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Now, this is the axis, this is the axis and that is vertical. So, the axis is vertical and that is what they are referring to. So, now, the advantages and disadvantages are like this. The one advantage is that it generates power independent of wind direction, it does not matter which direction the wind is coming because the axis is vertical and the wind is essentially horizontal. I mean unless the wind suddenly starts going vertical which is not what we see in a day from the perspective of the wind turbine typically the wind is horizontal. So, once it is horizontal it does not matter which side the wind is coming from because the axis of the generator axis of the wind turbine is vertical and since it is vertical the wind is always perpendicular to the axis it does not matter from which direction it is coming. So, and that you can see that here because as this thing rotates it says it does not matter whether the wind comes this way or it comes this way it does not matter the wind turbine will keep rotating and you do not have to do anything to re-orient the wind turbine it will rotate, it will just keep rotating. So, that is the one big advantage of it. It is a low cost, partly because of this thing that you do not need this strong tower since the generator is from the ground. So, the generator is placed in the ground here and therefore, you do not need, this tower does not have to be any fancy tower some basic requirements is all that it needs to meet and then it is in a position to operate. Disadvantages are that first of all it is a little low-efficiency type of a windmill or wind turbine, mainly because only one blade works at a time. So, why is this the case? If you look at the image you can see. So, let us say the wind is blowing this way. So, it pushes this blade here and then it runs off of this blade on the sides. So, it does not push this blade as much it pushes this blade more. So, as a result, it rotates this way. So, effectively at this point with these two blades available to you only the blade on your left is the one that is pushing and moving the axis, the blade on your right is not participating in the process if anything is providing a slight resistance to the process. So, it is not effectively participating in the process. And therefore, in terms of capturing energy, this is less efficient, you are wasting some energy whereas, in when you did the vertical windmill where the I mean horizontal axis windmill where the turbines were I mean where the axis was horizontal, the all the blades were always you know reacting to the wind it did not matter which position the blade was right. Whereas here as long as this blade is here, it does not respond to the wind when it rotates around and comes to this location it will be the one that is getting pushed the other one will stay benign. So, therefore, only one blade operates at a time and therefore, it is less efficient relative to the horizontal axis wind turbine. And it may need wires for support and this again depends on the structure because it is a very thin structure, so usually they will have some system by which you know they will take this turbine I mean this shaft and then they will tie it to the ground somewhere they will tie it like that, in some three places to keep it stable. So, that it does not apply. So, that is the activity that they would have to do. And it is usually since it is at the lower, lower location, it generally there is more turbulent flow it is not a very you know the smooth flow of air because there is a lot of you know resistance from the ground the air bounces off the ground. So, instead of air going flat it may suddenly go up and suddenly come down and you will have higher movement in all different directions closer to the ground and because of various obstructions that are present. And so, the flow is much more turbulent it is not very smooth laminar kind of flow so to speak. So, these are some disadvantages when you look at vertical axis wind turbines. (Refer Slide Time: 38:19) Just to give you an idea of what are we talking about let us look at the power generated. If you look at the commercially sold wind turbines some of the large ones that are being sold these days and are being installed internationally these days are having a capacity of the order of 2 to 3 megawatts, as of today that is the capacity that they are having and those are the larger ones. You may find once less than this 1 megawatt and even 500 kilowatts may be there and are probably, there these are the slightly larger ones and so, if there is a large scale investment maybe they are using these larger ones. So, let us look at what it generates per year. So, we have something called a 25 per cent capacity factor. So, what this means is that even though we are rating it at say 2 megawatts, 2 megawatts because the wind varies through the year through the day keeps on varying right. So, because of that, it is not going to give you 2 megawatts consistently there are times it is going to give a lot less than 2 megawatts sometimes it is going to get you closer to 2 megawatts so on. So, this factor simply says on average it is giving you 25 per cent is what it says, that is what it means 25 per cent capacity factor means on average across a year after if you average it across a significant period you will be getting one-fourth the capacity that it is rated for. So, in this case, you will get 0.25 into 2, let us just assume we are working with the 2-megawatt wind turbines. So, you will get about 0.5 megawatts is what you are going to get. So, if you take this thing and let us just see calculate what are we getting through the year. So, we will have this 2 megawatts, 2 into 10 power 6 into 0.25 and then let us look at what we get through the year. So, we have 3600 seconds in an hour 24 hours in a day 365 days in a year right, so you multiply all this you will get 1.6 into 10 power 13 Joules, so 1.6 into 10 power 13 Joules. We always said that you know humanity is using 500 exajoules per year so to speak. So, 500 exajoules is there, so that is 500 into 10 power 18 joules and if each wind turbine is giving us 1.6 into 10 power 13 Joules. How many turbines will you require? Well, it turns out you need 31 million turbines, assuming nothing else changes and this is all that we are going to do that today’s usage, today’s windmill all that we take into account, know. But, in reality, these numbers will change you may get better wind turbines you may get you to know higher capacity wind turbines, our power usage may go up, we may have more efficient ways of using power, power usage may come down. So, we do not know all that. So, just using today’s values this is the kind of number that we come up with. So, if you put up 31 million turbines around the world, you can take care of the entire requirement of humanity, the entire energy requirement of humanity it is just I mean I just wanted to do this calculation. So, you get some idea of the number we are talking of and so that is the number we have right 31 million turbines. So, how much area will this require? So that is another thing that we have to look at. (Refer Slide Time: 41:23) Generally what they say is that you know if you cannot keep wind turbines very close to each other because when one wind turbine is rotating it impacts the flow of air just past the wind turbine and therefore, if you keep the next wind turbine just next to it the second wind turbine works very ineffectively because it is getting a very bad flow of air you know airflow is just not back to its normal sense. So, normally they say a rule of thumb is that at least 7 times the diameter of that windmill. So, whatever the diameter of the wind means 7 times the diameter you should put between 2 windmills and only then you are reasonably sure that each windmill is roughly acting independently right. So, that it turns out that roughly you are looking at about 500 meters between turbines that is the kind of distance that you would like to keep between turbines so that they do not impact each other negatively. So, some calculations I have shown you. So, if you go down to the ground and you see what people have set up. So, various wind farms that have been set up at various places where they have sited it and you know map the site and then located it and distributed it across the site etcetera. It turns out that it seems like you need about half a square kilometre for each wind turbine you set up a wind turbine. So, half a square kilometre around it you should not sight another one. So, you should keep it past that point. So, half a square kilometre you should require for each wind turbine. So, we are looking at you know if you look at a half a square kilometre you will need about 15.5 million square kilometres. So, since you need 31 million you know turbines to power the entire world, I mean it is just a hypothetical calculation because just to get an idea of what we are dealing with here because we need to know what is the scale of it right. I mean if you just if you think something is interesting something is very fancy, oh let us go ahead and do it that is not how you are going to power the world. To power the world you need to know what does the world need, the world needs 500 exajoules you have to check whether the technology you are coming up with has a capability of handling 500 exajoules. And if it is going to use I mean supply 500 exajoules what is the impact of it what are all the other things that are going to be required for supplying 500 exajoules. So, this complete picture you need to have. And this kind of calculation you know gives you that scale of that complete picture and that is the reason why I am showing you this. So, we will need about 15.5 million square kilometres across which these windmills will be located and with that, you can power the entire world. Just to give you an idea that is about one and a half times the size of China or the United States. They are both around you know 9 million square kilometres something. So, this is one and half times the size of China, concerning India it may be like 4 or 5 times the size of India. So, that is the area across which you have to you know fully distribute the windmills to power the entire world. On the one hand, that may seem like a lot, but on the other hand, if this is something that you can distribute across the entire world. So, this is just to give you an idea that this is what is required you can distribute this across the entire world and there is no pollution involved there is nothing involved, and it is also off the ground. So, presumably, they have to think of windmill designs to see how you can integrate it concerning with the rest of society and still capture the wind energies without compromise so that it does not mean that this 15.5 million square kilometre is lost. So, you should be able to you know put it on top of tall buildings or something. So, you have to design buildings where on top of the building you can set up a windmill so you get the height because the building is there you already have a tall building on top of it you can set up a windmill. Already there are buildings of that nature. There are buildings where on the top of the building they set up a windmill and it generates enough electricity or more than enough electricity to power the entire building right. So, therefore, that is always an interesting thing to look at. So, for example, even if you see here no so, when I said 2-megawatt turbine. So, the 2-megawatt turbine at 0.25 per cent I mean sorry 25 per cent capacity right. So, that is what we are getting that is what we said here, 25 per cent capacity factor. So that is already we are looking at 2 megawatts giving us 500 kilowatts, 500 kilowatts right. So, as opposed to 2000 kilowatts, 2 megawatts would be 2000 kilowatts and from that, we are getting quarter of it, so 500 kilowatts we are getting. So, a house as I said we will typically you need anywhere from 2 to 5 kilowatts right. So, we will take half the value two and a half, somewhere in the middle it will over to say we will say 2.5 kilowatts per house or some or even if you take 5 kilowatts you can power 100 houses all right, 100 houses can be powered. If you take half of it you can power 200 houses. If you put a wind turbine on top of a tall building even you know you know say a 50 story building, 100 story building etcetera with the right capacity and that there you get very strong winds, so your you know utilization factor may be much higher than this your capacity factor may be much higher than 25 per cent if you do that the entire building can be powered by just that one wind turbine on top of the building. So, there is a model there. you can you know construct various buildings on top of them you can have appropriately sized windmills. So, you are not losing that area when I say 15.5 million square meters. So, square kilometres that area is not lost you are built a building there on top of the building you are placed it. At a location now where for example, these days they are placing all these towers for sending out the mobile signals mobile phone signals are being known sent off of towers which are on top of all sorts of buildings. So, you can do a combination of all these things, you can have wind you know I mean windmill, you can have a tower which is also doing all these communication signals, although they may have some interference we do not know about that, all these models are possible. So, that you are generating power in a clean way and no transmission loss because you are more or less powering this building right there. So, you do not have to transmit somewhere and you know have all the transmission losses, transmission infrastructure is avoided so that also sales cost. So, many many factors are there which are very interesting to look at and can be considered when you look at this kind of a picture right. So, this is very interesting to look at. (Refer Slide Time: 47:36) So, let us look at the conclusions here. First of all, there is considerable interest in tapping wind energy both internationally as well as in India and that is strongly seen by the fact that you know even in 10 years we have grown four and a half times which is huge. I mean 450 per cent growth is massive in any sector in 10 year time. I mean every year we seem to be growing about 15-20 per cent relative to where we were last year. And this trend is being seen in many countries, any country that has got into this seems to be actively pushing it. Geographical locations play an important role because as we saw you know this Muppandal area where they have set up this large wind farm is because geographically it is like that the wind flows there strongly and it can get you the kind of energy that we are interested in capturing a more effectively and therefore, that is a nice place to site it. So, therefore, you have to plan a little to site the windmills. So, that it gets you the energy that you want. And also I told you there are a lot of interesting models you can set it up on top of buildings, so it mixes up both the fact that you are living in a place and the fact that you are generating electricity right above that place and you make yourself self-sufficient, you make yourselves and environmentally free, clean your make yourself very efficient. I mean many times half the electricity bill that we are paying is for the transmission cost not for the generation cost. So, that transmission cost is gone. So, you are getting cheap electricity. So, you can power you are building and you can power a neighbouring building. So, that is great, so many such things that can be looked at. Various designs of windmills or wind turbines have been considered historically. We did not extensively look at it, but we did look at the idea that at least two of major design differences here are that the axis could be either vertical or it could be horizontal. And I showed you that the horizontal axis actually has many advantages whereas, the vertical axis has some advantages, but it has some disadvantages as well and as a result, you cannot you know it is not as effective. The horizontal axis windmills can capture the energy throughout their rotation process whereas the vertical axis ones are not able to do so, even though they are relatively cheap and economical to work with. So, those are our major conclusions for this class. We have many other things to look at with when it comes to wind energy, we have to look at say energy considerations what are the kind of calculations involved when you look at you know, what is the energy that is available to capture what is the energy that we are capturing what is the room there for us to actually improve this process and so on. So, that is something that we need to consider. And also these designs as I said a wide range of designs, a wide range of designs have been considered many new designs are also being considered they may have their pros and cons from any perspective. It could even be a psychological perspective of the people who have those windmills installed in their locations because as I said there is some level of resistance and reluctance to these technologies because they sort of impact the vision you know the view that you get off the place when you see these large set of forms of windmills that have been set up. So, several things to be looked at and we will look at them as we go forward. But for today I think this is your introduction to wind energy, we will take it from our next class. Thank you. Hello, in these classes we are now discussing wind energy and we are interested in trying to figure out what is the best that we can do with it. We have seen some of the statistics associated with it, we saw the countries that are significantly pushing towards wind energy, we saw even within India you know the various states the kind of effort that they are putting in towards capturing wind energy. And all this is because you know it is sort of an investment that once you put up it keeps collecting energy for you, relatively clean and the technology is also relatively mature at this point, people seem to understand what is happening and at least I mean how it is being captured is quite well established and people can do it quite effectively. So, therefore, it's being perceived quite actively, it can be set up at various locations as long as you know you are getting the wind there sufficiently and so there is a wide variety of advantages for trying out this technology and that is why you so many countries are pushing hard towards it. And not to mention the fact that it is completely clean, I mean in many ways nothing is coming out of it I mean it is just air that is already anyway moving you just tapping it to capture electricity. It has also been around as an age-old you know activity or in you know the technology that is been around for a very long time but in the middle its sort of lost its popularity because a lot of you know other gadgets came in and now it is sort of being rediscovered. But in the process, we have also understood a lot more about the science of how the wind turbines or windmills work and so the modern windmills are vastly more efficient than the sort of the ancient ones that we tend to see in you know magazines or pictures from you know maybe many places in Europe where they had these old-style windmills. So, we will look at the difference between those windmills as we go along. So, in today’s class, we are going to look at some specific energy-related considerations when it comes to capturing wind energy. So, some calculations relative to, related to this energy process, what is involved, what is likely that we can do with it and we will also increasingly get a sense for you know why is this structure; that the structure that you see in your picture here such a long structure here right. Why do not we just have it on top of our rooftop, why do not we just have it in garden etcetera and these blades are also so long, so many things are there today’s modern windmill has this kind of a design as what you see here. You can see you know how tall it is relative to the trees here these are all trees out here. So, the tree level is somewhere out here and this is significantly taller than that that you see there. So, it is interesting to understand what is the reason for all this and why are they setting it up this way and how significant is the reason. We may have some general idea that you know; oh there is wind there and therefore, you want a tall structure, but how significant is it what is the technical rationale behind it that is something that we would like to look at. (Refer Slide Time: 03:27) So, our learning objectives for today’s class are to determine the relationship between wind, speed and power, so wind speed and power. So, at least intuitively we understand that you know if the wind is very slow there is not much energy in it there is not much power in it and therefore, if you have a windmill that is trying to capture it, it is going to correspondingly capture less energy or less power and we also know that you know if the wind speed is higher correspondingly all these things are higher. But what is that relationship, how significant that relationship is that is something that we will try to get an understanding of. We will also try to understand or at least become familiar with typical performance characteristics associated with windmills and something about some at least an initial feel for what are the limits that we can expect or anticipate when you put this windmill out there and you are trying to capture energy from flowing wind. And we will also try to become aware of the theoretical limits associated with the capture of wind energy. So, that is the other thing that we will try to do. So, in I mean sort of the objective 2, we are sort of looking more in the practical aspects associated with it and here we are sort of looking at the more theoretical aspects associated with it. We will do brief discussions on those, we can do more elaborate discussions on those as well, but for the moment in this class, we will keep it to you know discussion that sort of sits within this framework of these topics that we are putting together and will have a corresponding level of detail right. So, this is what we are trying to do alright. So, we will begin by first doing some calculations. (Refer Slide Time: 05:07) So, we will start some energy calculations. So, now, let us just see here we have on this right extreme I will just draw something here. So, we have this tall tower and on that, we have a windmill right. So, this you have a windmill, now this is rotating. So, if you see it from the front the blade would look something like that, let us say I said I mean if there are 3 blades then you will typically see something like that, that is rotating right. So, now so that would be a tall tower there again. Now, we would like to understand what is the energy that we are captured. So, there is a lot of wind that is moving out there right. So, you have this entire you know the entire landscape has wind that is moving I mean you have moved have been moving the entire landscape. So, on what basis should we understand what is it that we have captured. So, what we are trying to do in this calculation is to see what is the energy or power that is available in the wind that is within the framework of this windmill. So, if I sort of draw a circle here and I mean, this is the breeze or wind that the windmill is accessing right. So, there is a breeze all around so that is not what is of relevance here, this is the breeze that the windmill is accessing. So, the breeze that goes through this circle that I have drawn here this I mean approximate circle that I have drawn here that is the breeze that the windmill is accessing. Now, we want to understand that given, the first thing we want to figure out is what is the energy or power that is available in this wind. So, in the wind that has gone through this region that is the first point that we want to understand. So, we have to make some assumptions, we would assume that first of all the wind is like you know perpendicular to this windmill. So, you have the windmill vertically present and then the breeze is going perpendicular to it and we would like to look at what is the power that is there this in the wind that has gone through this area this cross-sectional area the section of the area. So, to do that, first, we accept or we start with the assumption that the wind is having a velocity v, there is a velocity v associated with the wind and it is going perpendicular to this windmill and therefore, it's kinetic energy is simply half mv square. So, half mv square is the kinetic energy associated with any you know the object of mass m that is moving with a velocity v. So, the kinetic energy is half mv square. Now, in our case, it is not a solid object it is a gas basically air which is you know nitrogen-oxygen everything which is moving through this place. So, we have to estimate the mass. So, the mass here is we can say that the air has a density rho, rho and therefore, the mass would be if you understand, if you can figure out what is the volume of air that has gone through a particular region, the mass would simply be the density times the volume right. So, if a certain volume of air has gone through this region that volume times the density is the mass of air that has gone through this region. So, we do not know what that volume is for the moment we just assume it is V, volume V has gone through that region corresponding to the windmill blades which is the circle. So, that is what we have. So, now, the kinetic energy I just write that as KE is simply half instead of m we will have rho and V. So, rho V is the mass, v square small v square. So, this is kinetic energy. Now if this area is a, so we can say that the area associated with this circle that is a fixed area because we know that the radius of this blade is r right. So, we can say the radius of this blade is r and therefore, the area is known pi r square. So, the area would be, so the area is pi r square and we will assume that in whatever is the time frame that we are considering a certain length of air. So, the area times you know the amount of air that has gone through corresponds to this length of air this height of that air that goes through that the wind turbine is the amount of this is the volume. So, you have a circular area, a circular area and certain you know the depth of air corresponding to that circle has moved through that region corresponding to the windmill. So, we will assume that that depth is air in some time t. So, we do not worry about it some depth l. So, kinetic energy whatever is that value l depending on the value of then the kinetic energy is correspondingly higher. So, it is simply half rho, the cross-sectional area is A and some length which can be varying based on how long your you know waiting there and figuring out how much wind has gone by rho A l v square. So, this is what we have. Now, so this is the energy kinetic energy we will just call it as E which is the energy associated with the and all this energy is essentially kinetic energy at this point this is the amount of kinetic energy that was there in the air that went through that windmill right. So, the power is simply the amount of energy that the rate at which that energy is you know being consumed or being delivered. So, it is dE by dt, power is equal to P it is equal to dE by dt it is energy in unit time right. How much energy in unit time is power. So, Joules per second is watts that is basically what this thing is. So, if you differentiate your expression for E concerning t you find, half is a constant, rho is a constant that is the density of air, the area corresponding to the windmill is also a constant because the diameter or the radius of those blades is fixed, the radius of those windmill blades is fixed and we are using a horizontal axis windmill, the axis is perpendicular to this picture that we have drawn. So, the blades are you now sitting like that and the axis is perpendicular to it and so that is the area corresponding to that circle is fixed. So, the l is not fixed because that depends on how much time we are you know counting there. So, that is why when we differentiate concerning the time we have a dl by dt time v square the velocity is fixed, that is the velocity we will assume that it is a constant velocity of that is flowing then. So, that is also constant. Now, the dl by it is also velocity that is the rate at which the breeze is moving the wind is moving. So, the l was the distance the wind had moved during some time t which we did not I mean which we can which we could have kept track off, but more importantly now when we do differentiate we find that it is dl by dt that is the rate at which the wind is moving. So, that is v. So, this is equal to half rho A v into v square. So, this is essentially power is equal to half rho A v cube. So, half rho A v cube that is the power that is available in the wind which is travelling with a velocity v. So, that is the power that is available in the wind. So, we are not discussing right now on what the windmill is capturing. So, that is a different question, or that is also important, that is an important aspect in the end that is what is valuable to us. But first of all, what is available that is what we are calculating. So, what is available is this rho A v cube. Let us write it more clearly here half rho A v cube. So, this is what is available for us in the breeze.