Compare period maxima with signed instantaneous loads. Check seabed moment, wavelength and wave-only KC using reproducible examples. Educational single-cylinder model.
Wave & cylinder parameters
Presets
Wave height H
m
Wave period T
s
Water depth d
m
Cylinder diameter D
m
Current velocity Uc
m/s
Inertia coefficient Cm
Drag coefficient Cd
Changing an input recalculates results even while paused.
Results
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Maximum |force| [kN]
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Maximum |inertia| [kN]
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Maximum |drag| [kN]
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Maximum |seabed moment| [MN·m]
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Wave-only KC
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Wavelength [m]
Visualization
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Illustrative diagram: only one fixed vertical cylinder is calculated. Braces and neighbouring members are excluded.
Understand wave loading on one cylinder through inputs and phase
This educational model calculates horizontal loading on a vertical cylinder fixed to the seabed, using a linear Airy wave and a uniform current. It integrates inertia and drag per unit length over depth to obtain force and seabed moment. Seawater density is fixed at 1025 kg/m³ and gravity at 9.81 m/s².
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Student: Can I add the maximum inertia and drag values to obtain the maximum wave force?
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Professor: Generally, no. Velocity and acceleration have different phases, so their force components need not peak together. Add inertia and drag at the same phase, then find the largest absolute resultant over the period. Do not add the separate maximum cards.
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Student: Does a current create a moment even without waves?
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Professor: Yes. Select “Current only”: H=0 m and Uc=1 m/s. Drag is uniform over depth, so the 24.600 kN force acts at half the 60 m depth, or 30 m above the bed. The moment is 738 kN·m, equivalent to 0.738000 MN·m. Inertia and wave-only KC are both zero.
Examples you can reproduce in the calculator
Wave plus current: compare force and moment maxima separately
The reference example uses H=5 m, T=10 s, d=60 m, D=1 m, Uc=0.5 m/s, Cm=2 and Cd=0.8. Wavelength is 153.826 m, maximum |force| is 51.661 kN, maximum |seabed moment| is 2.022914 MN·m, and wave-only KC is 15.943. Changes in the loading height mean that maximum force and maximum moment occur at different phases.
Shallow water: check wavelength convergence
The shallow-wave example uses H=1 m, T=20 s, d=20 m, D=1 m, Uc=0, Cm=2 and Cd=0.8. The dispersion relation gives a wavelength of 270.722 m, maximum |force| of 3.423 kN and maximum |seabed moment| of 0.034836 MN·m. Depth is included in the solution rather than using the deep-water wavelength.
Steady current: check force and moment by hand
For H=0 the acceleration is zero: $F=\rho C_d D U_c|U_c|d/2$ and $M=Fd/2$. With Uc=1 m/s, d=60 m, D=1 m and Cd=0.8, F=24.600 kN and M=0.738000 MN·m. These steady-current results do not depend on wave period or inertia coefficient.
Reading the displays and using the controls
Each result card shows the maximum absolute value of that quantity over one wave period. The instantaneous readout below the diagram shows signed force and moment at the selected phase. Moving the phase slider pauses animation. Changing any of the seven physical inputs recalculates the results even while paused.
KC uses the wave-orbital velocity amplitude at still-water level: $KC=U_{wave}T/D$. Steady current Uc is excluded from KC but included in the velocity used for drag. KC alone does not determine load dominance or safety; compare the inertia and drag curves as well.
Model scope and unsuitable uses
The model assumes one constant-diameter cylinder, integration up to still-water level, constant Cm and Cd, a linear monochromatic wave and a depth-uniform current aligned with the wave motion. Braces in the jacket-style diagram are illustrative: their loads and interaction with neighbouring members are not calculated. Moving wet length, breaking, diffraction, current-induced wave changes, structural response, soil, stress, fatigue and safety factors are excluded.
Warnings flag large height/depth, height/wavelength or diameter/wavelength ratios. They are reminders, not a suitability test: the absence of a warning does not establish model validity or structural safety. Appropriate coefficients depend on flow, roughness and experimental evidence. Do not lower coefficients or alter environmental inputs just to obtain a smaller design load.
Calculation method and source
The wave number k solves $\omega^2=gk\tanh(kd)$ with a convergence check. Depth-integrated Morison inertia and signed drag give force; the seabed moment uses height above the bed as its weighting. If velocity changes sign over depth, the drag integral is split there. Periodic maxima are obtained by a full-cycle scan followed by refinement near candidate extrema.
See MIT OpenCourseWare: A. H. Techet’s Morison-equation lecture for fixed-cylinder force, depth integration and moment weighting. The examples were checked against independently solved dispersion roots, depth integration and period-maximization calculations for this simplified model. They do not certify real-sea prediction accuracy or standards compliance.
Frequently asked questions
Is maximum total force the sum of maximum inertia and drag?
Generally not. The separate components peak at different phases. Total force is formed by adding both components at the same phase before finding its maximum absolute value.
Is seabed moment maximum force times depth divided by three?
This tool does not use that approximation. It integrates signed loading weighted by height above the seabed, then finds the maximum absolute moment over the period. In a uniform steady current, the resultant acts at half the depth.
Why does changing current not change KC?
KC is defined here using wave-orbital velocity amplitude, excluding steady current. Current is included in drag, so force and moment still change.
Can these results verify offshore-platform safety?
No. This is an educational loading model for one fixed cylinder. It does not verify neighbouring members, breaking, diffraction, structural response, soil, stress, fatigue, safety factors or compliance.
Using the calculator
Choose the reference, shallow-wave or current-only preset, or change the seven inputs.
Compare period maximum absolute values in Results and the inertia, drag and total-force curves.
Use the phase slider to inspect signed instantaneous values while paused. Force and moment need not peak together.
Read warnings and model assumptions. Do not use these results to certify structural safety.
Changing height or coefficients explores load sensitivity. This tool cannot prescribe design coefficients or stress concentration factors. Conditions beyond the single-cylinder model need appropriate wave theory, experiments and structural assessment.