# Solar array using the Fibonacci formula

1. While most 13-year-olds spend their free time playing video games or cruising Facebook, one 7th grader was trekking through the woods uncovering a mystery of science. After studying how trees branch in a very specific way, Aidan Dwyer created a solar cell tree that produces 20-50% more power than a uniform array of photovoltaic panels.

2. His impressive results show that using a specific formula for distributing solar cells can drastically improve energy generation. The study earned Aidan a provisional U.S patent – it’s a rare find in the field of technology and a fantastic example of how biomimicry can drastically improve the design.

3. Aidan Dwyer took a hike through the trees last winter and took notice of patterns in the mangle of branches. His studies into how they branch in very specific ways lead him to a central guiding formula, the Fibonacci sequence. Take a number, add it to the number before it in a sequence like 1+1=2 then 2+1=3 then 3+2=5, 8, 13, 21 and so on a very specific pattern emerges.

4. Turns out the pattern and its corresponding ratios are reflected in nature all the time and Aidan’s keen observation of how trees branch according to the formula lead him to test the theory. First, he measured tree branches by how often they branch and at what degree from each other.

5. To see why they branch this way he built a small solar array using the Fibonacci formula, stepping cells at specific intervals and heights. He then compared the energy output with identical cells set in a row. Aidan reports the results: “The Fibonacci tree design performed better than the flat-panel model. The tree design made 20% more electricity and collected 2 1/2 more hours of sunlight during the day. But the most interesting results were in December when the Sun was at its lowest point in the sky. The tree design made 50% more electricity, and the collection time of sunlight was up to 50% longer!”

6. His work is certainly piquing the interest of the solar industry, and even more impressively he is demonstrating the power of biomimicry — a concept that many see as the pinnacle of good design, but one that thus far has been exceptionally difficult to achieve. Way to go!

By: Andrew Michler (Inhabitat)
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Linking Trees’ Fibonacci Sequence to Solar Power Wins Student A Young Naturalist Award

1. When 13-year-old Aidan took a winter hike through the Catskill Mountains, he noticed something spectacular about the bare trees. “I thought trees were a mess of tangled branches,” he would later recall, “But [then] I saw a pattern in the way the tree branches grew.”

2. Armed with a protractor, Aidan measured the angles of the branches and discovered they grew in a Fibonacci sequence—a mathematical pattern that can be observed throughout nature, from the curve of nautilus shells to the spirals of galaxies. In this famous sequence, each number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, continuing infinitely. Could this branch pattern help trees absorb more sunlight? Aidan’s pursuit of that question in his essay The Secret of the Fibonacci Sequence in Trees earned him a 2011 Young Naturalist Award.

3. To test his hypothesis, Aidan constructed a model tree based on the Fibonacci sequence of an oak, using PVC pipes as branches and PV solar panels as leaves. After testing his prototype against a flat solar panel, Aidan confirmed that trees outperformed the traditional model—in winter, by as much as 50 percent.

4. As it turns out, this distribution of branches minimizes the extent to which limbs shade the leaves below them. And unlike a flat solar panel—which must be mechanically readjusted to follow the Sun’s moving path—a Fibonacci-sequence tree can still absorb light when the Sun sits low in the sky. “Collecting the most sunlight is the difference between life and death,” wrote Aidan, who thinks humans can put treelike solar panel designs to use, especially in urban spaces where sunlight is scarce. He has already applied for a patent for his PV solar panel tree.

5. For his next project, Aidan plans on comparing the Fibonacci sequences of different trees to see if one species’ branch arrangement is more efficient than another. He knows he’ll find another secret in nature if he just keeps looking up.

(Courtesy: American Museum of Natural History)