Caster Angle Calculator

✖Camber 1 is the inward or outward tilt of the wheel at the first steering position, measured from the vertical axis of the vehicle.ⓘ Camber 1 [C₁]			+10% -10%
✖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.ⓘ Camber 2 [C₂]			+10% -10%
✖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.ⓘ Toe Angle 2 [T₂]			+10% -10%
✖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.ⓘ Toe Angle 1 [T₁]			+10% -10%
✖Steering Axis Inclination is the angle between the steering axis and the vertical line, affecting the vehicle's steering and handling characteristics.ⓘ Steering Axis Inclination [S]			+10% -10%

✖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.ⓘ Caster Angle [Ψ_c]

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Formula

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Caster Angle

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)}

Example

0.067547 rad = \sin (0.122 rad) - \sin (0.09 rad) - (\cos (0.09 rad) \cdot \cos (0.165 rad) - \cos (0.122 rad) \cdot \cos (0.19 rad)) \cdot \frac{\tan (0.11 rad)}{\cos (0.09 rad) \cdot \sin (0.165 rad) - \cos (0.122 rad) \cdot \sin (0.19 rad)}

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Caster Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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))
Ψ_c = sin(C₁)-sin(C₂)-(cos(C₂)*cos(T₂)-cos(C₁)*cos(T₁))*tan(S)/(cos(C₂)*sin(T₂)-cos(C₁)*sin(T₁))
This formula uses 3 Functions, 6 Variables

Functions Used

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., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., tan(Angle)

Variables Used

Caster Angle - (Measured in Radian) - 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.
Camber 1 - (Measured in Radian) - Camber 1 is the inward or outward tilt of the wheel at the first steering position, measured from the vertical axis of the vehicle.
Camber 2 - (Measured in Radian) - 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.
Toe Angle 2 - (Measured in Radian) - 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.
Toe Angle 1 - (Measured in Radian) - 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.
Steering Axis Inclination - (Measured in Radian) - Steering Axis Inclination is the angle between the steering axis and the vertical line, affecting the vehicle's steering and handling characteristics.

STEP 1: Convert Input(s) to Base Unit

Camber 1: 0.122 Radian --> 0.122 Radian No Conversion Required
Camber 2: 0.09 Radian --> 0.09 Radian No Conversion Required
Toe Angle 2: 0.165 Radian --> 0.165 Radian No Conversion Required
Toe Angle 1: 0.19 Radian --> 0.19 Radian No Conversion Required
Steering Axis Inclination: 0.11 Radian --> 0.11 Radian No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ψ_c = sin(C₁)-sin(C₂)-(cos(C₂)*cos(T₂)-cos(C₁)*cos(T₁))*tan(S)/(cos(C₂)*sin(T₂)-cos(C₁)*sin(T₁)) --> 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))

Evaluating ... ...

Ψ_c = 0.0675467386859745

STEP 3: Convert Result to Output's Unit

0.0675467386859745 Radian --> No Conversion Required

FINAL ANSWER

0.0675467386859745 ≈ 0.067547 Radian <-- Caster Angle

(Calculation completed in 00.005 seconds)

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Home » Physics » Automobile » Front Axle and Steering » Steering System » Mechanical » Angles Related to Steering System » Caster Angle

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Created by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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National Institute Of Technology (NIT), Hamirpur

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< Angles Related to Steering System Calculators

Caster Angle

Go 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))

Ackermann Steering Angle at High Cornering Speed

Go Ackermann Steering Angle at High Cornering Speed = 57.3*(Wheelbase of Vehicle/Radius of Turn)+(Slip Angle of Front Wheel-Slip Angle of Rear Wheel)

Ackermann Steering Angle at Low Speed Cornering

Go Ackermann Steering Angle in Slow Speed Cornering = Wheelbase of Vehicle/Radius of Turn

Slip Angle at High Cornering Speed

Go Slip Angle at High Cornering Speed = Cornering Force/Cornering Stiffness

Caster Angle Formula

What are the types of Caster?

Positive caster is when the vehicle's wheel (and lower pivot point) is in front of the upper pivot point. Negative caster has a lower pivot point behind the upper pivot point, and zero caster means the steering axis is perpendicular to the ground.

How to Calculate Caster Angle?

Caster Angle calculator 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 calculate 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 calculate Caster Angle using this online calculator? To use this online calculator 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. Here is how the Caster Angle calculation can be explained with given input values -> 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)).

FAQ

What is 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 and is represented as Ψ_c = sin(C₁)-sin(C₂)-(cos(C₂)*cos(T₂)-cos(C₁)*cos(T₁))*tan(S)/(cos(C₂)*sin(T₂)-cos(C₁)*sin(T₁)) or 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)). Camber 1 is the inward or outward tilt of the wheel at the first steering position, measured from the vertical axis of the vehicle, 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, 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, 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 & Steering Axis Inclination is the angle between the steering axis and the vertical line, affecting the vehicle's steering and handling characteristics.

How to calculate Caster Angle?

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