Length given Angle of Super Elevation Calculator

✖The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.ⓘ Acceleration due to Gravity [g]			+10% -10%
✖Super Elevation Angle is the angle with which the road or rail is raised for proper transportation for vehicles.ⓘ Super Elevation Angle [θ_e]			+10% -10%
✖Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Curve Radius [R_Curve]			+10% -10%
✖Rate of Radial Acceleration define the rate of change of radial acceleration. It is in the unit m/s^2 per second.ⓘ Rate of Radial Acceleration [α]			+10% -10%

✖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.ⓘ Length given Angle of Super Elevation [L_a]

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Length given Angle of Super Elevation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration
L_a = (g*tan(θ_e))^1.5*sqrt(R_Curve)/α
This formula uses 2 Functions, 5 Variables

Functions Used

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., 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., sqrt(Number)

Variables Used

Transition Curve Length - (Measured in Meter) - 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.
Acceleration due to Gravity - (Measured in Meter per Square Second) - The Acceleration due to Gravity is acceleration gained by an object because of gravitational force.
Super Elevation Angle - Super Elevation Angle is the angle with which the road or rail is raised for proper transportation for vehicles.
Curve Radius - (Measured in Meter) - Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.
Rate of Radial Acceleration - (Measured in Meter per Square Second) - Rate of Radial Acceleration define the rate of change of radial acceleration. It is in the unit m/s^2 per second.

STEP 1: Convert Input(s) to Base Unit

Acceleration due to Gravity: 9.8 Meter per Square Second --> 9.8 Meter per Square Second No Conversion Required
Super Elevation Angle: 95.4 --> No Conversion Required
Curve Radius: 200 Meter --> 200 Meter No Conversion Required
Rate of Radial Acceleration: 10 Meter per Square Second --> 10 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_a = (g*tan(θ_e))^1.5*sqrt(R_Curve)/α --> (9.8*tan(95.4))^1.5*sqrt(200)/10

Evaluating ... ...

L_a = 146.221394533313

STEP 3: Convert Result to Output's Unit

146.221394533313 Meter --> No Conversion Required

FINAL ANSWER

146.221394533313 ≈ 146.2214 Meter <-- Transition Curve Length

(Calculation completed in 00.020 seconds)

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< Length of Transition Curve Calculators

Length of Transition Curve given Time Rate

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

Time Rate given Length of Transition Curve

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

Rate of Change of Radial Acceleration

LaTeX Go Rate of Radial Acceleration = (Vehicle Velocity^2/(Curve Radius*Time taken to Travel))

Time Taken given Radial Acceleration

LaTeX Go Time taken to Travel = (Vehicle Velocity^2/(Curve Radius*Rate of Radial Acceleration))

Length given Angle of Super Elevation Formula

LaTeX Go

Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration
L_a = (g*tan(θ_e))^1.5*sqrt(R_Curve)/α

What is the Angle of Super Elevation?

The angle of super elevation is the angle at which the outer edge of a horizontal curve is raised above the inner edge to counteract the centrifugal force experienced by a vehicle.

How to Calculate Length given Angle of Super Elevation?

Length given Angle of Super Elevation calculator uses Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration to calculate 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 calculate Length given Angle of Super Elevation using this online calculator? To use this online calculator 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. Here is how the Length given Angle of Super Elevation calculation can be explained with given input values -> 146.2214 = (9.8*tan(95.4))^1.5*sqrt(200)/10.

FAQ

What is Length given Angle of Super Elevation?

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 and is represented as L_a = (g*tan(θ_e))^1.5*sqrt(R_Curve)/α or Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration. The Acceleration due to Gravity is acceleration gained by an object because of gravitational force, Super Elevation Angle is the angle with which the road or rail is raised for proper transportation for vehicles, Curve Radius is the radius of a circle whose part, say, arc is taken for consideration & Rate of Radial Acceleration define the rate of change of radial acceleration. It is in the unit m/s^2 per second.

How to calculate Length given Angle of Super Elevation?

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 is calculated using Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration. To calculate Length given Angle of Super Elevation, you need Acceleration due to Gravity (g), Super Elevation Angle (θ_e), Curve Radius (R_Curve) & Rate of Radial Acceleration (α). With our tool, you need to enter the respective value for Acceleration due to Gravity, Super Elevation Angle, Curve Radius & Rate of Radial Acceleration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Transition Curve Length?

In this formula, Transition Curve Length uses Acceleration due to Gravity, Super Elevation Angle, Curve Radius & Rate of Radial Acceleration. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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