Wheel Base of Vehicle using Retardation on Rear Wheel Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
b = ((a/[g]+sin(θ))*μ*h+μ*x*cos(θ))/(μ*cos(θ)-(a/[g]+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
Vehicle Wheelbase BRW - (Measured in Meter) - Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.
Braking Retardation BRW - (Measured in Meter per Square Second) - Braking Retardation BRW is the negative acceleration of the vehicle which reduces its speed.
Road Inclination Angle BRW - (Measured in Radian) - Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.
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.
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.
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.
STEP 1: Convert Input(s) to Base Unit
Braking Retardation BRW: 0.86885 Meter per Square Second --> 0.86885 Meter per Square Second No Conversion Required
Road Inclination Angle BRW: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Friction Coefficient between Wheels and Ground BRW: 0.48 --> No Conversion Required
Height of C.G. of Vehicle BRW: 0.007919 Meter --> 0.007919 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle BRW: 1.2 Meter --> 1.2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
b = ((a/[g]+sin(θ))*μ*h+μ*x*cos(θ))/(μ*cos(θ)-(a/[g]+sin(θ))) --> ((0.86885/[g]+sin(0.1745329251994))*0.48*0.007919+0.48*1.2*cos(0.1745329251994))/(0.48*cos(0.1745329251994)-(0.86885/[g]+sin(0.1745329251994)))
Evaluating ... ...
b = 2.70000020636146
STEP 3: Convert Result to Output's Unit
2.70000020636146 Meter --> No Conversion Required
FINAL ANSWER
2.70000020636146 2.7 Meter <-- Vehicle Wheelbase BRW
(Calculation completed in 00.004 seconds)

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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

Wheel Base of Vehicle using Retardation on Rear Wheel Formula

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

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 Wheel Base of Vehicle using Retardation on Rear Wheel?

Wheel Base of Vehicle using Retardation on Rear Wheel calculator uses 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))) to calculate the Vehicle Wheelbase BRW, Wheel Base of Vehicle using Retardation on Rear Wheel formula is used to find the center distance between the front and the rear axle of the vehicle. Vehicle Wheelbase BRW is denoted by b symbol.

How to calculate Wheel Base of Vehicle using Retardation on Rear Wheel using this online calculator? To use this online calculator for Wheel Base of Vehicle using Retardation on Rear Wheel, enter Braking Retardation BRW (a), Road Inclination Angle BRW (θ), Friction Coefficient between Wheels and Ground BRW (μ), Height of C.G. of Vehicle BRW (h) & Horizontal Distance of C.G. from Rear Axle BRW (x) and hit the calculate button. Here is how the Wheel Base of Vehicle using Retardation on Rear Wheel calculation can be explained with given input values -> 3.837431 = ((0.86885/[g]+sin(0.1745329251994))*0.48*0.007919+0.48*1.2*cos(0.1745329251994))/(0.48*cos(0.1745329251994)-(0.86885/[g]+sin(0.1745329251994))).

FAQ

What is Wheel Base of Vehicle using Retardation on Rear Wheel?
Wheel Base of Vehicle using Retardation on Rear Wheel formula is used to find the center distance between the front and the rear axle of the vehicle and is represented as b = ((a/[g]+sin(θ))*μ*h+μ*x*cos(θ))/(μ*cos(θ)-(a/[g]+sin(θ))) or 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))). Braking Retardation BRW is the negative acceleration of the vehicle which reduces its speed, Road Inclination Angle BRW is the angle which the road surface is making with the horizontal, Friction Coefficient between Wheels and Ground BRW is friction coefficient that is generated between wheels and ground when rear brakes are applied, 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 & 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.
How to calculate Wheel Base of Vehicle using Retardation on Rear Wheel?
Wheel Base of Vehicle using Retardation on Rear Wheel formula is used to find the center distance between the front and the rear axle of the vehicle is calculated using 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))). To calculate Wheel Base of Vehicle using Retardation on Rear Wheel, you need Braking Retardation BRW (a), Road Inclination Angle BRW (θ), Friction Coefficient between Wheels and Ground BRW (μ), Height of C.G. of Vehicle BRW (h) & Horizontal Distance of C.G. from Rear Axle BRW (x). With our tool, you need to enter the respective value for Braking Retardation BRW, Road Inclination Angle BRW, Friction Coefficient between Wheels and Ground BRW, Height of C.G. of Vehicle BRW & Horizontal Distance of C.G. from Rear Axle BRW and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Vehicle Wheelbase BRW?
In this formula, Vehicle Wheelbase BRW uses Braking Retardation BRW, Road Inclination Angle BRW, Friction Coefficient between Wheels and Ground BRW, Height of C.G. of Vehicle BRW & Horizontal Distance of C.G. from Rear Axle BRW. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • 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
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