What does the wake decay k control?

It sets how quickly a wake widens and recovers speed downstream — a higher k means downwind turbines recover more of the free-stream speed sooner.

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🌬️ Wind Farm

Interactive wind-farm simulator. Each turbine extracts P = ½ρAv³Cp (Betz limit Cp ≤ 0.593); downwind turbines lose output in the velocity-deficit wake via the Jensen/Park model. Drag turbines, set wind speed and direction, and track total power, wake loss and capacity factor.

Energy & Thermodynamics3DModerate60 FPS💨 Air & Wind

About this simulation

This top-down wind farm lets you drag turbines around a shared wind field and see, in real time, how each one's output depends on the air reaching it. Every turbine downstream of another sits partly inside a wake — a cone of slowed air modelled with the Jensen/Park deficit formula — so it produces less than an isolated machine would. Because power scales with the cube of wind speed, even a modest wake deficit costs real megawatts, which is exactly why farm layout, spacing and staggering matter so much in practice.

🔬 What it shows

A grid of turbines coloured red-to-green by their current power output, each with a wake cone stretching downwind. Turbines fully inside another's wake see reduced hub-height wind speed (shown as a number above each rotor) and their power drops as v³.

🎮 How to use

Drag any turbine directly on the canvas to reposition it, or use the wind speed, wind direction, spacing, rows × cols and wake decay k sliders, or jump to a preset (Aligned grid, Staggered, Single row, Strong wind) to watch total power, capacity factor and wake loss update.

💡 Did you know?

No turbine, however well engineered, can ever convert more than 59.3% of the wind's kinetic energy into power — the Betz limit — because slowing the air completely would simply mean it can't flow past the rotor at all.

Frequently asked questions

What is the Betz limit?

It's the theoretical ceiling on how much of the wind's kinetic energy a turbine can extract, Cp ≤ 16/27 ≈ 0.593. This simulator uses a realistic Cp of 0.45, comfortably below that limit, as real turbines do.

Why do downwind turbines produce less power?

They sit inside the velocity-deficit wake of turbines upstream, modelled here with the Jensen/Park formula: wake speed recovers gradually with downstream distance x at a rate set by the wake decay constant k. Since power scales with wind speed cubed, even a small speed deficit means a big power loss.

Why does staggering rows help?

Staggered turbines are offset sideways from the ones directly upstream, so fewer of them sit inside a narrow wake cone — try the "Staggered" preset and compare its wake loss to "Aligned grid" at the same spacing.

What does the "wake decay k" slider control?

It sets how quickly a wake widens and recovers speed downstream — a higher k means the wake spreads out and fills back in faster, so downwind turbines recover more of the free-stream speed sooner.

What is capacity factor?

It's total farm output divided by what the farm would produce if every turbine ran at its rated power continuously. Wake losses, and running below or above the turbines' optimal wind-speed range, both pull capacity factor down.

⚙ Under the hood

Lay out a turbine array and see how downwind wakes (Jensen/Park model) cut output. Each turbine extracts P=½ρAv³Cp under the Betz limit; drag turbines to minimise wake losses.

EnergyWind TurbineWake EffectBetz LimitJensen Model

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install