Moment due to Vertical Force on Wheels during Steering Calculator

✖Vertical Load on Left Wheels is the downward force exerted on the left wheels of a vehicle, affecting its steering and axle performance.ⓘ Vertical Load on Left Wheels [F_zl]			+10% -10%
✖Vertical Load on Right Wheels is the downward force exerted on the right wheels of a vehicle, affecting its steering system and axle performance.ⓘ Vertical Load on Right Wheels [F_zr]			+10% -10%
✖Lateral Offset at Ground Axles is the distance from the vertical plane of the axle to the point where the steering axis intersects the ground plane.ⓘ Lateral Offset at Ground [d_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%
✖Steer Angle is the angle at which the front wheels of a vehicle are turned from their normal straight-ahead position to steer the vehicle.ⓘ Steer Angle [δ]			+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%

✖Moment arising from Vertical Forces on Wheels is the total force exerted on the wheels and axles due to the weight of the vehicle and its cargo.ⓘ Moment due to Vertical Force on Wheels during Steering [M_v]

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Formula

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Moment due to Vertical Force on Wheels during Steering

Formula

M v = ((F zl - F zr) \cdot d L \cdot \sin (ν) \cdot \cos (δ)) - ((F zl + F zr) \cdot d L \cdot \sin (λ l) \cdot \sin (δ))

Example

0.108424 N*m = ((650 N - 600 N) \cdot 0.04 m \cdot \sin (4.5 °) \cdot \cos (0.32 °)) - ((650 N + 600 N) \cdot 0.04 m \cdot \sin (10 °) \cdot \sin (0.32 °))

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Moment due to Vertical Force on Wheels during Steering Solution

STEP 0: Pre-Calculation Summary

Formula Used

Moment arising from Vertical Forces on Wheels = ((Vertical Load on Left Wheels-Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Caster Angle)*cos(Steer Angle))-((Vertical Load on Left Wheels+Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Lateral Inclination Angle)*sin(Steer Angle))
M_v = ((F_zl-F_zr)*d_L*sin(ν)*cos(δ))-((F_zl+F_zr)*d_L*sin(λ_l)*sin(δ))
This formula uses 2 Functions, 7 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)

Variables Used

Moment arising from Vertical Forces on Wheels - (Measured in Newton Meter) - Moment arising from Vertical Forces on Wheels is the total force exerted on the wheels and axles due to the weight of the vehicle and its cargo.
Vertical Load on Left Wheels - (Measured in Newton) - Vertical Load on Left Wheels is the downward force exerted on the left wheels of a vehicle, affecting its steering and axle performance.
Vertical Load on Right Wheels - (Measured in Newton) - Vertical Load on Right Wheels is the downward force exerted on the right wheels of a vehicle, affecting its steering system and axle performance.
Lateral Offset at Ground - (Measured in Meter) - Lateral Offset at Ground Axles is the distance from the vertical plane of the axle to the point where the steering axis intersects the ground plane.
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.
Steer Angle - (Measured in Radian) - Steer Angle is the angle at which the front wheels of a vehicle are turned from their normal straight-ahead position to steer the vehicle.
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.

STEP 1: Convert Input(s) to Base Unit

Vertical Load on Left Wheels: 650 Newton --> 650 Newton No Conversion Required
Vertical Load on Right Wheels: 600 Newton --> 600 Newton No Conversion Required
Lateral Offset at Ground: 0.04 Meter --> 0.04 Meter No Conversion Required
Caster Angle: 4.5 Degree --> 0.0785398163397301 Radian (Check conversion here)
Steer Angle: 0.32 Degree --> 0.0055850536063808 Radian (Check conversion here)
Lateral Inclination Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

M_v = ((F_zl-F_zr)*d_L*sin(ν)*cos(δ))-((F_zl+F_zr)*d_L*sin(λ_l)*sin(δ)) --> ((650-600)*0.04*sin(0.0785398163397301)*cos(0.0055850536063808))-((650+600)*0.04*sin(0.1745329251994)*sin(0.0055850536063808))

Evaluating ... ...

M_v = 0.108424277153825

STEP 3: Convert Result to Output's Unit

0.108424277153825 Newton Meter --> No Conversion Required

FINAL ANSWER

0.108424277153825 ≈ 0.108424 Newton Meter <-- Moment arising from Vertical Forces on Wheels

(Calculation completed in 00.004 seconds)

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Home » Physics » Automobile » Front Axle and Steering » Mechanical » Forces on Steering System and Axles » Moment due to Vertical Force on Wheels during Steering

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Created by Syed Adnan

Ramaiah University of Applied Sciences (RUAS), bangalore

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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)

Moment due to Vertical Force on Wheels during Steering Formula

Why is the moment induced due to vertical forces during steering?

Vertical forces, primarily the vehicle's weight, also induce moments during steering, this occurs due to the offset between the tire contact patch and the suspension attachment points. As the vehicle turns, the vertical load distribution shifts, causing changes in the forces acting on these points. This imbalance generates a moment around the vehicle's roll axis, influencing steering feel and response. Engineers carefully consider these moments to optimize vehicle handling characteristics.

How to Calculate Moment due to Vertical Force on Wheels during Steering?

Moment due to Vertical Force on Wheels during Steering calculator uses Moment arising from Vertical Forces on Wheels = ((Vertical Load on Left Wheels-Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Caster Angle)*cos(Steer Angle))-((Vertical Load on Left Wheels+Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Lateral Inclination Angle)*sin(Steer Angle)) to calculate the Moment arising from Vertical Forces on Wheels, Moment due to Vertical Force on Wheels during Steering formula is defined as the measure of the turning effect of a force around a pivot point, specifically the vertical force exerted on the wheels of a vehicle during steering, which affects the vehicle's stability and maneuverability. Moment arising from Vertical Forces on Wheels is denoted by M_v symbol.

How to calculate Moment due to Vertical Force on Wheels during Steering using this online calculator? To use this online calculator for Moment due to Vertical Force on Wheels during Steering, enter Vertical Load on Left Wheels (F_zl), Vertical Load on Right Wheels (F_zr), Lateral Offset at Ground (d_L), Caster Angle (ν), Steer Angle (δ) & Lateral Inclination Angle (λ_l) and hit the calculate button. Here is how the Moment due to Vertical Force on Wheels during Steering calculation can be explained with given input values -> 0.108424 = ((650-600)*0.04*sin(0.0785398163397301)*cos(0.0055850536063808))-((650+600)*0.04*sin(0.1745329251994)*sin(0.0055850536063808)).

FAQ

What is Moment due to Vertical Force on Wheels during Steering?

Moment due to Vertical Force on Wheels during Steering formula is defined as the measure of the turning effect of a force around a pivot point, specifically the vertical force exerted on the wheels of a vehicle during steering, which affects the vehicle's stability and maneuverability and is represented as M_v = ((F_zl-F_zr)*d_L*sin(ν)*cos(δ))-((F_zl+F_zr)*d_L*sin(λ_l)*sin(δ)) or Moment arising from Vertical Forces on Wheels = ((Vertical Load on Left Wheels-Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Caster Angle)*cos(Steer Angle))-((Vertical Load on Left Wheels+Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Lateral Inclination Angle)*sin(Steer Angle)). Vertical Load on Left Wheels is the downward force exerted on the left wheels of a vehicle, affecting its steering and axle performance, Vertical Load on Right Wheels is the downward force exerted on the right wheels of a vehicle, affecting its steering system and axle performance, Lateral Offset at Ground Axles is the distance from the vertical plane of the axle to the point where the steering axis intersects the ground plane, 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, Steer Angle is the angle at which the front wheels of a vehicle are turned from their normal straight-ahead position to steer the vehicle & Lateral Inclination Angle is the angle between the vertical plane and the axis of the axle, affecting the stability and steering of a vehicle.

How to calculate Moment due to Vertical Force on Wheels during Steering?

Moment due to Vertical Force on Wheels during Steering formula is defined as the measure of the turning effect of a force around a pivot point, specifically the vertical force exerted on the wheels of a vehicle during steering, which affects the vehicle's stability and maneuverability is calculated using Moment arising from Vertical Forces on Wheels = ((Vertical Load on Left Wheels-Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Caster Angle)*cos(Steer Angle))-((Vertical Load on Left Wheels+Vertical Load on Right Wheels)*Lateral Offset at Ground*sin(Lateral Inclination Angle)*sin(Steer Angle)). To calculate Moment due to Vertical Force on Wheels during Steering, you need Vertical Load on Left Wheels (F_zl), Vertical Load on Right Wheels (F_zr), Lateral Offset at Ground (d_L), Caster Angle (ν), Steer Angle (δ) & Lateral Inclination Angle (λ_l). With our tool, you need to enter the respective value for Vertical Load on Left Wheels, Vertical Load on Right Wheels, Lateral Offset at Ground, Caster Angle, Steer Angle & Lateral Inclination 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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