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Total Vehicle Mass given Roll Gradient Formula

GoTotal Static Mass of Car given Effective Weight during Banking Formula

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Mass of Vehicle is the total mass of the vehicle. Check FAQs

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

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

Total Vehicle Mass given Roll Gradient Example

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Here is how the Total Vehicle Mass given Roll Gradient equation looks like with Values.

Here is how the Total Vehicle Mass given Roll Gradient equation looks like with Units.

Here is how the Total Vehicle Mass given Roll Gradient equation looks like.

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

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

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

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Total Vehicle Mass given Roll Gradient Solution

Follow our step by step solution on how to calculate Total Vehicle Mass given Roll Gradient?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

m = - (\frac{-0.03rad/m/s²}{[g] \cdot \frac{3.2111m}{94900Nm/rad + 67800Nm/rad}})

Next Step Substitute values of Constants

∴

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

Next Step Prepare to Evaluate

∴

m = - (\frac{-0.03}{9.8066 \cdot \frac{3.2111}{94900 + 67800}})

Next Step Evaluate

∴

m = 155.000012006571kg

LAST Step Rounding Answer

∴

m = 155kg

Total Vehicle Mass given Roll Gradient Formula Elements

Variables

Constants

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

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

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 to find Mass of Vehicle

Go Total Static Mass of Car given Effective Weight during Banking

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

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 Total Vehicle Mass given Roll Gradient?

Total Vehicle Mass given Roll Gradient evaluator uses Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate))) to evaluate the Mass of Vehicle, The Total vehicle mass given roll gradient formula is used to find the total mass of the vehicle. Mass of Vehicle is denoted by m symbol.

How to evaluate Total Vehicle Mass given Roll Gradient using this online evaluator? To use this online evaluator for Total Vehicle Mass given Roll Gradient, enter Roll Gradient (∂_Θ), 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 Total Vehicle Mass given Roll Gradient

What is the formula to find Total Vehicle Mass given Roll Gradient?

The formula of Total Vehicle Mass given Roll Gradient is expressed as Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate))). Here is an example- 1485.742 = -((-0.03)/([g]*3.211119/(94900+67800))).

How to calculate Total Vehicle Mass given Roll Gradient?

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

What are the other ways to Calculate Mass of Vehicle?

Here are the different ways to Calculate Mass of Vehicle-

Mass of Vehicle=Effective Weight/((Cornering Velocity^2)/(Corner Radius*[g])*(sin(Bank Angle)+cos(Bank Angle)))

Can the Total Vehicle Mass given Roll Gradient be negative?

No, the Total Vehicle Mass given Roll Gradient, measured in Weight cannot be negative.

Which unit is used to measure Total Vehicle Mass given Roll Gradient?

Total Vehicle Mass given Roll Gradient is usually measured using the Kilogram[kg] for Weight. Gram[kg], Milligram[kg], Ton (Metric)[kg] are the few other units in which Total Vehicle Mass given Roll Gradient can be measured.

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Total Vehicle Mass given Roll Gradient Formula

​GoTotal Static Mass of Car given Effective Weight during Banking Formula

Total Vehicle Mass given Roll Gradient Example

Total Vehicle Mass given Roll Gradient Solution

Total Vehicle Mass given Roll Gradient Formula Elements

Other Formulas to find Mass of Vehicle

Other formulas in Forces on Car category

How to Evaluate Total Vehicle Mass given Roll Gradient?

FAQs on Total Vehicle Mass given Roll Gradient

Variable Name

GoTotal Static Mass of Car given Effective Weight during Banking Formula