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Ruling Minimum Radius Calculator

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✖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.ⓘ Velocity [v_vehicle]			+10% -10%
✖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.ⓘ Rate of Super Elevation [e]			+10% -10%
✖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.ⓘ Coefficient of Lateral Friction [f_lateral]			+10% -10%

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

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Ruling Minimum Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction))
R_ruling = v_vehicle^2/([g]*(e+f_lateral))
This formula uses 1 Constants, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Ruling Minimum Radius - (Measured in Meter) - Ruling Minimum Radius is the minimum radius of a curve in a road design, ensuring safe and smooth traffic flow at desired speeds.
Velocity - (Measured in Meter per Second) - 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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Velocity: 28.23 Meter per Second --> 28.23 Meter per Second No Conversion Required
Rate of Super Elevation: 0.07 --> No Conversion Required
Coefficient of Lateral Friction: 0.15 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_ruling = v_vehicle^2/([g]*(e+f_lateral)) --> 28.23^2/([g]*(0.07+0.15))

Evaluating ... ...

R_ruling = 369.384272175235

STEP 3: Convert Result to Output's Unit

369.384272175235 Meter --> No Conversion Required

FINAL ANSWER

369.384272175235 ≈ 369.3843 Meter <-- Ruling Minimum Radius

(Calculation completed in 00.004 seconds)

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< Design of Superelevation Calculators

Distance between Front and Rear Wheel

LaTeX Go Distance between Front and Rear Wheel = 2*Radius of Outer Track Line of Front Wheel*Mechanical Widening on Horizontal Curves-Mechanical Widening on Horizontal Curves^2

Ruling Minimum Radius

LaTeX Go Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction))

Mechanical Widening needed for Large Radius of Road Curve

LaTeX Go Mechanical Widening on Horizontal Curves = (Number of Lanes*Distance between Front and Rear Wheel^2)/(2*Mean Radius of Curve)

Psychological Widening at Horizontal Curves

LaTeX Go Psychological Widening at Horizontal Curves = Velocity/(2.64*sqrt(Mean Radius of Curve))

Ruling Minimum Radius Formula

LaTeX Go

Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction))
R_ruling = v_vehicle^2/([g]*(e+f_lateral))

What is coefficient of longitudinal friction?

The coefficient of friction in the longitudinal direction of a highway is estimated as 0.396.It acts in the rolling direction of the tyres of vehicle

How to Calculate Ruling Minimum Radius?

Ruling Minimum Radius calculator uses Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)) to calculate 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 calculate Ruling Minimum Radius using this online calculator? To use this online calculator for Ruling Minimum Radius, enter Velocity (v_vehicle), Rate of Super Elevation (e) & Coefficient of Lateral Friction (f_lateral) and hit the calculate button. Here is how the Ruling Minimum Radius calculation can be explained with given input values -> 369.3843 = 28.23^2/([g]*(0.07+0.15)).

FAQ

What is 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 and is represented as R_ruling = v_vehicle^2/([g]*(e+f_lateral)) or Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)). 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, 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 & 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.

How to calculate 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 is calculated using Ruling Minimum Radius = Velocity^2/([g]*(Rate of Super Elevation+Coefficient of Lateral Friction)). To calculate Ruling Minimum Radius, you need Velocity (v_vehicle), Rate of Super Elevation (e) & Coefficient of Lateral Friction (f_lateral). With our tool, you need to enter the respective value for Velocity, Rate of Super Elevation & Coefficient of Lateral Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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