Coordinate systems

Suspension Explorer uses two right-handed coordinate spaces: a chassis-fixed space for modeling and solving the suspension, and an optional world space for placing a solved axle above a level road.

Both use the same axis convention:

Axis	Positive direction
X	Forwards
Y	Left
Z	Upwards

Left-side hardpoints therefore normally have positive Y coordinates, while right-side hardpoints normally have negative Y coordinates.

Chassis space

Chassis space is fixed to the sprung mass and follows the ISO 8855 vehicle axes. All authored hardpoints, solver variables, constraints, and solved point positions use this space. Fixed chassis hardpoints remain stationary while suspension, wheel, and tire points move relative to them.

The nonlinear solver never moves or converts this coordinate system. During an axle sweep, the current road plane instead moves relative to the chassis as the axle heaves or rolls.

Mirrored axles

For a symmetric axle, author the complete left-side geometry and omit the right-side hardpoints. Suspension Explorer mirrors the geometry and applicable side-local setup through chassis Y = 0.

World space

World space is an earth-fixed presentation frame. World X and Y lie in the straight, level road plane, world Z points upwards, and gravity points along world -Z. The road therefore lies at world Z = 0.

For each solved axle state, Suspension Explorer can derive a rigid chassis-to-world transform from the two wheel contact centers. That transform:

• Places the axle’s current road plane at world Z = 0.
• Keeps chassis +X exactly aligned with world +X.
• Rotates around that shared X axis to represent axle-local roll.
• Translates vertically to represent axle-local heave.

Because one axle cannot determine a complete vehicle pose, whole-vehicle pitch, yaw, and longitudinal translation are not inferred. The model assigns those unobservable degrees of freedom zero; an opposite axle is neither required nor approximated.

WorldSpace is calculated after solving. It does not feed back into the solver or metric calculations, and the solved positions remain in chassis coordinates. It is available on valid composed-axle results; a standalone corner cannot establish axle roll and therefore has no world transform.

The road plane

The road plane is not a third coordinate system. It is an axle-local geometric plane represented in chassis coordinates.

For a composed axle, the two current wheel contact centers define a lateral road line. Suspension Explorer models the tires as rigid discs, finds the plane tangent to both, and extends that line parallel to chassis X. This construction is why chassis X and world X always remain aligned: longitudinal road gradient is zero by construction.

A standalone corner cannot infer axle roll from one contact center, so calculations that need a local road datum use a chassis-horizontal plane with a +Z normal.

A tilted road plane in chassis coordinates describes axle roll relative to the level world road. It does not represent an authored banked road. Road grade, road bank, yaw, non-planar surfaces, tire deflection, and contact-patch extent are outside the current model.

Interpreting results

Result fields deliberately use the reference system appropriate to the quantity:

Result	Reference
Authored and solved point positions	Chassis space
Camber, caster, kingpin inclination, ISO steer angle, and toe	Chassis/vehicle axes
Wheel travel, heave, instant-center coordinates, rack displacement, and roll-center coordinates	Chassis axes
ISO track	Horizontal design ground
Scrub radius, mechanical trail, track change, ride-height change, swing-arm geometry, and geometric anti percentages	Axle-local road plane represented in chassis coordinates
world_space	Optional rigid placement of a solved axle state in world space
Damper, link, and other Euclidean lengths	Identical in either space

Metrics do not consume the world transform. In particular, suspension roll is the kinematic roll of the current wheel-center line, and ride-height change is the change in perpendicular clearance from the chassis origin to the axle-local road plane. Neither is a solved whole-vehicle attitude.

Units

• Authored hardpoints and linear outputs use millimeters.
• Tire section width uses millimeters.
• Rim diameter uses inches and is converted internally at 25.4 mm/in.
• Angles use degrees in configuration and output, and radians internally.
• Wheel offset follows the ET convention: positive offset moves the wheel center inboard.

Sweep values

Sweep targets can use either of two modes:

• relative values are offsets from the authored design condition.
• For point and actuator-position targets, absolute values are projected coordinates in chassis space.
• For element-length targets, absolute values are true pin-center lengths in millimeters.

For example, a relative Z target of -40 on wheel_center requests a position 40 mm below its design-condition location. A value of 0 returns it to the authored position. An absolute point Z target is a chassis-coordinate value, not a world-fixed height.