Month: January 2020

# How to Find Crossing Angle in Railway – Mathematical Problem & Solution

## Find the Crossing Angle – Problem & Solution

Mathematical Problem:

Find the crossing angle of 1 in $8\frac{1}{2}$ crossing by using all the three methods(Right angle, centre line and isosceles triangle method):

Solution:

1. By using right angle method

We know, $\cot \alpha = N = 8.5$ [N = $8\frac{1}{2}$ = 8.5]

So, Angle of Crossing = $\alpha = 6^{\circ} {42}’ {35}”$

2. By using centre line method

We know,

$\cot \frac{\alpha }{2} = 2N = 2 \times 8.5 = 17$

So, Angle of Crossing = $\alpha = 6^{\circ} {43}’ {59}”$

3. By using Isosceles triangle method

We know,

Or, $\alpha = 6^{\circ} {44}’ {41}”$

Angle of Railway Crossing Methods

Loop Line in Railway

# Loop Line in Railway and its Types

## Loop Line in Railway?

When a branch line leaves from a mainline and again this branch line terminates at the same mainline later, it is called a loop line. The main purpose of providing a loop line is to provide a bypass route. It helps to pass the fast-moving trains on time. The arrangement of the loop line can be either of the following types:

1. Split turnout
2. Trailing turnout
3. Straight and loop

➤ A split turnout is not suitable for fast-moving trains as they have to reduce their speed while nearing the facing points. Therefore, the use of split turnout is unacceptable when considering fast-moving trains.

➤ A trailing turnout is less objectionable as compared to a split turnout because there is a slight reduction in the speed of fast trains while leaving over a reverse curve.

➤ When considering fast through trains, straight and loop arrangement is always acceptable because there is no reduction in speed. Additional loops and other facilities are provided whenever needed.

Triangle – Railway Track Junction

Railway Water Columns

Switch Angle in Railway

# Triangle – Railway Track Junction

## Triangle – Railway Track Junction

The triangle is a junction of a railway track, which is constructed for changing the direction of engines. They require a large area and therefore they are constructed where there is enough land available for their construction.

Turntables are also used to change the direction of engines, but they are very costly. So, if enough area is available, then the construction of triangles is preferable to turntable installation. The triangle’s maintenance cost is less than that of the turntable.

Generally, a triangle junction consists of three tracks, they are PQ, QS, and SP, which are shown in the above fig. Usually, PQ and SQ tracks are curved and the PS track is straight. But sometimes all three tracks are laid on curves as shown in the figure.

A dead-end siding QR is provided at point Q to accommodate the length of the engine. If space permits, the QR length should be kept slightly longer than the lengths of two locomotives.

### Working Principle of Triangle

The working of triangle is very simple and it is very easy to understand. If an engine is standing at S facing towards P and the engine moves in the direction of arrows(i.e along SQ track) as shown[Now, in a simple way we can say a train moves from S to Q, then Q to R, then back R to Q, and then Q to P], it will be facing S when it reaches point P.

### Importance Features of Triangle

i. It consists of two simple turnouts (i.e., at S and P) and one symmetrical split at Q.

ii. This type of track junction has three acute angle crossings as shown in the figure.

iii. This is mainly used for turning the faces of engines where the provision of the turntable is costly.

Permanent Way in Railway

Types of Railway Platform

Types of Rails – Double Headed, Bull Headed, and Flat Footed Rails

Switch Angle in Railway

# Types of Railway Platform || Railway Engineering

## Types of Railway Platform

The platform is a raised level surface of a railway station, from where either passengers can get into the train, or the loading and unloading of goods are done. Generally, the following two types of railway platform are provided:

1. Passenger Platform
2. Goods Platform

### 1. Passenger Platform

As the name suggests, this type of platform is constructed for the movement of passengers who are using the railway. The following are the essentials of a passengers platform:

i. The passengers’ platform should be covered for a minimum distance of 60 to 61 m of their length.

ii. These types of railway platforms should be paved with a minimum width of 3.65 m.

iii. A ramp should be provided at the end of the platform of maximum slope 1: 6.

iv. Sufficient arrangement of light should be made for the efficient and safe running of trains at night.

v. The drinking water facility should be provided on the passenger platform, and also necessary sanitary arrangements should be made.

vi. The names of stations should be written on a R.C.C. or stone board in bold letters in Hindi, English, and the regional language. The station’s name is written on both sides of the board.

vii. The station’s name should be written on a yellow background in black letter with a size of 300 mm. The spacing between the letters, and also at the top and the bottom letter is 150 mm.

viii. The name board should be kept at least a height of 1.8 m from the platform level.

### Dimensions of the passenger platform

a. Length and Width of the passenger platform

• The minimum length recommended for passenger platform in case of all gauges is 180 m. But the desirable length for B.G is 305 m.
• The minimum permissible width in front of a station building for all gauge is 3.60 m.

b. Clearance between the center line of the adjacent track and the edge of the platform

• In India, the clearance is kept 1676 mm for Broad Gauge.
• 1346 mm for Meter Gauge.
• And 1219 mm for narrow gauge.

c. Height or elevation of the passenger platform

Generally, in India, there are three types of platform elevation, namely, the rail level, the low level and high-level platform. The height above rail level for different gauges and platform are as follows:

d. Slope of Platform

The platforms are provided with a slope of 1 in 30 across its width.

### 2. Goods Platform

As the name suggests, these types of railway platforms are used for the loading and unloading of goods. The following are the essentials of a goods platform.

i. Generally goods platforms are higher and the minimum width is 3 m.

ii. The goods sheds should be provided on the goods platforms and at the same time an arrangements for weighing the goods should be provided on these platforms.

iii. Proper drainage facility is very essential for a goods platform, hence proper arrangements for drainage should be made on these platforms.

The Permissible height of the goods platforms above the rail level is as follows:

Facilities Required at Railway Stations

Railway Gauge

Purpose of Providing Railway Station

# Calculate the Correct Length of the Tape – Mathematics Problem & Solution

Mathematics Problem – Example:

A line of true length 500 m, when measured by a 20 m tape, is reported to be 502 m long. The correct length of tape is?

Solution:

Given,

• True Length = 500 m
• Measured Length = 502 m

The line is measured long (502-500) = 2 m. Hence, the tape is short by some length and the actual length is not 20 m.

Hence,

True Length of Line = $\frac{{l}’}{l}\times$ measured length

Or, $500 = \frac{{l}’}{20}\times 502$

Or, $\frac{500\times 20}{502} = {l}’$

Or, ${l}’ = 19.92 m$

Different Types of Map Symbols

# 5 Purposes of Providing Superelevation in Roads

## 5 Purposes of Providing Superelevation

Following are the 5 purposes or advantages of providing superelevation on the curve portion of a road.

1. When a vehicle is moving on a curved path it is subject to an outward force known as centrifugal force. In order to counteract the effect of the centrifugal force, superelevation is provided.

Know more –Maximum And Minimum SuperElevation

2. It helps to keep your speed constant with comfort on a curve path.

3. It reduces the number of accidents.

4. It helps to drain off rainwater towards the inner side. so no need to provide camber at this portion of roads…(Analysis of Superelevation Formula)

5. It also helps to keep the vehicles to their proper side on the roads and thus prevents head collision of vehicles moving in opposite directions.

# Facilities Required at Railway Stations

## Facilities Required at Railway Stations

The features or requirements of a railway station can be grouped as under.

1. Public Requirements.
2. Traffic Requirements.
3. Requirements of the locomotive department.
4. General Requirement.

### 1. Public Requirements

i. A booking office for tickets.
ii. A platform for goods and passengers.
iii. A minimum platform covering.
iv. Proper lighting for night times.

v. Proper arrangement of drinking water.
vi. A refrigerator to supply cold water in hot weather if possible.
vii. Proper sanitary arrangements.
viii. Bathrooms

ix. Refreshment Rooms.
x. Waiting rooms and retiring rooms.
xi. Public telephone.
xii. Microphones to announce the arrival and departure of trains.

xiii. Guide map of the town.
xiv. A big board to show the timetable of the trains.
xv. Police office to help the passengers, and to avoid any violation.
xvi. Inquiry office.
xvii. Boards showing reservation charts.

### 2. Traffic Requirements

i. Proper arrangements for booking tickets, issuing of luggage labels and goods receipts, and also, the arrangement to collect all these things at the end of the journey should be made.

ii. The way for controlling and reporting the movement of trains by means of signals should be made.

iii. A sufficient number of sidings and platforms should be constructed to handle goods and traffic.

v. In the case of a big station, for moving luggage and heavy goods through lifts or underground passages should be constructed.

vi. Arrangements should be made to accommodate the staff of the traffic department.

### 3. Requirements of the Locomotive Department

Following are the requirements of the locomotive department.

i. Proper arrangements for supplying fuel and water to locomotives should be made.

ii. In a proper way, cleaning and examining the locomotives should be provided.

iii. The facility should be provided for maintaining and inspecting the locomotive.

### 4. General Requirement

General requirements or requirements for the development of railways are as follows:

i. Easy and suitable approach roads should be available towards the stations from the surrounding areas.
ii. Clocks for the correct time should be provided.
iii. Availability of coolies
iv. Foot bridges for connecting various platforms should be constructed.

Purpose of Providing Railway Station

Angle of Crossing in Railway

Top 10 Most Beautiful Railway Stations in the World

# Angle of Crossing in Railway & Methods Used to Determine it

## Angle of Crossing in Railway

The angle which is formed between the gauge faces of the Vee is known as the crossing angle or angle of the railway crossing. Following are the three methods used to determine the angle of crossing in railway.

### 1. Right Angle or Cole’s Method

In this method, a right angle triangle is used to determine the angle of crossing.

Notation:

• $\alpha$= Angle of Crossing
• N = Crossing Number

From this Figure, we can write

$\tan \alpha = \frac{1}{N}$

Or, $\cot \alpha = N$ …………(1.a)

Or, $N = \cot \alpha$ …………(1.b)

Equation (1.a) shows the angle of crossing.
Equation (1.b) shows the number of crossings.

Note: This is the standard method mostly adopted by the Indian Railways.

### 2. Centre Line Method

In this method, the measurement is taken along a line bisecting the crossing angle as shown in Fig.

Now,

$\tan \frac{\alpha}{2} = \frac{\frac{1}{2}}{N} = \frac{1}{2N}$

Or, $\cot \frac{\alpha}{2} = 2N$ …………..(2.a)

Or, $N = \frac{1}{2}.\cot \frac{\alpha}{2}$ ……….(2.b)

Equation (2.a) shows the angle of crossing.
Equation (2.b) shows the number of crossings.

Note: This method is adopted in some countries like U.K. and U.S.A.

### 3. Isosceles Triangle Method

In this case, the measurement is taken along one side of the isosceles triangle as shown in fig.

Then,

$\sin \frac{\alpha}{2} = \frac{\frac{1}{2}}{N} = \frac{1}{2N}$

Or, $cosec \frac{\alpha}{2} = 2N$ …………..(3.a)

Or, $N = \frac{1}{2}. cosec \frac{\alpha}{2}$ ……….(3.b)

Equation (3.a) shows the angle of crossing.
Equation (3.b) shows the number of crossings.

Note: This method is implemented in the case of tramway layout.

More the angle of crossing lesser will be permissible speed and vice versa