Tidal Barrage & Ocean Wave Hydrodynamic Energy Calculator

Marine Renewable Energy & Ocean Engineering: Tidal vs. Wave Power

Marine renewable energy captures the kinetic and potential energy stored in global oceans:

• Tidal Range (Barrage) Energy: Exploits the gravitational pull of the moon and sun on Earth's oceans. Water is impounded behind a barrage dam at high tide and released through low-head hydro turbines as the tide ebbs; potential energy scales with the square of the tidal range (R^2).

• Ocean Wave Power Flux (J): Wind blowing across vast open ocean fetches transfers kinetic energy into sinusoidal surface gravity waves. In deep water, wave energy flux density (J) is proportional to the square of significant wave height (H_s^2) multiplied by the wave period (T_e), frequently delivering 40 to 70 kW per meter of open ocean coastline.

• High Predictability: Unlike intermittent wind and solar, tidal cycles are 100% predictable centuries in advance based on lunar orbital mechanics.

How to Use This Calculator

Enter your Marine Renewable Energy Mode — choose from Tidal Range / Barrage Basin (E = 1/2 A ρ g R²), Ocean Wave Energy Converter (WEC Flux J = 0.491 · Hs² · Te), Tidal Basin / Estuary Area (km² [for tidal barrage]) (e.g. 12.0 (12 km² = 12,000,000 m²)), Tidal Range Head (R in meters [high to low tide]) (e.g. 6.5 (Typical tidal range: 4 to 12 meters)), Significant Wave Height (Hs in meters [for wave energy]) (e.g. 2.5 (Open ocean swell: 1.5 to 4.5 m)), Wave Energy Peak Period (Te in seconds) (e.g. 8.5 (Deepwater ocean swell: 7 to 14 s)), Wavefront / Device Capture Width (W in meters) (e.g. 100 (100-meter wave farm or attenuator array)), and Water-to-Wire Power Conversion Efficiency (%) (e.g. 35 (Wave converters: 25%–40%, Tidal barrage: 80%–90%)). Verify your units match the formula standard (SI vs imperial) before entering values.

The Formula

Ocean Hydrodynamics \& Marine Renewable Energy equations:

Tidal Barrage Energy Potential per Tide (Joules): E_tide = (1) / (2) A ρ g R^2

Tidal Annual Generation (GWh) = E_tide × 705 tides × η3.6 × 10^12

Deepwater Ocean Wave Energy Flux (kW/m): J = (ρ g^2) / (64 π) H_s^2 T_e ≈ 0.4906 · H_s^2 · T_e

Wave Power Output (kW) = J × W_capture × η_device

Average Continuous Electrical Output (MW) = (Annual GWh × 1,000) / (8,760 Hours)

Worked Example

For example, evaluating a tidal barrage in a 12.0 km^2 estuary with a 6.5 m mean tidal range and 35.0\% efficiency: Seawater density is . Potential energy per tide is 0.5 × (12 × 10^6) × 1,025 × 9.80665 × (6.5)^2 = 2,548.7 GJ (708.0 MWh). Across the barrage generates 628.7 MWh/tide delivered, totaling 174.67 GWh/year in electrical output (19.94 MW continuous average), powering 16,635 homes.

Understanding Your Result

Energy unit conversions: 1 kWh = 3,600,000 J (3.6 MJ), 1 kcal (food calorie) = 4,184 J, 1 BTU = 1,055 J. Power benchmarks: LED bulb 8–10 W, laptop 15–60 W, desktop PC 200–500 W, hair dryer 1,000–1,800 W, electric vehicle charger (Level 2) 7,200 W. A 100W device running 10 hours uses 1 kWh. At 15 cents/kWh (US average), that's 0.

• Energy efficiency is typically more cost-effective than energy generation — 1 unit of energy saved often costs 3–5× less than 1 unit generated.