Nozzle Mach-Field & Altitude-Compensation Map (2D)

A rocket nozzle's expansion ratio is a fixed trade-off: cut it for sea-level pressure and you throw away thrust in vacuum; cut it for vacuum and you risk flow separation at launch. This 2D companion solves the real isentropic area–Mach relation at dozens of stations along both a fixed-ε bell nozzle and a self-adjusting aerospike, painting the resulting Mach-number field directly onto each duct's cross-section, and pairs it with a full altitude × expansion-ratio heatmap of the thrust-coefficient gain so the whole design space — not just one flight point — is visible at once.