What Is the Ackermann Steering Geometry & Turning Radius Calculator?
Ackermann steering geometry solves the problem of wheels needing to trace out circles of different radii in a turn.
How Does the Ackermann Steering Geometry & Turning Radius Calculator Work?
Uses the cotangent difference equation to compute the geometrically ideal outer wheel steering angle.
Ackermann Steering Geometry & Turning Radius Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
cot(delta_o) - cot(delta_i) = rac{w}{L}, quad R = rac{L}{ andelta_{ ext{avg}}}
Ackermann condition for non-slipping pure rolling steering geometry.
How to Use the Ackermann Steering Geometry & Turning Radius Calculator
- Enter vehicle wheelbase length, track width between front steering pivots, and the inner wheel angle.
Step-by-Step Example Calculation
Midsize Passenger Car Turning Circle
Input Values:
wheelbaseM:2.7
trackWidthM:1.6
steerAngleInnerDeg:32
Worked Steps: Requires outer angle δ_o = 24.3° to achieve a smooth turning radius of 5.16 m.
Understanding Your Result
Provides outer wheel angle and turning radius to both vehicle centerline and rear axle.
Factors That Affect the Result
- High-speed driving introduces slip angles, where parallel or anti-Ackermann geometry may be preferred.
When Should You Use This Calculator?
- Automotive chassis design, autonomous mobile robot (AMR) steering, and go-kart suspension kinematics.
Assumptions & Limitations
- Applies low-speed kinematic rolling; ignores tire slip angles and centrifugal lateral load transfer.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard automotive chassis engineering kinematic model.