Slope of Road on Rear Wheel Calculator

✖Normal Reaction at Rear Wheel BRW is the reaction force offered by the ground surface onto the rear wheel.ⓘ Normal Reaction at Rear Wheel BRW [R_R]			+10% -10%
✖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%
✖Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.ⓘ Vehicle Wheelbase BRW [b]			+10% -10%

✖Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.ⓘ Slope of Road on Rear Wheel [θ]

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Formula

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Slope of Road on Rear Wheel

Formula

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

Example

`"9.999966°"=acos("5700N"/("13000N"*("1.2m"+"0.48"*"0.007919m")/("2.7m"+"0.48"*"0.007919m")))`

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Download Rear Wheel Braking for Racing Car Formulas PDF

Slope of Road on Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
θ = acos(R_R/(W*(x+μ*h)/(b+μ*h)))
This formula uses 2 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)
acos - The inverse cosine function, is the inverse function of the cosine function. It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., acos(Number)

Variables Used

Road Inclination Angle BRW - (Measured in Radian) - Road Inclination Angle BRW is the angle which the road surface is making with the horizontal.
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.
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

Normal Reaction at Rear Wheel BRW: 5700 Newton --> 5700 Newton No Conversion Required
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
Vehicle Wheelbase BRW: 2.7 Meter --> 2.7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_R/(W*(x+μ*h)/(b+μ*h))) --> acos(5700/(13000*(1.2+0.48*0.007919)/(2.7+0.48*0.007919)))

Evaluating ... ...

θ = 0.174532338183046

STEP 3: Convert Result to Output's Unit

0.174532338183046 Radian -->9.9999663664404 Degree (Check conversion here)

FINAL ANSWER

9.9999663664404 ≈ 9.999966 Degree <-- Road Inclination Angle 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) » Slope of Road on Rear Wheel

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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

Slope of Road 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 Slope of Road on Rear Wheel?

Slope of Road on Rear Wheel calculator uses 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))) to calculate the Road Inclination Angle BRW, Slope of Road on Rear Wheel formula is used to find the inclination of the road surface with the horizontal. Road Inclination Angle BRW is denoted by θ symbol.

How to calculate Slope of Road on Rear Wheel using this online calculator? To use this online calculator for Slope of Road on Rear Wheel, enter Normal Reaction at Rear Wheel BRW (R_R), 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) & Vehicle Wheelbase BRW (b) and hit the calculate button. Here is how the Slope of Road on Rear Wheel calculation can be explained with given input values -> 572.9559 = acos(5700/(13000*(1.2+0.48*0.007919)/(2.7+0.48*0.007919))).

FAQ

What is Slope of Road on Rear Wheel?

Slope of Road on Rear Wheel formula is used to find the inclination of the road surface with the horizontal and is represented as θ = acos(R_R/(W*(x+μ*h)/(b+μ*h))) or 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))). Normal Reaction at Rear Wheel BRW is the reaction force offered by the ground surface onto the rear wheel, 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 & Vehicle Wheelbase BRW is the center distance between the front and the rear axle of the vehicle.

How to calculate Slope of Road on Rear Wheel?

Slope of Road on Rear Wheel formula is used to find the inclination of the road surface with the horizontal is calculated using 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))). To calculate Slope of Road on Rear Wheel, you need Normal Reaction at Rear Wheel BRW (R_R), 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) & Vehicle Wheelbase BRW (b). With our tool, you need to enter the respective value for 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 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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