 So, let us look at the geometry of the sun and earth, how the position of the sun and earth changes with respect to each other and due to it, due to that changing how the solar radiation changes. Look at the diagram and see if it is making sense to you of any kind, how it reduces radiation. Any other thing that you can catch from the diagram? March 20th and September. So, two thing, one is the bright part is the day time where the sun earth is receiving light and other is dark time. Other important thing to notice the dot here is the north pole and look at the difference in the position of north pole here and here, right. In this happens because of this, the earth is inclined, inclined where? That is inclined with respect to the plane in which sun and earth is revolving around each other. So, there is a plane in which sun and earth is there, the earth axis of rotation is not perpendicular to that plane, it is inclined to that plane. So, therefore, if I look it from this direction, I see the pole towards the lighter side, but if in this position, the pole is exactly at the bisect half of it and in the, in this case, December 20th, the pole is at the darker side. If that is not clear to you, why how it is happening, you look at here, right. So, this is the because it is. So, this darker line is what is this line? Line of the plane connecting the sun and earth. The equator is the dotted line here, perpendicular to this, ok. So, this is the line which is connecting sun and earth, ok. So, what I am saying, the earth is inclined to the plane, which is connecting the sun and earth. So, it is inclined like this, right and the perpendicular to the, of course, the polar axis is the equator, which is here in the middle. And therefore, in this condition, in this condition, my north pole appears in the brighter spot, while in this condition, again my north pole appears in the darker spot, ok. So, we got it clear now, very important, because now we are going to find out why there is a change in the season, ok. So, for example, in one position, so suppose I am, so there is a equator and what is this, what you call this? Tropic of cancer and there is a Tropic of Capricorn, both are 23.5 degree away from the equator, right. So, suppose I am sitting in a position at the Tropic of cancer, in this position, this Tropic of cancer is the closest to the sun. Well, if somebody is leaving the Tropic of Capricorn, it is revealing some distance, it is away, right. What does it mean? This point is getting highest amount of solar radiation on the earth's surface. So, it is likely that this, the season here is summer, right, in this condition. Now, if it revolves and comes to this condition, same A point, my Tropic of Capricorn, cancer is here now, I am at the same location, but in this condition which is getting the highest radiation, Tropic of Capricorn, a location here is getting highest radiation, but here, now it is the lowest radiation, it is away from the perpendicular line, right. So, same location A which was having summer there, now having winter here, same location, nothing has happened, only thing is the position of the earth has changed. So, when it has some position, this side, it was the same location was having a summer because it is the closest to the earth's surface, sorry, sun and getting the highest amount of radiation, but when it is here, the same location is now away from it and this location is now having a summer, which was having a winter here. Is that clear to everybody? So, yes, then only I will move forward, very good. So, now and this, and this is for the, because this is 23 and half, I have taken this, this latitude also is 23 and half, then exactly it happens. Now, from this diagram, we can learn lot of things, from this diagram, we can learn lot of things. Now, this is the case when you are afternoon condition talking about. So, suppose now I want to install a solar panel, I am living in a location A, I am living at a location A, I want to install a solar panel and I want to make sure that my solar panel receives maximum amount of radiation throughout the year. How should I install? So, what should be the location of the module here? If I am at A, how should I install my module? I do not know what is, you tell me what is the condition at this condition, which is the 21st of June at location A, what should be the tilt of my module? 23.5? Corners. Corners? No, it is not, how much? So, let me repeat my question again. So, at this, this time I am living in location A in this condition, how should I put my module so that I get the maximum solar radiation? Perpendicular surface, parallel to the surface, 90 degree difference. So, you take average, like democratic way, put average in 45. Come on, any answer? Unanimous answer? No, in this case. How many of you feel that it has to be perpendicular, raise your hand? Fine. How many of you feel it has to be horizontal? How many of you feel that solar panels should not be there? It is making your life so difficult. It is making your life so difficult, it should not be there. The answer is that it has to be flat, lying on the ground. If I put it flat like this, which means then it is perpendicular. So, it is actually capturing everything. If it at this angle means the capture cross section area reduces. So, in this condition it has to be flat, exactly lying flat. Now, I have not changed my location, but after 6 months from 21st June, I go to 21st December. Same location, what do you think should be the angle now? So, this angle, this is here, 0, this is 23.5, right? Because this is my topic of capricorn, the angle between this is 23.5 and here another 23.5. So, I should not put flat here. If it is flat then it is pointing somewhere else. I should apply it, put tilted towards the sun like this, right? I should put like this. How much? 47 degrees. 47 degrees, right? So, if you want to keep your module getting lot of sunlight throughout the year, it has to go from 0 degree to 47 degree. What about that? Interesting? We keep on changing 0, 1, 2, 3, 4, 2, 47 and doing it back, keep it on 23.5 as one option. Another question. So, if I am not leaving at A, if I am not leaving at location A, I am leaving at equator, then how much angle I have to change? I am leaving an equator. In this case, it is, I have to do it like this. In this case, I have to do in opposite direction. So, my tilt is still 47 degree. So, one thing is clear. You leave at any part of the world, any latitude, the total tilt you have to do from the whole round year is 47 degree. That is clear. Everybody? 47. And that is lot of change, right? 47 degree is lot of change. And if you put it flat all the time, you are not going to generate enough electricity in this time. So, then what we do? Adjust. Adjust to a level so that the variation from the particular position is less and then in that case, it is 23 and half, in middle of the two, not 0, not 47, not 47, it is middle of the two, right? And what is the middle of the two? 23 and half. So, if you are living at a latitude, which is 23 and half degree because of the topic of cancer in this case, then your panels will be 23 and half with respect to what? Ground. 23 and half with respect to the ground. And if you are living at another location like Mumbai 19 degree, then your panel should be 19 degree or if you are living at the equator, your panel should be, if you are living at equator, your panel should be perpendicular. It should lie flat, ok. So, if you are living at equator, panel like a Patak though, installed. That is it. Panel like a Javinsa Patak though, it means it got installed automatically. It does not matter which angle. It is always going to be a perpendicular, right? Good. That is the advantage of saving the frame cost if you are living on an equator or closed equator. Is this ideas clear? Now, we will formulate this. Now, this is the conceptual. Now, we will put a formula. You can do it, right, without knowing anything now. Put the formula. Try to put the formula if we have to, if we have to find, write down the formula for optimum angle of inclination. What is that formula? Optimum angle of inclination. What is the formula? Very simple. Optimum angle of inclination is equal to latitude. That is it. So, phi. Normally, the symbol for the latitude is phi. So, optimum angle of inclination for your panel should be phi. That is it. That is a formula, nothing else. So, this is how I can try to confuse my students. To make a long question for which they keep on thinking, thinking, thinking of the answer is simply write equal to phi and answer is over. But it is just conceptual. You need to think about it. When you start the idea right, then you can answer any question. Fine. But, so if you, if you observe the motion of the sun, the sun always moves in one plane. So, if you look at the morning, 10 o'clock, 12 o'clock, 3 o'clock, 5 o'clock sunset, the motion of the sun is always in one plane. And that plane is always inclined with respect to perpendicular with angle equal to the latitude angle. So, if in Mumbai, the motion of the sun is always with vertical, it is always 19 degree. Mumbai latitude is 19 degrees, always 90 degree. So, this plane is, so if this is my vertical, the plane is always 90 degree. Only thing is the, the location of plane changes with respect to time. So, plane is fixed at 90 degree in which sun. So, you will always find sun. So, in the morning you will find sun here in the plane. 10 o'clock you will find here and the noon it will go there and come back here. So, because it is same plane, I am looking at the perpendicular to the plane. You are all looking at the perpendicular to the plane. So, sun is always in the same plane. What happens? During the air is the plane position keeps changing. So, plane is sometime here, sometime here, sometime here. In the winter it is away. Winter sun is down, it is away and it is come back. So, the plane in which suns move is always fixed in respect to the angle with respect to vertical, but the location of the plane keeps changing. Which is what I try to demonstrate here, but I am not sure that is clear to you. So, the motion of the sun in the green plane will be in the winter and the blue plane is in between and the red plane is in the summer. I think I have another slide. So, if you look at, if you look at here in this case and if you are at a location, if you are at location somewhere here, is it like latitude location? So, if you are looking at the location which is at 25 degree north latitude, if you are looking at this location, then what do you see sun moving? In this summer you will see sun moving in front of you, going up and setting in front of you. How much in front? Given by this angle. So, these are the angle given, right? So, it will rise in almost 70 degree. It will come to the, this circle which is 50 degree. So, even at the noon time, even at the noon time sun will be 50 degree from the vertical somewhere there and we know where you are, right? In the winter, even in the noon time sun does not come to overhead position, does it? In your house, for your village, your town does not come, right? For most of the India does not come to the overhead position in the winter, right? In the summer, it does come to overhead position, but then the sun rise is behind you. So, if you are looking here, if you are sitting facing the south, in the winter, I am sorry in the summer, at the afternoon time sun will be exactly on your head. Of course, depend on the latitude. If it is exactly on your head, the morning, it will not be exactly 90 degree. It will be behind you. And similarly, evening, it will not be 90 degree to the due south, it will be behind you, right here. The sun rises here, comes on the top of the head, goes behind you. So, this is how the sun moves. I am sure you are observing every since, ever since you, if not, then go back and start observing. Make an observation point in your house or in your roof and see what are the angles for the sunrise, sunset, what happens in the summer, in the afternoon of winter, what happens in the afternoon of summer, ok? Yes. What will be the gain in terms of power if we have module and we track the sun throughout the year? What will the gain in terms of power? Yes. What percentage, in terms of percentage? Ok. So, the question should be what percentage gain in terms of energy we generate, right? Yes. Because there is a time factor involved, right? Right. So, what percentage gain? So, if you always follow the sun at any given location, every time morning, evening, then you will get 40 percent more energy than if you are fixing it at the fixed angle. The energy, if you are always following the sun is 40 percent more. So, by fixing it, actually we lose lot of energy, right? Because you fix the module in this direction and your sun is here, then you are actually morning you are not generating, then afternoon you are generating and evening again you are generating very less. But instead of this, if sun is here, you follow it and wherever sun goes, you follow here. And even in the summer, if sun will go here, you make it horizontal, in the winter it go, you tilt it. If you do this, it is electricity that you can generate or you can interstate 40 percent more light energy either way, ok. And when we always follow the sun, it because moment is east-west and also north-south. Therefore, it is called two axis tracking. You have to follow in the both the axis, north-south axis. If you do only one axis, 20-25 percent there. And all this calculation, you can do yourself. I will teach you how. By the way, if you learn this solar radiation stuff very well, you can do lot of consultancy work. A lot of people going around the country asking how much radiation, where should I do it, what should I do it. So, very simple geometry that you need to understand, but it gives you lot of great tool. So, you can do all calculation yourself. When sun rises, one says how much extra energy I get, if I take it, if I do not take it, how much is the energy I am losing, what is the cost of taking things like this. So, lot of work can be done. There is some data sheet, how much solar total radiation. I will show some of the sheets. So, this is what happens eventually. So, first of all, the angle in the plane in which sun is moving. So, sun is in the morning gear, goes here, come back. So, it is always in the same plane. That plane is always tilted 90 minus latitude. That is phi. So, this is with respect to this. So, this is a vertical horizontal. So, with respect to this, this is 90 minus latitude. And what I also told you, the position of the sun, the plane keeps on changing. So, if it is summer, you see the sun in the noon time is exactly on top of you, over it. But in the morning, it will be behind you. You are facing the south. One thumb rule for this all solar collector, including thermal and PV, is that if you are in the south and southern hemisphere, if you are in the northern hemisphere, you should face your collector towards the south. In for us, India, the sun is always in the south, most of the time. But if you go to Australia, for most of the sun, some will be in the north for you. So, if you, because we are in the northern hemisphere. So, we are here, the sun is always in front of us. So, we are observer location here. The sun is always in front of us towards the south direction. So, therefore, our panel should always be focusing towards the south. So, and this position, change in position of the plane is given by a parameter called delta or declination angle. And declination angle change is 47 degree. That is what we are seeing. The declination angle over the year changes by 47 degree. So, sometimes it is plus, sometimes it is minus. Total change is 47 degree. So, the inclination angle. So, if I want to find out angle at a given sun, if sun is here at B position, I am here. What is that angle? I have to actually give 90 minus 5, which is this angle. N plus I have to add delta, which is the declination angle. So, now I want to install my collector. So, this surface here is my solar panel. This surface is my solar panel. And there are so many angles there. Can you see how many angles you can, you need to characterize. You want to find out where is your sun and how want to put. There are five different angles. Inclination of your panel itself, that is an angle. Azimuth angle, that is with respect to the vertical. And with respect to the sun's incoming ray, what is the angle? Inclination angle is with respect to the horizontal line. What is the inclination of the sun? Incident angle basically. This angle is important. Incident angle. If sun is at this angle and this is horizontal, what is that angle? Normal to the plane. Your sun, if your play normal to the z, south axis. So, if your plane, the module, it is focusing this way or this way or this way. Angle of the, with respect to same is focusing. So, if it is due south, if this is the south direction and my module is my perpendicular to the module is also lying in the south, then it is 0. It is this side, it is minus 180 is this side plus 180. So, that is another angle. All the angles are done. So, at any given time of the day, at any given day of the year, for any given inclination of the module, if you want to find out what is the inclination of the sun rays or what is the incident angle of the sun ray on your module. If you know that, then you can actually make. So, what is, if you want to absorb everything which is falling or if you want to intercept, maximize the interception of the light. What is your philosophy? Incidence angle should be 0, right, 0 with the perpendicular. So, incident angle sun should incident always perpendicular to the plane, should always be perpendicular, right. That is your philosophy, you always want to that, in case you want to maximize. So, we should know what is the relationship of all this angle with respect to alpha or the incident angle I want always want to be 0, right. I love the incident angle to be 0 and we should know what is the relationship. This is a very simple expression that is given for this, ok. The simple expression is this. If you calculate all this angle, you will know at any given time what is the incident angle, right. Sin phi sin delta cos beta cos delta cos gamma cos omega sin beta plus cos phi cos delta cos omega cos beta minus sin delta cos gamma sin beta plus cos delta sin gamma sin omega sin beta. You calculate this angle and you know exactly where is the sun. It is not difficult, we do not have to do it, computer have to do it, right. You have to just feed into that. You know phi, right, you know phi, phi is the latitude of the plane. You know delta, declination angle. I will tell about what is that. You know beta, angle of the, your panel with respect to horizontal. Gamma, you know, with respect to south, angle of your panel with respect to south and that is it. Omega, yeah. Omega also you need to have our angle with respect to the noon time. What is the angle of the sun with respect to the noon? So, this many angles you should know. So, I will go back. How much it can vary? Latitude, of course, we can vary plus minus 90. Any doubt? Azimuth angle with respect to south can vary 180. So, if I am due south, it is 0. If I go this way, it is minus 180. If I go other way, it is minus 180. So, where is 180? Our angle. What is our angle? As the name suggests, it is the angle measuring the time. It is the angle measuring the time. How many hours we have in the day? 3. 24 hours. 24 hours. And how many in one day? It revolves 360 degree. So, 360 degree divided by 24. So, 15 degree per hour. So, sun moves 15 degree in one hour, 15 degree in other hour. So, if I consider my noon time is a 0 hour angle. How many angle, how many degrees it moves? So, if I say noon time is 12, then 1 o'clock is 15 degree, 2 o'clock is 30 degree. So, our angle actually represents the time in terms of the angle, because all this we talk about angles. So, therefore, time is also converted into angles. Surface of the slope, it can vary from 0 to 180 degree. 180 degree means lying Ulta. This 0 means flat, surface is of 180 degree means passing to the surface, lying Ulta. And declination angle, very easy definition. Angle made by line joining the center of the sun and center of the earth with respect to equatorial plane. So, there is one plane which is joining the center of the sun to center of earth and there is equatorial plane. An equatorial plane, this angle keeps on changing. Can you imagine this process happening? Center of the sun joining center of the earth that is one line and the earth is inclined and there is equator. So, whatever plane it makes is equatorial plane. And how this angle is changing? This angle changes from 23.5 to 23 minus 23.5. Can you imagine this process? Declination angle here, right? In this case, this is the line joining center of the sun to center of the earth, right? And where is your equatorial plane? This one. So, this is making some angle with this line. You can say minus 20 or plus 23, whatever is your reference level. In this case, line joining center of the sun to center of the earth and equatorial plane, they are all in the same line, right? The angle is 0. In this case, the angle is in opposite direction, here, here. So, you can say minus 23 and in this case, angle is 0. So, in this case actually the sun ray is actually going exactly in the plane of the equator, perpendicular, exactly perpendicular. When it happens, you have the day time is equal to night time at that given location. When this happened, day time is equal because you are exactly in between the sun, day time is equal to night time. In this case, what will happen? Summer. So, this location will have longer summer time, longer days and this location you have the longer of winter days. So, depending on the position, the day length changes. If you go to the North Pole, what happens? The day length is 6 months and night length is 6 months, there is only one day. Exactly, you go to the pole, for the 6 months there is a light and for another 6 months there is no light. As you go away from the equator, in summer your day length keeps on changing. So, I was in Belgium for my PhD. So, the sunrise was some like 4 o'clock and sunset was 10 o'clock in the night. So, all shops were getting closed at 6 o'clock by the law. So, 6 o'clock it was looking as if something has happened to the city, nothing is there, nobody is around. In winter, it used to sunrise, we used to go to 8.39 or even up to 10 and sunset about 4 o'clock. So, we used to go to the office in the night, dark, we used to come from the office in the dark, in the winter. In the summer, of course, it was opposite. When you leave office, it looks as if it is afternoon time. So, as you go away further, further, further, the day length keeps on increasing. So, if you go to the pole, in summer, 6 months full light and 6 months full dark. It will also happen for the south pole. Anything that happens to north pole will also happen to the south pole, things will get you. Things will change only. So, we know the angle variation, we know the declination angle, how it changes, the equation for the declination angle. So, tomorrow you are going to do the calculation for all these angles. So, this is the expression for the declination angle. N is of course, the day of the year, N equal to 1 is January 1. So, if I ask you to find out the declination angle for 15th May, what you have to do? You have to find out how many days from the, from January 1. So, for which you know, we need to know which month is for how many days. You know that January for very right. That is very useful, that you must have learned in. Leap year. Yeah, leap year things will change. See, leap year is for our convenience. Only we cannot adjust quarter day, we cannot have quarter day every year, right. That is our problem, not sun's problem. Sun will actually move. So, you can see the, this will happen from minus 20 in December to go to 0 declination angle angle 2 days, September and March and go to the plus 23 at June and coming back. This is how the declination angle changes. Optimum tilt for the fixed collector. If you are, you want to fix the collector, then what is the optimum tilt? Let it in angle. For throughout the year, but if you want to have one fixed angle for each month, then one is for this throughout the year. That is, we cannot change every day, that is too much, but maybe we can change once in a month. So, this is the, so now you, the delta is also keeps on changing, right. 90 minus 5 is your inclination angle. And therefore, beta is 90 minus theta. So, your change, your, your inclination of the collector is 5 minus delta. Now, 5 is fixed, literally does not change, but delta changes, ok. So, if you want to find out what is the beta for a given month, what do you do? Find the average value of delta for that month, right. Find an average value of delta over period of one year is how much? Over one year, the average value of delta is 0. That is possibly minus value. So, over a period it is 0, that is fine. Over a period, this value is 0. And therefore, if you want to fix the, find out the optimum tilt for a year, then it is equal to 5. But for a given month, it should be, you should also calculate the value of delta, right. So, for a month, you should find out the average value of delta and do it, otherwise for the year it is 5, right. And if you are installing solar panels at your home and panels are very expensive, you would better like to change it every month. Once in a month, you can anyway do this, right. And because that will increase your energy generation by some 10, 15 percent easily, easily. So, when you are putting such expensive device, why not to track it? You need to find out how much to track it? This is the formula. You need to find out the delta for that given month, subtract it and you will get the, and delta can be plus and minus, right. It can be plus and minus also. Also, for some cases, you do not want to optimize for the given year. When you are using solar water heater, you want to optimize the collection in the, for the summer or winter? Winter. You want to optimize your collection for winter, not for the whole year. Then, beta equal to 5 is not a good answer. Beta equal to 5 is not a good answer. Then, you find what is the delta for a winter month and then adjusts for the winter month, right. So, with this small expression. Now, we are, all this adjustment, all this angle are with respect to noon position only. We are all talking about the noon time. But when you want to talk about every time morning, evening, then that simple expression that I have shown you, then you have to go to that, got it? This is only valid for the noon time, right. We are optimizing the angle for the noon time, this simple expression. But you really want to do for any other time, then you have to do that expression. Now, this is what I said. If you fix at the latitude and then I have tried to plot the, what happens if you put at latitude plus 15 and latitude is minus 15. What you see? January, February till December. If you put latitude minus 15, your generation is maximum in June, July, August. But if you put latitude plus 15, one minute, one minute, one minute. Yeah, latitude plus 15, your generation is, latitude minus 15, generation in June, July. If you put latitude plus 15, your generation is maximum in January, February. December, January, February, which is your winter month. What does it mean? If you want to maximize your collection in the winter month, you should put latitude plus 15. So, you will find that solar water heater are not at the latitude angle. They are latitude plus 15. They are little more than the latitude, about 15 degree more. Similarly, if you want, if you are using your solar panels, solar photovoltaic modules for running a fan, you want to run more fan in the summer. So, you should not put your solar panel to the, should not put to the latitude. Where should you put? How should you put? Minus 15. And latitude minus 15, then actually have the more in the summer. Right? So, there is not one solution, latitude equal to latitude is fine. It is, if you do not care about the extra energy that you can generate, fine. But if you really want to get best out of your solar collector, water heater or photovoltaic, then you should choose appropriate angle. This is true most of the location, I mean, with respect to latitude. In India, you can always do this. If you are at the equator, then also it is useful. The question is when the people are installing, whether they are doing all this calculation? Common feeling is they do not do it. My advice is they should do it. Actually, you should build the flexibility of changing the angle. That is the best. Yeah, they have some thumb rule and then thumb rule. But now you all are the smart people in the solar radiation. Right? So, now you make sure that people do measure the angle and put it appropriately, right? Very good. Okay, coming back to the expression here. Now, this expression is of course, little looks longer, but not that difficult. If the computer is doing the job, if you are doing the job, then it is difficult. But they can actually simplify in many, many conditions. What are the simplification you can make? For example, if you are putting always facing south, where gamma is 0. As soon as gamma is 0, sine gamma, so this term becomes 0. This term will not become 0. When you want to say delta for certain locations, you want to calculate only for June, no. Delta equals 0 in the September and February term, March term, sorry. Then you can actually find out that also. Zeroes are depending on the, there are several special cases. Beta equal to 0, when your module is on horizontal, beta equal to 0, then your expression is simple. It becomes like this. When gamma equal to 0, your collector is facing due south, then expression is like this. So, with this all possibilities, you can actually find out how much extra energy you get. If you do this or if you do not do this, how much extra, how much energy you lose. So, that is why I said by measuring, by doing the calculation, you can find out how much energy you are going to get extra. If you are doing this, if you are not doing, if you are doing monthly adjustment, if you are doing vehicle adjustment, if you are doing half yearly adjustment, if you are not doing any adjustment, if you are tracking all the time, things like that. There is another concept that you need to use is what is called local apparent time. So, when we say 12 o'clock in Mumbai, it is not actually 12 o'clock for the sun. When you say 12 o'clock in Mumbai, it is not 12 o'clock for the sun. Because for the whole country, we say 1 12 o'clock, but sun keeps on changing its position. So, when the time it takes to come overhead position to the east and then the middle and then the waist, it will take some time. So, what does it mean? As per the sun, 12 o'clock is different for every location. But for the whole country, we find one time. So, we need to adjust that time if you really want to do the right calculation. And therefore, you need to find out the local apparent time. And it is very simple again, 15 degree is what sun travel in 1 hour, right? And so, you need to find out the longitude of a standard time. Where is our longitude? What longitude we have? Standard time is based on our Indian standard time is based on? Lava. Lava, no? 80 something, right? 82.82 point something, yeah. So, you put that longitude and then you put the longitude where you are located. So, if you are in Mumbai or if you are in Calcutta somewhere, you put that longitude. And then there is something, some also other correction that you have to make equation of time. So, well-defined number equation you can put it. And there is a local time. So, you get the local apparent time. Because you are dividing with this, you will get in the hours, you can convert back into the degrees and you can use it. So, this equation of time, this is how changes. There are some other factors that actually results in the earth rotation. And that is again well known, then you can use it directly. So, then if you want to find out how much is the total radiation, then you know when is the sunrise happening, when is the sunset happening, how many hours, where is the sun coming, whether it is coming over at position or it is somewhere at that angle. So, you can find out how much energy is actually intercepting. So, from that equation, sunrise and sunset angles are simple. You put theta equal to 90, right? Theta is incident angle. So, if your panel is here, you put theta equal to 90. So, this 90 degree means sun is at somewhere down. So, that is your incidence angle and sunrise, sunset, sun is again down. So, you put that is 90 degree, you will get a simplified expression and this omega s is our angle, you will get this. So, this is, this will have two values because of the negative and there is a inverse you will have two values, one is positive, one is negative. So, the difference of the two is sunrise and sunset and the difference of the two is the day length, right? So, maximum sunshine hours you can get is like this. You are getting what you need to find out, when is the sunrise happening, when is the sunset happening, how many hours are passed by in between. So, maximum number of sun hours, possible sun hours. Now, there may be clouds in between. But this equation will give you the number of hours, possible hours. So, maximum number of sun shine hours from the morning to evening will be given by this equation. So, then this is the equation which is most commonly used model for estimating the global solar radiation is this. S max is what you have calculated the total day length which is this expression, the total day length, right? S a is the average day length, ok. Now, this number you cannot calculate. This is depending on the location. How many hours there is a clouds and things like that. So, depending on the location you will have this data are measured. Who will measure this? So, this is the maximum number of sun hours and this is average number of sun hours. Who will keep record of average number of sun hours? Metallurgical depart, they will keep on measuring the data for years and years and years and for tens of years they keep measuring how many times there is a cloud, how many times there is no cloud and they will find it, ok. As per this you may get the average day length may be 12 hours. But as per the measurement that average day length may be 10 hours. Why? Because other 2 hours average you will have the clouds. A and B are the constants that people have tried to fix it empirically there is no way you can you can do the calculation but it is all empirical ways of doing it. G is the global monthly averaged daily global radiation and O A is the monthly average extra terrestrial solar radiation extra terrestrial solar radiation outside the earth atmosphere. So, if you know A, if you know B, if you know S A, if you know S max A, if you know this you can find out the daily global solar radiation at a given location and this is monthly averaged. Take a average over the month and find out the daily global radiation at one particular location. Now, this is very important information for anybody who are doing business in the solar deployment, right. You know the national solar mission. Government is buying electricity at 17.91 rupees. So, what businessman will do? Business also, ok. I will put solar plant in Maharashtra. But he should be his business model will depend on how much radiation is falling on Maharashtra at that particular location. Because even 5 percent here and there can make a huge difference to his business plan, ok. So, estimating the global solar radiation is a very important plan, is a very important, right. And nevertheless, it is all estimation, right. So, you may still be wrong. It is not the real measurement. It is estimation, but still you have some idea to do this. So, I think you will do this calculations tomorrow morning be equipped with the scientific calculator. The constant A and B are given for various locations. Extra solar, terrestrial solar radiation H 0 or H 0, H A can be measured, can be calculated by this formula again. And there are various parameters. S is the solar constant, you know, 1, 3, 6, 7 watt per meter square. N is the day of the year. Omega S is the hour angle. Phi is the location, latitude. Delta is the declination angle. So, you know everything in this equation. You just put the numbers, right. You put the numbers and you will find the extra terrestrial solar radiation. Everything is known for you, ok. And these are the sum of the calculation that we have done and I have put also in my book for the global radiation, diffuse radiation and global radiation at the location which is tilted to the latitude, right. This global radiation is there at the horizontal surface. This is the diffuse radiation. This is the global radiation at the location, at the latitude, at the angle which is tilted equal to the latitude of the location. So, C dot of your publish and we have done it for the various cities. And this kind of maps you can generate then, ok. This is the map for January only. And the unit here is energy. So, mega joules per meter square per day. You can convert kilowatt hour into mega joules also. So, you can see how the map varies for the various locations. This is the radiation. So, red is 25 mega joules, blue is 2 mega joules. You can see very small radiation in January here and the north. But this part is well eliminated about 18, 20 mega joules. So, you can actually by knowing the… So, you can create your maps, your own maps. You can do the calculation and find out. So, this is in the May, ok. You can see most of the country May is now the radiation is gone to 24, 26 mega joules. In the January, it was 18, 20 mega joules. Now, it is 20, 20 mega joules. Questions? Is it interesting? So, just to know little more about the sun, you know, which is giving energy for since time we got birth, yeah. Angle can be positive, 15 and negative. Negative also, yeah. How to consider? How to? Which one can be positive and which one? So, all that was described in slide. There is some particular reference that people understand, ok. Go this side is positive and negative. That is all with respect to the noon position. Any other question? No, that is it. Thank you for your attention.