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Hello, today we continue our discussion on wind energy and in fact, we will wind up our discussion on wind energy we will sort of wrap things up with today’s class. And in the last few classes, we have looked at the whole wind energy concept and the area, from a wide range of different perspectives. So, we looked at economic aspects, we looked at geographical aspects, we looked at environmental aspects, scientific aspects associated with it and technological aspects. So, you have to look at all these aspects to get how you know much more complete you know feel for the feeling field when you make a decision long term decision on any particular technology. So, I, for example, I also told you to know this long term is a very important thing and the idea of you know looking at technology from its starting point to its finishing point, it is also another very important aspect when whenever you are discussing any kind of technology, which you want to put out as a mass-market application technology. So, for example, we discussed specifically the blades for the windmills, and the fact that they are presently being made out of composite materials; and so, it is very important that the composite material has a pathway for you know eventual reuse or recycling, that is you know somewhat reasonable, that you can do without creating a situation where the number of chemicals being used and you know perhaps wasted or released into the environment, during just the manufacture of the windmill being so high that it destroys the purpose of putting a windmill up therefore for clean energy. So, this kind of what they refer to as cradle to grave kind of analysis has to be done with any technology; not just windmills just any technology because the first thing that we see about the technology, often looks very promising and it that may also be a good thing to notice, but then we have to do this kind of analysis to understand if there is any other aspect of the technology where you need to tighten up. And it may just be quite possible that once you identify that problem you can solve it, and then after that the technology right from the beginning the cradle stage to you know till it is finished off and has to go for recycling, that entire lifecycle of that technology is a clean life cycle and then you have made a big difference. So, that’s the kind of point of view we have to take. So, concerning wind energy as we said you know, it’s clean because it is just wind it is already there you are not really burning anything to create this energy or any such thing it was already there, and in many ways, it is it’s a variation of the solar energy because the solar energy heats the atmosphere, and then you get these various you know densities at various locations of the atmosphere, and then you will have a weather pattern that develops. And based on that and location of you know planes, location of hills, mountains etcetera you have pathways for wind and so, accordingly, you can know to tap the wind energy. We saw how it the amount of power in the wind depends on the cube of the velocity and therefore, high velocities are very nice. And we also saw these issues like I said about the how the blades are manufactured, how the tower is manufactured and that you know the various materials are being looked at for all of these things, the idea that you can use permanent magnets, but then you need to have a lot more of neodymium, which may not be easy to get. So, all these issues have to be looked at as a totality to completely utilize that technology to be aware of what is the weak point so that you can simultaneously keep addressing that weak point because it is also true that you may never find a technology which has absolutely no weak points. So, you will have some weak point, you have to be aware of it, and keep addressing it as you go along so that, it is no longer a show-stopping weak point. It may still be something that is not the best that you are expecting it to be, but it will not be something that people who look at some years down the line and say you should never even have taken this path right. So, that is something that we have to be aware of. So, as I said if are going to put hundreds of thousands or millions of windmills out there, then it is important to know what is the path for recycling those blades. Because if you put out a win a million windmills and if they are all three-bladed windmills, you have three million you know wind blades that are out there that you have to do something about once they complete their life cycle. And these are very long blades these are you know 60-meter blades maybe 70-meter blades eventually will come. So, these are long objects these are not some small things that you can pack and you know to hide it away somewhere, you have to deal with them you have to do something about it. So, that’s an aspect that you have to look at. So, in today’s class, we will actually as I said you know sort of wind up this discussion on wind energy, in particular, we will look at some things associated with some overall design considerations. Overall design considerations for the windmill and see what sort of thought process is involved there, what kind of you know options are there maybe we are not fully aware of all those options. So, that kind of a discussion we will have a little broad-based discussion, which puts some perspective on the technology as a whole ok. (Refer Slide Time: 05:24) So, our learning objectives for today’s class are to differentiate between lift and drag designs of the windmill. So, this is something that we have briefly discussed actually in in in one of our earlier classes, that first of all that there are these variations in the design. So, although you see a windmill and you just see something moving as a result of the wind that is blowing. There is a large amount of difference that exists between one type of windmill and another type of windmill, in terms of the ability of that windmill to effectively capture the energy available in the wind. So, all of them will capture some energy, it’s not that they were not going to capture some energy there as long as there is something that is you know stable and has you know predictable or a consistent way in which it moves, we can always attach a generator to it and then tap that energy and that’s basically what is being done. But for various considerations, they may have done one design versus the other, but each design has some specific advantages and disadvantages and in that context, there is a difference between water considered as lift based designs versus drag designs. So, we will look at that. The other thing that maybe sometimes we think about, but maybe we don’t look at in any great detail is to understand the significance of the number of blades that are present in a windmill. So, and we traditionally tend to see three-bladed windmill designs, but what are the options there and why do people you know why most of them are setting a three-blade design. So, is there some great significance to it or is there no significance to it, is it simply a matter of symmetry things like that; we just need to get a sense of what is involved here in terms of the significance of the number of blades. And also alternate designs for wind energy capture. So, there may be a lot of interesting other designs that people are looking at. So, we will at least consider one which is you know significantly different than what we have discussed in the class so far, in some ways it is significantly different it is fundamentally there is something similar. So, I will highlight that to you, but in some ways, it looks significantly different. So, we will see that as well. So, we will look at differentiating between lift and drag, we will understand the significance of the number of blades that are present, and we will also examine alternate designs for the wind energy capture. So, these are the learning objectives for the class we will just see them as we go along ok. (Refer Slide Time: 07:53) So, in this context, there is a term that I defined a while earlier, but we didn’t discuss it in detail. So, I will highlight that here it’s called the tip speed ratio. It is reasonably significant in the context of windmills or wind turbines and we should at least get a sense of what it is, and maybe how it can be used to consider possibilities concerning a wind turbine. So, it is in terms of description and mathematics, it is relatively straightforward we are looking at the ratio of the linear speed of the tip of the blade ok. So, the linear speed of the tip of the blade to the wind speed. So, it’s a ratio of two speeds; the speed of the tip of the blade of the windmill to the ratio to the speed of the wind itself okay. So, what do we mean here? So, for example, you see a schematic here of a windmill right. So, you see a schematic of a windmill. So, let’s say based on how the breeze is blowing, let’s say it is rotating that way okay. So, let’s say it is rotating this way. So, if you take if this is how it is rotating, if you take the tip, this tip, tip of this blade the specific blade and that will be true for all the other blades, there will be a certain velocity with which it is moving. So, there is a certain. So, that velocity we are referring to as v tip, v subscript tip that is the velocity with which the tip of the blade is moving and why is it moving? It is moving because there is a wind coming from the front and moving backwards right. So, the wind is moving from the front of this windmill and moving backwards. So, going past the windmill and going backwards, and we will assume that the wind is coming horizontally. So, the wind is windmill is standing there and then the wind is just blowing this way. So, blowing past the windmill and then going continuing further. So, there is a velocity with which this wind is coming towards the windmill, and because of that, this windmill is rotating right. So, this windmill is rotating. So, we want to know as it rotates. So, for example, if these are the windmill blades if they are rotating, we want to know what is the velocity of the tip of this blade. So, what is the velocity of the tip of this blade is something that we want to calculate, and then having calculated the velocity of the tip of that blade we divide that by the velocity of the wind that is coming and that is referred to as this tip speed ratio. So, that’s basically what we have put here represented by lambda it is the ratio of the tip velocity, which is the v tip that I have up here and the numerator divided by v wind okay. So, this is what we have, and if you know, if you look at angular velocity versus you know if you look at rpm of something that is rotating you look at how many you know radians per second it is you know going through this angular motion. Then the linear velocity of that of any point based on this due to this as a result of this angular velocity is simply v equals omega R, where omega is the angular velocity and R is the radius of the point; of that point for which we want to know what’s the linear velocity right. So, if you have a longish blade and it is rotating, you can look consider various points here, you can consider the point here, you can consider point here, you can consider point here. So, I will just say this is A, this is B and this is C. So, even though omega is the same if they if the whole blade is rotating round and round and round and omega is the same. So, many radians per second you will have the angular velocity, the linear velocity of each of these is going to be different. So, if you look at this formula omega R, v equals omega R the R is more. So, this is I will just say this is R 1 this is R 2 up to here let’s say this is the centre R 1, R 2. So, let’s clear this. That would be R 1, this would be R 2 and this would be R 3. So, the linear velocity of C is higher than the linear velocity of B is higher than the linear velocity of A. So, v C is greater than v B is greater than v A. And that’s simply got to do with the fact that to travel the same angular you know movement to make the same angular moment the A has to had to travel a less distance, B had to travel a longer distance, C had to travel an even longer distance. So, and then as a result and that has happened in the same amount of time. As a result, the linear velocity of A is less than the linear velocity of B is less than the linear velocity of C even though or they all have the same angular velocity right. So, this is v equals omega R and so, if you want to know the velocity of the tip, once you know the rpm of that windmill you just have to sit there and what is the rpm of the windmill, then you will know how many radians per second it is revolving at. So, full 360 degrees would be 2 pi radians. So, based on that how many you know how many rpm it does that, when you rpm into 2 pi radians it would have covered in 60 seconds. So, you get the angular velocity and once you get the angular velocity you do v equals omega R and then you get the linear velocity. So, if you do that you will get this lambda which is the tip speed ratio omega R by v wind. Just to give you an idea in and we are going to see some values as we go along. We are looking at lambda values which could be lambda could be less than 1 in some cases, based on the design of the windmill it could be less than 1. Lambda could also be greater than 1 it can of course, also be equal to 1. So, it can be less than 1 greater than 1 etcetera. So, you are looking at a range of values and usually, I mean maybe towards the higher end of the spectrum we are looking at something like lambda could approximately say maybe 6 or 8 okay or maybe even 10. So, some something like that is what we are looking at as the value of lambda in the normal set of circumstances, that you are going to see a windmill in and for a set of types of a windmill that you are going to consider ok. So, that is the tip speed ratio which means what? I mean do we need to understand what it means by 6 or 8 or what is the significance of saying lambda is less than 1 or lambda is greater than 1. If lambda is less than 1 it means that the tip is moving at a speed linear velocity, which is less than this velocity of the wind okay. So, please remember in concerning the chi type of windmill that I have shown you on this plot, which is this three-bladed windmill; the wind is flowing perpendicular to the blades right it is flowing perpendicular to the blades. So, the tip of the blade is moving in a direction perpendicular to the direction of the movement of the wind okay. So, they are not in the same direction, they are in perpendicular directions. So, that is something that you have to keep in mind. So, they are moving perpendicular directions what we are saying is when lambda is less than 1, the blade the tip of the blade moves with a velocity that is less than the velocity of the wind that is crossing that blade ok. So, if the velocity of the wind crossing the blade is let’s say 10 kilometres an hour or let us say we want at least 10 to 16 before this thing starts moving, let’s say it is moving at 20 kilometres an hour. So, if I were moving at 20 kilometres an hour, the tip of the windmill is perhaps moving at 15 kilometres an hour okay. So, in that case, you will have 15 by 20. So, 0.75 right. So, that is that would be the ratio if you had something like that. If the tip we are moving at if and so, we will assume 20 kilometres an hour breeze and then relative to that we will think about it. Supposing you had 20 kilometres an hour breeze whereas, the tip was moving at 30 kilometres an hour, then you would have 1.5. So, 1.5 would be the lambda value or tip speed ratio, and if you have would something like you know when I say 6 to 8. So, what does it mean when it’s at 6 it means the wind is flowing at 20 kilometres an hour, the tip is moving in a direction perpendicular to the wind. Please remember that it’s the direction perpendicular to the wind at 120 kilometres an hour okay. So, that is the point that we have to remember. So, you may wonder how come you know that velocity is higher than this velocity, but that’s got to do with the fact that the phenomenon that is occurring is different and that is the reason there are some designs where it is where exactly what you are thinking is going to hold, and which is the case where lambda is less than or equal to 1. As long as lambda is less than or equal to 1, it is consistent with our you know intuitive process that with that says wind is flowing at some speed, the blade cannot go faster than that speed or something like that right. But what other designs the movement is different and the process is different as a result you can create a situation where the tip speed is different. In all cases energy is conserved. So, it’s not. So, that is I think the more fundamental aspect that you have to remember, you should not worry so much about the velocity, you should and you know be stuck on this idea that how can that velocity be higher than this velocity, that’s not the defining characteristic in this case in many of these windmill designs. What is more important is the energy is conserved. So, what the in terms of the movement of the windmill, whatever energy it has picked up is going to be less than or equal to the energy that the wind that. It is going to be less than the energy of the wind that arrived at the windmill, it is never going to be even equal to that energy right. So, it is going to be less than that energy. As a result that is the characteristic that we should feel satisfied has been met in this situation, and as long as that characteristic is met whatever is the velocity that ends up being there in the windmill is fine I mean. So, we need not worry you that you know that velocity is not matching this velocity etcetera, that that’s not how it works the energy conservation is the more fundamental defining idea right. So, that’s the way you should think about it ok.
 
 
 
 
(Refer Slide Time: 18:06) So, we spoke, I spoke in the just now about the idea that you know you have different designs of windmills and based on the design you may have this tip speed ratio which is greater than 1 right. So, that is the idea that I am pointing out here. So, there are certain types of design of movement based on flow. So, here we have a flow of wind, and based on that you have movement of the windmill blades. So, some of this movement of windmill blades happens, I mean again this is based on the design of the windmill. Based on the design of the windmill you can design the windmill such that the movement of the blade occurs due to a phenomenon referred to as lift okay so it occurs dues to a phenomenon called lift. This is the same lift concept that is there when an aircraft is trying to take off or even when it’s flying right. So, as it is flying it is the same concept that exists, there is a lift process which pushes the aircraft up and that is how the aircraft takes off and then stays in the air. So, the lift is very critical it is a phenomenon, a very important fundamental phenomenon that exists in the context of aerodynamics and this is the same concept that is being used in certain windmill designs. So, what it is, is something that we are just going to briefly look at. What you see here on your screen is an aerofoil. So, based on which part of the world you are looking at some places they will simply refer to it as an airfoil, but more specifically we call it aerofoil. So, you can see this shape this is a shape that I have drawn here. So, schematic of a shape, this shape is the cross-section of a surface of an object and if the object has this kind of cross-section, and it interacts with the wind it tends to create this lift okay. So so, for example, aircraft wings, if you look at aircraft wings and take a cross-section of the aircraft wing. So, if you have an aircraft wing that looks like that right. So, you have this aircraft wind wing and you take a cross-section of it. So, you cut the aircraft wing there right you cut the aircraft wing there and you take a cross-section of it, then it will have this shape this exact shape that I am showing you here something of that nature. So, it will have a shape that looks like that. So, some shape like that is what the cross-section of that aircraft wing will look like. Similarly, we have this windmill blades. So, you have a blade-like that, and you have a blade that looks like that, I mean that’s the hub and then you have a blade if you cut this here. So, we just cut it out here and you take the cross-section and then you look at the cross-section then this is what you will see okay. So, this shape is referred to as the aerofoil shape. So, what happens? So so, the point is in this kind of a circumstance and similarly with the wink of a plate, what you are seeing is if you see the aircraft. So, I just draw a schematic of some aircraft here, and then you have the wing right. So, you have something there. Now you must remember that the breeze as the aircraft moves forward, the wind is coming in this direction ok. So, this is the direction in which the wind is coming because the aircraft is moving in this direction. So, even if it is on a stationary day, you the engines of the aircraft switch on and then the aircraft moves forward okay. So, it moves forward gains speed on the runway it is picking up a lot of speed, and it let’s say it crosses some 300, 400 kilometres in are something like that. It is picking up some pretty good amount of speed. So, at that point relative to the aircraft the wind is coming backwards right. So, the wind is coming backwards. So, what happens the aircraft lifts off the ground right. So, the lift happens in this direction. So, the wings are helping the aircraft to move in that direction okay. So, that is the lift. On the other hand, the wind is also rubbing against this aircraft and that sort of like you know you can think of it as friction, which is holding the aircraft back. So, there is a force in this direction that is called drag, this is called lift ok. So, this is upward direction what is happening is lift what is pushing the aircraft back is a drag okay. Now the point you must notice here is that the wind is flowing in this direction the lift is happening in a perpendicular direction. So, the, that is an important thing that you have to remember. The lift is not happening in the direction of the wind, the lift is happening in a direction perpendicular to the wind. So, that’s a very important thing to keep in mind. So, now, if you keep that in mind and that is exactly what is happening in on an aircraft wing which I have shown here, that is also happening on the blade of a windmill of the design that I will just show you those three-blade windmill designs that I just showed you, which is a horizontal-axis windmill. So, in those designs the breeze is moving horizontally concerning the ground, the blade is moving in a direction perpendicular to the breeze right. So, the same in terms of directional orientation, that is consistent with what I am just showing you for an aircraft. So, what is happening? So, what is so special about the shape? So, there is this thing called the aerofoil shape and that is what you are seeing here. So, what happens is you have a lot of letting me just take some other colour here. So, it is easier for you to follow. So, we have some colour here. So, you have you know let’s say you have a breeze coming. So, this streamline will go off this way that will go that way ok. So, you will have a lot of breezes that are doing this. So, now, generally what is happening here is that the path travelled by the air molecules on top of the aerofoil is longer than the path travelled by the air molecules at the bottom be below this aerofoil. Now there is some analysis that people do and you know there are different approaches to looking at this. So, one approach says that let’s say you have two molecules, one molecule here and one molecule here. So, then they look at what is that path travelled by that molecule on top to arrive here and the molecule at the bottom to arrive here. And so, one sort of assumption or assumption that is made is that they travel they are both arrived here and they both start at the same point, and the arrival at the same point at the same time okay. So, the starting point is similar and the finishing point is similar and one assumption is that they all arrive at the same point to ensure continuity. So, if that is the case then the path travelled on top is longer than the path travelled at the bottom. So, therefore, the velocity of the wind above this aerofoil is higher than the velocity of the wind below this aerofoil okay. So, that is one approach although some people are suggesting that the velocity these particles on top in may even be coming faster than that. So, that is another angle you can think of, but that simply adds to this process not subtracts from this process, but the general assumption is they are all arriving at the same time, even when they are arriving at the same time you were going to see some difference. So, the idea is that the velocity on top is higher than the velocity at the bottom of the wind. So, now if you look at the fluid flow and you look at the idea that energy is conserved okay. So, that is the again the underlying phenomenon that I said, you know that’s the phenomenon that we should I know tie ourselves up to and within the context of that phenomenon whatever happens. So, we looked at Bernoulli’s principle. So, in Bernoulli’s principle, we say half rho V square plus rho GH plus P equals a constant right. So, in this context, we said that we said that you know this is the kinetic energy per unit volume. So, this is KE per unit volume, this is potential energy per unit volume and this is, of course, pressure. I showed you that the dimensions of kinetic energy per unit volume or and potential energy per unit volume which is energy per unit volume it’s the same as pressure. So, therefore, this equation is appropriate and correct as per dimensions and this says that this is the constant. So, if you look at situations where let’s say you are you know not worried about the change in height, because you know the breeze is flowing at the same height let’s say between the starting I mean compare the starting point and the endpoint there is no great variation in the height, they are essentially the same location. So, we can forget about or we can neglect potential energy per unit volume because that’s the same both of the starting point and the endpoint. So, we have only two terms here half rho V square and so, let’s say this is path 1, which is coming on top and path 2 which is coming at the bottom. So, half rho V 1 square plus P 1 should equal half rho V 2 square plus P 2. So, this is a P 2 comma V 2, where v is the velocity here not volume, velocity here and then on top, you have P 1 and V 1 which is the velocity on top. So, if you have created a situation. So, given that you know this has to be conserved, you have this equation here that has to hold as part of energy conservation of this fluid flowing around this airfoil. If this equation has to hold, then whenever the velocity goes up in any one location correspondingly the pressure goes down okay. So, to the extent that we find that in pathway 1 in pathway 1 because the distances travelled have to be are longer and it turns out that you know if you do the proper calculations and you understand all the dynamics that are happening there, the velocity in that path 1 for the molecules happens to be much higher than the velocity in path 2. Therefore, we find that you know because of the shape and how it is interacting with the breeze a V 1 happens to be greater than V 2 and how much greater it is will depend on exactly what assumptions you make and how correct those assumptions are. So, usually, the assumption made in most places where we discuss this is to say that the molecules start at the same point and they end up later also at the same point and therefore, they simply look at the path travel that one travels a longer path in the same duration of time, the other travels a shorter path in the same duration of point time and therefore, the velocity of 1 is greater than the velocity of 2. But like I said you know some people say that the there is some analysis which suggests that it may even be the difference maybe even more than that not just simply based on what is there when you when they both meet up there. So, in any case, the velocity is higher, there is you know there are no two opinions that the velocity is higher because the velocity is higher the pressure is lower. So, if pressure on top is less than the pressure at the bottom. So, if P 1 is less than P 2 then what happens? Pressure below that aerofoil is more than the pressure above the aerofoil right. So, velocity 1 is greater than velocity 2 and as a result pressure 1 is less than pressure 2, pressure 2 is below the aerofoil, pressure 1 is above the aerofoil and since you have low pressure on top and higher pressure below, it pushes that wing up. It pushes the wing up because you have this difference in pressure right.