Slope of Road at Rear Wheel Calculator

✖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%
✖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%
✖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 of Vehicle BFW [h]			+10% -10%

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

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Slope of Road at Rear Wheel Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
θ = acos(R_r/(W*(b-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 BFW - (Measured in Radian) - Road Inclination Angle BFW of Road is the angle which the road surface is making with the horizontal.
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.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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
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
Friction Coefficient Between Wheels And Ground BFW: 0.58 --> No Conversion Required
Height of C.G of Vehicle BFW: 0.0075 Meter --> 0.0075 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_r/(W*(b-x-μ*h)/(b-μ*h))) --> acos(6710.334/(15000*(2.4-1.3-0.58*0.0075)/(2.4-0.58*0.0075)))

Evaluating ... ...

θ = 0.209439403144593

STEP 3: Convert Result to Output's Unit

0.209439403144593 Radian -->11.9999938639264 Degree (Check conversion here)

FINAL ANSWER

11.9999938639264 ≈ 11.99999 Degree <-- Road Inclination Angle BFW

(Calculation completed in 00.008 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » Front Wheel Braking for Racing Cars » Mechanical » Effects on Rear Wheel » Slope of Road 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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< Effects on Rear Wheel Calculators

Normal Reaction Force on Rear Wheel

LaTeX 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

LaTeX 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))

Friction Coefficient between Wheels and Road Surface at Rear Wheel

LaTeX 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

LaTeX 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

Slope of Road at Rear Wheel Formula

LaTeX Go

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 at Rear Wheel?

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

How to calculate Slope of Road at Rear Wheel using this online calculator? To use this online calculator for Slope of Road at Rear Wheel, enter Normal Reaction at Rear Wheel BFW (R_r), Vehicle Weight BFW (W), Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. From Rear Axle BFW (x), Friction Coefficient Between Wheels And Ground BFW (μ) & Height of C.G of Vehicle BFW (h) and hit the calculate button. Here is how the Slope of Road at Rear Wheel calculation can be explained with given input values -> 687.549 = acos(6710.334/(15000*(2.4-1.3-0.58*0.0075)/(2.4-0.58*0.0075))).

FAQ

What is Slope of Road at Rear Wheel?

Slope of Road at 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*(b-x-μ*h)/(b-μ*h))) or 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 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, 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, Friction Coefficient Between Wheels And Ground BFW is the friction coefficient which is generated between wheels and ground 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.

How to calculate Slope of Road at Rear Wheel?

Slope of Road at Rear Wheel formula is used to find the inclination of the road surface with the horizontal is calculated using 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))). To calculate Slope of Road at Rear Wheel, you need Normal Reaction at Rear Wheel BFW (R_r), Vehicle Weight BFW (W), Vehicle Wheelbase BFW (b), Horizontal Distance of C.G. From Rear Axle BFW (x), Friction Coefficient Between Wheels And Ground BFW (μ) & Height of C.G of Vehicle BFW (h). With our tool, you need to enter the respective value for 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 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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