Calculation of Compensated Gradient for a Curve of Radius 120 m on a Highway:

Given:
Ruling Gradient = 1 in 20

To find:
Compensated Gradient for a Curve of Radius 120 m

Formula:
Compensated Gradient = Ruling Gradient + (Superelevation/Radius)
Superelevation = (V^2)/(127*R)
Where,
V = Design Speed in km/hr
R = Radius of Curve in meter

Calculation:
Assuming Design Speed = 80 km/hr

Superelevation = (80^2)/(127*120)
Superelevation = 0.42 m or 4.2%

Compensated Gradient = 1/20 + (4.2/120)
Compensated Gradient = 0.0525 + 0.035
Compensated Gradient = 0.0875 or 8.75%

Therefore, the Compensated Gradient for a Curve of Radius 120 m on a Highway is 8.75%.

Explanation:

- The ruling gradient is the maximum allowed gradient on a highway that can be used for a long distance without causing any discomfort to the passengers.
- The compensated gradient is the gradient that takes into account the effect of super-elevation on a curved road section.
- The super-elevation is the banking of a road at a curve to counter the centrifugal force acting on the vehicles.
- The formula for calculating the compensated gradient takes into account the ruling gradient and the super-elevation.
- The radius of the curve also affects the super-elevation, and hence, the compensated gradient.
- In this case, assuming a design speed of 80 km/hr, the super-elevation is calculated to be 4.2%.
- Substituting the values in the formula for compensated gradient gives a value of 8.75%.
- Therefore, for a highway with a ruling gradient of 1 in 20 and a curve of radius 120 m, the compensated gradient is 8.75%.