FormulaDen.com

Physics Chemistry Math Chemical Engineering Civil Electrical Electronics Electronics and Instrumentation Materials Science Mechanical Production Engineering Financial Health

Slope of Road using Retardation on Front Wheel Formula

Fx Copy

LaTeX Copy

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

θ = a \cos (\frac{a}{[g] \cdot \frac{μ \cdot x}{b - μ \cdot h}})

θ - Road Inclination Angle BFW?a - Braking Retardation BFW?μ - Friction Coefficient Between Wheels And Ground BFW?x - Horizontal Distance of C.G. From Rear Axle BFW?b - Vehicle Wheelbase BFW?h - Height of C.G of Vehicle BFW?[g] - Gravitational acceleration on Earth?

Slope of Road using Retardation on Front Wheel Example

With values

With units

Only example

Here is how the Slope of Road using Retardation on Front Wheel equation looks like with Values.

Here is how the Slope of Road using Retardation on Front Wheel equation looks like with Units.

Here is how the Slope of Road using Retardation on Front Wheel equation looks like.

12 = a \cos (\frac{3.0191}{9.8066 \cdot \frac{0.58 \cdot 1.3}{2.4 - 0.58 \cdot 0.0075}})

12° = a \cos (\frac{3.0191m/s²}{9.8066m/s² \cdot \frac{0.58 \cdot 1.3m}{2.4m - 0.58 \cdot 0.0075m}})

12 = a \cos (\frac{3.0191}{9.8066 \cdot \frac{0.58 \cdot 1.3}{2.4 - 0.58 \cdot 0.0075}})

Tip: Use pencil ( Pencil

) icon above to edit Input Values and Units.

Calculate

Recalculate

Solution

Copy

Reset

You are here -

Home » Category

Physics » Category

Mechanical » Category

Automobile » fx Slope of Road using Retardation on Front Wheel

Slope of Road using Retardation on Front Wheel Solution

Follow our step by step solution on how to calculate Slope of Road using Retardation on Front Wheel?

FIRST Step Consider the formula

θ = a \cos (\frac{a}{[g] \cdot \frac{μ \cdot x}{b - μ \cdot h}})

Next Step Substitute values of Variables

∴

θ = a \cos (\frac{3.0191m/s²}{[g] \cdot \frac{0.58 \cdot 1.3m}{2.4m - 0.58 \cdot 0.0075m}})

Next Step Substitute values of Constants

∴

θ = a \cos (\frac{3.0191m/s²}{9.8066m/s² \cdot \frac{0.58 \cdot 1.3m}{2.4m - 0.58 \cdot 0.0075m}})

Next Step Prepare to Evaluate

∴

θ = a \cos (\frac{3.0191}{9.8066 \cdot \frac{0.58 \cdot 1.3}{2.4 - 0.58 \cdot 0.0075}})

Next Step Evaluate

∴

θ = 0.209439595696502rad

Next Step Convert to Output's Unit

∴

θ = 12.0000048963382°

LAST Step Rounding Answer

∴

θ = 12°

Slope of Road using Retardation on Front Wheel Formula Elements

Variables

Constants

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.

Formulas to find Road Inclination Angle BFW

Braking Retardation BFW

Braking Retardation BFW is the negative acceleration of the vehicle which reduces its speed.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Braking Retardation BFW

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.

Formulas to find Friction Coefficient Between Wheels And Ground BFW

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.

Formulas to find Horizontal Distance of C.G. From Rear Axle BFW

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.

Formulas to find Vehicle Wheelbase BFW

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.

Formulas to find Height of C.G of Vehicle BFW

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

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 due to Retardation category

Go Braking Retardation on Front Wheel

a = [g] \cdot \frac{μ \cdot x \cdot \cos (θ)}{b - μ \cdot h}

Go Horizontal Distance of C.G. from Rear Axle using Retardation on Front Wheel

x = \frac{a}{[g] \cdot \frac{μ \cdot \cos (θ)}{b - μ \cdot h}}

Go Vehicle Wheel Base using Retardation on Front Wheel

b = [g] \cdot \frac{μ \cdot x \cdot \cos (θ)}{a} + μ \cdot h

Go Height of C.G. using Retardation on Front Wheel

h = \frac{b - [g] \cdot (μ \cdot x \cdot \frac{\cos (θ)}{a})}{μ}

How to Evaluate Slope of Road using Retardation on Front Wheel?

Slope of Road using Retardation on Front Wheel evaluator uses Road Inclination Angle BFW = acos(Braking Retardation BFW/([g]*(Friction Coefficient Between Wheels And Ground BFW*Horizontal Distance of C.G. From Rear Axle 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 using Retardation on Front 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 using Retardation on Front Wheel using this online evaluator? To use this online evaluator for Slope of Road using Retardation on Front Wheel, enter Braking Retardation BFW (a), Friction Coefficient Between Wheels And Ground BFW (μ), Horizontal Distance of C.G. From Rear Axle BFW (x), Vehicle Wheelbase BFW (b) & Height of C.G of Vehicle BFW (h) and hit the calculate button.

FAQs on Slope of Road using Retardation on Front Wheel

What is the formula to find Slope of Road using Retardation on Front Wheel?

The formula of Slope of Road using Retardation on Front Wheel is expressed as Road Inclination Angle BFW = acos(Braking Retardation BFW/([g]*(Friction Coefficient Between Wheels And Ground BFW*Horizontal Distance of C.G. From Rear Axle BFW)/(Vehicle Wheelbase BFW-Friction Coefficient Between Wheels And Ground BFW*Height of C.G of Vehicle BFW))). Here is an example- 4095.767 = acos(3.019069/([g]*(0.58*1.3)/(2.4-0.58*0.0075))).

How to calculate Slope of Road using Retardation on Front Wheel?

With Braking Retardation BFW (a), Friction Coefficient Between Wheels And Ground BFW (μ), Horizontal Distance of C.G. From Rear Axle BFW (x), Vehicle Wheelbase BFW (b) & Height of C.G of Vehicle BFW (h) we can find Slope of Road using Retardation on Front Wheel using the formula - Road Inclination Angle BFW = acos(Braking Retardation BFW/([g]*(Friction Coefficient Between Wheels And Ground BFW*Horizontal Distance of C.G. From Rear Axle BFW)/(Vehicle Wheelbase BFW-Friction Coefficient Between Wheels And Ground BFW*Height of C.G of Vehicle BFW))). This formula also uses Gravitational acceleration on Earth constant(s) and , Cosine (cos), Inverse Cosine (acos) function(s).

Can the Slope of Road using Retardation on Front Wheel be negative?

No, the Slope of Road using Retardation on Front Wheel, measured in Angle cannot be negative.

Which unit is used to measure Slope of Road using Retardation on Front Wheel?

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

Let Others Know

✖

Facebook

Twitter

Copied!

Slope of Road using Retardation on Front Wheel Formula

Slope of Road using Retardation on Front Wheel Example

Slope of Road using Retardation on Front Wheel Solution

Slope of Road using Retardation on Front Wheel Formula Elements

Other formulas in Effects due to Retardation category

How to Evaluate Slope of Road using Retardation on Front Wheel?

FAQs on Slope of Road using Retardation on Front Wheel

Variable Name