Steering and the force-feedback torque

The steer input sets the road-wheel angle through the steering ratio and Ackermann fraction; what comes back is the torque the tires put on the hand wheel, which is the signal a force-feedback wheel reproduces (ADR-0012).

Where the torque comes from

Each steered wheel turns about its kingpin axis, and three things put a moment on that axis:

• the tire's aligning moment, from the pneumatic trail: the lateral force acts behind the contact centre and tries to straighten the wheel, growing with slip angle until the trail goes to zero near the grip peak (combined slip);
• the mechanical trail from caster (steering.mechanicalTrail): the kingpin axis meets the ground ahead of the contact, so the lateral force acts on that arm too. Unlike the pneumatic trail it does not fade at the limit, which is why a car with more caster keeps some weight in the wheel when the front tires let go;
• the scrub radius (steering.scrubRadius): the contact sits outboard of the kingpin axis, so a longitudinal force steers. Equal forces on both wheels cancel; a limited-slip differential biasing drive to one wheel, a single locked wheel or a kerb on one side do not. That is torque steer.

The kingpin torques of both front wheels add up on the rack. Divided by the knuckle arm they are the rack force (RackForce); through the steering ratio, less the power assist fraction, they are the hand-wheel torque (SteeringTorque), reported in the sign of the steer input: turning right, the tires push back with a negative torque, and a force-feedback wheel is driven with that value directly.

What the device adds

The hand wheel is the input, so the core does not simulate the column. Its friction (columnFriction) and damping (columnDamping) are definition values the input package maps onto a wheel's own friction and damper effects, where the device's firmware applies them at its own rate.

Jacking

With caster and kingpin inclination, steering moves the wheels up and down relative to the chassis: the inner front wheel is pushed down, the outer lifted. A car's suspension absorbs most of it. A kart has no suspension, so the frame twists and the inner rear wheel unloads, which is the only way a solid rear axle can turn without pushing. steering.jackingRate is the linearised version: metres of front contact travel per radian of steer, inner down and outer up; the body's roll and pitch stiffness carry the difference diagonally.

Compliance steer

A real steering system is not rigid. The column, rack mounts and linkage wind up under the kingpin torque, and the suspension's rubber bushings let each wheel turn a little under its own lateral force. Both make a car understeer more as it corners harder, and both are standard kinematics-and-compliance rig measures (ADR-0027).

• steering.alignTorqueComplianceDeg: degrees of road-wheel steer per kN·m of the steered axle's total kingpin torque, with the hand wheel held. Both steered wheels turn in the direction the torque pushes them: out of the turn in steady cornering, and toward the harder-braking wheel on a split surface when the scrub radius is positive. A firm rack-and-pinion car is around 1 to 2; a recirculating-ball SUV can be near 10.
• axles[].lateralComplianceSteerDeg: each wheel's steer per kN of its own lateral force, positive understeer on either axle, so the front steers away from its force and the rear toward it. Typical values are a few hundredths to a few tenths; negative is oversteer compliance.

The understeer gradient grows by Gillespie's terms: c_at · (t_m + t_p) · W_f / g for the kingpin torque (mechanical plus pneumatic trail on the front axle load W_f), and (c_f · W_f + c_r · W_r) / (2 g) for the lateral compliances, with the rates in radians. Both act through the previous substep's forces and are in the snapshot. ComplianceSteer_FL … ComplianceSteer_RR report each wheel's compliance angle, which WheelSteer_* includes; SteerAngle stays the driver's. Both models carry it.