Floating Bodies Equilibrium Conditions Due to Waves: Part 1

Fundamental analysis of wave effects on ship dynamics is traditionally based on the Froude-Krylov hypothesis, which relies on the balance of hydrostatic forces. A byproduct of this conventional approach is the assumption that these forces generate a torque governed by the frequency of the incoming wave, inherently treating the standard horizontal surface as the continuous state of equilibrium. This study directly challenges that convention by investigating the exact physical orientation where the righting arm reaches zero and transitions from positive to negative. The core methodology models the local wave as an oblique surface, a fundamental geometric simplification to which any continuous wave can be reduced. Three distinct operational regimes are identified, with the primary regime analyzed in depth to establish the theoretical baseline for this approach. The mathematical model demonstrates that a ship reaches true dynamic equilibrium when its body inclination matches the wave slope. This finding is a profound departure from classical theory, which assumes the equilibrium equations must be balanced relative to a horizontal plane. Consequently, this paper proves that standard righting arm curves must be fundamentally redefined-taking on a completely different form and rsymmetry than traditional horizontal cases-to ensure accurate ship maneuvering and stability calculations in active seaways.