This partial calculator reconstructs the signed track and ideal rear-axle turning radii implied by an entered wheelbase and two selected front-wheel angles under ideal planar Ackermann geometry. It preserves incompatible angle order as a negative signed track. It does not design a steering linkage, steering arms, tie rod, rack, suspension or vehicle.
Steering Linkage - Ideal Ackermann Angle/Track Reconstruction
Explore the signed track and rear-axle turning radii implied by selected ideal Ackermann wheel angles.
Equation Used
- Wheelbase and the two positive steering-angle magnitudes are entered values.
- Angles are measured from straight ahead for one ideal low-speed planar turn.
- A positive-track Ackermann selection requires inside angle greater than outside angle.
- The signed track is not clamped, reordered or replaced by its absolute value.
- Linkage dimensions, tire slip, compliance, loads, dynamics and safety are excluded.
The secondary figure is an ideal Ackermann geometric construction, not a steering-linkage design.
Ideal Ackermann angle/track reconstruction
For ideal low-speed planar geometry, the inside angle must exceed the outside angle and cot(delta_o)-cot(delta_i)=T/L. The calculator solves that relation for signed track T, then reports the inside, outside and axle-center rear turning radii. A nonpositive reconstructed track is shown as an incompatible selected angle order rather than being hidden with an absolute value.
What the calculator determines
Use it to inspect whether two selected wheel angles are compatible with a positive ideal track at the entered wheelbase. The diagram is a kinematic construction only.
Selected relationships
R_i=L cot(delta_i); R_o=L cot(delta_o); T=R_o-R_i=L[cot(delta_o)-cot(delta_i)]; R_c=(R_i+R_o)/2.
Selected-input example
At 2.8 m wheelbase, 25 degrees inside angle and 18 degrees outside angle, the ideal construction gives inside rear radius about 6.005 m, outside rear radius about 8.618 m, signed reconstructed track about 2.613 m and axle-center radius about 7.311 m.
Not a linkage design
Steering-arm length and inclination, kingpin locations, tie-rod length and placement, rack travel, packaging, toe, suspension travel, compliance, backlash, tire slip, loads, steering effort, dynamic response and safety are excluded. Many real vehicles intentionally depart from ideal Ackermann behavior.
Questions
Why can reconstructed track be negative?
With positive left-turn angle magnitudes, ideal Ackermann geometry requires the inside angle to exceed the outside angle. The source input ranges permit the reverse, so the signed result is retained and flagged instead of silently taking its absolute value.
Does this calculate a steering-arm angle?
No. Steering-arm geometry depends on linkage dimensions and pivot locations that are not entered.
Does ideal geometry guarantee real tire behavior?
No. The cited SAE analysis distinguishes classic Ackermann from cases where it is not the design objective, and this calculator excludes tire slip and dynamics.
Authoritative references
- University of Florida dissertation: Simple Ackermann Steering Model — states cot(delta_o)-cot(delta_i)=t/L and the corresponding inner and outer turning-radius relations.
- University of Illinois Mechanics Reference: Steering geometry — explains why the fixed rear wheels and two front wheels require matched but different steering angles.
- SAE 2006-01-3638: Analysis of Ackermann Steering Geometry — describes classic Ackermann as orienting both tires perpendicular to a common turn center and notes that classic Ackermann is not always the objective.
References & Further Reading
- Wikipedia contributors. Ackermann steering geometry. Wikipedia
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