The maximum limit of super elevation on B.G. track in India is
165.1 mm
Understanding Super Elevation on Broad Gauge Railway Tracks
Super elevation, also known as cant, is the raising of the outer rail above the inner rail on a curved railway track. This is done to counteract the centrifugal force that acts on a train moving along a curve. Without super elevation, the train would tend to move outwards from the curve, causing discomfort to passengers and excessive wear on the rails and wheels, and potentially leading to derailment at higher speeds.
Super Elevation Requirements for Broad Gauge in India
In India, railway tracks are primarily classified into different gauges, with Broad Gauge (B.G.) being the most common. Broad Gauge has a track width of $\text{1676 mm}$. The design standards for railway tracks in India, including the limits for super elevation, are set by the Indian Railways.
The amount of super elevation provided on a curve depends on several factors, including the radius of the curve, the speed of the train, and the gauge of the track. However, there are maximum limits specified for super elevation to ensure safety and passenger comfort, especially for slower-moving trains which would experience excessive tilting if the super elevation is too high.
Maximum Limit of Super Elevation on B.G. Track
For Broad Gauge tracks in India, the maximum permissible limit for super elevation (cant) is specified. This limit is set keeping in mind various operational and safety considerations.
According to Indian Railway standards, the maximum limit of super elevation on B.G. track is $\text{165 mm}$. The options provided are in decimals, so we look for the closest value.
| Gauge Type | Track Width | Maximum Super Elevation Limit (India) |
|---|---|---|
| Broad Gauge (B.G.) | $\text{1676 mm}$ | $\text{165 mm}$ (or $\text{165.1 mm}$) |
| Metre Gauge (M.G.) | $\text{1000 mm}$ | $\text{100 mm}$ |
| Narrow Gauge (N.G.) | $\text{762 mm}$ and $\text{610 mm}$ | $\text{65 mm}$ (for $\text{762 mm}$ gauge) $\text{50 mm}$ (for $\text{610 mm}$ gauge) |
Looking at the options:
- Option 1: $\text{76.2 mm}$
- Option 2: $\text{83.2 mm}$
- Option 3: $\text{101.6 mm}$
- Option 4: $\text{165.1 mm}$
Comparing these values with the standard limit of $\text{165 mm}$ for B.G. track in India, the value $\text{165.1 mm}$ is the closest and represents the specified limit in some contexts (often rounded from imperial measurements). While $\text{165 mm}$ is commonly cited, $\text{165.1 mm}$ corresponds to $\text{6.5 inches}$, a common value in older specifications which is still often used.
Revision Table: Key Railway Track Limits
| Parameter | Broad Gauge (B.G.) | Metre Gauge (M.G.) |
|---|---|---|
| Track Width | $\text{1676 mm}$ | $\text{1000 mm}$ |
| Maximum Super Elevation (Cant) | $\text{165.1 mm}$ | $\text{100 mm}$ |
| Maximum Cant Deficiency (General) | $\text{75 mm}$ | $\text{50 mm}$ |
| Maximum Cant Deficiency (High Speed) | $\text{100 mm}$ | N/A |
Additional Information: Cant Deficiency and Equilibrium Speed
While maximum super elevation is one important limit, other related concepts are also crucial in railway track design:
- Cant Deficiency: This occurs when a train travels around a curve at a speed higher than the equilibrium speed for the provided super elevation. It is the difference between the theoretical super elevation required for the actual speed and the super elevation actually provided. The maximum permissible cant deficiency is also limited to ensure safety and prevent excessive lateral forces. For B.G. tracks in India, the general limit for cant deficiency is $\text{75 mm}$, but it can be increased to $\text{100 mm}$ on specific high-speed routes with approval.
- Equilibrium Speed: This is the speed at which the centrifugal force is perfectly balanced by the super elevation provided. At this speed, there is no lateral thrust on the rails, and passengers feel no discomfort from lateral forces. The formula for equilibrium speed ($v_{eq}$) is given by:
$\text{v}_{eq} = \sqrt{\frac{g \cdot C \cdot R}{W}}$
Where:
- $g$ is the acceleration due to gravity
- $C$ is the super elevation (cant)
- $R$ is the radius of the curve
- $W$ is the track gauge
A simplified formula often used in practice relates speed (V in kmph), gauge (G in meters), radius (R in meters), and cant (C in meters):
$\text{C} = \frac{\text{Gv}^2}{\text{127R}}$ (approximate, simplified for V in kmph)
Maximum super elevation limits are set to ensure that even for very slow trains (where cant excess occurs) or trains standing on a curve, the lateral tilt is not uncomfortable or unsafe.
- Cant Excess: This occurs when a train travels around a curve at a speed lower than the equilibrium speed. It is the difference between the super elevation provided and the theoretical super elevation required for the actual speed. Maximum cant excess is also limited, typically to prevent discomfort and excessive vertical load on the inner rail. For B.G. in India, the maximum cant excess limit is typically $\text{75 mm}$.
Important Questions from Basic Principles
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