Quantity-Dependent Bulk-to-Wall Observability of Surface Loading in Rarefied Hypersonic Flow over Triangular Protrusions

Localized protrusions on hypersonic vehicles generate pressure, heat-transfer, and shear loads whose rarefied response can depend on gas beyond the immediate wall neighborhood. This work quantifies that bulk-to-wall dependence for triangular protrusions and tests whether coordinate-conditioned surrogates preserve it. Geometry-consistent surrogates are trained for direct simulation Monte Carlo (DSMC) velocity, temperature, pressure, and wall-load profiles over Mach numbers 4–8, Knudsen numbers (Kn) 0.1–0.8, and three protrusion orientations. The central analysis is performed on raw DSMC fields. Around each wall point, circular neighborhoods of increasing radius are summarized by weighted statistics, extrema, nearest-point values, and tangent-normal gradients of velocity, temperature, and pressure. A fixed region-to-point diagnostic predicts the pressure coefficient ($C_p$), heat-transfer coefficient ($C_q$), and shear-stress magnitude ($\mathrm{\mid }\tau \mathrm{\mid }$). We define $R_{95}$ as the smallest tested radius whose complete wall-profile error lies within 5% of the full-domain descriptor error. The principal physical result is that rarefied surface loading has no single information length. Full-domain descriptors reduce errors from 45.5% to 13.8% for $C_p$ and from 72.6% to 12.9% for $C_q$, whereas shear improves only from 49.1% to 31.9%. Heat transfer exhibits the clearest order-$h_s$ nonlocal support, where $h_s$ is the protrusion-base length. Pressure is frequently right-censored beyond $3h_s$, and shear saturates at shorter radii but remains least identifiable. Ridge-regression and threshold controls preserve this hierarchy, while a closed-loop audit shows partial surrogate preservation, with the largest degradation in forward-facing heat transfer and shear.