The evolutionary design of wind turbines

Abstract

The human urge to achieve power from nature has shaped the evolution of wind turbines, enabling the conversion of wind into useful energy. This article unveils the evolutionary aeroelastic design of wind turbines from the perspective of Constructal Law, the physics of design that analyzes, explains, and predicts how energy flow configurations evolve to survive. Witnessing the evolution of wind turbines from early vertical axis to modern horizontal-axis configurations, the article highlights changes in tower height, rotor size, and material quantity that follow predictable patterns in design and performance, while identifying scaling relationships and structural constraints that influence efficiency. Key predictions include proportional relationships between rated power and tower mass, as well as among nacelle mass, rotor mass, and tower mass. The study demonstrates that several design shifts in history have consistently enhanced energy flow configurations, conceived as designs, and structural performance. These insights empower designers to fast-forward with confidence the evolution of wind turbine power systems.

Keywords

evolutionary design wind turbine Constructal Law wind power energy flow configuration

Introduction

Recent publications on wind turbine technology inspired our perspective on the long-term evolution of turbine design. Veers et al. emphasize the major technical unknowns that shape the future of large turbine systems, including limits in aerodynamic and aeroelastic modeling, wake interactions, control co-design, material behavior, and the need for high-fidelity prediction tools (Veers et al., 2023). Tavner et al. analyze Danish wind turbine data (1994–2004) to show how wind speed and weather conditions affect turbine reliability and identify the subassemblies most vulnerable, with implications for improving future onshore and offshore turbine designs (Tavner et al., 2006). Hansen et al. examine global wind turbine market penetration from 1998–2002, analyzing supplier data covering 76% of installed capacity to classify turbine concepts by speed and power control and identify prevailing design trends (Hansen et al., 2004). Al-Sanad et al. show how reliability-based optimization can reshape tower proportions when load and material uncertainties are treated explicitly (Al-Sanad et al., 2021). Hernandez-Estrada et al. review the structural and dynamic challenges of increasingly tall towers, from fatigue to vibration, highlighting the broader structural context in which modern turbines evolve (Hernandez-Estrada et al., 2021). Complementing these themes, Amano provides a broader synthesis of 21st-century wind turbine research, outlining the technological directions that continue to shape current design practice (Amano, 2017).

Complementary lines of research highlight how specific design choices respond to performance needs across different scales and operating conditions. Muchiri et al. (Muchiri et al., 2022) examine blade materials, pitch settings, and low-speed performance, while Torres et al. use geometric optimization to identify high-performance Savonius configurations (Torres et al., 2022). Shohag et al. review common damage mechanisms in wind turbine blades across manufacturing, transport, and operation, and survey early detection and mitigation techniques to reduce failure risk and repair costs (Shohag et al., 2017). Extensive work on small-scale and alternative rotor concepts further broadens this landscape. Jain and Saha review the state-of-the-art in H-type Darrieus rotors, covering aerodynamic modeling, CFD methods, dynamic stall, vortex interactions, and optimization strategies (Jain and Saha, 2020). Alom and Saha summarize four decades of augmentation techniques for Savonius rotors, showing how design modifications and flow-control devices can substantially increase power coefficients despite the rotor’s inherently low efficiency (Alom and Saha, 2018). Experimental work on small horizontal-axis turbines (SHAWTs) also sheds light on wake dynamics and array effects. Clausen et al. review technological advances in small wind turbines (≤ 50 kW), highlighting category-specific design challenges, recent improvements in aerodynamics, blades, and controls, and remaining gaps relative to large-turbine maturity (Clausen et al., 2000).

Siram et al. demonstrate how turbine spacing and low tip-speed-ratio operation influence power extraction and wake recovery, with implications for small wind farm configurations (Siram et al., 2022). van der Tempel et al. review dynamic design principles for lightweight, cost-effective wind turbines, emphasizing the integrated aero-hydro-structural dynamics of turbines and support structures, including offshore systems under wave loading (van der Tempel and Molenaar, 2002). Together, these studies broaden the range of evolutionary pathways for turbine design and motivate our examination of whether Constructal Law can help interpret these trends and identify the flow-based logic that links geometry, structure, and performance.

Witnessing earlier civilizations improves our understanding of the design evolution. The Persians, who lived in a region extending beyond the current borders of Iran, have been recognized for their innovative and efficient use of available resources such as food, water, and livestock. They refined their designs and practices to achieve a better life (greater efficiency). The first wind turbines (called Asbads) were built more than one thousand years ago (Zarrabi and Valibeig, 2021; UNESCO, 2025). Their purpose was to grind large quantities of wheat. The mill employed two heavy circular stones rotating against each other. Because of the seasonal 120-day winds, the region experiences drought. Among the region’s natural resources, wind offers the most accessible and cost-effective source of energy. The challenge was to engineer a mechanism that could capture wind power and convert it into rotational motion for grinding.

The Taftan Asbad, located in the Sistan region near Mount Taftan (Figure 1) (Dehghanpour, 2021), is widely recognized as the world’s first windmill. Vertical-axis windmills captured the strong seasonal winds, particularly the persistent “120-day wind” that blows during the summer across the Sistan basin. This historical use of wind as a practical and reliable source of power is consistent with modern assessments showing Iran’s substantial potential for renewable energy development. Slocum and Gessel demonstrate that even a modest allocation of hydrocarbon revenues toward wind and solar infrastructure could enable Iran to meet a large share of its future energy and freshwater needs through sustainable systems (Slocum and Gessel, 2022). In recognition of their cultural and technological significance, the Asbads of Iran have been inscribed on the UNESCO World Heritage List (UNESCO, 2025).

Figure 1.

World’s first windmill in Sistan, Iran (Dehghanpour, 2021).

Over time, the motivation for harnessing wind shifted from localized mechanical uses to large-scale electricity generation, driven by climate concerns and the need for cleaner energy. Modern wind turbines are now efficient, reliable systems with reduced environmental impact. Unlike early designs, current turbines are predominantly horizontal-axis with three-blade configurations optimized through advanced aerodynamics, real-time control, and grid integration. Wind farms, both onshore and offshore, now contribute significantly to electricity generation worldwide.

In recent decades, wind energy has become central to global decarbonization efforts, supported by policies such as the UN 2030 Agenda. Global capacity reached 906 GW in 2022 (Figure 2), with continued rapid growth projected in the coming years (GWEC, 2023). Alongside large-scale expansion, decentralized approaches such as Local Energy Communities are also emerging as part of the energy transition (Lakeman, 2024).

Figure 2.

New installations outlook 2022–2026 (GW). Adapted from Global Wind Energy Council, 2023) (GWEC, 2023).

The upward trend in rated power (Figure 3) reflects the growing demand for decarbonization, with global investments in wind energy expanding rapidly (The Wind Power EI, 2024). GWEC (2023) projects that installation rates must reach 320 GW per year by 2030 to meet climate targets. Modern turbines now exceed 10 MW, with rotor diameters over 100 m, benefiting from advances in aeroelastic design, materials, and maintenance technologies. Studies highlight key factors influencing performance, including atmospheric boundary layer interactions, turbulence, and wake effects (Porté-Agel et al., 2020), as well as aerodynamic design and structural optimization that improve efficiency and reliability (Balat, 2009; Schubel and Crossley, 2012).

Figure 3.

The historical trend in power from wind turbines (The Wind Power EI, 2024).

Blade design plays a central role in aeroelastic performance and stability, with studies highlighting improvements in structural and aerodynamic optimization (Hau and Renouard, 2006; Jureczko et al., 2005; Spera, 1994; Tong, 2010). Complementary work on control systems and noise management shows a shift toward multi-objective and predictive methods that enhance efficiency and durability (Menezes et al., 2018; Njiri and Söffker, 2016). Advances in generator technologies and data-driven diagnostics further improve reliability and scalability, including high-accuracy condition monitoring using SCADA data (Irfan et al., 2025; Polinder et al., 2013).

Convergent evolution of wind turbine design

Early wind turbines were small and inefficient, extracting only a fraction of the wind’s energy. During the past several decades, turbine designs have evolved to capture more energy from the wind, with modern turbines being 10 times more powerful than their predecessors (Gipe and Möllerström, 2022a; 2022b). Key in this evolution has been the improvement of airfoil design, which allows turbines to operate at higher “tip-speed ratios.” The tip-speed ratio, which is the speed of the blade tips relative to the wind speed on the ground, is an important parameter in turbine design (Manwell et al., 2009). Higher tip-speed ratios result in more efficient energy capture, allowing turbines to generate more power for the same rotor size. The rotor swept area of modern wind turbines has increased dramatically, with turbines now sweeping up to 100 times more wind area than those from the early 1980s.

The first practical application of wind energy was on sailing ships, where tall masts and large sails were used to capture wind and propel the vessel forward. Drawing inspiration from this principle, the earliest land-based wind-powered machines began to emerge. One example is the wind-powered pipe organ, described by the Greek engineer Heron of Alexandria. While records from antiquity are limited, it is likely that wind energy was harnessed for other purposes as well (Haskell, n.d). The first large-scale, practical windmills were developed in Persia, during the 7th century (Figure 1). These early windmills, known as panemone windmills (Zarrabi and Valibeig, 2021), were vertical-axis machines featuring rectangular sails mounted on a vertical shaft. Unlike the horizontal-axis turbines familiar today, these structures resembled revolving doors and could capture wind from any direction. They were used for grinding grain and irrigation. The simplicity and adaptability of the Persian design were in response to harsh environmental conditions.

In China, windmills appeared later, with the earliest written records dating to the 13th century, where they were similarly used for grinding and irrigation (Haskell, n.d). The electricity production from wind power began in 1887, when Scottish engineer James Blyth constructed the first turbine to generate electric power. Blyth’s wind turbine, as a vertical-axis design, produced small amounts of electricity for his home in Marykirk, Scotland. His design started the era of electricity production using wind, and provided some guiding principles for effective wind energy conversion that are applicable to this day (Gipe and Möllerström (2022a; 2022b)):

• A wind turbine should always be ready to work,

• It should operate for a long time without constant supervision,

• It should endure and take full advantage of adverse winds, such as strong gusts.

In the 20th century, horizontal-axis wind turbines (HAWTs) became the dominant design, resembling airplane propellers with blades optimized for aerodynamic efficiency by increasing lift and reducing drag. An early example is Charles Brush’s 1888 wind turbine in the U.S. (Figure 4), a large, self-regulated system with a 17.1 m rotor that generated up to 12 kW and operated for 20 years. Despite its innovative design, its complexity limited widespread adoption (USNRC, 2010).

Figure 4.

A: Brush’s wind turbine in Cleveland, Ohio (1888); B: La Cour’s 1891 electricity-generating wind turbine; C: Smith–Putnam wind turbine in Vermont (1941); D: Gedser mill, the grandfather of the Danish design concept; E: Mod-1 in Boone, North Carolina in 1978; F: Tvindkraft megawatt-scale turbine in Jutland (1978), repainted in 1999, the turbine’s 25th anniversary; G: Block Island offshore wind farm of GE’s Haliade 150 in the US (GE Vernova, 2024; Gipe and Möllerström, 2022).

Poul la Cour, often called “The Danish Edison,” established around 1891 an experimental wind energy facility in Denmark. His 11.6 m rotor windmill used self-regulating blades and drove an 18-kW dynamo (Figure 4). He conducted systematic experiments, including early wind tunnel studies, laying the foundation for modern turbine design and scalability. His designs remained in production into the 1950s (Gipe and Möllerström, 2022a; 2022b).

Many early low-speed multiblade turbines proved ineffective for electricity generation, but post–World War I developments introduced improved aerodynamic principles. A milestone was the 1919 Agricco turbine in Denmark, a 40-kW machine with airfoil blades connected to an AC network, marking a significant advancement in turbine technology.

Between the World Wars, engineers in Europe continued experimenting with wind turbine designs. Georges Darrieus in France explored both vertical- and horizontal-axis concepts, while Kurt Bilau in Germany advanced blade aerodynamics using airfoils, improving efficiency. A major milestone was the Smith–Putnam turbine (1941) in Vermont, the first megawatt-scale wind turbine with a 53 m rotor and 1,000 kW capacity (Figure 4). Despite its innovation, it failed in 1945, and similar scales were not revisited until the 1970s (Figure 5). After World War II, Denmark became a leader in wind turbine development, producing reliable two- and three-blade designs that operated for decades and contributed to grid electricity during fuel shortages.

Figure 5.

Historic trend of rotor diameter. (The Wind Power EI, 2024).

A major advancement came in the 1950s with Johannes Juul’s turbines, which introduced asynchronous generators and stall regulations. His 1957 Gedser turbine (Figure 4), a 24 m diameter machine, operated reliably for 16 years and became a model for modern Danish designs. After the 1970s oil crisis, wind energy development accelerated, driven by political and environmental pressures. While large, government-led prototypes were developed by aerospace firms, the modern wind industry was shaped primarily by smaller, scalable Danish turbines. During this period, horizontal-axis, three-bladed turbines with increasing rotor sizes became the standard (Gipe and Möllerström, 2022a; 2022b).

NASA led early large-scale wind turbine R&D through the Mod Program in the late 1970s, but these designs faced significant technical challenges. The General Electric Mod-1, a 2 MW turbine installed in 1978 (Figure 4), proved unsuccessful due to noise issues and reliability problems. Later models (Mod-2 and Mod-5b) improved in size but remained commercially unviable due to high costs and technical limitations, highlighting the risks of rapid scaling without incremental development. In contrast, Danish manufacturers achieved early success with the Nibe turbines, twin 630 kW units that demonstrated reliable and scalable design, setting the foundation for modern wind turbine development.

In the 1980s, Germany developed the Growian turbine, a 3 MW machine with a 100 m rotor, but it failed after limited operation and was decommissioned in 1987, highlighting the challenges of large prototypes. In contrast, the Tvindkraft turbine in Denmark (Figure 4), built by students with engineering support, demonstrated long-term reliability and became a symbol of scalable and robust design. During the same period, wind energy expanded rapidly in California, with over 11,000 turbines installed, many imported from Danish manufacturers such as Vestas and Nordtank. By the late 1980s, Danish designs, emphasizing gradual scaling and reliability, established the modern standard of horizontal-axis, three-bladed turbines.

According to Gipe and Möllerström (2022a; 2022b), American and European wind turbine designs in the 1980s reflected different engineering philosophies: U.S. designs emphasized lightweight structures, while Danish turbines prioritized durability and reliability. This difference proved critical in California, where Danish designs showed superior performance and longevity. Modern turbines are significantly more efficient, extracting up to 10 times more energy than early models due to advances in airfoil design and higher tip-speed ratios (Manwell et al., 2009). At the same time, turbine size has increased substantially, with rotor swept areas expanding dramatically, especially in offshore applications. More recently, designs have shifted toward greater efficiency in lower wind conditions, further broadening the applicability of wind energy systems.

Evolutionary aeroelastic design theory

The more recent advances reviewed above came at the same time as the Constructal Law, which is a unifying principle in physics that governs the emergence and evolution of flow configurations in both natural and engineered systems. This coincidence is an opportunity to view the evolution of wind turbines based on theory, and to predict their future.

From a thermodynamics viewpoint, the wind turbine is a live-state system in thermodynamics, not a dead-state system (Bejan, 2000, 2016a, 2016b). The live system contains flows and freely changing features: shape, structure, boundary, rhythm, and history. In short, the live system has evolution (form, movement, flow). The live system is not the “any” black box without configuration, which is the subject of classical thermodynamics.

In this section, we show how to predict the evolutionary tendencies documented in the preceding sections. Intuitively, it is to be expected that where the wind is stronger, the wind turbine installation should be stronger (more massive), and the power extracted from the wind should be greater. The dataset, compiled from Wind Power EI (The Wind Power EI, 2024), includes more than 400 commercial wind turbines spanning a wide range of sizes and designs, with no additional filtering criteria applied; the regressions in this section are presented in log–log form. Another point to note is that the scaling relationships developed in this study are intended for modern horizontal-axis wind turbines, as the theoretical framework is based on horizontal-axis configurations and is not directly applicable to vertical-axis designs. In addition, it should be noted that the dataset includes both onshore and offshore wind turbines; however, offshore turbines represent a small fraction of the sample (approximately 6%), and the analysis is intended to capture general scaling trends across the combined dataset.

The predictive path from speed to force, size, and power was proven in animal and engineering design. Early predictions were animal skeletons and the wheel (Bejan, 2010), and the evolution of airplanes (Bejan et al., 2014), helicopters (Chen et al., 2016), and boats with sails (Bejan et al., 2020). These demonstrations were educational because each addressed a familiar design that exhibits changes in a discernible direction. Along the way, these examples revealed the phenomenon (an inner tendency) that unites them, which is the evolutionary design of the flow of stresses through the moving and morphing flow structure (Bejan et al., 2024). This tendency makes itself visible in the evolution of loaded structures in motion, which is toward lightness and smaller size (Bejan, 2016a; 2016b, 2019).

Essential in the following analysis is the documented example of a cantilever beam that evolves with freedom toward lightness (Bejan, 2000). That is the shape visible from the outside, but the analysis is about moving and removing beam material so that the strangulation of the flow of stress is reduced at every turn, with every change in the configuration of the solid structure. The cantilever beam evolution is essential because, in their simplest models, the turbine tower and the rotor blade are beams in bending.

The wind turbine system has two main organs, the tower and the rotor. We describe them analytically in terms of the scales identified in Figure 6. The analysis employed here is scale analysis (Bejan and Lorente, 2008). The scales of the tower are the height H and the diameter d. We assume that the tower is a body of revolution. The diameter may vary with altitude; however, that variation is a secondary feature that does not deny the reality that the scale of the transversal dimension is d. In other words, if the tower is tapered, its diameter near the top is d multiplied by a factor of order 1 and less than 1. Near the base, the diameter is d multiplied by a factor of order 1 and greater than 1. Factors of order 1 are neglected in scale analysis. What matters is the order of magnitude of d, or the scale of the volume of structural material (V) invested in the tower, namely, V ∼ Hd².

Figure 6.

Left: Wind load and tower deflection. Right: Wind turbine general dimensions, Scale of wind turbine. Based on a 3D model by Naufal Kusumah on GrabCAD (Kusumah (n.d)).

Related to the height H is the wind speed U that impacts the rotor. Because of the air boundary layer near the ground, the wind speed is greater when the tower is taller. This relationship is postponed at this introductory stage; we assume that the U and H scales are independent.

The rotor scales are more numerous. The rotor diameter, D, is the same scale as the rotor radius and the length of one blade. The number of blades is n. The blade thickness (t) is measured in the direction perpendicular to the rotor disk of frontal area D². One blade has the scales D, t, and width w, which is measured in the plane of the disk (Figure 6). We simplify the analysis by regarding the scale t as the same as the scale of w. Other features and scales will recommend themselves as we proceed.

The power (P) extracted by the rotor from the wind has the scale F · U, where F is the drag force felt by the rotor,

F \sim C_{D} D^{2} σ \frac{1}{2} ρ_{a} U^{2}

(1)

The factor σ is the solidity of the rotor cross section, namely, the fraction of D² that is impacted by the wind:

σ \sim \frac{n w D}{D^{2}} \sim n \frac{w}{D}

(2)

We expect σ to be sensibly smaller than 1, but finite. The density of air is ρ_a. The drag coefficient is of order 1 and relatively insensitive to U and the corresponding Reynolds number (Bejan, 2019). Therefore, factors of order 1 such as C_D and 1/2 will be left out of equation (1).

We focus on the volume of material, which is predictable from the evolution of the configuration (external shape and internal structure) of a beam in pure bending. The tower is a beam of length H, loaded at the free end by a transversal force F, known as equation (1). At the end of an exhaustive program of changing the beam shape and structure (one at a time, or two at the same time), the scale of the tower volume is consistently of the order of

V \sim \frac{E F δ}{s_{m a}^{2}}

(3)

where s_ma is a known constant that accounts for the maximum allowable stress of the material. The factor E is the modulus of elasticity of the material. Finally, δ is the deflection of the free end, aligned with F. The tower is elastic; therefore, δ and F are proportional, F = kδ, where k is the spring constant of the tower modeled as a beam in pure bending. The volume V scale is

V \sim \frac{E}{s_{m a}^{2} k} F^{2}

(4)

The power extracted from the wind (P) increases with U as well,

P \sim F U

(5)

By eliminating F between equations (4) and (5), we arrive at the prediction that the power should increase monotonically with the tower size,

P \sim V^{1 / 2} U s_{m a} {(\frac{k}{E})}^{1 / 2}

(6)

Figure 7 shows a trend consistent with this prediction. The cloud of data is underpinned by the statistical correlation P = (25.6 kW) · (Tower Mass)^0.822, with R² = 0.17. By comparing the empirical fit with equation (6), and assuming that wind speed U, maximum allowable stress s_ma, and the ratio k/E remain approximately constant across the turbines, we can treat these terms as a constant C. Additionally, since mass is proportional to volume (Mass = ρV), equation (6) simplifies to P ∼ C · Mass^1/2. This theoretical prediction is consistent with the observed trend in the data, despite the scatter.

Figure 7.

Rated power versus tower mass (The Wind Power EI, 2024).

The corresponding analysis for the rotor follows the same steps. Again, the scale of the tower height H is the same as the scale of the rotor, D. The scale of H is one of the results of the analysis that led to equation (3). The details of that analysis can be found in chapter 2 of (Bejan, 2000), and chapter 10 of (Bejan and Lorente, 2008). For example, the V scale quoted in equation (3) was derived from two relations between the length (H) and diameter (d) of a solid rod implanted at one end and loaded transversally with F at the free end. Those relations are written in the present notation as follows:

s_{m a} \sim \frac{F H}{d^{3}}

(7)

δ \sim \frac{F H^{3}}{E d^{3}}

(8)

By solving the system (7, 8) for d and H, we obtain equation (3) and

d \sim s_{m a}^{- 3 / 5} {(E δ)}^{1 / 5} F^{2 / 5}

(9)

H \sim s_{m a}^{- 4 / 5} {(E δ)}^{3 / 5} F^{1 / 5}

(10)

From these follows the slenderness ratio of this simple model of the tower,

\frac{H}{d} \sim {(E δ)}^{2 / 5} {(s_{m a} F)}^{- 1 / 5}

(11)

or, after replacing δ with F/k,

\frac{H}{d} \sim {(\frac{E}{k})}^{2 / 5} {(\frac{F}{s_{m a}})}^{2 / 5}

(12)

The amount of structural material required by the rotor (n blades) follows from the same method. One blade is pushed horizontally by the force

F_{b} \sim C_{D} w D \frac{1}{2} ρ_{a} U^{2}

(13)

where C_D ∼ 1 and wD is the frontal area seen from the direction of the approaching air. The scale of the blade volume is

V_{b} \sim \frac{E F_{b} δ_{b}}{S_{m a}^{2}}

(14)

where δ_b is the blade deflection in pure bending. If the blade stiffness is k_b ∼ F_b/δ_b, the blade volume is

V_{b} \sim \frac{E}{s_{m a}^{2} k_{b}} F_{b}^{2}

(15)

The blade width w is also the length scale of the nacelle. In the simplest model, the nacelle is a roundish body with one length scale (w); therefore, the nacelle volume is of order w3, and the mass is

M_{n} \sim w^{3} ρ_{n}

(16)

where ρ_n is the volume averaged density of the nacelle. The volume estimates for the tower and one blade, Equation (4) and (15), can also be expressed as mass inventories, in order

M_{t} \sim \frac{E}{s_{m a}^{2} k} F^{2} ρ_{t}

(17)

M_{r} \sim n \frac{E}{s_{m a}^{2} k_{b}} F_{b}^{2} ρ_{t}

(18)

Interesting at this stage is the size of the rotor relative to the tower. Dividing equation (18) by equation (17), and using equations (13) and (1) for F_b and F, we obtain

\frac{M_{r}}{M_{t}} \sim \frac{1}{n} (\frac{k ρ_{r}}{k_{b} ρ_{t}})

(19)

Arguably, the factor in parentheses is a factor of order 1. The prediction is that in terms of mass (or weight), the rotor size should be proportional to the tower size, but smaller. Figure 8 confirms this prediction. The power-law formula correlates the data. P = (0.43 kg) · (Tower Mass)⁰.⁸⁶, with R² = 0.6.

Figure 8.

Top: Rotor mass versus tower mass; Bottom: Nacelle mass versus tower mass (The Wind Power EI, 2024).

Next is the size of the nacelle, equation (16), relative to the size of the rotor, or the tower. If we model one blade as a body of revolution (cone, approximately) with the scales D and w, the blade volume is of order w²D, and the rotor mass is

M_{r} \sim n w^{2} D ρ_{r}

(20)

The conclusion is that the rotor size should be roughly proportional to the tower size, and smaller, assuming that the group in round brackets is of order 1. Finally, from equations (16) and (18), we find the proportionality

\frac{M_{n}}{M_{r}} \sim \frac{σ}{n^{2}} \frac{ρ_{n}}{ρ_{r}}

(21)

Because ρ_n and ρ_r are comparable, and σ < 1 while n² > 1, the nacelle (M_n) should be proportionally smaller than the rotor (M_r):

\frac{M_{n}}{M_{r}} \sim \frac{σ}{n^{2}} o r \frac{M_{n}}{M_{t}} \sim \frac{σ}{n^{3}}

(22)

The statistical correlation of the data of Figure 8 is Nacelle Mass = (1.5 kg) · (Tower Mass)^0.8, with R² = 0.56.

The three correlations exhibit different levels of scatter, reflecting the nature of the variables involved. The relationships between structural masses (tower–rotor and tower–nacelle) show higher R2 values (0.60 and 0.56), indicating stronger geometric and structural coupling. In contrast, the relationship between power and tower mass has a lower R2 (0.17), as the two variables are not of the same nature. While tower mass is a structural quantity, rated power is a design parameter influenced by multiple considerations beyond structure. For example, two turbines with similar tower masses may be designed for different rated powers depending on rotor size, generator capacity, or target operating conditions. Therefore, the power–mass correlation should be interpreted as capturing an overall scaling trend rather than a strong predictive relationship, while the mass–mass correlations reflect tighter structural scaling.

Conclusions

This article outlined the historical evolution of wind turbines and showed how the Constructal Law accounts for the design proportions evident in the evolution of these flow architectures for power. From the earliest panemone windmills developed by Persians to the massive offshore turbines exceeding 10 MW in capacity, we have shown that this evolution is not random but follows a predictable and physics-based path.

By systematically analyzing global wind turbine data, we derived theoretical formulations that are consistent with observed trends, including relationships between tower weight and power output, rotor diameter and nacelle volume, and overall size versus power capacity. While the strength of these relationships varies, with tighter correlations observed among structural variables, the overall patterns indicate that wind turbines evolve in response to the fundamental tendency to provide access to everything that flows, fluid, power, and stresses through the solid structure.

More broadly, the Constructal Law provides a powerful framework for understanding how flow-based systems, from wind turbines to aircraft, morph over time to improve performance through freedom to change. The Constructal Law accounts for the phenomenon of design occurrence and evolution everywhere in nature. The Constructal Law is fundamentally distinct from the Second Law of Thermodynamics, which accounts for the distinct phenomenon of irreversibility everywhere in nature.

Evolutionary design is the staircase to design performance and permanence, as in all the persisting designs of nature, animate and inanimate. This article shows that the cost and time associated with trial-and-error design processes can be reduced significantly by relying on this predictive framework. Improvements are accessible not only in wind turbine design but also in the structural and aeroelastic development of systems such as high-aspect-ratio blades and offshore platforms. The application of evolutionary design across fields, from aerospace to environmental engineering, underscores the Law’s broad relevance.

Future research may consider more complex settings of power extraction from the wind, such as wind speed and tower height, the shift from vertical-axis to horizontal-axis turbines, new advances in lightweight materials, and offshore-specific design adaptations. Fundamentally, these are new opportunities to broaden the use of the Constructal Law by offering a roadmap for designing more efficient, sustainable, and resilient energy systems. Future work may also explore the connection between Constructal Law and the Betz limit, the fundamental aerodynamic bound on wind energy extraction, to further integrate evolutionary design principles with established efficiency constraints in wind turbine theory.

Successful designs with long lifespans emerge not randomly, but as part of a natural, law-governed phenomenon that favors flow efficiency and structural coherence. The future of wind power and sustainable technologies will continue to be shaped and heralded by this principle.

Footnotes

Acknowledgments

The U.S. Air Force Office of Scientific Research supports Prof. Mardanpour’s research through the grant numbers FA9550-22-1-0525 and & 23-1-0716.

ORCID iDs

Pezhman Mardanpour

Hadi Ebrahimi Fakhari

Author contributions

Author contributions are as follows:

• Pezhman Mardanpour, Conceptualization, Methodology, Writing Original Draft - Review & Editing, Supervision

• Adrian Bejan, Conceptualization, Methodology, Writing Original Draft, Review & Editing

• Natalia Rangel, Methodology, Formal analysis, Investigation, Resources, Data Curation - Original Draft, Writing - Review & Editing

• Hadi Ebrahimi Fakhari, Methodology, Formal analysis, Investigation, Resources, Data Curation, Writing - Review & Editing, Visualization.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Air Force Office of Scientific Research (FA9550-22-1-0525), (FA9550-23-1-0716).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability Statement

The data supporting the findings of this study are available from the authors upon request.*

Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT to improve the proficiency and readability of some parts of the text. After using it, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

Appendix

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