5.2 Design Speed and Superelevation Design

5.2 Design Speed and Superelevation Design

When a vehicle travels around a horizontal curve, it experiences centrifugal force that acts to push the vehicle radially outward. To maintain safety, stability, and passenger comfort, transportation engineers must counter this force. This is accomplished through a combination of two elements: the superelevation rate (e), which is the cross-slope of the road tilted inward, and the side friction factor (f), which represents the friction developed between the vehicle’s tires and the wet pavement surface.

The Minimum Radius Equation

The fundamental relationship governing vehicle stability on a horizontal curve is derived from the balance of lateral forces in circular motion. Under the AASHTO design guidelines (commonly referred to as the Green Book) and the NCEES PE Civil Reference Handbook, the minimum radius of curvature (R_min) for a given design speed (V) is determined using the following formula:

R = V^2 / (15 * (e + f))

Where:

• R = Radius of the curve (feet)
• V = Design speed of the highway (miles per hour, mph)
• e = Superelevation rate (expressed as a decimal, e.g., 0.06 for 6%)
• f = Side friction factor (dimensionless decimal)

[!NOTE] For SI units, the formula is: R = V^2 / (127 * (e + f)) Where R is in meters and V is in kilometers per hour (km/h). Ensure you verify the units of the inputs on the exam before selecting a formula.

Side Friction and Speed Relationship

The maximum allowable side friction factor (f_max) is not constant; it decreases as the design speed increases. This is a design decision based on driver comfort and vehicle handling characteristics. At higher speeds, passengers feel lateral acceleration more intensely, and tire-pavement friction capacity decreases. Typical values for f_max defined by AASHTO are summarized below:

Maximum Superelevation Rate (e_max)

The selection of the maximum superelevation rate (e_max) is governed by environmental and operational factors:

1. Climate and Icing: In regions subject to snow and ice, e_max is typically limited to 6% or 8%. This prevents slow-moving or stopped vehicles (such as heavy trucks or maintenance equipment) from sliding down the banked pavement toward the inside of the curve when the road is icy.
2. Terrain and Context: In rural areas with rolling or mountainous terrain and no ice, e_max up to 10% or 12% may be permitted to minimize earthwork. In contrast, urban areas with low-speed traffic, intersections, driveways, and pedestrian crossings typically limit e to 4% or 6% to facilitate cross-street alignments and avoid uneven sidewalk grades.

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Superelevation Transition Layout

A roadway cannot transition instantly from a normal crown cross-slope (typically -2.0% for drainage) to the full design superelevation rate (e_d). This transition must occur over a calculated distance, which is divided into two distinct parts: Tangent Runout (L_t) and Superelevation Runoff (L_r).

1. Superelevation Runoff (L_r)

The superelevation runoff is the distance required to transition the outside lane(s) of the pavement from a flat (0.0%) cross-slope to the full design superelevation rate (e_d). According to the NCEES PE Civil Reference Handbook, the minimum length of runoff is calculated as:

L_r = (w * n_1 * e_d * b_w) / Delta

Where:

• w = Width of a design lane (typically 12 ft)
• n_1 = Number of lanes rotated (usually 1 for a standard two-lane highway rotated about the centerline)
• e_d = Design superelevation rate (expressed as a decimal)
• b_w = Adjustment factor for the number of lanes rotated to account for larger pavement widths (AASHTO standard: 1.00 for 1 lane, 0.75 for 2 lanes, 0.67 for 3 lanes)
• Delta = Maximum relative gradient (expressed as a decimal, representing the slope of the outer edge of pavement relative to the centerline profile; see speed-gradient table above)

2. Tangent Runout (L_t)

The tangent runout is the distance required to transition the outside lane from a normal crown cross-slope (e_NC, usually -2.0%) to a flat (0.0%) cross-slope. It is calculated proportionally based on the runoff length:

L_t = (e_NC / e_d) * L_r

Where e_NC is the normal crown rate (decimal) and e_d is the design superelevation rate (decimal).

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Stationing of Superelevation Transitions

To balance steering comfort and passenger comfort, the transition length is distributed across the Point of Curvature (PC) and Point of Tangency (PT). The standard AASHTO practice is to locate two-thirds (2/3) of the superelevation runoff length (L_r) on the tangent section prior to the PC, and the remaining one-third (1/3) on the curve after the PC.

The critical stations along the transition are calculated as follows:

• Normal Crown Ends (NC): The point where the outside lane begins rotating. Station NC = Station PC - (2/3) * L_r - L_t
• Flat Crown (FC): The point where the outside lane is flat (0%). Station FC = Station PC - (2/3) * L_r
• Reverse Crown (RC): The point where the outside lane slope is equal but opposite to the inside lane (e.g., +2%). Station RC = Station PC - (2/3) * L_r + L_t
• Full Superelevation (FS): The point where the entire pavement achieves the design superelevation rate (e_d). Station FS = Station PC + (1/3) * L_r

The transition at the end of the curve (relative to the PT) is mirrored, with 1/3 of L_r on the curve before the PT and 2/3 of L_r plus L_t on the tangent after the PT.

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Axis of Rotation Selection

The axis of rotation is the longitudinal line along the highway profile about which the pavement cross-section is rotated. The choice of axis affects the profile grade lines of the pavement edges:

1. Revolving about the Centerline: This is the most common method. The centerline profile remains unchanged, while the inner edge drops by w * e / 2 and the outer edge rises by w * e / 2. This minimizes the vertical displacement of the pavement edges and is visually pleasing.
2. Revolving about the Inner Edge: The inner edge profile remains at the design grade. The centerline and outer edge are raised. This is commonly used on divided highways with a median, or in flat terrain where dropping the inner edge would create drainage ponding.
3. Revolving about the Outer Edge: The outer edge profile remains at the design grade, while the centerline and inner edge are depressed. This is useful when matching the outside edge to existing roadside features or structures.