Spa: Point-Mass Lap¶

This page explains examples/spa/spa_lap_point_mass.py.

Learning goal¶

Run a faster, lower-complexity baseline model and understand what is gained and lost relative to single-track.

What changes vs. single-track¶

The script keeps track and vehicle setup style identical, but swaps model backend:

model = build_point_mass_model(
    vehicle=vehicle,
    physics=PointMassPhysics(
        max_drive_accel=8.0,
        max_brake_accel=16.0,
        friction_coefficient=1.7,
    ),
)

Why this model is useful¶

Fast parameter sweeps and sensitivity studies.
Clean baseline for comparing model complexity.
Lower numerical and conceptual overhead for first experiments.

What this model cannot represent¶

Yaw-state dynamics are not modeled.
Yaw moment is zero by model structure.
Tire behavior is represented as isotropic envelope simplification.

Outputs to inspect first¶

examples/output/spa/point_mass/kpis.json
examples/output/spa/point_mass/speed_trace.png
examples/output/spa/point_mass/gg_diagram.png

Theoretical foundation¶

The point-mass model uses an isotropic acceleration envelope with aero coupling. Typical relations are:

Normal-acceleration budget:

\[ a_n(v) = g + \frac{F_{\mathrm{down}}(v)}{m} \]

Lateral limit (flat road simplification):

\[ a_{y,\mathrm{lim}}(v) = \mu \, a_n(v) \]

Friction-circle coupling:

\[ a_{x,\mathrm{avail}} = a_{x,\max}\sqrt{1 - \left(\frac{a_{y,\mathrm{req}}}{a_{y,\mathrm{lim}}}\right)^2} \]

This structure is intentionally compact and efficient for fast sweeps.

Assumptions and limits¶

Yaw dynamics and axle-specific tire behavior are not represented.
Tire behavior is condensed into scalar friction/envelope parameters.
Model fidelity is lower, but computational throughput is high.

Potential learnings from the data¶

Use this model for baseline trends and wide parameter scans.
Compare against single-track before drawing conclusions on yaw-sensitive effects.
Separate differences caused by calibration (\(\mu\)) from structural model differences.