What Is the Hydrodynamic Radiation Damping & Heave Resonance Calculator?
Radiation damping represents energy dissipated into radiating surface waves as a floating body oscillates.
How Does the Hydrodynamic Radiation Damping & Heave Resonance Calculator Work?
Added mass increases effective inertia, lowering the natural frequency below dry structural resonance.
Hydrodynamic Radiation Damping & Heave Resonance Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
C_{33} = \rho g A_w, \quad \omega_n = \sqrt{\frac{C_{33}}{M + A_{33}}}, \quad T_n = \frac{2\pi}{\omega_n}, \quad \zeta = \frac{B_{33}}{2\sqrt{C_{33}(M + A_{33})}}
Hydrostatic stiffness, virtual mass, heave natural period, and damping ratio.
How to Use the Hydrodynamic Radiation Damping & Heave Resonance Calculator
- Enter dry mass, added mass A33, waterplane area Aw, radiation damping B33, and fluid density.
Step-by-Step Example Calculation
Spar Buoy Heave Dynamics
Input Values:
heaveDisplacementMeters:0.5
bodyMassKg:10000
hydrodynamicAddedMassKg:5000
waterplaneAreaM2:8
radiationDampingCoeffNPerMS:3000
seawaterDensityKgPerM3:1025
Worked Steps: Predicts restoring stiffness C33 = 80.4 kN/m, natural period Tn = 2.71 s, and damping ratio = 0.043.
Understanding Your Result
Outputs natural heave period Tn, restoring stiffness C33, and non-dimensional damping ratio zeta.
Factors That Affect the Result
- Increasing waterplane area stiffens restoring forces, raising the resonant frequency.
When Should You Use This Calculator?
- Offshore spar platform design, semi-submersible stability, and wave energy converter resonance tuning.
Assumptions & Limitations
- Linear potential flow theory with uncoupled single degree of freedom heave.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Cummins equation and strip theory formulation in offshore engineering.