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Total Length of Valley Curve Formula

GoLength of Valley Curve given Time and Design Speed Formula

GoLength of Valley Curve Formula

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Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave. Check FAQs

L s = 2 \cdot \sqrt{\frac{N \cdot v^{3}}{C a}}

L_s - Length of Curve?N - Deviation Angle?v - Design Speed?C_a - Rate of Change of Acceleration?

Total Length of Valley Curve Example

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Here is how the Total Length of Valley Curve equation looks like with Values.

Here is how the Total Length of Valley Curve equation looks like with Units.

Here is how the Total Length of Valley Curve equation looks like.

10.2353 = 2 \cdot \sqrt{\frac{0.88 \cdot 5^{3}}{4.2}}

10.2353m = 2 \cdot \sqrt{\frac{0.88rad \cdot {5m/s}^{3}}{4.2m/s}}

10.2353 = 2 \cdot \sqrt{\frac{0.88 \cdot 5^{3}}{4.2}}

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Total Length of Valley Curve Solution

Follow our step by step solution on how to calculate Total Length of Valley Curve?

FIRST Step Consider the formula

L s = 2 \cdot \sqrt{\frac{N \cdot v^{3}}{C a}}

Next Step Substitute values of Variables

∴

L s = 2 \cdot \sqrt{\frac{0.88rad \cdot {5m/s}^{3}}{4.2m/s}}

Next Step Prepare to Evaluate

∴

L s = 2 \cdot \sqrt{\frac{0.88 \cdot 5^{3}}{4.2}}

Next Step Evaluate

∴

L s = 10.2353263143832m

LAST Step Rounding Answer

∴

L s = 10.2353m

Total Length of Valley Curve Formula Elements

Variables

Functions

Length of Curve

Length of Curve is the distance along the road where the alignment changes from upward to downward slope, creating a valley-shaped concave.

Symbol: L_s

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Length of Curve

Deviation Angle

Deviation Angle is the angle between the reference direction and the observed direction.

Symbol: N

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Deviation Angle

Design Speed

Design speed refers to the intended or planned operating speed for a particular section of a roadway or railway.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Design Speed

Rate of Change of Acceleration

Rate of Change of Acceleration refers to how quickly the acceleration of an object changes over time.

Symbol: C_a

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Rate of Change of Acceleration

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 Length of Curve

Go Length of Valley Curve given Time and Design Speed

L s = v \cdot t

Go Length of Valley Curve

L s = \frac{v^{3}}{R \cdot C a}

Other formulas in Design of Valley Curve category

Go Rate of Change of Acceleration

C a = \frac{v^{3}}{L s \cdot R}

Go Radius of Curve given Length of Valley Curve

R = \frac{v^{3}}{L s \cdot C a}

Go Design Speed given Length of Valley Curve

v = {(L s \cdot R \cdot C a)}^{\frac{1}{3}}

Go Time given Rate of Change of Acceleration

t = \frac{\frac{v^{2}}{R}}{C a}

How to Evaluate Total Length of Valley Curve?

Total Length of Valley Curve evaluator uses Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration) to evaluate 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 evaluate Total Length of Valley Curve using this online evaluator? To use this online evaluator 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.

FAQs on Total Length of Valley Curve

What is the formula to find Total Length of Valley Curve?

The formula of Total Length of Valley Curve is expressed as Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration). Here is an example- 10.48809 = 2*sqrt((0.88*5^3)/4.2).

How to calculate Total Length of Valley Curve?

With Deviation Angle (N), Design Speed (v) & Rate of Change of Acceleration (C_a) we can find Total Length of Valley Curve using the formula - Length of Curve = 2*sqrt((Deviation Angle*Design Speed^3)/Rate of Change of Acceleration). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Length of Curve?

Here are the different ways to Calculate Length of Curve-

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

Can the Total Length of Valley Curve be negative?

No, the Total Length of Valley Curve, measured in Length cannot be negative.

Which unit is used to measure Total Length of Valley Curve?

Total Length of Valley Curve is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Total Length of Valley Curve can be measured.

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Total Length of Valley Curve Formula

​GoLength of Valley Curve given Time and Design Speed Formula

​GoLength of Valley Curve Formula

Total Length of Valley Curve Example

Total Length of Valley Curve Solution

Total Length of Valley Curve Formula Elements

Other Formulas to find Length of Curve

Other formulas in Design of Valley Curve category

How to Evaluate Total Length of Valley Curve?

FAQs on Total Length of Valley Curve

Variable Name

GoLength of Valley Curve given Time and Design Speed Formula

GoLength of Valley Curve Formula