Vertical curve with horizontal curve, 45 degrees

Step 1: ruling radius and design speed

The horizontal curve has deflection $\Delta=45^\circ$ and length 180 m:

$$R=\frac{L}{\Delta\ (\text{rad})}=\frac{180}{0.7854}=229.2\ \text{m}$$

A ruling (minimum) radius uses $e_{max}=0.07$ and $f_{max}=0.15$ (IRC):

$$V=\sqrt{127R(e+f)}=\sqrt{127(229.2)(0.22)}=80.0\ \text{km/h}$$

So the design speed for both curves is 80 km/h.

Step 2: stopping sight distance

$$SSD=0.278(80)(2.5)+\frac{80^2}{254(0.35)}=127.6\ \text{m}$$

Step 3: summit curve

$g_1=+3\%,\ g_2=-1.5\%$, so $N=0.03+0.015=0.045$ (summit). With eye height 1.2 m and object height 0.15 m (IRC/NRS), assuming $L>S$:

$$L=\frac{NS^2}{2(\sqrt{H}+\sqrt{h})^2}=\frac{NS^2}{4.4}=\frac{0.045(127.6)^2}{4.4}=166.5\ \text{m}$$

$L>S$, so the assumption holds.

Answer: adopt a summit vertical curve of length L = 170 m (design speed 80 km/h, SSD = 127.6 m).