Braking Retardation on Rear Wheel Calculator

✖Friction Coefficient between Wheels and Ground BRW is friction coefficient that is generated between wheels and ground when rear brakes are applied.ⓘ Friction Coefficient between Wheels and Ground BRW [μ]			+10% -10%
✖Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.ⓘ Vehicle Wheelbase BRW [b]			+10% -10%
✖Horizontal Distance of C.G. from rear Axle BRW is the distance of vehicle's center of gravity (C.G.) form rear axle measured along wheelbase of vehicle.ⓘ Horizontal Distance of C.G. from Rear Axle BRW [x]			+10% -10%
✖Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.ⓘ Road Inclination Angle BRW [θ]			+10% -10%
✖Height of C.G. of Vehicle BRW is the theoretical point where the sum of all of the masses of each of its individual components effectively act.ⓘ Height of C.G. of Vehicle BRW [h]			+10% -10%

✖Braking Retardation BRW is the negative acceleration of the vehicle which reduces its speed.ⓘ Braking Retardation on Rear Wheel [a]

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Formula

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Braking Retardation on Rear Wheel

Formula

`"a" = "[g]"*(("μ"*("b"-"x")*cos("θ"))/("b"+"μ"*"h")-sin("θ"))`

Example

`"0.86885m/s²"="[g]"*(("0.48"*("2.7m"-"1.2m")*cos("10°"))/("2.7m"+"0.48"*"0.007919m")-sin("10°"))`

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Braking Retardation on Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Braking Retardation BRW = [g]*((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)-sin(Road Inclination Angle BRW))
a = [g]*((μ*(b-x)*cos(θ))/(b+μ*h)-sin(θ))
This formula uses 1 Constants, 2 Functions, 6 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

Braking Retardation BRW - (Measured in Meter per Square Second) - Braking Retardation BRW is the negative acceleration of the vehicle which reduces its speed.
Friction Coefficient between Wheels and Ground BRW - Friction Coefficient between Wheels and Ground BRW is friction coefficient that is generated between wheels and ground when rear brakes are applied.
Vehicle Wheelbase BRW - (Measured in Meter) - Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.
Horizontal Distance of C.G. from Rear Axle BRW - (Measured in Meter) - Horizontal Distance of C.G. from rear Axle BRW is the distance of vehicle's center of gravity (C.G.) form rear axle measured along wheelbase of vehicle.
Road Inclination Angle BRW - (Measured in Radian) - Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.
Height of C.G. of Vehicle BRW - (Measured in Meter) - Height of C.G. of Vehicle BRW is the theoretical point where the sum of all of the masses of each of its individual components effectively act.

STEP 1: Convert Input(s) to Base Unit

Friction Coefficient between Wheels and Ground BRW: 0.48 --> No Conversion Required
Vehicle Wheelbase BRW: 2.7 Meter --> 2.7 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle BRW: 1.2 Meter --> 1.2 Meter No Conversion Required
Road Inclination Angle BRW: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Height of C.G. of Vehicle BRW: 0.007919 Meter --> 0.007919 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = [g]*((μ*(b-x)*cos(θ))/(b+μ*h)-sin(θ)) --> [g]*((0.48*(2.7-1.2)*cos(0.1745329251994))/(2.7+0.48*0.007919)-sin(0.1745329251994))

Evaluating ... ...

a = 0.868849842475834

STEP 3: Convert Result to Output's Unit

0.868849842475834 Meter per Square Second --> No Conversion Required

FINAL ANSWER

0.868849842475834 ≈ 0.86885 Meter per Square Second <-- Braking Retardation BRW

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » Rear Wheel Braking for Racing Car » Effects on Rear Wheel (RW) » Braking Retardation on Rear Wheel

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Created by Peri Krishna Karthik

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

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

Verified by sanjay shiva

national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

sanjay shiva has verified this Calculator and 100+ more calculators!

< 12 Effects on Rear Wheel (RW) Calculators

Wheel Base of Vehicle using Retardation on Rear Wheel

Go Vehicle Wheelbase BRW = ((Braking Retardation BRW/[g]+sin(Road Inclination Angle BRW))*Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW+Friction Coefficient between Wheels and Ground BRW*Horizontal Distance of C.G. from Rear Axle BRW*cos(Road Inclination Angle BRW))/(Friction Coefficient between Wheels and Ground BRW*cos(Road Inclination Angle BRW)-(Braking Retardation BRW/[g]+sin(Road Inclination Angle BRW)))

Friction Coefficient using Retardation on Rear Wheel

Go Friction Coefficient between Wheels and Ground BRW = ((Braking Retardation BRW/[g]+sin(Road Inclination Angle BRW))*Vehicle Wheelbase BRW)/((Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW)-((Braking Retardation BRW/[g]+sin(Road Inclination Angle BRW))*Height of C.G. of Vehicle BRW))

Height of C.G. using Retardation on Rear Wheel

Go Height of C.G. of Vehicle BRW = ((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/((Braking Retardation BRW/[g])+sin(Road Inclination Angle BRW))-Vehicle Wheelbase BRW)/Friction Coefficient between Wheels and Ground BRW

Friction Coefficient between Wheel and Road Surface on Rear Wheel

Go Friction Coefficient between Wheels and Ground BRW = (Normal Reaction at Rear Wheel BRW*Vehicle Wheelbase BRW-Vehicle Weight BRW*Horizontal Distance of C.G. from Rear Axle BRW*cos(Road Inclination Angle BRW))/(Height of C.G. of Vehicle BRW*(Vehicle Weight BRW*cos(Road Inclination Angle BRW)-Normal Reaction at Rear Wheel BRW))

Height of C.G. from Road Surface on Rear Wheel

Go Height of C.G. of Vehicle BRW = (Normal Reaction at Rear Wheel BRW*Vehicle Wheelbase BRW-Vehicle Weight BRW*Horizontal Distance of C.G. from Rear Axle BRW*cos(Road Inclination Angle BRW))/(Friction Coefficient between Wheels and Ground BRW*(Vehicle Weight BRW*cos(Road Inclination Angle BRW)-Normal Reaction at Rear Wheel BRW))

Horizontal Distance of C.G. using Retardation on Rear Wheel

Go Horizontal Distance of C.G. from Rear Axle BRW = Vehicle Wheelbase BRW-((Braking Retardation BRW/[g]+sin(Road Inclination Angle BRW))*(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)/(Friction Coefficient between Wheels and Ground BRW*cos(Road Inclination Angle BRW)))

Braking Retardation on Rear Wheel

Go Braking Retardation BRW = [g]*((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)-sin(Road Inclination Angle BRW))

Slope of Road on Rear Wheel

Go Road Inclination Angle BRW = acos(Normal Reaction at Rear Wheel BRW/(Vehicle Weight BRW*(Horizontal Distance of C.G. from Rear Axle BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)))

Weight of Vehicle on Rear Wheel

Go Vehicle Weight BRW = Normal Reaction at Rear Wheel BRW/((Horizontal Distance of C.G. from Rear Axle BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)*cos(Road Inclination Angle BRW)/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW))

Horizontal Distance of C.G. from Rear Axle on Rear Wheel

Go Horizontal Distance of C.G. from Rear Axle BRW = Normal Reaction at Rear Wheel BRW*(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)/(Vehicle Weight BRW*cos(Road Inclination Angle BRW))-Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW

Normal Reaction Force at Rear Wheel

Go Normal Reaction at Rear Wheel BRW = Vehicle Weight BRW*(Horizontal Distance of C.G. from Rear Axle BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)*cos(Road Inclination Angle BRW)/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)

Wheel Base on Rear Wheel

Go Vehicle Wheelbase BRW = (Vehicle Weight BRW*(Horizontal Distance of C.G. from Rear Axle BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)*cos(Road Inclination Angle BRW)/Normal Reaction at Rear Wheel BRW)-Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW

Braking Retardation on Rear Wheel Formula

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.

Braking distribution 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 Braking Retardation on Rear Wheel?

Braking Retardation on Rear Wheel calculator uses Braking Retardation BRW = [g]*((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)-sin(Road Inclination Angle BRW)) to calculate the Braking Retardation BRW, Braking Retardation on Rear Wheel is used to find the negative acceleration of the vehicle which reduces its speed. Braking Retardation BRW is denoted by a symbol.

How to calculate Braking Retardation on Rear Wheel using this online calculator? To use this online calculator for Braking Retardation on Rear Wheel, enter Friction Coefficient between Wheels and Ground BRW (μ), Vehicle Wheelbase BRW (b), Horizontal Distance of C.G. from Rear Axle BRW (x), Road Inclination Angle BRW (θ) & Height of C.G. of Vehicle BRW (h) and hit the calculate button. Here is how the Braking Retardation on Rear Wheel calculation can be explained with given input values -> 0.86885 = [g]*((0.48*(2.7-1.2)*cos(0.1745329251994))/(2.7+0.48*0.007919)-sin(0.1745329251994)).

FAQ

What is Braking Retardation on Rear Wheel?

Braking Retardation on Rear Wheel is used to find the negative acceleration of the vehicle which reduces its speed and is represented as a = [g]*((μ*(b-x)*cos(θ))/(b+μ*h)-sin(θ)) or Braking Retardation BRW = [g]*((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)-sin(Road Inclination Angle BRW)). Friction Coefficient between Wheels and Ground BRW is friction coefficient that is generated between wheels and ground when rear brakes are applied, Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle, Horizontal Distance of C.G. from rear Axle BRW is the distance of vehicle's center of gravity (C.G.) form rear axle measured along wheelbase of vehicle, Road Inclination Angle BRW is the angle which the road surface is making with the horizontal & Height of C.G. of Vehicle BRW is the theoretical point where the sum of all of the masses of each of its individual components effectively act.

How to calculate Braking Retardation on Rear Wheel?

Braking Retardation on Rear Wheel is used to find the negative acceleration of the vehicle which reduces its speed is calculated using Braking Retardation BRW = [g]*((Friction Coefficient between Wheels and Ground BRW*(Vehicle Wheelbase BRW-Horizontal Distance of C.G. from Rear Axle BRW)*cos(Road Inclination Angle BRW))/(Vehicle Wheelbase BRW+Friction Coefficient between Wheels and Ground BRW*Height of C.G. of Vehicle BRW)-sin(Road Inclination Angle BRW)). To calculate Braking Retardation on Rear Wheel, you need Friction Coefficient between Wheels and Ground BRW (μ), Vehicle Wheelbase BRW (b), Horizontal Distance of C.G. from Rear Axle BRW (x), Road Inclination Angle BRW (θ) & Height of C.G. of Vehicle BRW (h). With our tool, you need to enter the respective value for Friction Coefficient between Wheels and Ground BRW, Vehicle Wheelbase BRW, Horizontal Distance of C.G. from Rear Axle BRW, Road Inclination Angle BRW & Height of C.G. of Vehicle BRW 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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