 So, let us start this day with the lecture 3 that is the continuation of lecture 2 that we have done yesterday. What we were discussing yesterday, if you recall, we looked at the solar radiation possibilities, we looked at how solar PV can be useful for fulfilling all our energy requirement. Then we actually looked, we are looking at the relative motion between sun and earth, so that we can find out at what angle we can collect the maximum solar radiation. Then we have also looked at that two facts that the sun moves always in a plane which is tilted at an angle equal to the latitude angle. So, the angle of the plane is fixed and this plane, so I am talking about the day motion of the sun, so morning and evening and afternoon. So, the sun moves in a plane, but the position of the plane can change and depending on the day. So, there are days which are equinox when the day length is equal to night length and there are days which are solstice where sun reaches to its extreme position either towards the southern hemisphere or towards the northern hemisphere. As a result of that, what we have seen that if you look at, if you look at the horizontal ground and if you are located at angle, so if this is normal to the ground, if you are located at some angle which is latitude angle called phi, then this is going to be the motion of your sun. This is peak position of the sun in the afternoon, this is where it starts and the plane, the angle remains same, the position of the plane will change. So, in the winter time the sun will appear to have the motion in this plane and therefore, this angle is phi and this angle here is delta. I told you the delta is the declination angle, it is the angle between the line joining the center of the sun to the center of earth with respect to the equatorial plane. Sometime delta can be 0, sometime delta can be plus 23.45, sometime it can be minus 23.5. So, in extreme position like this here, in extreme position here, the total angle with respect to normal, the total angle with respect to normal is phi plus delta and the tilt of the panel. Suppose you are installing a panel, so your panel should be perpendicular to the rays and particularly in the afternoon time. Why afternoon time? Because in the afternoon the radiation intensity is maximum and you want to collect the maximum solar radiation at the afternoon. So, if I want to make a solar panel perpendicular to this plane, perpendicular to this plane because the rays will be coming in this direction, then I have to install my panel like this. So, this is my PV panel or for that matter any solar collector. So, your water heater will also actually work on the same principle. Now, this angle I was measuring phi plus delta is measuring with respect to normal, but we can measure this angle with respect to horizontal plane. So, this angle, so this is the tilt with respect to the horizontal, then I would say that and this is referred as a beta, this is referred as a beta. So, this angle is beta which is the tilt of the collector, tilt of the solar panel. So, beta is actually you should have 90 minus because I am this angle phi plus beta with respect to perpendicular. So, I have to take 90 and subtract it. So, 90 minus phi plus delta and I know that my delta can be plus or minus. So, this is then beta is equal to your tilt of the solar collector. For that matter it can be solar photovoltaic or it can be solar thermal also or any other collector. And remember this, the whole equation is true for the noon time, the peak position of the sun, because in the morning sun will be here. So, your angle should be this in the in the before and afternoon your sun will be here. So, your angle should be this, but I am talking about the noon time. So, this is the angle beta equal to 90 minus phi plus minus delta. Phi is the latitude angle and delta is the declination angle, phi is the latitude angle delta is the declination angle. So, this is what we have discussed. So, for yesterday and let us continue our discussion to that. And we will come to this point also that this tilt of the earth with respect to its line joining the center of the sun to the center of earth, the earth axis is tilted by 23.545 degree and because of that there is a cause of season summer and winter. So, for example, this line in the center is the equator, this line at latitude 23.5 is a tropic of cancer and this line below 23.545 south is a tropic of capricorn. So, suppose you are living in a location at a point A, if you are living in a location point A which is at the tropic of cancer. So, your latitude angle is 23.45 degree right. This is extreme position of the earth and then the it will start moving in the other direction. So, at this point if you look at the sun, sun is directly overhead position in the afternoon it will be directly at overhead position which means this point A will get the maximum radiation as compared to any other point on the earth surface right. So, if you go above in the higher latitudes or lower latitudes you are going to get lower radiation. Now, the earth is revolving revolving and after six months it comes to this position. So, it is revolving in this plane. So, after six months it is coming to this position. So, note here that this is the equatorial plane. This plane if I continue this line like this, this is the equatorial plane here the equatorial plane is here. So, if this is my line joining the center of the center of earth my equatorial plane in the one extreme position is like this and in other extreme position it is like this. So, this is my because of the tilt right. Now, consider this position same point A tropic of cancer at 23.45 degree same point, but this point in the same condition is not actually overhead your sun is not on top of you now in the afternoon condition. So, therefore in this position here the sun was a point A or location A was getting a high amount of radiation. So, it will be summer here, but at this point in this time six months later the point A will get the lower amount of radiation you are as compared to this point because now this point is on the top. So, then this will become winter and that also you can understand how the angle of the sun is sun rays is changing. So, if your point A in this time which is June 21st what should be the tilt of your solar collector at this point what should be the tilt of your solar collector because the sun rays are coming exactly on the top sun rays are coming exactly from the tops here collector has to be flat on the ground. So, your collector has to be the flat on the ground, but in this location A in this location A what should be the angle let me draw the situation 21st December winter on a white board. So, if you are if you have this situation this is your line joining the center of the sun. So, this is your sun and earth I will draw little bit bigger. So, that it becomes clear now this is the tilt and this is your equator. So, this is your equator this is your north this is your south and at 23.45 year topic of cancer and below 23.45 year topic of capricorn. So, now you are sitting at this point and this point is obviously not getting the enough radiation. So, now you want to get the maximum solar radiation which is which will have this directions your collector has to install at this angle. Now, this angle will have actually this. So, you have to tilt by this angle which will be some of this angle will be some of some of the angle between the some of the angle between the line joining with the equator plane this is 23.45 and this is another 23.45. So, you will actually have almost about 47 degree tilt. So, this angle will be about 47. So, remember that one position when the earth was on the other side when the earth was at this side the collector was making a zero angle or the normal was aligned with the sun rays and your collector was flat on the ground in the extreme position here your collector has to be 47.47 degree. So, therefore, the angle of the collector will change from maximum 47 degree throughout the motion. So, this is what depicts here that how the different position of the earth with respect to sun result requires a different tilt of the module to collect the maximum radiation in the noon time and the maximum variation in this tilt will be about 47 degree. So, these are the various latitudes and longitudes that that is that India for example, in the south this point is 8 degree latitude it go to the north it is about 35 degree north. The longitudes varies from 68 degrees to 96 about 96 degree just to be clear. So, that whenever we talk about any location and we want to find out the angle of the PV module tilt then we should know the latitude. One other thing that we should note here is that because we are in the northern hemisphere the sun appears to us that it is always in a southern hemisphere. So, one thing is you have to tilt your collector with respect to the if this is a horizontal ground you have to tilt your collector, but what is the position tilt is this direction or this direction. So, this tilt the face of the module should always be in the southern direction because in the northern hemisphere and opposite is true when you go to the southern hemisphere. So, if you are putting your module in southern hemisphere then the face of your module should be towards the north if you are putting your modules in the northern hemisphere then the face of your module should be towards the south. So, same thing here that we already discussed that this altitude angle the altitude angle or the angle or the tilt of the module should be 90 minus 5 plus minus delta here it should be. So, now the declination angle that we are talking about the declination angle changes throughout the year every day and the equation is given 23.45 sin of 360 divided by 365 in the bracket 284 plus n. As we discussed yesterday the n is the day of the year n equal to 1 for January n equal to 2 for January 2 n equal to 3 for January 31st n equal to 365 for December 31st. So, here I have given some number n equal to 335 for December 1. So, just think quickly what should be the n for June 21st what should be the value of n to which day of the year June 21st is that is equal that is your n think about it quickly which day of the year June 21st is what is the value of n for June 21st. So, it is almost about the middle of the month it will have the value about 170 and 172. So, precise calculation you can do. So, now look at the variation of declination angle. The declination angle as I said on the on the equinox day that the day length equal to night length delta is 0. Delta is 0 means the equatorial plane is exactly in line with the line connecting the center of the sun to center of earth. So, these two days September 21st and March 21st are the equinox day these are the extreme position. So, for example, in December the sun December 21st sun goes to the extreme position. So, extreme what we call the chinion in our Hindi calendar and June 21st it goes to the other side in the extreme position. So, this is how the declination angle changes it crosses 0 2 points it reaches maximum value of minus 23.45 on December 21st plus 23.45 on June 21st. So, this we need to calculate. So, this is what I already discussed that I if I want to tilt my panel to collect the maximum solar radiation in the afternoon and this is what I told that most of the solar power plant in the country are designed are installed in a way that they collect maximum solar radiation in the afternoon because the intensity is higher in the afternoon. So, we are interested now in beta that is beta is the tilt of the module with respect to horizontal plane. So, this is how we can calculate 5 plus delta, but what is the problem now because my delta is changing every day. Remember the delta is a function of n changes every day. So, which means my delta changes every day and if my delta changes every day which means my tilt that is beta also changes every day. Beta changes every day means so which means you have to tilt your module almost on a daily basis. So, you have to tilt your module on a daily basis sorry. So, I think earlier I told you the beta equal to 90 minus 5 minus delta, but actually this is correct the beta is 90 minus theta that is the angle and if I put then beta is actually 5 minus delta or actually this should be 5 plus minus delta because delta can be plus or delta can be minus. So, this is the tilt beta equal to 5 plus minus delta. So, now because my delta keeps changing every day my beta should also keep changing every day. So, which is again a problem because I cannot tilt my modules on a daily basis. In practice it can be done, but it results in adding up the cost it results that extra facility in your power plant to actually adjust the module or even if you are installing a power solar panel on your rooftop you will have to actually do every day now that will become a problem. So, then what we should do then we should actually take the average value of the delta. So, if I take a average value of delta so this is how the delta is varying throughout the year. If I take a average value of delta what it will be? So, what do you think the average value of delta will be? So, that is the area of the curve positive side and negative side. So, because it is a symmetric curve the average value of delta over a period of year will be 0. Now, if you take a so you said fine. So, average value of delta over a period of year will be 0 which means if your beta is equal to phi plus minus delta and delta average delta average is equal to 0 over a year right. For the whole year if I take delta average is equal to 0 which means beta is equal to phi very simple. What does it mean? That it means the tilt of your module should be equal to the latitude angle of the location. So, if I am in Mumbai latitude angle of Mumbai is 19 degree then the I should always put the modules at tilted at 19 degree in which direction. So, if I am putting my module with respect to ground at 19 degree. So, this is my south and this is my north. So, module should always face towards the south the module should always face towards the south. So, this is the location but think about your location. So, if you are in the southern if you are in the down south then your angle can be you know 8 9 degree 10 degree depending on the latitude or if you are in the further north Delhi etcetera then your angle will be about 23 degree. So, this is the thumb rule that if you want to just fix your collector for once and if you do not want to change throughout the year then you should take the average value of delta and average value of delta is 0 or the declination angle is 0. And therefore, your beta that is the inclination of module is equal to 5. So, while the cases are simple but then you are going to lose some amount of radiation right because you know if you are fixing at this angle you know in the summer your sun will be on the top here. So, you are not collecting maximum in the winter your sun will go here. So, you are not collecting maximum radiation. So, therefore, some people what they some people what they do is that let us I cannot change the tilt of a module every day, but let me change the tilt of module once in a month. So, if you want to change the tilt of a module once in a month what you should do take the average monthly value of the delta what you should do take the average monthly value of the delta. So, then the average monthly value of the delta for summer will be a positive for winter it will be negative. So, then you can answer this question yourself what should be the fixed collector inclination in summer what should be the solar water heater inclination in the summer. Now, when you are when you are actually trying to install a solar water heater in the summer you do not want so much hot water, but you want more hot water in the winter. And therefore, you should optimize your tilt for the winter. And because the sun is more in the southern hemisphere tilt is more in the southern hemisphere you should actually tilt your module more for the winter location. And in winter and what happens in winter they are equal to beta equal to phi minus delta and the delta itself is a delta can be either plus or minus. So, in if I am taking winter situation then I have negative value of delta. So, then I have to have minus and then I have to put negative value of delta which is in winter the summer for example, it can be minus 23.45 then I will actually phi plus 23.45 degree. So, basically if you are installing your module for winter if you want to make a highest generation or highest collection of solar radiation for the winter case then and the extreme winter then you have to add 23.45. So, as a result that is why you will see that when you look at the solar water heater the angle of the solar water heater is normally more than the angle of the solar PV panels. Because in solar water heater you want to maximize your collection in the winter while for the solar PV panel you might want to maximize your collection in the summer because you want more electricity. But otherwise if you say if you are ready to change the angle every if you are ready to change the angle or the inclination angle every month then you should take a average value of you should take an average value of delta and that average value will change. So, therefore, so this is we already discussed that average delta is 0 over the year therefore, beta equal to phi, but otherwise beta average inclination should be phi minus delta and the delta by the way is already taking care of the plus and minus sign. So, I hope it is clear to all of you now that depending on the case when you want to maximize the collection you can actually decide the tilt and do the inclination of your collector accordingly and this applies to both solar water heater and a solar PV panel. So, this is an comparison that I show shown here that normally this horizontal line here is the case when you are installing your module at the latitude angle you are fixing you are not changing any time. So, this is a horizontal line now is suppose you are changing the tilt every month then what will happen. So, suppose you are changing the tilt if you are making it latitude minus 15 then you will say that this line will follow latitude minus 15. So, now latitude is minus 15 for the June-July you are going to get more collection. So, if you want your generation to be more and this is still case of the fixing. So, you are fixing it, but you are not fixing it to the latitude angle, but if you are fixing it to the latitude minus 15 degree on an average and therefore, your collection will be better in June and July, but look at the other case that is latitude plus 15. Latitude minus 15 means what? Latitude minus 15 means actually if this is the latitude angle you are actually putting at minus 15, putting it more trying to put it more horizontal, but if you are saying latitude plus 15 means if this is the normal angle then you are actually trying to put it more towards the south more tilt. So, this is 5 plus 15 degree case and this is 5 minus 15 degree case. So, because in the summer the sun is sun almost comes to the overhead position. So, this will give you more generation in summer. So, this is suitable this setting is suitable for summer and this setting because sun goes south, sun goes down in the south direction in winter and therefore, this setting will be more suitable for winter location, winter season. So, that is what is shown here in this graph. So, this was so far simple what we have discussed was simple because we are talking about one position of the sun that is afternoon position. So, all over this discussion so far is about the position of the sun at the noon time, but actually the angle made by the sun with respect to the solar rays at any given time on a same day are different. So, for example, if I if this is your module, this is your module they installed. Now, sun moves in a plane. Suppose, the sun is moving in a plane like this. So, this is the afternoon position, this is the morning position, this is the before noon and afternoon position. So, now look at the angle that is meant. So, now you normally you actually inclined your module for the afternoon position. So, in the afternoon this is the normal to the normal to the panel. So, the normal to the panel the angle is perfectly 90 degree here and this is what you want that rays should be perpendicular to this, but look at the morning position. So, morning angle is not optimum the rays will come from this direction, then it will come from this direction, it will come from this direction, then it will come from this direction. So, the if you are fixing a module then of course, you design it for the afternoon position, but if you are not fixing your module position then actually you will you want to collect the good radiation in the morning also, you want to collect good radiation at 9 o clock also, you want to collect the good radiation at 10 o clock also and so on. And your job is always to make that make sure that the solar radiation is always perpendicular to the solar panel in that case you are collecting maximum radiation. So, then it is called the trekking, then basically you have to follow this angle. So, in the when it is morning you have to make your module like this, when it is 9 o clock you have to make module perpendicular to this rays, when it is 12 o clock you have make a module perpendicular to this rays. So, basically it means that your solar radiation the angle of the solar radiation falling on the on the solar panel depends on other parameters also right. So, few things are very clear to us. So, let me repeat now we are thinking about following this in every minute every second. So, far earlier discussion was only to fix a module so that you can get a better collection at the afternoon, but now we are thinking that all the all the time I should get a better collection. So, the many parameters and this is actually long topic and what I have told you so far is good enough and we will not go into the details of this, but just to give a brief introduction that if you really want to calculate the angle that sun ray is making with respect to the normal to the plane, this respect to the normal to the plane. Look at here what is the normal this green lines is the normal to the plane and this is the sun position here. So, this angle theta this angle theta between the normal to the plane and the sun ray is what is important and you want what do what is the value of theta you want this angle theta here is the angle between the normal to the plane and sun rays. But what do you want the value of this angle this angle should be 0 all the time morning afternoon evening before noon afternoon summer winter anytime if you want maximum collection the angle theta that is the angle between normal to the plane and the sun rays should be 0. So, now we should see how theta depends on other angles. So, look at what are the other angles first term angle the beta which is the tilt of the module is one of the important angle fine. This is the angle which is called the gamma which is the if you take a dew south angle between the dew south or the angle between the dew south direction and the projection of the normal to the plane with respect to the dew south. So, basically with respect to south how is your how is your panel right. So, if your panel is exactly looking south then the gamma is 0 if your sun rays is in the morning in the east suppose this is east if sun rays are here and your panel is looking this way. So, you are making a 90 degree with respect to that in the evening sun will go the other side and you will make a 90 degree, but the the sign will be different. So, that is called gamma. So, that is orientation of the plane that gives gamma what are the other factors that will change your value of theta the factor that will change the value of theta is the latitude of the location. So, depending on the location that will change day of the year a declination also changes the angle right because declination defines the how how down the sun is or how up the sun is in the sky in the afternoon. So, there is a declination angle that will determine the angle time of the day you are talking about a 6 o clock 7 o clock 8 o clock 12 o clock or the morning and the beta n gamma already discussed. So, the theta which you always want to be 0 when you are completely following the sun will depend on the 5 different angles and this angle a latitude can vary plus minus 90. So, you can go to 90 degree north and 90 degree south surface azimuth angle or the orientation of the panel surface azimuth angle is this angle by the gamma with respect to south due south where is the sun rays that can vary 360 degree. So, one side 180 degree other side 180 degree our angle basically the time is given the time is given in terms of the angle. So, in a one day there is a 360 degree rotation. So, 360 divided by 24 hours. So, basically you will get 15 degree per hour rotation. So, the time of the day is measured in terms of angle because we are all talking about the angles here. So, 12 o clock is considered 0 hour angle and 11 o clock will be a 15 degree minus 15 degree hour angle 10 o clock will be minus 30 degree hour angle if you go to the afternoon time it is positive. So, 12 o clock is 0 hour angle 1 o clock is plus 15 degree hour angle 2 o clock is plus 30 degree hour angle and so on. So, 6 o clock is minus 90 degree in the morning and 6 o clock in the evening is plus 90 degree slope of the surface or the collector can be 0 or 180. 0 means it is lying flat on the ground. So, with respect to ground the angle of the panel is 0. So, it is lying flat on the ground and 90 degree is 90 degree means your panel is vertical and the declination angle as I said can vary minus 23.45 to plus 23.45. So, these are the various angles that can vary and I will come back to this slide, but I just want to give an idea that and we are not going to look at the details of this calculation. I just want to give it an idea that if you know the theta, if you know the theta you can find out the intensity of the light falling on your surface. So, here so, I b cos theta is the intensity of the light falling on your collector. Now, this value of theta cos the value of theta that we are interested is a function of all these angles and here is the simple equation that you can get or rather complicated equation. So, the value of angle that sun rays makes with the normal to the plane which is theta. So, this angle depends on so many other angles there are five angles. So, there is phi delta beta gamma and omega. So, the simple or the equation is this and if you can find out each angle at any given time at any given day at any given location at any given tilt of the collector you can find out what is the angle of the sun rays with respect to normal and remember what you want to do we want to make this angle theta as low as possible and preferably 0. So, when you are doing the sun tracking when you are doing the sun tracking actually you can feed this formula in your micro controller and your micro controller will calculate all this angle and will exactly align your panel perpendicular to the sun rays all the time. All the time means morning to evening all the seasons summer and winter all the location equator and the northern side or the southern side etcetera. This is the extra somebody wants to learn more about the radiations I am just giving you few slides and when you have time after this course you can actually go through this solar radiation and actually use this equations to estimate the amount of solar radiation availability given location and this is estimation only because the exact measurement requires long time. So, many people actually estimate. So, I very quickly go through the slide, but do not worry you are not supposed to learn this our main job here is to find out how much amount of the solar radiation and how to inclined a module for a year for a year or a month. So, these are the various equations that are there that are used in the estimation of the solar radiation you have to find the hour angle you have to do the various calculations. When you do all these calculations when you do all this calculation you can actually find out the find out the solar radiation. This is the main formula and again please do not worry about this I am just giving you this extra information in case anybody want to learn more about the solar radiation. This is also discussed in my book which is given to all the participants. So, when you have time after this course you can go through this slides and learn more about the radiation, but because we have to this is a PV course and we do not have enough time. So, we cannot afford to go through all these slides fine. So, let me come back to the solar radiation. So, far we have learned that if I want to install my collector at a fixed angle throughout the year I do not want to change then it is equal to the latitude angle it should be south facing, but if I want to maximize it for the summer then it is latitude minus 15 degree I should install. If I want to maximize the collection in the winter then it is a latitude my plus 15 degree I should install or if you want to maximize at a given month then I should take a average value of the delta the clinch angle for that month and then I should take proper care for the sign plus or minus and 8 to the phi and get that date. When we are talking about solar radiation solar power plants solar PV system we should always know what is the available fuel for us available fuel is basically solar radiation. So, solar radiation is now given in a various ways represented in various what are the ways solar radiation are many times it is also referred as insulation solar insulation for a given location is given on hourly basis many times you do not need hourly basis it can be given on a daily basis. So, solar radiation when you said daily basis means basically it is a total solar radiation energy calling on a given day which means you are actually integrating the total energy from morning to evening. So, basically we are when you are integrating means you are talking about the energy available solar radiation energy available for a day you can integrate over a month. So, you can get the monthly solar radiation energy available and you can integrate of course, over the year. So, this is one way of doing it per hour per month per year. Other way of talking about the solar radiation is whether it is a diffuse radiation direct radiation or a global radiation. So, you should know that whether the radiation given is diffuse direct or global fine. Other way of saying is whether the solar radiation is given in terms of the direct normal solar radiation it is always direct normal normal to the sun rays always always normal to the sun rays. If your collector is here then you are talking about this. So, sun rays basically is angle of the sun rays changes all the time. So, you are actually collecting the radiation all the time perpendicular to the sun rays and that is referred as a direct normal solar radiation. Direct normal solar radiation is particularly useful for concentrated technology because your concentrator optics can only concentrate the light which is coming perpendicular to the plane or the parallel rays only. So, therefore, many concentrated technology particularly concentrated solar thermal technology will require knowledge of DNI direct normal insulation. The normal global insulation will not do the job. Solar radiation can also be given in terms of the radiation whether it is at horizontal plane or the radiation with respect to some other plane. So, because as we discussed that your solar modules are installed normally not on the horizontal plane not flat on the ground normally they are inclined at some angle. So, rather than knowing the solar radiation on the horizontal plane it is more important to know the solar radiation at a inclined plane. So, that will give the correct picture. So, solar radiation can be represented in many ways and we have to be careful while using the information. So, let me go through again. So, it can be daily basis hourly basis monthly basis yearly basis it can be a diffuse direct global it can be a direct normal it can be a solar radiation on the horizontal plane or any other given plane. And that theta the complicated equation of theta that I have showed you actually if you know if you can use that equation you can find out any radiation that you want. So, when we say solar radiation when you say instantaneous value of solar radiation it is given remember as a given as a we were discussing yesterday as a solar constant what was the unit of solar constant instantaneous value of the radiation. The instantaneous value is what per meter square right and we also discussed that air mass 0 ok. So, instantaneous value air mass 1.5 we discussed yesterday that is 1000 watt per meter square ok. So, this is watt per meter square ok. This instantaneous will, but when we are talking about the daily or hourly or monthly solar radiation then we are actually talking about the integration of this instantaneous value over that period right. So, we are talking about daily solar radiation means we have to integrate the instantaneous value of solar intensity throughout the day. And once we integrate basically what we are doing we are multiplying with the time and when we multiply with the time what you will get watt you have to get multiply with the hour right. So, when you are multiplying with the hour this your watt per meter square will become watt hour per meter square ok. And typically this are presented in kilos. So, kilo watt hour. So, solar radiation value can easily be or the radiation or the radiation energy I would say is given in terms of kilo watt hour per meter square. And then depending on this case it can be per meter square per day it can be per meter square per month it can be per meter square per year ok. So, the daily solar radiation can be kilo watt hour per meter square per day monthly kilo watt hour per meter square per month and yearly kilo watt hour per meter square per year ok. Typically in India the solar radiation varies between 4 to 7 kilo watt hour per meter square per day ok 4 to 7 kilo watt hour per meter square per day. And if you multiply by 365 you will say that solar radiation value varies from 1400 to 2500 kilo watt hour per meter square per year. This is very good amount of solar radiation by the way ok that is why you might have heard several times now that India is placed with the solar radiation ok. Because our radiation intensities are very good and because your fuel density is higher your energy per unit area per unit year is higher your cost of electricity in India is lower than the cost of solar electricity in Europe for example right because your fuel is higher. So, this is an example of the solar intensity every solar intensity for the for India. I do not know if you can read this, but the darker side here represents about over 6 kilo watt hour per meter square per day ok 6 to 6.5. This lighter yellowish side represent here about 5 about 5 or little less than 5 kilo watt hour per meter square per day ok. This is very low intensity 4 4.5 kilo watt hour per meter square per day. But in general if you look at the overall country you will see that the solar radiation in general is pretty good and it is between 4 to 7, but more or less it is between 4.5 to 6 kilo watt hour per meter square per day ok. You can also look at the world map ok. So, this is in terms of the per day, but as I say an annual solar radiation if you look at India will vary between about 1400, 1500 kilo watt hour per meter square per day to about 2500 kilo watt hour per meter square per day. Remember this numbers are very important because when we are doing the solar PV system design you should know that what is the daily radiation or what is the monthly radiation or what is yearly radiation. If you do not know the precise number at least you should have the idea about how much is the solar radiation variation because you are going to use this number in our calculation in your tutorial also. So, remember this numbers. So, we can similarly have the world map that I have shown you yesterday, but I can have a look at today also. So, similarly in the world the solar radiation varies from very low values of 500 kilo watt hour per meter square per year by the way this numbers are per year and then it can be as high as 2500 watt hour kilo watt hour sorry per meter square per year ok. So, India is somewhere here and this belt which is the equatorial belt as you can see receives lot of solar radiation. So, as I told yesterday also that there is a plenty of sunshine that is available and if you use very fraction small fraction of it that all normally is good enough to generate all our energy requirement. So, with this I would like to stop this discussion on the solar radiation. I hope it has given you very brief idea about the solar radiation how it varies it has particularly given the idea about how to install a solar PV module particularly when you are installing a module fix you are not taking it when you are installing module at fixed angle then how to calculate that angle for a give optimum for a given month or a given year. So, you can actually calculate the value of delta and find out that angle ok. We also learnt the motion of the sun in a given plane and that plane keeps on changing depending on the day and the day is represented by angle delta which can be calculated ok. So, with this brief discussion I am sure that if I ask you to find out what should be the tilt of a solar panel on let us say March 31st to get a maximum solar radiation in the afternoon I am sure you should be able to do that ok. So, be ready with that kind of problems solve your problems and very simple you need to know just phi and delta and can discuss with your colleagues and find out that what is the solar what is the solar PV module is tilt for a year if you want to fix it for a year for your own location you for whatever village or city you are coming you can do that calculation for the same and it is going to be a simple calculation ok fine. So, let me take the question Amrita Coimbatore. Sir, the position of the sun is varying over a year. So, if you want to find the inclined angle is there any statistical method to calculate that. Yes sir, I want to generalize to that angle. Yes generalization is not possible you know because your latitude is different for different locations. So, there cannot be a single angle and it will vary with the latitude. So, if you go in the south the latitude angles are very small if you go to the north your latitude angles are large if you go to Europe your latitude angles are even higher. So, therefore, you cannot generalize and also your delta value changes every day ok, but so you have to take a you know delta phi and delta into account, but in general you have to you have to keep orientation towards the south and if you are fixing your module for the whole year then the angle is equal to the latitude angle, but as I said you can optimize your collection either for the summer or for the winter. If you are optimizing your collection if you want more collection in the summer then you should have the latitude angle minus 15 degree. If you want more collection in the in the winter then you have latitude angle plus 15 degree, but generalization is not possible this two parameter you must take into account. Sir you have said that during the tilt of the earth the angle that is 23.5 degree is that angle is same sir anywhere. So, 23.45 degree is an angle which is the extreme position of the plane equatorial plane with respect to the line joining the center of the sun to the center of earth ok, but yeah it and that is the extreme position at any given location that angle will change between plus 23.45 to minus 23.45. So, total variation in that angle will be 47 degree and at any given and at any given at any given location at any given location on earth that total variation in angle will always be 47 only whether it is equator or any north or any south the total variation is always be 47 degree ok, Naiti Surat. Basically I am a designer of wind solar hybrid system and in our hybrid configuration we do not have a good wind during winter. So, sorry it is advisable to have the angle as per the solar water heater for solar PV panel can you throw some light on that. For the wind you are talking about. No, not for wind turbine sir see for best consistency we do the hybrid of wind solar and in that the solar angle I think should be just like that of water heater during winter because in winter the wind is having a slack season and during summer wind is good even in monsoon it is good. Yeah. So, can you throw some light on that. Yeah. So, you are very correct that because your wind is low in the winter and you want more collection you want your panel to produce more power for for you in winter and if you do not want to change the angle of your panels then the best tilt for your panel will be that of corresponding to latitude angle plus 15 degree and that is that is what normally solar water heater do right they collect maximum in winter and what you are saying is true that it has to be latitude angle plus 15 degree. One last question I will take from Paramati. Is there any is there any mechanical sun tracking system instead of micro control? Yes, there are mechanical sun tracking system people have designed which is based on for example heating up a fluid and or it is similar to what is the time machine that you know we have seen the time machine. So, there are systems people have installed but actually because of the low cost and the more accuracy of electronic system normally for the sun tracking people go for electronic system but definitely it is possible to have the mechanical system also. There are there are many steplard is people use for the solar cooking where they use arrangement of similar to what we have the arrangement of the clock in the old clock you see that where the pendulum is is is using to maintain the time that kind of arrangement is possible. So, yes mechanical tracking is also possible. Okay, KG Somaya Mumbai. Is it true that in India catch receives maximum amount of solar radiation which will which can generate electricity which is sufficient for the whole country? Yeah definitely it is true and based on the numbers that I have given you you can yourself calculate the area now you know I have told you that suppose yesterday if you remember I told that if you just cover a 100 kilometer by 50 kilometer area of a of any catch region for example that will be sufficient to generate the whole electricity that India is generating today. Okay, and now we are using only 100 by 50 square kilometer and typically the area of the catch is much much more. Okay, so I think you all participant can also do the same calculation assume that your solar radiation is let us say 2000 kilowatt hour per meter square per year. Okay, take a 10 percent efficiency of that then you will find out that you will have 200 kilowatt hour per meter square per year that is the energy that you can generate. Now you divide whatever is your energy requirement if your energy requirement is 100 or 1000 billion units that is 1000 billion kilowatt hour divide it by 200 kilowatt hour per meter square you will get the area of your module in meter square. Right, so any participant should be able to do this calculation it is very simple calculation how much area is required to generate a given amount of energy. Okay, so do this calculation on your own and you will find precisely what how much area is required. I mean this is the for the country but you can see only in Mumbai for Maharashtra if you want to generate your electricity then how much area of the Maharashtra is required. Okay, some people can do it for Madhya Pradesh, Karnataka etc. So this is a simple calculation you should be able to do here. Okay, so let me stop here. Thank you.