Ruling Minimum Radius Calculator

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Design of Transition Curves and Setback Distances

✖Velocity is the rate of change of distance of the vehicle with respect to time.ⓘ Velocity [v_vehicle]			+10% -10%
✖Rate of Super Elevation is the transverse slope along the width of the road provided by rising the outer edge of the road with respect to the inner edge, throughout the length of the horizontal curve.ⓘ Rate of Super Elevation [e]			+10% -10%
✖Coefficient of Lateral Friction is a dimensionless value that represents the ratio of the lateral force required to move an object or surface laterally to the normal force acting on it.ⓘ Coefficient of Lateral Friction [f_lateral]			+10% -10%

✖The ruling minimum radius is a 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 [R_ruling]

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Formula

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Ruling Minimum Radius

Formula

`"R"_{"ruling"} = "v"_{"vehicle"}^2/("[g]"*("e"+"f"_{"lateral"}))`

Example

`"369.3843m"=("28.23m/s")^2/("[g]"*("0.07"+"0.15"))`

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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) - The ruling minimum radius is a 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.
Velocity - (Measured in Meter per Second) - Velocity is the rate of change of distance of the vehicle with respect to time.
Rate of Super Elevation - Rate of Super Elevation is the transverse slope along the width of the road provided by rising the outer edge of the road with respect to the inner edge, throughout the length of the horizontal curve.
Coefficient of Lateral Friction - Coefficient of Lateral Friction is a dimensionless value that represents the ratio of the lateral force required to move an object or surface laterally to the normal force acting on it.

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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Created by Avayjit Das

University of Engineering and Management,Kolkata (UEMK), Kolkata

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National Institute Of Technology (NIT), Hamirpur

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< 12 Design of Superelevation Calculators

Total Widening needed at Horizontal Curve

Go Total Widening Needed at Horizontal Curve = (Number of Lanes*Distance between Front and Rear Wheel^2)/(2*Mean Radius of Curve)+Velocity/(2.64*sqrt(Mean Radius of Curve))

Distance between Front and Rear Wheel

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

Velocity of Vehicle for Ruling Minimum Radius

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

Radius of Outer Track Line of Front Wheel

Go Radius of Outer Track Line of Front Wheel = sqrt(Radius of Outer Track Line of Rear Wheel^2+Distance between Front and Rear Wheel^2)

Radius of Outer Track Line of Rear Wheel

Go Radius of Outer Track Line of Rear Wheel = sqrt(Radius of Outer Track Line of Front Wheel^2-Distance between Front and Rear Wheel^2)

Ruling Minimum Radius

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

Mechanical Widening needed for Large Radius of Road Curve

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

Number of Lanes in Horizontal Curve

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

Psychological Widening at Horizontal Curves

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

Velocity of Vehicle for Psychological Widening

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

Rate of Super Elevation

Go Rate of Super Elevation = (0.75*Velocity^2)/([g]*Mean Radius of Curve)

Allowable Speed of Vehicle in Horizontal Curve

Go Allowable Speed = sqrt(0.22*[g]*Mean Radius of Curve)

Ruling Minimum Radius Formula

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 -> 107.5119 = 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 distance of the vehicle with respect to time, Rate of Super Elevation is the transverse slope along the width of the road provided by rising the outer edge of the road with respect to the inner edge, throughout the length of the horizontal curve & Coefficient of Lateral Friction is a dimensionless value that represents the ratio of the lateral force required to move an object or surface laterally to the normal force acting on it.

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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