Horizontal Distance of C.G. from Rear Axle at Rear Wheel Calculator

✖Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle.ⓘ Vehicle Wheelbase BFW [b]			+10% -10%
✖Friction Coefficient for Smooth Road BFW is the friction coefficient generated between wheels and smooth road when the brakes are applied.ⓘ Friction Coefficient for Smooth Road BFW [μ₀]			+10% -10%
✖Height of C.G. of Vehicle BFW 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 BFW [h]			+10% -10%
✖Normal Reaction at Rear Wheel BFW is the reaction force offered by the ground surface onto the rear wheel.ⓘ Normal Reaction at Rear Wheel BFW [R_R]			+10% -10%
✖Vehicle Weight BFW is the heaviness of the vehicle, generally expressed in Newtons.ⓘ Vehicle Weight BFW [W]			+10% -10%
✖Road Inclination Angle BFW of Road is the angle which the road surface is making with the horizontal.ⓘ Road Inclination Angle BFW [θ]			+10% -10%

✖Horizontal Distance of C.G. from rear Axle BFW 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 at Rear Wheel [x]

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Formula

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

Formula

`"x" = ("b"-"μ"_{"0"}*"h")*(1-"R"_{"R"}/("W"*cos("θ")))`

Example

`"1.301628m"=("2.4m"-"0.18"*"0.0075m")*(1-"6710.334N"/("15000N"*cos("12°")))`

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Download Weight Transfer during Braking Formula PDF

Horizontal Distance of C.G. from Rear Axle at Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

Horizontal Distance of C.G. from Rear Axle BFW = (Vehicle Wheelbase BFW-Friction Coefficient for Smooth Road BFW*Height of C.G. of Vehicle BFW)*(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW)))
x = (b-μ₀*h)*(1-R_R/(W*cos(θ)))
This formula uses 1 Functions, 7 Variables

Functions Used

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

Horizontal Distance of C.G. from Rear Axle BFW - (Measured in Meter) - Horizontal Distance of C.G. from rear Axle BFW is the distance of vehicle's center of gravity (C.G.) form rear axle measured along wheelbase of vehicle.
Vehicle Wheelbase BFW - (Measured in Meter) - Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle.
Friction Coefficient for Smooth Road BFW - Friction Coefficient for Smooth Road BFW is the friction coefficient generated between wheels and smooth road when the brakes are applied.
Height of C.G. of Vehicle BFW - (Measured in Meter) - Height of C.G. of Vehicle BFW is the theoretical point where the sum of all of the masses of each of its individual components effectively act.
Normal Reaction at Rear Wheel BFW - (Measured in Newton) - Normal Reaction at Rear Wheel BFW is the reaction force offered by the ground surface onto the rear wheel.
Vehicle Weight BFW - (Measured in Newton) - Vehicle Weight BFW is the heaviness of the vehicle, generally expressed in Newtons.
Road Inclination Angle BFW - (Measured in Radian) - Road Inclination Angle BFW of Road is the angle which the road surface is making with the horizontal.

STEP 1: Convert Input(s) to Base Unit

Vehicle Wheelbase BFW: 2.4 Meter --> 2.4 Meter No Conversion Required
Friction Coefficient for Smooth Road BFW: 0.18 --> No Conversion Required
Height of C.G. of Vehicle BFW: 0.0075 Meter --> 0.0075 Meter No Conversion Required
Normal Reaction at Rear Wheel BFW: 6710.334 Newton --> 6710.334 Newton No Conversion Required
Vehicle Weight BFW: 15000 Newton --> 15000 Newton No Conversion Required
Road Inclination Angle BFW: 12 Degree --> 0.20943951023928 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

x = (b-μ₀*h)*(1-R_R/(W*cos(θ))) --> (2.4-0.18*0.0075)*(1-6710.334/(15000*cos(0.20943951023928)))

Evaluating ... ...

x = 1.30162792568832

STEP 3: Convert Result to Output's Unit

1.30162792568832 Meter --> No Conversion Required

FINAL ANSWER

1.30162792568832 ≈ 1.301628 Meter <-- Horizontal Distance of C.G. from Rear Axle BFW

(Calculation completed in 00.020 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » Front Wheel Braking for Racing Cars » Effects on Rear Wheel » Horizontal Distance of C.G. from Rear Axle at 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!

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

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< 7 Effects on Rear Wheel Calculators

Slope of Road at Rear Wheel

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

Normal Reaction Force on Rear Wheel

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

Vehicle Weight at Rear Wheel

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

Height of C.G. at Rear Wheel

Go Height of C.G. of Vehicle BFW = (Vehicle Wheelbase BFW-Horizontal Distance of C.G. from Rear Axle BFW/(1-(Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW)))))/Friction Coefficient between Wheels and Ground BFW

Friction Coefficient between Wheels and Road Surface at Rear Wheel

Go Friction Coefficient between Wheels and Ground BFW = (Vehicle Wheelbase BFW-Horizontal Distance of C.G. from Rear Axle BFW/(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW))))/Height of C.G. of Vehicle BFW

Vehicle Wheel Base at Rear Wheel

Go Vehicle Wheelbase BFW = Horizontal Distance of C.G. from Rear Axle BFW/(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW)))+Friction Coefficient between Wheels and Ground BFW*Height of C.G. of Vehicle BFW

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

Go Horizontal Distance of C.G. from Rear Axle BFW = (Vehicle Wheelbase BFW-Friction Coefficient for Smooth Road BFW*Height of C.G. of Vehicle BFW)*(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW)))

Horizontal Distance of C.G. from Rear Axle at 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 Horizontal Distance of C.G. from Rear Axle at Rear Wheel?

Horizontal Distance of C.G. from Rear Axle at Rear Wheel calculator uses Horizontal Distance of C.G. from Rear Axle BFW = (Vehicle Wheelbase BFW-Friction Coefficient for Smooth Road BFW*Height of C.G. of Vehicle BFW)*(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW))) to calculate the Horizontal Distance of C.G. from Rear Axle BFW, Horizontal Distance of C.G. from Rear Axle at Rear Wheel formula is used to find the distance of vehicle's center of gravity(C.G.) from the rear axle measured along the wheelbase of the vehicle. Horizontal Distance of C.G. from Rear Axle BFW is denoted by x symbol.

How to calculate Horizontal Distance of C.G. from Rear Axle at Rear Wheel using this online calculator? To use this online calculator for Horizontal Distance of C.G. from Rear Axle at Rear Wheel, enter Vehicle Wheelbase BFW (b), Friction Coefficient for Smooth Road BFW (μ₀), Height of C.G. of Vehicle BFW (h), Normal Reaction at Rear Wheel BFW (R_R), Vehicle Weight BFW (W) & Road Inclination Angle BFW (θ) and hit the calculate button. Here is how the Horizontal Distance of C.G. from Rear Axle at Rear Wheel calculation can be explained with given input values -> 1.301628 = (2.4-0.18*0.0075)*(1-6710.334/(15000*cos(0.20943951023928))).

FAQ

What is Horizontal Distance of C.G. from Rear Axle at Rear Wheel?

Horizontal Distance of C.G. from Rear Axle at Rear Wheel formula is used to find the distance of vehicle's center of gravity(C.G.) from the rear axle measured along the wheelbase of the vehicle and is represented as x = (b-μ₀*h)*(1-R_R/(W*cos(θ))) or Horizontal Distance of C.G. from Rear Axle BFW = (Vehicle Wheelbase BFW-Friction Coefficient for Smooth Road BFW*Height of C.G. of Vehicle BFW)*(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW))). Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle, Friction Coefficient for Smooth Road BFW is the friction coefficient generated between wheels and smooth road when the brakes are applied, Height of C.G. of Vehicle BFW is the theoretical point where the sum of all of the masses of each of its individual components effectively act, Normal Reaction at Rear Wheel BFW is the reaction force offered by the ground surface onto the rear wheel, Vehicle Weight BFW is the heaviness of the vehicle, generally expressed in Newtons & Road Inclination Angle BFW of Road is the angle which the road surface is making with the horizontal.

How to calculate Horizontal Distance of C.G. from Rear Axle at Rear Wheel?

Horizontal Distance of C.G. from Rear Axle at Rear Wheel formula is used to find the distance of vehicle's center of gravity(C.G.) from the rear axle measured along the wheelbase of the vehicle is calculated using Horizontal Distance of C.G. from Rear Axle BFW = (Vehicle Wheelbase BFW-Friction Coefficient for Smooth Road BFW*Height of C.G. of Vehicle BFW)*(1-Normal Reaction at Rear Wheel BFW/(Vehicle Weight BFW*cos(Road Inclination Angle BFW))). To calculate Horizontal Distance of C.G. from Rear Axle at Rear Wheel, you need Vehicle Wheelbase BFW (b), Friction Coefficient for Smooth Road BFW (μ₀), Height of C.G. of Vehicle BFW (h), Normal Reaction at Rear Wheel BFW (R_R), Vehicle Weight BFW (W) & Road Inclination Angle BFW (θ). With our tool, you need to enter the respective value for Vehicle Wheelbase BFW, Friction Coefficient for Smooth Road BFW, Height of C.G. of Vehicle BFW, Normal Reaction at Rear Wheel BFW, Vehicle Weight BFW & Road Inclination Angle BFW 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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