Wind Farm Wake Power Loss Calculator

Jensen wake power loss estimate

This wind-farm wake calculator estimates the output reduction for a downstream turbine positioned in the fully aligned wake of one upstream turbine. It uses the classic Jensen (PARK) top-hat wake model to calculate the reduced wind speed at a chosen rotor-diameter spacing, then applies the turbine power equation to compare unwaked and waked output.

Use the result as a transparent first pass for turbine-layout decisions, such as comparing 6D and 8D downstream spacing, or seeing how a higher C_T changes the wake deficit. The calculator is a single-wake estimate rather than a complete annual-energy model. Check that the selected wind speed and coefficients represent the operating condition being compared, because turbine behavior can vary across its power curve.

Wind turbine wake loss inputs

These inputs define the inflow, turbine geometry, spacing, and aerodynamic coefficients used in the Jensen wake-power calculation.

• Free stream wind speed (m/s) (U): The undisturbed wind speed approaching the upstream turbine.
• Turbine rotor diameter (m) (D): Rotor diameter. The calculator uses the swept area A = π(D/2)² for both power estimates.
• Downstream spacing (rotor diameters) (s): Center-to-center streamwise distance in rotor diameters. The corresponding physical distance is x = s·D.
• Thrust coefficient (C_T): The rotor momentum-extraction coefficient used to solve for axial induction and the wake velocity deficit.
• Power coefficient (C_P): The assumed aerodynamic conversion coefficient in the free-stream and waked power calculations.

Jensen/PARK wake model equations

The Jensen wake-power calculation represents the wake as a uniformly reduced-speed flow that expands linearly behind the upstream rotor.

Wake radius: R_w = R + kx, where R = D/2, x is downstream distance, and the implementation uses k = 0.075.

The calculator obtains axial induction a from the actuator-disk thrust relation:

Thrust relation: C_T = 4a(1 − a)

For an aligned downstream turbine, the Jensen wake wind speed is:

The wake-power comparison then uses a constant-density, constant-C_P cubic-speed model:

Baseline power: P = ½ ρ A U³ C_P

Waked power: P_w = ½ ρ A U_w³ C_P

Therefore, with the same rotor and power coefficient on both sides of the comparison, P_w/P = (U_w/U)³. The displayed power values use air density ρ = 1.225 kg/m³ and are reported in kW.

Interpreting wind turbine wake-loss outputs

The reported values show how the Jensen velocity deficit propagates into a downstream turbine power estimate.

• Axial induction factor: The value solved from the entered thrust coefficient.
• Wake radius (R_w): The modelled wake radius at the entered downstream distance.
• Wake wind speed (U_w): Predicted aligned-wake speed at the downstream turbine.
• Baseline power (P): Estimated output at free-stream speed.
• Waked power (P_w): Estimated output at the reduced wake speed.
• Power loss: (1 − P_w/P)×100%. Because power follows wind speed cubed in this model, a modest speed deficit produces a larger percentage output loss.

Worked example: a 7D Jensen wake-power case

Consider an aligned downstream wind turbine with the calculator’s representative inputs:

• Free stream wind speed U = 10 m/s
• Rotor diameter D = 100 m
• Spacing s = 7D, so x = 700 m
• C_T = 0.80
• C_P = 0.45

For C_T = 0.80, the lower physical solution of C_T = 4a(1−a) gives a ≈ 0.276. The calculator’s fixed k = 0.075 makes the wake expand as it travels seven rotor diameters downstream, which reduces the modeled velocity deficit compared with a closer spacing. The resulting wake speed is then cubed in the waked-power calculation, so the reported loss is driven primarily by the speed ratio rather than by the entered power coefficient.

Jensen wake-model parameter guidance

These practical checks help put the wind-farm wake-loss inputs in context before using a single aligned-wake result for a layout comparison.

Jensen wake-power limitations and assumptions

This wind-turbine wake-loss result is intentionally simplified, so it should be read as an aligned single-wake screening estimate.

• Single-wake, aligned flow: The calculation models one upstream turbine and one downstream turbine directly in its wake, not a full turbine array.
• Top-hat wake profile: Jensen assumes one uniform velocity deficit across the wake; measured wakes commonly have non-uniform profiles.
• Fixed wake expansion: The code uses k = 0.075, so site turbulence, atmospheric stability, and offshore conditions do not alter recovery in the form calculation.
• No partial overlap: Lateral offset, yaw misalignment, and wind-direction changes can reduce rotor overlap and produce a different loss than this fully aligned estimate.
• Steady inflow: The model does not represent time-varying turbulence or unsteady structural loading.
• Simplified power curve: It assumes P ∝ U³ with constant C_P; rated-power limits, cut-in, cut-out, and turbine control transitions are excluded.
• No terrain or blockage treatment: Complex terrain, wind shear, and farm-scale blockage are outside the calculation.

When to move beyond a single Jensen wake estimate

For wind-farm energy assessment, use a more advanced engineering wake model or validated farm tool when the decision depends on multiple rows, directional wind distributions, turbulence, yaw and veer, partial overlap, terrain, or calibrated site measurements. Those analyses can combine wakes across turbines; this calculator is designed to make the basic spacing-and-thrust relationship easy to inspect.