Superelevation Design: Balancing e and f
Superelevation is the transverse banking applied to a roadway through a horizontal curve, tilting the pavement cross-slope to help counteract the centrifugal force acting on a vehicle traveling the curve. Without it — or with too little of it — side friction between tire and pavement has to do all the work of keeping the vehicle on its path.
The e + f = V²/15R Relationship
AASHTO's design equation splits the total centripetal force demand between superelevation (e) and side friction (f): e + f = V²/(15R), with V in mph and R in feet. For any given speed and radius, the two variables can be traded off against each other, but each has a practical ceiling — f is limited by tire-pavement friction and driver comfort, e by construction and drainage practicality. When the demand V²/(15R) is less than the side friction available at that speed alone, no superelevation is required at all and normal crown suffices — a common outcome on generous-radius curves at moderate speeds.
Selecting Maximum Superelevation (e_max)
AASHTO does not specify a single e_max — it varies by design context: 4–6% for urban streets or areas prone to ice, 8% for typical rural highways, and 10–12% for high-speed, limited-access facilities in climates without snow or ice concerns. Selecting e_max sets the minimum radius that can be built at a given design speed without exceeding the maximum allowable side friction factor, R_min = V²/[15(f_max + e_max/100)].
Superelevation Runoff Length
Superelevation cannot be applied instantaneously — the pavement must physically rotate from its normal crown to the full design superelevation over some length of roadway, called the superelevation runoff length (L_r). AASHTO limits this transition by a maximum relative gradient (Δ), the rate at which the profile of the outer edge of pavement may rise relative to the centerline, which itself varies by design speed and number of lanes rotated. Too short a runoff length creates an uncomfortable, potentially unsafe rate of cross-slope change; too long delays the start of full superelevation well before the curve actually needs it.
What happens if e + f exceeds the maximum values my agency allows?
The curve radius is too tight for the design speed under the selected e_max and f_max. Either increase the radius, reduce the design speed, or — where context allows — request a design exception, since exceeding both practical limits isn't a safe outcome to design around.
Why do urban streets use a lower e_max than rural highways?
Urban streets have more stop-and-go traffic, on-street parking, and driveways, so vehicles frequently travel through curves well below design speed. A high superelevation rate designed for fast-moving traffic becomes uncomfortable and even hazardous for slow-moving or stopped vehicles.
Does superelevation eliminate the need for adequate curve radius?
No — superelevation supplements side friction, it doesn't replace the geometric requirement for adequate radius. Even at maximum practical superelevation, there's a hard minimum radius below which no combination of e and f can safely serve a given design speed.
How is superelevation runoff length actually built into the roadway?
The outside edge of pavement is gradually raised (or the inside edge lowered, depending on rotation method) relative to the profile grade line over the runoff length, while cross-slope rotates linearly from normal crown to full superelevation.
Is ice or snow considered directly in this calculator?
Not directly — the AASHTO e+f equation itself is climate-agnostic. Climate is addressed indirectly through the choice of a lower e_max in regions with regular snow and ice, which this calculator lets you set explicitly.