Normal Reaction Force at Rear Wheel Calculator

✖Vehicle Weight BRW is the heaviness of the vehicle, generally expressed in Newtons.ⓘ Vehicle Weight BRW [W]			+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%
✖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%
✖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%
✖Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.ⓘ Road Inclination Angle BRW [θ]			+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%

✖Normal Reaction at Rear Wheel BRW is the reaction force offered by the ground surface onto the rear wheel.ⓘ Normal Reaction Force at Rear Wheel [R_R]

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Formula

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Normal Reaction Force at Rear Wheel

Formula

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

Example

`"5699.999N"="13000N"*("1.2m"+"0.48"*"0.007919m")*cos("10°")/("2.7m"+"0.48"*"0.007919m")`

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Download Rear Wheel Braking for Racing Car Formulas PDF PDF Image

Normal Reaction Force at Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
R_R = W*(x+μ*h)*cos(θ)/(b+μ*h)
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

Normal Reaction at Rear Wheel BRW - (Measured in Newton) - Normal Reaction at Rear Wheel BRW is the reaction force offered by the ground surface onto the rear wheel.
Vehicle Weight BRW - (Measured in Newton) - Vehicle Weight BRW is the heaviness of the vehicle, generally expressed in Newtons.
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.
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.
Road Inclination Angle BRW - (Measured in Radian) - Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.
Vehicle Wheelbase BRW - (Measured in Meter) - Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.

STEP 1: Convert Input(s) to Base Unit

Vehicle Weight BRW: 13000 Newton --> 13000 Newton No Conversion Required
Horizontal Distance of C.G. from Rear Axle BRW: 1.2 Meter --> 1.2 Meter No Conversion Required
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
Road Inclination Angle BRW: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Vehicle Wheelbase BRW: 2.7 Meter --> 2.7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_R = W*(x+μ*h)*cos(θ)/(b+μ*h) --> 13000*(1.2+0.48*0.007919)*cos(0.1745329251994)/(2.7+0.48*0.007919)

Evaluating ... ...

R_R = 5699.99941001216

STEP 3: Convert Result to Output's Unit

5699.99941001216 Newton --> No Conversion Required

FINAL ANSWER

5699.99941001216 ≈ 5699.999 Newton <-- Normal Reaction at Rear Wheel BRW

(Calculation completed in 00.020 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) » Normal Reaction Force at Rear Wheel

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Created by Peri Krishna Karthik

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

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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

Normal Reaction Force 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 Normal Reaction Force at Rear Wheel?

Normal Reaction Force at Rear Wheel calculator uses 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) to calculate the Normal Reaction at Rear Wheel BRW, Normal Reaction Force at Rear Wheel formula is used to find the reaction force offered by the road surface onto the front wheel. Normal Reaction at Rear Wheel BRW is denoted by R_R symbol.

How to calculate Normal Reaction Force at Rear Wheel using this online calculator? To use this online calculator for Normal Reaction Force at Rear Wheel, enter Vehicle Weight BRW (W), Horizontal Distance of C.G. from Rear Axle BRW (x), Friction Coefficient between Wheels and Ground BRW (μ), Height of C.G. of Vehicle BRW (h), Road Inclination Angle BRW (θ) & Vehicle Wheelbase BRW (b) and hit the calculate button. Here is how the Normal Reaction Force at Rear Wheel calculation can be explained with given input values -> 5765.906 = 13000*(1.2+0.48*0.007919)*cos(0.1745329251994)/(2.7+0.48*0.007919).

FAQ

What is Normal Reaction Force at Rear Wheel?

Normal Reaction Force at Rear Wheel formula is used to find the reaction force offered by the road surface onto the front wheel and is represented as R_R = W*(x+μ*h)*cos(θ)/(b+μ*h) or 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). Vehicle Weight BRW is the heaviness of the vehicle, generally expressed in Newtons, 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, 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, Road Inclination Angle BRW is the angle which the road surface is making with the horizontal & Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.

How to calculate Normal Reaction Force at Rear Wheel?

Normal Reaction Force at Rear Wheel formula is used to find the reaction force offered by the road surface onto the front wheel is calculated using 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). To calculate Normal Reaction Force at Rear Wheel, you need Vehicle Weight BRW (W), Horizontal Distance of C.G. from Rear Axle BRW (x), Friction Coefficient between Wheels and Ground BRW (μ), Height of C.G. of Vehicle BRW (h), Road Inclination Angle BRW (θ) & Vehicle Wheelbase BRW (b). With our tool, you need to enter the respective value for 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, Road Inclination Angle BRW & Vehicle Wheelbase 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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