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Rear Roll Rate given Rear Lateral Load Transfer Formula

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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. Check FAQs

K Φr = \frac{K Φf}{(\frac{\frac{A y}{[g]} \cdot \frac{m}{t r} \cdot H}{W r - \frac{a}{b} \cdot Z rr}) - 1}

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

Rear Roll Rate given Rear Lateral Load Transfer Example

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Here is how the Rear Roll Rate given Rear Lateral Load Transfer equation looks like with Values.

Here is how the Rear Roll Rate given Rear Lateral Load Transfer equation looks like with Units.

Here is how the Rear Roll Rate given Rear Lateral Load Transfer equation looks like.

67802.7957 = \frac{94900}{(\frac{\frac{9.81}{9.8066} \cdot \frac{155}{1.4} \cdot 3.4907}{161.87 - \frac{27}{2.7} \cdot 0.0762}) - 1}

67802.7957Nm/rad = \frac{94900Nm/rad}{(\frac{\frac{9.81m/s²}{9.8066m/s²} \cdot \frac{155kg}{1.4m} \cdot 3.4907m}{161.87kg - \frac{27m}{2.7m} \cdot 0.0762m}) - 1}

67802.7957 = \frac{94900}{(\frac{\frac{9.81}{9.8066} \cdot \frac{155}{1.4} \cdot 3.4907}{161.87 - \frac{27}{2.7} \cdot 0.0762}) - 1}

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Rear Roll Rate given Rear Lateral Load Transfer Solution

Follow our step by step solution on how to calculate Rear Roll Rate given Rear Lateral Load Transfer?

FIRST Step Consider the formula

K Φr = \frac{K Φf}{(\frac{\frac{A y}{[g]} \cdot \frac{m}{t r} \cdot H}{W r - \frac{a}{b} \cdot Z rr}) - 1}

Next Step Substitute values of Variables

∴

K Φr = \frac{94900Nm/rad}{(\frac{\frac{9.81m/s²}{[g]} \cdot \frac{155kg}{1.4m} \cdot 3.4907m}{161.87kg - \frac{27m}{2.7m} \cdot 0.0762m}) - 1}

Next Step Substitute values of Constants

∴

K Φr = \frac{94900Nm/rad}{(\frac{\frac{9.81m/s²}{9.8066m/s²} \cdot \frac{155kg}{1.4m} \cdot 3.4907m}{161.87kg - \frac{27m}{2.7m} \cdot 0.0762m}) - 1}

Next Step Prepare to Evaluate

∴

K Φr = \frac{94900}{(\frac{\frac{9.81}{9.8066} \cdot \frac{155}{1.4} \cdot 3.4907}{161.87 - \frac{27}{2.7} \cdot 0.0762}) - 1}

Next Step Evaluate

∴

K Φr = 67802.7957128244Nm/rad

LAST Step Rounding Answer

∴

K Φr = 67802.7957Nm/rad

Rear Roll Rate given Rear Lateral Load Transfer Formula Elements

Variables

Constants

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

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

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

Rear Track Width

Rear Track Width is the distance between the centres of the rear wheels.

Symbol: t_r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Rear Track Width

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

Rear Lateral Load Transfer

Rear Lateral Load Transfer is the load transfer in the rear wheels due to lateral acceleration.

Symbol: W_r

Measurement: WeightUnit: kg

Note: Value can be positive or negative.

Formulas to find Rear Lateral Load Transfer

Horizontal Distance of C.G. from Front Axle

Horizontal Distance of C.G. from Front Axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle.

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Horizontal Distance of C.G. from Front 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

Rear Roll Centre Height

Rear 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_rr

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Rear Roll Centre Height

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 Rear Lateral Load Transfer category

Go Rear Lateral Load Transfer

W r = \frac{A y}{[g]} \cdot \frac{m}{t r} \cdot H \cdot \frac{K Φr}{K Φf + K Φr} + \frac{a}{b} \cdot Z rr

Go Lateral Acceleration given Rear Lateral Load Transfer

A y = \frac{W r - \frac{a}{b} \cdot Z rr}{\frac{1}{[g]} \cdot \frac{m}{t r} \cdot H \cdot \frac{K Φr}{K Φf + K Φr}}

How to Evaluate Rear Roll Rate given Rear Lateral Load Transfer?

Rear Roll Rate given Rear Lateral Load Transfer evaluator uses Rear Roll Rate = Front Roll Rate/(((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/(Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1) to evaluate the Rear Roll Rate, The Rear roll rate given rear lateral load transfer formula is used to find the roll rate of rear suspension which is the stiffness of the rear suspension in roll mode. Rear Roll Rate is denoted by K_Φr symbol.

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

FAQs on Rear Roll Rate given Rear Lateral Load Transfer

What is the formula to find Rear Roll Rate given Rear Lateral Load Transfer?

The formula of Rear Roll Rate given Rear Lateral Load Transfer is expressed as Rear Roll Rate = Front Roll Rate/(((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/(Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1). Here is an example- 67494.5 = 94900/(((9.81/[g]*155/1.4*3.4907)/(161.87-27/2.7*0.0762))-1).

How to calculate Rear Roll Rate given Rear Lateral Load Transfer?

With Front Roll Rate (K_Φf), Lateral Acceleration (A_y), Mass of Vehicle (m), Rear Track Width (t_r), Centre of Gravity Distance to Roll Axis (H), Rear Lateral Load Transfer (W_r), Horizontal Distance of C.G. from Front Axle (a), Wheelbase of Vehicle (b) & Rear Roll Centre Height (Z_rr) we can find Rear Roll Rate given Rear Lateral Load Transfer using the formula - Rear Roll Rate = Front Roll Rate/(((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/(Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1). This formula also uses Gravitational acceleration on Earth constant(s).

Can the Rear Roll Rate given Rear Lateral Load Transfer be negative?

No, the Rear Roll Rate given Rear Lateral Load Transfer, measured in Torsion Constant cannot be negative.

Which unit is used to measure Rear Roll Rate given Rear Lateral Load Transfer?

Rear Roll Rate given Rear Lateral Load Transfer is usually measured using the Newton Meter per Radian[Nm/rad] for Torsion Constant. Newton Centimeter per Radian[Nm/rad] are the few other units in which Rear Roll Rate given Rear Lateral Load Transfer can be measured.

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Rear Roll Rate given Rear Lateral Load Transfer Formula

Rear Roll Rate given Rear Lateral Load Transfer Example

Rear Roll Rate given Rear Lateral Load Transfer Solution

Rear Roll Rate given Rear Lateral Load Transfer Formula Elements

Other formulas in Rear Lateral Load Transfer category

How to Evaluate Rear Roll Rate given Rear Lateral Load Transfer?

FAQs on Rear Roll Rate given Rear Lateral Load Transfer

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