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
La = (g*tan(θe))^1.5*sqrt(RCurve)/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
La = (g*tan(θe))^1.5*sqrt(RCurve)/α --> (9.8*tan(95.4))^1.5*sqrt(200)/10
Evaluating ... ...
La = 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 00.004 seconds)

Credits

Created by Chandana P Dev
NSS College of Engineering (NSSCE), Palakkad
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National Institute of Technology (NIT), Warangal
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10+ Length of Transition Curve Calculators

Length given Angle of Super Elevation
Go Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration
Length of Transition Curve given Time Rate
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
Go Super Elevation Time Rate = Railway Gauge*Vehicle Velocity^3/(Transition Curve Length*Acceleration due to Gravity*Curve Radius)
Hands-Off Velocity
Go Hands off Velocity = sqrt(Acceleration due to Gravity*Radius of Curve*tan(Angle of Super Elevation))
Rate of Change of Radial Acceleration
Go Rate of Radial Acceleration = (Vehicle Velocity^2/(Curve Radius*Time taken to Travel))
Time Taken given Radial Acceleration
Go Time taken to Travel = (Vehicle Velocity^2/(Curve Radius*Rate of Radial Acceleration))
Length of Transition Curve given Shift
Go Transition Curve Length = sqrt(Shift*24*Curve Radius)
Shift of Curve
Go Shift = Transition Curve Length^2/(24*Curve Radius)
Length when Comfort Condition Holds Good for Highways
Go Transition Curve Length = 12.80*sqrt(Curve Radius)
Length when Comfort Condition Holds Good for Railways
Go Transition Curve Length = 4.52*sqrt(Curve Radius)

Length given Angle of Super Elevation Formula

Transition Curve Length = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration
La = (g*tan(θe))^1.5*sqrt(RCurve)/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 La 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 e), Curve Radius (RCurve) & 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 La = (g*tan(θe))^1.5*sqrt(RCurve)/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 e), Curve Radius (RCurve) & 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 4 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)
  • Transition Curve Length = sqrt(Shift*24*Curve Radius)
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