Hurricanes are heat engines. Emanuel MPI scales as Vmax² ∝ (SST − T_out) × efficiency, with a practical threshold near 26.5 °C. Coriolis parameter f = 2Ω sin φ organises inflow into a cyclone — within ~5° of the equator f is too small and no closed eye forms. Vertical shear ventilates the warm core; above ~12–15 m/s most storms weaken. Central pressure uses a Holland-style vortex: V(r) = Vmax · (r/rm) · exp((1 − (r/rm)²)/2).