Total Vehicle Mass given Roll Gradient Calculator

✖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).ⓘ Roll Gradient [∂_Θ]			+10% -10%
✖Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis.ⓘ Centre of Gravity Distance to Roll Axis [H]			+10% -10%
✖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.ⓘ Front Roll Rate [K_Φ]			+10% -10%
✖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.ⓘ Rear Roll Rate [K_r]			+10% -10%

✖Mass of Vehicle is the total mass of the vehicle.ⓘ Total Vehicle Mass given Roll Gradient [m]

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Total Vehicle Mass given Roll Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate)))
m = -(∂_Θ/([g]*H/(K_Φ+K_r)))
This formula uses 1 Constants, 5 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Mass of Vehicle - (Measured in Kilogram) - Mass of Vehicle is the total mass of the vehicle.
Roll Gradient - (Measured in Radian per Meter per Square Second) - 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).
Centre of Gravity Distance to Roll Axis - (Measured in Meter) - Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis.
Front Roll Rate - (Measured in Newton Meter per Radian) - 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.
Rear Roll Rate - (Measured in Newton Meter per Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Roll Gradient: -0.03 Radian per Meter per Square Second --> -0.03 Radian per Meter per Square Second No Conversion Required
Centre of Gravity Distance to Roll Axis: 3.211119 Meter --> 3.211119 Meter No Conversion Required
Front Roll Rate: 94900 Newton Meter per Radian --> 94900 Newton Meter per Radian No Conversion Required
Rear Roll Rate: 67800 Newton Meter per Radian --> 67800 Newton Meter per Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

m = -(∂_Θ/([g]*H/(K_Φ+K_r))) --> -((-0.03)/([g]*3.211119/(94900+67800)))

Evaluating ... ...

m = 155.000012006571

STEP 3: Convert Result to Output's Unit

155.000012006571 Kilogram --> No Conversion Required

FINAL ANSWER

155.000012006571 ≈ 155 Kilogram <-- Mass of Vehicle

(Calculation completed in 00.004 seconds)

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Created by Peri Krishna Karthik

National Institute of Technology Calicut (NIT Calicut), Calicut, Kerala

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national institute of technology hamirpur (NITH ), hamirpur , himachal pradesh

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< Forces on Car Calculators

Effective Weight of Car due to Banking

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

Cornering Velocity given Horizontal Lateral Acceleration

LaTeX Go Cornering Velocity = sqrt(Horizontal Lateral Acceleration*Corner Radius)

Corner Radius given Horizontal Lateral Acceleration

LaTeX Go Corner Radius = (Cornering Velocity^2)/(Horizontal Lateral Acceleration)

Horizontal Lateral Acceleration

LaTeX Go Horizontal Lateral Acceleration = (Cornering Velocity^2)/(Corner Radius)

Total Vehicle Mass given Roll Gradient Formula

LaTeX Go

Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate)))
m = -(∂_Θ/([g]*H/(K_Φ+K_r)))

How does roll rate affect handling?

The ride and roll rates of your car determine a change in wheel load to a change in body position, be that in bump or roll. Roll rates determine the change in tire normal force side to side for a given applied torque to the chassis or a given amount of chassis roll. Ride rates determine the change in tire normal force for one wheel into a pure vertical change in body position.

How to Calculate Total Vehicle Mass given Roll Gradient?

Total Vehicle Mass given Roll Gradient calculator uses Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate))) to calculate 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 calculate Total Vehicle Mass given Roll Gradient using this online calculator? To use this online calculator 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. Here is how the Total Vehicle Mass given Roll Gradient calculation can be explained with given input values -> 1485.742 = -((-0.03)/([g]*3.211119/(94900+67800))).

FAQ

What is Total Vehicle Mass given Roll Gradient?

The Total vehicle mass given roll gradient formula is used to find the total mass of the vehicle and is represented as m = -(∂_Θ/([g]*H/(K_Φ+K_r))) or Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate))). 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), Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis, 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 & 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.

How to calculate Total Vehicle Mass given Roll Gradient?

The Total vehicle mass given roll gradient formula is used to find the total mass of the vehicle is calculated using Mass of Vehicle = -(Roll Gradient/([g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate))). To calculate Total Vehicle Mass given Roll Gradient, you need Roll Gradient (∂_Θ), Centre of Gravity Distance to Roll Axis (H), Front Roll Rate (K_Φ) & Rear Roll Rate (K_r). With our tool, you need to enter the respective value for Roll Gradient, Centre of Gravity Distance to Roll Axis, Front Roll Rate & Rear Roll Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Mass of Vehicle?

In this formula, Mass of Vehicle uses Roll Gradient, Centre of Gravity Distance to Roll Axis, Front Roll Rate & Rear Roll Rate. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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