Heave, pitch and two axle responses

Completed Transient Study Motion also supports local Engineering Video Export in Model or Vehicle view. Compare video is deferred.

Run a Half-Car Study

1. Open Studio in its default Half Car · 4 DOF Study. Quarter Car remains available for Transient, Frequency, Explore, Compare and Motion.
2. Start with the generic passenger-car parameters. Adjust body and suspension groups; tire, unsprung and initial-state controls are under Advanced inputs.
3. Use Front then rear for a smooth bump that excites pitch, Same at both axles for symmetry, or Independent to prescribe both axle roads.
4. Run Half-Car Study. Inspect body, pitch, suspension and tire responses, then export the completed evidence.

Inspect completed Motion

Response | Motion is available after a completed Half-Car Study. Model is a transparent longitudinal schematic; Vehicle is a contextual 3D representation with 3/4 and Side cameras. Both show body heave and pitch, independent front/rear axle vertical motion and synchronized front/rear road inputs from the same completed samples.

Play, pause, restart, speed and simulation time share one playback clock. Switching renderers preserves time; leaving Motion pauses playback. Edits retain the last completed Motion with the existing stale warning; exact restoration makes it current. Motion settings are not saved in engineering project files or included in PDF reports.

Positive pitch is nose-up, with Front on the right in Model and Side views. One vertical display scale amplifies both body attachment heights, wheels and roads. The visible body angle follows those amplified heights and is not the physical geometric angle; the physical pitch readout remains unscaled in degrees. Front road is solid and rear dashed.

Left/right wheels are mirrored: no roll, independent corners, lateral or yaw dynamics. Two local road pads show axle inputs only, not a reconstructed spatial road. Vehicle loads on demand; if WebGL is unavailable, Model, Response, road traces and readouts remain usable. Neither renderer runs a second simulation.

Road timing is scenario generation

The rear delay is wheelbase divided by speed: (a + b) / (speed in km/h / 3.6). The default 2.7 m wheelbase and 32.4 km/h speed yield 0.300 s. Speed must be 1–250 km/h, and both events must finish within the study duration. The solver consumes two explicit road definitions; speed is not part of the equations.

Equations and sign convention

Upward-positive displacements are offsets from static equilibrium. Pitch θ is positive nose-up. Front and rear suspension deflections are δf = zs + aθ − zuf and δr = zs − bθ − zur. Each suspension force is F = kδ + cδ̇.

State order: body heave, heave velocity, pitch angle, pitch rate, front unsprung displacement and velocity, rear unsprung displacement and velocity. Authoritative states use metres, seconds and radians. Model: vehiclelab.half-car.linear-passive v0.1.0; fixed-step RK4 v0.1.0.

Generic parameters

Evidence, units and freshness

Five separate plots keep heave displacement, heave acceleration, pitch angle, suspension travel and tire deflection on unambiguous axes. Front is solid and rear dashed. Display converts displacement to mm and pitch to degrees. CSV exports all 19 original channels in SI with stable unit-labelled columns, without smoothing or resampling.

The persistent Engineering Report action exports the last completed record and marks it stale after physics-affecting edits. Restoring the exact definition makes it current again. Switching models clears incompatible results. PNGs use the shared 1600 × 1000 Canvas2D renderer; PDFs use the same plots and never rerun physics.

Half-Car Transient Compare

In Compare, select Half Car · 4 DOF. Baseline and Variant A share explicit front/rear roads, all eight initial states, duration, timestep, model and solver. Variant A starts with 20% more damping at both axles. Add any of the twelve physical parameter differences; unlisted parameters follow Baseline. Axle-distance changes do not regenerate road timing.

Six grouped plots compare body acceleration, pitch, front/rear suspension travel and front/rear tire deflection. Eight metric deltas describe mathematical direction only; there is no ranking. Baseline is solid and Variant A dashed. Motion source selection preserves time, speed, camera, renderer and a display envelope covering both completed records. CSV retains original SI samples; PNG and PDF use the same evidence. Edited inputs retain the last completed comparison with a stale label; exact restoration makes it current again. Switching models clears incompatible comparison results.

Reproducible projects

The additive vehiclelab.project.v1 model union preserves existing quarter-car files. Half-car files contain definitions and project metadata only. Import restores explicit front/rear roads in Independent mode and preserves all initial states; run again to create authoritative results. Invalid files leave the workspace unchanged.

Model boundary

This is a small-angle, linear passive longitudinal half-car with generic parameters and prescribed road contact. It has no roll, lateral dynamics, nonlinear suspension, tire contact loss, active control or measured vehicle correlation. Independent numerical verification is not physical validation.

Half Car supports Transient Study, Explore and Compare, plus Study/Compare Motion and deterministic Study video export. Explore one physical parameterand promote a completed candidate deliberately. Half-Car Frequency Study and Compare are available through theshared-experiment comparison workflow.

Half-Car Frequency Study

Half-Car Frequency Study is available in Study → Half Car → Frequency. Transient response describes a road event over time; frequency response describes steady-state harmonic motion across frequency. The validated 4-DOF model retains nine complex responses with explicit rear-road delay and front-road normalization. Completed CSV, PNG and PDF exports preserve evidence; imported projects require rerunning.