L = eNW = 1/15 x 120 x 10 = 80m

Given: Maximum super elevation = 1 in 15, Rate of change of super elevation = 1 in 120, Road width = 10m.

To find: Minimum length of transition curve on either end.

Solution:

What is super elevation?

Super elevation is the banking of road curves to counteract the centrifugal force acting on a vehicle as it moves along the curve. The aim of providing super elevation is to increase the safe speed of a vehicle on a curve without skidding or overturning.

What is a transition curve?

A transition curve is a curve that is used to gradually introduce the super elevation on a road curve. It is a curve that connects the circular curve and the tangent of the road.

Formula:

The length of transition curve can be calculated using the following formula:

L = V^2/127R

Where,

L = Length of transition curve, in meters
V = Design speed, in km/hr
R = Radius of circular curve, in meters

Calculation:

Given: Maximum super elevation = 1 in 15, Rate of change of super elevation = 1 in 120, Road width = 10m.

To find: Minimum length of transition curve on either end.

Step 1: Calculation of Radius of Circular Curve:

The maximum super elevation that can be provided on a road curve is 1 in 15.

i.e. e = 1/15

The rate of change of super elevation is specified as 1 in 120.

i.e. de/dx = 1/120

The radius of the circular curve can be calculated using the following formula:

R = (W^2)/(2e) + (e/2)

Where,

W = Road width = 10m
e = Super elevation = 1/15

Putting the values, we get:

R = (10^2)/(2*(1/15)) + (1/2)

R = 375m

Step 2: Calculation of Design Speed:

The design speed of the road curve can be calculated using the following formula:

V = 3.6√(fR)

Where,

V = Design speed, in km/hr
f = Coefficient of friction = 0.15 (assumed)
R = Radius of circular curve, in meters

Putting the values, we get:

V = 3.6√(0.15*375)

V = 47.18 km/hr

Step 3: Calculation of Length of Transition Curve:

The length of transition curve can be calculated using the following formula:

L = V^2/127R

Putting the values, we get:

L = (47.18^2)/(127*375)

L = 80.17m

Therefore, the minimum length of the transition curve on either end will be 80m (approx).

Hence, the correct option is (C) 80m.