Rear Roll Rate given Front Lateral Load Transfer Calculator

✖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_Φf]			+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%
✖Front Track Width is the distance between the centers of front wheels.ⓘ Front Track Width [t_F]			+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 Lateral Load Transfer is the load transfer on to the front wheels due to lateral acceleration.ⓘ Front Lateral Load Transfer [W_f]			+10% -10%
✖Horizontal Distance of C.G. from Rear Axle is the distance of vehicle's center of gravity(C.G.) from rear axle measured along wheelbase of vehicle.ⓘ Horizontal Distance of C.G. from Rear Axle [x]			+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%
✖Front Roll Centre Height is the height of the notional point at which the cornering forces in the suspension are reacted to the vehicle body.ⓘ Front Roll Centre Height [Z_rf]			+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 Front Lateral Load Transfer [K_Φr]

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Rear Roll Rate given Front Lateral Load Transfer Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rear Roll Rate = Front Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Front Track Width*Centre of Gravity Distance to Roll Axis)/(Front Lateral Load Transfer-Horizontal Distance of C.G. from Rear Axle/Wheelbase of Vehicle*Front Roll Centre Height)-1)
K_Φr = K_Φf*((A_y/[g]*m/t_F*H)/(W_f-x/b*Z_rf)-1)
This formula uses 1 Constants, 10 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.
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.
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.
Front Track Width - (Measured in Meter) - Front Track Width is the distance between the centers of front 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.
Front Lateral Load Transfer - (Measured in Kilogram) - Front Lateral Load Transfer is the load transfer on to the front wheels due to lateral acceleration.
Horizontal Distance of C.G. from Rear Axle - (Measured in Meter) - Horizontal Distance of C.G. from Rear Axle is the distance of vehicle's center of gravity(C.G.) from rear 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.
Front Roll Centre Height - (Measured in Meter) - Front 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

Front Roll Rate: 94900 Newton Meter per Radian --> 94900 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
Front Track Width: 1.5 Meter --> 1.5 Meter No Conversion Required
Centre of Gravity Distance to Roll Axis: 0.335 Meter --> 0.335 Meter No Conversion Required
Front Lateral Load Transfer: 226 Kilogram --> 226 Kilogram No Conversion Required
Horizontal Distance of C.G. from Rear Axle: 2.3 Meter --> 2.3 Meter No Conversion Required
Wheelbase of Vehicle: 2.7 Meter --> 2.7 Meter No Conversion Required
Front Roll Centre Height: 245 Meter --> 245 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_Φr = K_Φf*((A_y/[g]*m/t_F*H)/(W_f-x/b*Z_rf)-1) --> 94900*((9.81/[g]*155/1.5*0.335)/(226-2.3/2.7*245)-1)

Evaluating ... ...

K_Φr = 95096.9695322439

STEP 3: Convert Result to Output's Unit

95096.9695322439 Newton Meter per Radian --> No Conversion Required

FINAL ANSWER

95096.9695322439 ≈ 95096.97 Newton Meter per Radian <-- Rear 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 » Front Lateral Load Transfer for Race Cars » Rear Roll Rate given Front Lateral Load Transfer

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< Front Lateral Load Transfer for Race Cars Calculators

Lateral Acceleration given Front Lateral Load Transfer

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

COG Position Distance from Rear Wheels given Front Lateral Load Transfer

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

Front Roll Centre Height given Front Lateral Load Transfer

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

Front Lateral Load Transfer

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

Rear Roll Rate given Front Lateral Load Transfer Formula

LaTeX Go

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 Rear Roll Rate given Front Lateral Load Transfer?

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

How to calculate Rear Roll Rate given Front Lateral Load Transfer using this online calculator? To use this online calculator for Rear Roll Rate given Front Lateral Load Transfer, enter Front Roll Rate (K_Φf), Lateral Acceleration (A_y), Mass of Vehicle (m), Front Track Width (t_F), Centre of Gravity Distance to Roll Axis (H), Front Lateral Load Transfer (W_f), Horizontal Distance of C.G. from Rear Axle (x), Wheelbase of Vehicle (b) & Front Roll Centre Height (Z_rf) and hit the calculate button. Here is how the Rear Roll Rate given Front Lateral Load Transfer calculation can be explained with given input values -> 95096.97 = 94900*((9.81/[g]*155/1.5*0.335)/(226-2.3/2.7*245)-1).

FAQ

What is Rear Roll Rate given Front Lateral Load Transfer?

The Rear roll rate given front lateral load transfer formula is used to find the roll rate of rear suspension when the front lateral load transfer is known and is represented as K_Φr = K_Φf*((A_y/[g]*m/t_F*H)/(W_f-x/b*Z_rf)-1) or Rear Roll Rate = Front Roll Rate*((Lateral Acceleration/[g]*Mass of Vehicle/Front Track Width*Centre of Gravity Distance to Roll Axis)/(Front Lateral Load Transfer-Horizontal Distance of C.G. from Rear Axle/Wheelbase of Vehicle*Front Roll Centre Height)-1). 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, Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering, Mass of Vehicle is the total mass of the vehicle, Front Track Width is the distance between the centers of front wheels, Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis, Front Lateral Load Transfer is the load transfer on to the front wheels due to lateral acceleration, Horizontal Distance of C.G. from Rear Axle is the distance of vehicle's center of gravity(C.G.) from rear axle measured along wheelbase of vehicle, Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle & Front 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 Rear Roll Rate given Front Lateral Load Transfer?

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