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

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

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

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

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

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

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

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

10.9611 = a \tan (\frac{0.88 \cdot {3.56}^{2} - 2 \cdot 0.75}{2 \cdot 3.56 \cdot 7})

10.9611° = a \tan (\frac{0.88rad \cdot {3.56m}^{2} - 2 \cdot 0.75m}{2 \cdot 3.56m \cdot 7m})

10.9611 = a \tan (\frac{0.88 \cdot {3.56}^{2} - 2 \cdot 0.75}{2 \cdot 3.56 \cdot 7})

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

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

α angle = a \tan (\frac{0.88rad \cdot {3.56m}^{2} - 2 \cdot 0.75m}{2 \cdot 3.56m \cdot 7m})

Next Step Prepare to Evaluate

∴

α angle = a \tan (\frac{0.88 \cdot {3.56}^{2} - 2 \cdot 0.75}{2 \cdot 3.56 \cdot 7})

Next Step Evaluate

∴

α angle = 0.191306613869968rad

Next Step Convert to Output's Unit

∴

α angle = 10.9610615676901°

LAST Step Rounding Answer

∴

α angle = 10.9611°

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

Variables

Functions

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

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

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

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)

atan

Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle.

Syntax: atan(Number)

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

Go Length of Valley Curve Greater than Stopping Sight Distance

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

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

Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance evaluator uses Inclination = atan((Deviation Angle*Sight Distance^2-2*Driver Sight Height)/(2*Sight Distance*Length of Curve)) to evaluate the Inclination, The Inclination Angle given Length of valley curve greater than stopping sight distance formula is defined asthe deviation angle multiplied by the square of the sight distance minus twice the product of the curve length and the driver's eye height, all divided by twice the sight distance multiplied by the curve length. Inclination is denoted by α_angle symbol.

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

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

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

The formula of Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance is expressed as Inclination = atan((Deviation Angle*Sight Distance^2-2*Driver Sight Height)/(2*Sight Distance*Length of Curve)). Here is an example- 628.0226 = atan((0.88*3.56^2-2*0.75)/(2*3.56*7)).

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

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

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

Yes, the Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance, measured in Angle can be negative.

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

Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Inclination Angle given Length of Valley Curve Greater than Stopping Sight Distance can be measured.

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

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

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

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

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

Variable Name