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For Students · Renewable Integration

Renewable Integration for a Class-D amp

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a Class-D amp live below — adjust the inputs and watch it respond, right in your browser.

Wind Power

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Wind Turbine PowerLive

the Betz limit

Controls

Presets

Rotor diameter (m)

Wind speed (m/s)

Power coefficient Cp

Wind power scales with the cube of wind speed and the square of rotor diameter — which is why turbines keep getting bigger and why a windy site is worth so much more. No turbine can extract more than 59.3% of the wind's energy (the Betz limit); real machines reach about 45%. Below cut-in and above cut-out speeds they produce nothing.

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Data Inspector

Power output1.64 MW

Rated power2.83 MW

Swept area6362 m²

% of Betz limit71%

Governing equation

P = \frac{1}{2} ρ A v^{3} C_{p} = \frac{1}{2} (1.225) (6362) (10)^{3} (0.42) = 1.64 MW

Reading this result: In the ramp region power climbs with the cube of wind speed, so even a small gust adds a large jump in output.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Solar Panel

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Solar PV SystemLive

panels to kilowatt-hours

Controls

Presets

Panel area (m²)

Panel efficiency (%)

Peak sun hours/day

Tilt angle (°)

A solar array's output is its rated power (area × efficiency at 1000 W/m²) multiplied by the peak sun hours your location receives — the equivalent full-intensity hours per day. Tilt matters too: aiming the panels near your latitude maximizes annual yield. Real systems lose a bit more to heat, wiring, and inverters.

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Data Inspector

System rating4.0 kW

Daily energy19.2 kWh

Annual energy6996 kWh

Homes powered0.7

Governing equation

P = η A G = 0.20 \times 20 \times 1000 = 4000 W

Reading this result: A 4.0 kW array in 5-sun-hour sun yields about 19.2 kWh/day — roughly 0.7 average homes.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Battery Storage

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Battery Energy StorageLive

capacity, efficiency & backup

Controls

Presets

Capacity (kWh)

Round-trip efficiency (%)

Depth of discharge (%)

Daily load from battery (kWh)

A battery's rated capacity is not all usable: depth-of-discharge limits protect its life, and round-trip efficiency means some energy is lost charging and discharging. What actually reaches your home is capacity × depth-of-discharge × round-trip efficiency. Together with cycle life, these set backup duration and the cost per stored kilowatt-hour.

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Data Inspector

Usable capacity12.2 kWh

Delivered / cycle10.9 kWh

Backup time26.2 hr

Lifetime throughput66 MWh

Governing equation

E_{del} = C \cdot DoD \cdot η_{r t} = 13.5 \times 0.90 \times 0.90 = 10.9 kWh

Reading this result: Usable energy is capacity × depth-of-discharge × round-trip efficiency, so only 10.9 of 13.5 kWh (81%) reaches your home each cycle — the discharge limit removes more here than efficiency does.

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Frequently asked questions

Is this good for students?: Yes — this version of "Renewable Integration for a Class-D amp" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.