INTEGRITY CODE SERIES Week 3 — F1 Lap Simulation

INTEGRITY CODE SERIES | Week 3

Physics-informed F1 lap simulation using six coupled ODEs integrated along arc length (space-marched scheme).

Integrity Code Series

Part of an ongoing series of physics-first integrity simulators by Felipe Rocha:

#	Repo	Domain
Week 3	integrity-code-series-week3-f1-lap-simulation	F1 lap simulation (six coupled ODEs) — this repo
Week 6	integrity-code-series-week6-smartphone-galvanic	Smartphone galvanic corrosion (Laplace + Butler-Volmer)
Week 7	integrity-code-series-week7-h2-lferw	LF-ERW H2 conversion (B31.12 + NACE TM0316)
Week 8	integrity-code-series-week8-creep-fatigue-heater	Creep-fatigue 9Cr-1Mo (Norton/Omega + Coffin-Manson)
Week 9	integrity-code-series-week9-cui	CUI thermohygro-electrochemical (3 PDEs, Strang)
Week 10	integrity-code-series-week10-nnph-scc	NNpHSCC full-physics (Chen-Sutherby-Xing + BS 7910)
Week 11	integrity-code-series-week11-erosion-corrosion-multiphase	Erosion-corrosion multiphase (NORSOK M-506 + DNV-RP-O501 + G119 + API 579)
Bonus	Vibration-Accelerated-Corrosion-Coupled-Mechano-Electrochemical-Simulation	Vibration-accelerated corrosion (SDOF + Butler-Volmer + Archard)
Bonus	synthetic-integrity-digital-twin-piml	Physics-informed neural-network surrogate
Bonus	integrity-data-foundation	Engineering data validation baseline

What this repository is

A reproducible, physics-grounded lap simulation with:

• Six simultaneous state variables: v, beta, SOC, fuel, T_tire, wear
• First-order spatial aero mode filter
• Gaussian thermal grip window
• ERS regen/deploy gate logic
• Full longitudinal dynamics with traction ceiling

No proprietary data. No ML. Classical numerical integration only.

Repository structure

integrity-code-series-week3-f1-lap-simulation/
├── src/
│   ├── simulation/
│   │   └── physics_model.py      # All governing equations + integrator
│   ├── visualization/
│   │   ├── plot_lap.py           # 5 static visualizations
│   │   └── generate_gif.py       # Animated GIF of tyre thermal evolution
│   └── validation/
│       └── validate_physics.py   # 9 physics consistency tests
├── docs/
│   └── equations.html            # Rendered (MathJax) governing-equations reference
├── notebooks/
│   └── explore_lap.ipynb         # Optional: interactive exploration
├── assets/
│   └── outputs/                  # Generated at run time — all figures + GIF saved here
├── run_all.py                    # Master execution script
├── pytest.ini                    # Test discovery config (collects the 9 validation tests)
├── requirements.txt
├── CHANGELOG.md
├── LICENSE
└── README.md

Execution order

# 1. Install dependencies
pip install -r requirements.txt

# 2. Run everything
python run_all.py

This single command runs validation, simulation, all visualizations, and the GIF generator in the correct dependency order.

Individual modules

# Physics validation only
python src/validation/validate_physics.py

# Simulation only
python src/simulation/physics_model.py

# Visualizations only (requires simulation to have run)
python src/visualization/plot_lap.py

# GIF only
python src/visualization/generate_gif.py

Governing Equations

view the full rendered reference

Full rendered (MathJax) reference: docs/equations.html — open in any browser. Every relation below is transcribed from src/simulation/physics_model.py; standard-mechanics relations are tagged [SOURCE] and model-specific proxies/coefficients [ASSUMED] in the rendered page.

Aero mode filter (spatial ODE):

$$ \frac{dm}{ds} ;=; \frac{m_{\text{raw}} - m}{\tau_{\text{aero}}}, \qquad \tau_{\text{aero}} = 40\ \text{m} $$

Aerodynamic drag and downforce:

$$ F_{\text{drag}} ;=; \tfrac{1}{2},\rho,C_d(m),A,v^{2}, \qquad F_{\text{down}} ;=; \tfrac{1}{2},\rho,C_l(m),A,v^{2} $$

Master equation of motion:

$$ m_{\text{car}},\frac{dv}{dt} ;=; F_{\text{drive}} - F_{\text{drag}} - F_{\text{roll}} - F_{\text{grade}} - F_{\text{brake}} $$

Tyre temperature ODE:

$$ \frac{dT}{dt} ;=; k_{\text{heat}},E_{\text{slip}} - k_{\text{cool}},(T - T_{\text{track}}), \qquad E_{\text{slip}} ;=; \bigl(|\beta| + 0.25,b\bigr),v^{2}\cdot 0.1 $$

Gaussian grip window:

$$ f_T ;=; \exp!\left(-\frac{(T - T_{\text{opt}})^{2}}{2,\sigma^{2}}\right), \qquad \mu_{\text{eff}} ;=; \mu_0,f_T,(1 - k_w,\text{wear}) $$

ERS SOC ODE:

$$ \frac{d,\text{SOC}}{dt} ;=; -\frac{P_{\text{bat}}}{E_{\text{bat}}} $$

Space-marched integration:

$$ \Delta t_i ;=; \frac{\Delta s}{v_i,\cos\beta_i + \varepsilon}, \qquad t_{\text{lap}} ;=; \sum_i \Delta t_i $$

Key parameters

Parameter	Value	Description
m_car	768 kg	Car + driver mass
L	3300 m	Track length
N	1600	Spatial nodes
T_opt	95 C	Peak grip temperature
sigma	20 C	Thermal window half-width
E_bat	4.0 MJ	Battery energy
P_deploy_max	350 kW	MGU-K deploy ceiling
P_regen_max	250 kW	Regen ceiling

Outputs

File	Description
lap_telemetry.png	6-panel: v, T, mu, SOC, P_MGUK, wear
thermal_grip_map.png	mu_eff contour vs T and wear
sensitivity_v_mu.png	Lap time sensitivity to mu0 and T_opt
residual_energy.png	ERS energy audit with SOC
track_heatmap.png	XY track colored by speed
tyre_thermal_evolution.gif	Animated thermal/grip/SOC evolution

Reproducibility

Results are deterministic. Random seed is fixed at 42 in track geometry generation. Running run_all.py twice produces identical outputs.

Escalation Table

Week	Topic	Key escalation
3	F1 lap	Six coupled state ODEs (v, β, SOC, fuel, T_tire, wear) space-marched along arc length, with a Gaussian thermal grip window, a first-order spatial aero-mode filter, and an ERS deploy/regen gate
9	CUI	3 coupled PDEs, Strang splitting
10	NNpHSCC	Chen-Sutherby-Xing crack growth, crack colony, COV=61.2% epistemic
11	Erosion-corrosion	Coupled DNV erosion + NORSOK CO2 + Beggs-Brill flow + G119 synergy + API 579 Part 5 FFS

Cybersecurity (STRIDE)

This is a self-contained, offline research simulation: no network calls, no external inputs, no secrets, and no persisted state beyond generated figures. The STRIDE attack surface is therefore limited to code and parameter integrity. Mitigations in scope:

• Tampering — deterministic run (fixed seed 42) makes any change to code or parameters reproducible and diff-visible; the physics-consistency suite (src/validation/validate_physics.py, 9 tests) fails closed if governing-equation behaviour drifts (grip peak, SOC/temperature bounds, wear monotonicity, lap-time range).
• Information disclosure — no proprietary data and no ML; all inputs are the published CarParams/TrackParams defaults.
• Denial of service — bounded work (N spatial nodes, single stint) and clipped state variables prevent runaway integration.

Repudiation, Spoofing, and Elevation-of-Privilege are out of scope for a local, single-user, no-I/O tool.

Anti-Hallucination Note

Every relation in this package is standard classical mechanics or an explicitly labelled modelling choice — nothing is attributed to a standard or paper it does not come from. The tiers below are applied honestly in docs/equations.html:

• T1 (SOURCE) — textbook physics reproduced as-is: Newton's second law (longitudinal EOM), the aerodynamic force law F = ½ρC A v², the Gaussian grip window, and the explicit space-marched integrator.
• T2 (derived) — quantities computed from T1 relations and the model parameters (traction ceiling from friction × downforce, slip-energy, lap time as the sum of local time steps).
• T3 (ASSUMED / heuristic) — model-specific proxies and tuned coefficients: the first-order aero-mode smoothing length, the curvature-based slip-angle and brake proxies, and the tyre heating/cooling/wear coefficients. These are engineering choices, not measured or standard values, and are tagged [ASSUMED] in the rendered equations. No external standard, DOI, or literature citation is claimed anywhere in this repository.

Disclaimer

Research tool only. Not for design, fitness-for-service, or safety-critical decisions without site-specific calibration and independent PE review.

This simulation is a physics-grounded teaching and exploration model. It uses no proprietary data, no measured tyre/aero maps, and no external standard; several coefficients are engineering assumptions (see the Anti-Hallucination Note). It is not a substitute for validated vehicle-dynamics tools.

License

MIT — Felipe Rocha. See LICENSE. Usage restrictions, if any, are covered by the Disclaimer above; the software itself is released under the MIT License.

How to Cite

If this software contributes to your work, please cite it:

Rocha, F. (2026). Integrity Code Series — Week 3 — F1 Lap Simulation (Six Coupled ODEs) [Computer software]. GitHub. https://github.com/felipearocha/integrity-code-series-week3-f1-lap-simulation

BibTeX:

@software{rocha_2026_ics_week3_f1_lap,
  author    = {Rocha, Felipe},
  title     = {{Integrity Code Series --- Week 3 --- F1 Lap Simulation
               (Six Coupled ODEs)}},
  year      = 2026,
  publisher = {GitHub},
  url       = {https://github.com/felipearocha/integrity-code-series-week3-f1-lap-simulation}
}

No archival DOI (e.g. Zenodo) has been minted for this repository yet; cite the GitHub URL above. When a DOI is issued it will be added here as concept (latest) and version (pinned) identifiers.

INTEGRITY CODE SERIES

Physics-first engineering. Secure digital integrity systems. Operationally defensible decisions. Verification over visibility.