Total Length of Valley Curve Calculator

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Vertical alignment

Design of Transition Curves and Setback Distances

Design of Superelevation

Marshall Mix Design

Pavement Materials

Sight Distance

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Length of Valley Curve

Length of Summit Curve greater than Sight Distance

Length of Summit Curve Less than Sight Distance

Length of Summit Curve with Grade Angles

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Design of Valley Curve

Length of Valley Curve greater than Stopping Sight Distance

Length of Valley Curve Less than Stopping Sight Distance

✖Deviation Angle is the angle between the reference direction and the observed direction.ⓘ Deviation Angle [N]			+10% -10%
✖Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.ⓘ Design Speed [v]			+10% -10%
✖Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.ⓘ Rate of Change of Acceleration [C_a]			+10% -10%

✖Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.ⓘ Total Length of Valley Curve [L_s]

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Formula

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Total Length of Valley Curve

Formula

`"L"_{"s"} = 2*sqrt(("N"*"v"^3)/"C"_{"a"})`

Example

`"10.23533m"=2*sqrt(("0.88rad"*("5m/s")^3)/"4.2m/s")`

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Total Length of Valley Curve Solution

STEP 0: Pre-Calculation Summary

Formula Used

Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration)
L_s = 2*sqrt((N*v^3)/C_a)
This formula uses 1 Functions, 4 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

Length of Curve - (Measured in Meter) - Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.
Deviation Angle - (Measured in Radian) - Deviation Angle is the angle between the reference direction and the observed direction.
Design Speed - (Measured in Meter per Second) - Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.
Rate of Change of Acceleration - (Measured in Meter per Second) - Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.

STEP 1: Convert Input(s) to Base Unit

Deviation Angle: 0.88 Radian --> 0.88 Radian No Conversion Required
Design Speed: 5 Meter per Second --> 5 Meter per Second No Conversion Required
Rate of Change of Acceleration: 4.2 Meter per Second --> 4.2 Meter per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

L_s = 2*sqrt((N*v^3)/C_a) --> 2*sqrt((0.88*5^3)/4.2)

Evaluating ... ...

L_s = 10.2353263143832

STEP 3: Convert Result to Output's Unit

10.2353263143832 Meter --> No Conversion Required

FINAL ANSWER

10.2353263143832 ≈ 10.23533 Meter <-- Length of Curve

(Calculation completed in 00.004 seconds)

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< 12 Design of Valley Curve Calculators

Total Length of Valley Curve

Go Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration)

Design Speed given Total Length of Valley Curve

Go Design Speed = ((Length of Curve/2)^2*Rate of Change of Acceleration/Deviation Angle)^(1/3)

Rate of Change of Acceleration given Total Length of Valley Curve

Go Rate of Change of Acceleration = (Length of Curve/2)^2*Deviation Angle*Design Speed^3

Deviation Angle given Total Length of Valley Curve

Go Deviation Angle = (Length of Curve/2)^2*Rate of Change of Acceleration/Design Speed^3

Design Speed given Length of Valley Curve

Go Design Speed = (Length of Curve*Radius of Curve*Rate of Change of Acceleration)^(1/3)

Radius of Curve given Length of Valley Curve

Go Radius of Curve = (Design Speed^3)/(Length of Curve*Rate of Change of Acceleration)

Rate of Change of Acceleration

Go Rate of Change of Acceleration = (Design Speed^3)/(Length of Curve*Radius of Curve)

Length of Valley Curve

Go Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration)

Time given Rate of Change of Acceleration

Go Time = ((Design Speed^2)/Radius of Curve)/Rate of Change of Acceleration

Length of Valley Curve given Time and Design Speed

Go Length of Curve = Design Speed*Time

Design Speed given Length of Valley Curve and Time

Go Design Speed = Length of Curve/Time

Time given Length of Valley Curve and Design Speed

Go Time = Length of Curve/Design Speed

Total Length of Valley Curve Formula

Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration)
L_s = 2*sqrt((N*v^3)/C_a)

Difference Between Length of Valley Curve and Total Length of Valley Curve

"Length of Valley Curve" refers to the curve segment itself, while "Total Length of Valley Curve" includes the approach and departure sections, providing a comprehensive view of the entire transition.

How to Calculate Total Length of Valley Curve?

Total Length of Valley Curve calculator uses Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration) to calculate the Length of Curve, The Total Length of Valley Curve formula is defined as twice the square root of the product of deviation angle, design speed cubed, and the inverse of the rate of change of acceleration. Length of Curve is denoted by L_s symbol.

How to calculate Total Length of Valley Curve using this online calculator? To use this online calculator for Total Length of Valley Curve, enter Deviation Angle (N), Design Speed (v) & Rate of Change of Acceleration (C_a) and hit the calculate button. Here is how the Total Length of Valley Curve calculation can be explained with given input values -> 10.48809 = 2*sqrt((0.88*5^3)/4.2).

FAQ

What is Total Length of Valley Curve?

The Total Length of Valley Curve formula is defined as twice the square root of the product of deviation angle, design speed cubed, and the inverse of the rate of change of acceleration and is represented as L_s = 2*sqrt((N*v^3)/C_a) or Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration). Deviation Angle is the angle between the reference direction and the observed direction, Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway & Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.

How to calculate Total Length of Valley Curve?

The Total Length of Valley Curve formula is defined as twice the square root of the product of deviation angle, design speed cubed, and the inverse of the rate of change of acceleration is calculated using Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration). To calculate Total Length of Valley Curve, you need Deviation Angle (N), Design Speed (v) & Rate of Change of Acceleration (C_a). With our tool, you need to enter the respective value for Deviation Angle, Design Speed & Rate of Change of 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 Length of Curve?

In this formula, Length of Curve uses Deviation Angle, Design Speed & Rate of Change of Acceleration. We can use 2 other way(s) to calculate the same, which is/are as follows -

Length of Curve = Design Speed*Time
Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration)

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