Valley curve 1 in 30 and 1 in 25

A descending 1 in 30 grade meeting an ascending 1 in 25 grade gives a valley curve.

Data

$N=\dfrac{1}{30}+\dfrac{1}{25}=0.07333$, $V=80$ km/h $=22.22$ m/s, SSD $S=160$ m (given). The allowable rate of change of centrifugal acceleration is taken as $C=0.6$ m/s³ (the units "m/s²" in the question are read as m/s³). Headlight height 0.75 m, beam angle 1°.

(a) Comfort condition

$$L=2\sqrt{\frac{NV^3}{C}}=2\sqrt{\frac{0.07333(22.22)^3}{0.6}}=73.2\ \text{m}$$

(b) Headlight sight distance

Assuming $L>S$:

$$L=\frac{NS^2}{2(h+S\tan\alpha)}=\frac{0.07333(160)^2}{1.5+0.035(160)}=264.4\ \text{m}$$

$L>S$, valid.

Design length

The larger value governs.

Answer: L = 264 m, adopt 265 m.