Question

A \(3\%\) downgrade curve is followed by a \(1\%\) upgrade curve and the rate of change of grade adopted is \(0.1\%\) per \(20\) m length. The length of the respective vertical curve is

• A. \(800\) m
• B. \(400\) m
• C. \(200\) m
• D. \(100\) m

Hint:

For vertical curves, \[ \boxed{ L=\frac{\text{Algebraic difference of grades}} {\text{Rate of change of grade}} \times \text{Specified length} } \] Always use the algebraic difference of the two gradients.

Answer 1

The Correct Option is A

Concept: The length of a vertical curve based on the permissible rate of change of grade is \[ \boxed{ L=\frac{N}{r}\times l } \] where \[ N=\text{Algebraic difference of grades (\%)}, \] \[ r=\text{Rate of change of grade (\% per interval)}, \] \[ l=\text{Specified interval length (m)}. \]

Step 1: Calculate the algebraic difference of grades. Given, \[ g_1=-3\% \] \[ g_2=+1\% \] Hence, \[ N = |(-3)-(+1)| = 4\%. \]

Step 2: Calculate the curve length. Rate of change of grade \[ = 0.1\% \text{ per }20\text{ m} \] Therefore, \[ L = \frac{4}{0.1}\times20 = 40\times20 = 800\text{ m} \] Hence, \[ \boxed{L=800\text{ m}} \] Therefore, the correct option is \[ \boxed{(A)\;800\text{ m}.} \]