Geometric Design: Sight Distance and Curves
Design speed governs everything
Nearly every geometric value - lane and shoulder width, superelevation, curve radius, clear zone, vertical curve length - is a function of design speed, not posted speed or operating speed. Candidates must know three sight distances: stopping sight distance (SSD), decision sight distance (DSD, longer, for complex or unexpected maneuvers), and passing sight distance (two-lane highways). SSD = 1.47Vt + V²/[30(f ± g)], with t = 2.5 s and f from the AASHTO table (f decreases as speed rises).
Horizontal alignment
Minimum radius is R = V²/[15(e + f)], where e is superelevation (typically capped at 0.04–0.10) and f is side friction. When a curve is shorter than the sight distance, the middle ordinate to a sight obstruction is M = R[1 − cos(28.65 S / R)].
Vertical alignment
Length of curve L = K × A, where A is the algebraic difference in grades in percent. Crest K values are set by SSD (and passing sight distance); sag K values are set by headlight sight distance and rider comfort.
Traps
- Entering grades as decimals instead of percent, producing an L that is off by 100×.
- Using the wrong K: crest versus sag criteria are entirely different curves.
- Sign errors: A on a crest is g1 − g2; on a sag it is g2 − g1.
- Applying the friction factor for the posted speed instead of the design speed.
Worked example
A crest vertical curve joins +3% and −3% grades at 60 mph design speed. A = 3 − (−3) = 6%. For 60 mph, crest K ≈ 151, so L = 151 × 6 = 906 ft, rounded to 910 ft.