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Positive Grade Angle with Deviation Angle Formula

GoPositive Grade Angle Given Sight Distance Formula

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A positive grade angle indicates an upward slope. Check FAQs

n 1 = \frac{N \cdot \sqrt{h 1 \cdot h 2} - N \cdot h 1}{h 2 - h 1}

n₁ - Positive Grade Angle?N - Deviation Angle?h₁ - Driver Sight Height?h₂ - The Height of The Obstruction?

Positive Grade Angle with Deviation Angle Example

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Here is how the Positive Grade Angle with Deviation Angle equation looks like with Values.

Here is how the Positive Grade Angle with Deviation Angle equation looks like with Units.

Here is how the Positive Grade Angle with Deviation Angle equation looks like.

29.7848 = \frac{0.88 \cdot \sqrt{0.75 \cdot 0.36} - 0.88 \cdot 0.75}{0.36 - 0.75}

29.7848° = \frac{0.88rad \cdot \sqrt{0.75m \cdot 0.36m} - 0.88rad \cdot 0.75m}{0.36m - 0.75m}

29.7848 = \frac{0.88 \cdot \sqrt{0.75 \cdot 0.36} - 0.88 \cdot 0.75}{0.36 - 0.75}

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Positive Grade Angle with Deviation Angle Solution

Follow our step by step solution on how to calculate Positive Grade Angle with Deviation Angle?

FIRST Step Consider the formula

n 1 = \frac{N \cdot \sqrt{h 1 \cdot h 2} - N \cdot h 1}{h 2 - h 1}

Next Step Substitute values of Variables

∴

n 1 = \frac{0.88rad \cdot \sqrt{0.75m \cdot 0.36m} - 0.88rad \cdot 0.75m}{0.36m - 0.75m}

Next Step Prepare to Evaluate

∴

n 1 = \frac{0.88 \cdot \sqrt{0.75 \cdot 0.36} - 0.88 \cdot 0.75}{0.36 - 0.75}

Next Step Evaluate

∴

n 1 = 0.519842530261068rad

Next Step Convert to Output's Unit

∴

n 1 = 29.7847829953666°

LAST Step Rounding Answer

∴

n 1 = 29.7848°

Positive Grade Angle with Deviation Angle Formula Elements

Variables

Functions

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

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

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

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

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 Positive Grade Angle

Go Positive Grade Angle Given Sight Distance

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

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 Negative Grade Angle Given Sight Distance

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

How to Evaluate Positive Grade Angle with Deviation Angle?

Positive Grade Angle with Deviation Angle evaluator uses Positive Grade Angle = (Deviation Angle*sqrt(Driver Sight Height*The Height of The Obstruction)-Deviation Angle*Driver Sight Height)/(The Height of The Obstruction-Driver Sight Height) to evaluate the Positive Grade Angle, The Positive Grade Angle with Deviation Angle formula is defined as the deviation angle multiplied by the square root of the product of the driver's eye height and the obstruction's height, minus the deviation angle times the driver's eye height, all divided by the difference between the obstruction's height and the driver's eye height. Positive Grade Angle is denoted by n₁ symbol.

How to evaluate Positive Grade Angle with Deviation Angle using this online evaluator? To use this online evaluator for Positive Grade Angle with Deviation Angle, enter Deviation Angle (N), Driver Sight Height (h₁) & The Height of The Obstruction (h₂) and hit the calculate button.

FAQs on Positive Grade Angle with Deviation Angle

What is the formula to find Positive Grade Angle with Deviation Angle?

The formula of Positive Grade Angle with Deviation Angle is expressed as Positive Grade Angle = (Deviation Angle*sqrt(Driver Sight Height*The Height of The Obstruction)-Deviation Angle*Driver Sight Height)/(The Height of The Obstruction-Driver Sight Height). Here is an example- 1706.542 = (0.88*sqrt(0.75*0.36)-0.88*0.75)/(0.36-0.75).

How to calculate Positive Grade Angle with Deviation Angle?

With Deviation Angle (N), Driver Sight Height (h₁) & The Height of The Obstruction (h₂) we can find Positive Grade Angle with Deviation Angle using the formula - Positive Grade Angle = (Deviation Angle*sqrt(Driver Sight Height*The Height of The Obstruction)-Deviation Angle*Driver Sight Height)/(The Height of The Obstruction-Driver Sight Height). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Positive Grade Angle?

Here are the different ways to Calculate Positive Grade Angle-

Positive Grade Angle=Driver Sight Height/(Sight Distance-Length of Curve/2-The Height of The Obstruction/Negative Grade Angle)

Can the Positive Grade Angle with Deviation Angle be negative?

No, the Positive Grade Angle with Deviation Angle, measured in Angle cannot be negative.

Which unit is used to measure Positive Grade Angle with Deviation Angle?

Positive Grade Angle with Deviation Angle is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Positive Grade Angle with Deviation Angle can be measured.

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Positive Grade Angle with Deviation Angle Formula

​GoPositive Grade Angle Given Sight Distance Formula

Positive Grade Angle with Deviation Angle Example

Positive Grade Angle with Deviation Angle Solution

Positive Grade Angle with Deviation Angle Formula Elements

Other Formulas to find Positive Grade Angle

Other formulas in Length of Summit Curve with Grade Angles category

How to Evaluate Positive Grade Angle with Deviation Angle?

FAQs on Positive Grade Angle with Deviation Angle

Variable Name

GoPositive Grade Angle Given Sight Distance Formula