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Caster Angle Formula

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Caster Angle is the angle between the vertical line and the steering axis, measured from the vertical line, affecting the steering system's stability and alignment. Check FAQs

Ψ c = \sin (C 1) - \sin (C 2) - (\cos (C 2) \cdot \cos (T 2) - \cos (C 1) \cdot \cos (T 1)) \cdot \frac{\tan (S)}{\cos (C 2) \cdot \sin (T 2) - \cos (C 1) \cdot \sin (T 1)}

Ψ_c - Caster Angle?C₁ - Camber 1?C₂ - Camber 2?T₂ - Toe Angle 2?T₁ - Toe Angle 1?S - Steering Axis Inclination?

Caster Angle Example

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With units

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Here is how the Caster Angle equation looks like with Values.

Here is how the Caster Angle equation looks like with Units.

Here is how the Caster Angle equation looks like.

0.0675 = \sin (0.122) - \sin (0.09) - (\cos (0.09) \cdot \cos (0.165) - \cos (0.122) \cdot \cos (0.19)) \cdot \frac{\tan (0.11)}{\cos (0.09) \cdot \sin (0.165) - \cos (0.122) \cdot \sin (0.19)}

0.0675rad = \sin (0.122rad) - \sin (0.09rad) - (\cos (0.09rad) \cdot \cos (0.165rad) - \cos (0.122rad) \cdot \cos (0.19rad)) \cdot \frac{\tan (0.11rad)}{\cos (0.09rad) \cdot \sin (0.165rad) - \cos (0.122rad) \cdot \sin (0.19rad)}

0.0675 = \sin (0.122) - \sin (0.09) - (\cos (0.09) \cdot \cos (0.165) - \cos (0.122) \cdot \cos (0.19)) \cdot \frac{\tan (0.11)}{\cos (0.09) \cdot \sin (0.165) - \cos (0.122) \cdot \sin (0.19)}

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Caster Angle Solution

Follow our step by step solution on how to calculate Caster Angle?

FIRST Step Consider the formula

Ψ c = \sin (C 1) - \sin (C 2) - (\cos (C 2) \cdot \cos (T 2) - \cos (C 1) \cdot \cos (T 1)) \cdot \frac{\tan (S)}{\cos (C 2) \cdot \sin (T 2) - \cos (C 1) \cdot \sin (T 1)}

Next Step Substitute values of Variables

∴

Ψ c = \sin (0.122rad) - \sin (0.09rad) - (\cos (0.09rad) \cdot \cos (0.165rad) - \cos (0.122rad) \cdot \cos (0.19rad)) \cdot \frac{\tan (0.11rad)}{\cos (0.09rad) \cdot \sin (0.165rad) - \cos (0.122rad) \cdot \sin (0.19rad)}

Next Step Prepare to Evaluate

∴

Ψ c = \sin (0.122) - \sin (0.09) - (\cos (0.09) \cdot \cos (0.165) - \cos (0.122) \cdot \cos (0.19)) \cdot \frac{\tan (0.11)}{\cos (0.09) \cdot \sin (0.165) - \cos (0.122) \cdot \sin (0.19)}

Next Step Evaluate

∴

Ψ c = 0.0675467386859745rad

LAST Step Rounding Answer

∴

Ψ c = 0.0675rad

Caster Angle Formula Elements

Variables

Functions

Caster Angle

Caster Angle is the angle between the vertical line and the steering axis, measured from the vertical line, affecting the steering system's stability and alignment.

Symbol: Ψ_c

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Caster Angle

Camber 1

Camber 1 is the inward or outward tilt of the wheel at the first steering position, measured from the vertical axis of the vehicle.

Symbol: C₁

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Camber 1

Camber 2

Camber 2 is the inward or outward tilt of the wheel at the second steering position, measured in degrees, affecting the vehicle's stability and handling.

Symbol: C₂

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Camber 2

Toe Angle 2

Toe Angle 2 is the angle between the vertical axis and the direction of the front wheels in a steering system, affecting vehicle stability and handling.

Symbol: T₂

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Toe Angle 2

Toe Angle 1

Toe Angle 1 is the angle between the vertical plane and the centerline of the front wheel when viewed from the front of the vehicle.

Symbol: T₁

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Toe Angle 1

Steering Axis Inclination

Steering Axis Inclination is the angle between the steering axis and the vertical line, affecting the vehicle's steering and handling characteristics.

Symbol: S

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Steering Axis Inclination

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

tan

The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle.

Syntax: tan(Angle)

Other formulas in Angles Related to Steering System category

Go Ackermann Steering Angle at Low Speed Cornering

δ S = \frac{L}{R}

Go Slip Angle at High Cornering Speed

α s = \frac{F y}{C α}

Go Ackermann Steering Angle at High Cornering Speed

δ H = 57.3 \cdot (\frac{L}{R}) + (α fw - α rw)

Go Vehicle Body Slip Angle at High Cornering Speed

β = \frac{v}{v t}

How to Evaluate Caster Angle?

Caster Angle evaluator uses Caster Angle = sin(Camber 1)-sin(Camber 2)-(cos(Camber 2)*cos(Toe Angle 2)-cos(Camber 1)*cos(Toe Angle 1))*tan(Steering Axis Inclination)/(cos(Camber 2)*sin(Toe Angle 2)-cos(Camber 1)*sin(Toe Angle 1)) to evaluate the Caster Angle, Caster Angle formula is defined as a measure of the angle created by the steering axis when viewed from the side of the vehicle, which affects the self-aligning torque and stability of the wheels, playing a crucial role in the overall handling and steering performance of a vehicle. Caster Angle is denoted by Ψ_c symbol.

How to evaluate Caster Angle using this online evaluator? To use this online evaluator for Caster Angle, enter Camber 1 (C₁), Camber 2 (C₂), Toe Angle 2 (T₂), Toe Angle 1 (T₁) & Steering Axis Inclination (S) and hit the calculate button.

FAQs on Caster Angle

What is the formula to find Caster Angle?

The formula of Caster Angle is expressed as Caster Angle = sin(Camber 1)-sin(Camber 2)-(cos(Camber 2)*cos(Toe Angle 2)-cos(Camber 1)*cos(Toe Angle 1))*tan(Steering Axis Inclination)/(cos(Camber 2)*sin(Toe Angle 2)-cos(Camber 1)*sin(Toe Angle 1)). Here is an example- 0.067547 = sin(0.122)-sin(0.09)-(cos(0.09)*cos(0.165)-cos(0.122)*cos(0.19))*tan(0.11)/(cos(0.09)*sin(0.165)-cos(0.122)*sin(0.19)).

How to calculate Caster Angle?

With Camber 1 (C₁), Camber 2 (C₂), Toe Angle 2 (T₂), Toe Angle 1 (T₁) & Steering Axis Inclination (S) we can find Caster Angle using the formula - Caster Angle = sin(Camber 1)-sin(Camber 2)-(cos(Camber 2)*cos(Toe Angle 2)-cos(Camber 1)*cos(Toe Angle 1))*tan(Steering Axis Inclination)/(cos(Camber 2)*sin(Toe Angle 2)-cos(Camber 1)*sin(Toe Angle 1)). This formula also uses Sine (sin)Cosine (cos), Tangent (tan) function(s).

Can the Caster Angle be negative?

No, the Caster Angle, measured in Angle cannot be negative.

Which unit is used to measure Caster Angle?

Caster Angle is usually measured using the Radian[rad] for Angle. Degree[rad], Minute[rad], Second[rad] are the few other units in which Caster Angle can be measured.

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Caster Angle Formula

Caster Angle Example

Caster Angle Solution

Caster Angle Formula Elements

Other formulas in Angles Related to Steering System category

How to Evaluate Caster Angle?

FAQs on Caster Angle

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