Positive Grade Angle with Deviation Angle Calculator

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Vertical alignment

Design of Transition Curves and Setback Distances

Design of Superelevation

Marshall Mix Design

Pavement Materials

Sight Distance

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Length of Summit Curve with Grade Angles

Length of Summit Curve greater than Sight Distance

Length of Summit Curve Less than Sight Distance

Length of Valley Curve

✖Deviation Angle is the angle between the reference direction and the observed direction.ⓘ Deviation Angle [N]			+10% -10%
✖Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle.ⓘ Driver Sight Height [h₁]			+10% -10%
✖The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety.ⓘ The Height of The Obstruction [h₂]			+10% -10%

✖A positive grade angle indicates an upward slope.ⓘ Positive Grade Angle with Deviation Angle [n₁]

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Formula

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Positive Grade Angle with Deviation Angle

Formula

`"n"_{"1"} = ("N"*sqrt("h"_{"1"}*"h"_{"2"})-"N"*"h"_{"1"})/("h"_{"2"}-"h"_{"1"})`

Example

`"29.78478°"=("0.88rad"*sqrt("0.75m"*"0.36m")-"0.88rad"*"0.75m")/("0.36m"-"0.75m")`

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Positive Grade Angle with Deviation Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
n₁ = (N*sqrt(h₁*h₂)-N*h₁)/(h₂-h₁)
This formula uses 1 Functions, 4 Variables

Functions Used

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., sqrt(Number)

Variables Used

Positive Grade Angle - (Measured in Radian) - A positive grade angle indicates an upward slope.
Deviation Angle - (Measured in Radian) - Deviation Angle is the angle between the reference direction and the observed direction.
Driver Sight Height - (Measured in Meter) - Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle.
The Height of The Obstruction - (Measured in Meter) - The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety.

STEP 1: Convert Input(s) to Base Unit

Deviation Angle: 0.88 Radian --> 0.88 Radian No Conversion Required
Driver Sight Height: 0.75 Meter --> 0.75 Meter No Conversion Required
The Height of The Obstruction: 0.36 Meter --> 0.36 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n₁ = (N*sqrt(h₁*h₂)-N*h₁)/(h₂-h₁) --> (0.88*sqrt(0.75*0.36)-0.88*0.75)/(0.36-0.75)

Evaluating ... ...

n₁ = 0.519842530261068

STEP 3: Convert Result to Output's Unit

0.519842530261068 Radian -->29.7847829953666 Degree (Check conversion here)

FINAL ANSWER

29.7847829953666 ≈ 29.78478 Degree <-- Positive Grade Angle

(Calculation completed in 00.004 seconds)

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< 8 Length of Summit Curve with Grade Angles Calculators

Positive Grade Angle with Deviation Angle

Go 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)

Deviation Angle with Positive Grade Angle

Go Deviation Angle = (Positive Grade Angle*(The Height of The Obstruction-Driver Sight Height))/(sqrt(Driver Sight Height*The Height of The Obstruction)-Driver Sight Height)

Negative Grade Angle Given Sight Distance

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

Positive Grade Angle Given Sight Distance

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

Height of Obstruction Given Angle Grades

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

Length of Summit Curve Given Angle Grades

Go Length of Curve = Sight Distance*2+Driver Sight Height/Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle

Driver Sight Height given Angle Grades

Go Driver Sight Height = Length of Curve/2+Sight Distance*Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle

Sight Distance Given Angle Grades

Go Sight Distance = Length of Curve/2+Driver Sight Height/Positive Grade Angle+The Height of The Obstruction/Negative Grade Angle

Positive Grade Angle with Deviation Angle Formula

Deviation Angle

The deviation angle refers to the angle between the line of sight and the horizontal plane. In various contexts, such as road construction or sightline analysis, it represents the angular difference between the direction of observation and a reference, usually the horizontal plane or a designated line of reference.

How to Calculate Positive Grade Angle with Deviation Angle?

Positive Grade Angle with Deviation Angle calculator 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 calculate 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 calculate Positive Grade Angle with Deviation Angle using this online calculator? To use this online calculator 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. Here is how the Positive Grade Angle with Deviation Angle calculation can be explained with given input values -> 1706.542 = (0.88*sqrt(0.75*0.36)-0.88*0.75)/(0.36-0.75).

FAQ

What is Positive Grade Angle with Deviation 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 and is represented as n₁ = (N*sqrt(h₁*h₂)-N*h₁)/(h₂-h₁) or 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). Deviation Angle is the angle between the reference direction and the observed direction, Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle & The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety.

How to calculate Positive Grade Angle with Deviation 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 is calculated using 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 calculate Positive Grade Angle with Deviation Angle, you need Deviation Angle (N), Driver Sight Height (h₁) & The Height of The Obstruction (h₂). With our tool, you need to enter the respective value for Deviation Angle, Driver Sight Height & The Height of The Obstruction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Positive Grade Angle?

In this formula, Positive Grade Angle uses Deviation Angle, Driver Sight Height & The Height of The Obstruction. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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