Angle of banking Calculator

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General Principal to Dynamics

Engineering Mechanics

Friction

Properties of Planes and Solids

Types of Motion

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Principal Parameters

Laws of Motion

✖Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.ⓘ Velocity [v]			+10% -10%
✖Radius of circular path is measure of radius of curved road path.ⓘ Radius of Circular Path [r]			+10% -10%

✖Angle of Banking is the angle of inclination of the road surface.ⓘ Angle of banking [θ_b]

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Formula

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Angle of banking

Formula

`"θ"_{"b"} = atan(("v"^2)/("[g]"*"r"))`

Example

`"74.76197°"=atan((("60m/s")^2)/("[g]"*"100m"))`

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Angle of banking Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path))
θ_b = atan((v^2)/([g]*r))
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., 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., atan(Number)

Variables Used

Angle of Banking - (Measured in Radian) - Angle of Banking is the angle of inclination of the road surface.
Velocity - (Measured in Meter per Second) - Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time.
Radius of Circular Path - (Measured in Meter) - Radius of circular path is measure of radius of curved road path.

STEP 1: Convert Input(s) to Base Unit

Velocity: 60 Meter per Second --> 60 Meter per Second No Conversion Required
Radius of Circular Path: 100 Meter --> 100 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ_b = atan((v^2)/([g]*r)) --> atan((60^2)/([g]*100))

Evaluating ... ...

θ_b = 1.30484245359045

STEP 3: Convert Result to Output's Unit

1.30484245359045 Radian -->74.7619655202416 Degree (Check conversion here)

FINAL ANSWER

74.7619655202416 ≈ 74.76197 Degree <-- Angle of Banking

(Calculation completed in 00.004 seconds)

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Created by Chilvera Bhanu Teja

Institute of Aeronautical Engineering (IARE), Hyderabad

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< 5 Principal Parameters Calculators

Maximum velocity to avoid overturning of vehicle along level circular path

Go Velocity = sqrt(([g]*Radius of Circular Path*Distance between Center Lines of two Wheels)/(2*Gauge of Track))

Force of attraction between two masses separated by distance

Go Gravitational Force of Attraction = ([G.]*Mass of First Particle*Mass of Second Particle)/(Distance between two Masses^2)

Maximum velocity to avoid skidding away of vehicle along level circular path

Go Velocity = sqrt(Coefficient of Friction between Wheels and Ground*[g]*Radius of Circular Path)

Superelevation in railways

Go Superelevation = (Gauge of Track*(Velocity^2))/([g]*Radius of Circular Path)

Angle of banking

Go Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path))

Angle of banking Formula

Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path))
θ_b = atan((v^2)/([g]*r))

What is banking of road?

In case of roadways, the outer edge is raised with respect to the inner edge of the road surface. The amount, by which the outer edge is raised is known as cant or superelevation. The process of providing superelevation is known as banking of the road.

How to Calculate Angle of banking?

Angle of banking calculator uses Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path)) to calculate the Angle of Banking, Angle of banking formula is defined as the inverse tan of ratio of the square of velocity of body to the product of acceleration due to gravity and radius of circular path. Angle of Banking is denoted by θ_b symbol.

How to calculate Angle of banking using this online calculator? To use this online calculator for Angle of banking, enter Velocity (v) & Radius of Circular Path (r) and hit the calculate button. Here is how the Angle of banking calculation can be explained with given input values -> 4283.545 = atan((60^2)/([g]*100)).

FAQ

What is Angle of banking?

Angle of banking formula is defined as the inverse tan of ratio of the square of velocity of body to the product of acceleration due to gravity and radius of circular path and is represented as θ_b = atan((v^2)/([g]*r)) or Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path)). Velocity is a vector quantity (it has both magnitude and direction) and is the rate of change of the position of an object with respect to time & Radius of circular path is measure of radius of curved road path.

How to calculate Angle of banking?

Angle of banking formula is defined as the inverse tan of ratio of the square of velocity of body to the product of acceleration due to gravity and radius of circular path is calculated using Angle of Banking = atan((Velocity^2)/([g]*Radius of Circular Path)). To calculate Angle of banking, you need Velocity (v) & Radius of Circular Path (r). With our tool, you need to enter the respective value for Velocity & Radius of Circular Path 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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