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Study / Full Car

Heave, pitch, roll and four corner responses

VehicleLab 1.3.0 exposes a linear passive vertical ride Study with seven mechanical degrees of freedom, fourteen states and independent prescribed corner roads.

Run a Full-Car Study

  1. Open Studio and choose Full Car · 7 DOF. Selecting Full-Car from any workspace reaches Study / Transient. Half-Car remains the initial Studio model.
  2. Configure Vehicle body & geometry, then Front Left (FL), Front Right (FR), Rear Left (RL) and Rear Right (RR) corner properties. The generic preset deliberately retains small left/right differences.
  3. Set four explicit road histories under Prescribed corner road inputs. Flat, smooth step, half-sine and raised-cosine inputs share the existing temporal road evaluator.
  4. Use Advanced inputs for fourteen initial-state values, duration and fixed RK4 time step. All quantities in the definition use SI.
  5. Run Full-Car Study to create immutable completed evidence in the production browser Web Worker. Edits retain the previous record and mark it stale; rerun to create current evidence. A failed run preserves the last valid record.

Coordinates and body attachment kinematics

Seven DOFs: rigid-body CG heave, pitch and roll, plus four independent unsprung vertical displacements. Fourteen interleaved states pair each displacement/angle with its velocity/rate. The state order is heave, pitch, roll, FL, FR, RL, RR, each followed by its derivative.

Coordinates are offsets from loaded static equilibrium: upward heave z, nose-up pitch θ, left-side-up roll φ. Longitudinal x is forward and lateral y is left. Gravity is balanced at equilibrium. Let a/b be CG-to-front/rear axle distances and t_f/t_r the full track widths.

zsFL=z+aθ+tf2ϕ,zsFR=z+aθ−tf2ϕz_{sFL}=z+a\theta+\frac{t_f}{2}\phi,\quad z_{sFR}=z+a\theta-\frac{t_f}{2}\phi
zsRL=z−bθ+tr2ϕ,zsRR=z−bθ−tr2ϕz_{sRL}=z-b\theta+\frac{t_r}{2}\phi,\quad z_{sRR}=z-b\theta-\frac{t_r}{2}\phi

At corner i, suspension extension is δ_i = z_si − z_ui and F_i = k_si δ_i + c_si (ż_si − ż_ui). Positive F_i acts downward on the body and upward on the unsprung mass. Tire deflection is z_ui − z_ri; linear tire stiffness supplies the restoring wheel force. Attachment velocities use the same linear kinematics.

msz¨=−∑iFi,Iyθ¨=−a(FFL+FFR)+b(FRL+FRR)m_s\ddot z=-\sum_i F_i,\quad I_y\ddot\theta=-a(F_{FL}+F_{FR})+b(F_{RL}+F_{RR})
Ixϕ¨=tf2(FFR−FFL)+tr2(FRR−FRL)I_x\ddot\phi=\frac{t_f}{2}(F_{FR}-F_{FL})+\frac{t_r}{2}(F_{RR}-F_{RL})
muiz¨ui=Fi−kti(zui−zri)m_{ui}\ddot z_{ui}=F_i-k_{ti}(z_{ui}-z_{ri})

Prescribed roads are temporal inputs

Each of the four roads is a vertical displacement versus time. They do not reconstruct a traveling spatial road surface, contact patch, vehicle trajectory or speed-dependent road. There is no Full-Car speed-to-delay helper. Independent input timing is authored explicitly and stored in projects.

Primary results and complete evidence

Six primary plots show body heave displacement (mm), body heave acceleration (m/s²), pitch angle (deg), roll angle (deg), four suspension travels (mm), and four dynamic tire deflections (mm). FL / FR / RL / RR have labels and distinct solid, dashed, dotted and dash-dot styles. Plots convert display units only; no smoothing, filtering, resampling or numerical recomputation.

Six body metrics give peak absolute and RMS heave/pitch/roll acceleration. Four suspension and four tire metrics give peak absolute corner displacement. Sample count and simulated duration complete the sixteen metrics. Angular accelerations display in deg/s² and remain rad/s² in evidence. These are neutral quantities with no comfort score, ranking or pass/fail rating.

Data & project exports all 34 authoritative CSV channels in SI, including road histories, body states/accelerations, attachment displacements, wheel displacements/velocities, suspension travels and tire deflections. Every primary plot exports PNG through the existing EngineeringPlot action. The global Engineering Report includes completed configuration, metrics, primary plots, provenance and limitations.

Reproducible definitions and provenance

Full-Car projects extend vehiclelab.project.v1 additively. They preserve model/solver identity, four roads, fourteen initial states, solver settings and metadata, with no numerical result arrays. Import restores Full-Car Study / Transient and requires Run. Incompatible or malformed files reject atomically. Quarter/Half-Car projects remain compatible, and switching model contexts preserves separate authoring and completed evidence.

Model: vehiclelab.full-car.linear-passive v0.1.0. Solver: vehiclelab.rk4.fixed-step v0.1.0. Product: VehicleLab 1.3.0; implementation milestone 1.3.0-alpha.1. Execution: Browser Web Worker, local Float64 computation.

Solver and input safeguards

The existing generic fixed-step RK4 integrates fourteen states; Full-Car introduces no second solver. Duration is 0.01–30 s, time step 0.0001–0.02 s, with at most 100,001 samples. Events must finish within the simulation duration. Finite parameter and initial-state bounds are enforced before execution. These input rails do not guarantee numerical stability for every combination of coefficients and step size.

Generic configuration

ParameterValueSI unit
Sprung mass1200kg
Pitch inertia2000kg·m²
Roll inertia550kg·m²
CG to front axle1.2m
CG to rear axle1.5m
Front track1.6m
Rear track1.58m
Front Left · FL unsprung mass30kg
Front Left · FL suspension stiffness15000N/m
Front Left · FL suspension damping1250N·s/m
Front Left · FL tire stiffness110000N/m
Front Right · FR unsprung mass31kg
Front Right · FR suspension stiffness15500N/m
Front Right · FR suspension damping1300N·s/m
Front Right · FR tire stiffness112000N/m
Rear Left · RL unsprung mass32kg
Rear Left · RL suspension stiffness16000N/m
Rear Left · RL suspension damping1350N·s/m
Rear Left · RL tire stiffness115000N/m
Rear Right · RR unsprung mass33kg
Rear Right · RR suspension stiffness16500N/m
Rear Right · RR suspension damping1400N·s/m
Rear Right · RR tire stiffness117000N/m

Relationship to Half-Car and verification

The Full-Car foundation uses the same force conventions, road evaluator and RK4 as the existing models. With identical left/right corner inputs and parameters, zero roll initial state, and axle stiffness/damping/mass/tire values split equally between corners, Full-Car reduces exactly to the longitudinal Half-Car model.

FC-001 through FC-008 verify exact zero equilibrium, left/right symmetry, exact Half-Car reduction, independent M/K/C free/forced state-space agreement, fourth-order RK4 convergence, hand-derived signs, Worker transfer integrity and strict rejection without fallback. The existing 5,003-point literature reproduction remains unchanged. Numerical verification does not establish measured vehicle correlation.

Half-Car Study · Numerical method · Verification & Validation

Assumptions and limitations

  • Linear passive vertical ride model: rigid sprung-body heave, pitch and roll plus four independent unsprung vertical motions (7 DOF / 14 interleaved states).
  • Small pitch/roll angles about static equilibrium; upward heave, nose-up pitch and left-side-up roll. Body attachments: front z + a*theta, rear z - b*theta, with left + track/2*phi and right - track/2*phi.
  • Four independent prescribed temporal corner road inputs. They are not a traveling spatial road surface; no spatial-road reconstruction.
  • Constant linear springs, dampers and tire stiffness. No contact-loss physics, nonlinear suspension, bump stops, bushings or chassis flexibility.
  • No lateral dynamics, yaw, longitudinal tire dynamics or active control.
  • Generic passenger-car preset has no measured-vehicle correlation or production-vehicle validation claim. Independent numerical verification is not physical validation.
  • Full-Car release 1.3.0 supports Transient Study only. Motion, Vehicle visualization, Engineering Video, Frequency, Explore and Compare are unavailable.