Centre of Gravity Distance to Roll Axis 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%
✖Mass of Vehicle is the total mass of the vehicle.ⓘ Mass of Vehicle [m]			+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%

✖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 given Roll Gradient [H]

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Centre of Gravity Distance to Roll Axis given Roll Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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).
Mass of Vehicle - (Measured in Kilogram) - Mass of Vehicle is the total mass of the vehicle.
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
Mass of Vehicle: 155 Kilogram --> 155 Kilogram 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

H = -(∂_Θ/(m*[g]/(K_Φ+K_r))) --> -((-0.03)/(155*[g]/(94900+67800)))

Evaluating ... ...

H = 3.21111924873888

STEP 3: Convert Result to Output's Unit

3.21111924873888 Meter --> No Conversion Required

FINAL ANSWER

3.21111924873888 ≈ 3.211119 Meter <-- Centre of Gravity Distance to Roll Axis

(Calculation completed in 00.008 seconds)

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Created by Peri Krishna Karthik

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

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Centre of Gravity Distance to Roll Axis given Roll Gradient Formula

LaTeX Go

Centre of Gravity Distance to Roll Axis = -(Roll Gradient/(Mass of Vehicle*[g]/(Front Roll Rate+Rear Roll Rate)))
H = -(∂_Θ/(m*[g]/(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 tyre 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 tyre normal force for one wheel into a pure vertical change in body position.

How to Calculate Centre of Gravity Distance to Roll Axis given Roll Gradient?

Centre of Gravity Distance to Roll Axis given Roll Gradient calculator uses Centre of Gravity Distance to Roll Axis = -(Roll Gradient/(Mass of Vehicle*[g]/(Front Roll Rate+Rear Roll Rate))) to calculate the Centre of Gravity Distance to Roll Axis, The Centre of Gravity distance to roll axis given roll gradient formula is used to find the distance between the centre of gravity and the roll axis. Centre of Gravity Distance to Roll Axis is denoted by H symbol.

How to calculate Centre of Gravity Distance to Roll Axis given Roll Gradient using this online calculator? To use this online calculator for Centre of Gravity Distance to Roll Axis given Roll Gradient, enter Roll Gradient (∂_Θ), Mass of Vehicle (m), Front Roll Rate (K_Φ) & Rear Roll Rate (K_r) and hit the calculate button. Here is how the Centre of Gravity Distance to Roll Axis given Roll Gradient calculation can be explained with given input values -> 3.211119 = -((-0.03)/(155*[g]/(94900+67800))).

FAQ

What is Centre of Gravity Distance to Roll Axis given Roll Gradient?

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

The Centre of Gravity distance to roll axis given roll gradient formula is used to find the distance between the centre of gravity and the roll axis is calculated using Centre of Gravity Distance to Roll Axis = -(Roll Gradient/(Mass of Vehicle*[g]/(Front Roll Rate+Rear Roll Rate))). To calculate Centre of Gravity Distance to Roll Axis given Roll Gradient, you need Roll Gradient (∂_Θ), Mass of Vehicle (m), Front Roll Rate (K_Φ) & Rear Roll Rate (K_r). With our tool, you need to enter the respective value for Roll Gradient, Mass of Vehicle, 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.

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