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Track Width of Vehicle using Ackermann Condition Formula

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Track Width of Vehicle is the distance between the centerlines of the left and right wheels of a vehicle's axles, affecting its stability and steering. Check FAQs

a tw = (\cot (δ o) - \cot (δ i)) \cdot L

a_tw - Track Width of Vehicle?δ_o - Steering Angle Outer Wheel?δ_i - Steering Angle Inner Wheel?L - Wheelbase of Vehicle?

Track Width of Vehicle using Ackermann Condition Example

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Here is how the Track Width of Vehicle using Ackermann Condition equation looks like with Values.

Here is how the Track Width of Vehicle using Ackermann Condition equation looks like with Units.

Here is how the Track Width of Vehicle using Ackermann Condition equation looks like.

1.9978 = (\cot (16) - \cot (20)) \cdot 2.7

1.9978m = (\cot (16°) - \cot (20°)) \cdot 2.7m

1.9978 = (\cot (16) - \cot (20)) \cdot 2.7

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Track Width of Vehicle using Ackermann Condition Solution

Follow our step by step solution on how to calculate Track Width of Vehicle using Ackermann Condition?

FIRST Step Consider the formula

a tw = (\cot (δ o) - \cot (δ i)) \cdot L

Next Step Substitute values of Variables

∴

a tw = (\cot (16°) - \cot (20°)) \cdot 2.7m

Next Step Convert Units

∴

a tw = (\cot (0.2793rad) - \cot (0.3491rad)) \cdot 2.7m

Next Step Prepare to Evaluate

∴

a tw = (\cot (0.2793) - \cot (0.3491)) \cdot 2.7

Next Step Evaluate

∴

a tw = 1.99782996584333m

LAST Step Rounding Answer

∴

a tw = 1.9978m

Track Width of Vehicle using Ackermann Condition Formula Elements

Variables

Functions

Track Width of Vehicle

Track Width of Vehicle is the distance between the centerlines of the left and right wheels of a vehicle's axles, affecting its stability and steering.

Symbol: a_tw

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Track Width of Vehicle

Steering Angle Outer Wheel

Steering Angle Outer Wheel is the angle at which the outer wheel of a vehicle is turned in response to steering input, affecting axle movement and vehicle direction.

Symbol: δ_o

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Steering Angle Outer Wheel

Steering Angle Inner Wheel

Steering Angle Inner Wheel is the angle at which the inner wheel of a vehicle is turned in response to the driver's steering input.

Symbol: δ_i

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Steering Angle Inner Wheel

Wheelbase of Vehicle

Wheelbase of Vehicle is the distance between the center of the front and rear axles, affecting the stability and steering of a vehicle.

Symbol: L

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Wheelbase of Vehicle

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

Other formulas in Forces on Steering System and Axles category

Go Self Aligning Moment or Torque on Wheels

M at = (M zl + M zr) \cdot \cos (λ l) \cdot \cos (ν)

Go Rear Slip Angle due to High Speed Cornering

α r = β - (\frac{b \cdot r}{v t})

Go Front Slip Angle at High Cornering Speed

α f = β + ((\frac{a \cdot r}{v t}) - δ)

Go Load on Front Axle at High Speed Cornering

W fl = \frac{W \cdot b}{L}

How to Evaluate Track Width of Vehicle using Ackermann Condition?

Track Width of Vehicle using Ackermann Condition evaluator uses Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle to evaluate the Track Width of Vehicle, Track Width of Vehicle using Ackermann Condition formula is defined as the distance between the center of the left and right wheels of a vehicle, which is a critical parameter in vehicle dynamics and stability, particularly during cornering and steering maneuvers. Track Width of Vehicle is denoted by a_tw symbol.

How to evaluate Track Width of Vehicle using Ackermann Condition using this online evaluator? To use this online evaluator for Track Width of Vehicle using Ackermann Condition, enter Steering Angle Outer Wheel (δ_o), Steering Angle Inner Wheel (δ_i) & Wheelbase of Vehicle (L) and hit the calculate button.

FAQs on Track Width of Vehicle using Ackermann Condition

What is the formula to find Track Width of Vehicle using Ackermann Condition?

The formula of Track Width of Vehicle using Ackermann Condition is expressed as Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle. Here is an example- 1.99783 = (cot(0.27925268031904)-cot(0.3490658503988))*2.7.

How to calculate Track Width of Vehicle using Ackermann Condition?

With Steering Angle Outer Wheel (δ_o), Steering Angle Inner Wheel (δ_i) & Wheelbase of Vehicle (L) we can find Track Width of Vehicle using Ackermann Condition using the formula - Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle. This formula also uses Cotangent (cot) function(s).

Can the Track Width of Vehicle using Ackermann Condition be negative?

No, the Track Width of Vehicle using Ackermann Condition, measured in Length cannot be negative.

Which unit is used to measure Track Width of Vehicle using Ackermann Condition?

Track Width of Vehicle using Ackermann Condition is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Track Width of Vehicle using Ackermann Condition can be measured.

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