A semi-analytical triangular-cell surrogate model is presented for the rapid prediction of shock-system structure and intake-capture geometry in supersonic external-compression inlets. The method couples classical two-dimensional oblique-shock relations with a discrete triangular-cell discretization implemented in open-source Octave, and it is intended for rapid preliminary-design and system-level modeling and simulation of air-breathing defense systems. The inlet is idealized as a planar, piecewise-ramped compression system so that each station is solved sequentially for shock angle, static pressure rise, total pressure recovery, downstream Mach number, and cowl-tip placement with minimal computational cost. The model is benchmarked against a curated set of published planar and piecewise-planar inlet cases, while conical and axisymmetric references are retained for context because they exceed the strict assumptions of the present surrogate. For geometry-matched planar cases, the model reproduces the principal shock and performance trends with small errors, whereas the larger divergence observed for conical or strongly curved references is explicitly attributable to the planar idealization and incomplete geometric reporting in the source literature. The resulting implementation is orders of magnitude faster than Reynolds Averaged Navier-Stokes compressible fluid dynamics (RANS CFD) and is therefore suitable for rapid parametric sweeps, sensitivity studies, uncertainty quantification, and integration into multi-physics design workflows. The Octave code and benchmark cases are provided to support a reproducible early-stage intake design.
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