6. Introduction to Railway Engineering.pdf

Transportation Planning and Engineering
Abhash Acharya | Introduction to Railway Engineering
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Introduction to Railway Engineering
- Abhash Acharya
M.Sc. In Transportation Engineering
acharyaabhash@gmail.com
www.abhashacharya.com.np

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Classification of railways
Components of the railway section
Geometric design of railway track
Design of track structure
Railway switches and crossings
Railway side tracks and yards

3
Railway Engineering
The branch of civil engineering which deals with the design, construction and maintenance of the railway tracks for safe and
efficient movements of trains.

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Advantages of Railway
• Handle heavier loads at higher speeds
• Lower operation costs
• High speed rails are much faster than roads
• Convenient for long haul distances
• Electric railways are very environment friendly
• Safe

5
Disadvantages of Railway
• Requires a large investment of capital
• High construction and maintenance cost
• Restricted to be in one direction
• Less suitable for hilly areas with curves
• Cannot provide door to door service as it is tied to a particular track
• Intermediate loading or unloading involves greater cost, more wear and tear and wastage of time
• Unsuitable and uneconomical for short distances and small traffic of goods

6
Rail Gauges
The gauge of a railway track is defined as the clear minimum perpendicular distance between the inner faces of the two rails.
Types of Rail Gauges
• Broad Gauge
• Standard Gauge
• Meter Gauge
• Narrow Gauge
• Mixed Gauge
Broad Gauge
1676 mm to 1524 mm, 1676 (India,
Pakistan, Srilanka, Brazil, Argentina)
1670 (Spain, Portugal), 1600 (Ireland),
1524 (Russia, Finland)
Standard Gauge/International/Normal
1435 mm and 1451 mm (England, USA, Canada, China, Turkey)
Meter Gauge
1067mm (Japan, Australia, New Zeland, South Africa, Indonesia),
1000mm (India, France, Argentina), 915mm (Ireland)
Narrow Gauge
762mm and 610mm
Mixed Gauge
1435mm (Standard) and 760mm (Narrow) – Czech
1435mm (Standard) and 1000mm (Meter) – Switzerland
1435mm (Standard) and 1067mm (Cape) - Japann

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Rail Gauge
Selection of Gauges
• Cost of Construction
• Marginal increase in cost of earthwork, rails, ballasts, sleepers and other track accessories
• Volume and nature of traffic
• Heavy and high speed – wider gauges are required
• Speed
• Depends on wheel and wheel diameter
• Development of area
• Narrow gauge to join underdeveloped area with developed area
• Topography
• Narrow gauge for hilly terrain due to sharp curve and steep gradient

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Rail Gauge
Problems caused by change of gauge
• Inconvenience to passengers (to change trains in the mid journey along with luggage)
• Difficult in trans-shipment of goods
• Inefficient use of rolling stocks
• Hindrance to fast movement of goods and passenger traffic
• Additional facilities at stations and yards
• Difficulties in balanced economic growth
• Difficulties in future gauge conversion projects

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Railway Components
• Rolling Stock
• Permanent Way (Track)
• Stations and Terminals
• Signaling and Control
• Depot and Workshop

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Rolling Stock
• Refers to any vehicles that move on a railway.
• Includes locomotives, coaches, wagons, metro cars, light rails/trams and train brakes
• Locomotives
• Powerhouse mounted on a frame that produces the power needed for traction on railways.
• Types of traction
• Steam traction by steam locomotives
• Diesel traction by diesel locomotives
• Electric traction by electric locomotives

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Rolling Stock
• Locomotives
• Parts of locomotives
• Fire box and boiler: Fuel is burnt in fire box and
steam is generated in the boiler.
• Proper engine: Heat consists of cylinders, pistons
and other various moving parts. Converts heat
energy of steam into mechanical energy of
motion.
• Framework: Mounted on wheels. It has a draw
bar which transmits the tractive force to the train.
• Tender: To store the fuel, a small bogie is
attached with the locomotives.

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Rolling Stock
• Coaches
• Compartments which provide accommodation to the passenger in trains are called coaches.
• Wagons
• Unpowered railway vehicles that are used for the transportation of cargo.
• Timber wagons
• Cattle wagons
• Oil wagons, petrol wagons
• Hoper wagons: ballast, minerals, coals
• Well wagons: bulky articles of excessive height
• Power wagons: for explosives and chemicals
• Refrigerated wagons: milk, fruits, meats and fishes

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Rolling Stock
• Train brakes
• Function of train brakes are to stop moving locomotives
• Types
• Hand brakes
• Steam brakes
• Continuous automatic brakes
• Hand and steam brakes

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Railway Components
The track or permanent way is the railroad on which train runs.

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Railway Components
Consists: Rails, Sleepers, Fasteners, Ballast as shown.

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Railway Components
Requirements of a good permanent way
• Correct and uniform gauge
• Proper level in straight portion and proper amount of super elevation in curves
• An uniform and gentle gradient
• Resilient and elastic
• Uniformly distributed load on both the rails
• Good lateral strength to maintain its stability
• Proper drainage facilities
• Easy replacement of various track components
• Low initial as well as maintenance cost

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Railway Components
• Rails
• Members of the track laid in two parallel lines to provide an
unchanging, continuous and level surface for movement of trains
• Steel girders for the purpose carrying axle loads.
• Rails are joined by welding and fish plates and bolts.
• Functions
• Provide hard, smooth and continuous surface.
• To give minimum wear surface.
• To bear stresses due to vertical load and transmit loads to the
sleepers.
• Serve as a lateral guide for the running of wheels.

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Railway Components
• Rails
• Requirement of Rails
• Proper composition of steel
• High vertical stiffness
• Withstand lateral force
• Sufficient deep head for an adequate margin of vertical wear
• Sufficiently thick web
• Wide enough foot to prevent overturning
• CG at mid height to equalize maximum tensile and compressive stresses

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Railway Components
• Rails
• Types of Rail Sections
• Double Headed Rails (D.H. Rails)
• Double Headed of a dumb-bell section
• The idea behind using of these rails was that when the
head was worn out in course of time, the rail can be
inverted or reused.

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Railway Components
• Rails
• Bull Headed Rails (B.H Rails)
• The head is made little thicker and stronger than the
lower part, by adding more metal to it, so that even
after wear, it can withstand stresses.

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Railway Components
• Rails
• Flat footed Rails (F.F Rails)
• It could be directly fixed into sleepers.
• It would eliminate the need for chairs and keys
required for the full headed rails.
• Demerits – Heavy train load cause the foot of rail to
sink into wooden sleeper.

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Railway Components
• Rails
• Details of standard rail sections
• 90R rails are suitable for annual traffic of about 10 gross million tonnes (GMT) speeds upto 100 kmph
and service life upto 20 to 25 years.
• 52MR (i.e. 52kg/m) rails are suitable for use of speed of 130 kmph and traffic density of 20 to 25 GMT.
• 60MR (i.e. 60kg/m) rails are suitable for use upto a speed of 160 kmph and traffic density of about 35
GMT.
Type Wt/m
(kg)
Area
(mm2)
90R 44.61 5795
52 MR 51.89 6615
60 MR 60.34 7686

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Railway Components
• Rails
• Length of Rails
• The most common length for BG rails is 13 m (42’8”) although double-length rails (26 m, 85’4”) are
seen in some places.
• MG rails are usually 12m (39’4”) in length.
• NG rails vary, but the commonest length is 9m (29’6”).
• Minimum rail length: should not be less than the distance between the two adjacent axles which has been
kept 3.6m in India

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Railway Components
• Rails
• Factors governing length of rails
• Manufacturing cost
• Transportation facility
• Lifting and handling operation
• Big expansion joints
• Weight of rails
• Maximum axle load = 560*sectional weight of rail kg per meter

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Railway Components
• Sleepers
• Transverse ties that are laid to support the rails.
• Rails are fixed to sleepers by different types of fixtures and fastenings.
• The typical length of a BG sleeper is 2.7m.
• Classification of sleepers
• Wooden sleepers
• Metal sleepers
• Concrete sleepers

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Railway Components
• Sleepers

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Railway Components
• Sleepers
• Functions of sleeper
• To hold the rails to correct gauge and alignment
• To act an elastic medium between the ballast and the rail
• To distribute load from the rail to the wider area
• To support rails at proper level in straight tracks, and at proper super elevation on curves
• Sleepers also provide longitudinal and lateral stability of the track

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Railway Components
• Sleepers
• Requirements of sleepers
• Initial and maintenance cost should be minimum
• Weight should be moderate (convenient for handling)
• Should be designed such that fixing and removing of rails are easy
• Should have sufficient bearing area
• Maintain and adjust the gauge properly
• Should not break or get damaged during packing
• Should be able to have track circuiting
• Should be capable of resisting vibrations and shocks caused by the moving trains

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Railway Components
• Sleepers
• Spacing of sleeper
• Sleeper density = Number of sleepers per unit rail length (per unit track length for welded rail).
• Factors affecting spacing
• Axle load and speed
• Type and section of rails
• Type and strength of sleepers
• Type of ballast and ballast cushion
• Nature of formation

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Railway Components
• Sleepers
• No. of sleepers per rail length = M + 7 (BG), where, M is the length of the rail in m.
• If the sleeper density is M+7 on a broad gauge route and the length of the rail is 13m, it means that 13+7
= 20 sleepers will be used per rail on that route.
• Spacing are closer near the joints.

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Railway Components
• Sleepers

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Railway Components
• Ballast
• Layer of broken stones, gravels, moorum or any other
gritty materials placed and packed below and around
sleepers.
• Functions of ballast
• Provide a hard and level bed for sleepers
• Hold sleepers in place during passage of trains
• Transfer and distribute load from sleepers to larger area
• Increase elasticity and resilience of the track for getting
good riding comfort
• Provide effective drainage and keep sleepers dry
• Prevent vegetation growth

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Railway Components
• Ballast
• Desirable properties of ballast
• Cubical with sharp edge
• Tough and wear resistant
• Durable and should not get pulverized or disintegrated
• Good bearing capacity and crushing value
• Good drainage property
• Non porous
• Weather resistant
• Low lifecycle cost

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Railway Components
• Ballast
• Ballast materials/Types of ballasts
• Broken stone – Best to be used as ballast. The size of the ballast is generally is 40 to 50 mm at points and
crossing 25 mm size may be used.
• Gravel ballast - Cheaper
• Cinder or coal ash – Used in yards or sidings or as the initial ballast in new construction. Harmful for
steel sleepers and fittings (corrosive action).
• Sand ballast – Coarse sand is cheap if available locally. Used primarily for cast iron pots. Is also used
with wooden and steel through sleepers in areas where traffic density is low. Causes excessive wear of
the rail top and the moving parts of the rolling stock.
• Moorum ballast – Decomposed laterite rocks. Used as the initial ballast in new construction.
• Brick ballast

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Railway Components
• Ballast
• Size of ballast materials
• Depends upon
• Type of sleepers
• Maintenance methods
• Location of the track
• For wooden sleepers - 51 mm
• For steel sleepers – 38 mm
• For under switches, points and crossings - 25.4 mm

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Railway Components
• Ballast
• Depth of ballast section
• The wheel load dispersion in the ballast is
assumed at 45o to the vertical.
• For uniform distribution of load on the
formation, ballast depth should be such
that the depression lines should not
overlap each other.
• Depth of ballast (Db) can be calculated by
Sleeper spacing (s) = Width of sleeper (w) + 2*depth of ballast

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Railway Components
• Ballast
• Depth of ballast section
• To provide lateral stability to the track, the width of the
ballast section should be sufficient.
• Should be extended by 30cm on BG track and 23cm on MG
track beyond the edge of sleepers.
• This ballast is known as shoulder ballast.
• Ballast under sleeper is known as ballast cushion.
• Ballast outside the sleeper is known as shoulder and in
between the sleeper is called crib ballast.

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Railway Components
• Ballast
• Test for ballast
• Abrasion test - <30%
• Aggregate impact test - <20%
• Flakiness index - <50%

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Railway Components
• Rail joints
• Weakest part of rail
• Rail joints are provided for expansion and
contraction due to variation in temperatures.
• Certain gap is provided at each joint.
• Rail joints hold the adjoining ends of the rails
in the correct position both in horizontal and
vertical planes.
• The joint cause severe blows to the passenger
due to moving of wheels over this gap.

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Railway Components
• Rail joints
• Types of rail joints
• According to the position of joints
• Square joints
• Staggered joints
• According to the position of sleepers
• Suspended joints
• Supported joints
• Bridge joints

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Railway Components
• Rail joints
• Square joints
• Joint in one rail is exactly opposite to the joint in the other parallel rail.
• Common in straight tracks.

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Railway Components
• Rail joints
• Staggered joints
• Joint in one rail is exactly opposite to the center of the other parallel rail.
• Usually used in curves.
• Gives smoother running to the track.

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Railway Components
• Rail joints
• Suspended joints
• The rail joint placed at the centre of two consecutive sleepers.
• The load is evenly distributed on two sleepers.
• When joint is depressed both rails are pressed down evenly.

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Railway Components
• Rail joints
• Supported joints
• The sleeper is placed exactly below the rail joint.
• Do not give sufficient support with heavy axle loads.

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Railway Components
• Rail joints
• Bridge joints
• Similar to suspended joint, but a metal serves as a bridge to connect the ends of two rails.
• Bridge is placed at the bottom of rails and it rests on two sleepers.

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Railway Components
• Fittings and Fastenings
• Hold the rails in their proper position in order to ensure the smooth running of trains.
• Functions of fittings and fastenings
• Join rails together as well as fixing them to the sleepers.
• Maintain the level, alignment and gauge of the railway track within permissible limits even during the
passage of trains.

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Railway Components
• Rail to rail fastenings
• Rail to rail fastening involves the use of fish plates
and bolts for joining rails in series.
• Fish plates
• Railway fish plate is a pair of metal bar bolted to
the ends of two rails to join them together.
• Four or six suits of fish bolt per pair of fish plates.
• Function of fish plates
• Used in rail joints to maintain the continuity of the
rails and to allow expansion and contraction.

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Railway Components
• Fish bolts
• Made up of medium or high carbon steel used to
hold fish plate together.
• Gets loose by the traffic variations and require
tightening from time to time.

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Railway Components
• Spikes
• Large nail with an offset head that is used to secure rails and base plates to sleepers in railroad ties in the
track.
• Requirements of spikes
• Strong
• Enough resistance against motion
• Deep for better holding power
• Easy in fixing and removal from the sleepers
• Cheap in cost
• Capable of maintaining the gauge

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Railway Components
• Bolts
• Form of threaded fastener used for fixing various track components in position.

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Railway Components
• Chairs
• Device to hold bull headed rails and double headed rails in position.
• Helps in distributing the load from the rails to the sleepers.
• Made up of cast iron and consists of two jaws and a rail seat.
• The web of the rail is held tightly against the inner jaws on the chair and a key is driven between the rail
and the outer jaw of the chair.
• The chairs are fixed with the sleepers by means of spikes.
• The shape of chairs depend upon the types of rails used.

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Railway Components
• Chairs

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Railway Components
• Blocks
• When two rails run very close as in case of check rails, etc. small blocks are inserted between the two
rails and bolted to maintain the required distance.

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Railway Components
• Keys
• Wedge shaped timber or steel pieces to fix
rails to chairs on the metal sleepers.
• Wooden keys are small straight or
tapered pieces of timber.
• Metal keys are much more durable
than wooden keys.

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Railway Components
• Bearing plates
• Rectangular plates of mild steel or cast iron used below F.F. rails to distribute the load on a larger area of
timber sleeper.
• Advantages
• To distribute the load coming on rails to the sleepers
• To prevent the destruction of the sleeper

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Railway Components
• Elastic fastening
• Due to shocks and vibrations caused by moving loads, the conventional rigid fastenings get loose.
• Elastic fastening could safeguard track parameters and dampen the vibrations against shock and
vibrations.

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Railway Components
• Subgrade and formation
• Naturally occurring soil which is prepared to receive the ballast.
• The prepared flat surface, which is ready to receive the ballast, sleepers, and rails, is called the formation.
• Functions
• To provide a smooth and uniform bed for laying the track.
• To bear the load transmitted to it from the moving load through the ballast.
• To facilitate drainage.
• To provide stability to the track.

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Railway Components
• Subgrade and formation

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Materials requirement per km of railway track
• No. of rails per km length = 1000*2 rail length
• For BG track 60 kg rail and 13m length of rail recommended
• No. of rails per km length = (2*1000)/13 = 154
• Weight of rail per km length = 154*13*60 = 120120 kg
• No. of sleepers per km length = (No. of rails per km)/2*(sleeper density)
• On BG track, sleeper density = 13+7 = 20
• No. of sleepers per km track = (154/2)*20 = 1540 nos.
• No. of fish plates per one km of track length = No. of rails per km * 2 = 154*2 = 308 nos.
• No. of fish bolts = 4*No. of rails per km = 4*154 = 616 nos.
• No. of bearing plates = 2*No. of sleepers per km length = 2*1540 = 3080 nos.
• No. of labors required to lay one km of track (with 8 hour shift) = Total tonnage + 20%

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Points and Crossings

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• Points and crossings are provided to help transfer railway vehicles from one track to another.
• A complete set of points and crossings, along with lead rails is called a turnout.
• 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 turnout – Designated as a right-hand or a left-hand turnout depending on whether it diverts the traffic
to the right or to the left.
• Tongue rail – 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 – Running rail against which a tongue rail operates.

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• Points and crossings are provided to help transfer railway vehicles from one track to another.
• Points and crossings are necessary because the wheels or 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.

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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 turnout – Designated as a right-hand or a left-hand turnout depending on whether it diverts the traffic
to the right or to the left.
• Tongue rail – 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 – Running rail against which a tongue rail operates.

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Turnout
Ds is the degree of the outer rail of the turnout curve from the straight track, Dm is the degree of the rail of the main track on
which the crossing lies, i.e. the inner rail, Dt is the degree of the rail of the turnout curve on which the crossing lies, i.e. outer
rail, Rs is the radius of the outer rail of the turnout curve from the straight track and Rt is the radius of the rail of the turnout
curve on which the crossing lies, i.e. the outer rail.

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Turnout
• Components
• A pair of tongue rails
• A pair of stock rails
• Two check rails
• Four lead rails
• A vee crossing
• Slide chairs
• Stretcher bar
• A pair of heel blocks
• Switch tie plate or gauge tie chair
• Parts for operating points – Rods, cranks, levers, etc.
• Locking system which includes locking box, lock bar,
plunger bar, etc.

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Turnout

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Points or Switch
A pair of tongue and stock rails with necessary connections and fittings
form a switch
• A pair of stock rails, AB and CD
• A pair of tongue rails (switch rails), PQ and RS.
• The tongue rails are machined to a very thin section
to obtain a snug fit with the stock rail.
• A pair of heel bocks which hold the heel of the
tongue rails.
• A number of slide chairs to support the tongue rail
and enable its movement towards or away from the
stock rail.
• Two or more stretcher bars connecting both the
tongue rail close to the toe, for the purpose of
holding them at a fixed distance from each other.
• A gauge tie plate to fix gauges and ensure correct
gauge at the points.

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Crossings/Frog
• 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.

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Crossings
• Requirements
• Crossing assembly should be rigid enough to withstand severe vibrations
• Wing rails and nose of crossing should be able to resist heavy wear due to movement of wheels
• The nose of crossing should have adequate thickness to take all stresses acting on the crossing
• Components
• A Vee piece
• A point rail
• A splice rail
• Two check rails
• Two wing rails
• Heel blocks at throat, nose and heel of crossing
• Chairs at crossing, at toe and at heel

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Crossings
• Types of crossings
• On the basis of shape of crossing
• Square crossing
• Acute angle or V-crossing or frog
• Obtuse angle or diamond crossing
• On the basis of assembly of crossing
• Ramped crossing
• Spring or movable crossing

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Crossings

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Crossings

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Crossings

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Station and Yards

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Station
• Railway facility where trains regularly stop to load or unload passengers and/or freight.
• Factors to be considered while selecting site for railway stations
• Adequate land
• Level area with good drainage
• Straight alignment
• Easy accessibility
• Adequate water supply

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Station
• Functions of railway stations
• To entrain or detrain passengers
• For load or unload goods or parcels
• To enable the trains on a single line track to cross from opposite directions
• To enable the following express trains to overtake
• For fueling
• For detaching or attaching of compartment and wagons
• For detaching engines
• For repairing engines and changing their directions
• To enable sorting out of wagons to form new trains
• To provide facilities and give shelter to passengers in the case of emergencies such as floods and accidents,
which disrupt traffic.

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Station
• Types of stations
• Wayside stations
• Junction stations
• Terminal stations
• Made for crossing or for overtaking trains
• Halt stations
• Flag stations
• Crossing stations

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Station
• Halt stations
• Simplest station
• Usually unstaffed and with few or no facilities
• Has only a rail level platform with a name board at either end
• Small waiting shed may also be provided that serves as a booking office
• Trains stop only on request. Some selected trains are allotted a stoppage time to enable passengers to
board or alight.
• Booking of passengers is done by travelling ticket examiners or booking clerks.

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Station
• Flag stations
• Stopping point at which trains stop only if there are
passengers to be picked up or dropped off.
• These stations do not have overtaking or crossing facilities
and arrangements to control the movement of trains.
• However, these stations have buildings, staff and telegraph
facilities.
• Some of the flag stations have sidings also in the form of
loops.

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Station
• Provided with facilities for crossing
• At least one loop line is provided to
allow another train if one track is
already occupied by a waiting train
• Generally, the train to be stopped is
taken on the loop line and the
through train is allowed to pass on
the main line

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Station

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Station
• Junction station
• Meeting point of three or more lines emerging from different directions.
• Following arrangements are necessary
• Facilities for the interchange of traffic between main and branch line
• Facilities for repair and cleaning of the compartments
• Facilities of goods siding engine sheds, turn table, etc.

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Station
• Junction station

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Station
• Terminal station
• Station at which a railway line or one of its
branches terminates
• Facilities required at terminal stations are
• Watering, coaling, cleaning, servicing the
engine
• Turn table for the change of direction of the
engine
• Facilities for dealing goods traffic as
marshalling yard, engine sheds, sidings, etc.
• Circulating area, ticket office, restaurant, etc.

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Station
• General Requirements of Railway Stations
• Public requirements
• Booking office
• Platform
• Drinking water
• Refreshment room
• Sanitary arrangement
• Enquiry office
• Station name board
• Waiting rooms
• Lighting arrangements
• Public telephone
• Traffic requirements
• Machines for dating tickets
• Weighing machine
• Controlling and recording
the movement of trains
• Siding to cross or overtake
trains
• Sidings for good traffic
• Platform for loading,
unloading and storing of
goods
• Locomotive requirements
• Water column
• Fuel storage and supply
• Cleaning and examining of
locomotives
• Inspection of vehicles and
locomotives
• Turntable
• General
• Suitable roads to station
• Clock for accurate time
• Availability of coolies

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Platform (passenger and goods platform)
• Passenger platform
• Place from where the passengers to entrain or
detrain.
• Loading space.
• Length of platform for all gauges should not be
less than 180m.
• Generally about 305m length of a BG railway
platform is desirable.
• The edge of the platform from center of the
nearest track is kept 1.7m away for BG, 1.39m for
MG and 1.2 for NG.

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• Essentials of passenger platform
• Minimum length should not be less than 180m.
• Minimum width should not be less than 3.67m and should be paved fully.
• Platform should be covered atleast for the length of 60m.
• End of high level platform should be in the form of ramp with slope of 1:6.
• Adequate lighting should be arranged for night.
• Adequate drinking water.
• The slope in its width should be 1 in 30.
• The top width of masonry wall should be about 46cm.

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• Essentials of passenger platform
• There is different level (height) of platforms
• Rail level platform
• The height of such platform is equal to the height of the rail.
• Low level platform
• The height of such platform should be kept about 45 cm above rail level.
• High level platform
• The height is kept about 76 to 85 cm above the rail level.

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• Goods platform
• To facilitate the goods handling, generally height of goods platform is kept up to the floor level of the
wagon.
• Essentials of good platform
• Weighing arrangement
• Goods shed
• Proper drainage facility
• Facility for direct access from goods platform to goods sidings and to marshalling yards

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Yard
• System of tracks laid out to deal with the passenger as well as goods traffic being handled by the railways.
• Types
• Passenger yards
• Goods yards
• Marshalling yards
• Locomotive yards

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Yard
• Passenger yards
• To provide all the facilities for the safe movement of passengers.
• Facilities in passenger yards
• Booking office, enquiry office, luggage booking room, cloak room and waiting room for passengers
• Parking space for vehicles
• Signals for reception and dispatch of trains
• Platforms and sidings for shunting facilities
• Facilities for changing batteries
• Facilities for passing a through train
• Washing lines, sick lines facilities

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Yard
• Goods yards
• For loading or unloading of goods from ships or road vehicles and/or where goods wagons are transferred to
local sidings
• Requirements of goods yard
• Approach road
• Loop lines
• Loading and unloading platforms
• Space for good sorting
• Car weighing machine
• Cranes for very heavy goods
• Booking office

93
Yard
• Space where goods wagons received from different centers are sorted out and placed in order to be detached
at different stations
• Distribution centers
• Empty wagons are also kept in marshalling yards
• Functions include – Reception of trains, sorting of trains, departure off trains
• Design consideration for marshalling yards
• Shunting operations should not be distributed by the regular trains
• Marshalling yard should be kept parallel to the running lines
• Movement of trains in only one direction is desirable
• Repair facilities

94
Yard

95
Yard
• Locomotive yards
• Houses the locomotives for various facilities such as watering, fueling, cleaning, repairing, servicing, etc.
• Following facilities must be provided
• Sufficient, number of tracks, engine shed, inspection, repair shed, turn table
• Should be situated near the passenger and goods yards
• Water column
• Hydraulic jack
• Overhead tank

96
Loops and sidings
• Loops
• When a branch line from a main line meets or terminates
at the same main line, this arrangement is called as loops.
• Can be subdivided into three groups
• Split turn out
• Not suitable for fast through trains
• Trailing turn out
• Fast through train has to reduce speed slightly
while crossing over a reverse curve
• Straight and loop
• For the fast through trains it is suitable as there
is no need reducing speed

97
Loops and sidings
• Sidings
• When a branch line from a main line or a loop line
terminates at a dead end with buffer stop, is called sidings.
• Function of siding is to improve temporary storage of
wagons.
• Four type of sidings.
• Trap sidings
• Shunting sidings
• Catch sidings
• Private and assisted sidings

98
Staff quarters
• Residential quarters for the staff
• The minimum clear distance from the center of the existing track to the boundary of quarters should be 8 meters
• The proposed site should not interfere with the future expansion of the station and should be provided in three
years.

99
Signaling
• Railway signaling is a system used to control railway traffic safely, essentially to prevent trains from colliding.
• Signaling consists of the systems, device and means by which trains are operated efficiently and tracks are used to
maximum extent, maintaining the safety of the passengers, the staff and the rolling stock.
• It includes the use and working of signals, points, block instruments and other equipment.

100
Depots and Workshops
• A depot offer both equipment for the maintenance of rolling stock (cleaning, daily maintenance, current
maintenance, schedule maintenance, corrective maintenance, etc.) and the maintenance of the infrastructure and
systems.
• Depot facilities consists
• Workshops and the storage of tools and equipment required
• Storage space for the vehicles used for maintenance
• Space for the maintenance of these vehicle

101
Geometric Design

102
Geometric Design
• Includes all those parameters which determine or affect the geometric of the track.
Necessity for Geometric Design
• To ensure the smooth and safe running of trains
• To achieve maximum speeds
• To carry heavy axle loads
• To avoid accidents and derailments due to a defective permanent way
• To ensure that the track requires less maintenance
• For good aesthetics

103
Gradients
• Provided to negotiate the rise or fall in the level of the railway
track.
• Gradient is normally represented by the distance travelled for a rise
or fall of one unit.
• Gradients are provided to meet the following objectives
• To reach various stations at different elevations
• To follow the natural contours of the ground to the extent
possible
• To reduce the cost of earthwork

104
Gradients
• Factors affecting the selection of gradient
• Nature of the ground
• Safety requirements
• Drainage requirements
• Total height to be covered
• Hauling capacity of railway engines
• Types of Gradient
• Ruling gradient
• Momentum gradient
• Pusher gradient
• Station yard gradient

105
Gradients
• Types of gradient
• Ruling gradient
• Steepest gradient that exists in a section
• Determines the maximum load that can be hauled by locomotive on that section
• Power of locomotive plays an important role in taking the decision
• 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 = Wsin𝜃 = Wtan𝜃 = W*gradient
In plain terrain: 1 in 150 to 1 in 250
In hilly terrain: 1 in 100 to 1 in 150
* All other gradients provided in that section should be flatter than the ruling gradient after making due
compensation for curvature.

106
Gradients
• Momentum gradient
• 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 acquire good speed and momentum, which gives additional kinetic
energy to he train and allows it to negotiate gradients steeper than the ruling gradient.

107
Gradients
• Pusher gradient/Helper gradient
• 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 is
required to pull the entire load, and an extra locomotive 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

108
Gradients
• Gradients in station yards
• Gradients in station yards are quite flat due to the following reasons
• To prevent standing vehicles from rolling and moving away from the yard due to the combined
effect of gravity and strong winds
• To reduce the additional resistive forces required to start a locomotive to the extent possible
• The maximum gradient prescribed in station yards on Indian Railway is 1 in 400, while the
recommended gradient is 1 in 1000.

109
Gradients
• 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
• On BG tracks, 0.04% per degree of the curve or 70/R, whichever is minimum
• On MG tracks, 0.03% per degree of curve or 52.5/R, whichever is minimum
• On NG tracks, 0.02% per degree of curve or 35/R, whichever is minimum
where, R is the radius of the curve in meters.
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.

110
Gradients [Numerical]
Find the steepest gradient on a 2o curve for a BG line with a ruling gradient of 1 in 200.
Ruling gradient = 1 in 200 = 0.5%
Compensation for a 2o curve = 0.04*2 = 0.085
Compensated gradient = 0.5 – 0.08 = 0.42% = 1 in 238
The steepest gradient on the curved track is 1 in 238

111
Horizontal curves
• Provided when a change in the direction of the track is required
• Defined either by its radius or by its degree
• Degree of the curve is defined as the angle subtended at the center of curve by a chord of 100 ft length
D = 5730/R (when R is in feet)
D = 1750/R (when R is in metres)
• Elements of curve

112
Horizontal curves
• Maximum degree of a curve
• Maximum permissible degree of a curve on a track depends on various factors as gauge, wheel base of the
vehicle, maximum permissible super elevation, etc.
• The maximum degree or the minimum radius of the curve permitted on Indian Railways for various
gauges is given below:

113
Horizontal curves
• Superelevation on curves (cant)
• Difference in height difference between the outer and the inner rail on a curve
• 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 gradient rail
• Function includes
• To ensure a better distribution of load on both rails
• To reduce the wear and tear of the rails and rolling stock
• To neutralize the effect of lateral forces
• To provide comfort to passengers

114
Horizontal curves
• Equilibrium speed
• Speed at which the effect of centrifugal force is exactly balanced by the super elevation provided.
• Maximum permissible speed
• The highest speed which may be allowed or permitted on a curved track taking into consideration of the
radius of curvature, actual cant, cant deficiency, cant excess and the length of the transition curve
• When the maximum permissible speed on the curve is less than the maximum sanctioned speed of the
section of the line, permanent speed restriction become necessary on such curves

115
Horizontal curves
• Cant deficiency (Cd)
• Occurs when a train travels around a curve at a speed higher
• It is the difference between the theoretical cant required for such high speeds and the actual cant provided
• 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 with the theoretical cant required for such a low
speed
• Cant gradient and cant deficiency gradient
• 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 1mm is attained or lost in every 1000
mm of transition length

116
Horizontal curves
• Rate of change of cant or cant deficiency
• Rate at which cant deficiency increases while passing over the transition curve
• A rate of 35mm per second means that a vehicle will experience a change in cant or a cant deficiency of
35mm in each second of travel over the transition when travelling at the maximum permissible speed

117
Horizontal curves
• 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.
• Vehicle is subjected to constant radial acceleration g =
𝑉2
𝑅
• Where, V is the velocity (meter per second), R is the radius of curve (meters).
• The radial acceleration produces a centrifugal force which acts in a radial direction away from the center.
• The value of the centrifugal force is given by
• Force = mass * acceleration
• F = m *
𝑉2
𝑅

118
Horizontal curves
• Centrifugal force on a curved track
• 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.

119
Horizontal curves
• Equilibrium Superelevation
• If 𝜃 is the angle that the inclined plane makes with the horizontal line, then, Tan
𝜃 =
𝑆𝑢𝑝𝑒𝑟𝑒𝑙𝑒𝑣𝑎𝑡𝑖𝑜𝑛
𝑔𝑎𝑢𝑔𝑒
=
𝑒
𝐺
Also, Tan 𝜃 =
𝐶𝑒𝑛𝑡𝑟𝑖𝑓𝑢𝑔𝑎𝑙 𝑓𝑜𝑟𝑐𝑒
𝑊𝑒𝑖𝑔ℎ𝑡
=
𝐹
𝑊
We have,
𝑒
𝐺
=
𝐹
𝑊
→ e = F *
𝐺
𝑊
→ e =
𝑊
𝑔
*
𝑉2
𝑅
*
𝐺
𝑊
=
𝐺𝑉2
𝑔𝑅
Where, e is the equilibrium superelevation, G is the gauge, V is the velocity,
R is the radius.
e =
𝐺𝑉2
127𝑅
, where e is in mm, V is in kmph, R is in m, G is dynamic gauge in
mm which is equal to the sum of the gauge and width of the rail head in mm.
(1750 mm for BG, 1058 mm for MG, 772 mm for NG)

120
Horizontal curves
• Thumb Rules for Calculating Superelevation in the field
• Superelevation for BG in cm = (
𝑠𝑝𝑒𝑒𝑑 𝑖𝑛 𝑘𝑚𝑝ℎ
10
)2
*
𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑐𝑢𝑟𝑣𝑒
13
• For MG tracks, the value of superelevation is taken as three-fifths of the value calculated using the preceding formula.
• The equilibrium speed is used in this formula.

121
Horizontal curves
• Equilibrium speed for providing superelevation
• The amount of superelevation depends not only on the maximum speed of the fastest train but also on the average
speed of the goods traffic moving on that section.
• A compromise has to be achieved by providing superelevation in a way that fast trains run smoothly without
causing any discomfort to the passengers and slow trains run safely without fear of derailment due to excessive
superelevation.
• The equilibrium speed to be provided should be decided taking into consideration of the following factors
• The maximum permissible speed which can actually be achieved both by fast trains and by goods train.
• Permanent and temporary speed restriction.
• Number of stoppage.
• Gradients
• Combination of both slow and fast trains.

122
Horizontal curves
• Equilibrium speed for providing superelevation
• The amount of superelevation to be provided is calculated as
e =
𝐺𝑉2
127𝑅
=
13.7 𝑉2
𝑅
(for BG)
e =
8.33 𝑉2
𝑅
(for MG)
Where, e is the superelevation in mm
V is the speed in kmph
G is the dynamic gauge
R is the radius of the curve in meteres

123
Horizontal curves
• Maximum Value of Superelevation
• Maximum value of the superelevation generally adopted is 1/10th to 1/12th of the gauge.

124
Horizontal curves
• Cant deficiency and cant excess
• Difference between the equilibrium cant that is necessary for the maximum permissible speed on a curve
and the actual cant provided.
• Limited due to two considerations
• Higher cant deficiency causes greater discomfort to passengers and
• 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

125
Horizontal curves
• Cant deficiency and cant excess
• Maximum value of cant deficiency prescribed for Indian Railways is shown as
• Limiting values of cant excess have also been prescribed.
• Cant excess should not be more than 75mm on BG and 65mm on MG for all types of rolling stock.

126
Horizontal curves
• Negative superelevation
• 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.

127
Horizontal curves
• Negative superelevation
• The provision of negative superelevation for the branch line and the reduction in speed over the main line can be
calculated as:
• The equilibrium superelevation for the branch line curve is first calculated as e =
𝐺𝑉2
127𝑅
• The equilibrium superelevation e is reduced by the permissible cant deficiency Cd and the resultant superelevation to
be provided is x = e – Cd
where, x is the superelevation, e is the equilibrium superelevation, and Cd is 75mm for BG and 50 mm for MG.
the value of Cd is generally higher than that of e, therefore x is normally negative. Thus, the branch line has a
negative superelevation of x.
• The maximum permissible speed on the main line, which has a superelevation 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.

128
Horizontal curves
• Safe speed on curves
• Speed which protects a carriage from the danger of overturning and derailment and provides a certain
margin of safety.
• For BG and MG
• Transitioned curves
V = 4.4 𝑅 − 70
Where, V is the speed in kmph and R is the radius in meters
• Non-transitioned curves
Safe speed = Four-fifths of the speed calculated for transitioned curves

129
Horizontal curves
• Speed which protects a carriage from the danger of overturning and derailment and provides a certain
margin of safety.
• For NG
• Transitioned curves
V = 3.65 𝑅 − 6 subject to a maximum of 50 kmph
• Non-transitioned curves
V = 2.92 𝑅 − 6 subject to a maximum of 40 kmph
• For high speeds
V = 4.58 𝑅
Note: Indian Railways no longer follows this concept of safe speed on curves.

130
Horizontal curves
• Maximum permissible speed considering superelevation (Rational formula)
• On BG
where, Ca is the actual cant provided in mm
Cd is the cant deficiency permitted in mm
R is the radius in m
V is the maximum speed in kmph
• On MG
• On NG

131
Horizontal curves
• Maximum permissible speed considering superelevation
• Minimum value of speed calculated from the following consideration
• Maximum sanctioned speed of the section – Maximum permissible speed authorized by the
commissioner of rail safety.
• Maximum speed of section taking into account the superelevation and cant deficiency (Use of
rational formula)
• Speed corresponding to the length of transition curve

132
Horizontal curves
• Maximum permissible speed considering superelevation
• Minimum value of speed calculated from the following consideration

133
Horizontal curves - Superelevation on curves (cant) [Numerical]
Calculate the superelevation and the maximum permissible speed for a 2o BG transitioned curved on a high-speed route with a
maximum sanctioned speed of 110 kmph. The speed for calculating the equilibrium superelevation as decided by the chief
engineer is 80 kmph and the booked speed of goods trains is 50 kmph.
1. Calculation of radius
R = 1750 / D = 1750 / 2 = 875 m
2. Superelevation for equilibrium speed
e =
𝐺𝑉2
127𝑅
, G = 1750mm (BG rail)
e =
1750∗802
127∗875
= 100.80mm
3. Superelevation for maximum speed
e = 190.60 mm (V=110kmph)
Cant deficiency = 190.6–100.8 = 89.8mm < 100mm (OK)
4. Superelevation for goods trains
e = 39.4mm (V=50kmph)
Cant excess = 100.8-39.4 = 61.4mm → 61.4 mm < 75mm (OK)
Maximum speed potential or safe speed of the curve based on theoretical
consideration
V = 0.27 𝐶𝑎 + 𝐶𝑑 ∗ 𝑅 where, Ca = 100.80mm, Cd = 89.8mm, R = 875 m
V = 110.1 kmph
6. Maximum permissible speed = Min(Maximum sanctioned speed, safe speed)
Maximum permissible speed = 110kmph and e = 100.80 mm

134
Horizontal curves - Superelevation on curves (cant) [Numerical] – Simplified Method
Step 1: Calculate the cant for the maximum sanctioned speed of the section, say, 110kmph, using the standard formula
C = GV2/127R. This is C110.
Step 2: Calculate the cant using the same standard formula as for the slowest traffic, i.e., for a goods train which may be
running at, say, 50kmph. This is C50. To this, add cant excess. This becomes C50 + Ce.
Step 3: Calculate the cant for equilibrium speed (if decided) using the same standard formula. Let it be 80kmph. This
value is C80.
Step 4: Adopt the lowest of the three values obtained from the preceding steps and that becomes the permissible cant (Ca).
The three values are C110, C50 + Ce and C80.
Step 5: Taking this cant value (Ca), add the cant deficiency and find the maximum permissible speed using the formula.

135
Step 1: Calculate the cant for the maximum sanctioned speed of the section, say, 110kmph, using the standard formula
C = GV2/127R. This is C110.
C110 =
𝐺𝑉2
127𝑅
=
1750∗1102
127∗875
= 190.6 mm
Step 2: Calculate the cant using the same standard formula as for the slowest traffic, i.e., for a goods train which may be
running at, say, 50kmph. This is C50. To this, add cant excess. This becomes C50 + Ce.
C50 =
1750 ∗50 ∗ 50
127∗875
= 39.4 mm
On adding cant excess, C50 + Ce = 114.4 mm
Step 3: Calculate the cant for equilibrium speed (if decided) using the same standard formula. Let it be 80kmph. This
value is C80.
C80 =
1750∗80∗80
127∗875
= 100.8 mm

136
Step 4: Adopt the lowest of the three values obtained from the preceding steps and that becomes the permissible cant (Ca).
The three values are C110, C50 + Ce and C80.
Ca = 100.80 mm
Step 5: Taking this cant value (Ca), add the cant deficiency and find the maximum permissible speed using the formula.
V = 0.27 𝐶𝑎 + 𝐶𝑑 ∗ 𝑅
V = 0.27 100.80 + 75 ∗ 875
V = 110.10 kmph

137
Calculate the superelevation, maximum permissible speed, and transition length for a 3o curve on a high-speed BG
section with a maximum sanctioned speed of 110 kmph. Assume the equilibrium speed to be 80kmph and the booked
speed of the goods train to be 50kmph.

138
Calculate the maximum permissible speed on a curve of a high speed BG group A route having the following particulars:
degree of the curve = 1o, superelevation = 80mm, length of transition curve = 120m, maximum speed likely to be
sanctioned for the section = 160kmph.
R = 1750 / D = 1750 / 1 = 1750 m
2. Safe speed over the curve as per theoretical consideration
V = 0.27 𝐶𝑎 + 𝐶𝑑 ∗ 𝑅 where, Cd = 100 mm (assumed),
Ca = 80mm, R = 1750 m
V = 151.3 kmph
3. Speed based on transition length
a) Rate of gain of cant
Vm = 198L/E = 198*120/80 = 297 kmph
b) Rate of gain of cant deficiency
Vm = 198L/Cd = 198*120/100 = 237.6kmph
c) Cant gradient = 1 in
120∗1000
80
= 1 in 1500 (not steeper than 1 in 720)
4. Maximum permissible speed = Min(Maximum sanctioned speed, safe speed based on theoretical consideration, speed based on
transition length) = 150kmph

139
A BG branch line track takes off as a contrary flexure through a 1 in 12 turnout from a main line track of a 3o curvature.
Due to the turnout, the maximum permissible speed on the branch line is 30kmph. Calculate the negative superelevation
to be provided on thee branch line track and the maximum permissible speed on the main line track.
1. Degree of curve of branch track = Turnout ± Degree of main curve (+ve for similar, -ve for contrary flexure) = 4o – 3o = 1o
Radius = 1750/D = 1750m
e = GV2/127R = 1750*30*30/127*1750 = 7.08 mm
After rounding it off to a higher multiple of 5, it is taken as 10 mm.
2. The value of negative superelevation for a branch line track: x = e – Cd = 10 – 75 = 65 mm (negative)
3. The superelevation to be provided on the main line track is 65 mm, which is the same as the superelevation of the branch line but in
opposite direction. Now, taking e = x + Cd = 65 + 75 = 140mm. Calculating R for main track = 1750/3 = 583.33m
4. V =
127∗583.3∗140
1750
= 76.98kmph and now Alternatively, V = 0.27 𝐶𝑎 + 𝐶𝑑 ∗ 𝑅 = 0.27 65 + 75 ∗ 583.3 = 77.15kmph
Take V = 75kmph

140
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 curves so that the centrifugal force is built up gradually as the superelevation slowly runs out at a
uniform rate.
• Therefore, a transition curve is a 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.

141
Transition Curve
• Objectives of transition curve
• 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.
• To provide a gradual increase of the superelevation starting from zero at the straight line to the desired
superelevation at the circular curve.
• To ensure a gradual increase or decrease of centrifugal forces so as to enable the vehicles to negotiate a
curve smoothly.

142
Transition Curve
• Requirements of an ideal transition curve
• 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.
• It should join the circular curve tangentially, i.e. it should finally have the same curvature as that of the
circular curve.
• Its curvature should increase at the same rate as the superelevation.
• The length of the transition curve should be adequate to attain the final superelevation, which increases
gradually at a specified rate.

143
Transition Curve
• Types of transition curve
• Euler’s spiral – Ideal transition curve but
not preferred due to mathematical
complications.
𝜙 =
𝑙2
2𝑅𝐿
• Cubical spiral – Good transition curve but
quite difficult to set on the field.
y =
𝑙2
6𝑅𝐿
• Bernoulli’s lemniscate – Not used in
railways.

144
Transition Curve
• Cubical parabola
• Indian Railway mostly uses cubical parabola.
• 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 throughout the length of the curve. A
straight line ramp is provided for such transition curves.
y =
𝑥3
6𝑅𝑙

145
Transition Curve
• S-shaped transition curve
• Curvature and superelevation assume the shape of two
quadratic parabolas.
• S-type parabola ramp is provide instead of a straight line
ramp.
• Shift required is half the shift required for the normal
shift provided for a straight line ramp.
S =
𝐿2
48𝑅
• Desirable when the shift is restricted due to site
conditions.

146
Transition Curve
• 𝜙 = angle between the straight line track and the tangent to
the transition curve
• l = distance of any point on the transition curve from the
take-off point
• L = length of the transition curve
• x = horizontal coordinate on the transition curve
• y = vertical coordinate on the transition curve
• R = radius of the circular curve

147
Transition Curve
• Shift
• For the main curve to fit in the
transition curve, it is required to be
moved by a measure known as the shift.
S =
𝐿2
24𝑅
Where, S is the shift in m, L is the length
of the transition curve in m and R is the
radius in m.

148
Transition Curve
• Length of the transition curve
• Maximum of the following three values
• L = 0.008Ca * Vm =
𝐶𝑎 ∗ 𝐶𝑑
125
(Based on rate of change of a cant or cant deficiency of 35mm/secs)
• L = 0.008Cd * Vm =
𝐶𝑑 ∗ 𝑉𝑚
125
(Based on rate of change of a cant or cant deficiency of 35mm/secs)
• L = 0.72Ca (Based on a maximum cant gradient of 1 in 720 or 1.4mm/m)
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.

149
Transition curves - [Numerical]
Calculate the superelevation, maximum permissible speed, and transition length for a 3o curve on a high-speed BG section with
a maximum sanctioned speed of 110 kmph. Assume the equilibrium speed to be 80kmph and the booked speed of the goods
train to be 50kmph.
R = 1750 / D = 1750 / 3 = 583.3 m
2. Superelevation for equilibrium speed
e =
𝐺𝑉2
127𝑅
, G = 1750mm (BG rail)
e =
1750∗802
127∗583.3
= 151.2mm
3. Superelevation for maximum speed
e = 285.8 mm (V=110kmph)
Cant deficiency = 285.8–151.2 = 134.6mm > 100mm
Take Cd = 100mm. Actual cant = 285.8 – 100 = 185.8mm
However, actual cant is limited to 165mm, therefore this value will be adopted.
4. Superelevation for goods trains
e = 59mm (V=50kmph)
Cant excess = 165-59 = 106mm > 75mm. With 75mm taken as cant excess, the
actual cant now provided is 75+59 = 134mm. Take 135mm.
Maximum speed potential or safe speed of the curve based on theoretical
consideration
V = 0.27 𝐶𝑎 + 𝐶𝑑 ∗ 𝑅 where, Ca = 135 mm, Cd = 100mm, R = 583.3 m
V = 99.96 kmph

150
Transition curves - [Numerical]
Calculate the superelevation, maximum permissible speed, and transition length for a 3o curve on a high-speed BG
section with a maximum sanctioned speed of 110 kmph. Assume the equilibrium speed to be 80kmph and the booked
speed of the goods train to be 50kmph.
6. Maximum permissible speed = Min(Maximum sanctioned speed, safe speed)
Maximum permissible speed = 99.96kmph
7. Length of transition curve
Maximum of
• L = 0.008 * Ca * Vm = 0.008 * 135 * 99.96 = 107.95m
• L = 0.008 * Cd * Vm = 0.008 * 100 * 99.96 = 79.96m
• L = 0.72*e = 0.72*135 = 97.20m
• Therefore, e = 135mm, Vm = 99.96kmph (approx. 100kmph) and L = 107.95m (approx. 108m)

151
Widening of gauge on curves
• Due to rigidity of the wheel base, it is sometimes found on the curve that the rails are tilted outwards so that
actual gauge is more than the theoretical value.
• Possibility of tilting rail outwards.
• To prevent this tendency, the gauge of the track is sometimes widened on sharp curves. Amount of widening
depends upon the radius of the curve, gauge width, and the rigid wheel base of the vehicle likely to be used on
the track. Rigid wheel base for BG and MG tracks are taken as 610cm and 488cm respectively.
• The amount of widening of gauge is
w =
(𝐵+𝐿)2∗13
𝑅
where, B = rigid wheel base in m, R = radius of curve in m
L = lap of flange in m
L = 0.02 ℎ2 + 𝐷ℎ, where, h = flange projection (cm) and D = diameter of the wheel (cm)

152
Widening of gauge on curves

153
Widening of gauge on curves [Numerical]
The wheel base of a vehicle moving on a BG track is 6m. The diameter of the wheels is 1524 mm and the flanges
project 32mm below the top of the rail. Determine the extra width of the gauge required if the radius of the curve is
168m. Also indicate the extra width of the gauge actually provided as per Indian Railway Standards.
• Lap of flange L = 0.02 ℎ2 + 𝐷ℎ
• Lap of flange L = 0.02 3.22 + (152.4 ∗ 3.2) = 0.446m
• Extra width of gauge (w) =
13(𝐵+𝐿)2
𝑅
• Extra width of gauge (w) =
13∗(6+0.446)2
168
= 3.21 cm = 32.1 mm
• As per Indian Railways standards, an extra width of 5 mm is provided for curves with a radius less than 400m in actual practice.

154
Vertical Curves
• Problems with the meeting of two gradients
• Angular formation
• Rough run of the vehicles on track
• Bunching of vehicles in the sags
• Variation in the tension of couplings in the summits
• Vertical curves are provided at points where two gradients meet or where a gradient meets level ground.
• 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.

155
Vertical Curves

156
Vertical Curves
• Length of vertical curve (Old Method)
• 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 30.5m
chords, whereas the corresponding figure for sags is 0.05% per 30.5m chord.
• The required length of a vertical curve for achieving the maximum permissible speed is given by the
formula
L = (a/r) * 30.5m
where, L is the length of the vertical curve in m, a is the percent 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.

157
Vertical Curves
• Existing provisions on Indian Railways
• Vertical curves are only provided at the junction of gradients, when the algebraic difference between the
gradients is equal to or more than 0.4 percent.
• The minimum radii for vertical curves is presented in the table.

158
Vertical Curves [Numerical]
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.
• Gradient of the rising track (1 in 100) = 1% (+ve) = +0.01
• Gradient of the falling track (1 in 200) = 0.5% (-ve) = - 0.005
• Change of gradient (a) = 1 – (-0.5) = 1.5% (+ve) = 0.015
• Rate of change of gradient (r) for summit curves = 0.1% = 0.001
• Length of vertical curve (L) = (a/r)*30.50
• Length of vertical curve (L) = (0.015/0.001)*30.50
• Length of vertical curve (L) = 457.50 m

159
Vertical Curves
• Length of vertical curve (New Method)
• The length of the vertical curve is calculated as
L = RQ
where, L is the length of the vertical curve, R is the radius of the vertical curve as per the existing provisions
and Q is the difference in the percentage of gradients.

160
Vertical Curves [Numerical]
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 1000m and its RL is 100m. Calculate the length of the vertical curve and the RL and the chainage of the
beginning and end of the curve.
Refer to Setting of curve
• First gradient = 1 in 100 (rising) = +1%
• Second gradient = 1 in 200 (falling0 = -0.5%
• Difference in gradient = +1 – (-0.5) = +1.5%
• Length of vertical curve (L) = RQ = 4000*(1.5/100) = 60m
• Chainage of point A = 1000 – 30 = 970m
• Chainage of point B = 970 + 60 = 1030m
• RL of point A = 100 – (0.01*30) = 99.70 m
• RL of point B = 100 – (0.005*30) = 99.85 m

161
Thank You!
- Abhash Acharya
M.Sc. In Transportation Engineering
acharyaabhash@gmail.com
www.abhashacharya.com.np

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