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Rate of Super Elevation Formula

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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. Check FAQs

e = \frac{0.75 \cdot {v vehicle}^{2}}{[g] \cdot R mean}

e - Rate of Super Elevation?v_vehicle - Velocity?R_mean - Mean Radius of Curve?[g] - Gravitational acceleration on Earth?

Rate of Super Elevation Example

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Here is how the Rate of Super Elevation equation looks like with Values.

Here is how the Rate of Super Elevation equation looks like with Units.

Here is how the Rate of Super Elevation equation looks like.

0.1793 = \frac{0.75 \cdot {28.23}^{2}}{9.8066 \cdot 340}

0.1793 = \frac{0.75 \cdot {28.23m/s}^{2}}{9.8066m/s² \cdot 340m}

0.1793 = \frac{0.75 \cdot {28.23}^{2}}{9.8066 \cdot 340}

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Rate of Super Elevation Solution

Follow our step by step solution on how to calculate Rate of Super Elevation?

FIRST Step Consider the formula

e = \frac{0.75 \cdot {v vehicle}^{2}}{[g] \cdot R mean}

Next Step Substitute values of Variables

∴

e = \frac{0.75 \cdot {28.23m/s}^{2}}{[g] \cdot 340m}

Next Step Substitute values of Constants

∴

e = \frac{0.75 \cdot {28.23m/s}^{2}}{9.8066m/s² \cdot 340m}

Next Step Prepare to Evaluate

∴

e = \frac{0.75 \cdot {28.23}^{2}}{9.8066 \cdot 340}

Next Step Evaluate

∴

e = 0.179260014437982

LAST Step Rounding Answer

∴

e = 0.1793

Rate of Super Elevation Formula Elements

Variables

Constants

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

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

Mean Radius of Curve

Mean Radius of Curve is the average radius of a curve section in road design, used to calculate superelevation and widening of the road.

Symbol: R_mean

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Mean Radius of Curve

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 Ruling Minimum Radius

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

How to Evaluate Rate of Super Elevation?

Rate of Super Elevation evaluator uses Rate of Super Elevation = (0.75*Velocity^2)/([g]*Mean Radius of Curve) to evaluate the Rate of Super Elevation, The Rate of Super Elevation formula is defined as the banking of a roadway to offset the effect of centripetal acceleration. Rate of Super Elevation is denoted by e symbol.

How to evaluate Rate of Super Elevation using this online evaluator? To use this online evaluator for Rate of Super Elevation, enter Velocity (v_vehicle) & Mean Radius of Curve (R_mean) and hit the calculate button.

FAQs on Rate of Super Elevation

What is the formula to find Rate of Super Elevation?

The formula of Rate of Super Elevation is expressed as Rate of Super Elevation = (0.75*Velocity^2)/([g]*Mean Radius of Curve). Here is an example- 0.17926 = (0.75*28.23^2)/([g]*340).

How to calculate Rate of Super Elevation?

With Velocity (v_vehicle) & Mean Radius of Curve (R_mean) we can find Rate of Super Elevation using the formula - Rate of Super Elevation = (0.75*Velocity^2)/([g]*Mean Radius of Curve). This formula also uses Gravitational acceleration on Earth constant(s).

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