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Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Formula

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Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis. Check FAQs

H = \frac{W f - \frac{x}{b} \cdot Z rf}{\frac{A y}{[g]} \cdot \frac{m}{t F} \cdot \frac{K Φf}{K Φf + K Φr}}

H - Centre of Gravity Distance to Roll Axis?W_f - Front Lateral Load Transfer?x - Horizontal Distance of C.G. from Rear Axle?b - Wheelbase of Vehicle?Z_rf - Front Roll Centre Height?A_y - Lateral Acceleration?m - Mass of Vehicle?t_F - Front Track Width?K_Φf - Front Roll Rate?K_Φr - Rear Roll Rate?[g] - Gravitational acceleration on Earth?

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Example

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Here is how the Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer equation looks like with Values.

Here is how the Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer equation looks like with Units.

Here is how the Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer equation looks like.

0.2869 = \frac{226 - \frac{2.3}{2.7} \cdot 245}{\frac{9.81}{9.8066} \cdot \frac{155}{1.5} \cdot \frac{94900}{94900 + 67800}}

0.2869m = \frac{226kg - \frac{2.3m}{2.7m} \cdot 245m}{\frac{9.81m/s²}{9.8066m/s²} \cdot \frac{155kg}{1.5m} \cdot \frac{94900Nm/rad}{94900Nm/rad + 67800Nm/rad}}

0.2869 = \frac{226 - \frac{2.3}{2.7} \cdot 245}{\frac{9.81}{9.8066} \cdot \frac{155}{1.5} \cdot \frac{94900}{94900 + 67800}}

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Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Solution

Follow our step by step solution on how to calculate Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

FIRST Step Consider the formula

H = \frac{W f - \frac{x}{b} \cdot Z rf}{\frac{A y}{[g]} \cdot \frac{m}{t F} \cdot \frac{K Φf}{K Φf + K Φr}}

Next Step Substitute values of Variables

∴

H = \frac{226kg - \frac{2.3m}{2.7m} \cdot 245m}{\frac{9.81m/s²}{[g]} \cdot \frac{155kg}{1.5m} \cdot \frac{94900Nm/rad}{94900Nm/rad + 67800Nm/rad}}

Next Step Substitute values of Constants

∴

H = \frac{226kg - \frac{2.3m}{2.7m} \cdot 245m}{\frac{9.81m/s²}{9.8066m/s²} \cdot \frac{155kg}{1.5m} \cdot \frac{94900Nm/rad}{94900Nm/rad + 67800Nm/rad}}

Next Step Prepare to Evaluate

∴

H = \frac{226 - \frac{2.3}{2.7} \cdot 245}{\frac{9.81}{9.8066} \cdot \frac{155}{1.5} \cdot \frac{94900}{94900 + 67800}}

Next Step Evaluate

∴

H = 0.286870365007323m

LAST Step Rounding Answer

∴

H = 0.2869m

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Formula Elements

Variables

Constants

Centre of Gravity Distance to Roll Axis

Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis.

Symbol: H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Centre of Gravity Distance to Roll Axis

Front Lateral Load Transfer

Front Lateral Load Transfer is the load transfer on to the front wheels due to lateral acceleration.

Symbol: W_f

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Formulas to find Front Lateral Load Transfer

Horizontal Distance of C.G. from Rear Axle

Horizontal Distance of C.G. from Rear Axle is the distance of vehicle's center of gravity(C.G.) from 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

Wheelbase of Vehicle

Wheelbase of Vehicle 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 Wheelbase of Vehicle

Front Roll Centre Height

Front Roll Centre Height is the height of the notional point at which the cornering forces in the suspension are reacted to the vehicle body.

Symbol: Z_rf

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Front Roll Centre Height

Lateral Acceleration

Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering.

Symbol: A_y

Measurement: AccelerationUnit: m/s²

Note: Value can be positive or negative.

Formulas to find Lateral Acceleration

Mass of Vehicle

Mass of Vehicle is the total mass of the vehicle.

Symbol: m

Measurement: WeightUnit: kg

Note: Value should be greater than 0.

Formulas to find Mass of Vehicle

Front Track Width

Front Track Width is the distance between the centers of front wheels.

Symbol: t_F

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Front Track Width

Front Roll Rate

Front Roll Rate is the stiffness of your car in the roll mode. Or one can say, it is the roll angle per unit lateral acceleration.

Symbol: K_Φf

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Front Roll Rate

Rear Roll Rate

Rear Roll Rate is the stiffness of your car in the roll mode. Or one can say, it is the roll angle per unit lateral acceleration.

Symbol: K_Φr

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Rear Roll Rate

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

Other formulas in Front Lateral Load Transfer for Race Cars category

Go Front Lateral Load Transfer

W f = \frac{A y}{[g]} \cdot \frac{m}{t F} \cdot H \cdot \frac{K Φf}{K Φf + K Φr} + \frac{x}{b} \cdot Z rf

Go Front Roll Centre Height given Front Lateral Load Transfer

Z rf = (W f - \frac{A y}{[g]} \cdot \frac{m}{t F} \cdot H \cdot \frac{K Φf}{K Φf + K Φr}) \cdot \frac{b}{x}

How to Evaluate Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer evaluator uses Centre of Gravity Distance to Roll Axis = (Front Lateral Load Transfer-Horizontal Distance of C.G. from Rear Axle/Wheelbase of Vehicle*Front Roll Centre Height)/(Lateral Acceleration/[g]*Mass of Vehicle/Front Track Width*Front Roll Rate/(Front Roll Rate+Rear Roll Rate)) to evaluate the Centre of Gravity Distance to Roll Axis, The Height of Centre of Gravity from Roll Axis given front lateral load transfer formula is used to find the distance of centre of gravity from the roll axis when other parameters are known. Centre of Gravity Distance to Roll Axis is denoted by H symbol.

How to evaluate Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer using this online evaluator? To use this online evaluator for Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer, enter Front Lateral Load Transfer (W_f), Horizontal Distance of C.G. from Rear Axle (x), Wheelbase of Vehicle (b), Front Roll Centre Height (Z_rf), Lateral Acceleration (A_y), Mass of Vehicle (m), Front Track Width (t_F), Front Roll Rate (K_Φf) & Rear Roll Rate (K_Φr) and hit the calculate button.

FAQs on Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer

What is the formula to find Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

The formula of Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer is expressed as Centre of Gravity Distance to Roll Axis = (Front Lateral Load Transfer-Horizontal Distance of C.G. from Rear Axle/Wheelbase of Vehicle*Front Roll Centre Height)/(Lateral Acceleration/[g]*Mass of Vehicle/Front Track Width*Front Roll Rate/(Front Roll Rate+Rear Roll Rate)). Here is an example- 0.28687 = (226-2.3/2.7*245)/(9.81/[g]*155/1.5*94900/(94900+67800)).

How to calculate Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

With Front Lateral Load Transfer (W_f), Horizontal Distance of C.G. from Rear Axle (x), Wheelbase of Vehicle (b), Front Roll Centre Height (Z_rf), Lateral Acceleration (A_y), Mass of Vehicle (m), Front Track Width (t_F), Front Roll Rate (K_Φf) & Rear Roll Rate (K_Φr) we can find Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer using the formula - Centre of Gravity Distance to Roll Axis = (Front Lateral Load Transfer-Horizontal Distance of C.G. from Rear Axle/Wheelbase of Vehicle*Front Roll Centre Height)/(Lateral Acceleration/[g]*Mass of Vehicle/Front Track Width*Front Roll Rate/(Front Roll Rate+Rear Roll Rate)). This formula also uses Gravitational acceleration on Earth constant(s).

Can the Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer be negative?

No, the Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer, measured in Length cannot be negative.

Which unit is used to measure Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer can be measured.

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Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Formula

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Example

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Solution

Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer Formula Elements

Other formulas in Front Lateral Load Transfer for Race Cars category

How to Evaluate Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer?

FAQs on Height of Centre of Gravity from Roll Axis given Front Lateral Load Transfer

Variable Name