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Negative Grade Angle Given Sight Distance Formula

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A negative grade angle indicates an incline slope. Check FAQs

n 2 = \frac{h 2}{S - \frac{L s}{2} - \frac{h 1}{n 1}}

n₂ - Negative Grade Angle?h₂ - The Height of The Obstruction?S - Sight Distance?L_s - Length of Curve?h₁ - Driver Sight Height?n₁ - Positive Grade Angle?

Negative Grade Angle Given Sight Distance Example

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Here is how the Negative Grade Angle Given Sight Distance equation looks like with Values.

Here is how the Negative Grade Angle Given Sight Distance equation looks like with Units.

Here is how the Negative Grade Angle Given Sight Distance equation looks like.

-0.4023 = \frac{0.36}{3.56 - \frac{7}{2} - \frac{0.75}{45}}

-0.4023 = \frac{0.36m}{3.56m - \frac{7m}{2} - \frac{0.75m}{45°}}

-0.4023 = \frac{0.36}{3.56 - \frac{7}{2} - \frac{0.75}{45}}

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Negative Grade Angle Given Sight Distance Solution

Follow our step by step solution on how to calculate Negative Grade Angle Given Sight Distance?

FIRST Step Consider the formula

n 2 = \frac{h 2}{S - \frac{L s}{2} - \frac{h 1}{n 1}}

Next Step Substitute values of Variables

∴

n 2 = \frac{0.36m}{3.56m - \frac{7m}{2} - \frac{0.75m}{45°}}

Next Step Convert Units

∴

n 2 = \frac{0.36m}{3.56m - \frac{7m}{2} - \frac{0.75m}{0.7854rad}}

Next Step Prepare to Evaluate

∴

n 2 = \frac{0.36}{3.56 - \frac{7}{2} - \frac{0.75}{0.7854}}

Next Step Evaluate

∴

n 2 = -0.402266252503758

LAST Step Rounding Answer

∴

n 2 = -0.4023

Negative Grade Angle Given Sight Distance Formula Elements

Variables

Negative Grade Angle

A negative grade angle indicates an incline slope.

Symbol: n₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Negative Grade Angle

Open Variable

The Height of The Obstruction

The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety.

Symbol: h₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find The Height of The Obstruction

Open Variable

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

Open Variable

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

Open Variable

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

Open Variable

Positive Grade Angle

A positive grade angle indicates an upward slope.

Symbol: n₁

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Positive Grade Angle

Open Variable

Other formulas in Length of Summit Curve with Grade Angles category

Go Height of Obstruction Given Angle Grades

h 2 = (S - \frac{L s}{2} - \frac{h 1}{n 1}) \cdot n 2

Go Driver Sight Height given Angle Grades

h 1 = \frac{L s}{2} + S \cdot n 1 + \frac{h 2}{n 2}

Go Length of Summit Curve Given Angle Grades

L s = S \cdot 2 + \frac{h 1}{n 1} + \frac{h 2}{n 2}

Go Positive Grade Angle Given Sight Distance

n 1 = \frac{h 1}{S - \frac{L s}{2} - \frac{h 2}{n 2}}

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How to Evaluate Negative Grade Angle Given Sight Distance?

Negative Grade Angle Given Sight Distance evaluator uses Negative Grade Angle = The Height of The Obstruction/(Sight Distance-Length of Curve/2-Driver Sight Height/Positive Grade Angle) to evaluate the Negative Grade Angle, The Negative Grade Angle Given Sight Distance formula is defined as the height of the obstruction divided by the difference between the sight distance, half the curve length, and the driver's eye height divided by the positive grade angle. Negative Grade Angle is denoted by n₂ symbol.

How to evaluate Negative Grade Angle Given Sight Distance using this online evaluator? To use this online evaluator for Negative Grade Angle Given Sight Distance, enter The Height of The Obstruction (h₂), Sight Distance (S), Length of Curve (L_s), Driver Sight Height (h₁) & Positive Grade Angle (n₁) and hit the calculate button.

FAQs on Negative Grade Angle Given Sight Distance

What is the formula to find Negative Grade Angle Given Sight Distance?

The formula of Negative Grade Angle Given Sight Distance is expressed as Negative Grade Angle = The Height of The Obstruction/(Sight Distance-Length of Curve/2-Driver Sight Height/Positive Grade Angle). Here is an example- -0.402266 = 0.36/(3.56-7/2-0.75/0.785398163397301).

How to calculate Negative Grade Angle Given Sight Distance?

With The Height of The Obstruction (h₂), Sight Distance (S), Length of Curve (L_s), Driver Sight Height (h₁) & Positive Grade Angle (n₁) we can find Negative Grade Angle Given Sight Distance using the formula - Negative Grade Angle = The Height of The Obstruction/(Sight Distance-Length of Curve/2-Driver Sight Height/Positive Grade Angle).

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