Uncovering The Genius of Fibonnaci Turbines

this is the Fibonacci sequence and this the golden ratio and the golden spiral closely related and seem to appear everywhere and it seems that

turbines

may be no exception when I read about how the golden ratio helps optimize energy harvesting in the floors. I had to find out if the engineers who design

turbines

are using this ancient knowledge for more modern applications. This led me to discover a number of fascinating turbines that not only look like art installations but also promise impressive efficiencies with a host of other potential benefits with increasing demand for energy independence. clean and affordable sources, it is no surprise that research into more efficient ways for these small distributed turbines is a hot topic when looking for engineering inspiration.

I have often heard that nature is the best source because it has a history of 4 billion years, so what is it? the truth about these spirals we keep seeing in nature that could reshape the turbines that power our lives and what the Fibonacci sequence has to do with them the entire Fibonacci sequence and the golden ratio have gained a lot of traction in modern mythology the patterns The infinitely repeating patterns that they generate have been used to reveal God, codify beauty and everything from architecture to human faces, explain the harmony of musical greatness, the

genius

behind the Mona Lisa and apparently even predict the financial market. .

It's hard to talk about the Fibonacci sequence without going down a rabbit hole. myths, literally the first myth is that Fibonacci came up with the famous sequence calculating rabbit populations. This is actually not true. Leonardo, the traveler of Pisa, as he was known in his time, learned about the Hindu Arabic numeral system from traders and merchants throughout the Mediterranean. Coast, in the late 12th century, was so excited about how useful these nine Indian figures were compared to clumsy Roman numerals for things like accounting, commerce, and weighing things, that he wrote a book about it. This book, Libra Bachi, included an explanation of a sequence of numbers that Indian mathematicians had been talking about for centuries and which later acquired its name Fibonacci sequence because it was he who explained it to a European audience.

This is where the rabbit puzzle comes back. Calculating how many rabbits would emerge from a single pair within a year under idolized conditions simply illustrates the sequence where each number is the sum of the two numbers preceding it, so if that is the sequence of Fibonacci, how does it relate to the golden ratio and where do spirals come into all of this? According to the work of Plato and Pythagoras they found what he called the division into extreme and mean ratio. This is what you get when you divide a line so that the ratio between the smaller section and the larger section is the same as the ratio between the larger section and the staves inside. of pentagons can go on and on without losing shape rectangles with sides in this proportion They nest perfectly within each other forever the curves drawn around the proportion points of these rectangles create a logarithmic spiral that grows or contracts in the same proportion with each quarter turn, this astonishing proportion was called the divine proportion in the 15th century and would only acquire its golden name in the 20th century.

Mathematical historians say that this was the first number found that could not be expressed as a fraction. The first known numerical expression of this relationship was apparently in Germany in 1567. It was like 1.618 3988 7 dot dot dot and the dots show that the number continues forever without repeating itself, so it was shortened to 1.618 and much later, in the 20th century, the even most beautiful. simple fi now this is where fi meets Fibonacci around the 15th and 16th centuries. It was also found that fi about 1.618 is roughly what you get if you go back through the higher numbers of the Fibonacci sequence, you can see that the ratio between a number and the previous one gets closer to five as you go down.

The Fibonacci sequence is not exactly the same, but it is very close. The Fibonacci spiral is generated by squares with proportions of the Fibonacci sequence. This is instead of the golden ratio rectangles used for the very similar golden ratio. spiral again, these are not exactly the same but they are very close to be honest as an engineer, the approximation that the Fibonacci spiral and the golden spiral are the same seems perfectly fine to me. I've made much broader assumptions before, but it's an interesting distinction and one that mathematicians probably take very seriously, however, the combination of the Fibonacci sequence and the golden ratio is nothing compared to the many myths in around the golden ratio and the golden spiral, it has been related to almost everything, such as the proportions of the human body, another is that the Mona Lisa follows the golden ratio like some painting by numbers exercises, other fables are that it was used in the pathon design and pyramids, the problem is that we can retrospectively go back and adjust the golden spiral to almost anything, as for the silly spiral.

I'm not really sure what it is, maybe you can let me know in the comments below that there are also some amazing spirals in nature that are often said to be in the golden ratio, but are not actually galaxies and waves of the ocean. bands of tropical Cy clones these are logarithmic spirals in a logarithmic spiral a straight line drawn outward from the center always intercepts the spiral at a constant angle this expansion could be in the golden ratio since the golden spiral is a logarithmic spiral however Not all logarithmic spirals have to be in the golden ratio.

Another type of spiral is the aredi spiral, which will be another important one to remember as we start to look at these new turbine designs. I found a great video that described a spiral as a complicated circle that moves. the center, but over time it goes further and further away; However, unlike logarithmic spirals, the growth of an Archimedean spiral is constant, so if Fibonacci occurrences and golden spirals appear to be false, what's all the fuss about? After all, there must be reasons for it. Engineers like those on a research team in Spain want to use it in their BS turbine before revealing where and why these patterns actually appear in nature.

I want to show you the first Fibonacci inspired turbine to give you an idea of ​​what this pattern could unlock. I have this little turbine model to help me describe this development and if you want to understand more deeply easily and for free what happens inside designs like this, then you should check out today's sponsor, shiny shiny, it allows you to learn by doing and is the better way. To help you achieve your goals of understanding mathematics, science and engineering at your own pace during my PhD, I have to keep learning new skills and when my project started going down the machine learning route, I was brilliant as it was a unbeatable interactive resource. catch me up, they have thousands of lessons from basics to advanced levels that got me up to speed so I could start understanding the academic literature on a new topic.

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Now let's get back to this little model and how the Fibonacci sequence could improve it. This is half of a Savonus wind turbine. These turbines depend on resistance when the wind pushes them. The reason these simple vertical axis wind turbines still exist today is because they are cheap, quiet and reliable and can be small in size. Plus, they don't require a lot of wind to move or worry about where the wind is coming from. They are a good option for urban environments where the wind can be quite chaotic, however their efficiency is also quite low, which is what a team of researchers from Spain wanted to see if they could change it.

It's still in the research phase, but the results are exciting. The team examined the blade profile of a simple Savonus turbine that was first patented in 1926 using blades that curved following the Fibonacci spiral instead of the standard Savonus blade curve. The team showed a 14% increase in efficiency with increased power and thrust. coefficient since power is produced primarily by drag, they say the increase is because the Fibonacci shape increases the drag force of the advancing blade and reduces the drag force of the returning blade, increasing the net driving force . However, I wonder how much of this improvement is just due to a logarithmic spiral and how it would have fed if it hadn't followed the Fibonacci or Golden spiral exactly.

Either way, there is clearly something about the PN spiral pattern that makes sense when we step back. and we look more closely at the natural world. My favorite. A real example of the Fibonacci sequence in nature has to be sunflowers, the seeds spiral out in two directions so they can pack tightly without overlapping. If we take a look, the number of spirals in each direction matches the Fibonacci sequence, although as a side note there are exceptions. It does happen in the Royal Society's sunflower research and, after checking 657 flowers, they found that about 1 in five had even more complex patterns that will no doubt be studied intensively in the coming years;

However, the vast majority of sunflowers follow the Fibonacci sequence. This is also true and pine cones are a fascinating example built from adjacent hexagons. Three types of spirals appear: eight to the right, 13 to the left, and 21 vertically, adding to the Fibonacci mystique. The magic continues when we look at the placement of leaves around some plants. the angle between the leaves is 137.5 De, which is what you get if you fold the golden ratio around a circle and measure the smallest angle. It turns out that this golden angle minimizes how much one leaf blocks the next, allowing each leaf to have optimal exposure to sunlight and rainwater to nourish the plant, but what about wind turbines?

Could we take inspiration from nature and use the golden ratio or golden angle to help wind turbines maximize the amount of energy from wind or water? Could you maximize the turbine's exposure to energy sources to help capture more? energy like electricity, just like it helps plants get more water or sun, the answer is that people are trying and it is giving rise to forms of turbines that I have never seen before, but the question is can they match the efficiency of traditional AIS horizontal wind turbines. We can see an experimental setup of a hydroelectric power turbine that follows the golden spiral.

The spiral was designed to rotate around the core so that the width of the blade expands by a ratio of 1.618. The researchers tested the prototype in a water channel and found that Compared to a more conventional propeller turbine with the same blade diameter, the three-bladed golden spiral was 15% more efficient at low water speeds, although these No benefits were seen as the water became faster. The idea here is that the golden ratio means a maximum. A large amount of energy can be harvested from gently flowing water, in the same way that plant leaves carry a maximum amount of rain to the roots, and this idea seems to be working.

This might be a good option for small scale slow flow turbines and I will be interested. I'm interested to see how it works as they expand the design and eventually a real world turbine that came out of the research papers, Liam F1 Archimedes. I have to be honest, the name of this turbine confuses me a little, as we learned before. the aredi spiral is not logarithmic and it is definitely not a golden spiral, however in an interview the CTO said that it was based on the golden spiral and by looking at videos and images of the turbine, at least it is using a logarithmic spiral, Perhaps the name is just a nod to the Archimedean screw, which bears a vague resemblance, it is possible to make an Archimedean spiral wind turbine like theshows Robert Mari Smith, but this is not one of them by any means, it is a great demonstration of how you can create a spiral design.

It is used in place of a blade configuration as in many conventional horizontal axis wind turbines. So how does it work? The wind blows from the front creating a pressure difference that forces the blades to start rotating and it doesn't take much wind to get them going. As it spins and blows more air into the spiral, its shape causes it to fire again almost like jet thrusters and creates an equal and opposite force that spins the turbine further. This is a key difference from conventional horizontal axis wind turbines as they use both lifts. and drag to spin the turbine, the findings first emerged in a 2014 paper co-authored by the inventor of Liam f1 and I managed to 3D print the model from that paper thanks to a model that became available at easycad Solutions in Youtube.

It was an unusually calm day outside when I was filming, so there was no real wind to test this; However, even the very slow air from my mini heater was more than enough to get it spinning and I could feel the side air starting to shoot out. On the outside it goes without saying that with a hair dryer this went completely crazy, it seems that the marketed Liam F1 turbine is based on this design where we have three equally spaced expanding circular blades wrapped around each other and although The full size turbine can not be too portable, Yore is passively controlled by the drag force, so the turbine always follows the wind direction automatically.

I don't know about you, but I could definitely imagine it being a pretty fancy energy harvesting device for commercial and residential buildings in populated areas and for powering auxiliary loads of things like ships, as for the efficiency of this turbine, it's supposed to be more efficient than competing urban turbine designs. In the research work it was found that it was approximately 25% efficient in converting wind energy into electricity. The commercial turbine website indicates 40%, which is similar to the best conventional bladed turbines. The manufacturer also says that it is much quieter, possibly because it does not have large VES at the tips of the blades, as conventional turbine blades comply with this principle of reducing tip vortices.

This is similar to the tidal propeller that I have covered in a couple of my other videos where the vortices created spread along the blade rather than shooting noisily from the tips of the blades. Spiral turbines can be an interesting way to increase the efficiency of low-cost urban turbines. turbines and look quite impressive while doing it, these small spiral systems could also be much easier to manufacture than bladed turbines, as they could simply be formed from lightweight sheets of metal or plastic folded into a spiral, which which could also make them easier to recycle, leading to less waste.

I would really like to see more research done on the use of Fibonacci sequences and golden spirals, as early research looks very promising, although I think weight and strength limitations will prevent them from ever replacing the huge turbines we see in many parks. Wind spirals are also as cool as golden and Fibonacci spirals. I think the real heroes here are logarithmic spirals given the long and rich history of discoveries about the Fibonacci sequence, the golden ratio and spirals in all their forms, it is definitely a technology to watch out for. If you liked this video, please subscribe as it helps me make more videos about the exciting technology that helps improve the efficiency and sustainability of Our Lives.

You might also like this other video I made about a compact desalination system that MIT has released and If you have any other interesting research you want to investigate, leave it in the comments below. I also left another Joe Hansen video from Bart in the description below so you can check it out if you want to learn even more about the golden ratio and golden spirals thanks for watching