How Wind Farm Wake Losses Are Calculated

Every turbine that produces power must slow the air passing through it, because the energy it extracts comes directly from the kinetic energy of that air. The slowed, turbulent column trailing behind the rotor is the wake, and it is the single largest source of energy loss unique to arranging turbines in groups rather than operating them alone. This calculator uses the Jensen model, also called the Park model, which represents the wake as a cone expanding linearly downstream from the rotor plane.

The velocity deficit immediately behind the rotor follows from the thrust coefficient as one minus the square root of one minus Ct. Downstream, that deficit is diluted by the square of the expansion factor, which grows as one plus twice the wake decay constant times the distance in rotor diameters. When a turbine sits in the wakes of several upstream machines, the individual deficits are combined by the sum of squares rule rather than added directly, reflecting the observation that deficits do not accumulate linearly in deep arrays.

Converting the velocity deficit into a power deficit is where the numbers become dramatic. Power available in moving air scales with the cube of velocity, so a wake that reduces wind speed by ten percent removes roughly twenty seven percent of the available power at that rotor. This cubic relationship is why layout decisions that look minor on a site plan translate into millions of dollars of lifetime revenue.

Choosing Turbine Spacing

The industry rule of thumb calls for seven to ten rotor diameters of separation along the prevailing wind direction and three to five diameters perpendicular to it. Those figures are not arbitrary. At seven diameters in typical onshore conditions a single wake has recovered enough that the downstream turbine loses only a few percent of its output, and the incremental gain from stretching to nine or ten diameters rarely justifies the additional land lease, access road and collector cable cost.

Offshore the calculation shifts. Sea surfaces are aerodynamically smooth, ambient turbulence is low, and wakes persist far downstream. Wake decay constants near 0.04 are appropriate, and spacing of eight to twelve diameters is common. Since offshore foundations and cabling are extremely expensive, developers face a genuinely difficult optimisation between packing turbines close enough to keep infrastructure costs down and separating them enough to avoid crippling array losses.

Lateral staggering offers a way to escape part of the trade-off. Offsetting alternate rows sideways moves downstream rotors partly or entirely out of the wake core without requiring additional downwind distance. Professional Mode includes a lateral offset input so you can see how much of the loss a staggered layout recovers for a given site footprint.

Reading Array Efficiency

Array efficiency compares the actual farm output against what the same turbines would generate standing alone in undisturbed flow. It is the number that appears in energy yield assessments and that lenders scrutinise during due diligence. An efficiency above ninety two percent indicates a generously spaced layout. The high eighties is normal for a commercially optimised onshore array. Anything below eighty five percent means the layout is trading a substantial slice of annual energy for site compactness, and deserves a hard look at whether the land savings truly justify it.

The figure this calculator reports for a single wind direction is a worst case, because it assumes the wind blows exactly along the rows. Real annual losses are considerably lower, since for most of the year the wind arrives from directions where turbines are effectively in free stream. Professional Mode applies a directional weighting so the annual energy and revenue figures reflect how often the aligned sector actually occurs at your site.

Limitations and What to Check Next

The Jensen model is a screening tool. It handles array-level energy loss well and runs instantly, which is exactly what you want when comparing dozens of candidate layouts. It does not capture the detailed near-wake structure within two or three rotor diameters, it assumes a uniform deficit across the wake cross section rather than the Gaussian profile that measurements show, and it takes the thrust coefficient as a constant rather than following the full Ct curve across the operating wind speed range.

Three further effects are absent entirely. Added turbulence intensity in the wake drives fatigue loading on downstream turbines and is frequently the real constraint on tight spacing, sometimes overriding the energy argument completely. Global blockage, the upstream deceleration ahead of a large array, has been measured at one to three percent of production and is not modelled here. Wake steering, in which upstream turbines yaw deliberately to deflect their wakes aside, can recover a meaningful fraction of array losses on modern control systems.

Treat the output as a well-grounded first estimate that tells you which layouts are worth pursuing. Before committing capital, confirm with a full resource assessment using measured site wind data, a complete wind rose, turbine-specific power and thrust curves, and a wake code validated against operating farms in comparable terrain.