Calculate the number of sleepers required for 1 km railway track, if sleeper density is (n + 4) for broad gauge and the length of one rail for a broad gauge is 13 m.
1308
Calculating Sleepers for Railway Tracks: A Step-by-Step Guide
This question asks us to determine the total number of sleepers required for a 1 km length of broad gauge railway track, given a specific sleeper density and the length of a single rail.
Understanding Sleeper Density
Sleeper density is a measure used in railway engineering to specify how many sleepers are placed per length of rail. It is often expressed in the form of (n + x), where 'n' represents the length of the rail in meters, and 'x' is an additional number of sleepers placed within that rail length.
In this problem, the sleeper density is given as (n + 4) for a broad gauge track. The length of one rail for broad gauge is provided as 13 m. Therefore, we substitute n = 13 m into the density formula:
Sleeper Density = (n + 4) sleepers per rail length
Sleeper Density = (13 + 4) sleepers per rail length
Sleeper Density = 17 sleepers per rail length
This means that for every 13-meter length of rail, 17 sleepers are needed.
Calculating the Number of Rail Lengths in 1 km
We need to find out how many 13-meter rail lengths are there in a 1 km railway track. First, we convert the total track length from kilometers to meters:
Total Track Length = 1 km
1 km = 1000 meters
Now, we divide the total track length by the length of a single rail to find the number of rail lengths:
Number of Rail Lengths = \frac{\text{Total Track Length}}{\text{Length of one rail}}
Number of Rail Lengths = \frac{1000 \text{ m}}{13 \text{ m}}
Number of Rail Lengths \approx 76.923
Since we cannot have a fraction of a rail length in this calculation context (we are calculating how many segments equivalent to one rail length fit), we consider the full length. The track is made up of approximately 76.923 segments of 13m each. The number of rail joints will influence the exact count, but for a continuous 1 km section, this is the total coverage needed.
Total Number of Sleepers Calculation
To find the total number of sleepers required for the entire 1 km track, we multiply the number of rail lengths by the number of sleepers per rail length (the sleeper density).
Total Number of Sleepers = (Number of Rail Lengths) \times (Sleeper Density)
Total Number of Sleepers = \frac{1000}{13} \times 17
Total Number of Sleepers \approx 76.923 \times 17
Total Number of Sleepers \approx 1307.69
Since the number of sleepers must be a whole number, and to ensure the entire track length is supported correctly, we round this number up to the nearest integer.
Total Number of Sleepers = 1308
Summary of Calculation Steps
| Parameter | Value |
|---|---|
| Total track length | 1 km = 1000 m |
| Broad gauge rail length (n) | 13 m |
| Sleeper density formula | (n + 4) sleepers per rail length |
| Calculated sleeper density | (13 + 4) = 17 sleepers per rail length |
| Number of rail lengths in 1 km | \frac{1000 \text{ m}}{13 \text{ m}} \approx 76.923 |
| Total number of sleepers | \approx 76.923 \times 17 \approx 1307.69 |
| Rounded number of sleepers | 1308 |
Based on the calculation, approximately 1308 sleepers are required for a 1 km broad gauge railway track with a sleeper density of (n+4).
Conclusion on Required Sleepers
The calculation shows that for a 1 km broad gauge railway track with a 13m rail length and (n+4) sleeper density, the total number of sleepers needed is 1308. This is a standard calculation in railway track design and construction to estimate material requirements.
Revision Table: Railway Track Sleepers
| Term | Description | Calculation Method |
|---|---|---|
| Railway Sleeper | A rectangular support for the rails in railroad tracks. Transfers load to ballast. | N/A |
| Sleeper Density | Number of sleepers placed per length of rail (e.g., n+x). | Substitute rail length for 'n'. |
| Broad Gauge | A railway track gauge wider than standard gauge (typically 1676 mm in many countries). | Affects standard rail length used. |
| Rail Length (n) | The standard length of a single rail section (e.g., 13m for broad gauge). | Provided in the problem or standard specifications. |
| Total Sleepers | Total number of sleepers for a given track length. | (Total Track Length / Rail Length) \times Sleeper Density |
Additional Information: Railway Track Components
A railway track is composed of several key components that work together to provide a stable and smooth path for trains. Understanding these parts helps in appreciating calculations like sleeper density.
- Rails: The steel beams that guide the wheels of the train.
- Sleepers (Ties): Placed perpendicular to the rails, they support the rails and transfer the load to the ballast. They maintain the gauge (distance between rails). Can be made of wood, concrete, or steel.
- Ballast: A layer of crushed stone or gravel placed beneath the sleepers. It distributes the load from the sleepers to the formation, provides drainage, and holds the track in place.
- Fastenings: Clips, bolts, or spikes used to secure the rails to the sleepers.
- Formation (Subgrade): The prepared ground surface upon which the ballast is laid.
The spacing of sleepers (dictated by sleeper density) is crucial for evenly distributing the load from the train to the ballast and subgrade, affecting the stability and longevity of the railway track.
Important Questions from Basic Principles
The longitudinal movement of a rail is known as:
Match the designated component in List 1 with its purpose at airports in List 2.
List 1
A. Basic Runway length
B. Runway Capacity
C. Runway geometric design
D. Hanger
List 2
1. Width and length of safety area of airport
2. Housing, servicing of aircrafts
3. Location of exit taxiways
4. Engine failure class
In the North India, the first train was operated from Allahabad to Kanpur in the year:
Who was the Governor-General during the first train run in India?
_______ represents the maximum width and height to which a rolling stock, namely, a locomotive, coach or wagon, can be built.
