Electro-Aero-Magnetic 5-Phase Propulsion Model: Multi-Physics Power Partitioning, Dimensional Homogeneity, Transonic Shock Scaling, and Self-Consistent Mass Closure

We establish an exhaustive, multi-physics analytical energy and power partitioning architecture spanning five distinct velocity bands of high-speed ground, subterranean, and aerial transportation: an electric hypercar (350–500 km/h), an electrodynamic maglev train (500–600 km/h), a commercial transonic airliner (600–900 km/h), a supersonic interceptor (900–1250 km/h), and an evacuated-tube hyperloop pod operating at 1250 km/h. The master power equation replaces unphysical magnetic pressure terms and redundant enthalpy losses with rigorous 3D swept aerodynamic wave-drag, velocity-dependent tire rolling resistance incorporating aerodynamic downforce, velocity-scaled electrodynamic levitation (EDS), and parasitic thermal cooling loads. Rigorous dimensional homogeneity [ML²T⁻³] is established across all terms, ensuring exact equality between electrical supply power and mechanical dissipation (LHS ≡ RHS). In the hyperloop regime (M = 1.012 in a 100 Pa tube), aerodynamic resistance is derived via normal detached shock jump conditions and Rayleigh Pitot stagnation mechanics, establishing an exact electrical power requirement of 0.593 MW. Sizing an electric airliner (70 t dry mass) reveals asymptotic closed-form quadratic convergence to an all-up mass of 108.85 tonnes (M_batt = 38.85 tonnes, E_total = 7.771 MWh), proving aerodynamic viability at a realistic battery mass fraction of 35.7%. A comprehensive 8-point validation matrix, a 200,000-sample Monte Carlo uncertainty propagation, and exhaustive historical mapping matrices are fully documented. Author / Inventor Statement: Author: Navneet Dwivedi (Independent Innovator) Originality Declaration: This transportation architecture, aerodynamic shock formulation, and recursive battery mass convergence framework represent original multi-physics investigation unifying electric, magnetic, and aerodynamic propulsion modes across five distinct vehicle classes without ad-hoc empirical scaling.