How the Fibonacci Sequence Inspired Turbines

The Fibonacci sequence appears so often in nature that it has captured the human imagination for centuries. It’s also inspired human design in several industries.

In this blog, we’ll specifically look into how it inspired the design of turbines in the industrial and energy sectors. 

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Other examples include snail shells and nautilus shells growing in logarithmic spirals, allowing for expansion without changing shape. 

Sunflowers and pinecones arrange seeds in the Fibonacci sequence to maximize space and sunlight exposure. Tornadoes and whirlpools use spiral dynamics to channel energy efficiently. In animals, spiral body structures, like a seahorse’s curled tail, provide grip and stability. 

By studying natural spirals, scientists and engineers develop innovations in robotics, aerodynamics, and sustainable design, enhancing efficiency and resilience in human-made systems.

These patterns show up everywhere… and they may even be reshaping the future of renewable energy.

Interested in patterns? Read: 10 Patterns in Nature that Solve Design Problems

When researchers first observed how the golden ratio helps plants optimize sunlight and water, the question emerged: could the same principles apply to turbines? The answer has led to some remarkable and highly efficient designs.

In this article, we explore how the Fibonacci sequence inspired turbines, as explained in this thought-provoking youtube video by Ziroth: Uncovering The Genius of Fibonacci Turbines.

The Mathematics Behind the Fibonacci sequence

Closely related to the Fibonacci Sequence is the golden ratio, approximately 1.618, which generates spirals and proportions we often see in leaves, shells, and flowers. This undeniably reflects efficiencies in natural growth.

The Fibonacci sequence is a series of numbers where each is the sum of the two before it. Credit: Randaum via Wikimedia Commons

In sunflowers, for instance, seeds spiral outwards in both directions, following Fibonacci numbers. This arrangement allows them to pack tightly without overlap. Leaves, too, are often spaced at the golden angle (137.5 degrees), ensuring each gets maximum exposure to light and rain. These optimizations sparked the idea: could turbine blades harness the same efficiencies?

The Golden Ratio Meets Turbines

Traditional turbines, such as the Savonius design first patented in 1926, are reliable but not very efficient. 

A team of Spanish researchers tested a bold idea: replace the standard blade curve with one shaped by the Fibonacci sequence. The result was a 14% increase in efficiency! Credit: "Investigation of an innovative savonius turbine in practice" via nature.com

In a world defined by exponential growth and ever-increasing numbers, 14% might seem small at first glance - but in reality it represents a significant leap forward. For context, even single-digit improvements can shift entire industries, and a 14% gain translates into a major win. 

By enhancing the drag on advancing blades and reducing resistance on returning blades, the Fibonacci-inspired shape produced more usable power.

Other experimental projects have gone further. A hydro turbine designed with blades expanding according to the golden spiral achieved 15% greater efficiency at slow water speeds compared to traditional propellers. While the advantage diminished at higher speeds, the design shows promise for small-scale, low-flow applications.

Why is the Golden Ratio so efficient?

Nature moves and grows in precise, turbulent, spiraling flows. It exploits the energy that is rolled up in turbulence. 

Human-made technology, on the other hand, tries to suppress turbulence. 

Birds, insects, fish, and the human heart clearly demonstrate the advantage of this strategy. 

In the words of Jay Harman: “Humans insist on traveling in straight lines and guzzle energy. Nature travels in spirals and sips energy. Truly grasping the significance of this simple fact throws open the door to reinventing the industrial world and gives us the tools to rescue our ailing planet, populations, and economy.”

The success of our designs lie in the properties of logarithmic spirals, which expand consistently, making them effective for channeling flows of air or water. Here’s how.

The Fibonacci Sequence’s Flow Efficiency

The golden ratio creates a curve that naturally matches the way fluids (air or water) swirl in vortices. Turbine blades shaped or arranged with this spiral allow air or water to flow smoothly with less turbulence and drag. This reduces energy loss and makes the turbine more efficient.

Even Distribution of Forces

When blades are positioned following the Golden Angle (~137.5°), forces like pressure and vibration get distributed more evenly. This reduces wear on the turbine, extends its lifespan, and lowers maintenance needs.

Compact, High-Output Design

The spiral arrangement allows blades to be packed closely while still maintaining optimal spacing for airflow. This can produce more power from a smaller device, making turbines lighter, quieter, and more effective in both wind and water.

Nature-Inspired Innovation

Just like pinecones, sunflower seeds, and shells optimize space and energy capture through spiral patterns, turbines modeled on the golden ratio harness nature’s blueprint for maximum efficiency with minimal wasted energy.

Real-World Example: The Liam F1 Archimedes Turbine

Perhaps the most striking real-world application is the Liam F1 Archimedes, a spiral-shaped wind turbine that looks more like a sculpture than a machine. Instead of relying solely on lift, it combines lift and drag, channeling wind through its spiral blades in a way that boosts rotation while minimizing noise.

In tests, the Liam F1 achieved efficiency levels on par with some of the best conventional turbines, while being quieter and more suitable for urban settings. Its spiral shape also allows for easier manufacturing and potential recyclability, benefits that could help expand renewable energy access.

What is the Future of Fibonacci Turbines?

The Fibonacci sequence may have started as a mathematical curiosity, but its spirals could soon power parts of our everyday lives. 

While Fibonacci and golden spiral turbines are not going to replace massive wind farms in the next few years, they hold real potential for smaller, distributed energy systems. 

From urban rooftops to boats and off-grid homes, there are a range of potential applications. By taking cues from sunflowers, pinecones, and seashells, engineers are unlocking new ways to harvest clean energy more beautifully and efficiently.

Something which struck me was what Jay Harman mentioned whilst on a call in the Biomimicry Confluence… that there exists 500+ spiral / flow innovations that have yet to be applied today.

Interested in renewable energy? Read: 10 Biomimicry Examples in Renewable Energy

In Summary 

The Fibonacci sequence and golden ratio are patterns found widely in nature, and when designers use these patterns in turbine design, they’re tapping into natural efficiencies that have evolved over millions of years. 

Engineers often use it as a starting point and then refine the design with fluid dynamics simulations, materials science, and practical testing.

Wild regards

Anita and the Learn Biomimicry team

PS - If you are interested in learning more about spirals and other patterns in nature that inspire human designs, we highly recommend signing up for a free trial of our Biomimicry Short Course Set. 

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