Question

It is proposed to insert a circular curve of radius 300 m with a transition curve of 90 m length at each end. The spiral angle and central angle are respectively:
$(\text{Deflection angle = 40}{}^{\circ }\text{)}$

• A. $8^{\circ }{36}^{\prime }and{31}^{\circ }{24}^{\prime }$
• B. $8^{\circ }{36}^{\prime }and{22}^{\circ }{48}^{\prime }$
• C. ${17}^{\circ }{12}^{\prime }and{22}^{\circ }{48}^{\prime }$
• D. ${17}^{\circ }{36}^{\prime }and{31}^{\circ }{24}^{\prime }$

Answer 1

The correct option is B $8^{\circ }{36}^{\prime }and{22}^{\circ }{48}^{\prime }$

$Spiralangle\left(\varphi \right)=\frac{L}{2R}radians$

$=\frac{90}{2\times 300}\times \frac{180}{\pi }=8^{\circ }{36}^{\prime }$

$Centralangle=\Delta -2\varphi ={40}^{\circ }-2\times 8^{\circ }{36}^{\prime }={22}^{\circ }{48}^{\prime }$