Height of C.G. 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%
✖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 BFW [x]			+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%
✖Friction Coefficient between Wheels and Ground BFW is the friction coefficient which is generated between wheels and ground when the brakes are applied.ⓘ Friction Coefficient between Wheels and Ground BFW [μ]			+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. at Rear Wheel [h]

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Formula

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Height of C.G. at Rear Wheel

Formula

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

Example

`"0.0075m"=("2.4m"-"1.3m"/(1-("6710.334N"/("15000N"*cos("12°")))))/"0.58"`

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Height of C.G. at Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
h = (b-x/(1-(R_R/(W*cos(θ)))))/μ
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

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.
Vehicle Wheelbase BFW - (Measured in Meter) - Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle.
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.
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.
Friction Coefficient between Wheels and Ground BFW - Friction Coefficient between Wheels and Ground BFW is the friction coefficient which is generated between wheels and ground when the brakes are applied.

STEP 1: Convert Input(s) to Base Unit

Vehicle Wheelbase BFW: 2.4 Meter --> 2.4 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle BFW: 1.3 Meter --> 1.3 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)
Friction Coefficient between Wheels and Ground BFW: 0.58 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (b-x/(1-(R_R/(W*cos(θ)))))/μ --> (2.4-1.3/(1-(6710.334/(15000*cos(0.20943951023928)))))/0.58

Evaluating ... ...

h = 0.00749992075603395

STEP 3: Convert Result to Output's Unit

0.00749992075603395 Meter --> No Conversion Required

FINAL ANSWER

0.00749992075603395 ≈ 0.0075 Meter <-- Height of C.G. of Vehicle BFW

(Calculation completed in 00.004 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 » Height of C.G. 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)))

Height of C.G. 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 Height of C.G. at Rear Wheel?

Height of C.G. at Rear Wheel calculator uses 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 to calculate the Height of C.G. of Vehicle BFW, Height of C.G. at Rear Wheel formula is used to find the height of 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 is denoted by h symbol.

How to calculate Height of C.G. at Rear Wheel using this online calculator? To use this online calculator for Height of C.G. at Rear Wheel, enter Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. from Rear Axle BFW (x), Normal Reaction at Rear Wheel BFW (R_R), Vehicle Weight BFW (W), Road Inclination Angle BFW (θ) & Friction Coefficient between Wheels and Ground BFW (μ) and hit the calculate button. Here is how the Height of C.G. at Rear Wheel calculation can be explained with given input values -> 0.325225 = (2.4-1.3/(1-(6710.334/(15000*cos(0.20943951023928)))))/0.58.

FAQ

What is Height of C.G. at Rear Wheel?

Height of C.G. at Rear Wheel formula is used to find the height of the theoretical point where the sum of all of the masses of each of its individual components effectively act and is represented as h = (b-x/(1-(R_R/(W*cos(θ)))))/μ or 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. Vehicle Wheelbase BFW is the center distance between the front and the rear axle of the vehicle, 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, 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 & Friction Coefficient between Wheels and Ground BFW is the friction coefficient which is generated between wheels and ground when the brakes are applied.

How to calculate Height of C.G. at Rear Wheel?

Height of C.G. at Rear Wheel formula is used to find the height of the theoretical point where the sum of all of the masses of each of its individual components effectively act is calculated using 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. To calculate Height of C.G. at Rear Wheel, you need Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. from Rear Axle BFW (x), Normal Reaction at Rear Wheel BFW (R_R), Vehicle Weight BFW (W), Road Inclination Angle BFW (θ) & Friction Coefficient between Wheels and Ground BFW (μ). With our tool, you need to enter the respective value for Vehicle Wheelbase BFW, Horizontal Distance of C.G. from Rear Axle BFW, Normal Reaction at Rear Wheel BFW, Vehicle Weight BFW, Road Inclination Angle BFW & Friction Coefficient between Wheels and Ground 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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