Length of Transition Curve given Shift Calculator

✖Shift is the distance by which the curve moves in order to accommodate the shape of transition curve.ⓘ Shift [S]			+10% -10%
✖Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.ⓘ Curve Radius [R_Curve]			+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 of Transition Curve given Shift [L_a]

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Formula

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Length of Transition Curve given Shift

Formula

`"L"_{"a"} = sqrt("S"*24*"R"_{"Curve"})`

Example

`"120m"=sqrt("3m"*24*"200m")`

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Length of Transition Curve given Shift Solution

STEP 0: Pre-Calculation Summary

Formula Used

Transition Curve Length = sqrt(Shift*24*Curve Radius)
L_a = sqrt(S*24*R_Curve)
This formula uses 1 Functions, 3 Variables

Functions Used

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.
Shift - (Measured in Meter) - Shift is the distance by which the curve moves in order to accommodate the shape of transition curve.
Curve Radius - (Measured in Meter) - Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.

STEP 1: Convert Input(s) to Base Unit

Shift: 3 Meter --> 3 Meter No Conversion Required
Curve Radius: 200 Meter --> 200 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_a = sqrt(S*24*R_Curve) --> sqrt(3*24*200)

Evaluating ... ...

L_a = 120

STEP 3: Convert Result to Output's Unit

120 Meter --> No Conversion Required

FINAL ANSWER

120 Meter <-- Transition Curve Length

(Calculation completed in 00.004 seconds)

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Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

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Meerut Institute of Engineering and Technology (MIET), Meerut

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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 of Transition Curve given Shift Formula

Transition Curve Length = sqrt(Shift*24*Curve Radius)
L_a = sqrt(S*24*R_Curve)

What are the Ideal Mathematical Expressions for Transition Curves?

1. Cubic spiral, or clothoid, or Euler spiral
2. Bernoulli’s lemniscate
3. Cubic parabola or Froude’s curve
Within the limits used in practice, all the above curves give substantially the same curve on ground. However, consideration of their relative merits from three important viewpoints—mathematical, simplicity, adaptability to variety of conditions and ease to laying out in field—has lead most of the surveyors to favour clothoid.

What is the Purpose of a Transition Curve?

The purpose of a transition curve is to allow a train to smoothly transition from a straight track to a curved track without experiencing any sudden changes in direction or lateral forces. This helps to reduce wear and tear on the track and rolling stock, as well as increasing safety for passengers and crew.

How to Calculate Length of Transition Curve given Shift?

Length of Transition Curve given Shift calculator uses Transition Curve Length = sqrt(Shift*24*Curve Radius) to calculate the Transition Curve Length, The Length of Transition Curve given Shift formula is defined as the length of the transition curve in its cubic parabolic shape. Transition Curve Length is denoted by L_a symbol.

How to calculate Length of Transition Curve given Shift using this online calculator? To use this online calculator for Length of Transition Curve given Shift, enter Shift (S) & Curve Radius (R_Curve) and hit the calculate button. Here is how the Length of Transition Curve given Shift calculation can be explained with given input values -> 120 = sqrt(3*24*200).

FAQ

What is Length of Transition Curve given Shift?

The Length of Transition Curve given Shift formula is defined as the length of the transition curve in its cubic parabolic shape and is represented as L_a = sqrt(S*24*R_Curve) or Transition Curve Length = sqrt(Shift*24*Curve Radius). Shift is the distance by which the curve moves in order to accommodate the shape of transition curve & Curve Radius is the radius of a circle whose part, say, arc is taken for consideration.

How to calculate Length of Transition Curve given Shift?

The Length of Transition Curve given Shift formula is defined as the length of the transition curve in its cubic parabolic shape is calculated using Transition Curve Length = sqrt(Shift*24*Curve Radius). To calculate Length of Transition Curve given Shift, you need Shift (S) & Curve Radius (R_Curve). With our tool, you need to enter the respective value for Shift & Curve Radius 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 Shift & Curve Radius. 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 = (Acceleration due to Gravity*tan(Super Elevation Angle))^1.5*sqrt(Curve Radius)/Rate of Radial Acceleration
Transition Curve Length = 4.52*sqrt(Curve Radius)
Transition Curve Length = 12.80*sqrt(Curve Radius)

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