Slope of Road from Braking with Front Wheel Reaction Calculator

✖Normal Reaction at the Front Wheel is the reaction force offered by the ground surface onto the front wheels.ⓘ Normal Reaction at the Front Wheel [R_F]			+10% -10%
✖Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons.ⓘ Vehicle Weight [W]			+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%
✖Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle.ⓘ Vehicle Wheelbase [b]			+10% -10%

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

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Formula

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Slope of Road from Braking with Front Wheel Reaction

Formula

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

Example

`"5.000027°"=acos("4625.314N"/("11000N"*("1.15m"+"0.49"*"0.065m")/("2.8m")))`

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Download Weight Transfer during Braking Formula PDF

Slope of Road from Braking with Front Wheel Reaction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inclination Angle of Road = acos(Normal Reaction at the Front Wheel/(Vehicle Weight*(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_F/(W*(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 the Front Wheel - (Measured in Newton) - Normal Reaction at the Front Wheel is the reaction force offered by the ground surface onto the front wheels.
Vehicle Weight - (Measured in Newton) - Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons.
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.
Vehicle Wheelbase - (Measured in Meter) - Vehicle Wheelbase 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 the Front Wheel: 4625.314 Newton --> 4625.314 Newton No Conversion Required
Vehicle Weight: 11000 Newton --> 11000 Newton 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
Vehicle Wheelbase: 2.8 Meter --> 2.8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

θ = acos(R_F/(W*(x+μ*h)/(b))) --> acos(4625.314/(11000*(1.15+0.49*0.065)/(2.8)))

Evaluating ... ...

θ = 0.0872669421311205

STEP 3: Convert Result to Output's Unit

0.0872669421311205 Radian -->5.00002747512653 Degree (Check conversion here)

FINAL ANSWER

5.00002747512653 ≈ 5.000027 Degree <-- Inclination Angle of Road

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » All Wheel Braking for Racing Car » Effects on Front Wheel » Slope of Road from Braking with Front 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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< 7 Effects on Front Wheel Calculators

Slope of Road from Braking with Front Wheel Reaction

Go Inclination Angle of Road = acos(Normal Reaction at the Front Wheel/(Vehicle Weight*(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 Front Wheel Brake

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

Height of C.G. from Road Surface with Front Wheel Brake

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

Vehicle Weight with All Wheel Brake on Front Wheel

Go Vehicle Weight = Normal Reaction at the Front Wheel/((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))

Horizontal Distance of C.G from Rear Axle with Front Wheel Brake

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

Wheel Base with All Wheel Braking on Front Wheel

Go Vehicle Wheelbase = Vehicle Weight*(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)/(Normal Reaction at the Front Wheel)

Front Wheel Reaction with All Wheel Braking

Go Normal Reaction at the Front Wheel = Vehicle Weight*(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 Front Wheel Reaction 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.

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 Front Wheel Reaction?

Slope of Road from Braking with Front Wheel Reaction calculator uses Inclination Angle of Road = acos(Normal Reaction at the Front Wheel/(Vehicle Weight*(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 Front 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 Front Wheel Reaction using this online calculator? To use this online calculator for Slope of Road from Braking with Front Wheel Reaction, enter Normal Reaction at the Front Wheel (R_F), Vehicle Weight (W), 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) & Vehicle Wheelbase (b) and hit the calculate button. Here is how the Slope of Road from Braking with Front Wheel Reaction calculation can be explained with given input values -> 1864.906 = acos(4625.314/(11000*(1.15+0.49*0.065)/(2.8))).

FAQ

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

Slope of Road from Braking with Front Wheel Reaction formula is used to find the inclination of the road surface with the horizontal and is represented as θ = acos(R_F/(W*(x+μ*h)/(b))) or Inclination Angle of Road = acos(Normal Reaction at the Front Wheel/(Vehicle Weight*(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 the Front Wheel is the reaction force offered by the ground surface onto the front wheels, Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons, 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 & Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle.

How to calculate Slope of Road from Braking with Front Wheel Reaction?

Slope of Road from Braking with Front 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 the Front Wheel/(Vehicle Weight*(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 Front Wheel Reaction, you need Normal Reaction at the Front Wheel (R_F), Vehicle Weight (W), 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) & Vehicle Wheelbase (b). With our tool, you need to enter the respective value for Normal Reaction at the Front Wheel, Vehicle Weight, 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 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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