Understanding Design Super Elevation Calculation

The question asks us to calculate the design rate of super elevation for a highway curve in a plain terrain. We are given the design speed and the radius of the curve.

Super elevation (often denoted as 'e') is the banking of a highway curve to counteract the centrifugal force acting on a vehicle. It helps vehicles navigate curves safely and comfortably. The design of super elevation is based on specific guidelines, like those provided by the Indian Road Congress (IRC).

Key Parameters Given:

• Design Speed (V) = 80 kmph
• Radius of Curve (R) = 400 m
• Terrain Type = Plain terrain

Formula for Super Elevation

The general formula relating super elevation (e), lateral friction (f), speed (v), gravitational acceleration (g), and radius (R) is:

\( e + f = \frac{v^2}{gR} \)

where 'v' is in m/s, 'g' is in m/s², and 'R' is in m.

Design Procedure for Super Elevation

According to standard highway design practices (like IRC), the design super elevation is calculated considering a specific percentage of the design speed and neglecting lateral friction initially. The maximum allowed super elevation depends on the terrain type.

For plain or rolling terrain, the maximum permissible super elevation is typically 7% (or 0.07).

The first step in the design calculation is to determine the super elevation required for 75% of the design speed, neglecting friction:

\( e_{calc} = \frac{(0.75V)^2}{gR} \)

Where V is in m/s.

Step-by-Step Calculation

1. Convert the design speed from kmph to m/s:

\( V_{kmph} = 80 \text{ kmph} \)

\( V_{m/s} = 80 \times \frac{1000 \text{ m}}{3600 \text{ s}} = 80 \times \frac{5}{18} = \frac{400}{18} = \frac{200}{9} \text{ m/s} \)

2. Calculate the speed for super elevation design (75% of design speed):

\( v = 0.75 \times V_{m/s} = 0.75 \times \frac{200}{9} = \frac{3}{4} \times \frac{200}{9} = \frac{3 \times 50}{9} = \frac{150}{9} = \frac{50}{3} \text{ m/s} \)

3. Calculate the required super elevation using the formula, neglecting friction (f=0):

\( e_{calc} = \frac{v^2}{gR} \)

Using \( g \approx 9.81 \text{ m/s}^2 \) and \( R = 400 \text{ m} \):

\( e_{calc} = \frac{(\frac{50}{3})^2}{9.81 \times 400} = \frac{\frac{2500}{9}}{3924} = \frac{2500}{9 \times 3924} = \frac{2500}{35316} \approx 0.07078 \)

As a percentage, \( e_{calc} \approx 0.07078 \times 100\% \approx 7.08\% \)

Checking Against Maximum Permissible Super Elevation

For plain terrain, the maximum permissible super elevation is 7% (or 0.07).

Our calculated value (\( e_{calc} \approx 7.08\% \)) is slightly greater than the maximum permissible limit (7%).

According to design guidelines, if the calculated super elevation exceeds the maximum permissible value, the design super elevation is limited to the maximum permissible value.

Therefore, the design rate of super elevation for this curve is 7%.

Conclusion on Design Super Elevation

Since the calculated super elevation (7.08%) is greater than the maximum allowed for plain terrain (7%), the design rate of super elevation is set at 7%.

This is a crucial step in highway design to ensure safety while keeping construction practical and cost-effective.

Revision Table: Highway Curve Design Concepts

Additional Information: Why Limit Super Elevation?

The design rate of super elevation is limited for several practical reasons:

• Slow-Moving Vehicles: High super elevation can cause slow-moving heavy vehicles to feel unstable or even tip inwards when navigating the curve.
• Construction Issues: Constructing and maintaining pavements with very steep cross slopes (high super elevation) is difficult and costly.
• Snow/Ice Conditions: In regions with snow or ice, high super elevation can make steering difficult and increase the risk of vehicles sliding off the road when traction is low. For these areas, the maximum super elevation is often restricted to 7%.
• Mixed Traffic: Highways carry a mix of fast and slow vehicles. The design must accommodate all users safely.

The calculation procedure involving 75% of design speed and the maximum limit ensures a balance between safety for fast-moving vehicles and stability for slow-moving vehicles, while also considering construction and environmental factors.