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Horizontal Distance of C.G. using Retardation on Rear Wheel Formula

GoHorizontal Distance of C.G. from Rear Axle on Rear Wheel Formula

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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. Check FAQs

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

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

Horizontal Distance of C.G. using Retardation on Rear Wheel Example

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

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

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

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

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

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

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Horizontal Distance of C.G. using Retardation on Rear Wheel Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

x = 2.7m - ((\frac{0.8688m/s²}{[g]} + \sin (10°)) \cdot \frac{2.7m + 0.48 \cdot 0.0079m}{0.48 \cdot \cos (10°)})

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

x = 2.7m - ((\frac{0.8688m/s²}{9.8066m/s²} + \sin (0.1745rad)) \cdot \frac{2.7m + 0.48 \cdot 0.0079m}{0.48 \cdot \cos (0.1745rad)})

Next Step Prepare to Evaluate

∴

x = 2.7 - ((\frac{0.8688}{9.8066} + \sin (0.1745)) \cdot \frac{2.7 + 0.48 \cdot 0.0079}{0.48 \cdot \cos (0.1745)})

Next Step Evaluate

∴

x = 1.19999990812263m

LAST Step Rounding Answer

∴

x = 1.2m

Horizontal Distance of C.G. using Retardation on Rear Wheel Formula Elements

Variables

Constants

Functions

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

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

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

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

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

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

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 Horizontal Distance of C.G. from Rear Axle

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

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

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 Horizontal Distance of C.G. using Retardation on Rear Wheel?

Horizontal Distance of C.G. using Retardation on Rear Wheel evaluator uses Horizontal Distance of C.G. from Rear Axle = Vehicle Wheelbase-((Braking Retardation/[g]+sin(Road Inclination Angle))*(Vehicle Wheelbase+Friction Coefficient on Rear Wheel*Height of C.G. of Vehicle)/(Friction Coefficient on Rear Wheel*cos(Road Inclination Angle))) to evaluate the Horizontal Distance of C.G. from Rear Axle, Horizontal Distance of C.G. using Retardation on Rear Wheel formula is defined as the distance from the center of gravity to the point where the rear wheel is braked, taking into account the retardation, angle of inclination, and other factors that affect the vehicle's motion. Horizontal Distance of C.G. from Rear Axle is denoted by x symbol.

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

FAQs on Horizontal Distance of C.G. using Retardation on Rear Wheel

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

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

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

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

What are the other ways to Calculate Horizontal Distance of C.G. from Rear Axle?

Here are the different ways to Calculate Horizontal Distance of C.G. from Rear Axle-

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

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

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

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

Horizontal Distance 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 Horizontal Distance of C.G. using Retardation on Rear Wheel can be measured.

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Horizontal Distance of C.G. using Retardation on Rear Wheel Formula

​GoHorizontal Distance of C.G. from Rear Axle on Rear Wheel Formula

Horizontal Distance of C.G. using Retardation on Rear Wheel Example

Horizontal Distance of C.G. using Retardation on Rear Wheel Solution

Horizontal Distance of C.G. using Retardation on Rear Wheel Formula Elements

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

Other formulas in Effects on Rear Wheel (RW) category

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

FAQs on Horizontal Distance of C.G. using Retardation on Rear Wheel

Variable Name

GoHorizontal Distance of C.G. from Rear Axle on Rear Wheel Formula