What is the curve resistance for a 50 tonnes train on a BG track on a 4°curve?
0.08 tonne
Calculating Railway Curve Resistance
Curve resistance is a type of resistance encountered by a train when it moves along a curved track. This resistance is mainly due to the friction between the wheel flanges and the rail, as well as the slipping of wheels. It depends on factors like the weight of the train and the degree of curvature of the track.
Formula for Curve Resistance on Broad Gauge (BG) Track
For Broad Gauge (BG) tracks, the curve resistance ($R_c$) is commonly calculated using the following empirical formula:
\[ R_c = 0.0004 \times W \times D \] যেখানে:
- $R_c$ হলো কার্ভ রেজিস্ট্যান্স (tonne-এ).
- $W$ হলো ট্রেনের ওজন (tonne-এ).
- $D$ হলো কার্ভের ডিগ্রী (° -এ).
Step-by-Step Calculation
Given in the question:
- ট্রেনের ওজন ($W$) = 50 tonnes
- কার্ভের ডিগ্রী ($D$) = 4°
- ট্র্যাক গেজ = ব্রড গেজ (BG)
Using the formula for curve resistance on BG track:
\[ R_c = 0.0004 \times W \times D \]
Substitute the given values into the formula:
\[ R_c = 0.0004 \times 50 \times 4 \]
Now, perform the multiplication:
\[ R_c = 0.0004 \times 200 \]
\[ R_c = 0.08 \text{ tonnes} \]
Result and Analysis
The calculated curve resistance for the 50 tonnes train on a 4° curve on a BG track is 0.08 tonnes.
Let's compare this result with the given options:
| Option | Value (tonne) | Matches Calculation |
|---|---|---|
| 1 | 0.06 | No |
| 2 | 0.01 | No |
| 3 | 0.05 | No |
| 4 | 0.08 | Yes |
The calculated value matches Option 4.
Revision Table: Railway Resistances
| Type of Resistance | Description | Factors Affecting It |
|---|---|---|
| Rolling Resistance | Resistance due to friction at axles, contact between wheel and rail, and air resistance. | Speed, train weight, condition of track and rolling stock. |
| Gradient Resistance | Resistance encountered when a train moves up an incline. | Weight of the train and the steepness of the gradient. |
| Curve Resistance | Resistance encountered when a train moves along a curve. | Weight of the train, degree of curve, gauge of the track. |
Additional Information: Railway Curves and Gauges
Degree of Curve: The degree of curve ($D$) is defined as the angle subtended by an arc of length 100 feet (or 30 meters depending on the system) at the center. On Indian Railways (which follows the 30m chord definition), a relationship exists between the radius ($R$) and the degree of curve ($D$): $R \approx \frac{1750}{D}$ for chord definition, or $R \approx \frac{1719}{D}$ for arc definition. The problem uses the degree directly in the resistance formula.
Railway Gauges in India:
- Broad Gauge (BG): 1676 mm (5 ft 6 in) - The most common gauge in India.
- Meter Gauge (MG): 1000 mm (3 ft 3 3/8 in) - Less common now.
- Narrow Gauge (NG): 762 mm (2 ft 6 in) or 610 mm (2 ft) - Used in hilly areas or for specific purposes.
The formula for curve resistance might slightly differ for different gauges or based on specific railway standards, but $0.0004 WD$ is a standard formula for BG tracks.
Important Questions from Track Design
To effectively control creep in rails on broad gauge tracks, how many rail anchors are typically installed per $13$ meter rail length?
Which one of the following is the CORRECT sequence for a train in order to pass over the turnout from the facing direction?
Which of the following types of track fittings are fixed with the help of tie bars and cotters?
The railway device primarily used to rotate locomotives or individual wagons, typically $180^\circ$, to change their direction, especially within engine sheds or depots with limited space, is known as a:-
In horizontal curves of Railway Tracks, Negative Super elevation means-
