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

✖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.ⓘ Friction Coefficient on Rear Wheel [μ_RW]			+10% -10%
✖Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.ⓘ Vehicle Wheelbase [b]			+10% -10%
✖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.ⓘ Horizontal Distance of C.G. from Rear Axle [x]			+10% -10%
✖Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.ⓘ Road Inclination Angle [θ]			+10% -10%
✖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.ⓘ Braking Retardation [a]			+10% -10%

✖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.ⓘ Height of C.G. using Retardation on Rear Wheel [h]

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Formula

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Height of C.G. using Retardation on Rear Wheel

Formula

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

Example

0.007919 m = \frac{\frac{0.48 \cdot (2.7 m - 1.2 m) \cdot \cos (10 °)}{(\frac{0.86885 m/s²}{[g]}) + \sin (10 °)} - 2.7 m}{0.48}

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

STEP 0: Pre-Calculation Summary

Formula Used

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
h = ((μ_RW*(b-x)*cos(θ))/((a/[g])+sin(θ))-b)/μ_RW
This formula uses 1 Constants, 2 Functions, 6 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Height of C.G. of Vehicle - (Measured in Meter) - 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.
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.
Vehicle Wheelbase - (Measured in Meter) - Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car.
Horizontal Distance of C.G. from Rear Axle - (Measured in Meter) - 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.
Road Inclination Angle - (Measured in Radian) - Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability.
Braking Retardation - (Measured in Meter per Square Second) - 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.

STEP 1: Convert Input(s) to Base Unit

Friction Coefficient on Rear Wheel: 0.48 --> No Conversion Required
Vehicle Wheelbase: 2.7 Meter --> 2.7 Meter No Conversion Required
Horizontal Distance of C.G. from Rear Axle: 1.2 Meter --> 1.2 Meter No Conversion Required
Road Inclination Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Braking Retardation: 0.86885 Meter per Square Second --> 0.86885 Meter per Square Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = ((μ_RW*(b-x)*cos(θ))/((a/[g])+sin(θ))-b)/μ_RW --> ((0.48*(2.7-1.2)*cos(0.1745329251994))/((0.86885/[g])+sin(0.1745329251994))-2.7)/0.48

Evaluating ... ...

h = 0.00791865497482558

STEP 3: Convert Result to Output's Unit

0.00791865497482558 Meter --> No Conversion Required

FINAL ANSWER

0.00791865497482558 ≈ 0.007919 Meter <-- Height of C.G. of Vehicle

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Weight Transfer during Braking » Rear Wheel Braking for Racing Car » Mechanical » Effects on Rear Wheel (RW) » Height of C.G. using Retardation on Rear Wheel

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< Effects on Rear Wheel (RW) Calculators

Friction Coefficient using Retardation on Rear Wheel

Go Friction Coefficient on Rear Wheel = ((Braking Retardation/[g]+sin(Road Inclination Angle))*Vehicle Wheelbase)/((Vehicle Wheelbase-Horizontal Distance of C.G. from Rear Axle)*cos(Road Inclination Angle)-((Braking Retardation/[g]+sin(Road Inclination Angle))*Height of C.G. of Vehicle))

Friction Coefficient between Wheel and Road Surface on Rear Wheel

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

Weight of Vehicle on Rear Wheel

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

Normal Reaction Force at Rear Wheel

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

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

What is Retardation in Vehicle?

Retardation in a vehicle refers to the process of slowing down or decelerating. It is the rate at which a vehicle's speed decreases when brakes are applied or when other decelerating forces, like engine braking, are used. Retardation is crucial for controlled stopping and safe driving, and it depends on factors such as the braking system's effectiveness, road conditions, and the vehicle's weight. Proper retardation ensures stability and helps prevent accidents.

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

Height of C.G. using Retardation on Rear Wheel calculator 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 calculate 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 calculate Height of C.G. using Retardation on Rear Wheel using this online calculator? To use this online calculator 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. Here is how the Height of C.G. using Retardation on Rear Wheel calculation can be explained with given input values -> 0.007919 = ((0.48*(2.7-1.2)*cos(0.1745329251994))/((0.86885/[g])+sin(0.1745329251994))-2.7)/0.48.

FAQ

What is Height of C.G. using Retardation on Rear Wheel?

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 and is represented as h = ((μ_RW*(b-x)*cos(θ))/((a/[g])+sin(θ))-b)/μ_RW or 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. 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, Vehicle Wheelbase is the distance between the center of the rear wheel and the point where the brake is applied in a racing car, 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, Road Inclination Angle is the angle at which the road is inclined, affecting the racing car's rear wheel braking performance and overall stability & 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.

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

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 is calculated using 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 calculate Height of C.G. using Retardation on Rear Wheel, you need 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). With our tool, you need to enter the respective value for Friction Coefficient on Rear Wheel, Vehicle Wheelbase, Horizontal Distance of C.G. from Rear Axle, Road Inclination Angle & Braking Retardation and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Height of C.G. of Vehicle?

In this formula, Height of C.G. of Vehicle uses Friction Coefficient on Rear Wheel, Vehicle Wheelbase, Horizontal Distance of C.G. from Rear Axle, Road Inclination Angle & Braking Retardation. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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