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Length of Valley Curve Greater than Stopping Sight Distance 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{N \cdot S^{2}}{2 \cdot h 1 + 2 \cdot S \cdot \tan (α angle)}

L_s - Length of Curve?N - Deviation Angle?S - Sight Distance?h₁ - Driver Sight Height?α_angle - Inclination?

Length of Valley Curve Greater than Stopping Sight Distance Example

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Here is how the Length of Valley Curve Greater than Stopping Sight Distance equation looks like with Values.

Here is how the Length of Valley Curve Greater than Stopping Sight Distance equation looks like with Units.

Here is how the Length of Valley Curve Greater than Stopping Sight Distance equation looks like.

6.378 = \frac{0.88 \cdot {3.56}^{2}}{2 \cdot 0.75 + 2 \cdot 3.56 \cdot \tan (2)}

6.378m = \frac{0.88rad \cdot {3.56m}^{2}}{2 \cdot 0.75m + 2 \cdot 3.56m \cdot \tan (2°)}

6.378 = \frac{0.88 \cdot {3.56}^{2}}{2 \cdot 0.75 + 2 \cdot 3.56 \cdot \tan (2)}

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Length of Valley Curve Greater than Stopping Sight Distance Solution

Follow our step by step solution on how to calculate Length of Valley Curve Greater than Stopping Sight Distance?

FIRST Step Consider the formula

L s = \frac{N \cdot S^{2}}{2 \cdot h 1 + 2 \cdot S \cdot \tan (α angle)}

Next Step Substitute values of Variables

∴

L s = \frac{0.88rad \cdot {3.56m}^{2}}{2 \cdot 0.75m + 2 \cdot 3.56m \cdot \tan (2°)}

Next Step Convert Units

∴

L s = \frac{0.88rad \cdot {3.56m}^{2}}{2 \cdot 0.75m + 2 \cdot 3.56m \cdot \tan (0.0349rad)}

Next Step Prepare to Evaluate

∴

L s = \frac{0.88 \cdot {3.56}^{2}}{2 \cdot 0.75 + 2 \cdot 3.56 \cdot \tan (0.0349)}

Next Step Evaluate

∴

L s = 6.37798190883142m

LAST Step Rounding Answer

∴

L s = 6.378m

Length of Valley Curve Greater than Stopping Sight Distance 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

Sight Distance

Sight Distance is s the minimum distance between two vehicles moving along a curve, when the driver of one vehicle can just see the other vehicle on the road.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Sight Distance

Driver Sight Height

Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle.

Symbol: h₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Driver Sight Height

Inclination

Inclination refers to the angle or slope of an object or surface concerning the horizontal plane.

Symbol: α_angle

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Inclination

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.

Syntax: tan(Angle)

Other formulas in Length of Valley Curve greater than Stopping Sight Distance category

Go Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance

α angle = a \tan (\frac{N \cdot S^{2} - 2 \cdot h 1}{2 \cdot S \cdot L s})

Go Deviation Angle given Length of Valley Curve Greater than Stopping Sight Distance

N = \frac{L s \cdot (2 \cdot h 1 + 2 \cdot S \cdot \tan (α angle))}{S^{2}}

Go Driver Eye Height given Length of Valley Curve Greater than Stopping Sight Distance

h 1 = \frac{N \cdot S^{2} - 2 \cdot L s \cdot S \cdot \tan (α angle)}{2 \cdot L s}

How to Evaluate Length of Valley Curve Greater than Stopping Sight Distance?

Length of Valley Curve Greater than Stopping Sight Distance evaluator uses Length of Curve = (Deviation Angle*Sight Distance^2)/(2*Driver Sight Height+2*Sight Distance*tan(Inclination)) to evaluate the Length of Curve, The Length of valley curve greater than stopping sight distance formula is defined as the product of the deviation angle and the square of the sight distance divided by twice the driver's eye height, added to two times the sight distance multiplied by the tangent of the inclination angle. Length of Curve is denoted by L_s symbol.

How to evaluate Length of Valley Curve Greater than Stopping Sight Distance using this online evaluator? To use this online evaluator for Length of Valley Curve Greater than Stopping Sight Distance, enter Deviation Angle (N), Sight Distance (S), Driver Sight Height (h₁) & Inclination (α_angle) and hit the calculate button.

FAQs on Length of Valley Curve Greater than Stopping Sight Distance

What is the formula to find Length of Valley Curve Greater than Stopping Sight Distance?

The formula of Length of Valley Curve Greater than Stopping Sight Distance is expressed as Length of Curve = (Deviation Angle*Sight Distance^2)/(2*Driver Sight Height+2*Sight Distance*tan(Inclination)). Here is an example- 6.377982 = (0.88*3.56^2)/(2*0.75+2*3.56*tan(0.03490658503988)).

How to calculate Length of Valley Curve Greater than Stopping Sight Distance?

With Deviation Angle (N), Sight Distance (S), Driver Sight Height (h₁) & Inclination (α_angle) we can find Length of Valley Curve Greater than Stopping Sight Distance using the formula - Length of Curve = (Deviation Angle*Sight Distance^2)/(2*Driver Sight Height+2*Sight Distance*tan(Inclination)). This formula also uses Tangent function(s).

Can the Length of Valley Curve Greater than Stopping Sight Distance be negative?

No, the Length of Valley Curve Greater than Stopping Sight Distance, measured in Length cannot be negative.

Which unit is used to measure Length of Valley Curve Greater than Stopping Sight Distance?

Length of Valley Curve Greater than Stopping Sight Distance 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 Greater than Stopping Sight Distance can be measured.

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Length of Valley Curve Greater than Stopping Sight Distance Formula

Length of Valley Curve Greater than Stopping Sight Distance Example

Length of Valley Curve Greater than Stopping Sight Distance Solution

Length of Valley Curve Greater than Stopping Sight Distance Formula Elements

Other formulas in Length of Valley Curve greater than Stopping Sight Distance category

How to Evaluate Length of Valley Curve Greater than Stopping Sight Distance?

FAQs on Length of Valley Curve Greater than Stopping Sight Distance

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