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Roll Gradient Formula

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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). Check FAQs

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

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

Roll Gradient Example

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

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

Here is how the Roll Gradient equation looks like.

-0.03 = - 155 \cdot 9.8066 \cdot \frac{3.2111}{94900 + 67800}

-0.03rad/m/s² = - 155kg \cdot 9.8066m/s² \cdot \frac{3.2111m}{94900Nm/rad + 67800Nm/rad}

-0.03 = - 155 \cdot 9.8066 \cdot \frac{3.2111}{94900 + 67800}

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Roll Gradient Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

∂ Θ = - 155kg \cdot [g] \cdot \frac{3.2111m}{94900Nm/rad + 67800Nm/rad}

Next Step Substitute values of Constants

∴

∂ Θ = - 155kg \cdot 9.8066m/s² \cdot \frac{3.2111m}{94900Nm/rad + 67800Nm/rad}

Next Step Prepare to Evaluate

∴

∂ Θ = - 155 \cdot 9.8066 \cdot \frac{3.2111}{94900 + 67800}

Next Step Evaluate

∴

∂ Θ = -0.0299999976761478rad/m/s²

LAST Step Rounding Answer

∴

∂ Θ = -0.03rad/m/s²

Roll Gradient Formula Elements

Variables

Constants

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

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

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

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

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 Roll Gradient?

Roll Gradient evaluator uses Roll Gradient = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate) to evaluate the Roll Gradient, The Roll gradient formula is used to find the vehicle body roll angle derivative concerning the lateral acceleration acting at its centre of gravity (CG). Roll Gradient is denoted by ∂_Θ symbol.

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

FAQs on Roll Gradient

What is the formula to find Roll Gradient?

The formula of Roll Gradient is expressed as Roll Gradient = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate). Here is an example- -0.00313 = -155*[g]*3.211119/(94900+67800).

How to calculate Roll Gradient?

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

Can the Roll Gradient be negative?

Yes, the Roll Gradient, measured in Roll Gradient can be negative.

Which unit is used to measure Roll Gradient?

Roll Gradient is usually measured using the Radian per Meter per Square Second[rad/m/s²] for Roll Gradient. Radian per Acceleration of Gravity[rad/m/s²], Degree per Acceleration of Gravity[rad/m/s²] are the few other units in which Roll Gradient can be measured.

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Roll Gradient Formula

Roll Gradient Example

Roll Gradient Solution

Roll Gradient Formula Elements

Other formulas in Forces on Car category

How to Evaluate Roll Gradient?

FAQs on Roll Gradient

Variable Name