Moment about Steeraxis due to Driveline Torque Solution

STEP 0: Pre-Calculation Summary
Formula Used
Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal)))
Msa = Fx*((d*cos(ν)*cos(λl))+(Re*sin(λl+ζ)))
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 about Steeraxis due to Driveline Torque - (Measured in Newton Meter) - Moment about Steeraxis due to Driveline Torque is defined as the moment arising on the steeraxis because of the driveline torque.
Tractive Force - (Measured in Newton) - Tractive Force is defined as the component of force acting on the wheel in the direction of travel which is in x_direction.
Distance between Steeraxis and Tire center - (Measured in Meter) - Distance between steeraxis and tire center is defined as the horizontal distance between the center of the tire and the bottom side of steeraxis.
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.
Lateral Inclination Angle - (Measured in Radian) - Lateral Inclination Angle is the inclination of the kingpin with respect to the vertical axis laterally.
Radius of Tire - (Measured in Meter) - Radius of Tire is defined as the radius of a tire of a car.
Angle made by Front Axle with Horizontal - (Measured in Radian) - Angle made by Front Axle with Horizontal is defined as the inclination of the front axle from the horizontal axis.
STEP 1: Convert Input(s) to Base Unit
Tractive Force: 450 Newton --> 450 Newton No Conversion Required
Distance between Steeraxis and Tire center: 0.21 Meter --> 0.21 Meter No Conversion Required
Caster Angle: 4.5 Degree --> 0.0785398163397301 Radian (Check conversion here)
Lateral Inclination Angle: 10 Degree --> 0.1745329251994 Radian (Check conversion here)
Radius of Tire: 0.35 Meter --> 0.35 Meter No Conversion Required
Angle made by Front Axle with Horizontal: 19.5 Degree --> 0.34033920413883 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Msa = Fx*((d*cos(ν)*cos(λl))+(Re*sin(λl+ζ))) --> 450*((0.21*cos(0.0785398163397301)*cos(0.1745329251994))+(0.35*sin(0.1745329251994+0.34033920413883)))
Evaluating ... ...
Msa = 170.334157096998
STEP 3: Convert Result to Output's Unit
170.334157096998 Newton Meter --> No Conversion Required
FINAL ANSWER
170.334157096998 170.3342 Newton Meter <-- Moment about Steeraxis due to Driveline Torque
(Calculation completed in 00.004 seconds)

Credits

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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4 Moments Acting on Steering System and Axles Calculators

Moment due to Vertical Force on Wheels during Steering
Go 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))
Moment about Steeraxis due to Driveline Torque
Go Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal)))
Moment Arising due to Lateral Forces on Wheels during Steering
Go Moment on Wheels Arising from Lateral Force = (Lateral Force on Left Wheels+Lateral Force on Right Wheels)*Radius of Tire*tan(Caster Angle)
Moment Arising from Traction Force on Wheels during Steering
Go Moment Arising from Traction Force = (Tractive Force on Left Wheels-Tractive Force on Right Wheels)*Lateral Offset at Ground

Moment about Steeraxis due to Driveline Torque Formula

Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal)))
Msa = Fx*((d*cos(ν)*cos(λl))+(Re*sin(λl+ζ)))

Why does the moment induce on the steeraxis due to driveline torque?

The forward force introduces a moment in the steering system which opposes the steer angle trying to steer the vehicle out of turn-make the vehicle understeer. That is why in Front wheel drive vehicles toe out is provided.

How to Calculate Moment about Steeraxis due to Driveline Torque?

Moment about Steeraxis due to Driveline Torque calculator uses Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal))) to calculate the Moment about Steeraxis due to Driveline Torque, The Moment about steeraxis due to driveline torque formula is defined as the moment induced on the steer axis due to the driveline torque which acts on the front axle. Moment about Steeraxis due to Driveline Torque is denoted by Msa symbol.

How to calculate Moment about Steeraxis due to Driveline Torque using this online calculator? To use this online calculator for Moment about Steeraxis due to Driveline Torque, enter Tractive Force (Fx), Distance between Steeraxis and Tire center (d), Caster Angle (ν), Lateral Inclination Angle l), Radius of Tire (Re) & Angle made by Front Axle with Horizontal (ζ) and hit the calculate button. Here is how the Moment about Steeraxis due to Driveline Torque calculation can be explained with given input values -> 165.9162 = 450*((0.21*cos(0.0785398163397301)*cos(0.1745329251994))+(0.35*sin(0.1745329251994+0.34033920413883))).

FAQ

What is Moment about Steeraxis due to Driveline Torque?
The Moment about steeraxis due to driveline torque formula is defined as the moment induced on the steer axis due to the driveline torque which acts on the front axle and is represented as Msa = Fx*((d*cos(ν)*cos(λl))+(Re*sin(λl+ζ))) or Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal))). Tractive Force is defined as the component of force acting on the wheel in the direction of travel which is in x_direction, Distance between steeraxis and tire center is defined as the horizontal distance between the center of the tire and the bottom side of steeraxis, 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, Lateral Inclination Angle is the inclination of the kingpin with respect to the vertical axis laterally, Radius of Tire is defined as the radius of a tire of a car & Angle made by Front Axle with Horizontal is defined as the inclination of the front axle from the horizontal axis.
How to calculate Moment about Steeraxis due to Driveline Torque?
The Moment about steeraxis due to driveline torque formula is defined as the moment induced on the steer axis due to the driveline torque which acts on the front axle is calculated using Moment about Steeraxis due to Driveline Torque = Tractive Force*((Distance between Steeraxis and Tire center*cos(Caster Angle)*cos(Lateral Inclination Angle))+(Radius of Tire*sin(Lateral Inclination Angle+Angle made by Front Axle with Horizontal))). To calculate Moment about Steeraxis due to Driveline Torque, you need Tractive Force (Fx), Distance between Steeraxis and Tire center (d), Caster Angle (ν), Lateral Inclination Angle l), Radius of Tire (Re) & Angle made by Front Axle with Horizontal (ζ). With our tool, you need to enter the respective value for Tractive Force, Distance between Steeraxis and Tire center, Caster Angle, Lateral Inclination Angle, Radius of Tire & Angle made by Front Axle with Horizontal 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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