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At a road curve of radius 450 m, for a vehicle speed of 120 km/h, the total super elevation required is ___________ m. Take the width of the road as 20 m and the coefficient of friction as 0.20. (Answer up to two decimal places)
Correct answer is '1.04'. Can you explain this answer?
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At a road curve of radius 450 m, for a vehicle speed of 120 km/h, the...
Given: R = 450 m, V = 120 km/h,
w = 20 m and f = 0.20
Super elevation e is
Total super elevation is ew = 0.052(20) = 1.04
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At a road curve of radius 450 m, for a vehicle speed of 120 km/h, the...
The super elevation required for a road curve can be calculated using the following formula:
Super elevation = (v^2) / (g * r)
Where:
v = vehicle speed in m/s
g = acceleration due to gravity (9.81 m/s^2)
r = radius of the curve in meters
Step 1: Convert the vehicle speed from km/h to m/s.
Given vehicle speed = 120 km/h
Convert km/h to m/s:
120 km/h = (120 * 1000) / 3600 = 33.33 m/s
Step 2: Calculate the super elevation using the formula.
Given radius of the curve = 450 m
Super elevation = (33.33^2) / (9.81 * 450) = 0.254
Step 3: Convert the super elevation to the width of the road.
Given width of the road = 20 m
To convert the super elevation to the width of the road, we need to consider the coefficient of friction.
Coefficient of friction = 0.20
The equation for calculating the super elevation required is:
Super elevation = (v^2) / (g * r)
Rearranging the equation, we get:
r = (v^2) / (g * Super elevation)
Substituting the given values:
r = (33.33^2) / (9.81 * 0.20) = 569.47
This is the radius of the curve required to generate the required super elevation.
Step 4: Calculate the super elevation required for the width of the road.
We can calculate the super elevation required for the width of the road using the following formula:
Super elevation (width of road) = (Super elevation * width of road) / radius of the curve
Substituting the given values:
Super elevation (width of road) = (0.254 * 20) / 569.47 = 0.0089 m
Step 5: Calculate the total super elevation required.
The total super elevation required is the sum of the super elevation for the width of the road and the super elevation calculated in step 2.
Total super elevation required = 0.0089 + 0.254 = 0.2629 m
Rounding the answer to two decimal places, the total super elevation required is approximately 0.26 m.
Therefore, the correct answer is '1.04' is incorrect. The correct answer is approximately '0.26' m.
Super elevation = (v^2) / (g * r)
Where:
v = vehicle speed in m/s
g = acceleration due to gravity (9.81 m/s^2)
r = radius of the curve in meters
Step 1: Convert the vehicle speed from km/h to m/s.
Given vehicle speed = 120 km/h
Convert km/h to m/s:
120 km/h = (120 * 1000) / 3600 = 33.33 m/s
Step 2: Calculate the super elevation using the formula.
Given radius of the curve = 450 m
Super elevation = (33.33^2) / (9.81 * 450) = 0.254
Step 3: Convert the super elevation to the width of the road.
Given width of the road = 20 m
To convert the super elevation to the width of the road, we need to consider the coefficient of friction.
Coefficient of friction = 0.20
The equation for calculating the super elevation required is:
Super elevation = (v^2) / (g * r)
Rearranging the equation, we get:
r = (v^2) / (g * Super elevation)
Substituting the given values:
r = (33.33^2) / (9.81 * 0.20) = 569.47
This is the radius of the curve required to generate the required super elevation.
Step 4: Calculate the super elevation required for the width of the road.
We can calculate the super elevation required for the width of the road using the following formula:
Super elevation (width of road) = (Super elevation * width of road) / radius of the curve
Substituting the given values:
Super elevation (width of road) = (0.254 * 20) / 569.47 = 0.0089 m
Step 5: Calculate the total super elevation required.
The total super elevation required is the sum of the super elevation for the width of the road and the super elevation calculated in step 2.
Total super elevation required = 0.0089 + 0.254 = 0.2629 m
Rounding the answer to two decimal places, the total super elevation required is approximately 0.26 m.
Therefore, the correct answer is '1.04' is incorrect. The correct answer is approximately '0.26' m.
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At a road curve of radius 450 m, for a vehicle speed of 120 km/h, the total super elevation required is ___________ m. Take the width of the road as 20 m and the coefficient of friction as 0.20. (Answer up to two decimal places)Correct answer is '1.04'. Can you explain this answer?
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