Front Roll Rate given Rear Lateral Load Transfer Calculator

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Race Car Vehicle Dynamics

Driveline

Front Axle and Steering

Suspension Geometry

Vehicle Collision

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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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Rear Lateral Load Transfer

Load on Wheels in Race Cars

Front Lateral Load Transfer for Race Cars

✖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%
✖Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering.ⓘ Lateral Acceleration [A_y]			+10% -10%
✖Mass of Vehicle is the total mass of the vehicle.ⓘ Mass of Vehicle [m]			+10% -10%
✖Rear Track Width is the distance between the centres of the rear wheels.ⓘ Rear Track Width [t_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 [H]			+10% -10%
✖Rear Lateral Load Transfer is the load transfer in the rear wheels due to lateral acceleration.ⓘ Rear Lateral Load Transfer [W_R]			+10% -10%
✖Horizontal Distance of C.G. from Front Axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle.ⓘ Horizontal Distance of C.G. from Front Axle [a]			+10% -10%
✖Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.ⓘ Wheelbase of Vehicle [b]			+10% -10%
✖Rear Roll Centre Height is the height of the notional point at which the cornering forces in the suspension are reacted to the vehicle body.ⓘ Rear Roll Centre Height [Z_RR]			+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 Rear Lateral Load Transfer [K_ΦF]

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Formula

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Front Roll Rate given Rear Lateral Load Transfer

Formula

`"K"_{"ΦF"} = "K"_{"ΦR"}*(("A"_{"y"}/"[g]"*"m"/"t"_{"R"}*"H")/(("W"_{"R"}-"a"/"b"*"Z"_{"RR"}))-1)`

Example

`"41030.71Nm/rad"="67800Nm/rad"*(("9.81m/s²"/"[g]"*"155kg"/"1.4m"*"2.335m")/(("161.87kg"-"27m"/"2.7m"*"0.0762m"))-1)`

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Front Roll Rate given Rear Lateral Load Transfer Solution

STEP 0: Pre-Calculation Summary

Formula Used

Front Roll Rate = Rear Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/((Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1)
K_ΦF = K_ΦR*((A_y/[g]*m/t_R*H)/((W_R-a/b*Z_RR))-1)
This formula uses 1 Constants, 10 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.
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.
Lateral Acceleration - (Measured in Meter per Square Second) - Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering.
Mass of Vehicle - (Measured in Kilogram) - Mass of Vehicle is the total mass of the vehicle.
Rear Track Width - (Measured in Meter) - Rear Track Width is the distance between the centres of the rear wheels.
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.
Rear Lateral Load Transfer - (Measured in Kilogram) - Rear Lateral Load Transfer is the load transfer in the rear wheels due to lateral acceleration.
Horizontal Distance of C.G. from Front Axle - (Measured in Meter) - Horizontal Distance of C.G. from Front Axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle.
Wheelbase of Vehicle - (Measured in Meter) - Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
Rear Roll Centre Height - (Measured in Meter) - Rear Roll Centre Height is the height of the notional point at which the cornering forces in the suspension are reacted to the vehicle body.

STEP 1: Convert Input(s) to Base Unit

Rear Roll Rate: 67800 Newton Meter per Radian --> 67800 Newton Meter per Radian No Conversion Required
Lateral Acceleration: 9.81 Meter per Square Second --> 9.81 Meter per Square Second No Conversion Required
Mass of Vehicle: 155 Kilogram --> 155 Kilogram No Conversion Required
Rear Track Width: 1.4 Meter --> 1.4 Meter No Conversion Required
Centre of Gravity Distance to Roll Axis: 2.335 Meter --> 2.335 Meter No Conversion Required
Rear Lateral Load Transfer: 161.87 Kilogram --> 161.87 Kilogram No Conversion Required
Horizontal Distance of C.G. from Front Axle: 27 Meter --> 27 Meter No Conversion Required
Wheelbase of Vehicle: 2.7 Meter --> 2.7 Meter No Conversion Required
Rear Roll Centre Height: 0.0762 Meter --> 0.0762 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_ΦF = K_ΦR*((A_y/[g]*m/t_R*H)/((W_R-a/b*Z_RR))-1) --> 67800*((9.81/[g]*155/1.4*2.335)/((161.87-27/2.7*0.0762))-1)

Evaluating ... ...

K_ΦF = 41030.7110657445

STEP 3: Convert Result to Output's Unit

41030.7110657445 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

41030.7110657445 ≈ 41030.71 Newton Meter per Radian <-- Front Roll Rate

(Calculation completed in 00.020 seconds)

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Created by Peri Krishna Karthik

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

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< 7 Rear Lateral Load Transfer Calculators

Lateral Acceleration given Rear Lateral Load Transfer

Go Lateral Acceleration = (Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height)/(1/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis*Rear Roll Rate/(Front Roll Rate+Rear Roll Rate))

Total Vehicle Mass given Rear Lateral Load Transfer

Go Mass of Vehicle = (Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height)/(Lateral Acceleration/[g]*1/Rear Track Width*Centre of Gravity Distance to Roll Axis*Rear Roll Rate/(Front Roll Rate+Rear Roll Rate))

Height of Centre of Gravity from Roll Axis given Rear Lateral Load Transfer

Go Centre of Gravity Distance to Roll Axis = (Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height)/(Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Rear Roll Rate/(Front Roll Rate+Rear Roll Rate))

Rear Track Width given Rear Lateral Load Transfer

Go Rear Track Width = (Lateral Acceleration/[g]*Mass of Vehicle*Centre of Gravity Distance to Roll Axis*Rear Roll Rate/(Front Roll Rate+Rear Roll Rate))/(Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height)

Rear Lateral Load Transfer

Go Rear Lateral Load Transfer = Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis*Rear Roll Rate/(Front Roll Rate+Rear Roll Rate)+Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height

Front Roll Rate given Rear Lateral Load Transfer

Go Front Roll Rate = Rear Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/((Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1)

Rear Roll Rate given Rear Lateral Load Transfer

Go Rear Roll Rate = Front Roll Rate/(((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/(Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1)

Front Roll Rate given Rear Lateral Load Transfer Formula

How does lateral load transfer occur?

Lateral load transfer occurs during cornering and is the shift of mass across the wheels due to the centrifugal force and the lateral acceleration. When a car is cornering it creates a force called centrifugal force. This force works against the lateral acceleration which is created by the grip from the tyres known as the tyre cornering forces.

What are the three mechanisms of lateral load transfer?

Lateral Load Transfer from Unsprung Mass: The simplest component of load transfer. If unsprung mass is isolated, it’s possible to find its own CG. When the car corners, lateral acceleration is applied at this CG, generating a centrifugal force which will result in a moment, that can be divided by the axle track to yield a lateral load transfer component.; Load Transfer from Direct Lateral Force (Kinematic Load Transfer Component): It is one of the two components related to the lateral force acting upon the sprung mass. It arises from the force coupling effect that roll centres have, directly linking forces on sprung mass to the unsprung mass.; Load Transfer Due to Roll Angle (Elastic Load Transfer Component): During spring displacements, a force on each spring arises, and these forces generate a moment that tends to resist the rotation of the body. These forces are reacted by the tyres, and that contributes to lateral load transfer. This component is also referred as the elastic weight transfer component.

How to Calculate Front Roll Rate given Rear Lateral Load Transfer?

Front Roll Rate given Rear Lateral Load Transfer calculator uses Front Roll Rate = Rear Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/((Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1) to calculate the Front Roll Rate, The Front roll rate given rear lateral load transfer formula is used to find the roll rate of front suspension which is the stiffness in the roll mode. Front Roll Rate is denoted by K_ΦF symbol.

How to calculate Front Roll Rate given Rear Lateral Load Transfer using this online calculator? To use this online calculator for Front Roll Rate given Rear Lateral Load Transfer, enter Rear Roll Rate (K_ΦR), Lateral Acceleration (A_y), Mass of Vehicle (m), Rear Track Width (t_R), Centre of Gravity Distance to Roll Axis (H), Rear Lateral Load Transfer (W_R), Horizontal Distance of C.G. from Front Axle (a), Wheelbase of Vehicle (b) & Rear Roll Centre Height (Z_RR) and hit the calculate button. Here is how the Front Roll Rate given Rear Lateral Load Transfer calculation can be explained with given input values -> -52186.172074 = 67800*((9.81/[g]*155/1.4*2.335)/((161.87-27/2.7*0.0762))-1).

FAQ

What is Front Roll Rate given Rear Lateral Load Transfer?

The Front roll rate given rear lateral load transfer formula is used to find the roll rate of front suspension which is the stiffness in the roll mode and is represented as K_ΦF = K_ΦR*((A_y/[g]*m/t_R*H)/((W_R-a/b*Z_RR))-1) or Front Roll Rate = Rear Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/((Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1). 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, Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering, Mass of Vehicle is the total mass of the vehicle, Rear Track Width is the distance between the centres of the rear wheels, Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis, Rear Lateral Load Transfer is the load transfer in the rear wheels due to lateral acceleration, Horizontal Distance of C.G. from Front Axle is the distance of vehicle's center of gravity(C.G.) form front axle measured along wheelbase of vehicle, Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle & Rear Roll Centre Height is the height of the notional point at which the cornering forces in the suspension are reacted to the vehicle body.

How to calculate Front Roll Rate given Rear Lateral Load Transfer?

The Front roll rate given rear lateral load transfer formula is used to find the roll rate of front suspension which is the stiffness in the roll mode is calculated using Front Roll Rate = Rear Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Rear Track Width*Centre of Gravity Distance to Roll Axis)/((Rear Lateral Load Transfer-Horizontal Distance of C.G. from Front Axle/Wheelbase of Vehicle*Rear Roll Centre Height))-1). To calculate Front Roll Rate given Rear Lateral Load Transfer, you need Rear Roll Rate (K_ΦR), Lateral Acceleration (A_y), Mass of Vehicle (m), Rear Track Width (t_R), Centre of Gravity Distance to Roll Axis (H), Rear Lateral Load Transfer (W_R), Horizontal Distance of C.G. from Front Axle (a), Wheelbase of Vehicle (b) & Rear Roll Centre Height (Z_RR). With our tool, you need to enter the respective value for Rear Roll Rate, Lateral Acceleration, Mass of Vehicle, Rear Track Width, Centre of Gravity Distance to Roll Axis, Rear Lateral Load Transfer, Horizontal Distance of C.G. from Front Axle, Wheelbase of Vehicle & Rear Roll Centre Height 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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