How do you design a rocket nozzle for optimal performance?

Rocket nozzle design aims to maximize thrust coefficient through efficient expansion. Key considerations: Area ratio (exit/throat) sized for operating altitude - under-expansion loses thrust, over-expansion causes flow separation; Contour design using bell (shorter, lighter) or ideal (conical, simple) profiles, typically 80% bell for balance; Cooling requirements for high heat flux at throat (regenerative, film, or ablative); Structural design for high temperatures and pressures; and Thrust vector control integration (gimbaling, fluid injection). Analysis uses isentropic flow relations, method of characteristics for supersonic flow, and CFD for detailed optimization. Trade studies balance performance, weight, and complexity.