Friction Coefficient between Wheel and Road Surface with Retardation Calculator

✖Retardation Produced by Braking is the negative acceleration of the vehicle which reduces its speed.ⓘ Retardation Produced by Braking [a]			+10% -10%
✖Inclination Angle of Road is the angle which the road surface is making with the horizontal.ⓘ Inclination Angle of Road [θ]			+10% -10%

✖Friction Coefficient between Wheels and Ground is the friction coefficient which is generated between wheels and ground when the brakes are applied.ⓘ Friction Coefficient between Wheel and Road Surface with Retardation [μ]

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Formula

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Friction Coefficient between Wheel and Road Surface with Retardation

Formula

`"μ" = ("a"/"[g]"+sin("θ"))/cos("θ")`

Example

`"0.489768"=("3.93m/s²"/"[g]"+sin("5°"))/cos("5°")`

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Download Weight Transfer during Braking Formula PDF

Friction Coefficient between Wheel and Road Surface with Retardation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road)
μ = (a/[g]+sin(θ))/cos(θ)
This formula uses 1 Constants, 2 Functions, 3 Variables

Constants Used

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

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

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.
Retardation Produced by Braking - (Measured in Meter per Square Second) - Retardation Produced by Braking is the negative acceleration of the vehicle which reduces its speed.
Inclination Angle of Road - (Measured in Radian) - Inclination Angle of Road is the angle which the road surface is making with the horizontal.

STEP 1: Convert Input(s) to Base Unit

Retardation Produced by Braking: 3.93 Meter per Square Second --> 3.93 Meter per Square Second No Conversion Required
Inclination Angle of Road: 5 Degree --> 0.0872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

μ = (a/[g]+sin(θ))/cos(θ) --> (3.93/[g]+sin(0.0872664625997001))/cos(0.0872664625997001)

Evaluating ... ...

μ = 0.489767929283873

STEP 3: Convert Result to Output's Unit

0.489767929283873 --> No Conversion Required

FINAL ANSWER

0.489767929283873 ≈ 0.489768 <-- Friction Coefficient between Wheels and Ground

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » All Wheel Braking for Racing Car » Vehicle Braking Dynamics » Friction Coefficient between Wheel and Road Surface with Retardation

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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< 11 Vehicle Braking Dynamics Calculators

Braking Torque of Leading Shoe

Go Leading Shoe Braking Torque = (Leading Shoe Actuating Force*Distance of Actuating Force from Horizontal*Friction Coefficient between Drum and Shoe*Effective Radius of Normal Force)/(Force of Trailing Shoe Distance from Horizontal+(Friction Coefficient between Drum and Shoe*Effective Radius of Normal Force))

Braking Torque of Trailing Shoe

Go Trailing Shoe Braking Torque = (Trailing Shoe Actuating Force*Force of Trailing Shoe Distance from Horizontal*Friction Coefficient for Smooth Road*Effective Radius of Normal Force)/(Force of Trailing Shoe Distance from Horizontal-Friction Coefficient for Smooth Road*Effective Radius of Normal Force)

Mean Lining Pressure of Brake Lining

Go Mean Lining Pressure = (180/(8*pi))*(Brake Drum Braking Force*Effective Wheel Radius)/(Friction Coefficient between Drum and Shoe*Brake Drum Radius^2*Brake Lining Width*Angle between Linings of Brake Shoes)

Gradient Descend Brake Drum Force

Go Brake Drum Braking Force = Vehicle Weight/Acceleration due to Gravity*Vehicle Deceleration+Vehicle Weight*sin(Angle of Inclination of Plane to Horizontal)

Friction Coefficient between Wheel and Road Surface with Retardation

Go Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road)

All Wheel Braking Retardation

Go Retardation Produced by Braking = [g]*(Friction Coefficient between Wheels and Ground*cos(Inclination Angle of Road)-sin(Inclination Angle of Road))

Braking Torque of Disc Brake

Go Disc Brake Braking Torque = 2*Line Pressure*Area of One Piston per Caliper*Friction Coefficient of Pad Material*Mean Radius of Caliper Unit to Disc Axis*Number of Caliper Units

Normal Force at Brake Shoe Contact Point

Go Normal Force between Shoe and Drum = (Brake Drum Braking Force*Effective Wheel Radius)/(8*Friction Coefficient between Drum and Shoe*Angle between Linings of Brake Shoes)

Ground Speed of Track Laying Vehicle

Go Ground Speed of Track Laying Vehicle = (Engine RPM*Driving Sprocket Circumference)/(16660*Overall Gear Reduction)

Braking Force on Brake Drum on Level Road

Go Brake Drum Braking Force = Vehicle Weight/Acceleration due to Gravity*Vehicle Deceleration

Wheel Heat Generation Rate

Go Heat Generated per Second at Each Wheel = (Brake Drum Braking Force*Vehicle Speed)/4

Friction Coefficient between Wheel and Road Surface with Retardation Formula

Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road)
μ = (a/[g]+sin(θ))/cos(θ)

How weight transfer occurs during braking?

The inertial force acts at the centre of gravity of the vehicle, while the retarding force due to the application of brakes acts at the road surface. These two forms an overturning couple. This overturning couple increases the perpendicular force between the front wheels and ground by an amount, while the perpendicular force between rear wheels and ground is decreased by an equal amount. Some of the vehicle weight is thus transferred from the rear to the front axle.

How does the braking distribution occurs among front and rear brakes?

It is observed that in vehicles either the distribution of weight over the two axles is equal, or the front axle carries more weight, the braking effect has to be more at the front wheels for efficient braking. It is seen that in general for achieving maximum efficiency, about 75% of the total braking effect should be on front wheels. However, in such case the trouble would arise while travelling over wet road. where hight braking effect at the front would cause skidding of front wheels, because of decrease of weight transfer. In practice, about 60% of the braking effort is applied on the front wheels.

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

Friction Coefficient between Wheel and Road Surface with Retardation calculator uses Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road) to calculate 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 calculate Friction Coefficient between Wheel and Road Surface with Retardation using this online calculator? To use this online calculator 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. Here is how the Friction Coefficient between Wheel and Road Surface with Retardation calculation can be explained with given input values -> 0.238983 = (3.93/[g]+sin(0.0872664625997001))/cos(0.0872664625997001).

FAQ

What is Friction Coefficient between Wheel and Road Surface with Retardation?

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 and is represented as μ = (a/[g]+sin(θ))/cos(θ) or Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road). Retardation Produced by Braking is the negative acceleration of the vehicle which reduces its speed & Inclination Angle of Road is the angle which the road surface is making with the horizontal.

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

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 is calculated using Friction Coefficient between Wheels and Ground = (Retardation Produced by Braking/[g]+sin(Inclination Angle of Road))/cos(Inclination Angle of Road). To calculate Friction Coefficient between Wheel and Road Surface with Retardation, you need Retardation Produced by Braking (a) & Inclination Angle of Road (θ). With our tool, you need to enter the respective value for Retardation Produced by Braking & Inclination Angle of Road 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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