Near-limit emergency maneuvers are dominated by nonlinear tire saturation and stability constraints, calling for a short-horizon handling envelope that can be queried online. We formulate a stability-constrained finite-time reachability tube for a planar single-track vehicle with Magic-Formula tires. For a discretized primitive library and an environment channel \(e=(\mu ,s,w)\), where \(\mu\) denotes tire–road friction, s road grade, and w a crosswind surrogate, the tube \(\mathscr {T}(t,e)\) aggregates all states that remain dynamically admissible and reachable for \(0\le t\le T\). We prove compactness and, under a local robustness-of-admissibility condition, a Hausdorff-continuity result, and derive sampling-complexity scaling with time resolution, geometric tolerance, and environment dimension. Offline, we construct tube slices using analytic stability screening and nonconvex \(\alpha\)-shape reconstruction in a normalized feature space, enabling fast membership queries for online feasibility screening. The main high-fidelity benchmark is carried out on the nominal flat-road/no-wind slice \(e=(\mu ,0,0)\) with friction-only variation; the Supplementary Information extends the study to fixed grade-only, wind-only, and combined off-nominal slices, and includes a stratified CarSim spot-check on the separated grade-only and wind-only cases. On an extreme-scenario benchmark, the tube screen provides a conservative triage gate and deployment-oriented diagnostics, including conflict-time statistics, risk–coverage frontiers, baseline comparisons, and guard-band sensitivity. The approach bridges reachability analysis and reliability-facing safety screening for near-limit vehicle operation.
