An interactive tool for evaluating wave attenuation and mooring design of floating breakwaters used at marinas and aquaculture sites. Adjust the form, floater width, draft, wave height, and period to see the Macagno (1953) transmission coefficient Ct, horizontal wave force, mooring tension, and heave natural period update in real time.
Parameters
Breakwater type
Type changes the trend of added mass and drag coefficient
Floater width B
m
Effective width in the wave direction. B/L is the dominant driver of transmission
Draft D
m
Submerged depth. Governs the heave natural period T_n
Floater length L_f
m
Length perpendicular to the wave. Scales the total wave force linearly
Significant wave height Hs
m
Wave period Tp
s
Sets the deep-water wavelength L = gT²/(2π). Longer periods hurt the floater
Water depth d
m
Number of mooring lines n
Lines on one side of the floater. 4-8 is typical
Results
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Wavelength L (m)
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Transmission coeff. Ct
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Transmitted Ht (m)
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Total horiz. load (kN)
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Mooring tension (kN)
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Heave natural period (s)
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Floating breakwater — incident, reflected and transmitted waves
The incident wave from the left hits the floater; part reflects, and part travels under the hull as the transmitted wave. The orange mooring lines indicate the load direction, and the blue wave heights correspond to Hs and Ht.
Transmission Ct vs. width-to-wavelength ratio B/L
Transmission coefficient — comparison across types
Macagno (1953) simplified transmission coefficient. B = floater width, D = draft, k = 2π/L is the wavenumber, Ct is the transmission coefficient (ideally below 0.3), Hs is the incident wave height. For numerical stability this tool uses Ct = 1/√(1+(kB)²).
$$F_h = \tfrac{1}{2}\rho g H_s^{2}\!\left(1+\frac{\cosh k(d-D)}{\cosh kd}\right) \cdot L_f$$
Horizontal wave force (Morison-like simplified form). ρ = seawater density 1025 kg/m³, d = water depth, L_f = floater length.
$$T_n = 2\pi\sqrt{\frac{D}{g}}$$
Heave natural period of a rectangular floater. It depends only on draft D, and avoiding the resonance band 0.8 < Tp/T_n < 1.2 is the key design rule.
A "floating breakwater" — you just float a box on the sea and it blocks the waves? How is that different from a regular concrete breakwater?
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Good catch. A standard breakwater is gravity-type or caisson-type, stacked from the seabed up, and the cost explodes in deep water or soft soil. A floating breakwater simply floats a box at the surface and uses mooring lines to keep it in place. Wave energy is concentrated near the surface, so blocking the top few meters can already make the marina or harbor behind it much calmer. Famous examples are the MC2 marina in Monaco and Sandy Hook in the US.
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I see. So what decides how much wave you can reduce? On the left, when I raised "floater width" the "transmission coefficient Ct" dropped.
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Exactly — the dominant factor is essentially the ratio of floater width B to wavelength L. The Macagno (1953) formula gives Ct ≈ 1/√(1+(kB)²), so the larger kB = (2π × B / L), the smaller Ct. A common rule is that B/L > 0.5 brings Ct below 0.5, while B/L < 0.2 lets almost all the wave through. That is why for long-period swells (Tp ≥ 10 s) you need either a 20 m+ wide floater or a Catamaran that gains effective width.
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What if you can't go that big? A marina rarely has room for a 20 m floater.
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Realistically, that's right. So floating breakwaters are limited to sites where short-period waves dominate. Typical targets are harbor wind waves (Tp = 3-5 s), ferry and vessel wake, and small everyday waves at aquaculture sites. Open-ocean swells (Tp > 8 s) are essentially impossible to block. The design routine is to first fix "what period the target wave is", then size the floater from there. In this tool you can see Ct degrade sharply when you raise Tp with B fixed.
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The mooring tension comes out pretty high. 660 kN per line — that's enough to hang a car…
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Yes, that is the weak point of a floating breakwater. All horizontal wave force is taken by the mooring lines, so even at Hs = 2 m and a 50 m floater with 4 lines, each line ends up in the few hundred kN range. In practice you compute the storm wave (50-year return period), keep MBL safety factor > 3, and select chain, synthetic rope or spiral strand. And if the anchor pulls out, it is an immediate catastrophic failure, so anchor holding capacity matters just as much. "Designing to attenuate waves" and "designing not to drift away" come as a pair.
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The heave natural period shows 2.84 s. If that is close to Tp, that's bad — right?
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That's right. When the heave natural period T_n and incident wave period Tp have a ratio between 0.8 and 1.2, resonance amplifies the response 3-5 times and mooring tension jumps accordingly. The remedies are (1) increase draft to lengthen T_n, (2) attach heave plates or skirts under the hull to gain added mass, and (3) switch to a Catamaran so the twin-hull added mass pushes T_n above 5 s. This tool flags NG inside the resonance band, so play with Tp and D to feel where the "safe zone" is.
Frequently Asked Questions
This tool applies the simplified Macagno (1953) form, Ct = 1/√(1+(kB)²), where B is the floater width and k = 2π/L is the wavenumber (L is the deep-water wavelength gT²/2π). The wider the floater and the shorter the wave (larger kB), the smaller Ct, meaning more wave attenuation. The transmitted wave height Ht = Ct·Hs controls the calmness behind the breakwater. Ct ≤ 0.5 is the usual design target, and Ct ≤ 0.3 is the benchmark for high-quality marinas.
A floating breakwater works better as the ratio of floater width B to wavelength L (B/L) increases. Empirically, B/L ≥ 0.5 gives Ct ≤ 0.5, while B/L ≤ 0.2 lets almost all the wave through (Ct ≥ 0.8). In deep water the wavelength is long, so for swells with Tp ≥ 8 s you need a wide floater (B ≥ 20 m) or a Catamaran (twin-hull) to gain effective width. Conversely, short-period harbor waves (Tp = 3-5 s) can be attenuated with a B = 5-8 m Pontoon.
The tool divides the total horizontal wave force by the number of mooring lines and assumes a 45° angle: T = F_h / (n · cos 45°). In practice you must (1) apply the storm wave (50-year return period) and keep at least a safety factor of 3 against MBL (minimum breaking load), (2) select chain, synthetic rope, or spiral strand, and (3) verify anchor holding capacity (piles, concrete blocks, or suction anchors). Adding more lines reduces tension linearly, but 4-8 lines is typical given cost and interference.
The heave natural period of a rectangular floater is approximated by T_n = 2π√(D/g), so D = 2 m gives T_n ≈ 2.84 s. If Tp falls within 0.8-1.2 times T_n, resonance amplifies the response and mooring tension spikes. Remedies are (1) increase draft to lengthen T_n, (2) add skirts or heave plates beneath the hull to gain added mass, and (3) switch to a Catamaran form for a longer T_n. This tool flags NG when the design enters the resonance zone.
Real-world applications
Marinas and yacht harbors: Sites such as the MC2 marina in Monaco, Sandy Hook in the US, and Yokohama Bayside Marina sit in deep water where fixed breakwaters are prohibitively expensive, so Pontoon or Caisson floating breakwaters are the mainstream. In sheltered bays where short-period waves dominate, a B = 6-10 m Pontoon can achieve Ct ≤ 0.4 and secure berthing calmness for yachts.
Wave attenuation for aquaculture (oysters, fish): Aquaculture sites near open water suffer facility damage and fish escapes from swells. HDPE modular floaters connected in a mat configuration (SF Marina, EZ Dock, etc.) are easy to install, can be removed or relocated, and fit well with fishing-rights constraints.
Harbor entrances and ferry terminals: Catamaran types are used to block vessel wake (short period) and to ensure user safety at terminals. The twin-hull configuration gains effective width B while keeping an opening for water exchange, so it can be designed for environmental considerations such as preventing water-quality and sediment deterioration.
Renewable-energy integration: Recent research mounts solar panels on top of floating breakwaters for combined generation, or integrates wave-energy converters (WEC such as Oscillating Water Column or Point Absorber) to harvest kinetic wave energy as electricity. Demonstration projects are running in Scotland and South Korea.
Common misconceptions and caveats
The biggest pitfall is "applying the Macagno equation directly to long-period waves (Tp > 10 s)". Macagno (1953) holds for mid-to-short period waves where B/L > 0.2; in the long-period regime where B/L is very small, the actual Ct tends to be higher than the theoretical value. Always validate the final design with physical wave-tank testing or CFD such as OpenFOAM or STAR-CCM+. This tool is for early-stage estimates only.
Next is "evaluating mooring tension with the mean wave". Real design must use the maximum wave height Hmax (about 1.8 × Hs) or the 50-year return-period wave. This tool returns values based on Hs, so for actual design work multiply by a factor of 1.8-2.5 and then keep MBL safety factor 3 — guidance from PIANC WG124 or ASCE COPRI 95-1.
Finally, "ignoring under-hull flow and sediment changes". The floater blocks water circulation, which can cause water-quality degradation (anoxia) or sediment accumulation behind it. In waters with fishing rights or in enclosed bays, leave intermittent gaps along the floater length, or use a Catamaran form to keep the bottom open. An environmental impact assessment (EIA) early in the design phase is essential.
How to Use
Enter floater dimensions: width (m), draft (m), and length (m) for your floating breakwater structure
Input significant wave height (Hs) in meters based on site wave climate data
The simulator calculates wavelength using dispersion relation, transmission coefficient via energy dissipation, and resulting mooring tension in kN
Review outputs including heave natural period to verify resonance avoidance with local wave spectra
Worked Example
A marina floating breakwater with width 3.5 m, draft 1.2 m, length 25 m encounters Hs = 1.5 m storm waves. The simulator returns wavelength L ≈ 18.6 m (for 8 s peak period), transmission coefficient Ct ≈ 0.45, transmitted wave height 0.68 m, total horizontal load 62 kN, mooring tension 78 kN per anchor line, and heave natural period 2.1 s. This 0.45 attenuation satisfies typical marina protection requiring 50% energy reduction.
Practical Notes
Increase draft to 1.8 m for winter conditions (Hs 2.0+ m) to reduce transmission coefficient below 0.35 and prevent resonance coupling with 2–3 s mooring sway periods
Verify mooring tension against anchor holding capacity; 90 kN loads typically require concrete deadweight or pile embedment in soft seabeds
Wave period dominates attenuation—short-period wind waves (4–6 s) transmit more than swell; design for spectral scatter
Heave period under 1.5 s indicates over-stiffness; soft moorings reduce impact loads on craft behind structure