Ruling Minimum Radius Calculator

Ruling Minimum Radius Formula:

\[ R_{ruling} = \frac{v_{vehicle}^2}{[g] \times (e + f_{lateral})} \]

Velocity:

m/s

Rate of Super Elevation:

(dimensionless)

Coefficient of Lateral Friction:

(dimensionless)

Ruling Minimum Radius:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Ruling Minimum Radius?

The Ruling Minimum Radius is a limiting value of curvature for a given design speed in road engineering. It represents the smallest radius that a curve can have while still maintaining safe vehicle operation at the design speed, considering both super elevation and lateral friction.

2. How Does the Calculator Work?

The calculator uses the Ruling Minimum Radius formula:

\[ R_{ruling} = \frac{v_{vehicle}^2}{[g] \times (e + f_{lateral})} \]

Where:

\( R_{ruling} \) — Ruling Minimum Radius (m)
\( v_{vehicle} \) — Vehicle velocity (m/s)
\( [g] \) — Gravitational acceleration (9.80665 m/s²)
\( e \) — Rate of Super Elevation (dimensionless)
\( f_{lateral} \) — Coefficient of Lateral Friction (dimensionless)

Explanation: The formula calculates the minimum curve radius that allows a vehicle to safely navigate a curve at a given speed, accounting for the combined effects of road banking (super elevation) and tire-road friction.

3. Importance of Ruling Minimum Radius Calculation

Details: Accurate calculation of ruling minimum radius is crucial for road design, ensuring safe vehicle operation on curved sections. It helps prevent accidents by providing adequate curve radii that accommodate the design speed while considering vehicle dynamics and road conditions.

4. Using the Calculator

Tips: Enter velocity in meters per second, rate of super elevation (typically between 0.04-0.08 for roads), and coefficient of lateral friction (typically 0.15-0.35 for dry pavement). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the typical range for super elevation rates?
A: For highways, super elevation typically ranges from 4% to 8% (0.04 to 0.08), with maximum values around 10% in some jurisdictions.

Q2: How does lateral friction coefficient vary?
A: Lateral friction coefficients range from 0.15-0.35 for dry pavement, decreasing significantly on wet or icy surfaces (0.05-0.15).

Q3: Why is gravitational acceleration included?
A: Gravitational acceleration is needed to account for the gravitational forces acting on the vehicle during curved motion and banking.

Q4: What factors affect the ruling minimum radius?
A: The radius is primarily affected by design speed, available super elevation, and pavement friction characteristics.

Q5: How is this used in actual road design?
A: Engineers use this calculation to determine minimum curve radii for different design speeds, ensuring that road geometries provide safe navigation for vehicles.