Self Aligning Moment or Torque on Wheels Calculator

✖Aligning Moment Acting on Left Tires is the force that tends to steer the left tires of a vehicle in a particular direction.ⓘ Aligning Moment Acting on Left Tires [M_zl]			+10% -10%
✖Aligning Moment on Right Tires is the force that tends to steer the right tires and axles in a specific direction, affecting the vehicle's stability and handling.ⓘ Aligning Moment on Right Tires [M_zr]			+10% -10%
✖Lateral Inclination Angle is the angle between the vertical plane and the axis of the axle, affecting the stability and steering of a vehicle.ⓘ Lateral Inclination Angle [λ_l]			+10% -10%
✖Caster Angle is the angle between the vertical line and the pivot line of the steering axis, affecting the stability and directional control of a vehicle.ⓘ Caster Angle [ν]			+10% -10%

✖Self Aligning Moment is the torque that tries to align the wheels with the direction of travel, reducing the effort required to steer the vehicle.ⓘ Self Aligning Moment or Torque on Wheels [M_at]

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Formula

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Self Aligning Moment or Torque on Wheels

Formula

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

Example

100.1407 N*m = (27 N*m + 75 N*m) \cdot \cos (10 °) \cdot \cos (4.5 °)

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Download Forces on Steering System and Axles Formulas PDF PDF Image

Self Aligning Moment or Torque on Wheels Solution

STEP 0: Pre-Calculation Summary

Formula Used

Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)
M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν)
This formula uses 1 Functions, 5 Variables

Functions Used

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

Variables Used

Self Aligning Moment - (Measured in Newton Meter) - Self Aligning Moment is the torque that tries to align the wheels with the direction of travel, reducing the effort required to steer the vehicle.
Aligning Moment Acting on Left Tires - (Measured in Newton Meter) - Aligning Moment Acting on Left Tires is the force that tends to steer the left tires of a vehicle in a particular direction.
Aligning Moment on Right Tires - (Measured in Newton Meter) - Aligning Moment on Right Tires is the force that tends to steer the right tires and axles in a specific direction, affecting the vehicle's stability and handling.
Lateral Inclination Angle - (Measured in Radian) - Lateral Inclination Angle is the angle between the vertical plane and the axis of the axle, affecting the stability and steering of a vehicle.
Caster Angle - (Measured in Radian) - Caster Angle is the angle between the vertical line and the pivot line of the steering axis, affecting the stability and directional control of a vehicle.

STEP 1: Convert Input(s) to Base Unit

Aligning Moment Acting on Left Tires: 27 Newton Meter --> 27 Newton Meter No Conversion Required
Aligning Moment on Right Tires: 75 Newton Meter --> 75 Newton Meter No Conversion Required
Lateral Inclination Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Caster Angle: 4.5 Degree --> 0.0785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν) --> (27+75)*cos(0.1745329251994)*cos(0.0785398163397301)

Evaluating ... ...

M_at = 100.14073577601

STEP 3: Convert Result to Output's Unit

100.14073577601 Newton Meter --> No Conversion Required

FINAL ANSWER

100.14073577601 ≈ 100.1407 Newton Meter <-- Self Aligning Moment

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Front Axle and Steering » Mechanical » Forces on Steering System and Axles » Self Aligning Moment or Torque on Wheels

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Created by Syed Adnan

Ramaiah University of Applied Sciences (RUAS), bangalore

Syed Adnan has created this Calculator and 200+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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< Forces on Steering System and Axles Calculators

Self Aligning Moment or Torque on Wheels

Go Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)

Front Slip Angle at High Cornering Speed

Go Slip Angle of Front Wheel = Vehicle Body Slip Angle+(((Distance of c.g from Front Axle*Yaw Velocity)/Total Velocity)-Steer Angle)

Track Width of Vehicle using Ackermann Condition

Go Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle

Rear Slip Angle due to High Speed Cornering

Go Slip Angle of Rear Wheel = Vehicle Body Slip Angle-((Distance of c.g from Rear Axle*Yaw Velocity)/Total Velocity)

Self Aligning Moment or Torque on Wheels Formula

Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle)
M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν)

What is self aligning moment on wheels?

Self-aligning moment is a torque generated by a tire as it rolls, which tries to steer the tire back towards the direction it's moving. This happens due to the tire's deformation and the offset between the tire's contact patch and the steering axis. It helps in vehicle stability by counteracting forces that might cause it to veer off course.

How to Calculate Self Aligning Moment or Torque on Wheels?

Self Aligning Moment or Torque on Wheels calculator uses Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle) to calculate the Self Aligning Moment, Self Aligning Moment or Torque on Wheels formula is defined as a measure of the torque generated by the wheels of a vehicle, which affects the vehicle's directional stability and steering behavior, and is influenced by factors such as wheel alignment, load, and road conditions. Self Aligning Moment is denoted by M_at symbol.

How to calculate Self Aligning Moment or Torque on Wheels using this online calculator? To use this online calculator for Self Aligning Moment or Torque on Wheels, enter Aligning Moment Acting on Left Tires (M_zl), Aligning Moment on Right Tires (M_zr), Lateral Inclination Angle (λ_l) & Caster Angle (ν) and hit the calculate button. Here is how the Self Aligning Moment or Torque on Wheels calculation can be explained with given input values -> 100.1407 = (27+75)*cos(0.1745329251994)*cos(0.0785398163397301).

FAQ

What is Self Aligning Moment or Torque on Wheels?

Self Aligning Moment or Torque on Wheels formula is defined as a measure of the torque generated by the wheels of a vehicle, which affects the vehicle's directional stability and steering behavior, and is influenced by factors such as wheel alignment, load, and road conditions and is represented as M_at = (M_zl+M_zr)*cos(λ_l)*cos(ν) or Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle). Aligning Moment Acting on Left Tires is the force that tends to steer the left tires of a vehicle in a particular direction, Aligning Moment on Right Tires is the force that tends to steer the right tires and axles in a specific direction, affecting the vehicle's stability and handling, Lateral Inclination Angle is the angle between the vertical plane and the axis of the axle, affecting the stability and steering of a vehicle & Caster Angle is the angle between the vertical line and the pivot line of the steering axis, affecting the stability and directional control of a vehicle.

How to calculate Self Aligning Moment or Torque on Wheels?

Self Aligning Moment or Torque on Wheels formula is defined as a measure of the torque generated by the wheels of a vehicle, which affects the vehicle's directional stability and steering behavior, and is influenced by factors such as wheel alignment, load, and road conditions is calculated using Self Aligning Moment = (Aligning Moment Acting on Left Tires+Aligning Moment on Right Tires)*cos(Lateral Inclination Angle)*cos(Caster Angle). To calculate Self Aligning Moment or Torque on Wheels, you need Aligning Moment Acting on Left Tires (M_zl), Aligning Moment on Right Tires (M_zr), Lateral Inclination Angle (λ_l) & Caster Angle (ν). With our tool, you need to enter the respective value for Aligning Moment Acting on Left Tires, Aligning Moment on Right Tires, Lateral Inclination Angle & Caster Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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