Rao Revisited: A Reproducible Pareto Atlas of Supersonic Nozzle Contours via the Method of Characteristics with Compressible Boundary-Layer Correction
Ansh Pathak - 2026 - Preprint · Open dataset
The Method of Characteristics has drawn every supersonic nozzle since the 1950s - it turns supersonic flow into geometry, where waves are lines - yet the field lacked an open, tested, DOI-archived reference implementation. nozzlemoc fills that gap: an open-source Method-of-Characteristics design code for supersonic rocket-nozzle contours with compressible boundary-layer correction, published together with a reproducible Pareto atlas of nozzle designs. The solver agrees with the classical textbook benchmark to 0.011% and reproduces the 1952 NACA Mach-10 nozzle contour. Across the atlas, the maximum wall angle settles at a near-universal 0.550 of the exit Prandtl-Meyer angle - a sharpening of the classical half-nu rule - and a sensitivity analysis built on 8,192 coupled simulations ranks which design inputs actually govern the contour. Code is MIT-licensed; the paper, dataset and figures are archived at DOI 10.5281/zenodo.21438122.
- 0.011% - Agreement with the textbook benchmark
- 0.550 - Universal turning ratio discovered
- 1952 - NACA Mach-10 nozzle reproduced
- 8,192 - Coupled simulations · sensitivity analysis