Wind Turbine Wake Effect Calculator
Calculate the reduced wind speed experienced by a downstream turbine due to wake effects from an upstream rotor. Essential for wind farm layout optimisation and accurate annual energy production modelling.
About this calculator
When a wind turbine extracts energy from the wind, it creates a wake — a cone of slower, more turbulent air behind the rotor. The Jensen (Park) model estimates the downstream wind speed as: v_d = v_u × [1 − (1 − √(1 − Cₜ)) / (1 + 2k·x/D)²], where v_u is upstream wind speed, Cₜ is the thrust coefficient, k is the wake decay constant, x is the downstream distance, and D is the rotor diameter. The term (1 − √(1 − Cₜ)) is the initial velocity deficit at the rotor plane derived from actuator-disc theory. The denominator (1 + 2k·x/D)² describes how the wake expands and recovers with distance. Since power scales with speed cubed, even a 10% speed reduction causes a ~27% power loss. Typical Cₜ values are 0.7–0.9 and k ranges from 0.04 (offshore) to 0.075 (onshore).
How to use
Upstream wind speed v_u = 10 m/s, rotor diameter D = 80 m, downstream distance x = 400 m, thrust coefficient Cₜ = 0.8, wake decay constant k = 0.05. Step 1 – Initial deficit: 1 − √(1 − 0.8) = 1 − √0.2 = 1 − 0.4472 = 0.5528. Step 2 – Denominator: (1 + 2 × 0.05 × 400/80)² = (1 + 0.5)² = 1.5² = 2.25. Step 3 – Velocity ratio deficit: 0.5528 / 2.25 = 0.2457. Step 4 – Downstream speed: v_d = 10 × (1 − 0.2457) = 10 × 0.7543 ≈ 7.54 m/s. Step 5 – Power loss: (7.54/10)³ ≈ 0.429, meaning the downstream turbine captures only ~43% of the power it would in free-stream wind.
Frequently asked questions
How far apart should wind turbines be spaced to minimise wake losses?
Industry practice typically spaces turbines 5–9 rotor diameters (D) apart in the prevailing wind direction and 3–5 D in the cross-wind direction. At 5 D separation, wake losses per turbine can be 10–20% of free-stream power; at 10 D they fall to 2–5%. However, wider spacing reduces the number of turbines that fit on a site, so developers optimise for total farm output rather than individual turbine performance. Offshore farms, with lower wake decay (k ≈ 0.04), require larger separations than onshore sites. Advanced wake steering — intentionally yawing upstream turbines to deflect the wake away from downstream rotors — can recover 3–10% of otherwise lost energy.
What is the thrust coefficient of a wind turbine and how does it affect wake losses?
The thrust coefficient Cₜ is a dimensionless measure of the axial force a turbine exerts on the wind relative to the kinetic energy flux through the rotor disc. It is defined as Cₜ = T / (½ρAv²), where T is thrust force. For most modern turbines, Cₜ peaks near rated wind speed at values of 0.7–0.9 and decreases at very low and very high wind speeds. A higher Cₜ means the rotor is extracting more momentum from the flow, creating a deeper and longer-lasting wake. Paradoxically, very high Cₜ values (above 0.96, the Betz actuator-disc limit) are physically impossible — the Jensen model uses √(1−Cₜ) to convert thrust into initial velocity deficit, so Cₜ must be below 1.0 for the formula to be valid.
What is the wake decay constant k and how do I choose the right value?
The wake decay constant k (also written as α in some literature) governs how quickly the turbine wake widens and the velocity deficit recovers with downstream distance. Higher k means faster wake recovery: offshore sites use k ≈ 0.04 because low surface roughness and stable stratification suppress ambient turbulence; onshore flat terrain sites use k ≈ 0.05–0.06; and complex or forested terrain can reach k ≈ 0.075. The appropriate value should ideally be calibrated from wake measurements or SCADA data at the specific site. Using an offshore k value for an onshore farm will overestimate wake losses and underestimate farm energy output, while the reverse error will lead to an overly optimistic layout design.