Track Width of Vehicle using Ackermann Condition Solution

STEP 0: Pre-Calculation Summary
Formula Used
Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle
atw = (cot(δo)-cot(δi))*L
This formula uses 1 Functions, 4 Variables
Functions Used
cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
Variables Used
Track Width of Vehicle - (Measured in Meter) - Track Width of Vehicle is the distance between the center line of each of the two wheels on the same axle (front/rear axle).
Steering Angle Outer Wheel - (Measured in Radian) - Steering Angle Outer Wheel is the angle made by the front outer wheel with respect to vertical while taking a turn.
Steering Angle Inner Wheel - (Measured in Radian) - Steering Angle Inner Wheel is the angle made by the front inner wheel with respect to vertical while taking a turn.
Wheelbase of Vehicle - (Measured in Meter) - Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
STEP 1: Convert Input(s) to Base Unit
Steering Angle Outer Wheel: 16 Degree --> 0.27925268031904 Radian (Check conversion here)
Steering Angle Inner Wheel: 20 Degree --> 0.3490658503988 Radian (Check conversion here)
Wheelbase of Vehicle: 2.7 Meter --> 2.7 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
atw = (cot(δo)-cot(δi))*L --> (cot(0.27925268031904)-cot(0.3490658503988))*2.7
Evaluating ... ...
atw = 1.99782996584333
STEP 3: Convert Result to Output's Unit
1.99782996584333 Meter --> No Conversion Required
FINAL ANSWER
1.99782996584333 1.99783 Meter <-- Track Width of Vehicle
(Calculation completed in 00.004 seconds)

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Created by Syed Adnan
Ramaiah University of Applied Sciences (RUAS), bangalore
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11 Moments, Loads, Angles acting 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)
Critical Speed for Oversteer Vehicle
Go Critical Speed for Oversteer Vehicles = -sqrt((57.3*Wheelbase of Vehicle*Acceleration due to Gravity)/(Understeer Gradient))
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
Characteristic Speed for Understeer Vehicles
Go Characteristic Speed for Understeer Vehicles = sqrt((57.3*Wheelbase of Vehicle*Acceleration due to Gravity)/Understeer Gradient)
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)
Load on Front Axle at High Speed Cornering
Go Load on Front Axle at High Speed Cornering = (Total Load of Vehicle*Distance of c.g from Rear Axle)/Wheelbase of Vehicle
Load on Rear Axle at High Speed Cornering
Go Load on Rear Axle at High Speed Cornering = (Total Load of Vehicle*Distance of c.g from Front Axle)/Wheelbase of Vehicle
Centripetal Acceleration during Cornering
Go Centripetal Acceleration during Cornering = (Total Velocity*Total Velocity)/Radius of Turn
Lateral Acceleration during Cornering of Car
Go Horizontal Lateral Acceleration = Centripetal Acceleration during Cornering/Acceleration due to Gravity
Driveline Torque
Go Driveline Torque = Tractive Force*Radius of Tire

Track Width of Vehicle using Ackermann Condition Formula

Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle
atw = (cot(δo)-cot(δi))*L

What is ackermann steering condition?

The Ackermann steering geometry is a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii.
It was invented by the German carriage builder Georg Lankensperger in Munich in 1817, then patented by his agent in England, Rudolph Ackermann (1764–1834) in 1818 for horse-drawn carriages.

How to Calculate Track Width of Vehicle using Ackermann Condition?

Track Width of Vehicle using Ackermann Condition calculator uses Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle to calculate the Track Width of Vehicle, Track width of vehicle using Ackermann condition formula is defined as a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii. Track Width of Vehicle is denoted by atw symbol.

How to calculate Track Width of Vehicle using Ackermann Condition using this online calculator? To use this online calculator for Track Width of Vehicle using Ackermann Condition, enter Steering Angle Outer Wheel o), Steering Angle Inner Wheel i) & Wheelbase of Vehicle (L) and hit the calculate button. Here is how the Track Width of Vehicle using Ackermann Condition calculation can be explained with given input values -> 11.79331 = (cot(0.27925268031904)-cot(0.3490658503988))*2.7.

FAQ

What is Track Width of Vehicle using Ackermann Condition?
Track width of vehicle using Ackermann condition formula is defined as a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii and is represented as atw = (cot(δo)-cot(δi))*L or Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle. Steering Angle Outer Wheel is the angle made by the front outer wheel with respect to vertical while taking a turn, Steering Angle Inner Wheel is the angle made by the front inner wheel with respect to vertical while taking a turn & Wheelbase of Vehicle is the center distance between the front and the rear axle of the vehicle.
How to calculate Track Width of Vehicle using Ackermann Condition?
Track width of vehicle using Ackermann condition formula is defined as a geometric arrangement of linkages in the steering of a car or other vehicle designed to solve the problem of wheels on the inside and outside of a turn needing to trace out circles of different radii is calculated using Track Width of Vehicle = (cot(Steering Angle Outer Wheel)-cot(Steering Angle Inner Wheel))*Wheelbase of Vehicle. To calculate Track Width of Vehicle using Ackermann Condition, you need Steering Angle Outer Wheel o), Steering Angle Inner Wheel i) & Wheelbase of Vehicle (L). With our tool, you need to enter the respective value for Steering Angle Outer Wheel, Steering Angle Inner Wheel & Wheelbase of Vehicle 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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