# Grade Compensation Mathematical Problems and Solution

7th April 2019## Grade Compensation Problems and Solution

Here one mathematical example is taken for, how to determine grade compensation when the gradient and radius of curve is given.

### Mathematical Problems

The **gradient** on a highway is 1 in 15. The radius of curve is 160 m. After grade compensation, the grade to be provided should not be less than 4%. **What is grade compensation**?

### Mathematical Solution

Gradient, N = 1/15 = (1/15)⨯100 = 6.67 %.

Grade compensation = (30+R)/R

= (30+160)/160 = 1.1875%

Or, 75/R = 75/160 = 0.47%

Use minimum i.e., 0.47%.

After grade compensation the gradient to be provided on the road is 6.67 -0.47 = 6.2 % (Which is more than 4%, hence OK)

So, Grade compensation = 0.47%.

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