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Slope of Road from Braking with Rear Wheel Reaction Formula

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Inclination Angle of Road is the angle which the road surface is making with the horizontal. Check FAQs

θ = a \cos (\frac{R R}{W \cdot \frac{b - x - μ \cdot h}{b}})

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

Slope of Road from Braking with Rear Wheel Reaction Example

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Here is how the Slope of Road from Braking with Rear Wheel Reaction equation looks like with Values.

Here is how the Slope of Road from Braking with Rear Wheel Reaction equation looks like with Units.

Here is how the Slope of Road from Braking with Rear Wheel Reaction equation looks like.

4.9997 = a \cos (\frac{6332.83}{11000 \cdot \frac{2.8 - 1.15 - 0.49 \cdot 0.065}{2.8}})

4.9997° = a \cos (\frac{6332.83N}{11000N \cdot \frac{2.8m - 1.15m - 0.49 \cdot 0.065m}{2.8m}})

4.9997 = a \cos (\frac{6332.83}{11000 \cdot \frac{2.8 - 1.15 - 0.49 \cdot 0.065}{2.8}})

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Slope of Road from Braking with Rear Wheel Reaction Solution

Follow our step by step solution on how to calculate Slope of Road from Braking with Rear Wheel Reaction?

FIRST Step Consider the formula

θ = a \cos (\frac{R R}{W \cdot \frac{b - x - μ \cdot h}{b}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{6332.83N}{11000N \cdot \frac{2.8m - 1.15m - 0.49 \cdot 0.065m}{2.8m}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{6332.83}{11000 \cdot \frac{2.8 - 1.15 - 0.49 \cdot 0.065}{2.8}})

Next Step Evaluate

∴

θ = 0.0872619231137437rad

Next Step Convert to Output's Unit

∴

θ = 4.99973990661354°

LAST Step Rounding Answer

∴

θ = 4.9997°

Slope of Road from Braking with Rear Wheel Reaction Formula Elements

Variables

Functions

Inclination Angle of Road

Inclination Angle of Road is the angle which the road surface is making with the horizontal.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Inclination Angle of Road

Normal Reaction at Rear Wheel

Normal Reaction at Rear Wheel is the reaction force offered by the ground surface onto the rear wheel.

Symbol: R_R

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Normal Reaction at Rear Wheel

Vehicle Weight

Vehicle Weight is the heaviness of the vehicle, generally expressed in Newtons.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Vehicle Weight

Vehicle Wheelbase

Vehicle Wheelbase is the center distance between the front and the rear axle of the vehicle.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Vehicle Wheelbase

Horizontal Distance of C.G. from Rear Axle

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.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance of C.G. from Rear Axle

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.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Friction Coefficient Between Wheels and Ground

Height of Center of Gravity (C.G.) of Vehicle

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.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Center of Gravity (C.G.) of Vehicle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: acos(Number)

Other formulas in Effects on Rear Wheel category

Go Friction Coefficient between Wheel and Road Surface with Rear Wheel Brake

μ = \frac{b - x - \frac{R R \cdot b}{W \cdot \cos (θ)}}{h}

Go Rear Wheel Reaction with All Wheel Braking

R R = W \cdot (b - x - μ \cdot h) \cdot \frac{\cos (θ)}{b}

How to Evaluate Slope of Road from Braking with Rear Wheel Reaction?

Slope of Road from Braking with Rear Wheel Reaction evaluator 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 evaluate 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 evaluate Slope of Road from Braking with Rear Wheel Reaction using this online evaluator? To use this online evaluator 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.

FAQs on Slope of Road from Braking with Rear Wheel Reaction

What is the formula to find Slope of Road from Braking with Rear Wheel Reaction?

The formula of Slope of Road from Braking with Rear Wheel Reaction is expressed as 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))). Here is an example- 286.464 = acos(6332.83/(11000*(2.8-1.15-0.49*0.065)/(2.8))).

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

With 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) we can find Slope of Road from Braking with Rear Wheel Reaction using the formula - 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))). This formula also uses Cosine (cos), Inverse Cosine (acos) function(s).

Can the Slope of Road from Braking with Rear Wheel Reaction be negative?

No, the Slope of Road from Braking with Rear Wheel Reaction, measured in Angle cannot be negative.

Which unit is used to measure Slope of Road from Braking with Rear Wheel Reaction?

Slope of Road from Braking with Rear Wheel Reaction is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Slope of Road from Braking with Rear Wheel Reaction can be measured.

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Slope of Road from Braking with Rear Wheel Reaction Formula

Slope of Road from Braking with Rear Wheel Reaction Example

Slope of Road from Braking with Rear Wheel Reaction Solution

Slope of Road from Braking with Rear Wheel Reaction Formula Elements

Other formulas in Effects on Rear Wheel category

How to Evaluate Slope of Road from Braking with Rear Wheel Reaction?

FAQs on Slope of Road from Braking with Rear Wheel Reaction

Variable Name