Unit 2 Geometric Design of railway .pdf

Unit No. 2
Geometric Design
 Introduction
The geometric design of a railway track includes all those parameters which determine
or affect the geometry of the track.
These parameters are as follows.
1. Gradients in the track, including grade compensation, rising gradient, and falling
gradient.
2. Curvature of the track, including horizontal and vertical curves, transition curves,
sharpness of the curve in terms of radius or degree of the curve, cant or
superelevation on curves, etc.
3. Alignment of the track, including straight as well as curved alignment.
It is very important for tracks to have proper geometric design in order to ensure the
safe and smooth running of trains at maximum permissible speeds, carrying the heaviest
axle loads.
The speed and axle load of the train are very important and sometimes are also
included as parameters to be considered while arriving at the geometric design of the
track.
 Necessity for Geometric Design
The need for proper geometric design of a track arises because of the following
considerations
(a) To ensure the smooth and safe running of trains
(b) To achieve maximum speeds
(c) To carry heavy axle loads
(d) To avoid accidents and derailments due to a defective permanent way
(e) To ensure that the track requires least maintenance.
(f) For good aesthetics.
 Alignment of Railway Lines:
Alignment of railway line refers to the direction and position given to the centre line
of the railway track on the ground in the horizontal and vertical planes.
Horizontal alignment means the direction of the railway track in the plan including the
straight path and the curves it follows.
Vertical alignment means the direction it follows in a vertical plane including the level
track, gradients, and vertical curves.
 Importance of Good Alignment

A new railway line should be aligned carefully after proper considerations, as
improper alignment may ultimately prove to be more costly and may not be able to fulfill
the desired objectives. Railway line constructions are capital-intensive projects, once
constructed, it is very difficult to change the alignment of a railway line because of the
costly structures involved, difficulty in getting additional land for the new alignment, and
such other considerations.
 Basic Requirements of an Ideal Alignment
The ideal alignment of a railway line should meet the following requirements.
1. Purpose of the New Railway Line
The alignment of a new railway line should serve the basic purpose for which
the railway line is being constructed. As brought out earlier, the purpose may include
strategic considerations, political considerations, developing of backward areas,
connecting new trade centres, and shortening existing rail lines.
2. Integrated Development
The new railway line should fit in with the general planning and form a part of
the integrated development of the country.
3. Economic Considerations
The construction of the railway line should be as economical as possible.
The following aspects require special attention.
a) Shortest route
It is desirable to have the shortest and most direct route between the connecting
points. The shorter the length of the railway line, the lower the cost of its construction,
maintenance, and operation. There can, however, be other practical considerations that
can lead to deviation from the shortest route.
b) Construction and maintenance cost
The alignment of the line should be so chosen that the construction cost is
minimum. This can be achieved by a balanced cut and fill of earthwork, minimizing
rock cutting and drainage crossings by locating the alignment on watershed lines, and
such other technical considerations. Maintenance costs can be reduced by avoiding
steep gradients and sharp curves, which cause heavy wear and tear of rails and rolling
stock.
c) Minimum operational expenses
The alignment should be such that the operational or transportation expenses
are minimum. This can be done by maximizing the haulage of goods with the given
power of the locomotive and traction mix. This can he achieved by providing easy
gradients, avoiding sharp curves, and adopting a direct route.
4. Maximum Safety and Comfort

The alignment should be such that it provides maximum safety and comfort to
the travelling public. This can be achieved by designing curves with proper transition
lengths, providing vertical curves for gradients, and incorporating other such technical
features.
5. Aesthetic Considerations
While deciding the alignment, aesthetic aspects should also be given due
weightage. A journey by rail should be visually pleasing. This can be done by
avoiding views of borrow pits and passing the alignment through natural and beautiful
surroundings with attractive beauty.
 Selection of a Good Alignment
Normally, a direct straight route connecting two points is the shortest and most
economical route for a railway line, but there are practical problems and other
compulsions which necessitate deviation from this route. The various factors involved is
the selection of a good alignment for a railway line are given below.
Choice of Gauge
The gauge can be a BG (1676 mm), an MG (1000 mm), or even an NG (762 mm). As
per the latest policy of the Government of India, new railway lines are constructed on BG
only.
1. Obligatory or Controlling Points
These are the points through which the railway line must pass due to political,
strategic, and commercial reasons as well as due to technical considerations. The
following are obligatory or controlling points.
 Important cities and towns
This is mostly intermediate important towns, cities, or places which of
commercial, strategic, or political importance.
 Major bridge sites and river crossings
The construction of major bridges for large rivers is very expensive and suitable
bridge sites become obligatory points for a good alignment.
 Existing passes and saddles in hilly terrain
Existing passes and saddles should be identified for crossing a hilly terrain in
order to avoid deep cuttings and high banks.
 Sites for tunnels
The option of a tunnel in place of a deep cut in a hilly terrain is better from the
economical viewpoint. The exact site of such a tunnel becomes an obligatory point.
2. Topography of the Country
The alignment of a new railway line depends upon the topography of the
country it traverses. The following few situations may arise.

 Plane alignment
When the topography is plane and flat, the alignment presents no problems and can
pass through obligatory points and yet have very easy gradients.
 Valley alignment
The alignment of a railway line in valley is simple and does not pose any problem. If
two control points lie in the same valley, a straight line is provided between these
points with a uniform gradient.
 Cross-country alignment
The alignment of a railway line in such terrain crosses the watersheds of two or more
streams of varied sizes. As the levels vary in crosscountry, the gradients are steep and
varying and there are sags and summits. The controlling or obligatory points for cross-
country alignment may be the lowest saddles or tunnels. It may be desirable to align
the line for some length along the watersheds so that some of the drainage crossings
may be avoided.
 Mountain alignment
The levels in mountains vary considerably, and if normal alignment is adopted, the
grades would become too steep, much more than the ruling gradient (allowable
gradient). In order to remain within the ruling gradient, the length of the railway line
is increased artificially by the ‘development processes.
The following are the standard methods for the development technique:
a) Zigzag line method
In this method, the railway line traverses in a zigzag alignment and follows a
convenient side slope which is at nearly right angles to the general direction of the
alignment. The line then turns about 180° in a horseshoe pattern to gain height.
b) Switch-back method

In the case of steep side slopes, a considerable gain in elevation is accomplished
the switch-back method. This method involves a reversal of direction achieved by a
switch, for which the train has to necessarily stop. The switch point is normally
located in a station yard.
In Fig., A and B are two switches and A1 and B1 are two buffer stops. A train
coming from D will stop at B1 and move in back gear to line BA. It will stop at A1
again and then follow the line AC
c) Spiral or complete loop method
This method is used in a narrow valley where a small bridge or viaduct has been
constructed at a considerable height to span the valley. In this case, normally a
complete loop of the railway line is constructed, so that the line crosses the same point
a second time at a height through a flyover or a tunnel.

5. Geometrical Standards
Geometrical standards should be so adopted as to economize as much as
possible as well as provide safety and comfort to passengers. This can be done by
adopting gradients and curves within permissible limits. Transition as well as vertical
curves should be used to provide better comfort and safety.
6. Geological Formation
The alignment should be so selected that it normally runs on good and stable
soil formation as far as possible. Weak soil and marshy land present a number of
problems including those of maintenance. Though rocky soil, provides a stable
formation, it is a costly proposal.
7. Effect of Flood and Climate
The alignment should normally pass through areas which are not likely to be
flooded. The climatic conditions should also be taken into consideration for
alignment.
In hot climate and sandy areas, the alignment should pass by those sides of sand
dunes that face away from the direction of the wind. Similarly, in cold regions, the
alignment should pass by those sides of hills that face away from the direction of the
wind. A sunny side is more desirable.
8. Position of Roads and Road Crossings
A railway line should cross a road at right angles so as to have a perpendicular
level crossing and avoid accidents.
9. Proximity of Labour and Material
The availability and proximity of local labour and good and cheap building
material should also be considered when deciding the alignment.
10. Location of Railway Stations and Yards
Railway stations and yards should be located on level stretches of land,
preferably on the outskirts of a town or village so as to have enough area for the free
flow of traffic.
11. Religious and Historical Monuments
The alignment should avoid religious and historical monuments, as it is
normally not possible to dismantle these buildings.
12. Cost Considerations
The alignment should be such that the cost of construction of the railway line is
as low as possible. Not only the initial cost of construction but also the maintenance
cost should be as low as possible. For this purpose, the alignment should be as straight
as possible, with least earthwork, and should pass through terrain with good soil.
12. Traffic Considerations

The alignment should be so selected that it attracts maximum traffic. In this
context, traffic centres should be well planned; so that the railway line is well
patronized and the gross revenue arising out of traffic receipts is as high as possible.
13. Economic Considerations
Keeping in mind the various considerations, it should be ensured that the
alignment is overall economic. For this purpose, various alternate alignments are
considered and the most economical one, which is cost effective and gives the
maximum returns, is chosen.
14. Political Considerations
The alignment should take into account political considerations. It should not
enter foreign soil and should preferably be away from common border areas.
 Gradients
Gradients are provided to negotiate the rise or fall in the level of the railway track. A
rising gradient is one in which the track rises in the direction of the movement of traffic
and a down or falling gradient is one in which the track loses elevation in the direction of
the movement of traffic.
A gradient is normally represented by the distance travelled for a rise or fall of one
unit. Sometimes the gradient is indicated as % rise or fall.
For example, if there is a rise of 1 m in 400 m, the gradient is 1 in 400 or 0.25%, as
shown in Fig.
Gradients are provided to meet the following objectives.
(a) To reach various stations at different elevations
(b) To follow the natural contours of the ground to the extent possible
(c) To reduce the cost of earthwork.
The following types of gradients are used on the railways.
(a) Ruling gradient
(b) Pusher or helper gradient

(c) Momentum gradient
(d) Gradients in station yards
1 Ruling Gradient
The ruling gradient is the steepest gradient that exists in a section. It determines the
maximum load that can be hauled by a locomotive on that section. While deciding the
ruling gradient of a section, it is not only the severity of the gradient but also its length as
well as its position with respect to the gradients on both sides that have to be taken into
consideration.
The power of the locomotive (engine) to be put into service on the track also plays an
important role in taking this decision, as the locomotive should have adequate power to
haul the entire load over the ruling gradient at the maximum permissible speed.
The extra force P required by a locomotive to pull a train of weight W on a gradient
with an angle of inclination θ is P = W Sinθ
= W tanθ (approximately, as θ is very small)
= W × gradient
Indian Railways does not specify any fixed ruling gradient owing to enormous
variations in the topography of the country, the traffic plying on various routes, and the
speed and type of locomotive in use on various sections. Generally, the following ruling
gradients are adopted on Indian Railways when there is only one locomotive pulling the
train.
In plain terrain: 1 in 150 to 1 in 250
In hilly terrain: 1 in 100 to 1 in 150
Once a ruling gradient has been specified for a section, all other gradients provided in
that section should be flatter than the ruling gradient after making due compensation for
curvature.
2 Pusher or Helper Gradient
In hilly areas, the rate of rise of the terrain becomes very important when trying to
reduce the length of the railway line and, therefore, sometimes gradients steeper than the
ruling gradient are provided to reduce the overall cost. In such situations, one locomotive
is not adequate to pull the entire load, and an extra locomotive (engine) is required.
When the gradient of the ensuing section is so steep as to necessitate the use of an
extra engine for pushing the train, it is known as a pusher or helper gradient.
3 Momentum Gradient
The momentum gradient is steeper than the ruling gradient and can be overcome by a
train because of the momentum it gathers while running on the section. In valleys, a
falling gradient is sometimes followed by a rising gradient.

In such a situation, a train coming down a falling gradient acquires good speed and
momentum, which gives additional kinetic energy to the train and allows it to negotiate
gradients steeper than the ruling gradient.
In sections with momentum gradients there are no obstacles provided in the form of
signals, etc., which may bring the train to a critical juncture.
4 Gradients in Station Yards
The gradients in station yards are quite flat due to the following reasons.
(a) To prevent standing vehicles from rolling and moving away from the yard due to
the combined effect of gravity and strong winds.
(b) To reduce the additional resistive forces required to start a locomotive to the extent
possible.
It may be mentioned here that generally, yards are not leveled completely and certain
flat gradients are provided in order to ensure good drainage.
The maximum gradient prescribed in station yards on Indian Railways is 1 in 400,
while the recommended gradient is 1 in 1000.
 Grade Compensation on Curves
Curves provide extra resistance to the movement of trains. As a result, gradients are
compensated to the following extent on curves
(a) On BG tracks, 0.04% per degree of the curve or 70/R, whichever is minimum.
(b) On MG tracks, 0.03% per degree of curve or 52.5/R, whichever is minimum.
(c) On NG tracks, 0.02% per degree of curve or 35/R, whichever is minimum
where R is the radius of the curve in metres.
The gradient of a curved portion of the section should be flatter than the ruling
gradient because of the extra resistance offered by the curve.
Example
Find the steepest gradient on a 2° curve for a BG line with a ruling gradient of 1 in 200.
Solution
(i) Ruling gradient = 1 in 200 = 0.5%
(ii) Compensation for a 2° curve = 0.04 × 2 = 0.08%
(iii) Compensated gradient = 0.5 – 0.08 = 0.42% = 1 in 238
The steepest gradient on the curved track is 1 in 238.
 Horizontal curves:
 Introduction
Curves are introduced on a railway track to bypass obstacles, to provide longer and
easily traversed gradients, and to pass a railway line through obligatory or desirable
locations.

Horizontal curves are provided when a change in the direction of the track is required
and vertical curves are provided at points where two gradients meet or where a gradient
meets level ground.
To provide comfortable ride on a horizontal curve, the level of the outer rail is raised
above the level of the inner rail. This is known as super elevation.
 Circular curves
This section describes the defining parameters, elements, and methods of setting out
circular curves.
 Radius or degree of a curve
A curve is representing either by its radius or by its degree. The degree of a curve (D)
is the angle subtended at its centre by a 30.5 m or 100 ft arc.
The value of the degree of the curve can be determined as indicated below.
Circumference of a circle = 2πR
Angle subtended at the centre by a circle with this circumference = 360°
Angle subtended at the centre by a 30.5 m arc,
or degree of curve = 360°/2πR x30.5 = 1750/ (approximately R is in meter)
In cases where the radius is very large, the arc of a circle is almost equal to the chord
connecting the two ends of the arc.
The degree of the curve is thus given by the following formulae:
D = 1750/R (when R is in metres)
D = R 5730/R (when R is in feet)
A 2° curve, therefore, has a radius of 1750/2 = 875 m.
Relationship between radius and versine of a curve
The versine is the perpendicular distance of the midpoint of a chord from the arc of a
circle.
The relationship between the radius and versine of a curve can be established as shown in
Fig.
Let R be the radius of the curve, C be the length of the chord, and V be the versine of
a chord of length C.

Unit 2 Geometric Design of railway .pdf

 Determination of degree of a curve in field
For determining the degree of the curve in the field, a chord length of either 11.8 m or
62 ft is adopted. The relationship between the degree and versine of a curve is very
simple for these chord lengths as indicated below.

This important relationship is helpful in determining the degree of the curve at any
point by measuring the versine either in centimetres on a 11.8-m chord or in inches on a
62-ft chord. The curve can be of as many degrees as there are centimetres or inches of the
versine for the chord lengths given above.
 Maximum Degree of a Curve
The maximum permissible degree of a curve on a track depends on various factors
such as gauge, wheel base of the vehicle, maximum permissible superelevation, and other
such allied factors. The maximum degree or the minimum radius of the curve permitted on
Indian Railways for various gauges is given in below table.
 Elements of a circular curve
In Fig., AO and BO are two tangents of a circular curve which meet or intersect at a
point O, called the point of intersection or apex.
T1 and T2 are the points where the curve touches the tangents, called tangent points
(TP).
OT1 and OT2 are the tangent lengths of the curve and are equal in the case of a simple
curve. T1T2 is the chord and EF is the versine of the same.
The angle AOB formed between the tangents AO and OB is called the angle of
intersection (< 1) and the angle BOO1 is the angle of deflection (< φ) .
The following are some of the important relations between these elements:

∠1 +∠ φ = 180°
 Superelevation
The following terms are frequently used in the design of horizontal curves.
Superelevation or cant Superelevation or cant (Ca ) is the difference in height
between the outer and the inner rail on a curve. It is provided by gradually lifting the
outer rail above the level of the inner rail. The inner rail is taken as the reference rail and
is normally maintained at its original level. The inner rail is also known as the gradient
rail.
The main functions of superelevation are the following.
(a) To ensure a better distribution of load on both rails
(b) To reduce the wear and tear of the rails and rolling stock
(c) To neutralize the effect of lateral forces
(d) To provide comfort to passengers
 Equilibrium speed
When the speed of a vehicle negotiating a curved track is such that the resultant
force of the weight of the vehicle and of radial acceleration is perpendicular to the
plane of the rails, the vehicle is not subjected to any unbalanced radial acceleration
and is said to be in equilibrium. This particular speed is called the equilibrium speed.
The equilibrium speed, as such, is the speed at which the effect of the centrifugal force
is completely balanced by the cant provided.
 Maximum permissible speed
This is the highest speed permitted to a train on a curve taking into
consideration the radius of curvature, actual cant, cant deficiency, cant excess, and the
length of transition. On cruves where the maximum permissible speed is less than the
maximum sectional speed of the section of the line, permanent speed restriction
becomes necessary.
 Cant deficiency
Cant deficiency (Cd) occurs when a train travels around a curve at a speed
higher than the equilibrium speed. It is the difference between the theoretical cant
required for such high speeds and the actual cant provided.
 Cant excess

Cant excess (Ce) occurs when a train travels around a curve at a speed lower
than the equilibrium speed. It is the difference between the actual cant provided and
the theoretical cant required for such a low speed.
 Cant gradient and cant deficiency gradient
These indicate the increase or decrease in the cant or the deficiency of cant in a
given length of transition. A gradient of 1 in 1000 means that a cant or a deficiency of
cant of 1 mm is attained or lost in every 1000 mm of transition length.
 Rate of change of cant or cant deficiency
This is the rate at which cant deficiency increases while passing over the
transition curve, e.g., a rate of 35 mm per second means that a vehicle will experience
a change in cant or a cant deficiency of 35 mm in each second of travel over the
transition when travelling at the maximum permissible speed.
 Centrifugal Force on a Curved Track
A vehicle has a tendency to travel in a straight direction, which is tangential to the
curve, even when it moves on a circular curve. As a result, the vehicle is subjected to a
constant radial acceleration:
Radial acceleration = g = V 2
/R
Where V is the velocity (metres per second) and R is the radius of curve (metres). This radial
acceleration produces a centrifugal force which acts in a radial direction away from the
centre.
The value of the centrifugal force is given by the formula
Force = mass × acceleration
F = m × (V 2
/R)
= (W/g) × (V 2
/R)
Where F is the centrifugal force (tonnes),
W is the weight of the vehicle (tonnes),
V is the speed (metre/sec),
g is the acceleration due to gravity (metre/sec2
),
R is the radius of the curve (metres).
To counteract the effect of the centrifugal force, the outer rail of the curve is elevated
with respect to the inner rail by an amount equal to the superelevation.
A state of equilibrium is reached when both the wheels exert equal pressure on the
rails and the superelevation is enough to bring the resultant of the centrifugal force and the
force exerted by the weight of the vehicle at right angles to the plane of the top surface of the
rails.
In this state of equilibrium, the difference in the heights of the outer and inner rails of
the curve known as equilibrium superelevation.
 Equilibrium Superelevation

In Fig. , if θ is the angle that the inclined plane makes with the horizontal line, then
where
e is the equilibrium superelevation,
G is the gauge,
V is the velocity, g is the acceleration due to gravity, and
R is the radius of the curve.
In the metric system equilibrium superelevation is given by the formula

where
e is the superelevation in millimetres,
V is the speed in km/h,
R is the radius of the curve in metres, and
G is the dynamic gauge in millimetres,
which is equal to the sum of the gauge and the width of the rail head in millimetres.
This is equal to 1750 mm for BG tracks and 1058 mm for MG tracks.
 MAXIMUM VALUE OF SUPERELEVATION
The maximum value of super elevation has been laid down based on experiments
carried out in Europe on a standard gauge for the overturning velocity, taking into
consideration the track maintenance standards. The maximum value of super elevation
generally adopted on many railways around the world is one-tenth to one-twelfth of the
gauge. The values of maximum super elevation prescribed on Indian Railways are given in
Table below.
Cant Deficiency and Cant Excess
Cant deficiency is the difference between the equilibrium cant that is necessary for the
maximum permissible speed on a curve and the actual cant provided. Cant deficiency is
limited due to two considerations:
(a) Higher cant deficiency causes greater discomfort to passengers and
(b) Higher cant deficiency leads to greater unbalanced centrifugal forces, which in turn lead
to the requirement of stronger tracks and fastenings to withstand the resultant greater lateral
forces.
The maximum values of cant deficiency prescribed for Indian Railways are given in
Table 13.3.

The limiting values of cant excess have also been prescribed. Cant excess should not
be more than 75 mm on broad gauge and 65 mm on meter gauge for all types of rolling
stock.
Cant excess should be worked out taking into consideration the booked speed of the
trains running on a particular section. In the case of a section that carries predominantly
goods traffic, cant excess should be kept low to minimize wear on the inner rail. Table 13.4
lists the limiting values of the various parameters that concern a curve.
Negative Super elevation
When the main line lies on a curve and has a turnout of contrary
flexure leading to a branch line, the super elevation necessary for the average speed of
trains running over the main line curve cannot be provided. In Fig. 13.9, AB, which is

the outer rail of the main line curve, must be higher than CD. For the branch line,
however, CF should be higher than AE or point C should be higher than point A. These
two contradictory conditions cannot be met within one layout. In such cases, the
branch line curve has a negative super elevation and, therefore, speeds on both tracks
must be restricted, particularly on the branch line.
The provision of negative super elevation for the branch line and the reduction in speed
over the main line can be calculated as follows.
(i) The equilibrium super elevation for the branch line curve is first calculated
using the formula,
e= 127 x GV² / R
(ii) The equilibrium super elevation e is reduced by the permissible cant
deficiency Cd and the resultant super elevation to be provided is
x = e – Cd
Where, x is the super elevation, e is the equilibrium super elevation, and
Cd is 75 mm for BG and 50 mm for MG.
The value of Cd is generally higher than that of e, and, therefore, x is
normally negative. The branch line thus has a negative super elevation of x.
(iii) The maximum permissible speed on the main line, which has a super
elevation of x, is then calculated by adding the allowable cant deficiency (x +
Cd), The safe speed is also calculated and smaller of the two values is taken
as the maximum permissible speed on the main line curve.
 Maximum Permissible Speed on a Curve
The maximum permissible speed on a curve is the minimum value of the speed that is
calculated after determining the four different speed limits mentioned here. The first three
speed limits are taken into account for the calculation of maximum permissible speed,

particularly if the length of the transition curve can be increased. For high-speed routes,
however, the fourth speed limit is also very important, as cases may arise when the length of
the transition curve cannot be altered easily.
(i) Maximum sanctioned speed of the section
This is the maximum permissible speed authorized by the commissioner of railway safety.
This is determined after an analysis of the condition of the track, the standard of
interlocking, the type of locomotive and rolling stock used, and other such factors.
(ii) Maximum speed of the section taking into consideration cant deficiency
This is the speed calculated using the formula given in Table 13.5. First, the
equilibrium speed is decided after taking various factors into consideration and the
equilibrium superelevation (Ca ) calculated. The cant deficiency (Cd ) is then added to the
equilibrium superelevation and the maximum speed is calculated as per this increased
superelevalion (Ca + Cd ).
(iii) Maximum speed taking into consideration speed of goods train and cant excess
Cant (Ca ) is calculated based on the speed of slow moving traffic, i.e., goods train. This
speed is decided for each section after taking various factors into account, but generally its
value is 65 km/h for BG and 50 km/h for MG. The maximum value of cant excess (Ce ) is
added to this cant and it should be ensured that the cant for the maximum speed does not
exceed the value of the sum of the actual cant + and the cant excess (Ca + Ce ).
(iv) Speed corresponding to the length of the transition curves
This is the least value of speed calculated after taking into consideration the various
lengths of transition curves given by the formulae listed in Table 13.6. The following points
may be noted when calculating the maximum permissible speed on a curve.
(a) Criterion (iv) is to be used only in cases where the length of the transition curve
cannot be increased due to site restrictions. The rate of change of cant or cant deficiency has
been permitted at a rate of 55 mm/sec purely as an interim measure for the existing curves
on BG tracks.
(b) For high-speed BG routes, when the speed is restricted as a result of the rate of
change of cant deficiency exceeding 55 mm/sec, it is necessary to limit the cant deficiency to
a value lower than 100 mm in such a way that optimum results are obtained. In this situation,
the maximum permissible speed is determined for a cant deficiency less than 100 mm, but
gives a higher value of the maximum permissible speed.

 Transition Curve
As soon as a train commences motion on a circular curve from a straight line track, it
is subjected to a sudden centrifugal force, which not only causes discomfort to the
passengers but also distorts the track alignment and affects the stability of the rolling stock.
In order to smoothen the shift from the straight line to the curve, transition curves are
provided on either side of the circular curve so that the centrifugal force is built up gradually
as the superelevation slowly runs out at a uniform rate .
A transition curve is, therefore, the cure for an uncomfortable ride, in which the
degree of the curvature and the gain of superelevation are uniform throughout its length,
starting from zero at the tangent point to the specified value at the circular curve.
The following are the objectives of a transition curve.
(a) To decrease the radius of the curvature gradually in a planned way from infinity at
the straight line to the specified value of the radius of a circular curve in order to help the
vehicle negotiate the curve smoothly.
(b) To provide a gradual increase of the superelevation starting from zero at the
straight line to the desired superelevation at the circular curve.
(c) To ensure a gradual increase or decrease of centrifugal forces so as to enable the
vehicles to negotiate a curve smoothly.
 Requirements of an Ideal Transition Curve
The transition curve should satisfy the following conditions.
(a) It should be tangential to the straight line of the track, i.e., it should start from
the straight part of the track with a zero curvature.
(b)It should join the circular curve tangentially, i.e., it should finally have the
same curvature as that of the circular curve.
(c) Its curvature should increase at the same rate as the superelevation.
(d)The length of the transition curve should be adequate to attain the final
superelevation, which increases gradually at a specified rate.
 Types of Transition Curves

The types of transition curves that can be theoretically provided are described
here. The shapes of these curves are illustrated in Fig.
 Euler’s spiral
This is an ideal transition curve, but is not preferred due to mathematical
complications. The equation for Euler’s sprial is
 Cubical spiral
This is also a good transition curve, but quite difficult to set on the field.
 Bernoulli’s lemniscate
In this curve, the radius decreases as the length increases and this causes the
radial acceleration to keep on falling. The fall is, however, not uniform beyond a 30°
deflection angle. This curve is not used on railways.
 Cubic parabola
Indian Railways mostly uses the cubic parabola for transition curves. The
equation of the cubic parabola is
In this curve, both the curvature and the cant increase at a linear rate. The cant of the
transition curve from the straight to the curved track is so arranged that the inner rail
continues to be at the same level while the outer rail is raised in the linear form
thought out the length of the curve. A straight line ramp is provided for such transition
curves.
Where,

φ is the angle between the straight line track and the tangent to the transition
curve,
l is the distance of any point on the transition curve from the take-off point,
L is the length of the transition curve,
x is the horizontal coordinate on the transition curve,
y is the vertical coordinate on the transition curve, and R is the radius of the
circular curve.
 S-shaped transition curve
In an S-shaped transition curve, the curvature and superelevation assume the
shape of two quadratic parabolas. Instead of a straight line ramp, an S-type parabola
ramp is provided with this transition curve.
The special feature of this curve is that the shift required in this case is only half
of the normal shift provided for a straight line ramp.
The value of shift is
Further, the gradient is at the centre and is twice steeper than in the case of a
straight line ramp. This curve is desirable in special conditions—when the shift is
restricted due to site conditions.
The Railway Board has decided that on Indian Railways, transition curves will
normally be laid in the shape of a cubic parabola.
 Shift
For the main circular curve to fit in the transition curve, which is laid in the
shape of a cubic parabola, it is required be moved inward by a measure known as the
‘shift’.
The value of shift can be calculated using the formula
Where,
S is the shift in m, L is the length of the transition curve in m, and R is the radius in
m.

The offset (in centimetres) from the straight line to any point on the transition curve is
calculated using the equation.
where y is the offest from the staight line in cm, x is the distance from the
commencement of the curve in m, L is the length of transition in m, and R is the
radius of curve in m.
 Length of Transition Curve
The length of the transition curve prescribed on Indian Railways is the maximum of
the following three values:
……a)
…..b)
……c)
Where,
L is the length of the curve in m,
Ca is the actual cant or superelevation in mm, and
Cd is the cant deficiency in mm.
Formulae (a) and (b) are based on a rate of change of a cant or cant deficiency of 35
mm/sec. Formula (c) is based on a maximum cant gradient of 1 in a 720 or 1.4 mm/m.

Problem: A curve of 600 m radius on a BG section has a limited transition of 40 m
length. Calculate the maximum permissible speed and superelevation for the same. The
maximum sectional speed (MSS) is 100 km/h.
Solution
In a normal situation, a curve of a 600 m radius will have quite a long transition curve for
an MSS of 100 km/h. However, as the transition curve has been restricted to 40 m, the
cant should be so selected that the speed on the main circular curve is equal to the speed
on the transition curve as a whole.
(i) For the circular curve, the maximum speed is calculated from Eqn :
The most favourable value of speed is obtained when Ca = Cd .
(ii) For the transition curve, the maximum change of cant is taken as 55 mm/sec and the
maximum speed is then calculated:
Therefore,
Or
On solving this equation, Ca = 89.50 mm = 90 mm.
(iii) On limiting the value of Cd to 75 mm,
which is within the permissible limits of 1:360. Therefore, the maximum permissible
speed is 85 km/h and the superelevation to be provided is 90 mm.
 Laying a Transition Curve
A transition curve is laid in the following steps.

1. Calculate the length of transition curve.
2. This transition length is divided into an even number of equal parts, usually eight.
3. The equations for a cubic parabola and the shift, reproduced here, are used for
calculations.
4. Calculate the shift.
5. The ordinates are then calculated at points 1, 2, 3, etc.

6. The point at which the transition curve starts is then determined approximately by
shifting the existing tangent point backwards by distance equal to half the length of
the transition curve.
7. The offsets y1 , y2 , y3 , etc. are measured perpendicular to the tangent to get the
profile of the transition curve.
 Compound Curve
A compound curve is formed by the combination of two circular curves of different
radii curving in the same direction. A common transition curve may be provided between
the two circular curves of a compound curve.
Assuming that such a connecting curve is to be traversed at a uniform speed, the
length of the transition curve connecting the two circular curves can be obtained from the
formula
where Ca1 and Cd1 are the cant and cant deficiency for curve 1 and Ca2 and Cd2 are
the cant and cant deficiency for curve 2 in millimetres. L is the length of the transition
curve, in m, and Vm is the maximum permissible speed in km/h.
 Reverse Curve

A reverse curve is formed by the combination of two circular curves with opposite
curvatures. A common transition curve may be provided between the two circular curves
of a reverse curve.
The total length of the transition curve, from the common circular curve to the
individual circular curve, may be obtained in the same manner as explained for a
compound curve.
It has been stipulated that for high-speed group A and B routes, a minimum straight
length of 50 m should be kept between the two curves constituting a reverse curve. In the
case of a high-speed MG route, the distance to be kept should be 30 m.
Straight lines between the circular curves measuring less than 50 m on BG sections of
group A and B routes and less than 30 m on high-speed MG routes should be eliminated
by suitably extending the transition lengths.
When doing so, it should be ensured that the rate of change of cant and versine along
the two transition lengths being extended is kept the same. When such straight lines
between reverse curves cannot be eliminated and their lengths cannot be increased to
over 50 m in the case of BG routes and 30 m in the case of MG routes, speeds in excess
of 130 km/h on BG routes and 100 km/h on MG routes should not be permitted.
Vertical Curves
An angle is formed at the point where two different gradients meet, forming a
summit or sag as explained in Fig.
The angle formed at the point of contact of the gradients is smoothened by providing a
curve called the vertical curve in the vertical plane. In the absence of a vertical curve,
vehicles are likely to have a rough run on the track. Besides this, a change in the gradient
may also cause bunching of vehicles in the sags and a variation in the tension of
couplings in the summits, resulting in train parting and an uncomfortable ride.

To avoid these ill effects, the change in gradient is smoothened by providing a vertical
curve. A rising gradient is normally considered positive and a failing gradient is
considered negative. A vertical curve is normally designed as a circular curve.
The circular profile ensures a uniform rate of change of gradient, which controls the
rotational acceleration.
 Calculating the Length of a Vertical Curve (Old Method)
The length of a vertical curve depends upon the algebraic difference between the
gradients and the type of curve formed (summit or sag).
The rate of change of gradient in the case of summits should not exceed 0. 1%
between successive 30.5- m (100-ft) chords, whereas the corresponding figure for sags is
0.05% per 30.5-m (100-ft) chord. The required length of a vertical curve for achieving
the maximum permissible speed is given by the formula

L = (a/r) × 30.5 m
Where L is the length of the vertical curve in m, a is the per cent algebraic difference
between successive gradients, and r is the rate of change of the gradient, which is 0.1%
for summit curves and 0.05% for sag curves.
 Setting a Vertical Curve
A vertical curve can be set by various methods, such as the tangent correction method
and the chord deflection method. The tangent correction method, which is considered
simpler than the other methods and is more convenient for the field staff.
It involves the following steps.
1. The length of the vertical curve is first calculated. The chainages and reduced levels
(RL) of the tangent points and apex are then worked out.
2. Tangent corrections are then computed with the help of the following equation:
where y is the vertical ordinate, x is the horizontal distance from the springing point,
g1 is gradient number 1 (positive for rising gradients), g2 is gradient number 2 (negative
for falling gradients), and n is the number of chords up to half the length of the curve.
3. The elevations of the stations on the curve are determined by algebraically adding the
tangent corrections on tangent OA.
Problem:
Calculate the length of the vertical curve between two gradients meeting in a summit,
one rising at a rate of 1 in 100 and the other falling at a rate of 1 in 200.
Solution
Gradient of the rising track (1 in 100) = 1% (+)
Gradient of the falling track (1 in 200) = 0.5% (–)
Change of gradient (a) = 1 – (–0.5) = 1 + 0.5% = + 1.5%

Rate of change of gradient (r) for summit curve = 0.1%
 New Method of Calculating Length of Vertical Curve
According to the new method, the length of a vertical curve is calculated as follows:
L = RQ
where
L is the length of the vertical curve,
R is the radius of the vertical curve
Q is the difference in the percentage of gradients (expressed in radians).
It is seen that the length of the vertical curve calculated as per the new practice is
relatively small compared to the length calculated using the old method. The length of the
vertical curve according to the new practice is considered very reasonable for the purpose
of laying the curve in the field, as can be seen from the next solved example.
Note that when the change in gradient (a) is positive it forms a summit and when it is
negative it forms a sag.
Problem:
A rising gradient of 1 in 100 meets a falling gradient of 1 in 200 on a group A route. The
intersection point has a chainage of 1000 m and its RL is 100 m. Calculate the length of
the vertical curve, and the RL and the chainage of the various points in order to set a
vertical curve at this location.

Points and Crossings
 Introduction
Points and crossings are provided to help transfer railway vehicles from one track to
another. The tracks may be parallel to, diverging from, or converging with each other.
Points and crossings are necessary because the wheels of railway vehicles are provided
with inside flanges and, therefore, they require this special arrangement in order to
navigate their way on the rails.
The points or switches aid in diverting the vehicles and the crossings provide gaps in
the rails so as to help the flanged wheels to roll over them. A complete set of points and
crossings, along with lead rails, is called a turnout.
 Important Terms
The following terms are often used in the design of points and crossings.

 Turnout
It is an arrangement of points and crossings with lead rails by means of which the rolling
stock may be diverted from one track to another.
Direction of a turnout
A turnout is designated as a right-hand or a left-hand turnout depending on whether it
diverts the traffic to the right or to the left.
The direction of a point (or turnout) is known as the facing direction if a vehicle
approaching the turnout or a point has to first face the thin end of the switch. The
direction is trailing direction if the vehicle has to negotiate a switch in the trailing
direction i.e., the vehicle first negotiates the crossing and then finally traverses on the
switch from its thick end to its thin end.
Therefore, when standing at the toe of a switch, if one looks in the direction of the
crossing, it is called the facing direction and the opposite direction is called the trailing
direction.
 Tongue rail
It is a tapered movable rail, made of high-carbon or -manganese steel to
withstand wear. At its thicker end, it is attached to a running rail. A tongue rail is also
called a switch rail.
 Stock rail
It is the running rail against which a tongue rail operates.
 Points or switch
A pair of tongue and stock rails with the necessary connections and fittings
forms a switch.
 Crossing
A crossing is a device introduced at the junction where two rails cross each
other to permit the wheel flange of a railway vehicle to pass from one track to another.
 Switches
A set of points or switches consists of the following main constituents.

a. A pair of stock rails, AB and CD, made of medium-manganese steel.
b. A pair of tongue rails, PQ and RS, also known as switch rails, made of medium-
manganese steel to withstand wear. The tongue rails are machined to a very thin
section to obtain a snug fit with the stock rail. The tapered end of the tongue rail is
called the toe and the thicker end is called the heel.
c. A pair of heel blocks which hold the heel of the tongue rails is held at the standard
clearance or distance from the stock rails.
d. A number of slide chairs to support the tongue rail and enable its movement towards
or away from the stock rail.
e. Two or more stretcher bars connecting both the tongue rails close to the toe, for the
purpose of holding them at a fixed distance from each other.
f. A gauge tie plate to fix gauges and ensure correct gauge at the points.
 Types of Switches
Switches are of two types, namely, stud switch and split switch.
In a stud type of switch, no separate tongue rail is provided and some portion of the
track is moved from one side to the other side. Stud switches are no more in use on
Indian Railways.
They have been replaced by split switches. These consist of a pair of stock rails and a
pair of tongue rails. Split switches may again be of two types—loose heel type and
fixed heel type. These are discussed below.
1. Loose heel type

In this type of split switch, the switch or tongue rail finishes at the heel of
the switch to enable movement of the free end of the tongue rail. The fish plates
holding the tongue rail may be straight or slightly bent. The tongue rail is
fastened to the stock rail with the help of a fishing fit block and four bolts. All
the fish bolts in the lead rail are tightened while those in the tongue rail are kept
loose or snug to allow free movement of the tongue. As the discontinuity of the
track at the heel is a weakness in the structure, the use of these switches is not
preferred.
2. Fixed heel type
In this type of split switch, the tongue rail does not end at the heel of the
switch but extends further and is rigidly connected. The movement at the toe of
the switch is made possible on account of the flexibility of the tongue rail.
 Toe of switches
The toe of the switches may be of the following types.
Undercut switch:
In this switch the foot of the stock rail is planned to accommodate the tongue rail (Fig.
14.3).
Fig. 14.3 Undercut switch
Overriding switch:
In this case, the stock rail occupies the full section and the tongue rail is planed
to a 6-mm (0.25") -thick edge, which overrides the foot of the stock rail (Fig. 14.4).

The switch rail is kept 6 mm (0.25") higher than the stock rail from the heel to the
point towards the toe where the planning starts. This is done to eliminate the possibility
of splitting caused by any false flange moving in the trailing direction. This design is
considered to be an economical and superior design due to the reasons given below.
(a) Since the stock rail is uncut, it is much stronger.
(b) Manufacturing work is confined only to the tongue rail, which is very economical.
(c) Although the tongue rail has a thin edge of only 6 mm (0.25"), it is supported by the
stock rail
for the entire weakened portion of its length. As such, the combined strength of the
rails
between the sleepers is greater than that of the tongue rail alone in the undercut
switch.
Overriding switches have been standardized on the Indian Railways.
 Important Terms Pertaining to Switches
The following terms are common when discussing the design of switches.
Switch angle:
This is the angle between the gauge face of the stock rail and that of the tongue rail at
the theoretical toe of the switch in its closed position. It is a function of the heel
divergence and the length of the tongue rail.
Flange way clearance:
This is the distance between the adjoining faces of the running rail and the check
rail/wing rail at the nose of the crossing. It is meant for providing a free passage to

wheel flanges. Table 14.2 gives the minimum and maximum values of flange way
clearance for BG and MG tracks.
Heel divergence
This is the distance between the gauge faces of the stock rail and the tongue rail
at the heel of the switch. It is made up of the flange way clearance and the width of the
tongue rail head that lies at the heel.
Throw of the switch
This is the distance through which the tongue rail moves laterally at the toe of
the switch to allow movement of the trains. Its limiting values are 95–115 mm for BG
routes and 89–100 mm for MG routes.
 Crossing
A crossing or frog is a device introduced at the point where two gauge faces cross
each other to permit the flanges of a railway vehicle to pass from one track to another. To
achieve this objective, a gap is provided from the throw to the nose of the crossing, over
which the flanged wheel glides or jumps.
In order to ensure that this flanged wheel negotiates the gap properly and does not
strike the nose, the other wheel is guided with the help of check rails.
A crossing consists of the following components, shown in Fig

a) Two rails, the point rail and splice rail, which are machined to form a nose. The point rail
ends at the nose, whereas the splice rail joins it a little behind the nose. Theoretically,
the point’s rail should end in a point and be made as thin as possible, but such a knife
edge of the point rail would break off under the movement of traffic. The point rail,
therefore, has its fine end slightly cut off to form a blunt nose, with a thickness of 6 mm
(1/4"). The toe of the blunt nose is called the actual nose of crossing (ANC) and the
theoretical point where gauge faces from both sides intersect is called the theoretical nose
of crossing (TNC). The ‘V’ rail is planed to a depth of 6 mm (1/4") at the nose and runs
out in 89 mm to stop a wheel running in the facing direction from hitting the nose.
b) Two wing rails consisting of a right-hand and a left-hand wing rail that converge to form
a throat and diverge again on either side of the nose. Wing rails are flared at the ends to
facilitate the entry and exit of the flanged wheel in the gap.
c) A pair of check rails to guide the wheel flanges and provide a path for them, thereby
preventing them from moving sideways, which would otherwise may result in the wheel
hitting the nose of the crossing as it moves in the facing direction.
 Types of Crossings

A crossing may be of the following types.
(a) An acute angle crossing or ‘V’ crossing in which the intersection of the two gauge
faces forms an acute angle. For example, when a right rail crosses a left rail, it makes an
acute crossing. Thus, unlike rail crossings form acute crossings (A and C of Fig. 15.9).
(b) An obtuse or diamond crossing in which the two gauge faces meet at an obtuse
angle. When a right or left rail crosses a similar rail, it makes an obtuse crossing (B and D
of Fig. 15.9).
(c) A square crossing in which two tracks cross at right angles. Such crossings are rarely
used in actual practice (Fig. 14.7).
For manufacturing purposes, crossings can also be classified as follows.
1. Built up crossing
In a built-up crossing, two wing rails and a V section consisting of splice and
point rails are assembled together by means of bolts and distance blocks to form a
crossing. This type of crossing is commonly used on Indian Railways. Such crossings
have the advantage that their initial cost is low and that repairs can be carried out
simply by welding or replacing each constituent separately.
A crossing becomes unserviceable when wear is more than 10 mm (3/8"). A
built-up crossing, however, lacks rigidity. The bolts require frequent checking and
sometimes break under fast and heavy traffic.
2. Cast steel crossing
This is a one-piece crossing with no bolts and, therefore, requiring very little
maintenance. Comparatively, it is a more rigid crossing since it consists of one
complete mass. The initial cost of such a crossing is, however, quite high and its repair
and maintenance pose a number of problems. Recently cast manganese steel (CMS)
crossings, which have longer life, have also been adopted.
3. Combined rail and cast crossing

This is a combination of a built-up and cast steel crossing and consists of a cast
steel nose finished to ordinary rail faces to form the two legs of the crossing. Though it
allows the welding of worn out wing rails, the nose is still liable to fracture suddenly.
4. CMS Crossing
Due to increase in traffic and the use of heavier axle loads, the ordinary built-up
crossings manufactured from medium-manganese rails are subjected to very heavy
wear and tear, specially in fast lines and suburban sections with electric traction. Past
experience has shown that the life of such crossings varies from 6 months to 2 years,
depending on their location and the service conditions. CMS crossings possess higher
strength, offer more resistance to wear, and consequently have a longer life. The
following are the main advantages of CMS crossings.
(a) Less wear and tear.
(b) Longer life: The average life of a CMS crossing is about four times more
than that of an ordinary built-up crossing.
CMS crossings are free from bolts as well as other components that normally
tend to get loose as a result of the movement of traffic.
These days CMS crossings are preferred on Indian Railways. Though their
initial cost is high, their maintenance cost is relatively less and they last longer.
However, special care must be taken in their laying and maintenance. Keeping this in
view, CMS crossings have been standardized on Indian Railways. On account of the
limited availability of CMS crossings in the country, their use has, however, been
restricted for the time being to group. A routes and those lines of other routes on
which traffic density is over 20 GMT. These should also be reserved for use on heavily
worked lines of all the groups in busy yards.
5. Spring or Movable Crossing
In a spring crossing, one wing rail is movable and is held against the V of the
crossing with a strong helical spring while the other wing rail is fixed (Fig. 14.8).When
a vehicle passes on the main track, the movable wing rail is snug with the crossing and
the vehicle does not need to negotiate any gap at the crossing. In case the vehicle has to
pass over a turnout track, the movable wing is forced out by the wheel flanges and the
vehicle has to negotiate a gap as in a normal turnout.
This type of crossing is useful when there is high-speed traffic on the main track
and slow-speed traffic on the turnout track.

Turnouts
The simplest arrangement of points and crossing can be found on a turnout taking off
from a straight track. There are two standard methods prevalent for designing a
turnout.
These are
(a) Cole’s method
(b) IRS method.
These methods are described in detail in the following sections.
The important terms used in describing the design of turnouts are defined as follows.
 Curve lead (CL)
This is the distance from the tangent point (T) to the theoretical nose of crossing
(TNC) measured along the length of the main track.
 Switch lead (SL)
This is the distance from the tangent point (T) to the heel of the switch (TL)
measured along the length of the main track.
 Lead of crossing (L)
This is the distance measured along the length of the main track as follows:
Lead of crossing (L) = curve lead (CL) – switch lead (SL)
 Gauge (G)
This is the gauge of the track.
 Heel divergence (D)
This is the distance between the main line and the turnout side at the heel.
 Angle of crossing (a )
This is the angle between the main line and the tangent of the turnout line.
 Radius of turnout (R)
This is the radius of the turnout. It may be clarified that the radius of the turnout
is equal to the radius of the centre line of the turnout (R1) plus half the gauge
width.
R = R1 + 0.5G
As the radius of a curve is quite large, for practical purposes, R may be taken to
be equal to R1.
 Special fittings with turnouts
Some of the special fittings required for use with turnouts are enumerated below.
o Distance blocks
Special types of distance blocks with fishing fit surfaces are provided at the nose
of the crossing to prevent any vertical movement between the wing rail and the nose of
the crossing.

 Flat bearing plates
As turnouts do not have any cant, flat bearing plates are provided under the
sleepers.
 Spherical washers
These are special types of washers and consist of two pieces with a spherical
point of contact between them. This permits the two surfaces to lie at any angle to
each other. These washers are used for connecting two surfaces that are not parallel
to one another. Normally, tapered washers are necessary for connecting such
surfaces. Spherical washers can adjust to the uneven bearings of the head or nut of a
bolt and so are used on all bolts in the heel and the distance blocks behind the heel
on the left-hand side of the track.
 Slide chairs
These are provided under tongue rails to allow them to move laterally. These are
different for ordinary switches and overriding switches.
 Grade off chairs
These are special chairs provided behind the heel of the switches to give a
suitable ramp to the tongue rail, which is raised by 6 mm at the heel.
 Gauge tie plates
These are provided over the sleepers directly under the toe of the switches, and
under the nose of the crossing to ensure proper gauge at these locations.
 Stretcher bars
These are provided to maintain the two tongue rails at an exact distance.
 Cole’s method
This is a method used for designing a turnout taking off from a straight track
(Fig. 14.11). The curvature begins from a point on the straight main track ahead of the
toe of the switch at the theoretical toe of switch (TTS) and ends at the theoretical nose
of crossing (TNC).
The heel of the switch is located at the point where the offset of the curve is
equal to the heel divergence. Theoretically, there would be no kinks in this layout, had
the tongue rail been curved as also the wing rail up to the TNC. Since tongue rails and
wing rails are not curved generally, there are the following three kinks in this layout.

(a) The first kink is formed at the actual toe of the switch.
(b) The second kink is formed at the heel of the switch.
(c) The third kink is formed at the first distance block of the crossing.

 IRS method
In this layout (Fig.), the curve begins from the heel of the switch and ends at the
toe of the crossing, which is at the centre of the first distance block. The crossing is
straight and no kink is experienced at this point. The only kink occurs at the toe of
the switch. This is the standard layout used on Indian Railways. The calculations
involved in this method are somewhat complicated and hence this method is used
only when precision is required.

 Types of Track Juctions:
1. Diamond Crossing
A diamond crossing is provided when two tracks of either the same gauge or of
different gauges cross each other. It consists of two acute crossings (A and C) and
two obtuse crossings (B and D).
A typical diamond crossing consisting of two tracks of the same gauge crossing
each other, is shown in the Fig. In the layout, ABCD is a rhombus with four equal
sides.
The length of the various constituents may be calculated as follows.
EB =DF =AE cot α =GN
AB= BC = G cosec α
Diagonal AC= G cosec α /2
Diagonal BD= sec α /2

It can be seen from the layout that the length of the gap at points B and D
increases as the angle of crossing decreases. Longer gaps increase the chances of
the wheels, particularly of a small diameter, being deflected to the wrong side of the
nose.
On Indian Railways, the flattest diamond crossing permitted for BG and MG
routes is 1 in 8.5. Along with diamond crossings, single or double slips may also be
provided to allow the vehicles to pass from one track to another.
2 Single Slip and Double Slip
In a diamond crossing, the tracks cross each other, but the trains from either
track cannot change track. Slips are provided to allow vehicles to change track. The
slip arrangement can be either single slip or double slip. In single slips, there are
two sets of joints, the vehicle from only one direction can change tracks.
In the single slip shown in Fig., the train on track A can change to track D,
whereas the train on track C remains on the same track, continuing onto track D.
In the case of double slips, there are four sets of points, and trains from both
directions can change tracks. In the double slip shown in Fig., the trains on both
tracks A and C can move onto either track B or D.

3. Scissors Crossover
A scissors crossover is meant for transferring a vehicle from one track to another
track and vice versa. It is provided where lack of space does not permit the
provision of two separate crossovers. It consists of four pairs of switches, six acute
crossings, two obtuse crossings, check rails, etc.
The scissors crossovers commonly used are of three types depending on the
distance between the two parallel tracks they join.
A brief description of these crossovers follows.
a. In the first type, the acute crossing of the diamond falls within the lead of the
main line turnout. In this case, the lead of the main line turnout is considerably
reduced and hence this is not a satisfactory arrangement.
b. In the second type, the acute crossing of the diamond falls opposite the crossing
of the main line turnout. Here, both the crossings lie opposite each other,
resulting in a simultaneous drop of the wheel and these results in jolting. This is
also not a desirable type of layout.
c. In the third type of scissors crossover, the acute crossing falls outside the lead of
the main crossing. Thus, the acute crossing of the diamond is far away from the
crossing of the main line track. This is the most satisfactory arrangement out of
these three layouts.
4. Gauntleted Track:
This is a temporary diversion provided on a double-line track to allow one of the
tracks to shift and pass through the other track. Both the tracks run together on the
same sleepers. It proves to be a useful connection when one side of a bridge on a

double-line section is required to be blocked for major repairs or rebuilding. The
specialty of this layout is that there are two crossings at the ends and no switches.
5. Triangle
A triangle (Fig. 15.16) is mostly provided in terminal yards for changing the
direction of an engine. Turntables are also used for this purpose, but are costly,
cumbersome, and present a lot of problems in maintenance. Normally, a triangle is
provided if enough land is available. A triangle consists of one symmetrical split at R
and two turnouts at P and Q along with lead rails, check rails, etc.

6. Double Junctions
A double junction (Fig. 15.17) is required when two or more main line tracks are
running and other tracks are branching off from these main line tracks in the same
direction. The layout of a double junction consists of ordinary turnouts with one or
more diamond crossings depending upon the number of parallel tracks.
Double junctions may occur either on straight or curved main lines and the branch
lines may also be either single or double lines. These types of junctions are quite
common in congested yards.

PROBLEMS ON SUPERELEVATION SPEED:

Unit 2 Geometric Design of railway .pdf

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Unit 2 Geometric Design of railway .pdf