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%
✖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%

✖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]

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Roll Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
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

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
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

∂_Θ = -m*[g]*H/(K_Φ+K_r) --> -155*[g]*3.211119/(94900+67800)

Evaluating ... ...

∂_Θ = -0.0299999976761478

STEP 3: Convert Result to Output's Unit

-0.0299999976761478 Radian per Meter per Square Second --> No Conversion Required

FINAL ANSWER

-0.0299999976761478 ≈ -0.03 Radian per Meter per Square Second <-- Roll Gradient

(Calculation completed in 00.018 seconds)

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Credits

Created by Peri Krishna Karthik

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

Peri Krishna Karthik has created this Calculator and 200+ more calculators!

Verified by sanjay shiva

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

sanjay shiva has verified this Calculator and 100+ more calculators!

< 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)

Roll Gradient Formula

LaTeX Go

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

Roll Gradient calculator uses Roll Gradient = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate) to calculate 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 calculate Roll Gradient using this online calculator? To use this online calculator 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. Here is how the Roll Gradient calculation can be explained with given input values -> -0.00313 = -155*[g]*3.211119/(94900+67800).

FAQ

What is 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) and is represented as ∂_Θ = -m*[g]*H/(K_Φ+K_r) or Roll Gradient = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear 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, 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 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) is calculated using Roll Gradient = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/(Front Roll Rate+Rear Roll Rate). To calculate Roll Gradient, you need Mass of Vehicle (m), 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 Mass of Vehicle, 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.

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