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Extra widening required at a horizontal curve on a single lane road of radius 100m for a design speed of 60 kmph and for a vehicle with wheel base 6m is:
- a)0.12m
- b)0.18m
- c)0.63m
- d)0.80m
Correct answer is option 'B'. Can you explain this answer?
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Calculation of Extra Widening Required at a Horizontal Curve on a Single Lane Road
Given parameters:
Radius of the curve (R) = 100m
Design speed (V) = 60 kmph
Wheelbase of the vehicle (L) = 6m
Step 1: Calculation of Design Speed in m/s
Design speed (V) is given in kmph, but for calculation purposes, it needs to be converted to m/s.
V = 60 kmph
= (60 x 1000) / 3600 m/s
= 16.67 m/s
Step 2: Calculation of Coefficient of Lateral Friction (f)
The coefficient of lateral friction (f) determines the ability of a vehicle to negotiate a curve without skidding.
Assuming a dry road surface, the value of f can be taken as 0.15.
Step 3: Calculation of Centrifugal Force (Fc)
Centrifugal force is the force acting on a vehicle when it takes a curve. It is given by the formula:
Fc = (mv^2) / R
where m = mass of the vehicle, and v = velocity of the vehicle.
Assuming a vehicle mass of 1500 kg, the value of Fc is:
Fc = (1500 x 16.67^2) / 100
= 418.5 N
Step 4: Calculation of Extra Widening Required (W)
Extra widening required is the additional width required on the outer edge of the curve to compensate for the centrifugal force.
W = (L^2 / 8R) + (fV^2 / gR)
where g = acceleration due to gravity (9.81 m/s^2)
Substituting the values of L, R, f, V, and g, we get:
W = (6^2 / 8 x 100) + (0.15 x 16.67^2 / 9.81 x 100)
= 0.18 m
Therefore, the extra widening required at a horizontal curve on a single lane road of radius 100m for a design speed of 60 kmph and for a vehicle with wheelbase 6m is 0.18m.
Given parameters:
Radius of the curve (R) = 100m
Design speed (V) = 60 kmph
Wheelbase of the vehicle (L) = 6m
Step 1: Calculation of Design Speed in m/s
Design speed (V) is given in kmph, but for calculation purposes, it needs to be converted to m/s.
V = 60 kmph
= (60 x 1000) / 3600 m/s
= 16.67 m/s
Step 2: Calculation of Coefficient of Lateral Friction (f)
The coefficient of lateral friction (f) determines the ability of a vehicle to negotiate a curve without skidding.
Assuming a dry road surface, the value of f can be taken as 0.15.
Step 3: Calculation of Centrifugal Force (Fc)
Centrifugal force is the force acting on a vehicle when it takes a curve. It is given by the formula:
Fc = (mv^2) / R
where m = mass of the vehicle, and v = velocity of the vehicle.
Assuming a vehicle mass of 1500 kg, the value of Fc is:
Fc = (1500 x 16.67^2) / 100
= 418.5 N
Step 4: Calculation of Extra Widening Required (W)
Extra widening required is the additional width required on the outer edge of the curve to compensate for the centrifugal force.
W = (L^2 / 8R) + (fV^2 / gR)
where g = acceleration due to gravity (9.81 m/s^2)
Substituting the values of L, R, f, V, and g, we get:
W = (6^2 / 8 x 100) + (0.15 x 16.67^2 / 9.81 x 100)
= 0.18 m
Therefore, the extra widening required at a horizontal curve on a single lane road of radius 100m for a design speed of 60 kmph and for a vehicle with wheelbase 6m is 0.18m.
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Extra widening required at a horizontal curve on a single lane road of radius 100m for a design speed of 60 kmph and for a vehicle with wheel base 6m is:a)0.12mb)0.18mc)0.63md)0.80mCorrect answer is option 'B'. Can you explain this answer?
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