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Height of C.G. using Retardation on Rear Wheel Formula

GoHeight of C.G. from Road Surface on Rear Wheel Formula

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Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a racing car during rear wheel braking. Check FAQs

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

h - Height of C.G. of Vehicle?μ_RW - Friction Coefficient on Rear Wheel?b - Vehicle Wheelbase?x - Horizontal Distance of C.G. from Rear Axle?θ - Road Inclination Angle?a - Braking Retardation?[g] - Gravitational acceleration on Earth?

Height of C.G. using Retardation on Rear Wheel Example

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Here is how the Height of C.G. using Retardation on Rear Wheel equation looks like with Values.

Here is how the Height of C.G. using Retardation on Rear Wheel equation looks like with Units.

Here is how the Height of C.G. using Retardation on Rear Wheel equation looks like.

0.0079 = \frac{\frac{0.48 \cdot (2.7 - 1.2) \cdot \cos (10)}{(\frac{0.8688}{9.8066}) + \sin (10)} - 2.7}{0.48}

0.0079m = \frac{\frac{0.48 \cdot (2.7m - 1.2m) \cdot \cos (10°)}{(\frac{0.8688m/s²}{9.8066m/s²}) + \sin (10°)} - 2.7m}{0.48}

0.0079 = \frac{\frac{0.48 \cdot (2.7 - 1.2) \cdot \cos (10)}{(\frac{0.8688}{9.8066}) + \sin (10)} - 2.7}{0.48}

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Height of C.G. using Retardation on Rear Wheel Solution

Follow our step by step solution on how to calculate Height of C.G. using Retardation on Rear Wheel?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \frac{\frac{0.48 \cdot (2.7m - 1.2m) \cdot \cos (10°)}{(\frac{0.8688m/s²}{[g]}) + \sin (10°)} - 2.7m}{0.48}

Next Step Substitute values of Constants

∴

h = \frac{\frac{0.48 \cdot (2.7m - 1.2m) \cdot \cos (10°)}{(\frac{0.8688m/s²}{9.8066m/s²}) + \sin (10°)} - 2.7m}{0.48}

Next Step Convert Units

∴

h = \frac{\frac{0.48 \cdot (2.7m - 1.2m) \cdot \cos (0.1745rad)}{(\frac{0.8688m/s²}{9.8066m/s²}) + \sin (0.1745rad)} - 2.7m}{0.48}

Next Step Prepare to Evaluate

∴

h = \frac{\frac{0.48 \cdot (2.7 - 1.2) \cdot \cos (0.1745)}{(\frac{0.8688}{9.8066}) + \sin (0.1745)} - 2.7}{0.48}

Next Step Evaluate

∴

h = 0.00791865497482558m

LAST Step Rounding Answer

∴

h = 0.0079m

Height of C.G. using Retardation on Rear Wheel Formula Elements

Variables

Constants

Functions

Height of C.G. of Vehicle

Height of C.G. of Vehicle is the vertical distance of the center of gravity from the ground level of a racing car during rear wheel braking.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of C.G. of Vehicle

Friction Coefficient on Rear Wheel

Friction Coefficient on Rear Wheel is a measure of the resistance to motion between the rear wheel and the road surface during racing car braking.

Symbol: μ_RW

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Friction Coefficient on Rear Wheel

Vehicle Wheelbase

Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.

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 from the center of gravity to the rear axle, affecting the racing car's stability during rear wheel braking.

Symbol: x

Measurement: LengthUnit: m

Note: Value should be greater than 0.

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

Road Inclination Angle

Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.

Symbol: θ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Road Inclination Angle

Braking Retardation

Braking Retardation is the rate of decrease in speed of a racing car when the rear wheel brake is applied to slow down or stop the vehicle.

Symbol: a

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Braking Retardation

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

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

Syntax: cos(Angle)

Other Formulas to find Height of C.G. of Vehicle

Go Height of C.G. from Road Surface on Rear Wheel

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

Other formulas in Effects on Rear Wheel (RW) category

Go Friction Coefficient between Wheel and Road Surface on Rear Wheel

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

Go Friction Coefficient using Retardation on Rear Wheel

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

Go Normal Reaction Force at Rear Wheel

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

Go Weight of Vehicle on Rear Wheel

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

How to Evaluate Height of C.G. using Retardation on Rear Wheel?

Height of C.G. using Retardation on Rear Wheel evaluator uses Height of C.G. of Vehicle = ((Friction Coefficient on Rear Wheel*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle))/((Braking Retardation/[g])+sin(Road Inclination Angle))-Vehicle Wheelbase)/Friction Coefficient on Rear Wheel to evaluate the Height of C.G. of Vehicle, Height of C.G. using Retardation on Rear Wheel formula is defined as a method to determine the height of the center of gravity of a vehicle when the rear wheel is braked, taking into account the frictional coefficient, distance, angle of inclination, and acceleration due to gravity. Height of C.G. of Vehicle is denoted by h symbol.

How to evaluate Height of C.G. using Retardation on Rear Wheel using this online evaluator? To use this online evaluator for Height of C.G. using Retardation on Rear Wheel, enter Friction Coefficient on Rear Wheel (μ_RW), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Road Inclination Angle (θ) & Braking Retardation (a) and hit the calculate button.

FAQs on Height of C.G. using Retardation on Rear Wheel

What is the formula to find Height of C.G. using Retardation on Rear Wheel?

The formula of Height of C.G. using Retardation on Rear Wheel is expressed as Height of C.G. of Vehicle = ((Friction Coefficient on Rear Wheel*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle))/((Braking Retardation/[g])+sin(Road Inclination Angle))-Vehicle Wheelbase)/Friction Coefficient on Rear Wheel. Here is an example- 0.007919 = ((0.48*(2.7-1.2)*cos(0.1745329251994))/((0.86885/[g])+sin(0.1745329251994))-2.7)/0.48.

How to calculate Height of C.G. using Retardation on Rear Wheel?

With Friction Coefficient on Rear Wheel (μ_RW), Vehicle Wheelbase (b), Horizontal Distance of C.G. from Rear Axle (x), Road Inclination Angle (θ) & Braking Retardation (a) we can find Height of C.G. using Retardation on Rear Wheel using the formula - Height of C.G. of Vehicle = ((Friction Coefficient on Rear Wheel*(Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle))/((Braking Retardation/[g])+sin(Road Inclination Angle))-Vehicle Wheelbase)/Friction Coefficient on Rear Wheel. This formula also uses Gravitational acceleration on Earth constant(s) and , Sine, Cosine function(s).

What are the other ways to Calculate Height of C.G. of Vehicle?

Here are the different ways to Calculate Height of C.G. of Vehicle-

Height of C.G. of Vehicle=(Normal Reaction at Rear Wheel*Vehicle Wheelbase-Vehicle Weight*Horizontal Distance of C.G. from Rear Axle*cos(Road Inclination Angle))/(Friction Coefficient on Rear Wheel*(Vehicle Weight*cos(Road Inclination Angle)-Normal Reaction at Rear Wheel))

Can the Height of C.G. using Retardation on Rear Wheel be negative?

No, the Height of C.G. using Retardation on Rear Wheel, measured in Length cannot be negative.

Which unit is used to measure Height of C.G. using Retardation on Rear Wheel?

Height of C.G. using Retardation on Rear Wheel is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of C.G. using Retardation on Rear Wheel can be measured.

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Height of C.G. using Retardation on Rear Wheel Formula

​GoHeight of C.G. from Road Surface on Rear Wheel Formula

Height of C.G. using Retardation on Rear Wheel Example

Height of C.G. using Retardation on Rear Wheel Solution

Height of C.G. using Retardation on Rear Wheel Formula Elements

Other Formulas to find Height of C.G. of Vehicle

Other formulas in Effects on Rear Wheel (RW) category

How to Evaluate Height of C.G. using Retardation on Rear Wheel?

FAQs on Height of C.G. using Retardation on Rear Wheel

Variable Name

GoHeight of C.G. from Road Surface on Rear Wheel Formula