How to calculate superelevation?

To calculate superelevation, you typically consider two main aspects: determining the design superelevation rate (the "e" value) and calculating the rate of change in superelevation during the transition along the roadway.

Superelevation (often referred to as banking or cant) is the transverse slope of a roadway on a horizontal curve that counteracts the centrifugal force generated by a vehicle's motion, improving safety and comfort.

Calculating the Design Superelevation Rate (e)

The design superelevation rate (e) is a dimensionless value, often expressed as a percentage or decimal, representing the ratio of the cross-slope rise to the width of the roadway. It is primarily determined by the design speed of the road, the radius of the curve, and the maximum allowable side friction.

The fundamental formula used in highway design for calculating the required superelevation rate is:

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

Where:

• e: Superelevation rate (decimal, e.g., 0.06 for 6%)
• f: Side friction factor (dimensionless), representing the friction between the tires and the road surface that prevents skidding.
• V: Design speed (miles per hour, mph)
• R: Radius of the curve (feet)
• 15: A constant to adjust units for common imperial measurements.

Key Factors Influencing 'e':

• Design Speed (V): Higher speeds require greater superelevation.
• Radius of Curve (R): Tighter curves (smaller radius) require greater superelevation.
• Side Friction Factor (f): This factor accounts for the lateral forces that tires can withstand before skidding. It varies with speed and pavement conditions.
• Maximum Superelevation Rate (e_max): Highway agencies typically set maximum allowable e values (e.g., 4%, 6%, 8%, 10%, or 12%) based on climate, terrain, and urban/rural context to ensure drainage and safety at low speeds.

Calculating the Rate of Change in Superelevation During Transition

While the design superelevation rate (e) determines how much the road is banked, the rate of change in superelevation dictates how smoothly this banking is introduced along the length of the road. This is crucial for driver comfort, safety, and proper drainage. This "rate of change" typically refers to the longitudinal slope of the pavement edge relative to the axis of rotation as the cross-slope transitions from a normal crown to full superelevation.

According to design principles, the rate of change in superelevation is found by:

Rate of Change = (Difference between Normal Crown and Full Super) / Transition Length

This calculation defines the slope at which the outer and inner edges of the pavement change their elevation relative to the axis of rotation over the transition length.

Understanding the Components:

• Difference between Normal Crown and Full Super: This refers to the total change in cross-slope elevation that occurs between the point where the road has a standard drainage crown (normal crown) and the point where it achieves its full design superelevation. This "difference" is a vertical elevation change of the pavement edge relative to the axis of rotation, proportional to the total change in cross-slope percentage multiplied by the lane width.
• Transition Length: This is the horizontal distance over which the change in cross-slope is introduced. It's the length of the roadway section where the banking gradually increases from the normal crown to the full superelevation.

Practical Example from Reference:

The provided reference illustrates this calculation with specific numbers:

"The rate of change in superelevation is found by dividing the difference between normal crown and full super by the transition length. 11000 – 10971.61 = 28.39. The rate of change is the same as for the transition at the beginning end of the curve (. 0004177)."

Breakdown of the Example:

• Transition Length Calculation: The reference states "11000 – 10971.61 = 28.39". This indicates that the transition length is 28.39 units (likely feet or meters, representing a stationing difference).
• Resulting Rate of Change: The reference then states, "The rate of change is the same as for the transition at the beginning end of the curve (. 0004177)." This means the calculated rate of change in superelevation is 0.0004177.

Therefore, in this example, the "difference between normal crown and full super" (the total vertical elevation change over the transition length) divided by 28.39 results in a rate of 0.0004177. This rate represents the longitudinal slope of the pavement edge during the superelevation runoff.

Superelevation Design Summary Table (Example)

This table is illustrative; actual values depend on specific design standards and local conditions.