TRANSPORTATION ENGINEERING: Railway engineering Study Notes

By Deepanshu Rastogi|Updated : July 29th, 2021



  • Railway track is a combination of rails, fitted on sleepers and resting on ballast and subgrade.
  • Essential function of railway track is to support and guide the vehicles that run over it.
  • The conventional railway track consists of two rails located at fixed distance apart. The pressure exerted over by the rails is in turn transmitted to the formation with the help of sleepers and ballast.
  • Railway track is also known as permanent way. In a permanent way, rails are joined in series by fish plates and bolts and then they are fixed to sleepers by different types of fastenings.
  • The sleepers properly spaced, resting on ballast, are suitably packed and fixed with ballast.
  • The layer of ballast rests on the prepared subgrade called as the formation.



2.1.   Formation

The formation (also called subgrade level) is the ground surface prepared to support the track surface. It is the top layer of the extended subsoil. A subgrade protection layer applied to the formation is an integral part of track construction today.

Formation protective layer:

The fine-grained formation protective layer  is applied on the formation, possibly on an additional layer of geosynthetics (geotextiles). It is also called "track bed layer", because it is intended to increase the load-bearing capacity of the soil and can be used for soil improvement with a lime-cement mixture.

2.2.   Ballast

  • Ballast is composed of hard rocks with sharp edges and a particle size of between 32 and 65 mm. It is broken in special ballast plants.
  • It is important that the particles have sharp edges so that the ballast bed can provide a secure location in the ballast bed.
  • The materials used are granite, diabase or basalt. Different materials are used from region to region.
  • The quantity of ballast required per metre of track is 3.5 to 4 tonnes on average, which is slightly more than 2 m³.
  • After about 30 to 50 years, the ballast needs to be completely renewed.

Ballast bed:

  • The ballast bed carries the track grid and ensures that it is retained in a stable position, but at the same time must be elastic and enables a certain amount of track deflection under load.
  • In addition, the ballast bed must allow rain water to drain away effectively. Regular maintenance of the ballast bed (use of tamping machines, with selective hand tamping at certain points) ensures that it retains its properties.
  • At longer time intervals, depending on load and ambient conditions, the ballast bed must be cleaned partially machines), or completely replaced.
  • Inadequate maintenance reduces the carrying capacity of the track bed, leading to the introduction of speed restrictions and finally up to the destruction of the ballast.
  • Some amount of elasticity will be generated by ballast. Minimum size ensures drainage conditions whereas maximum size ensures shear strength.

Depth of ballast =

Here, SS = spacing between sleepers

WS = Width of sleeper

DB = Depth of ballast

2.3.   Sleepers:

The sleeper laid transverse to the direction of travel in general keeps both rails parallel to each other, distributes the load and ensures the correct track gauge.

Types of Sleepers:

  • General: Typical forms are the classic wooden sleeper, the steel-reinforced concrete and steel sleeper, as well as the so-called Y-steel sleeper. With the so-called bi-block-sleeper two concrete elements are connected under the rails by steel rods. Sleepers lying under both rails along the direction of travel, which require additional tie rods or other elements to maintain the correct distance apart, are also designated as Long sleepers; they can also be concreted (type of ballast less track). Sleeper provides elasticity on the railway track.

(i) Wooden sleeper: Dog spikes were used for wooden sleeper.

Composite sleeper index is an index to check the suitability of a particular timber to be used as a sleeper.

Here, S: strength of timber

H: hardness of timber

(ii) Steel sleeper: Steel sleeper provides maximum rigidity to the rail movement

(iii) Concrete sleeper:Pandrol clip is used for concrete sleeper.

Sleeper density:

Number of sleeper used for one rail length are denoted by M + x, where M = length of rail in meter. Sleeper density for B.G. should lie between (M + 4) to (M + 7).

2.4.   Rails

  • There would be no railway without rails. There is a variety of different rail sections, some of which have limited use (e.g. crane rails).
  • In principle, each rail is a rolled, long steel beam.
  • The widest part is always the rail foot and above it there is the rail web and at the top of this there is the rail head. The rail foot is located next to the sleeper. Where appropriate, it is separated by an elastic rail pad.
  • If rails are connected by bolted joints, holes are provided in the rail web and the rail ends are connected by steel bolts in the "fishplate surface", which connect the fishplates. Normally, rails are continuously welded today.
  • In general usage, "rail" and "track" are often used as synonyms, but this is not correct. In general, the track is formed of two rails with sleepers and ballast or slab track. In special cases such as the integration of narrow-gauge railways, the track can have three or even four rails. Routes with just one central, paved guide rail have been laid for rubber tyre vehicles similar to bus and coach lanes especially in French cities.

2.5.   Fixtures & Fastenings:

  • All those fittings which are required for connecting the rails end to end and for fixing the rails to the sleepers in a track are known as fixtures and fastenings. 

They include -

1) Fish plates

2) Spikes

3) Bolts

4) Chairs

5) Keys

6) Blocks

7) Bearing plates

  • The different functions of these fittings are:

1) To keep the rails in the proper positions.

2) Connection of rail to rail.

3) To set points and crossings properly

4) To allow for expansion and contraction of rails.

  • The various types of fixtures and fastenings listed above are briefly described below:

FISH PLATES: These plates are used to maintain proper alignment of the rail line. They maintain the continuity of the rails and also allow expansion or contraction of rails caused due to temperature variations.

Generally these plates are made of mild steel and 20 mm in thickness.  

They are 45.6 cm long and provided with 4 no. of 32 mm diameter holes at 11.4 centre to centre.

Indian railways generally adopt following two types of fish plates:-

1.Bone shaped fish plate

2.Increased depth fish plate

SPIKES: They are used to hold the rails to the wooden sleeper. A good spike should have following qualities:

1) It should have sufficient strength to hold the rail in position.

2) It should help in maintaining proper gauge.

3) It should be easy to fix and replace from the sleepers.

Indian Railways use following types of spikes:-

  1. Dog spikes
  2. Screw spikes
  3. Round spikes
  4. Standard spikes
  5. Elastic spikes

BOLTS: They are used for connecting:

1) Fish plates to the rails at each rail joint.

2) Chairs or bearing plates to timber sleepers.

3) Sleepers to bridge girders, etc.

The different types of bolts used in Indian Railways are:

  1. Hook bolts
  2. Fish bolts
  3. Fang bolts
  4. Rag bolts

CHAIRS: They are used to hold the double headed and bull headed rails in required position. They are made of cast iron having two jaws and a rail seat. In order to fix the double headed or bull headed rail to a chair, the rail is placed between the two jaws of the chair.

KEYS:  They are small tapered pieces of timber or steel to connect rails to chairs on metal sleepers.

Types of keys generally used are:

1) Timber keys

2) Metal keys

3) Stuart's keys

4) Morgan keys

BLOCKS: They are inserted in between the two rails running close to each other and bolted to maintain the required distance. They may touch either the webs or the finishing faces or both.

BEARING PLATES: They are the plates placed in between the flat footed rails and timber sleepers on a track. They serve as chairs for flat footed rails. They are made of cast iron, wrought iron or steel. Generally, they are of following types: 

1.Flat bearing plates: Flat bearing plates are used at locations where rails are laid flat. Also they are used in turn out tracks under points and crossings.

2.Canted bearing plates: Canted Bearing plates are used on soft timber sleepers beneath outside rail on curves, on sleepers placed on either side of rail joints, bridges etc. where rails are laid at an inward tilt of 1 in 20.


It is the distance between inner faces of rails or running faces of rail section.

3.1.   Type of Gauge:

(i) Broad Gauge: 1.676 m

(ii) Standard Gauge: 1.435 m

(iii) Meter Gauge: 1.00 m

(iv) Narrow Gauge: 0.762 m

(v) Feder Gauge: 0.610 m



The wheels are made cone shaped having different diameters at different cross sections. Diameter near flange is more than the diameter near other ends. The rails are also laid at a slope of lin20 (same slope of wheel face) this is called coning of wheels.

Purpose of coning

1.On a straight track: To keep the wheel assembly in central position to avoid derailment.
2. To reduce wear and tear of centrifugal force the wheel assembly in move in outward direction, so diameter on outer rail will increase. So the distance travelled on outer rail will become more as required. Due to difference of diameter on two rails, the trains will be moving on a circular track and distance travelled on two tracks will be adjusted as required.

2.Only some part of difference is adjusted due to coning. Remaining part is covered by slip or skid on the surface.
Due to cone shaped wheels, diameter of wheel is not same at each section.

3.On straight track, the wheel will always move in central position in such a way that diameter at contact point with rail is same on the two rails. If the train or axle of wheel tries to move in any direction, diameter of wheel on one rail will increase. So the axle will start moving on a circular track. Thus the wheel assembly will be automatically returned back in its central position.


Welding methods:

·       Gas pressure welding

·       Electric arc welding/Metal arc welding

·       Flash butt welding

·       Thermite welding


6.1.   Maximum speed on a railway track:

It is the minimum of,

(i)Speed decided by Railway board

(ii)Speed decided by Martin’s formula

(iii)Speed calculated by Online Classroom Program elevation formula

(iv)Speed calculated by length of transition curve formula

  • Martin’s formula : a) On a Transition Curve
  1. For BG/MG

Vmax= 4.35 √(R-67)

ii.For NG

Vmax= 3.6 √(R-61)

  1. b) On a Non- Transition Curve

Vmax= 0.8 (Vmax of transition curve)

  1. c) For High Speed Trains

Vmax= 4.58 √(R)

6.2.   Radius of the curve,

   [For 1 chain length = 30 m]

6.3.   Online Classroom Program elevation: 

In the above figure, if Ө is the angle that the inclined plane makes with the horizontal line, then

tan Ө = Online Classroom Program Elevation/ Gauge = e/G

Also, tan Ө = Centrifugal Force/ Weight = F/W

From these equations

e/G = F/W

e= F. (G/W)

e= (W/g). (V2/R). (G/W) = G V2 / gR

Where e is the equilibrium Online Classroom Program elevation, 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 Online Classroom Program elevation is given by the formula

e= G V2/ 127R

Where e is the Online Classroom Program elevation 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.

Equilibrium Online Classroom Program Elevation:

Here G = gauge in ‘meter’

V = velocity in km/h

R = radius in 'meter'

e = is in 'meter'

Different trains have different speed on the railway track and actual cant is provided for average speed and that is also called as equilibrium cant.

6.3.1.Permissible value of actual cant


Speed 120 km/h

Speed > 120 km/h


16.5 cm

18.5 cm


10.0 cm


7.6 cm




For high speed train cant requirement will be more than actual cant provided so the train will be forced to move on a lower value of cant. This deficiency of cant for high speed train movement is called cant deficiency.

etheoretical = eactual + cant deficiency

7.1.   Limits of cant deficiency


Speed 100 km/hr

Speed > 100 km/hr









8.1.   Types of gradients

(i) Ruling Gradient: It is the maximum gradient that can be provided in the most general condition and that determines maximum load that a locomotive can carry on that particular section.

(ii) Momentum gradient: For a practical situation as shown in figure, gradient may be increased more than ruling gradient (with no stoppage)

(iii) Pulling/helper/pusher gradient: When gradient is greater than ruling gradient then extra locomotive is provided for that particular section.

Note: Greater gradient reduce the cutting cost

Minimum gradient at station yard: 1/100

Maximum gradient at station yard: 1/400

8.2.   Grade compensation: If the gradient is provided on a curved location then gradient value is reduced to compensate curve resistance. Reduction in gradient for broad gauge is 0.04% per degree of the curve.


It is required for

(i) Introduction the Online Classroom Program elevation in a gradual manner within the length of transition curve in outer railway track.

(ii) Reducing the radius of the curve from infinite to some value

(iii) Curve should be perfectly tangential at joining points

(iv) If the centrifugal force is to be increased at a constant rate, centrifugal force must vary   with time.

(v) The ideal condition for transition curve is:

(vi) Cubical parabola equation for transition curve:

h = in ‘m’

e = actual cant in ‘cm’

Vmax = in km/hr

CD = in cm 


Spiral and Deflection Angles:


shift → because of transition curve, the path shifted w.r.t. circular curve

L = length of transition curve


It is an arrangement on railway track to direct the trains from one track to another track.

(i) Tongue rail: They are provided on sliding plate and each plate of tongue rail is connected by structure bars.

(ii) Flare: It is provided to guide the wheel such that range of wheel enter and leave the turnout smoothly.

(iii) Heel Block

  • Flangwayclearance : It is the distance between adjacent faces of stock rail and tongue rail
  • Flange way depth: It is the vertical distance from top of the rail surface to top of the heel block.
  • Heel divergence :It is the distance between the running faces of stock rail and tongue rail

It is the combination of 2 turnouts with intermediate portion as straight portion or curved portion i.e., used to drive the trains from one track to another track.

From ∆ABC,

from ∆ CDE,

Also, we know

So total cross-over length

= 2GN + 2GN + DE


Maximum functional force that can be generated between rail surface and driving wheels.

Hauling capacity = µWN

Here, µ = functional co-efficient

W = load on each driving axle (in tonnes)

N = No. of pairs of driving wheel


Longitudinal movement of rails w.r.t. sleeper is k/a creep of rails.

Dominating traffic theory (also called drag theory):

P = AE ∝ T, here l = length of rail in one direction

T = temperature are valuation

∝ = thermal coefficient

 = no. of sleeper required.  {Ro: resistance offered by one single sleeper}

Length of rail in one direction = l = (n – 1) s

Here, s = spacing between two sleepers


A vehicle normally assumes the central position on a straight track and the flanges of the wheels stay clear of the rails. The situation, however, changes on a curved track. As soon as the vehicle moves onto a curve, the flange of the outside wheel of the leading axle continues to travel in a straight line till it rubs against the rail. Due to the coning of wheels, the outside wheel travels a longer distance compared to the inner wheel. This, however, becomes impossible for the vehicle as a whole since the rigidity of the wheel base causes the trailing axle to occupy a different position. In an effort to make up for the difference in the distance travelled by the outer wheel and the inner wheel, the inside wheels slip backward and the outer wheels skid forward. A close study of the running of vehicles on curves indicates that the wear of flanges eases the passage of the vehicle round curves, as it has the effect of increasing the gauge. The widening of the gauge on a curve has, in fact, the same effect and tends to decrease the wear and tear on both the wheel and the track.

The widening of the gauge on curves can be calculated using the formula:

Extra Width on curves=w = 13 (B+L)2/ R

Where B is the wheel base of the vehicle in metres, R is the radius of the curve in metres, 

L = 0.02 (h2 + D.h)0.5 is the lap of the flange in metres, h is the depth of flange below top of the rail, and D is the diameter of the wheel of the vehicle.

Example: The wheel base of a vehicle moving on a BG track is 6 m. The diameter of the wheels is 1524 mm and the flanges project 32 mm below the top of the rail. Determine the extra width of the gauge required if the radius of the curve is 168 m. Also indicate the extra width of gauge actually provided as per Indian Railways standards.


(i) Lap of flange

Where h = 3.2 cm is the depth of the flange below the top of the rail and

D = 152.4 cm is the diameter of the wheel. Therefore,

(ii) Extra width of gauge (w)

(iii) As per Indian Railways standards, an extra width of 5 mm is provided for curves with a radius less than 400 in actual practice.


  1. NEGATIVE Online Classroom Program ELEVATION

When the main line lies on a curve and has a turnout of contrary flexure leading to a branch line, the Online Classroom Program elevation necessary for the average speed of trains running over the main line curve cannot be provided. In the figure below, 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 Online Classroom Program elevation and, therefore, speeds on both tracks must be restricted, particularly on the branch line.

The provision of negative Online Classroom Program elevation for the branch line and the reduction in speed over the main line can be calculated as follows:

(i)The equilibrium Online Classroom Program elevation for the branch line curve is first calculated using the formula:

(ii)  The equilibrium Online Classroom Program elevation e is reduced by the permissible cant deficiency CD and the resultant Online Classroom Program elevation to be provided is

x = e - CD

Where, x is the Online Classroom Program elevation, e is the equilibrium Online Classroom Program 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 Online Classroom Program elevation of x.

(iii) The maximum permissible speed on the main line, which has a Online Classroom Program 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.



Railways are modernized with the objective of allowing heavier trains to run safely and economically at faster speeds, of improving productivity, and of providing better customer service to rail users. This consists of upgrading the track, use of better designed rolling stock, adopting a superior form of traction, better signalling and telecommunication arrangements, and using other modern techniques in the various operations of a railways system.

A railway track is modernized by incorporating the following features in the track:

(a) Use of heavier rail sections such as 52 kg/m and 60 kg/m and the use of wear-resistant rails for heavily used sections so as to increase the life of the rails.

(b) Use of curved switches of 1 in 16 and 1 in 20 type for smoother arrival at yards.

(c) Use of pre stressed concrete sleepers and elastic fastenings such as Pandrol clips to provide resilience to the track and ensure the smooth movement of trains at high speeds.

(d) Use of long welded rails and switch expansion joints to ensure a smooth and fast rail journey.

(e) Modernization of track maintenance methods to include mechanized maintenance, measured shovel packings, etc., in order to ensure better track geometry, to facilitate high speeds and smooth travel.

(f) Track monitoring using the Amsler car, portable accelerometer, Hallade track recorder, etc. to assess the standards of track maintenance and plan for better maintenance, if required.

Other aspects of modernization of the railways generally include making the following provisions:

(a) Use of better designed all-coiled, anti-telescope ICF coaches with better spring arrangements and better braking systems for safe and smoother rail travel.

(b) Provisions of universal couples to ensure uniformity in the coupling of the coaches.

(c) Introduction of diesel and electric traction in order to haul heavier loads at faster speeds.

(d) Introduction of modern signalling techniques to enable trains to move at high speeds without any risks.

(e) Setting up of a management information system for monitoring and moving freight traffic in order to avoid idle time and increase productivity.

(f) Computerization of the train reservation system to avoid human error and provide better customer service for reservation of berths.

(g) Use of computers and other modern management techniques to design and maintain railway assets more efficiently and economically, to ensure efficient human resource development (HRD), to increase productivity, and to provide better customer service.







1.1.   Investigation

(i) Before planning:-

(a) To determine relation between bed rock and top soil when exploration at the surface in form of knowing morphology, petrology, stratigraphy etc.

(b) Electrical resistivity methods are used to locate positions of work zone like faults and shear zones.

(ii) At the time of planning :-

(a) Investigations at the time of planning are made through drilling holes either by


Rotary percussion


(iii) At the time of construction :-

Information is achieved by driving either of the following.


driving drift

1.2.   Blasting :-

(i) Types of explosives :-

(a) Straight dynamites

(b) Ammonia dynamites

(c) Ammonia gelatine

(d) Semi-gelatine

(ii) Theory of blasting :- Processes by which rock can be blasted

(a) Impact

(b) Abrasion

(c) Thermally induced spalling

(d) Fusion and vaporization

(e) Chemical reaction


1.3.   Shape and Size:-

(i) D-section :- This section is suitable for sub-ways or navigation tunnels.

(ii) Circular section :- For tunnels which may have to withstand heavy internal or external radial pressure.

(iii) Rectangular section: Suitable in case of hard rocks.

(iv) Egg shaped section:- Used for carrying sewage because it gives self  cleaning velocity.

(v) Horse shoe form :- Used for traffic purposes and as the floor of the tunnel is nearly flat, it gives working space to store material during construction.

1.4.   Various types of Construction Technique

(i) Cut and cover method                 (iv) Shaft method

(ii) Bored tunnel method                  (v) Box jacking method

(iii) Clay kicking method                  (iv) Under water tunnels.


2.1.   Types of Bridges

(i) Arch Bridges :-

(a) It is very strong and wide range of materials can be used.

(b) It is quiet expensive.

(ii) Truss Bridges:-

(a) It is frequently used as a draw bridge or as an overpass for railroad train.

(b) It is difficult to construct, high maintenance.

(iii) Suspension Bridges:-

(a) It has span distances up to 7000 feet,

(b) It allows large boats and heavy boat traffic to pass underneath.

(c) Expensive construction

(iv) Cable Stayed Bridges:-

(a) Not expensive and faster to build

2.2.   Factors for Selection of Types of Bridges

(i) Geography                      (ii) Loading

(iii) Aesthetics                      (iv) Cost

2.3.   Section Criteria for Bridge Site

(i) Topography                     (ii) Catchment area

(iii) Hydrology                      (iv) Geo-technical

(v) Seismology                     (vi) Navigation

(vii) Construction resources    (viii) Traffic data

2.4.   Types of Bridge Foundation

(i) Spread or open foundation is suitable for bridges of moderate height to be built on dry ground which is sufficiently firm to support the bridge structure.

(ii) Raft foundation is suitable when bed of water course consists of soft clay and silt.

(iii) Grillage Foundation is suitable for heavy load and located footing of piers where deep foundations are to be avoided.

(iv) Inverted arch foundation is suitable when depth of excavation for foundation is less. It is best suited where bearing capacity of soil is less.

(v) Pile formation is suitable when the soil is very soft and the hard strata are not available at reasonable depth.

(vi) Well foundation is suitable where good soil is available at about 3 to 4m below the bed level of the river the bed consist of sandy soil.

(vii) Caisson foundation is suitable when a hard is available near to the river bed but the depth of water is excessive and it is not economically possible to exclude water from a dry bed for sinking the wells to provide well foundation. 


3.1.   Introduction:

Airports are classified by 2 organisations:

(i) ICAO: International Civil Aviation Organization.

(ii) FAA: Federal Aviation Agency.

ICAO classified airport into 2 categories-

(i) Based on basic runway length

A → longest runway

B → shortest runway

  1. Equivalent Single Wheel Load of the aircraft.

Important Points related to Wind- Rose Diagrams:

(i) Length of runway requirements will be more if landing and take-off operation are performed along the wind direction.

(ii) Wind parameters (direction and intensity) are graphically represented by diagrams called as wind rose diagrams.

(iii) Wind parameters should be collected for a period of 3 years.

(iv) Normal component of the wind is called as cross-wind component & it may interrupt safe landing & take-off of the aircraft. For the smaller size of aircraft, max. Permissible limit is 15 km/hr & for bigger →25 km/hr of (due to more weight, its higher) of cross-wind component.

The % age of time during which in a year, the cross wind component remains within the permissible limit is called as wind coverage.

3.2.   Basic runway length requirements

  1. Airport altitude is at MSL.
  2. Temperature at airport is standard 15°c.
  3. Runway is levelled in the longitudinal direction.
  4. Aircraft is loaded through its full loading capacity. They themselves are worst cases. So no correction required for them.
  5. Speed of wind should be zero on the runway.

Correction for elevation

ICAO recommends that the basic runway length should be increased by 7% per 300 m rise in elevation above MSL.

Correction for temperature

Std. Atmospheric temperature at rest altitude is calculated as

Local body temperature of a particular area is called as airport reference temperature & that is defined for hottest month of the year.

Τa→ monthly mean of avg. Daily temperature.

Τm→ monthly mean of max. Daily temperature.

ICAO recommends that the basic runway length after corrected for elevation should be increased by 1% for every 1°c rise of art above the std. Atmospheric temperature at that elevation (air density).

If the total correction for elevation & temperature is less than or equal to 35% of basic runway length, no corrections are >35%, scientific analysis must be performed at site conditions again (economical).

Correction for gradient

[Only as per FAA].

After corrected runway length for elevation & temperature, runway length should be increased by 20% for every 1% of effective gradient.

Example: Basic runway length = 1620 m. [under std. Condition]

ART = 32.94°c

Elevation- of airport site = 270m.

If the runway is to be constructed with 0.2% eff. Gradient.

Calculate corrected runway length.

Ans. Correction for elevation→

Corrected runway length = 1620 + 102.06 = 1722.06 m.

(2) change in standard temperature→

= 15° – (0.0065 × change in el. Above MSL)

= 15° – (0.0065 × 270)

= 13. 24°c

ART = = 32.94°c (given)

ΔT °c = 32.94°c – 13.24°c

        = 19.7°c

So correction for temperature:

= 339.24 m.

Corrected runway length = 2061.3 m

  1. Correction for gradient:

Corrected runway length

= 2143.75 m.

Example: Determine actual length of runway for them given parameter⇒ basic runway length = 1800 m.

El. Of airport site = 600 m, τa = 15°c, τm = 21.6°c,Eff grad = 0.6%     


Correction for elevation →

Corrected length = 1800 + 252


  1. Temperature correction:

Std. Temperature

= 15° – (0.0065 × 600) = 11.1°c

So rise in ART = 17.2 – 11.1

(δt°C) = 6.1°c

So correction =

= 125.172 m.

So corrected length

= 2052 + 125.172



  1. Grad. Correction [FAA]

So final corrected length

= 2177.172 + 261. 26

=   2438.43 m

  • In case of take-off elevation, temperature & gradient corrections are necessary.

In case of landing, only elevation correction is necessary.

3.3.   Turning radius at taxiway

4)  R> 120 m for Sub sonic jets.

Example: Evaluate taxiway radius for supersonic aircraft with

w = 35 m & tread of landing gear = 7.5 m.

Speed of aircraft = 50 km/hr

Ans. 1.

Let t = 22.5m,



  1. For supersonic = r ≥ 180 m

= max = 316.86 m

3.4.   Some Important elements of an Airport:

Stop way is used in case of engine failure conditions.

Length of runway is decided on the basis of:

  1. Normal landing case
  2. Normal take off care
  3. Engine failure case

Circling radius depends on

  1. Type of aircraft
  2. Weathering conditions & volume of aircrafts.

Aircraft movements will be more in case visual flight rules as compared to instrumental flight rules (which are applicable in bad weathering conditions.)

Size of hanger building is decided on basis of size of aircraft (length, width, height).


4.1.   Some Important Definitions:

  • HARBOURS provide safe anchorage to ships in conditions of bad weather.
  • PORTS are used for loading & unloading of passengers, cargo, etc.
  • Every port is a harbour but reverse is not true.
  • Docks which are used for ships to facilitate loading & unloading of passengers & cargo are known as Wet Docks.
  • Docks which are used for serving & maintenance of ships are called as Dry Docks.
  • WHARF → it is a type of fixed platform usually on file foundations where ships are loaded or unloaded.
  • FENDER → Dock wall receives large amount of impact and to avoid this, cushions are provided permanently with dock walls & these are known as FENDERS. [In India, we use TYRES].
  • DOLPHIN PILES → used to tie-up the ships.
  • LITTORAL DRIFT → Sea waves are generated by prevailing winds & they move lighter particles of sand in suspension. This suspended sand is carried in a zig-zag manner & deposition of this sand is called LITTORAL DRIFT.
  • Excavation below water surface is called as DREDGING.

NAVIGATIONAL AID: Any device which is used to help travelers in navigation. Example: BOOYS, LIGHTHOUSE, etc.


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Deepanshu RastogiDeepanshu RastogiMember since Jul 2020
cracked GATE DTU AIR 1130-GATE
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