Front 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%
✖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%

✖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 given Roll Gradient [K_Φ]

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Front Roll Rate given Roll Gradient Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

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

Variables Used

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.
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).
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
Roll Gradient: -0.03 Radian per Meter per Square Second --> -0.03 Radian per Meter per Square Second 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

K_Φ = -m*[g]*H/∂_Θ-K_r --> -155*[g]*3.211119/(-0.03)-67800

Evaluating ... ...

K_Φ = 94899.987396975

STEP 3: Convert Result to Output's Unit

94899.987396975 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

94899.987396975 ≈ 94899.99 Newton Meter per Radian <-- Front Roll Rate

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Race Car Vehicle Dynamics » Vehicle Cornering in Race Cars » Mechanical » Forces on Car » Front Roll Rate given Roll Gradient

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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

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Horizontal Lateral Acceleration

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

Front Roll Rate given Roll Gradient Formula

LaTeX Go

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

Front Roll Rate given Roll Gradient calculator uses Front Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Rear Roll Rate to calculate the Front Roll Rate, The Front roll rate given roll gradient formula is used to find the stiffness of the car in the roll mode. Front Roll Rate is denoted by K_Φ symbol.

How to calculate Front Roll Rate given Roll Gradient using this online calculator? To use this online calculator for Front Roll Rate given Roll Gradient, enter Mass of Vehicle (m), Centre of Gravity Distance to Roll Axis (H), Roll Gradient (∂_Θ) & Rear Roll Rate (K_r) and hit the calculate button. Here is how the Front Roll Rate given Roll Gradient calculation can be explained with given input values -> -50826.323292 = -155*[g]*3.211119/(-0.03)-67800.

FAQ

What is Front Roll Rate given Roll Gradient?

The Front roll rate given roll gradient formula is used to find the stiffness of the car in the roll mode and is represented as K_Φ = -m*[g]*H/∂_Θ-K_r or Front Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-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, 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) & 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 Front Roll Rate given Roll Gradient?

The Front roll rate given roll gradient formula is used to find the stiffness of the car in the roll mode is calculated using Front Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Rear Roll Rate. To calculate Front Roll Rate given Roll Gradient, you need Mass of Vehicle (m), Centre of Gravity Distance to Roll Axis (H), Roll Gradient (∂_Θ) & 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, Roll Gradient & 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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