Unified Continuous Propulsion from Rest to Hypersonic Flight

Version 3 — corrective revision (August 2026). This version corrects a sign error inEquation (5) as published in versions 1 and 2.2, and withdraws the claims of Sections 4 and 5that depended on the erroneous form. The membrane stress of a pressurized oblate ellipsoidalshell varies as 1/sqrt(1 − ε² sin²θ), not 1/sqrt(1 + ε² sin²θ). The error was identified by theauthor through independent numerical verification against classical thin-shell theory and iscorrected at the author's initiative. Five statements are withdrawn: the quasi-uniform stressdistribution claim; the interior optimum in eccentricity derived from Equation (5); the 18–25 %area-to-volume advantage over an equivalent-volume cylinder; the wall-thickening penaltyattributed to cylindrical geometry; and the derived 40–50 % structural mass reduction. Alsowithdrawn is the statement that peak-stress reduction had been verified through coupled CFD-FEManalysis. Section 4.2 now states the classical upper bound instead: the circumferential stressof an oblate spheroid becomes compressive at the equator for ε ≥ 1/√2, beyond which the designis buckling-governed. Section 11 (new) records the erratum in citable form. The HEC principleand Equation (2) are unaffected. The geometric optimization of the chamber remains undercontinuing evaluation and continues to be the subject of the corresponding patent application.Reserved parameters remain reserved. The companion method paper (10.31224/7957) is not affected. The unification of propulsion across the full Mach 0 to Mach 12 envelope within a single enginearchitecture has remained an open problem in aerospace engineering for over seven decades.Existing combined-cycle approaches (TBCC, RBCC) rely on discrete mode-switching betweenspecialized propulsion units, incurring thrust losses of 10 to 25 percent during transitionwindows and imposing substantial structural and operational penalties. This paper presents aconceptual framework for unified continuous propulsion based on two integrated principles:(i) continuous transition of oxidizer source from catalytically-decomposed hydrogen peroxide toatmospheric air, governed by a smooth monotonic function of Mach number, and (ii) oblateellipsoidal combustion chamber geometry that accommodates radial catalytic gradient distributionand a continuous chamber-to-nozzle transition. The synergistic integration of these twoprinciples is shown qualitatively to enable continuous operation from static thrust throughhypersonic regimes without mode-switching, with improved thermal management compared tocylindrical alternatives. This version corrects a sign error in Equation (5) of the earlierversions and withdraws the claims that depended on it; see Section 11. The conceptual frameworkhas been assessed through computational fluid dynamics simulations across discrete operationalpoints spanning the full envelope. The two founding equations underlying the framework have beenformally registered with the Portuguese Institute of Industrial Property (INPI) in February 2026under provisional patent numbers 121103 L and 121102 K, with PCT international filing scheduledfor February 2027. The work positions itself within the evolving context of European hypersonicpropulsion, including the structural disruption following the dissolution of Reaction EnginesLtd. in late 2024, the consolidation of GCAP/Edgewing in April 2026 with the £686 milliondevelopment contract, and adjacent European initiatives in distinct hypersonic segments such asHypersonica (Munich/London) which demonstrated a Mach 6 solid-rocket missile flight in February2026. The work proposes a development roadmap from current TRL 2 to TRL 4 through laboratoryprototype validation.