Scrub radius, kingpin inclination, caster and trail

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Scrub radius, kingpin inclination, caster and mechanical trail all describe one line: the steering axis, through the upper and lower ball joints. Kingpin inclination and caster are its tilt in the front and side views; scrub radius and trail are where it meets the ground relative to the contact patch.

Quantity	View	Definition	Positive means
Kingpin inclination (KPI)	Front	Tilt of the steering axis from vertical	Top of the axis leans inward
Scrub radius	Front	Lateral distance on the ground from the steering axis to the contact patch center	Contact patch is outboard of the axis
Caster	Side	Tilt of the steering axis from vertical	Top of the axis leans rearward
Mechanical trail	Side	Longitudinal distance on the ground from the contact patch to the steering axis	Axis meets the ground ahead of the contact patch

Formulas

With the lower ball joint at $(x_{L}, y_{L}, z_{L})$ and the upper at $(x_{U}, y_{U}, z_{U})$ , and the contact patch at $(x_{C P}, y_{C P}, 0)$ :

KPI = arctan \frac{y _{L} - y _{U}}{z _{U} - z _{L}} caster = arctan \frac{x _{L} - x _{U}}{z _{U} - z _{L}}

Following the axis down to the ground ( $z = 0$ ):

scrub = y_{C P} - (y_{L} + z_{L} \frac{y _{L} - y _{U}}{z _{U} - z _{L}}) trail = x_{L} + z_{L} \frac{x _{L} - x _{U}}{z _{U} - z _{L}} - x_{C P}

Worked example

In the docs example double wishbone the ball joints are at $(5, 550, 120)$ and $(- 15, 530, 340)$ , and the contact patch is at $(0, 600, 0)$ . The axis rises 220 mm while moving 20 mm inboard and 20 mm rearward, so

KPI = caster = arctan \frac{20}{220} = 5.1 9^{\circ}

Below the lower ball joint the axis travels another 120 mm to the ground, moving $120 \times 20/220 = 10.9$ mm outboard and forward. It meets the ground at $y = 560.9$ mm and $x = 15.9$ mm:

scrub = 600 - 560.9 = 39.1 mm trail = 15.9 - 0 = 15.9 mm

opensus reports the same four values in the readout.

What they do

Scrub radius is the lever arm that braking and drive forces have about the steering axis. A large scrub radius makes a front wheel's braking force pull the steering; small or slightly negative is common. Wheel offset and wider tires change it.
KPI raises the car as the wheels steer, which gives self-centring at low speed, and reduces scrub radius for a given wheel packaging.
Caster gains negative camber on the outside wheel as you steer, and with trail gives the driver steering feel.
Mechanical trail is the lever arm that cornering forces have about the steering axis, adding to the tire's own pneumatic trail. More trail means heavier steering and stronger self-alignment. Compliance shows how the resulting aligning torque deflects the steering.

opensus computes these at every position and steering angle, including multilinks with a virtual steering axis. See the readout as you move the Steer slider under the 3D view.

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Last updated 2026-11-07 · View as Markdown