Highway Geometric Design: Sight Distance and Curves

Geometric design fixes the visible shape of a road: how far drivers can see, how curves are banked, and how grades change. Indian practice follows IRC guidelines.

Stopping sight distance (SSD)

The distance to perceive, react and stop:

SSD = v t + v²/(2 g f) (v in m/s)

• Reaction time t = 2.5 s (IRC); longitudinal friction f = 0.35–0.40.
• On a gradient n (as a fraction): v²/(2g(f ± n)), + going uphill.
• Intermediate sight distance = 2 × SSD.
• On two-way single-lane roads, SSD is doubled.

Overtaking sight distance (OSD)

OSD = d₁ + d₂ + d₃ = v_b t + (v_b T + 2s) + v T, with s = 0.7v_b + 6 m and T = √(4s/a). It applies on two-lane roads; overtaking zones are marked where OSD is available.

Horizontal curves

Superelevation: e + f = v²/(g R).

• IRC design: e = (0.75v)²/(gR) (superelevation for 75% of the design speed, no friction), limited to e_max = 0.07 (plain and rolling terrain), and f = 0.15.
• Ruling minimum radius: R = v²/(g(e + f)).
• Extra widening = mechanical (n l²/(2R)) + psychological (V/(9.5√R)), with l = wheelbase, n = number of lanes, V in km/h.
• Set-back distance to keep sight distance on a curve: m = R − (R − d) cos(α/2), with α/2 = S/(2(R − d)) for S < curve length.

Transition curves

Spiral (clothoid) curves introduce curvature and superelevation gradually. Length from the rate of change of centrifugal acceleration:

L = v³/(C R), with C = 80/(75 + V) (V in km/h), limited to 0.5–0.8 m/s³.

Also checked against the rate of introducing superelevation and IRC empirical minimums.

Vertical curves

• Deviation angle N = |n₁ − n₂| (difference of gradients).
• Valley (sag) curves: designed for headlight sight distance and comfort; cubic parabola. For L > S: L = N S²/(1.5 + 0.035 S).
• Summit curves: designed for sight distance, square parabola. For L > SSD: L = N S²/4.4 (driver eye height 1.2 m, object height 0.15 m). For OSD (both heights 1.2 m): L = N S²/9.6.

Worked example

Design speed 80 km/h (22.22 m/s), f = 0.35, t = 2.5 s, level road.

• SSD = 22.22 × 2.5 + 22.22²/(2 × 9.81 × 0.35) = 55.6 + 71.9 = 127.5 m.

Practice