The original work, by Simão Ferreira and colleagues, proposed a ceiling on the capacity factor of offshore wind farms, the ratio of actual electricity produced to the maximum a fleet of turbines could generate if running flat out at rated power. The authors built their limit from simplified analytical models: a Weibull distribution describing the wind speed climate at a site, an idealized turbine power curve, and a classical representation of how an infinitely large wind farm interacts with the atmospheric boundary layer, drawing on formulations by Frandsen from 1992 and Sørensen and Larsen from 2021. To make the infinite-farm model usable for real, finite wind farms, they applied a correction that accounts for turbines at the edges of a farm that still see undisturbed freestream wind. The model was then validated against the measured net capacity factors of 72 offshore wind farms across the Baltic, North, and Irish seas.

The stakes became political when the original authors calculated that Dutch national policy for planned offshore wind farms assumes capacity factors significantly in excess of their proposed limit, reportedly by as much as 49 percent when assuming ten percent additional losses. That finding suggested the Netherlands was planning more electricity from its crowded patch of the North Sea than physics would allow, and it fed directly into parliamentary debate. Van der Laan and Watson do not dispute that wake losses, the slowing of wind as turbines extract energy and leave turbulent, depleted flow behind them, are a genuine and growing problem for densely packed seas. What they dispute is whether the proposed ceiling deserves the label “theoretical.”

Their central argument is that the limit rests on heuristic model assumptions and unknown parameters rather than on a fundamental physical constraint. They contrast it with the Betz limit, the celebrated 59.3 percent cap on the power coefficient of a single wind turbine, which follows rigorously from momentum theory. The proposed wind farm limit, by comparison, is an analytical expression for normalized gross annual energy production multiplied by an ad hoc loss factor, and, crucially, different choices of its embedded parameters would yield distinctly different limits. The comment authors also point out that the plotted “theoretical limit” in the original paper actually represents normalized gross annual energy production, a subtlety they say is not clear from the original text and has been frequently misunderstood by readers.

The most damaging critique concerns reproducibility. To apply the infinite-farm model to real wind farms, the original authors corrected it by manually counting the number of freestream turbines at each of the 72 sites, taking into account the farm layout, the prevailing wind rose, and the wakes of neighboring wind farms. This manual procedure was only briefly described, and no scientific method was provided, meaning the results cannot be independently reproduced. Van der Laan and Watson built their own automated version of the procedure, fitting a polygon to the farm boundary, computing outward normal vectors for edge turbines, flagging inflow-edge turbines for each of twelve wind direction sectors, and filtering out turbines shadowed by upstream farms using a ray-casting method. For the Amrumbank West wind farm, their automated approach yielded 11.3 freestream turbines averaged over the wind rose, while the original manual method had reported 15.

The discrepancies run deeper than a single site. In community comments published during the open review process, the original authors themselves attempted an updated automated version of their correction and failed to reproduce their own manual results, with differences exceeding 30 percent for twenty wind farms, including Anholt, DanTysk, London Array, East Anglia One, and Borkum Riffgrund I and II. Van der Laan and Watson show that the weight given to the freestream-turbine count has an enormous influence on the predicted capacity factor, which can slide anywhere between the no-wake-loss gross value and the deep depletion of an infinite farm. When they replot the validation data using alternative correction methods, the quality of the fit degrades substantially, and the high correlation coefficient of 0.87 reported in the original work could not be replicated. A data point can even cross the normalized gross energy line, which the comment authors describe as a serious flaw in the validation.

There is also a measurement problem. The validation relied on net capacity factors, which bundle together wake losses with grid faults, curtailment, and turbine downtime. That mixture makes it impossible to isolate the wake losses the model is supposed to capture. The original authors attempted to correct for this with an additional loss factor of 0.9, but van der Laan and Watson find no compelling evidence for that particular value, noting that the choice directly shifts the apparent limit.

To expose how little of the model’s behavior is truly fixed by physics, the comment authors derived a striking simplification. Although the infinite-farm wake loss equation is implicit, requiring numerical solution of a geostrophic drag law, the 72 wind farms in question share such similar latitudes, hub heights, roughness lengths, and thrust characteristics that the entire expression collapses to a simple explicit formula depending on a single variable: the turbine spacing normalized by rotor diameter. The approximation matches the full implicit calculation to within 2.3 percent for all 72 farms. Likewise, the so-called wind farm wind factor, which condenses wake effects into one number, turns out to depend mainly on just two quantities, the freestream turbine fraction and the turbine spacing. That fragility, the authors argue, undercuts any claim that the model pins down a unique physical ceiling. They add that wake losses are strongly dependent on atmospheric turbulence intensity and stability, so collapsing them into a single variable may not even be possible in principle.

When these uncertainties are propagated to the Dutch policy case, the dramatic 49 percent overestimate dissolves. Van der Laan and Watson note that the references cited by the original study itself give a range of planned capacity densities between 4 and 10.5 megawatts per square kilometer and expected full-load hours between 3700 and 5100, corresponding to capacity factors between 0.42 and 0.58. While 0.58 is indeed optimistic, the lower value of 0.42 sits comfortably within the range of measured capacity factors of the 72 existing wind farms. Moreover, treating a planned 10-gigawatt Dutch build-out as one gigantic uniform wind farm is unrealistic; the more plausible scenario is a cluster of separate 1000 to 2000 megawatt farms built over time with gaps between them, a configuration the analytical framework can actually accommodate with far milder losses.

The comment’s conclusion is blunt: the proposed ceiling should be regarded as a model-derived estimate resting on a non-reproducible finite-farm correction, not a theoretical limit, and given the model’s sensitivity it cannot be used to judge the feasibility of national offshore wind policies. The episode is a cautionary tale for the energy transition, illustrating how a simple spreadsheet-friendly model, precisely because of its accessibility to policymakers, can acquire political force before its assumptions have been scrutinized. Robust tools for estimating large-scale wake losses do exist, from engineering wake models to mesoscale simulations, but they come with complexity and computational cost. As European seas fill with turbines and farms begin to shadow one another, the debate over how much energy the wind can truly deliver is far from settled, and the researchers argue it must be settled with reproducible science rather than ad hoc corrections.

Subject of Research: Critique of a proposed theoretical upper limit for offshore wind farm energy extraction and its reproducibility

Article Title: Comment on “A theoretical upper limit for offshore wind energy extraction” by Simão Ferreira et al. (2026)

Article References: van der Laan, M. P., & Watson, S. (2026). Comment on “A theoretical upper limit for offshore wind energy extraction” by Simão Ferreira et al. (2026). Wind Energy Science, 11(10), 3763-3774. https://doi.org/10.5194/wes-11-3763-2026

Image Credits: AI Generated

DOI: 10.5194/wes-11-3763-2026

Keywords: offshore wind, capacity factor, wake losses, wind farm modeling, atmospheric boundary layer, reproducibility, Betz limit, Dutch energy policy, North Sea, wind energy science, geostrophic drag law, peer review