Front Roll Rate given Roll Gradient Calculator

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Race Car Vehicle Dynamics

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Front Axle and Steering

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Vehicle Cornering in Race Cars

Rates for Axle Suspension in Race Car

Ride Rate and Ride Frequency for Race Cars

Tire Behavior in Racing Car

Weight Transfer during Braking

Wheel Centre Rates for Independent Suspension

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Load on Wheels in Race Cars

Front Lateral Load Transfer for Race Cars

Rear Lateral Load Transfer

✖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∂A_y]			+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_ΦR]			+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_ΦF]

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Formula

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Front Roll Rate given Roll Gradient

Formula

`"K"_{"ΦF"} = -"m"*"[g]"*"H"/"∂θ∂A"_{"y"}-"K"_{"ΦR"}`

Example

`"50509.06Nm/rad"=-"155kg"*"[g]"*"2.335m"/"-0.03rad/m/s²"-"67800Nm/rad"`

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Download Vehicle Cornering in Race Cars Formula PDF

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_ΦF = -m*[g]*H/∂θ∂A_y-K_ΦR
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: 2.335 Meter --> 2.335 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_ΦF = -m*[g]*H/∂θ∂A_y-K_ΦR --> -155*[g]*2.335/(-0.03)-67800

Evaluating ... ...

K_ΦF = 50509.0600416667

STEP 3: Convert Result to Output's Unit

50509.0600416667 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

50509.0600416667 ≈ 50509.06 Newton Meter per Radian <-- Front Roll Rate

(Calculation completed in 00.020 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!

< 12 Vehicle Cornering in Race Cars Calculators

Cornering Velocity given Effective Weight of Car due to Banking

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

Total Static Mass of Car given Effective Weight during Banking

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

Corner Radius given Effective Weight of Car due to Banking

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

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))

Centre of Gravity Distance to Roll Axis given Roll Gradient

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

Total Vehicle Mass given Roll Gradient

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

Roll Gradient

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

Front Roll Rate given Roll Gradient

Go Front Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Rear Roll Rate

Rear Roll Rate given Roll Gradient

Go Rear Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Front Roll Rate

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)

Front Roll Rate given Roll Gradient Formula

Front Roll Rate = -Mass of Vehicle*[g]*Centre of Gravity Distance to Roll Axis/Roll Gradient-Rear Roll Rate
K_ΦF = -m*[g]*H/∂θ∂A_y-K_ΦR

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 your car in the roll mode. Front Roll Rate is denoted by K_ΦF 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∂A_y) & Rear Roll Rate (K_ΦR) 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]*2.335/(-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 your car in the roll mode and is represented as K_ΦF = -m*[g]*H/∂θ∂A_y-K_ΦR 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 your 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∂A_y) & Rear Roll Rate (K_ΦR). 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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