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Friction Coefficient between Wheel and Road Surface with Retardation Formula

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Friction Coefficient between Wheels and Ground is the friction coefficient which is generated between wheels and ground when the brakes are applied. Check FAQs

μ = \frac{\frac{a}{[g]} + \sin (θ)}{\cos (θ)}

μ - Friction Coefficient Between Wheels and Ground?a - Retardation Produced by Braking?θ - Inclination Angle of Road?[g] - Gravitational acceleration on Earth?

Friction Coefficient between Wheel and Road Surface with Retardation Example

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Here is how the Friction Coefficient between Wheel and Road Surface with Retardation equation looks like with Values.

Here is how the Friction Coefficient between Wheel and Road Surface with Retardation equation looks like with Units.

Here is how the Friction Coefficient between Wheel and Road Surface with Retardation equation looks like.

0.4898 = \frac{\frac{3.93}{9.8066} + \sin (5)}{\cos (5)}

0.4898 = \frac{\frac{3.93m/s²}{9.8066m/s²} + \sin (5°)}{\cos (5°)}

0.4898 = \frac{\frac{3.93}{9.8066} + \sin (5)}{\cos (5)}

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Friction Coefficient between Wheel and Road Surface with Retardation Solution

Follow our step by step solution on how to calculate Friction Coefficient between Wheel and Road Surface with Retardation?

FIRST Step Consider the formula

μ = \frac{\frac{a}{[g]} + \sin (θ)}{\cos (θ)}

Next Step Substitute values of Variables

∴

μ = \frac{\frac{3.93m/s²}{[g]} + \sin (5°)}{\cos (5°)}

Next Step Substitute values of Constants

∴

μ = \frac{\frac{3.93m/s²}{9.8066m/s²} + \sin (5°)}{\cos (5°)}

Next Step Convert Units

∴

μ = \frac{\frac{3.93m/s²}{9.8066m/s²} + \sin (0.0873rad)}{\cos (0.0873rad)}

Next Step Prepare to Evaluate

∴

μ = \frac{\frac{3.93}{9.8066} + \sin (0.0873)}{\cos (0.0873)}

Next Step Evaluate

∴

μ = 0.489767929283873

LAST Step Rounding Answer

∴

μ = 0.4898

Friction Coefficient between Wheel and Road Surface with Retardation Formula Elements

Variables

Constants

Functions

Friction Coefficient Between Wheels and Ground

Friction Coefficient between Wheels and Ground is the friction coefficient which is generated between wheels and ground when the brakes are applied.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Friction Coefficient Between Wheels and Ground

Retardation Produced by Braking

Retardation Produced by Braking is the negative acceleration of the vehicle which reduces its speed.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Retardation Produced by Braking

Inclination Angle of Road

Inclination Angle of Road is the angle which the road surface is making with the horizontal.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Inclination Angle of Road

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Vehicle Braking Dynamics category

Go Braking Force on Brake Drum on Level Road

F = \frac{W}{g} \cdot f

Go Gradient Descend Brake Drum Force

F = \frac{W}{g} \cdot f + W \cdot \sin (α inc)

Go Braking Torque of Leading Shoe

T l = \frac{W l \cdot m \cdot μf \cdot k}{n t + (μf \cdot k)}

Go Braking Torque of Trailing Shoe

T t = \frac{W t \cdot n t \cdot μ 0 \cdot k}{n t - μ 0 \cdot k}

How to Evaluate Friction Coefficient between Wheel and Road Surface with Retardation?

Friction Coefficient between Wheel and Road Surface with Retardation evaluator uses Friction Coefficient Between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road) to evaluate the Friction Coefficient Between Wheels and Ground, Friction Coefficient between Wheel and Road Surface with Retardation formula is used to find the measure of the amount of friction existing between ground and wheel. Friction Coefficient Between Wheels and Ground is denoted by μ symbol.

How to evaluate Friction Coefficient between Wheel and Road Surface with Retardation using this online evaluator? To use this online evaluator for Friction Coefficient between Wheel and Road Surface with Retardation, enter Retardation Produced by Braking (a) & Inclination Angle of Road (θ) and hit the calculate button.

FAQs on Friction Coefficient between Wheel and Road Surface with Retardation

What is the formula to find Friction Coefficient between Wheel and Road Surface with Retardation?

The formula of Friction Coefficient between Wheel and Road Surface with Retardation is expressed as Friction Coefficient Between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road). Here is an example- 0.489768 = (3.93/[g]+sin(0.0872664625997001))/cos(0.0872664625997001).

How to calculate Friction Coefficient between Wheel and Road Surface with Retardation?

With Retardation Produced by Braking (a) & Inclination Angle of Road (θ) we can find Friction Coefficient between Wheel and Road Surface with Retardation using the formula - Friction Coefficient Between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road). This formula also uses Gravitational acceleration on Earth constant(s) and , Sine (sin), Cosine (cos) function(s).

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