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Mathematics Behind Operating Passenger Trains: Types, Formula and Functionality

It is surprising to know that Mathematics is used to maintain the railways. Unlike our boring mathematics text book, Indian Railways uses its own kind of maths to operate trains. From algebra to trigonometry, it is used to find routes (either shortest or longest), calculate speed of trains and various other factors. The Indian Railways run about 20,000 trains regularly including passenger trains, express trains, and Rajdhani to carry over 23 million travelers which is equivalent to entire population of Australia. It connects more than 7,349 stations along with major and suburban routes. It is the financial backbone of our nation. It is an honour to say that it is the fourth largest rail network of world. Indian Railways is the cheapest way to travel from one place to another. There’re thousands of passengers train running daily. Still, new passenger trains’ are launched every year. The core concept of launching passenger trains is the increasing influx of travelers. There was a time when India had limited number of trains. But with growing population, many new trains have been launched and railways maintain the train schedule and its operations smoothly.

If there’s only Express or Superfast train in our Railways, the travelers’ load on these trains will increase with an upward spike. Passenger trains were specially launched for short duration train journeys. Some of those trains are duty special train, some are ladies special and rest locomotive trains are general. The Indian Railways always gives preference to express or superfast trains in comparison to locomotive trains. But, some specific passengers’ trains like the duty special train, its timing lies between 5:00 am to 9:00 am. Since its duty special, so Indian Railways care for its timing. For the safety of women passengers’ eight ladies special train runs between the location of Church gate, Borivali, Bhayander, Vasai road and Virar. Indian Railways has more than 3,300 electric and diesel passenger trains which run in a cyclic schedule known as locomotive links. The time table of passenger train is in dynamic mode.

Types of Passengers’ Train:
These passenger train services of Indian Railways, transports almost 2.5 crore passengers daily in 16 zones over a route of 65,808 km with 7,112 stations. Types of passengers’ trains are:

  • Suburban Trains: They’re the major transport system in the metro city eg. Like Mumbai Suburban Railway, Chennai Suburban Railway and the Kolkata Suburban Railway.
  • Local Trains: Slow Passenger Trains are called as local trains in India, which are convenient for getting off at small towns and villages.
  • Intercity: These’re the Indian inter-city trains used for longer distances run by Indian Railways.
  • Fast Passenger: Fast Passenger trains are Fast Passenger local train rail service of India, generally run on long distance single line routes.

Formula Behind the maintenance of passengers’ Trains by Indian Railways:
There’re three important mathematical formulas through which the Indian Railways’ operate the passenger train.

Passengers’ Train Punctuality:
Punctuality = RL+NLT/Total number of Mail express Trains*100
RT = Trains arriving Right Time
NLT= Trains not Loosing time

Shunting Kilometres per 100 Train Kilometres
This figure indicates the amount of unproductive service that has to be performed per 100 train kilometres (Passenger including proportion of mixed). Formula to calculate the same is:
Shunting Kms/Train Kms x 100

Vehicle Kilometres per Vehicles Day:
This figure indicates by the vehicle days which are the product of average number of coaching vehicles on line /in use and the number of days in the period under reference. The formula for the same are:
Vehicle km. Per Vehicle day= Coaching Vehicle Km/Vehicle day.

How to know which train is for suburban areas?
A train number is designed with 5 digits. All the digits of a train contain information about their functions.
First digit of a train number indicates its type; either it is express, superfast or passenger trains.

First Digit – Types of trains (0xxxx)
0 – Special trains, like Holiday or Exam Special
1 or 2 – Long distance trains, like Superfast or Express trains
3 – Kolkata Suburban Railways
4 – Other Suburban trains of Chennai, Delhi or Hyderabad Multi Modal Transport System
5 – Passengers trains with conventional coaches
6 – Memu Services
7 – Diesal multiple units or railcars
8 – Suvidha Express Trains
9 – Mumbai Suburban Railways

Second digit, indicates its zone Second Digit – Zone (x0xxx)
0 – Konkan Railways trains
1 – Central Railways, some are west central and North Central Railways trains
2 – Rajdhani, Shatabdi and all other superfast trains
3 – Eastern or East Central Railways trains
4 – Northern, North Central and North Western Railways trains
5 – North Eastern Railways trains
6 – Southern and South Western Railways trains
7 – South Central and South Western Railways trains
8 – South Eastern, South East Central and East Coast Railways trains
9 – Western, West Central and North Western Railways trains

Third digit shows where the train will be maintained
Third Digit – Maintanance Zone (xx0xx)
1 – Central and some West Central Zones trains
2 – Some Northern, North Central, north Western and Southern zone trains
3 – Eastern and East Central Zone trains
4 – Some Northern, North Central and North Western zone trains
5 – Northeast Frontier and North Eastern Zone trains
6 – Some Southern and South Western zone trains
7 – South Central and Some South Western zone trains
8 – South Eastern, South East Central and East Coast Zone trains
9 – Western, Some West Central and North Western Zone trains

Fourth and Fifth digit are random numbers for making each train numbers unique
Fourth & Fifth Digit- Random numbers
0 to 2 – Memu
3 to 5 – Electric multiple unit
6 and 7 – Conventional passenger coach
8 – Diesel multiple unit
9 – Other rolling stock

As for example, train number 63261
First digit is 6 – Memu service
Second digit, 3 – Eastern Railways
Third digit, 2 – Maintained in Danapur
Fourth & Fifth digit 61 – Conventional Passenger Coach
(Image Credit: news18.com, Indiatimes.com)