Rear Roll Rate given Roll Gradient Calculator

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

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Formula

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Rear Roll Rate given Roll Gradient

Formula

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

Example

67799.99 Nm/rad = - 155 kg \cdot [g] \cdot \frac{3.211119 m}{-0.03 rad/m/s²} - 94900 Nm/rad

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Rear Roll Rate given Roll Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

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

Variables Used

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

STEP 1: Convert Input(s) to Base Unit

Mass of Vehicle: 155 Kilogram --> 155 Kilogram No Conversion Required
Centre of Gravity Distance to Roll Axis: 3.211119 Meter --> 3.211119 Meter No Conversion Required
Roll Gradient: -0.03 Radian per Meter per Square Second --> -0.03 Radian per Meter per Square Second No Conversion Required
Front Roll Rate: 94900 Newton Meter per Radian --> 94900 Newton Meter per Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_r = -m*[g]*H/∂_Θ-K_Φ --> -155*[g]*3.211119/(-0.03)-94900

Evaluating ... ...

K_r = 67799.987396975

STEP 3: Convert Result to Output's Unit

67799.987396975 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

67799.987396975 ≈ 67799.99 Newton Meter per Radian <-- Rear Roll Rate

(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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< Forces on Car Calculators

Effective Weight of Car due to Banking

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

Cornering Velocity given Horizontal Lateral Acceleration

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

Corner Radius given Horizontal Lateral Acceleration

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

Horizontal Lateral Acceleration

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

Rear Roll Rate given Roll Gradient Formula

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

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 Rear Roll Rate given Roll Gradient?

Rear Roll Rate given Roll Gradient calculator uses Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate to calculate 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 calculate Rear Roll Rate given Roll Gradient using this online calculator? To use this online calculator 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. Here is how the Rear Roll Rate given Roll Gradient calculation can be explained with given input values -> -77926.323292 = -155*[g]*3.211119/(-0.03)-94900.

FAQ

What is Rear Roll Rate given Roll Gradient?

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

How to calculate Rear Roll Rate given Roll Gradient?

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 is calculated using Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate. To calculate Rear Roll Rate given Roll Gradient, you need Mass of Vehicle (m), Centre of Gravity Distance to Roll Axis (H), Roll Gradient (∂_Θ) & Front Roll Rate (K_Φ). With our tool, you need to enter the respective value for Mass of Vehicle, Centre of Gravity Distance to Roll Axis, Roll Gradient & Front 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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