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Vehicle Turning Circle Design Equations and Calculator

Power Transmission Design and Engineering
Engineering and Design Applications

Vehicle Turning Circle Design and Engineering Equations and Calculators.

When a vehicle is cornering, each wheel describes a turning circle. The outer turning circle, or its radius, is the main subject of interest. The calculation is not precise because when a vehicle is cornering the perpendiculars through the centers of all wheels do not intersect at the curve center point (Ackermann condition). In addition, while the vehicle is moving dynamic forces will arise that will affect the cornering maneuver. However, the following formulae can be used for estimation purposes:

Calculator Preview: Vehicle Turning Circle Equations and Calculators

Distance Between steering axis

j = s - 2r_O

Theorectical value of the outer steering angle

cotΒ_a0 = cotβ_i + j / I_kt

Steering angle deviation

Β_F = Β_a - Β_a0

Turning circle radius

r_s = I_kt / sinΒ_a0 + r_O - 50 ·Β_F

Where:

j = Distance between steering axles (mm)
I_kt = Wheelbase center to center (mm)
s = Track or whele to wheel center width (mm)
r_o = Scrub radius (mm) the distance in front view between the king pin axis and the center of the contact patch of the wheel, where both would theoretically touch the road.
β_i = Inner steering angle
β_a = Outer steering angle
r_s = Turning circule radius (mm)
β_F = Steering deviation (deg)
'a0 = Theorectical value for outer steer angle