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Length given Angle of Super Elevation Formula

GoLength of Transition Curve given Time Rate Formula

GoLength when Comfort Condition Holds Good for Railways Formula

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Transition Curve Length should be such that full super elevation is attained at the end of the transition curve and applied at a suitable rate. Check FAQs

L a = {(g \cdot \tan (θ e))}^{1.5} \cdot \frac{\sqrt{R Curve}}{α}

L_a - Transition Curve Length?g - Acceleration due to Gravity?θ_e - Super Elevation Angle?R_Curve - Curve Radius?α - Rate of Radial Acceleration?

Length given Angle of Super Elevation Example

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Here is how the Length given Angle of Super Elevation equation looks like with Values.

Here is how the Length given Angle of Super Elevation equation looks like with Units.

Here is how the Length given Angle of Super Elevation equation looks like.

146.2214 = {(9.8 \cdot \tan (95.4))}^{1.5} \cdot \frac{\sqrt{200}}{10}

146.2214m = {(9.8m/s² \cdot \tan (95.4))}^{1.5} \cdot \frac{\sqrt{200m}}{10m/s²}

146.2214 = {(9.8 \cdot \tan (95.4))}^{1.5} \cdot \frac{\sqrt{200}}{10}

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Length given Angle of Super Elevation Solution

Follow our step by step solution on how to calculate Length given Angle of Super Elevation?

FIRST Step Consider the formula

L a = {(g \cdot \tan (θ e))}^{1.5} \cdot \frac{\sqrt{R Curve}}{α}

Next Step Substitute values of Variables

∴

L a = {(9.8m/s² \cdot \tan (95.4))}^{1.5} \cdot \frac{\sqrt{200m}}{10m/s²}

Next Step Prepare to Evaluate

∴

L a = {(9.8 \cdot \tan (95.4))}^{1.5} \cdot \frac{\sqrt{200}}{10}

Next Step Evaluate

∴

L a = 146.221394533313m

LAST Step Rounding Answer

∴

L a = 146.2214m

Length given Angle of Super Elevation Formula Elements

Variables

Functions

Transition Curve Length

Transition Curve Length should be such that full super elevation is attained at the end of the transition curve and applied at a suitable rate.

Symbol: L_a

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Transition Curve Length

Acceleration due to Gravity

The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.

Symbol: g

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Acceleration due to Gravity

Super Elevation Angle

Super Elevation Angle is the angle with which the road or rail is raised for proper transportation for vehicles.

Symbol: θ_e

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Super Elevation Angle

Curve Radius

Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.

Symbol: R_Curve

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Curve Radius

Rate of Radial Acceleration

Rate of Radial Acceleration define the rate of change of radial acceleration. It is in the unit m/s^2 per second.

Symbol: α

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Rate of Radial Acceleration

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Transition Curve Length

Go Length of Transition Curve given Time Rate

L a = G \cdot \frac{V^{3}}{x \cdot g \cdot R Curve}

Go Length when Comfort Condition Holds Good for Railways

L a = 4.52 \cdot \sqrt{R Curve}

Go Length when Comfort Condition Holds Good for Highways

L a = 12.80 \cdot \sqrt{R Curve}

Go Length of Transition Curve given Shift

L a = \sqrt{S \cdot 24 \cdot R Curve}

Other formulas in Length of Transition Curve category

Go Time Rate given Length of Transition Curve

x = G \cdot \frac{V^{3}}{L a \cdot g \cdot R Curve}

Go Rate of Change of Radial Acceleration

α = (\frac{V^{2}}{R Curve \cdot t})

Go Time Taken given Radial Acceleration

t = (\frac{V^{2}}{R Curve \cdot α})

Go Shift of Curve

S = \frac{{L a}^{2}}{24 \cdot R Curve}

How to Evaluate Length given Angle of Super Elevation?

Length given Angle of Super Elevation evaluator uses Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration to evaluate the Transition Curve Length, The Length given Angle of Super Elevation formula is defined as the full superelevation attained at the end of the transition curve and applied at a suitable rate. Transition Curve Length is denoted by L_a symbol.

How to evaluate Length given Angle of Super Elevation using this online evaluator? To use this online evaluator for Length given Angle of Super Elevation, enter Acceleration due to Gravity (g), Super Elevation Angle (θ_e), Curve Radius (R_Curve) & Rate of Radial Acceleration (α) and hit the calculate button.

FAQs on Length given Angle of Super Elevation

What is the formula to find Length given Angle of Super Elevation?

The formula of Length given Angle of Super Elevation is expressed as Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration. Here is an example- 146.2214 = (9.8*tan(95.4))^1.5*sqrt(200)/10.

How to calculate Length given Angle of Super Elevation?

With Acceleration due to Gravity (g), Super Elevation Angle (θ_e), Curve Radius (R_Curve) & Rate of Radial Acceleration (α) we can find Length given Angle of Super Elevation using the formula - Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration. This formula also uses Tangent (tan), Square Root (sqrt) function(s).

What are the other ways to Calculate Transition Curve Length?

Here are the different ways to Calculate Transition Curve Length-

Transition Curve Length=Railway Gauge*Vehicle Velocity^3/(Super Elevation Time Rate*Acceleration due to Gravity*Curve Radius)
Transition Curve Length=4.52*sqrt(Curve Radius)
Transition Curve Length=12.80*sqrt(Curve Radius)

Can the Length given Angle of Super Elevation be negative?

Yes, the Length given Angle of Super Elevation, measured in Length can be negative.

Which unit is used to measure Length given Angle of Super Elevation?

Length given Angle of Super Elevation is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Length given Angle of Super Elevation can be measured.

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: Value
: Unit

Length given Angle of Super Elevation Formula

​GoLength of Transition Curve given Time Rate Formula

​GoLength when Comfort Condition Holds Good for Railways Formula

Length given Angle of Super Elevation Example

Length given Angle of Super Elevation Solution

Length given Angle of Super Elevation Formula Elements

Other Formulas to find Transition Curve Length

Other formulas in Length of Transition Curve category

How to Evaluate Length given Angle of Super Elevation?

FAQs on Length given Angle of Super Elevation

Variable Name

GoLength of Transition Curve given Time Rate Formula

GoLength when Comfort Condition Holds Good for Railways Formula