Horizontal Curve Design

Simple curve

Two straights joined by one circular curve of constant radius R.

Reverse curve

Two curves in opposite directions; better practice = short tangent of 0.7V metres between them.

Compound curve

Two or more contiguous curves, same direction, different radii.

Degree of curvature (D)

Angle subtended by a 100 m arc; larger R → smaller D (inverse relationship).

Δ (deflection angle)

Central angle of the circular curve, equal to the deflection angle between the tangents at PI.

PI / TC / CT

Point of Intersection of tangents / Tangent-to-Curve (start) / Curve-to-Tangent (end).

T / E / M / L

Tangent length (TC-PI) / External distance (PI to curve midpoint) / Middle ordinate (chord midpoint to curve) / curve arc length (TC to CT).

Superelevation (e)

Banking of the pavement on a curve to counteract centrifugal force.

Side friction factor (f)

Tyre-pavement friction resisting skidding on curves.

f selection rule

If a table offers different f values for the same operating speed, choose the absolute maximum.

Minimum radius

Smallest radius preventing skidding (from V, emax, fmax); too small = skid risk.

Steep downgrade rule

Increase Rmin by 10% for each 1% of grade over 3%.

Transition curve (spiral)

Spiral path between tangent and circular curve.

Why spirals

Smooth path from straight to curve; better appearance; gradual superelevation introduction; lets driver negotiate changing curvature.

When spirals not needed

May not be required below 60 km/h or for sufficiently large radii (not an automatic exemption). Spirals must give ≥ 2 s transition path. Spiral theory/drawing: Appendix I in the 2026 guide (lecture cites Appendix K

Tangent runout (Tro)

Length to change crossfall from normal crown to flat.

Superelevation runoff (Sro)

Length to change crossfall from flat to fully superelevated.

Development length

Method 1

Development length

Method 2

Choosing Le

Must satisfy BOTH methods → take the greater length.

Runoff placement, no spiral

50% on tangent, 50% on curve.

Runoff placement, with spiral

The runoff is accommodated through the transition curve.

Adopted spiral length

Lsp,adopted = max(Lsp,min, Sro): take the greater of the minimum required spiral length and the superelevation runoff. Also check min curve length TS-to-ST (Table 7.6/7.8).

Optimising e

Linear relation between 1/e and R: higher e → smaller required Rmin. After selecting the adopted elevation ea, recalculate optimised friction: fa = V²/(127R) − ea.