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Slope of Road at Rear Wheel Formula

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Road Inclination Angle BFW 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 - μ \cdot h}})

θ - Road Inclination Angle BFW?R_r - Normal Reaction at Rear Wheel BFW?W - Vehicle Weight BFW?b - Vehicle Wheelbase BFW?x - Horizontal Distance of C.G. From Rear Axle BFW?μ - Friction Coefficient Between Wheels And Ground BFW?h - Height of C.G of Vehicle BFW?

Slope of Road at Rear Wheel Example

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Here is how the Slope of Road at Rear Wheel equation looks like with Values.

Here is how the Slope of Road at Rear Wheel equation looks like with Units.

Here is how the Slope of Road at Rear Wheel equation looks like.

12 = a \cos (\frac{6710.334}{15000 \cdot \frac{2.4 - 1.3 - 0.58 \cdot 0.0075}{2.4 - 0.58 \cdot 0.0075}})

12° = a \cos (\frac{6710.334N}{15000N \cdot \frac{2.4m - 1.3m - 0.58 \cdot 0.0075m}{2.4m - 0.58 \cdot 0.0075m}})

12 = a \cos (\frac{6710.334}{15000 \cdot \frac{2.4 - 1.3 - 0.58 \cdot 0.0075}{2.4 - 0.58 \cdot 0.0075}})

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Home » Physics » Mechanical » Automobile » Slope of Road at Rear Wheel

Slope of Road at Rear Wheel Solution

Follow our step by step solution on how to calculate Slope of Road at Rear Wheel?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{6710.334N}{15000N \cdot \frac{2.4m - 1.3m - 0.58 \cdot 0.0075m}{2.4m - 0.58 \cdot 0.0075m}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{6710.334}{15000 \cdot \frac{2.4 - 1.3 - 0.58 \cdot 0.0075}{2.4 - 0.58 \cdot 0.0075}})

Next Step Evaluate

∴

θ = 0.209439403144593rad

Next Step Convert to Output's Unit

∴

θ = 11.9999938639264°

LAST Step Rounding Answer

∴

θ = 12°

Slope of Road at Rear Wheel Formula Elements

Variables

Functions

Road Inclination Angle BFW

Road Inclination Angle BFW 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.

Normal Reaction at Rear Wheel BFW

Normal Reaction at Rear Wheel BFW 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.

Vehicle Weight BFW

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

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Vehicle Wheelbase BFW

Vehicle Wheelbase BFW 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.

Horizontal Distance of C.G. From Rear Axle BFW

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.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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.

Symbol: μ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Height of C.G of Vehicle BFW

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.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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)

Credits

Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

Peri Krishna Karthik has created this Formula and 200+ more formulas!

Verified by

national institute of technology hamirpur (NITH ), Hamirpur, Himachal Pradesh

sanjay shiva has verified this Formula and 100+ more formulas!

Other formulas in Effects on Rear Wheel category

Go Friction Coefficient between Wheels and Road Surface at Rear Wheel

μ = \frac{b - \frac{x}{1 - \frac{R r}{W \cdot \cos (θ)}}}{h}

Go Normal Reaction Force on Rear Wheel

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

How to Evaluate Slope of Road at Rear Wheel?

Slope of Road at Rear Wheel evaluator 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 evaluate 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 evaluate Slope of Road at Rear Wheel using this online evaluator? To use this online evaluator 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.

FAQs on Slope of Road at Rear Wheel

What is the formula to find Slope of Road at Rear Wheel?

The formula of Slope of Road at Rear Wheel is expressed as 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))). Here is an example- 687.549 = acos(6710.334/(15000*(2.4-1.3-0.58*0.0075)/(2.4-0.58*0.0075))).

How to calculate Slope of Road at Rear Wheel?

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

Can the Slope of Road at Rear Wheel be negative?

No, the Slope of Road at Rear Wheel, measured in Angle cannot be negative.

Which unit is used to measure Slope of Road at Rear Wheel?

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

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Slope of Road at Rear Wheel Formula

Slope of Road at Rear Wheel Example

Slope of Road at Rear Wheel Solution

Slope of Road at Rear Wheel Formula Elements

Credits

Other formulas in Effects on Rear Wheel category

How to Evaluate Slope of Road at Rear Wheel?

FAQs on Slope of Road at Rear Wheel

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