Bow Diving Planes in Submarines: Analytical Sensitivity to Longitudinal Position and Finite-Element Assessment of Hull–Plane Connection Geometry

The positioning and geometry of submarine bow diving planes govern not only their contribution to pitch control but also the mechanical demand ultimately transmitted to the hull–plane connection. This study develops a sequential hydrodynamic–structural framework that traces this complete load path, from hydrodynamic force generation and pitching-moment authority to root bending and local connection stability. A conventional diesel–electric submarine is adopted as the reference configuration, combining analytical hydrodynamic formulations with finite-element assessment of the supporting structure. The results reveal that hydrodynamically equivalent solutions can produce markedly different structural consequences. Under the adopted linear formulation, a 10% increase in the longitudinal moment arm and a 10% increase in incidence provide the same relative increase in pitching moment; however, only the latter requires a proportional increase in transmitted force. Operating-condition sensitivity is dominated by local incident speed, whereas pressure-induced density variations between 50 and 300 m produce only a minor effect. Planform geometry introduces a further hydrodynamic–structural trade-off: increasing the equivalent aspect ratio from 4.00 to 6.25 reduces the incidence required for a prescribed pitching moment by approximately 12% while increasing root bending by 25%, despite an unchanged resultant lift. At the connection level, geometric redistribution and targeted stiffening outperform uniform thickness increases, with the most effective stiffening configuration increasing the elastic buckling metric by 83.8% while reducing structural weight relative to the thickest unstiffened bracket. These findings demonstrate that bow-plane design is fundamentally a load-path management problem, requiring longitudinal position, planform geometry, operating condition and connection architecture to be assessed as components of a single hydrodynamic–structural system.