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Ruling Minimum Radius Formula

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Ruling Minimum Radius is the minimum radius of a curve in a road design, ensuring safe and smooth traffic flow at desired speeds. Check FAQs

R ruling = \frac{{v vehicle}^{2}}{[g] \cdot (e + f lateral)}

R_ruling - Ruling Minimum Radius?v_vehicle - Velocity?e - Rate of Super Elevation?f_lateral - Coefficient of Lateral Friction?[g] - Gravitational acceleration on Earth?

Ruling Minimum Radius Example

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Here is how the Ruling Minimum Radius equation looks like with Values.

Here is how the Ruling Minimum Radius equation looks like with Units.

Here is how the Ruling Minimum Radius equation looks like.

369.3843 = \frac{{28.23}^{2}}{9.8066 \cdot (0.07 + 0.15)}

369.3843m = \frac{{28.23m/s}^{2}}{9.8066m/s² \cdot (0.07 + 0.15)}

369.3843 = \frac{{28.23}^{2}}{9.8066 \cdot (0.07 + 0.15)}

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Ruling Minimum Radius Solution

Follow our step by step solution on how to calculate Ruling Minimum Radius?

FIRST Step Consider the formula

R ruling = \frac{{v vehicle}^{2}}{[g] \cdot (e + f lateral)}

Next Step Substitute values of Variables

∴

R ruling = \frac{{28.23m/s}^{2}}{[g] \cdot (0.07 + 0.15)}

Next Step Substitute values of Constants

∴

R ruling = \frac{{28.23m/s}^{2}}{9.8066m/s² \cdot (0.07 + 0.15)}

Next Step Prepare to Evaluate

∴

R ruling = \frac{{28.23}^{2}}{9.8066 \cdot (0.07 + 0.15)}

Next Step Evaluate

∴

R ruling = 369.384272175235m

LAST Step Rounding Answer

∴

R ruling = 369.3843m

Ruling Minimum Radius Formula Elements

Variables

Constants

Ruling Minimum Radius

Ruling Minimum Radius is the minimum radius of a curve in a road design, ensuring safe and smooth traffic flow at desired speeds.

Symbol: R_ruling

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Ruling Minimum Radius

Velocity

Velocity is the rate of change of an object's position with respect to time, used in superelevation design to ensure safe and efficient traffic flow.

Symbol: v_vehicle

Measurement: SpeedUnit: m/s

Note: Value should be between 0 to 500.

Formulas to find Velocity

Rate of Super Elevation

Rate of Super Elevation is the rate at which the outer rail is raised above the inner rail in a curve to balance centrifugal force.

Symbol: e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Rate of Super Elevation

Coefficient of Lateral Friction

Coefficient of Lateral Friction is a measure of the frictional force that opposes the motion of a vehicle on a curved path in superelevation design.

Symbol: f_lateral

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Coefficient of Lateral Friction

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Other formulas in Design of Superelevation category

Go Distance between Front and Rear Wheel

l fr = 2 \cdot R 2 \cdot W m - {W m}^{2}

Go Psychological Widening at Horizontal Curves

W ps = \frac{v vehicle}{2.64 \cdot \sqrt{R mean}}

Go Mechanical Widening needed for Large Radius of Road Curve

W m = \frac{n \cdot {l fr}^{2}}{2 \cdot R mean}

Go Radius of Outer Track Line of Rear Wheel

R 1 = \sqrt{{R 2}^{2} - {l fr}^{2}}

How to Evaluate Ruling Minimum Radius?

Ruling Minimum Radius evaluator uses Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)) to evaluate the Ruling Minimum Radius, The Ruling Minimum Radius formula is defined as limiting value of curvature for a given design speed. A ruling minimum radius is calculated on the basis of maximum super-elevation and coefficient of friction. Ruling Minimum Radius is denoted by R_ruling symbol.

How to evaluate Ruling Minimum Radius using this online evaluator? To use this online evaluator for Ruling Minimum Radius, enter Velocity (v_vehicle), Rate of Super Elevation (e) & Coefficient of Lateral Friction (f_lateral) and hit the calculate button.

FAQs on Ruling Minimum Radius

What is the formula to find Ruling Minimum Radius?

The formula of Ruling Minimum Radius is expressed as Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)). Here is an example- 369.3843 = 28.23^2/([g]*(0.07+0.15)).

How to calculate Ruling Minimum Radius?

With Velocity (v_vehicle), Rate of Super Elevation (e) & Coefficient of Lateral Friction (f_lateral) we can find Ruling Minimum Radius using the formula - Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)). This formula also uses Gravitational acceleration on Earth constant(s).

Can the Ruling Minimum Radius be negative?

No, the Ruling Minimum Radius, measured in Length cannot be negative.

Which unit is used to measure Ruling Minimum Radius?

Ruling Minimum Radius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Ruling Minimum Radius can be measured.

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