Railway Engineering is one of the very diverse fields of Engineering that focuses on Geometric Design of railway tracks, sleepers, formation and other components along with maintenance of entire facilities. It also lays frameworks for design of stations, Railway structures and other elements that form the backbone of Railway transportation.

Basic Formulas and Numerical Terms

This section provides all numerical concepts and formulas related to Railway Engineering. We will also cover geometric design of Railway tracks.

Minimum depth of Railway ballast cushion

\large\textcolor{blue}{D_{b}= \frac{S-W}{2}}

S = Centre to Centre distance between two railway sleeper

W = width of sleeper

Sleeper Density

Number of sleepers to be used for one rail length.

\large\textcolor{blue}{S =Spacing = \frac{Rail\, Length}{Sleeper\,density}}

Length of each rail (BG) = 1280 cm = 12.8 m

It is denoted by (n + X) [n+3 to N+6]

n= length of each rail

Composite Sleeper Index

Index of strength and hardness as well as mechanical suitability.

\large\textcolor{blue}{CSI = \frac{S+10H}{20}}

S = General strength for 12% moisture

H = General hardness.

Geometric design of Railway track

Safe speed on Railway curves:

[1] For Transition curve

(A) Broad gauge and Meter gauge:

\large\textcolor{black}{V= 4.35\sqrt{R-67}}

(B) Narrow gauge:

\large\textcolor{black}{V= 3.65\sqrt{R-6}}

For non transition curves: V = 0.8 X speed(a)

For high speed train:

\large\textcolor{black}{V= 4.58\sqrt{R}}

Safe speed based on Super elevation:

[1] For Transition curve : Speed (Km/h) BG. and MG respectively

\large\textcolor{black}{V= 0.27\sqrt{(C_{a}+C_{d})R}}

\large\textcolor{black}{V= 0.347\sqrt{(C_{a}+C_{d})R}}

R = radius of curve in mm

G= 1750 mm ( BG)

G = 1057 mm (MG)

Railway Super Elevation

\large\textcolor{black}{e_{1}=\frac{GV_{1}^2}{127R}}

\large\textcolor{black}{e_{2}=\frac{GV_{2}^2}{127R}}

\large\textcolor{black}{V_{2}=V_{avg}=\frac{3}{4}V}

\large\textcolor{black}{V_{1}=V_{max}=V}

e_max = 16.5 cm ; V is in Kph

[2]

\large\textcolor{black}{V=3.67\sqrt{R-6}}

\large\textcolor{black}{L_{T}=0.073\times e\times V_{max}}

C_a = Actual cant in mm

C_d = Cant deficiency in mm (e₁-e₂)

e – cm, V – Kph

Radius and Degree of Railway curve

30 m Chain

\large\textcolor{black}{D=\frac{1720}{R}}

20 m Chain

\large\textcolor{black}{D=\frac{11150}{R}}

D = 10˚ (BG), 16˚ (MG), 40˚ (NG)

Equation of parabola of transition curve

\large\textcolor{black}{Y= \frac{x^3}{6RL}}

\large\textcolor{black}{Shift (S)= \frac{L^2}{24R}}

L = Length of chord (m)

Versine of Curve : V(m)

\large\textcolor{black}{V= \frac{L^2}{8R}}

Grade Compensation

To reduce curve resistance

BG : 0.04 % per degree of curve or 70/R (Minimum)

MG : 0.03 % per degree of curve or 52.5/R (Minimum)

NG : 0.02 % per degree of curve or 35/R (Minimum)

R : radius of curvature ; Ruling gradient ( 1 in R)

For Broad gauge

Railway Point and Crossing

Length of straight portion of cross over along the track

\large\textcolor{black}{S= (D-G)N-G\sqrt{1+N^2}}

G = Gauge ( BG=1.676m,MG=1m,NG=0.762m)

N : number of crossing ( crossover 1 in N)

D : centre to centre distance between tracks.

α = Crossing angle.

\large\textcolor{black}{N=Cot\alpha }

\large\textcolor{black}{Overall\: Length= 4NG+S}

Hauling Capacity

\large\textcolor{black}{H.C= \mu n w}

w : weight of one pair of driving wheels (or one axle)

μ : coefficient of friction (1/6)

n : number of driving wheels.

Resistance due to Curve

Increase with speed, depend on central angle of curve

w : weight of train in tonnes

D : degree of curve

Total frictional resistance

\large\textcolor{black}{R_{f}=0.0016w}

Atmospheric resistance

\large\textcolor{black}{R_{a}=0.000000wv^2}

Resistance due to gradient

g : gradient ( 1 in g)

\large\textcolor{black}{R_{g}=w\sin\theta =\frac{w}{g}}

Components of Railways

This Part elaborates about several components of Railways like rail track, sleeper, ballast, formation and track fittings. It also covers conceptual details about geometric design of Railway Tracks along with terms like hammer blow effects, coning of wheels and more.

Gauge

Minimum distance between the rails.

Mountain Railway

Steep Gradient ( greater than or equal to 3%)

Narrow gauge

Curvature : 40 degree

Method of plate or Railway track laying

Train line method : temporary train line by side of track to transport material.

Side Method : Trucks on service road parallel to track.

Ballast of specified thickness is spread above ground called Formation. Ballast provides level, drainage and transfer load to larger area.

Railway Track consists of following

• Rail
• Ballast
• Formation ( 6.1 m wide for B.G and 4.8 m for M.G)
• Sleeper ( thickness 20-30 cm)
• Fitting and Fastenings

Rail

R : Revised British Specification (lb./yard)

BG : 60 kg , 52 kg , 13m length

MG : 90R , 75 R , 60R ; 12 m length

Welded by flash-butt, thermite welding (repair)

Fastening : elastic rail clip, IRN 202

Railway Track Modulus

Index of measurement of resistance to deformation.

Defined by load per unit rail length required to produce one unit depression in rail bottom.

Unit : Kg / Cm²

It depends on gauge, rail type, sleeper and ballast.

Railway Speed Factor

Factor multiplied to convert stationary load to dynamic load.

Unit : miles/hour

μ : Track modulus (psi)

\large\textcolor{black}{Speed\: Factor = \frac{V}{{\sqrt[3]{\mu }}}}

Hammer blow effect

Vertical component of centrifugal force of weight introduced to balance the reciprocating mass cause variation in wheel pressure.

Lateral force cause twist in rail and bending in rail.

Longitudinal stress is developed by locomotive and braking forces.

Total breathing length of LWR = 2(N-1)S

N : No. of sleeper

S : Spacing between sleeper (cm)

Rail Stress : Photo-elastic method – IR uses it.

Coning of Wheel

The tread of wheels of railway vehicle is made sloped like cone in order to enable vehicle to move smoothly on curves as well as straight tracks.

Slope : 1 in 20

Result in tread circumference of wheel to increase over other to negotiate curve.

It reduces wear and tear of wheel flanges.

Slip for Broad Gauge : 0.029 m/degree of curve.

Tilting of rail is done inward at 1 in 20 to reduce wear and tear.

Steel for rail : 880 grade : C (0.6-0.8), Mn (0.8-1.3), Si (1.3-0.5)

IRS – 52 Kg (A= 156 mm , B = 136 mm)- 710 (grade of rail section) – TISCO (manufacturer) – II 1991 (month and date) – OB (Open hearth basic method of steel making).

Permissible Variation : length of rail (+2 mm to -10 mm); Height ( +0.8 mm to – 0.4 mm).

Test for Rail

• Falling Weight : withstand blow without fracture
• Tensile Test : should be greater than or equal to 72 Kg/mm² ; Minimum elongation = 14% or 12 % (for high quality)
• Hammer Test : head is struck blows; fracture test.

Defects in Rail

• Hogging of rail
• Scrabbing (depression)
• Wheel burns
• Shelling and blackspot
• Corrugation – cause roaring sound of rail; removed by grinding

Ultrasonic rail flow detector : send vibrations to check defect.

Sleeper

Transverse ties to support rail.

Transfer wheel load from rail to ballast.

Material : Cast Iron, Steel, Wood (teak , Sal , rosewood) and Concrete (PSC 14 standard)

Adzing : cutting of sleeper to slope 1 in 20 Cant.

Ballast

Distribute load from sleeper to formation.

Provides Cushion effect

Should be hard, angular along edge and no weathered portion.

Material : Sand, Moorum, Coal, ash or cinder, broken stone(granite, quartzite) , gravel, kankar

Should be machine crushed.

Size specified : Concrete wooden sleeper (2”), Metal (1.5″)

Dispersion of load can be assumed to be roughly 45˚ to the vertical.

Minimum depth of ballast cushion = 250 mm

Sleeper Spacing = Width of Sleeper + 2 X depth of ballast

Water absorption < 1%

Measurement of quantity : stock and wagon measurement.

Aggregate abrasion = 30 % max

Aggregate impact = 20 % max

Railway Subgrade and Formation

Naturally occurring soil prepared to receive ballast. It bears the load by ballast.

Side slope depend on shearing strength of soil and angle of repose. (Slip circle method)

Sand or Clay Soil : 2:1 (H:V)

Rocky : 1:1 to 0.5:1

Compaction is done in layers of thickness not exceeding 300mm to 650mm .

Top Formation Slope : 1 in 30 away from centre.

Railway Track fittings and fastenings

Hold rails in their proper position. Join rails to sleeper and with each other.

Fish Plate

Join two rails horizontally and vertically

Steel :

0.3-0.42 % C , < 0.6% Mn , < 0.15% Si , S , P

Combination of fish plate, nut and bolt makes different section of rails.

Fang Bolts

Under switches for fastening slide chair to sleeper.

Bearing Plate

Fit and forget , irremovable and cheap

Pandrol Clip

• Fit and forget type elastic
• Made of silica-manganese spring steel
• Φ = 20.6 mm
• Heat treated
• Toe load : 710 Kg, cause indention
• Driven by 4 pound hammer
• Easily taken out

For RCC Sleeper : IRN 2.2 – Two coils, bolt and clamp arrangement

Creep of railway

Longitudinal movement of rail with respect to sleeper.

Railway Creep Theories

[1] Wave motion theory : wave motion in track, causes deflection in rail under load. The portion of rail immediately below wheels get depressed. As the wheel move forward, so is depression and previous depression swing back to normal position.

[2] Percussion Theory : Creep is developed by impact of wheel at rail end ahead of joint.

[3] Drag Theory : Backward thrust of driving wheels has tendency to push rail backward.

Cause of Railway Creep

• Ironing effect of wheel
• Starting and stopping operation
• Change in temperature
• unbalanced traffic
• Poor maintenance (bad joint)

Effect of Creep

• Sleeper out of square
• expansion gap widens and close
• distortion of point and crossing
• possible buckling of track
• difficulty in changing rail.

Measurement

By creep indicator : Two Creep post at 1 km distance on side of track. Distance between chisel mark and string is measured.

Geometric Design of Railway Tracks

Railway Gradient

It is the distance travelled per rise or fall.

Types of Railway Gradient

[1] Ruling Gradient : Steepest gradient in section

Plain : 1 in 150 to 1 in 250

Hilly : 1 in 150 to 1 in 150

[2] Pusher or helper gradient : to reduce cost in hilly areas gradient steeper than ruling gradient are provided.

To reduce the length of track required.

[3] Momentum gradient : It is steeper than ruling gradient and can be overcomed by train because of its momentum.

Falling gradient followed by rising gradient.

[4] Gradient in Station/Yard : it is quite flat.

It is made so that good drainage is maintained.

Maximum gradient : 1 in 400 or 1 in 1000 (recommended)

Points and Crossing

Transfer vehicle from one track to another.

Turnout

Arrangement of points and crossing with lead rails.

May be right handled or left handled.

Toe of switch to crossing : Facing direction

Crossing to toe : Trailing direction

Tongue rail

It is tapered movable rail, made of high carbon or manganese steel to withstand wear. At its thickness end ,it is attached to a running rail.

It is also called Switch rail.

1 in 8.5, 1 in 12 (turnout) ; longer length : smoother in entry switch.

Stock Rail

Running rail against which tongue rail operate.

Tongue and stock rail with fitting: Switch

Crossing (Frog)

Device introduced at junction of two rail cross point to permit wheel flange of railway to pass from one track to another.

Type:

• Acute angle (V) : right cross left rail
• Obtuse angle (diamond) : right/left crosses.
• Square Crossing : rare
• Built Up : two wing rail
• Cast Iron Crossing : no bolt, one piece

Switch Angle

Angle between gauge face of stock and tongue rail.

Flange way Clearance

Distance between running rail and check rail or wing rail at nose

It provides passage to wheel.

BG : 44 – 48 mm

MG : 41 – 44 mm

Limiting wear on crossing : 10 mm

Method of turnout design : Coles method and IRS method

Special Fitting

• Distance Block : prevent vertical movement between wing and nose.
• Flat bearing plate : provided under sleeper
• Spherical washer : move two surface to lie at any angle.

Gauntleted Track

Temporary diversion provided on double line track to allow one of the tracks to shift and pass through other track.

Both tracks run on same sleeper, on mixed gauge.

Used when one line is under repair.

No switches and there are two crossing at ends.

Gathering line

Called ladder track.

Tracks where number of parallel track gather or merge.

Diamond Crossing

\textcolor{blue}{Tan\alpha=\frac{1}{N}}

\textcolor{blue}{AB=BC=CD=DA=GCosec\alpha}

\textcolor{blue}{BD=GSec\frac{\alpha}{2}}

\textcolor{blue}{AC=GCosec\frac{\alpha}{2}}

\textcolor{blue}{BF=ED=GCot\alpha}

Railway Stations Yards and Maintenance

This part is dedicated to several practices used for maintenance of rail tracks and sleepers. It also covers railway defects, measurement instruments used in railways and Types of stations.

Railway Track Maintenance

[1] Through Packing

[2] Systemic Overhauling

[3] Picking Up Slacks

Through packing

• Opening of road : ballast is dug on either side with shovel or wire claw.
• Examination of rail, sleeper and fastening : damaged parts are removed using Jim crow.
• Squaring of Sleeper : position of sleeper is checked with reference to second rail by the help of T-Square.
• Aligning the track : Small errors are corrected by slewing the track.
• Gauging : Spacing is maintained
• Packing of Sleeper : Scissor packing method using beaters.
• Boxing Ballast : section and dressing by special template.

Systematic Overhauling

• Shallow Screening and making of ballast section.
• Replacement of damaged or broken fitting
• Packing
• Making up the cess

Picking up slacks

Slacks are point of faulty running in track that should be fixed.

Measuring Instruments and Maintenance tools

• Rail Gauge : check length (gauge)
• Spirit level : check alignment and cross level.
• Gauge cum level : gauge and cross level both.
• Cant board : difference in cross level and super elevation.
• Mallet : packing of sleeper
• Canne-a-boule : assess void under sleepers.
• T Square : check squaring of sleeper
• Stepped feeler gauge : measure wear or clearness
• Sleeper Tong : carry slipper
• Rail Tong : carry rail.
• Beater : pack ballast
• Crowbar : lift track and correct alignment
• Jim Crow : to bend or break rail.
• Spanner : to tighten bolt
• Wire claw and ballast ruke : to draw or pull out ballast while screening.
• Phowrah (Shovel) : to cut earth or ballast
• Auger : to bore holes in wood sleeper
• Box spanner : driving rail screw or plate screw
• Wire basket : screening the ballast.
• Pan Iron meter : leading earth or ballast.

Defects in Railway

Hogging of joint : use of liners and shims dehogging machine.

High Joint : due to change in track structure and sinking of sleeper. It is removed by packing of intermediate sleeper.

Blowing and pumping joint : blowing joint blow out fine dust during passage. It also pumps water and mud in rain. It is caused because of bad packing and bad drainage.

Lifting of track : maximum of 3″ of track should be lifted at time.

Longitudinal Sag : track between two rigid structures.

Centre bound sleeper : ballast at sleeper end depress more, sleeper start to rest at centre. It causes rocking of train.

Railway Station and Yard

Station

Block – A, B, C – need authority to proceed

Flag- D – no arrangement of traffic

A Class : line clear signal granted only when line is clear, double line

Signal in A Class

1. Warner : to indicate section is clear or not
2. Home : first stop signal
3. Starter : line should be clear so train can be given permission.
4. Advance Starter : provided beyond switches.

B Class

Single as well as double line

Line should be clear upto adequate distance.

Signal : Outer (first step reception) , home, starter

C Class

Block hat, split a long black section

Signal : warner, home

DK station : require key to be opened by ball token. It is used as siding.

Railway Yards

[1] Coaching Yard : deal with reception and dispatch of passenger train. Facilities such as watering , fuelling and charging are provided.

[2] Goods Yard : reception, stabling, loading, unloading and dispatch of goods wagon.

[3] Marshalling Yard : A Goods yard deals with goods, wagons to form new Goods train.

Reception, sorting and departure

Types : Gravitational , jump, flat yard.

[4] Locomotive Yard : house the locomotive

[5] Sick Line Yard : repair of defective wagon or coach.

Signals Types

Operational : detonating, hand and fixed signal

Functional : stop, warner, shunting, colored light

Locational : Reception and departure

Special : repeater or co acting, routing (at point of diversion), calling on (permit rail to proceed cautiously) and point indicator (obstructed vision by curvature or overbridge).