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-3	F1 lap simulation (six coupled ODEs)
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-week-10_nnph_scc	NNpHSCC full-physics (Chen-Sutherby-Xing + BS 7910)
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

ics2_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
├── assets/
│   └── outputs/                  # All generated figures saved here
├── notebooks/
│   └── explore_lap.ipynb         # Optional: interactive exploration
├── linkedin/
│   └── post_draft.txt            # LinkedIn post text
├── run_all.py                    # Master execution script
├── requirements.txt
└── 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 summary

Aero mode filter (spatial ODE): dm/ds = (m_raw - m) / tau tau = 40 m

Aerodynamic forces: F_drag = 0.5 * rho * Cd(m) * A * v^2 F_down = 0.5 * rho * Cl(m) * A * v^2

Traction ceiling: F_trac_max = mu_eff * F_down * 4

Tyre temperature ODE: dT/dt = k_heat * E_slip - k_cool * (T - T_track)

Gaussian grip window: f_T = exp( -(T - T_opt)^2 / (2 * sigma^2) ) mu_eff = mu0 * f_T * (1 - k_w * wear)

ERS SOC ODE: dSOC/dt = -P_bat / E_bat

Master equation of motion: m * dv/dt = F_drive - F_drag - F_roll - F_grade - F_brake

Integration: dt_i = ds / (v_i * cos(beta_i) + eps) t_lap = sum(dt_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.