Explore how much the wake of an upstream turbine cuts the power of the turbines behind it. Adjust the wind speed, rotor diameter, turbine spacing, thrust coefficient and turbine count to see the velocity deficit, array efficiency and wake loss from the Jensen (Park) wake model update in real time.
Parameters
Free-stream wind speed
m/s
Upstream wind speed not yet affected by any wake
Rotor diameter D
m
Rotor diameter used as the reference for spacing
Turbine spacing (rotor diameters)
×D
Spacing between consecutive turbines, x/D
Thrust coefficient Ct
Dimensionless force the rotor takes from the wind; higher means a stronger wake
Turbines per row
units
Number of turbines lined up along the prevailing wind
Results
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Velocity deficit (%)
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Waked turbine wind speed (m/s)
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Waked turbine power ratio (%)
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Array efficiency (%)
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Wake loss (%)
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Spacing rating
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Turbine row and wake cones — animation
Behind each turbine an expanding wake cone of reduced wind speed forms. Longer arrows mean faster wind; darker shading means a larger speed deficit. The wind-speed profile steps down along the row.
Velocity deficit from the Jensen (Park) wake model and the downstream turbine's power ratio. x/D is the spacing in rotor diameters, k the wake decay constant (about 0.075 onshore) and Ct the thrust coefficient. Power scales with the cube of wind speed.
Wind speed V_waked seen by a waked turbine, and array efficiency η_array of a row of N turbines. The first turbine sees the free stream; every following turbine is taken to sit in the single wake. Wake loss is (1 − η_array) × 100 [%].
What is Wake Loss?
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Wind farms line turbines up in rows, right? Doesn't the turbine behind lose out by sitting in the "wind shadow" of the one in front?
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That is exactly the big problem. A turbine generates power by taking kinetic energy out of the wind. As a basic consequence of energy conservation, the air leaving the rotor must be slower than the wind that came in — and more turbulent too. That slowed, churned-up region is called the wake. A downstream turbine sitting in the wake of one in front only gets a weaker wind that has already had energy removed.
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But if the wind speed drops only a little, the power just drops a little too, doesn't it?
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It is not "a little". Turbine power scales with the cube of wind speed. So a 10% drop in wind speed costs roughly a 27% drop in power. Try raising the thrust coefficient Ct on the left. The harder the upstream turbine pulls energy from the wind, the stronger its wake — and you will see the downstream power ratio fall sharply.
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A cube? So packing turbines close together must waste a lot of energy.
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Right. That is why turbines are spaced many rotor diameters apart. As the wake travels downstream it mixes with the faster surrounding air and the wind speed gradually recovers. In the Jensen model the deficit shrinks with the square of distance. Slide the "Turbine spacing" up and the "array efficiency vs spacing" chart below climbs steadily. Typically you use 7-10 diameters along the prevailing wind.
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If widening the spacing fixes it, that sounds easy — but I guess it's not that simple?
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Only if land were free. In reality land, cabling and grid connection are all limited, so you want to pack in more turbines. But packing them in costs energy through wake losses. A large wind farm typically loses 5-15% of the energy it would make if every turbine saw clean wind. So spacing is a tug-of-war between land cost and wake loss.
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Apart from spacing, are there other ways to cut wake losses?
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Yes. One is to angle the rows relative to the prevailing wind or use a staggered layout so turbines do not line up directly behind each other. And the hot topic lately is "wake steering": deliberately yawing an upstream turbine a few degrees to deflect its wake sideways. Its own output drops slightly, but the turbines behind get stronger wind, and the farm as a whole produces more. It is a central problem in layout design.
Frequently Asked Questions
A wind turbine generates power by taking kinetic energy out of the wind, so the air that has passed through the rotor is always slower — and more turbulent — than the wind that arrived. That slowed region is the turbine's wake. When turbines are placed in rows, any downstream turbine sitting in the wake of one in front receives a weaker wind and produces less power. Because turbine power scales with the cube of wind speed, even a small speed drop causes a large power loss. The reduction in energy across the whole row is the wake loss.
The Jensen model, proposed by N.O. Jensen in 1983 and also known as the Park model, is the most basic wake model. It assumes the wake expands as a cone whose diameter grows linearly downstream, and the velocity deficit is deficit = (1 - sqrt(1 - Ct)) / (1 + 2k*x/D)^2. Here Ct is the thrust coefficient, x/D is the downstream distance divided by rotor diameter, and k is the wake decay constant (about 0.075 onshore). Simple yet accurate enough for practice, it is still widely used in wind-farm layout design.
The velocity deficit in a wake recovers as it mixes with the faster surrounding air downstream. In the Jensen model the deficit shrinks with the square of distance, so a wider spacing means downstream turbines see a stronger wind and the wake loss falls. A typical layout uses 7-10 rotor diameters along the prevailing wind direction and 3-5 diameters across it. Tighter spacing saves land but costs energy, so spacing is a trade-off between land cost and power loss.
There are three main levers. First, widen the turbine spacing. Second, orient the rows relative to the prevailing wind and use a staggered (offset) layout so turbines do not line up directly behind each other. Third, use wake steering, in which upstream turbines are deliberately yawed a few degrees to deflect their wakes aside. Wake losses typically rob a large wind farm of 5-15% of the energy it would produce if every turbine saw clean wind, so minimising them is a central problem in layout design.
Real-World Applications
Onshore wind-farm layout design: Given the prevailing wind direction from wind measurements, turbines are placed in rows 7-10 diameters apart along the wind and staggered across it. A Jensen-model calculation like this tool is used to screen layout options before moving to detailed CFD (computational fluid dynamics). Adding turbines raises the energy per unit of land, but it also raises wake loss, so engineers search for the combination of count and spacing that maximises the annual energy production (AEP).
Offshore wind farms: Over the sea the surface friction is low and the wake decay constant k is around 0.04 — smaller than onshore — so wakes trail far downstream and losses tend to be larger. At Denmark's Horns Rev and North Sea projects in the UK, satellite observations have confirmed wakes reaching tens of kilometres. Because foundation costs are high offshore, spacing is often widened (8-12 diameters) to maximise the energy per turbine.
Wake steering control: An upstream turbine is deliberately yawed a few degrees to deflect its wake away from the next turbine. Field demonstrations by NREL and the Technical University of Denmark (DTU) have shown a few-percent gain in total farm output. Lowering the "thrust coefficient" in this tool conceptually shows how a weaker wake helps downstream turbines, giving an intuitive feel for the benefit of steering control.
Energy yield prediction and project finance: The revenue of a wind project depends directly on the accuracy of its annual energy estimate. Underestimating wake loss leads to a project that "does not generate as much as expected" after commissioning. In financial due diligence, the validity of P50/P90 energy figures including wake loss is checked rigorously. This tool helps quickly grasp how sensitive the loss is to spacing and turbine count.
Common Misconceptions and Pitfalls
The biggest caveat is that the Jensen model is a simplified single-wake formula. This tool adopts the standard simplification that "every following turbine sits in the same single wake as the first one". In a real wind farm, the wakes of several turbines overlap (multi-wake), and that superposition needs an approximation such as the root-sum-of-squares (RSS) rule. The wind speed inside the wake is also assumed uniform — a "top-hat" profile — rather than the bell-shaped distribution seen in reality. Accurate energy prediction needs Gaussian wake models, CFD, and comparison with measured data.
Next, the wake decay constant k is not a fixed value. This tool uses the representative onshore value k=0.075, but k depends strongly on atmospheric turbulence intensity. More turbulence mixes and recovers the wake faster, so k is larger; in low-turbulence environments such as offshore, k can drop to around 0.04 and the wake persists far downstream. It also varies with atmospheric stability (day/night, season). Treating k as a single constant tends to underestimate the loss, especially offshore.
Finally, it is easy to forget that wake loss varies strongly with wind direction. This tool computes the worst case, with the wind blowing straight along the row. Real wind constantly changes direction, so over a full year the turbines line up directly behind one another only a fraction of the time. An annual energy assessment must combine the wind rose (the frequency of each wind direction) and average the wake loss over all directions. Mistaking "the head-on loss" for "the annual loss" overestimates the loss.
How to Use
Set free-stream wind speed (8–15 m/s typical for utility-scale farms) using the windSpeedNum input or windSpeedRange slider.
Define rotor diameter (80–220 m for modern turbines) and downstream spacing in rotor diameters (3–10 D recommended). Tighter spacing increases wake losses exponentially.
Adjust thrust coefficient (0.7–0.95 for operating turbines) to model different blade pitch angles and operating conditions. Run the simulation to calculate velocity deficit, waked turbine power ratio, and array efficiency losses.
Worked Example
Free-stream wind speed 12 m/s, rotor diameter 150 m, turbine spacing 5 D (750 m apart), thrust coefficient 0.85. The downstream turbine experiences approximately 18% velocity deficit, reducing its wind speed from 12 m/s to 9.84 m/s. This velocity reduction causes power output to drop to 58% of the upstream turbine value due to cubic power law (P ∝ V³). For a 10-turbine linear array with this spacing, overall wake loss reaches 12–15%, reducing farm capacity factor by 1.5–2 percentage points compared to isolated operation.
Practical Notes
Onshore farm design typically targets 4–5 D spacing to balance wake losses (8–10%) against land-use efficiency; offshore farms use 6–8 D spacing where real estate cost is negligible.
Yaw control strategies can redirect wake deflection 20–25°, reducing downstream velocity deficit by 30–50% in some operating conditions but requiring active wake management systems.
Wind shear and atmospheric stability dramatically affect wake recovery; neutral stability assumes faster recovery than stable conditions typical of night operations, where wake losses increase 20–30%.