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Rear Roll Rate given Roll Gradient 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 r = - m \cdot [g] \cdot \frac{H}{∂ Θ} - K Φ

K_r - Rear Roll Rate?m - Mass of Vehicle?H - Centre of Gravity Distance to Roll Axis?∂_Θ - Roll Gradient?K_Φ - Front Roll Rate?[g] - Gravitational acceleration on Earth?

Rear Roll Rate given Roll Gradient Example

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Here is how the Rear Roll Rate given Roll Gradient equation looks like with Values.

Here is how the Rear Roll Rate given Roll Gradient equation looks like with Units.

Here is how the Rear Roll Rate given Roll Gradient equation looks like.

67799.9874 = - 155 \cdot 9.8066 \cdot \frac{3.2111}{-0.03} - 94900

67799.9874Nm/rad = - 155kg \cdot 9.8066m/s² \cdot \frac{3.2111m}{-0.03rad/m/s²} - 94900Nm/rad

67799.9874 = - 155 \cdot 9.8066 \cdot \frac{3.2111}{-0.03} - 94900

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Rear Roll Rate given Roll Gradient Solution

Follow our step by step solution on how to calculate Rear Roll Rate given Roll Gradient?

FIRST Step Consider the formula

K r = - m \cdot [g] \cdot \frac{H}{∂ Θ} - K Φ

Next Step Substitute values of Variables

∴

K r = - 155kg \cdot [g] \cdot \frac{3.2111m}{-0.03rad/m/s²} - 94900Nm/rad

Next Step Substitute values of Constants

∴

K r = - 155kg \cdot 9.8066m/s² \cdot \frac{3.2111m}{-0.03rad/m/s²} - 94900Nm/rad

Next Step Prepare to Evaluate

∴

K r = - 155 \cdot 9.8066 \cdot \frac{3.2111}{-0.03} - 94900

Next Step Evaluate

∴

K r = 67799.987396975Nm/rad

LAST Step Rounding Answer

∴

K r = 67799.9874Nm/rad

Rear Roll Rate given Roll Gradient 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_r

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Rear Roll Rate

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

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

Roll Gradient

The Roll Gradient is defined as the derivative of the vehicle body roll angle with respect to the lateral acceleration acting at its centre of gravity (CG).

Symbol: ∂_Θ

Measurement: Roll GradientUnit: rad/m/s²

Note: Value can be positive or negative.

Formulas to find Roll Gradient

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_Φ

Measurement: Torsion ConstantUnit: Nm/rad

Note: Value should be greater than 0.

Formulas to find Front 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 Forces on Car category

Go Horizontal Lateral Acceleration

A α = \frac{V^{2}}{R}

Go Effective Weight of Car due to Banking

W e = \frac{m \cdot V^{2}}{R \cdot [g]} \cdot (\sin (Φ) + \cos (Φ))

Go Corner Radius given Horizontal Lateral Acceleration

R = \frac{V^{2}}{A α}

Go Cornering Velocity given Horizontal Lateral Acceleration

V = \sqrt{A α \cdot R}

How to Evaluate Rear Roll Rate given Roll Gradient?

Rear Roll Rate given Roll Gradient evaluator uses Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate to evaluate the Rear Roll Rate, The Rear roll rate given roll gradient formula is used to find the stiffness of the rear suspension of the car in the roll mode. Rear Roll Rate is denoted by K_r symbol.

How to evaluate Rear Roll Rate given Roll Gradient using this online evaluator? To use this online evaluator for Rear Roll Rate given Roll Gradient, enter Mass of Vehicle (m), Centre of Gravity Distance to Roll Axis (H), Roll Gradient (∂_Θ) & Front Roll Rate (K_Φ) and hit the calculate button.

FAQs on Rear Roll Rate given Roll Gradient

What is the formula to find Rear Roll Rate given Roll Gradient?

The formula of Rear Roll Rate given Roll Gradient is expressed as Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate. Here is an example- -77926.323292 = -155*[g]*3.211119/(-0.03)-94900.

How to calculate Rear Roll Rate given Roll Gradient?

With Mass of Vehicle (m), Centre of Gravity Distance to Roll Axis (H), Roll Gradient (∂_Θ) & Front Roll Rate (K_Φ) we can find Rear Roll Rate given Roll Gradient using the formula - Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate. This formula also uses Gravitational acceleration on Earth constant(s).

Can the Rear Roll Rate given Roll Gradient be negative?

No, the Rear Roll Rate given Roll Gradient, measured in Torsion Constant cannot be negative.

Which unit is used to measure Rear Roll Rate given Roll Gradient?

Rear Roll Rate given Roll Gradient 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 Roll Gradient can be measured.

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Rear Roll Rate given Roll Gradient Formula

Rear Roll Rate given Roll Gradient Example

Rear Roll Rate given Roll Gradient Solution

Rear Roll Rate given Roll Gradient Formula Elements

Other formulas in Forces on Car category

How to Evaluate Rear Roll Rate given Roll Gradient?

FAQs on Rear Roll Rate given Roll Gradient

Variable Name