Aerospike vs Bell Nozzle — Altitude Compensation

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 simulator solves the real isentropic nozzle-flow and thrust-coefficient equations for a conventional bell nozzle climbing through an exponential atmosphere, and compares it side by side against an altitude-compensating aerospike nozzle whose exhaust plume expands freely against ambient pressure instead of being confined by a fixed wall. Tune the bell's design expansion ratio and chamber pressure, watch both plumes change shape with altitude — flaring when under-expanded, necking and diamond-shocking when over-expanded — and read the live thrust-coefficient gap between the two designs on the graph.