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Length of Valley Curve Formula

GoLength of Valley Curve given Time and Design Speed Formula

GoTotal Length 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 = \frac{v^{3}}{R \cdot C a}

L_s - Length of Curve?v - Design Speed?R - Radius of Curve?C_a - Rate of Change of Acceleration?

Length of Valley Curve Example

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

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

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

12.7188 = \frac{5^{3}}{2.34 \cdot 4.2}

12.7188m = \frac{{5m/s}^{3}}{2.34m \cdot 4.2m/s}

12.7188 = \frac{5^{3}}{2.34 \cdot 4.2}

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Length of Valley Curve Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

L s = \frac{{5m/s}^{3}}{2.34m \cdot 4.2m/s}

Next Step Prepare to Evaluate

∴

L s = \frac{5^{3}}{2.34 \cdot 4.2}

Next Step Evaluate

∴

L s = 12.7187627187627m

LAST Step Rounding Answer

∴

L s = 12.7188m

Length of Valley Curve Formula Elements

Variables

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

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

Radius of Curve

Radius of Curve typically represents the minimum radius of the curve.

Symbol: R

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Curve

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

Other Formulas to find Length of Curve

Go Length of Valley Curve given Time and Design Speed

L s = v \cdot t

Go Total Length of Valley Curve

L s = 2 \cdot \sqrt{\frac{N \cdot v^{3}}{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 Length of Valley Curve?

Length of Valley Curve evaluator uses Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration) to evaluate the Length of Curve, The Length of Valley Curve formula is defined as the cube of the design speed and dividing it by the product of the radius of the curve and the rate of change of acceleration. Length of Curve is denoted by L_s symbol.

How to evaluate Length of Valley Curve using this online evaluator? To use this online evaluator for Length of Valley Curve, enter Design Speed (v), Radius of Curve (R) & Rate of Change of Acceleration (C_a) and hit the calculate button.

FAQs on Length of Valley Curve

What is the formula to find Length of Valley Curve?

The formula of Length of Valley Curve is expressed as Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration). Here is an example- 5.57339 = (5^3)/(2.34*4.2).

How to calculate Length of Valley Curve?

With Design Speed (v), Radius of Curve (R) & Rate of Change of Acceleration (C_a) we can find Length of Valley Curve using the formula - Length of Curve = (Design Speed^3)/(Radius of Curve*Rate of Change of Acceleration).

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

Can the Length of Valley Curve be negative?

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

Which unit is used to measure Length of Valley Curve?

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 Length of Valley Curve can be measured.

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Length of Valley Curve Formula

​GoLength of Valley Curve given Time and Design Speed Formula

​GoTotal Length of Valley Curve Formula

Length of Valley Curve Example

Length of Valley Curve Solution

Length of Valley Curve Formula Elements

Other Formulas to find Length of Curve

Other formulas in Design of Valley Curve category

How to Evaluate Length of Valley Curve?

FAQs on Length of Valley Curve

Variable Name

GoLength of Valley Curve given Time and Design Speed Formula

GoTotal Length of Valley Curve Formula