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

GoHeight of C.G. using Retardation 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{R R \cdot b - W \cdot x \cdot \cos (θ)}{μ RW \cdot (W \cdot \cos (θ) - R R)}

h - Height of C.G. of Vehicle?R_R - Normal Reaction at Rear Wheel?b - Vehicle Wheelbase?W - Vehicle Weight?x - Horizontal Distance of C.G. from Rear Axle?θ - Road Inclination Angle?μ_RW - Friction Coefficient on Rear Wheel?

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

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Here is how the Height of C.G. from Road Surface on Rear Wheel equation looks like with Values.

Here is how the Height of C.G. from Road Surface on Rear Wheel equation looks like with Units.

Here is how the Height of C.G. from Road Surface on Rear Wheel equation looks like.

0.0079 = \frac{5700 \cdot 2.7 - 13000 \cdot 1.2 \cdot \cos (10)}{0.48 \cdot (13000 \cdot \cos (10) - 5700)}

0.0079m = \frac{5700N \cdot 2.7m - 13000N \cdot 1.2m \cdot \cos (10°)}{0.48 \cdot (13000N \cdot \cos (10°) - 5700N)}

0.0079 = \frac{5700 \cdot 2.7 - 13000 \cdot 1.2 \cdot \cos (10)}{0.48 \cdot (13000 \cdot \cos (10) - 5700)}

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

Follow our step by step solution on how to calculate Height of C.G. from Road Surface on Rear Wheel?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = \frac{5700N \cdot 2.7m - 13000N \cdot 1.2m \cdot \cos (10°)}{0.48 \cdot (13000N \cdot \cos (10°) - 5700N)}

Next Step Convert Units

∴

h = \frac{5700N \cdot 2.7m - 13000N \cdot 1.2m \cdot \cos (0.1745rad)}{0.48 \cdot (13000N \cdot \cos (0.1745rad) - 5700N)}

Next Step Prepare to Evaluate

∴

h = \frac{5700 \cdot 2.7 - 13000 \cdot 1.2 \cdot \cos (0.1745)}{0.48 \cdot (13000 \cdot \cos (0.1745) - 5700)}

Next Step Evaluate

∴

h = 0.00791946791317697m

LAST Step Rounding Answer

∴

h = 0.0079m

Height of C.G. from Road Surface on Rear Wheel Formula Elements

Variables

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

Normal Reaction at Rear Wheel

Normal Reaction at Rear Wheel is the upward force exerted by the ground on the rear wheel of a racing car during braking, affecting its stability and control.

Symbol: R_R

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Normal Reaction at 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

Vehicle Weight

Vehicle Weight is the total weight of the racing car, including the driver, fuel, and other components, affecting the rear wheel braking performance.

Symbol: W

Measurement: ForceUnit: N

Note: Value should be greater than 0.

Formulas to find Vehicle Weight

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

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

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. using Retardation on Rear Wheel

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

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)}

How to Evaluate Height of C.G. from Road Surface on Rear Wheel?

Height of C.G. from Road Surface on Rear Wheel evaluator uses 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)) to evaluate the Height of C.G. of Vehicle, Height of C.G. from Road Surface on Rear Wheel formula is defined as the vertical distance from the road surface to the center of gravity of a vehicle's rear wheel, which is a critical parameter in determining the vehicle's stability and rollover propensity. Height of C.G. of Vehicle is denoted by h symbol.

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

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

What is the formula to find Height of C.G. from Road Surface on Rear Wheel?

The formula of Height of C.G. from Road Surface on Rear Wheel is expressed as 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)). Here is an example- 0.007919 = (5700*2.7-13000*1.2*cos(0.1745329251994))/(0.48*(13000*cos(0.1745329251994)-5700)).

How to calculate Height of C.G. from Road Surface on Rear Wheel?

With Normal Reaction at Rear Wheel (R_R), Vehicle Wheelbase (b), Vehicle Weight (W), Horizontal Distance of C.G. from Rear Axle (x), Road Inclination Angle (θ) & Friction Coefficient on Rear Wheel (μ_RW) we can find Height of C.G. from Road Surface on Rear Wheel using the formula - 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)). This formula also uses 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=((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

Can the Height of C.G. from Road Surface on Rear Wheel be negative?

No, the Height of C.G. from Road Surface on Rear Wheel, measured in Length cannot be negative.

Which unit is used to measure Height of C.G. from Road Surface on Rear Wheel?

Height of C.G. from Road Surface 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. from Road Surface on Rear Wheel can be measured.

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

​GoHeight of C.G. using Retardation on Rear Wheel Formula

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

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

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

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

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