Question

An ascending gradient of 1 in 45 meets a descending gradient of 1 in 60. A summit curve has to be designed gradient for design speed of 80 km/h so as to provide a safe overtaking sight distance of 230 m. Estimate the length of the summit curve.

• A. 213.143

Answer 1

The correct option is A 213.143

$N=\frac{1}{45}-(-\frac{1}{60})=\frac{7}{180}$

$\text{Assume}L>S$

Length of summit curve
$L=\frac{N{S}^2}{2(\sqrt{h_1}+\sqrt{h_2}{)}^2}$

For OSD
$h_1=1.2m$
$h_2=1.2m$

$L=\frac{\frac{7}{180}\times {230}^2}{2(\sqrt{1.2}+\sqrt{1.2}{)}^2}$

$=214.294m<230m\text{NOT OK}$

$\text{If,}L<S$

$L=2S-\frac{2(\sqrt{h_1}+\sqrt{h_2}{)}^2}{N}$

$=2\times 230-\frac{2(\sqrt{1.2}+\sqrt{1.2}{)}^2}{\frac{7}{180}}$

$=213.143m<230m\text{OK}$

$L=213.143m$