Slope of Road from Braking with Rear Wheel Reaction Calculator

✖Normal Reaction at Rear Wheel is the reaction force offered by the ground surface onto the rear wheel.ⓘ Normal Reaction at Rear Wheel [R_R]			+10% -10%
✖Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons.ⓘ Vehicle Weight [W]			+10% -10%
✖Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle.ⓘ Vehicle Wheelbase [b]			+10% -10%
✖Horizontal Distance of C.G. from Rear Axle 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 [x]			+10% -10%
✖Friction Coefficient between Wheels and Ground is the friction coefficient which is generated between wheels and ground when the brakes are applied.ⓘ Friction Coefficient Between Wheels and Ground [μ]			+10% -10%
✖Height of Center of Gravity (C.G.) of Vehicle is the theoretical point where the sum of all of the masses of each of its individual components effectively act.ⓘ Height of Center of Gravity (C.G.) of Vehicle [h]			+10% -10%

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

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Slope of Road from Braking with Rear Wheel Reaction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inclination Angle of Road = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle-Friction Coefficient Between Wheels and Ground*Height of Center of Gravity (C.G.) of Vehicle)/(Vehicle Wheelbase)))
θ = acos(R_R/(W*(b-x-μ*h)/(b)))
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

Inclination Angle of Road - (Measured in Radian) - Inclination Angle of Road is the angle which the road surface is making with the horizontal.
Normal Reaction at Rear Wheel - (Measured in Newton) - Normal Reaction at Rear Wheel is the reaction force offered by the ground surface onto the rear wheel.
Vehicle Weight - (Measured in Newton) - Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons.
Vehicle Wheelbase - (Measured in Meter) - Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle.
Horizontal Distance of C.G. from Rear Axle - (Measured in Meter) - Horizontal Distance of C.G. from Rear Axle 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 - Friction Coefficient between Wheels and Ground is the friction coefficient which is generated between wheels and ground when the brakes are applied.
Height of Center of Gravity (C.G.) of Vehicle - (Measured in Meter) - Height of Center of Gravity (C.G.) of Vehicle 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: 6332.83 Newton --> 6332.83 Newton No Conversion Required
Vehicle Weight: 11000 Newton --> 11000 Newton No Conversion Required
Vehicle Wheelbase: 2.8 Meter --> 2.8 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle: 1.15 Meter --> 1.15 Meter No Conversion Required
Friction Coefficient Between Wheels and Ground: 0.49 --> No Conversion Required
Height of Center of Gravity (C.G.) of Vehicle: 0.065 Meter --> 0.065 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_R/(W*(b-x-μ*h)/(b))) --> acos(6332.83/(11000*(2.8-1.15-0.49*0.065)/(2.8)))

Evaluating ... ...

θ = 0.0872619231137437

STEP 3: Convert Result to Output's Unit

0.0872619231137437 Radian -->4.99973990661354 Degree (Check conversion here)

FINAL ANSWER

4.99973990661354 ≈ 4.99974 Degree <-- Inclination Angle of Road

(Calculation completed in 00.333 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » All Wheel Braking for Racing Car » Mechanical » Effects on Rear Wheel » Slope of Road from Braking with Rear Wheel Reaction

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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!

Verified by sanjay shiva

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

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< Effects on Rear Wheel Calculators

Slope of Road from Braking with Rear Wheel Reaction

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

Friction Coefficient between Wheel and Road Surface with Rear Wheel Brake

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

Vehicle Weight with All Wheel Brake on Rear Wheel

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

Rear Wheel Reaction with All Wheel Braking

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

Slope of Road from Braking with Rear Wheel Reaction 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.

How the braking distribution occurs 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 from Braking with Rear Wheel Reaction?

Slope of Road from Braking with Rear Wheel Reaction calculator uses Inclination Angle of Road = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle-Friction Coefficient Between Wheels and Ground*Height of Center of Gravity (C.G.) of Vehicle)/(Vehicle Wheelbase))) to calculate the Inclination Angle of Road, Slope of Road from Braking with Rear Wheel Reaction formula is used to find the inclination of the road surface with the horizontal. Inclination Angle of Road is denoted by θ symbol.

How to calculate Slope of Road from Braking with Rear Wheel Reaction using this online calculator? To use this online calculator for Slope of Road from Braking with Rear Wheel Reaction, enter Normal Reaction at Rear Wheel (R_R), Vehicle Weight (W), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient Between Wheels and Ground (μ) & Height of Center of Gravity (C.G.) of Vehicle (h) and hit the calculate button. Here is how the Slope of Road from Braking with Rear Wheel Reaction calculation can be explained with given input values -> 286.464 = acos(6332.83/(11000*(2.8-1.15-0.49*0.065)/(2.8))).

FAQ

What is Slope of Road from Braking with Rear Wheel Reaction?

Slope of Road from Braking with Rear Wheel Reaction 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))) or Inclination Angle of Road = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle-Friction Coefficient Between Wheels and Ground*Height of Center of Gravity (C.G.) of Vehicle)/(Vehicle Wheelbase))). Normal Reaction at Rear Wheel is the reaction force offered by the ground surface onto the rear wheel, Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons, Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle, Horizontal Distance of C.G. from Rear Axle 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 is the friction coefficient which is generated between wheels and ground when the brakes are applied & Height of Center of Gravity (C.G.) of Vehicle 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 from Braking with Rear Wheel Reaction?

Slope of Road from Braking with Rear Wheel Reaction formula is used to find the inclination of the road surface with the horizontal is calculated using Inclination Angle of Road = acos(Normal Reaction at Rear Wheel/(Vehicle Weight*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle-Friction Coefficient Between Wheels and Ground*Height of Center of Gravity (C.G.) of Vehicle)/(Vehicle Wheelbase))). To calculate Slope of Road from Braking with Rear Wheel Reaction, you need Normal Reaction at Rear Wheel (R_R), Vehicle Weight (W), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Friction Coefficient Between Wheels and Ground (μ) & Height of Center of Gravity (C.G.) of Vehicle (h). With our tool, you need to enter the respective value for Normal Reaction at Rear Wheel, Vehicle Weight, Vehicle Wheelbase, Horizontal Distance of C.G. from Rear Axle, Friction Coefficient Between Wheels and Ground & Height of Center of Gravity (C.G.) of Vehicle 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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