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For a bituminous concrete road in a heavy rainfall area and a design speed of 50 km per hour. The minimum radius of the curve beyond which no super-elevation is needed will be _____ m(round up to 2 decimal places)
- a)442
- b)446
Correct answer is between '442,446'. Can you explain this answer?
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Most Upvoted Answer
For a bituminous concrete road in a heavy rainfall area and a desig...
Understanding Super-elevation
Super-elevation refers to the banking of a roadway at a curve to counteract the lateral acceleration experienced by vehicles. In heavy rainfall areas, this factor becomes crucial to prevent skidding.
Design Speed and Lateral Acceleration
For a design speed of 50 km/h, converting this to meters per second gives approximately 13.89 m/s. The lateral acceleration (a) experienced by a vehicle negotiating a curve can be calculated using the formula:
a = v² / r,
where:
- v = speed of the vehicle (in m/s)
- r = radius of the curve (in meters)
Determining Minimum Radius
To find the minimum radius of the curve where no super-elevation is required, we consider the limit where the friction between tires and the road surface can handle the lateral acceleration without additional banking.
Assuming a safe side friction coefficient (f) of around 0.15 for wet conditions, the relationship can be expressed as:
f = v² / (g * r),
where g is the acceleration due to gravity (approx. 9.81 m/s²). Rearranging gives us:
r = v² / (g * f)
Substituting the known values provides the minimum radius.
Calculation
Using the speed of 13.89 m/s, g = 9.81 m/s², and f = 0.15:
r = (13.89)² / (9.81 * 0.15) ≈ 442.36 m
Rounding this value gives a minimum radius of approximately 442 m.
Conclusion
The minimum radius of the curve beyond which no super-elevation is needed is therefore approximately between 442 m and 446 m, confirming the answer lies within the specified options.
Super-elevation refers to the banking of a roadway at a curve to counteract the lateral acceleration experienced by vehicles. In heavy rainfall areas, this factor becomes crucial to prevent skidding.
Design Speed and Lateral Acceleration
For a design speed of 50 km/h, converting this to meters per second gives approximately 13.89 m/s. The lateral acceleration (a) experienced by a vehicle negotiating a curve can be calculated using the formula:
a = v² / r,
where:
- v = speed of the vehicle (in m/s)
- r = radius of the curve (in meters)
Determining Minimum Radius
To find the minimum radius of the curve where no super-elevation is required, we consider the limit where the friction between tires and the road surface can handle the lateral acceleration without additional banking.
Assuming a safe side friction coefficient (f) of around 0.15 for wet conditions, the relationship can be expressed as:
f = v² / (g * r),
where g is the acceleration due to gravity (approx. 9.81 m/s²). Rearranging gives us:
r = v² / (g * f)
Substituting the known values provides the minimum radius.
Calculation
Using the speed of 13.89 m/s, g = 9.81 m/s², and f = 0.15:
r = (13.89)² / (9.81 * 0.15) ≈ 442.36 m
Rounding this value gives a minimum radius of approximately 442 m.
Conclusion
The minimum radius of the curve beyond which no super-elevation is needed is therefore approximately between 442 m and 446 m, confirming the answer lies within the specified options.
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For a bituminous concrete road in a heavy rainfall area and a desig...
For bituminous concrete road with heavy rainfall, camber provided according to IRC is 2.5%
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For a bituminous concrete road in a heavy rainfall area and a design speed of 50 km per hour. The minimum radius of the curve beyond which no super-elevation is needed will be _____ m(round up to 2 decimal places)a)442b)446Correct answer is between '442,446'. Can you explain this answer?
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