Divergence Half-Angle Optimisation in Conical De Laval Nozzles: Reconciling CFD and Experimental Disagreements Through Nozzle Pressure Ratio Analysis

The divergence half-angle of a convergent-divergent nozzle is the primary geometric determinant of thrust performance, yet current literature reports optimal angles ranging widely with no consensus and no agreed explanation for this spread. This review investigates whether the disagreement can be explored through a single governing variable: Nozzle Pressure Ratio (NPR), the ratio of chamber to ambient pressure that varies continuously as a rocket ascends. Combining analytical derivations from the thrust equation, numerical solution across a range of operating conditions, and a synthesis of fourteen hybrid studies organized by NPR regime, the paper establishes that the thrust-optimal divergence angle is not a fixed geometric constant but increases with NPR. The reviewed studies confirm this predicted trend while sitting systematically above the idealized theoretical curve, and experimental optima consistently exceeds computational predictions at matched NPR, indicating systematic conservatism in prevailing CFD methods. The review provides directionality, but further quantification is necessary, specifically in the transitional NPR regime.