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AASHTO Superelevation

Required superelevation rate (cross-slope) on a highway horizontal curve. Per AASHTO Green Book Method 5: e + f = V²/(15R) (US) or V²/(127R) (SI). Reports minimum radius for the chosen emax and design speed.

mph
ft
—— (AASHTO design value)
—% (= e + f − f, distributed)
——
—ft

Defaults: 55 mph design speed, 1000 ft radius, e_max = 8%. Method 5 distributes e and f according to a curve-radius-dependent formula in AASHTO §3.3.4. Output e is the full-superelevation cross-slope at the apex of the curve.

$$ e + f = \frac{V^2}{15 R} \text{ (US, with V in mph and R in ft)} $$
$$ e + f = \frac{V^2}{127 R} \text{ (SI, with V in km/h and R in m)} $$
Minimum radius for chosen emax:
$$ R_{min} = \frac{V^2}{15 \,(e_{max} + f_{max})} $$
e superelevation rate (cross-slope, decimal or percent) · f side-friction factor (AASHTO design values, much less than max friction available) · emax maximum allowable superelevation by region (4% to 12%) · V design speed.

What e + f means

A vehicle on a banked, curved roadway is held in the curve by two forces: the horizontal component of pavement reaction (from cross-slope = e), plus tire-pavement friction (from f). The kinematic equation V² / (gR) = e + f balances centripetal acceleration to those two forces. The factor 15 in US units (or 127 in SI) embeds 1/g and conversion from mph² to ft/s² (or km/h² to m/s²).

AASHTO design f values

AASHTO design values for f are well below maximum tire-pavement friction — they're calibrated for driver comfort and to leave reserve friction for braking on the curve. Typical AASHTO design f at typical e_max:

Higher speeds get lower f because driver comfort tolerance for lateral acceleration decreases. These are far below max tire-pavement friction (0.4–0.7) — there's reserve for emergency braking.

Method 5 — distributed e and f

For curves sharper than Rmin for V, AASHTO Method 5 (the modern preferred method) distributes e and f along a quartic relationship, so that f reaches the maximum allowable only at the minimum radius. For radii larger than Rmin, e is reduced from emax while f stays at zero or low values. This makes the design responsive to the curve's actual sharpness, instead of using emax on every curve.

emax — regional choices

Transitioning into superelevation

The cross-slope must transition from normal crown (typically 2% downward to each side) to full superelevation (e% rotated to the inside) over a runoff length Lr. AASHTO §3.3.6 specifies the runoff:

Lr = (W × n × e) / Δ, where W is rotation width (lane + shoulder), n is the number of rotated lanes, e is the rate, and Δ is the relative gradient (typically 0.45–0.65% for highways).

Distribute the runoff: 2/3 on the tangent before PC, 1/3 on the curve itself. For ramps/turning roadways with spirals, the spiral length serves as the runoff.

Reference: AASHTO (2018). A Policy on Geometric Design of Highways and Streets, 7th ed., §3.3.4 and Tables 3-7 to 3-12. Garber, N.J., Hoel, L.A. (2015). Traffic and Highway Engineering, 5th ed., Cengage, ch. 16.

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