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Lateral Acceleration given Rear Lateral Load Transfer Formula

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Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering. Check FAQs
Ay=Wr-ab⋅Zrr1[g]⋅mtr⋅H⋅KΦrKΦf+KΦr
Ay - Lateral Acceleration?Wr - Rear Lateral Load Transfer?a - Horizontal Distance of C.G. from Front Axle?b - Wheelbase of Vehicle?Zrr - Rear Roll Centre Height?m - Mass of Vehicle?tr - Rear Track Width?H - Centre of Gravity Distance to Roll Axis?KΦr - Rear Roll Rate?KΦf - Front Roll Rate?[g] - Gravitational acceleration on Earth?

Lateral Acceleration given Rear Lateral Load Transfer Example

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Here is how the Lateral Acceleration given Rear Lateral Load Transfer equation looks like with Values.

Here is how the Lateral Acceleration given Rear Lateral Load Transfer equation looks like with Units.

Here is how the Lateral Acceleration given Rear Lateral Load Transfer equation looks like.

9.8102Edit=161.87Edit-27Edit2.7Edit⋅0.0762Edit19.8066⋅155Edit1.4Edit⋅3.4907Edit⋅67800Edit94900Edit+67800Edit
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Lateral Acceleration given Rear Lateral Load Transfer Solution

Follow our step by step solution on how to calculate Lateral Acceleration given Rear Lateral Load Transfer?

FIRST Step Consider the formula
Ay=Wr-ab⋅Zrr1[g]⋅mtr⋅H⋅KΦrKΦf+KΦr
Next Step Substitute values of Variables
∴ Ay=161.87kg-27m2.7m⋅0.0762m1[g]⋅155kg1.4m⋅3.4907m⋅67800Nm/rad94900Nm/rad+67800Nm/rad
Next Step Substitute values of Constants
∴ Ay=161.87kg-27m2.7m⋅0.0762m19.8066m/s²⋅155kg1.4m⋅3.4907m⋅67800Nm/rad94900Nm/rad+67800Nm/rad
Next Step Prepare to Evaluate
∴ Ay=161.87-272.7⋅0.076219.8066⋅1551.4⋅3.4907⋅6780094900+67800
Next Step Evaluate
∴Ay=9.81023594081167m/s²
LAST Step Rounding Answer
∴Ay=9.8102m/s²

Lateral Acceleration given Rear Lateral Load Transfer Formula Elements

Variables
Constants
Lateral Acceleration
Lateral Acceleration is the acceleration in the lateral direction when the vehicle is cornering.
Symbol: Ay
Measurement: AccelerationUnit: m/s²
Note: Value can be positive or negative.
Formulas to find Lateral AccelerationOpen Variable
Rear Lateral Load Transfer
Rear Lateral Load Transfer is the load transfer in the rear wheels due to lateral acceleration.
Symbol: Wr
Measurement: WeightUnit: kg
Note: Value can be positive or negative.
Formulas to find Rear Lateral Load TransferOpen Variable
Horizontal Distance of C.G. from Front Axle
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.
Symbol: a
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Horizontal Distance of C.G. from Front AxleOpen Variable
Wheelbase of Vehicle
Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
Symbol: b
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Wheelbase of VehicleOpen Variable
Rear Roll Centre Height
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.
Symbol: Zrr
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Rear Roll Centre HeightOpen Variable
Mass of Vehicle
Mass of Vehicle is the total mass of the vehicle.
Symbol: m
Measurement: WeightUnit: kg
Note: Value should be greater than 0.
Formulas to find Mass of VehicleOpen Variable
Rear Track Width
Rear Track Width is the distance between the centres of the rear wheels.
Symbol: tr
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Rear Track WidthOpen Variable
Centre of Gravity Distance to Roll Axis
Centre of Gravity Distance to Roll Axis is the distance between the centre of gravity and the roll axis.
Symbol: H
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Formulas to find Centre of Gravity Distance to Roll AxisOpen Variable
Rear Roll Rate
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.
Symbol: KΦr
Measurement: Torsion ConstantUnit: Nm/rad
Note: Value should be greater than 0.
Formulas to find Rear Roll RateOpen Variable
Front Roll Rate
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.
Symbol: KΦf
Measurement: Torsion ConstantUnit: Nm/rad
Note: Value should be greater than 0.
Formulas to find Front Roll RateOpen Variable
Gravitational acceleration on Earth
Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.
Symbol: [g]
Value: 9.80665 m/s²

Other formulas in Rear Lateral Load Transfer category

​Go Rear Lateral Load Transfer
Wr=Ay[g]⋅mtr⋅H⋅KΦrKΦf+KΦr+ab⋅Zrr
​Go Rear Track Width given Rear Lateral Load Transfer
tr=Ay[g]⋅m⋅H⋅KΦrKΦf+KΦrWr-ab⋅Zrr

How to Evaluate Lateral Acceleration given Rear Lateral Load Transfer?

Lateral Acceleration given Rear Lateral Load Transfer evaluator uses 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)) to evaluate the Lateral Acceleration, The Lateral acceleration given rear lateral load transfer formula is used to find the acceleration along the lateral direction of the vehicle during the cornering when the rear lateral load transfer is known. Lateral Acceleration is denoted by Ay symbol.

How to evaluate Lateral Acceleration given Rear Lateral Load Transfer using this online evaluator? To use this online evaluator for Lateral Acceleration given Rear Lateral Load Transfer, enter Rear Lateral Load Transfer (Wr), Horizontal Distance of C.G. from Front Axle (a), Wheelbase of Vehicle (b), Rear Roll Centre Height (Zrr), Mass of Vehicle (m), Rear Track Width (tr), Centre of Gravity Distance to Roll Axis (H), Rear Roll Rate (KΦr) & Front Roll Rate (KΦf) and hit the calculate button.

FAQs on Lateral Acceleration given Rear Lateral Load Transfer

What is the formula to find Lateral Acceleration given Rear Lateral Load Transfer?
The formula of Lateral Acceleration given Rear Lateral Load Transfer is expressed as 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)). Here is an example- 9.784169 = (161.87-27/2.7*0.0762)/(1/[g]*155/1.4*3.4907*67800/(94900+67800)).
How to calculate Lateral Acceleration given Rear Lateral Load Transfer?
With Rear Lateral Load Transfer (Wr), Horizontal Distance of C.G. from Front Axle (a), Wheelbase of Vehicle (b), Rear Roll Centre Height (Zrr), Mass of Vehicle (m), Rear Track Width (tr), Centre of Gravity Distance to Roll Axis (H), Rear Roll Rate (KΦr) & Front Roll Rate (KΦf) we can find Lateral Acceleration given Rear Lateral Load Transfer using the formula - 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)). This formula also uses Gravitational acceleration on Earth constant(s).
Can the Lateral Acceleration given Rear Lateral Load Transfer be negative?
Yes, the Lateral Acceleration given Rear Lateral Load Transfer, measured in Acceleration can be negative.
Which unit is used to measure Lateral Acceleration given Rear Lateral Load Transfer?
Lateral Acceleration given Rear Lateral Load Transfer is usually measured using the Meter per Square Second[m/s²] for Acceleration. Kilometer per Square Second[m/s²], Micrometer per Square Second[m/s²], Mile per Square Second[m/s²] are the few other units in which Lateral Acceleration given Rear Lateral Load Transfer can be measured.
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