Caster Angle Calculator

⤿

Front Axle and Steering

Driveline

Race Car Vehicle Dynamics

Suspension Geometry

Vehicle Collision

⤿

Steering System

Moments, Loads, Angles acting on Steering system and Axles

Movement Ratio

Pivot Centre, Wheel Base and Track

Turning Radius

⤿

Angles Related to Steering System

✖Camber 1 is the inward or outward tilt of the front tires as viewed from the front of the vehicle.ⓘ Camber 1 [C₁]			+10% -10%
✖Camber 2 is the inward or outward tilt of the front tires as viewed from the front of the vehicle.ⓘ Camber 2 [C₂]			+10% -10%
✖The Toe Angle 2 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above.ⓘ Toe Angle 2 [T₂]			+10% -10%
✖The Toe Angle 1 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above.ⓘ Toe Angle 1 [T₁]			+10% -10%
✖Steering Axis Inclination is defined as the angle measured in the front elevation between the steering axis and the vertical.ⓘ Steering Axis Inclination [S]			+10% -10%

✖Caster Angle is the angle that identifies the forward or backward slope of a line that is drawn through the upper and lower steering pivot points.ⓘ Caster Angle [K]

⎘ Copy

👎

Formula

✖

Caster Angle

Formula

`"K" = sin("C"_{"1"})-sin("C"_{"2"})-(cos("C"_{"2"})*cos("T"_{"2"})-cos("C"_{"1"})*cos("T"_{"1"}))*tan("S")/(cos("C"_{"2"})*sin("T"_{"2"})-cos("C"_{"1"})*sin("T"_{"1"}))`

Example

`"0.067547rad"=sin("0.122rad")-sin("0.09rad")-(cos("0.09rad")*cos("0.165rad")-cos("0.122rad")*cos("0.19rad"))*tan("0.11rad")/(cos("0.09rad")*sin("0.165rad")-cos("0.122rad")*sin("0.19rad"))`

Calculator

LaTeX

Reset

👍

Download Steering System Formulas PDF PDF Image

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))
K = 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 that identifies the forward or backward slope of a line that is drawn through the upper and lower steering pivot points.
Camber 1 - (Measured in Radian) - Camber 1 is the inward or outward tilt of the front tires as viewed from the front of the vehicle.
Camber 2 - (Measured in Radian) - Camber 2 is the inward or outward tilt of the front tires as viewed from the front of the vehicle.
Toe Angle 2 - (Measured in Radian) - The Toe Angle 2 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above.
Toe Angle 1 - (Measured in Radian) - The Toe Angle 1 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above.
Steering Axis Inclination - (Measured in Radian) - Steering Axis Inclination is defined as the angle measured in the front elevation between the steering axis and the vertical.

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

K = 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 ... ...

K = 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 00.004 seconds)

You are here -

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

Credits

Created by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has created this Calculator and 10+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 6 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))

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)

Steer Angle given Understeer Gradient

Go Steer Angle = (57.3*(Wheelbase of Vehicle/Radius of Turn))+(Understeer Gradient*Horizontal Lateral Acceleration)

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

Vehicle Body Slip Angle at High Cornering Speed

Go Vehicle Body Slip Angle = Lateral Velocity Component/Total Velocity

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, The Caster Angle castor angle is the angular displacement of the steering axis from the vertical axis of a steered wheel in a car, motorcycle, bicycle, other vehicle or a vessel, as seen from the side of the vehicle. Caster Angle is denoted by K 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 -> 0.06814 = 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?

The Caster Angle castor angle is the angular displacement of the steering axis from the vertical axis of a steered wheel in a car, motorcycle, bicycle, other vehicle or a vessel, as seen from the side of the vehicle and is represented as K = 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 front tires as viewed from the front of the vehicle, Camber 2 is the inward or outward tilt of the front tires as viewed from the front of the vehicle, The Toe Angle 2 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above, The Toe Angle 1 is the direction the tires are pointed, in relation to the vehicle centerline, viewed from above & Steering Axis Inclination is defined as the angle measured in the front elevation between the steering axis and the vertical.

How to calculate Caster Angle?

The Caster Angle castor angle is the angular displacement of the steering axis from the vertical axis of a steered wheel in a car, motorcycle, bicycle, other vehicle or a vessel, as seen from the side of the vehicle is calculated using 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 Caster Angle, you need Camber 1 (C₁), Camber 2 (C₂), Toe Angle 2 (T₂), Toe Angle 1 (T₁) & Steering Axis Inclination (S). With our tool, you need to enter the respective value for Camber 1, Camber 2, Toe Angle 2, Toe Angle 1 & Steering Axis Inclination and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search