Deviation Angle with Positive Grade 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

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

✖Deviation Angle is the angle between the reference direction and the observed direction.ⓘ Deviation Angle with Positive Grade Angle [N]

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Formula

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Deviation Angle with Positive Grade Angle

Formula

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

Example

`"1.329538rad"=("45°"*("0.36m"-"0.75m"))/(sqrt("0.75m"*"0.36m")-"0.75m")`

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Deviation Angle with Positive Grade Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
N = (n₁*(h₂-h₁))/(sqrt(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

Deviation Angle - (Measured in Radian) - Deviation Angle is the angle between the reference direction and the observed direction.
Positive Grade Angle - (Measured in Radian) - A positive grade angle indicates an upward slope.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Positive Grade Angle: 45 Degree --> 0.785398163397301 Radian (Check conversion here)
The Height of The Obstruction: 0.36 Meter --> 0.36 Meter No Conversion Required
Driver Sight Height: 0.75 Meter --> 0.75 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N = (n₁*(h₂-h₁))/(sqrt(h₁*h₂)-h₁) --> (0.785398163397301*(0.36-0.75))/(sqrt(0.75*0.36)-0.75)

Evaluating ... ...

N = 1.32953797266746

STEP 3: Convert Result to Output's Unit

1.32953797266746 Radian --> No Conversion Required

FINAL ANSWER

1.32953797266746 ≈ 1.329538 Radian <-- Deviation 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

Deviation Angle with Positive Grade 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 Deviation Angle with Positive Grade Angle?

Deviation Angle with Positive Grade Angle calculator uses 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) to calculate the Deviation Angle, The Deviation Angle with Positive Grade Angle formula is defined as the positive grade angle multiplied by the difference between the height of the obstruction and the driver's eye height, divided by the square root of the product of the driver's eye height and the height of the obstruction, minus the driver's eye height. Deviation Angle is denoted by N symbol.

How to calculate Deviation Angle with Positive Grade Angle using this online calculator? To use this online calculator for Deviation Angle with Positive Grade Angle, enter Positive Grade Angle (n₁), The Height of The Obstruction (h₂) & Driver Sight Height (h₁) and hit the calculate button. Here is how the Deviation Angle with Positive Grade Angle calculation can be explained with given input values -> 1.329538 = (0.785398163397301*(0.36-0.75))/(sqrt(0.75*0.36)-0.75).

FAQ

What is Deviation Angle with Positive Grade Angle?

The Deviation Angle with Positive Grade Angle formula is defined as the positive grade angle multiplied by the difference between the height of the obstruction and the driver's eye height, divided by the square root of the product of the driver's eye height and the height of the obstruction, minus the driver's eye height and is represented as N = (n₁*(h₂-h₁))/(sqrt(h₁*h₂)-h₁) or 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). A positive grade angle indicates an upward slope, The Height of The Obstruction refers to its vertical dimension, blocking a line of sight or path, often in transportation, construction or safety & Driver Sight Height refers to the vertical distance between the driver's eye level and the road surface while seated in a vehicle.

How to calculate Deviation Angle with Positive Grade Angle?

The Deviation Angle with Positive Grade Angle formula is defined as the positive grade angle multiplied by the difference between the height of the obstruction and the driver's eye height, divided by the square root of the product of the driver's eye height and the height of the obstruction, minus the driver's eye height is calculated using 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). To calculate Deviation Angle with Positive Grade Angle, you need Positive Grade Angle (n₁), The Height of The Obstruction (h₂) & Driver Sight Height (h₁). With our tool, you need to enter the respective value for Positive Grade Angle, The Height of The Obstruction & Driver Sight Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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