CHAPTER Environmental Characteristics 2 Thesunisasphereofintenselyhotgaseous matter with a diameter of 1.39  109 m(see Figure 2.1). The sun is about 1.5  108 km away from earth, so, because thermal radiation travels with the speed of light in vacuum (about 300,000 km/s), after leaving the sun solar energy reaches our planet in 8 min and 20 s. As observed from the earth, the sun disk forms an angle of 32 min of a degree. This is important in many applications, especially in concentrator optics, where the sun cannot be considered as a point source and even this small angle is significant in the analysis of the optical behavior of the collector. The sun has an effective blackbody temperature of 5760 K. The temperature in the central region is much higher. In effect, the sun is a continuous fusion reactor in which hydrogen is turned into helium. The sun’s total energy output is 3.8  1020 MW, which is equal to 63 MW/m2 of the sun’s surface. This energy radiates outward in all directions. The earth receives only a tiny fraction of the total radiation emitted, equal to 1.7  1014 kW; however, even with this small fraction, it is estimated that 84 min of solar radiation falling on earth is equal to the world energy demand for 1 year (about 900 EJ). As seen from the earth, the sun rotates around its axis about once every 4 weeks. As observed from earth, the path of the sun across the sky varies throughout the year. The shape described by the sun’s position, considered at the same time each day for a complete year, is called the analemma and resembles a figure 8 aligned along a north–south axis. The most obvious variation in the sun’s apparent position through the year is a north–south swing over 47 of angle (because of the 23.5 tilt of the earth axis with respect to the sun), called declination (see Section 2.2). The north–south swing in apparent angle is the main cause for the existence of seasons on earth. Knowledge of the sun’s path through the sky is necessary to calculate the solar radiation falling on a surface, the solar heat gain, the proper orientation of solar collectors, the placement of collectors to avoid shading, and many more factors that are not of direct interest in this book. The objective of this Diameter ϭ 1.39 109 m Diameter ϭ 1.27 107 m Sun Angle 32Ј Earth Distance ϭ 1.496 1011 m FIGURE 2.1 Sun–earth relationship. Solar Energy Engineering. http://dx.doi.org/10.1016/B978-0-12-397270-5.00002-9 51 Copyright Ó 2014 Elsevier Inc. All rights reserved. 52 CHAPTER 2 Environmental Characteristics chapter was to describe the movements of the sun relative to the earth that give to the sun its east–west trajectory across the sky. The variation of solar incidence angle and the amount of solar energy received are analyzed for a number of fixed and tracking surfaces. The environment in which a solar system works depends mostly on the solar energy availability. Therefore, this is analyzed in some detail. The general weather of a location is required in many energy calculations. This is usually presented as a typical meteorological year (TMY) file, which is described in the last section of this chapter. 2.1 Reckoning of time In solar energy calculations, apparent solar time (AST) must be used to express the time of day. AST is based on the apparent angular motion of the sun across the sky. The time when the sun crosses the meridian of the observer is the local solar noon. It usually does not coincide with the 12:00 o’clock time of a locality. To convert the local standard time (LST) to AST, two corrections are applied; the equation of time (ET) and longitude correction. These are analyzed next. 2.1.1 Equation of time Due to factors associated with the earth’s orbit around the sun, the earth’s orbital velocity varies throughout the year, so the AST varies slightly from the mean time kept by a clock running at a uniform rate. The variation is called the equation of time (ET). The ET arises because the length of a day, that is, the time required by the earth to complete one revolution about its own axis with respect to the sun, is not uniform throughout the year. Over the year, the average length of a day is 24 h; however, the length of a day varies due to the eccentricity of the earth’s orbit and the tilt of the earth’s axis from the normal plane of its orbit. Due to the ellipticity of the orbit, the earth is closer to the sun on January 3 and furthest from the sun on July 4. Therefore the earth’s orbiting speed is faster than its average speed for half the year (from about October through March) and slower than its average speed for the remaining half of the year (from about April through September). The values of the ET as a function of the day of the year (N) can be obtained approximately from the following equations: ET ¼ 9:87 sinð2BÞ7:53 cosðBÞ1:5 sinðBÞ½min (2.1) and 360 B ¼ðN À 81Þ (2.2) 364 A graphical representation of Eq (2.1) is shown in Figure 2.2, from which the ET can be obtained directly. 2.1.2 Longitude correction The standard clock time is reckoned from a selected meridian near the center of a time zone or from the standard meridian, the Greenwich, which is at longitude of 0. Since the sun takes 4 min to transverse 2.1 Reckoning of time 53 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 20 15 10 5 0 Minutes –5 –10 –15 –20 0 30 60 90 120 150 180 210 240 270 300 330 360 Day number FIGURE 2.2 Equation of time. 1 of longitude, a longitude correction term of 4 (Standard longitude [SL] À Local longitude [LL]) should be either added or subtracted to the standard clock time of the locality. This correction is constant for a particular longitude, and the following rule must be followed with respect to sign convention. If the location is east of the standard meridian, the correction is added to the clock time. If the location is west, it is subtracted. The general equation for calculating the AST is: AST ¼ LST þ ET Æ 4ðSLÀ LLÞDS (2.3) where LST ¼ local standard time. ET ¼ equation of time. SL ¼ standard longitude. LL ¼ local longitude. DS ¼ daylight saving (it is either 0 or 60 min). If a location is east of Greenwich, the sign of Eq (2.3) is minus (À), and if it is west, the sign is plus (þ). If a daylight saving time is used, this must be subtracted from the LST. The term DS depends on whether daylight saving time is in operation (usually from end of March to end of October) or not. This term is usually ignored from this equation and considered only if the estimation is within the DS period. 54 CHAPTER 2 Environmental Characteristics EXAMPLE 2.1 Find the equation of AST for the city of Nicosia, Cyprus. Solution For the locality of Cyprus, the SL is 30E. The city of Nicosia is at a LL of 33.33 east of Greenwich. Therefore, the longitude correction is À4  (30e33.33) ¼þ13.32 min. Thus, Eq (2.3) can be written as: AST ¼ LST þ ET þ 13:32 ðminÞ 2.2 Solar angles The earth makes one rotation about its axis every 24 h and completes a revolution about the sun in a period of approximately 365.25 days. This revolution is not circular but follows an ellipse with the sun at one of the foci, as shown in Figure 2.3. The eccentricity, e, of the earth’s orbit is very small, equal to 0.01673. Therefore, the orbit of the earth round the sun is almost circular. The sun–earth distance, R,at perihelion (shortest distance, at January 3) and aphelion (longest distance, at July 4) is given by Garg (1982): R ¼ að1 Æ eÞ (2.4) where a ¼ mean sun–earth distance ¼ 149.5985  106 km. The plus sign in Eq (2.4) is for the sun–earth distance when the earth is at the aphelion position and the minus sign for the perihelion position. The solution of Eq (2.4) gives values for the longest distance Spring equinox—March 21 Earth 24 h Ecliptic 23.45° axis Sun Polar axis 152.1 106 km 147.1 106 km Summer solstice—June 21 Winter solstice—December 21 24.7 days 365.25 days Fall equinox—September 21 FIGURE 2.3 Annual motion of the earth about the sun. 2.2 Solar angles 55 equal to 152.1  106 km and for the shortest distance equal to 147.1  106 km, as shown in Figure 2.3. The difference between the two distances is only 3.3%. The mean sun–earth distance, a, is defined as half the sum of the perihelion and aphelion distances. The sun’s position in the sky changes from day to day and from hour to hour. It is common knowledge that the sun is higher in the sky in the summer than in winter. The relative motions of the sun and earth are not simple, but they are systematic and thus predictable.