Uncovering The Genius of Fibonnaci Turbines

this is the Fibonacci sequence and this the closely related golden ratio and golden spiral and they seem to appear everywhere and it seems like turbines may be no exception when I read about how the golden ratio helps optimize energy harvesting in Plants I had to find out whether Engineers designing turbines are using this ancient knowledge for more modern applications this led me to discovering a number of spellbinding turbines that not only look like art installation but also promise impressive efficiencies with a host of other potential benefits with an ever increasing demand for energy independence from clean and affordable sources it's no surprise that research into more efficient shapes for these small distributed turbines is a Hot Topic when looking for engineering inspiration I've often heard that nature is the best source because it has a 4 billion year track record so what is the truth about these spirals we keep seeing in nature that could reshape the turbines that power our lives and what does the Fibonacci sequence have to do with it all the Fibonacci sequence and golden ratio have gained a lot of traction in modern mythology the infinitely repeating patterns 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 Financial Market it's hard to talk about the Fibonacci sequence without going down a rabbit hole of myths literally the first myth is that Fibonacci came up with the famous sequence by calculating rabbit populations this isn't actually true Leonardo The Traveler from Pisa as he was known in his day learned about the Hindu Arabic numerical system from Traders and Merchants around the Mediterranean Coast in the late 12th century he was so excited about how useful these nine Indian Figures were compared to the clumsy Roman numerals for things like bookkeeping trading 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 have been talking about for centuries and that later acquired his name the Fibonacci sequence because he was the one who explained it to a European audience this is where the rabbit puzzle comes back in working out how many rabbits would spring from a single pair within one year in idolized conditions just illustrates the sequence where each number is the sum of the two numbers preceding it so if that's the Fibonacci sequence how does it relate to the golden ratio and where do spirals come into it all based on the work of Plato and Pythagoras uid found what he called the division in extreme and mean ratio this is what you get when a line is divided so that the ratio between the smaller SE section and the larger section is the same as the ratio between the larger section and the whole line following these proportions pentagrams within pentagons can go on and on without losing shape rectangles with sides in this ratio Nest perfectly into each other forever curves drawn around the ratio points of these rectangles create a logarithmic spiral that grows or shrinks by the same ratio with every quarter turn this amazing ratio was called the Divine proportion in the 15th century and would only go on to acquire its golden name in the 20th century math historians say that this was the first number that was found that couldn't be expressed as a fraction the first known numerical expression of this ratio was apparently in Germany in 1567 it was as 1.618 3988 7 dot dot dot with the dots showing that the number goes on forever without repeating so it's shortened to 1.618 and much later in the 1900s the even more beautifully simple fi now this is where fi meets Fibonacci around the 15th and 16th centuries it was also discovered that fi approximately 1.618 is more or less what you get if you go backwards through the higher numbers of the Fibonacci sequence you can see that the ratio between a number and the one before it gets closer to five as you go along the Fibonacci sequence it's not exactly th but very close the Fibonacci spiral is generated by squares with ratios of the Fibonacci sequence this is instead of golden ratio rectangles used for the very similar golden spiral again these are not exactly the same but 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 is an interesting distinction and one that mathematicians are probably very serious about however the conflation of the Fibonacci sequence and the golden ratio is nothing compared to the many myths around the golden ratio and golden spiral it's been linked to just about everything like proportions of the human body another one is that the Mona Lisa follows the golden ratio like some paint by numbers exercise other fables are that it was used in the design of the pathon and pyramids the issue is we can retrospectively go back and fit the golden spiral to just about anything as for the chump spiral I'm not really sure what that one's all about maybe you can let me know in the comments below there are also some amazing spirals in nature that are often said to be in the golden ratio but actually aren't from galaxies and ocean waves to bands of tropical Cy clones these are instead logarithmic spirals in a logarithmic spiral a straight line drawn outwards from the center always intercepts the spiral at a constant angle this expansion out could be in the golden ratio as the golden spiral is a logarithmic spiral however not all logarithmic spirals have to be in the golden ratio another kind 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 moving around the center but over time just going further and further out however unlike logarithmic spirals the growth of an Archimedes spiral is constant so if the occurrences of the Fibonacci and golden spirals seem to be false what is all the hype about after all there must be reasons why Engineers like those in a research team in Spain want to use it in their turbine BS before revealing where and why these patterns actually do appear in nature I want to show you the first Fibonacci inspired turbine to give you a taste of what this pattern might unlock I have this small turbine model to help me describe this development and if you want to easily and for free understand more deeply what's happening inside designs like this then you need to check out today's sponsor brilliant brilliant lets you learn by doing and is the best way to help reach your goals for understanding maths science and engineering at your own pace during my PhD I have to keep learning new skills and when my project started to go down the route of machine learning I went to brilliant as it was an unbeatable interactive resource to get me up to speed they have thousands of lessons from the basics up to Advanced levels that got me up to speed so I could start understanding academic literature on a new topic the lessons are seriously fun and can be done in bite-sized bits to make sure it fits around your busy schedules whether you're an academic student professional or lifetime learner as well as as binging the data and computer science courses it's been great to sharpen my knowledge of other topics with real world examples like finding out what really makes a strong password and if you're finding the mathematical sequences in this video interesting you're going to love all of the Math's courses that are available whether it's for career progression or your own curiosity go check out brilliant with my link below brilliant.org zeroth for 30 days free and the first 200 subscribers will get 20% off an annual plan now now back to this little model and how the Fibonacci sequence could improve it this is half of a savonus wind turbine these turbines rely on drag as the wind pushes them round the reason these simple vertical axis wind turbines are still around today is because they're cheap quiet reliable and can be small in size they also don't require much wind to get them moving or mind which way that wind is coming from which makes them a good choice for urban environments where the wind can be quite C chaotic however their efficiency is also pretty low which is what a team of researchers from Spain wanted to see if they could change it's still in the research phase but the results are exciting the team looked at the blade profile of a simple savonus turbine which was first patented way back in 1926 by using blades that curved following the Fibonacci spiral instead of the standard savonus blade curve the team showed a 14% increase in efficiency with an increased power and thrust coefficient as power is mainly produced 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 I do however wonder how much of this Improvement is just due to a logarithmic spiral and how it would have fed if it didn't exactly follow the Fibonacci or golden spiral either way there is clearly something to the spiral pattern PN which makes sense when we go back and look closer at the natural world my favorite real example of the Fibonacci sequence in nature has to be sunflowers the seeds spiral out in two directions so that they can pack in tightly without overlapping if we take a look the number of spirals in each Direction matches the Fibonacci sequence although as an aside note exceptions do occur the Royal Society crowdsourced sunflower research and after verifying 657 flowers they found that about 1 in five had even more complex patterns which will no doubt be studied intensely in years to come however the vast majority of sunflowers do follow the Fibonacci sequence pine cones are also like this and pineapples are a fascinating example built from adjacent hexagons three kinds of spirals appear eight to the right 13 to the left and 21 vertically adding to the the Fibonacci Mystique the magic continues when we look at the placement of leaves around some plants too the angle between leaves is at 137.5 De which is what you get if you bend the golden ratio around a circle and measure the smaller angle it turns out this golden angle minimizes how much one leaf blocks out the next allowing every leaf 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 it maximize the turbin exposure to energy sources to help capture more energy as electricity just like it helps plants get more water or sun the answer is people are trying and it's leading to turbine shapes that I'd never never seen before but the question is can they match the efficiency of traditional horizontal AIS wind turbines firstly we can look at an experimental setup of a hydro energy turbine that follows the golden spiral the spiral was designed to turn around the core so that the width of the blade expands at a ratio of 1.618 the researchers tested the prototype in a water canal and found that compared to a more conventional propeller turbine with the same blade diameter the three-blade golden spiral had 15% greater efficiency at slow water speeds though these benefits weren't seen as the water got faster the idea here is that the golden ratio means a maximum amount of energy can be harvested from gently flowing water just like how plant leaves get a maximum amount of rain to the roots and this idea seems to be working this could be a good choice for small scale slow flow rate turbines and I'll be interested interested to see how it works as they scale the design up and finally a real world turbine that has made it out of the research papers the Liam F1 Archimedes I have to be honest here the naming of this turbine is slightly confusing me as we learned before the aredi spiral isn't logarithmic and definitely isn't a golden spiral however in an interview the CTO said it was based on the golden spiral and looking at videos and images of the turbine it is at least using a logarithmic spiral perhaps the name is just a nod to the Archimedes screw which does have a vague resemblance it is possible to make an Archimedes spiral wind turbine as shown by Robert Mari Smith but this isn't one of them either way it's a great demonstration of how a spiral design can be used instead of a bladed configuration like 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 spinning and it doesn't take a lot of wind to get it going as it turns and more air blows into the spiral their shape makes it shoot out again almost like jet thrusters and creates an equal and opposite force that spins the turbine more this is a key difference to Conventional horizontal axis wind turbines as it is using both lift and drag to spin the turbine the findings first came out in a 2014 paper that the Liam f1's inventor co-authored and I've managed to 3D print the model from that paper thanks to a model that was made available from easycad Solutions on YouTube it was an unusually still day outside when I was filming so there was no real wind to try this out with however even the very slow air from my mini heater was more than enough to get it spinning and I could feel the sideways air starting to be shot out of the side needless to say with a hair dryer this thing went absolutely crazy it appears that the commercialized Liam F1 turbine is based on this design where we have three equally spaced expanding circular blades wrapped around one another and although the full-size turbine may not be overly portable the 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 this as a pretty stylish energy harvesting device for commercial and residential buildings in populated areas and to power auxiliary loads of things like boats as for the efficiency this turbine is meant to be more efficient than competing Urban turbine designs in the research paper it was found to be approximately 25% efficient at converting wind power to electricity though the website for the commercial turbine States 40% which is similar to the best conventional bladed turbines the manufacturer also says it is much quieter possibly because it doesn't have large VES at the blade tips which conventional turbine blades do this principle of reducing tip vortices here is similar to the thidal propeller that I've covered in a couple of my other videos where the vortices created are spread along the blade instead of noisily rocketing off the blade tips spiral turbines may be an interesting way to boost the efficiency of lowcost urban turbines and look pretty awesome while they do it these small spiral systems could also be much easier to manufacture than bladed turbines as they could be simply formed from lightweight sheets of metal or plastic bent into spiral shapes this could also make them easier to recycle leading to less waste I'd really like to see more research done on the use of Fibonacci sequences and golden spirals as the early research is looking really promising though I do think that weight and drag limitations will stop them ever replacing the huge turbines we see in many wind farms also as cool as the golden and Fibonacci spirals are I think the real heroes here are the logarithmic spirals given the very long and Rich history of discoveries about the Fibonacci sequence the golden ratio and spirals in all their forms it's definitely a technology to watch if you've enjoyed this video please subscribe as it helps me to make more videos about the interesting technology helping to improve the efficiency and sustainability of Our Lives you might also like this other video I made on a compact desalination system that MIT have released and if you got any other cool research you want to look into please leave it in the comments below I've also left another video from Joe Hansen from Bart in the description below so you can go and watch that if you want to learn even more about the golden ratio and golden spirals thanks for watching

Channel: Ziroth

Views: 507,757

Keywords: Science, Engineering, STEM, Electric, Zero, Tesla, News, Research, EV, Battery, wind, energy

Id: i4TEMZ5dyPo

Length: 17min 42sec (1062 seconds)

Published: Wed Jan 31 2024