular curve or

between two branches of a compound curve.

It is necessary to provide an easy change from a tangent to the

radius selected for a particular curve.

It is essential that the curvature and superelevation in the

outer rail and the curvature in the inner rail are attained

gradually, by the use of easement curve or transition curve.

Transitional Curves…. Objects:

Primary objects:

To decrease the radius of curve gradually from infinite at the

straight to that of circular curve of selected radius.

To attain gradual rise for the desired superelevation. This is

applicable for outer rail.

Secondary objects:

The gradual increase or decrease of the centrifugal force on

the vehicle by use of this curve provides smooth running of

vehicle & comfort to the passengers.

No sudden application, so the chances of derailment are gently

reduced.

Transitional Curves….

Requirements of a Transition Curve;

It should be perfectly tangential to the straight.

The length of the transition curve should be such that

curvature may increase at the same rate as the superelevation .

This curve should join the circular arc tangentially i.e.,

curvature of transition curve should conform with that of

circular curve.

Superelevation for B.G, M.G & N.G….

Relationship of superelevation (e), with gauge(G),

speed (V) and radius of the curve ( R ).W= Weight of moving vehicle in kg.

v = Speed of vehicle in m/sec

V = Speed of vehicle in km.ph

R = Radius of curve in meters

G = Gauge of track in meters

g = Acceleration due to gravity in m/sec2

α = Angle of inclination

S = Length of inclined surface in meters

Centrifugal force is given by the following expression.

F = Wv2/gR -------------(1)

Now resolving the forces along the inclined surface we get

F cosα = W sinα -------- (2)

Superelevation for B.G, M.G & N.G….

F = Wv2/gR , cosα = G/S & sinα = e/S

Therefore equation (2) becomes Wv2/gR * G/S = W*e/S

Therefore, e = v2/gR * G meters

Where, v in m/sec.

= G ( 0,278V)2/9.81R

= GV2/127 R meter

e = GV2/1.27 R centimeter

For B.G., e = GV2/1.27 R = 1.676 V2/1.27 R centimeter

For M.G., e = GV2/1.27 R = 1.0 V2/1.27 R centimeter

For N.G., e = GV2/1.27 R = 0.762 V2/1.27 R centimeter

geometric design of the track

Engineering