Three relations decide whether a geometry is safe at a speed. They chain: how far a driver needs to see, then how long a crest must be to deliver it, then how hard a bend may be taken.

Stopping sight distance: $d = v\,t_r + \dfrac{v^{2}}{2a}$ — d equals v t-r plus v squared over two a. $d$ is the distance in metres, $v$ the design speed in metres per second, $t_r$ the perception-reaction time in seconds — 2.5 s by standard, and it is generous on purpose — and $a$ the deceleration in m/s², taken as 3.4 m/s² on a wet road. The two terms are two separate events: the distance covered while nothing has happened yet, and the distance covered once the brakes bite. The first is linear in speed, the second quadratic, and that asymmetry is the entire engineering case for a speed limit.

Speeds arrive in km/h and the relation eats m/s. Divide by 3.6 before anything else — a speed left in km/h is squared in the second term, and the answer comes back thirteen times too large while still looking like a number.

Crest curve length: $L = \dfrac{A S^{2}}{200\left(\sqrt{h_1} + \sqrt{h_2}\right)^{2}}$, for the usual case where the sight distance $S$ is shorter than the curve. $A$ is the grade change in percent, $S$ the required sight distance in metres, $h_1$ the driver's eye height and $h_2$ the object height. Both heights are conventions, not measurements: metric AASHTO uses $h_1 = 1.08$ m and $h_2 = 0.60$ m, which makes the denominator 658. The imperial pair, 3.5 ft and 2.0 ft, makes 2158. Mixing a metric height into an imperial constant is the named mistake of this lesson, and it under-lengths every crest on the job.

Superelevation: $\dfrac{e}{100} + f = \dfrac{v^{2}}{gR}$. $e$ is the superelevation rate — the pavement's cross-slope, in percent; $f$ is the side friction factor, a bare number the standard allows at each speed (0.10 to 0.17, and chosen for comfort long before tyres actually slide); $v$ is speed in m/s, $R$ the curve radius in metres, $g$ is 9.80665 m/s². Read it as a budget: the turn demands $v^{2}/gR$, the tilt of the road pays part and the grip of the tyres pays the rest. Fix the two allowances and the sharpest permissible curve follows.