Iqbal An Introduction To Solar Radiation

1. Auflage 2012
ISBN: 978-0-323-15181-8
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 408 Seiten

An Introduction to Solar Radiation is an introductory text on solar radiation, with emphasis on the methods of calculation for determining the amount of solar radiation incident on a surface on the earth. Topics covered include the astronomical relationship between the sun and the earth; thermal radiation; the solar constant and its spectral distribution; and extraterrestrial solar irradiation. This book is comprised of 12 chapters and begins with an overview of the trigonometric relationships between the sun-earth line and the position of an inclined surface, followed by a discussion on the characteristics of blackbody radiation. The next chapter focuses on the solar constant and its spectral distribution, paying particular attention to extraterrestrial solar spectral irradiance and the sun's blackbody temperature. Subsequent chapters explore extraterrestrial and radiation incident on inclined planes; the optics of a cloudless-sky atmosphere; solar spectral radiation and total (broadband) radiation under cloudless skies; and solar radiation arriving at horizontal surfaces on the earth through cloudy skies. The ground albedo and its spectral and angular variation are also described, along with insolation on inclined surfaces. The last chapter is devoted to instruments for measuring solar radiation, including pyrheliometers and pyranometers. This monograph will serve as a useful guide for energy analysts, designers of thermal devices, architects and engineers, agronomists, and hydrologists as well as senior graduate students.

Muhammad Iqbal joined Jamia Hamdard (Hamdard University), New Delhi, as Professor of Botany and was Head of the Botany Department, Dean of Science Faculty, and Vice-Chancellor of Jamia Hamdard. Specializing in the Developmental, Environmental and Medicinal Botany, he has produced over 425 publications, His research interests include radial growth in vascular plants, plant-pollution interaction, heavy metals influence on plants, stress crop physiology, phytoremediation and traditional herbal medicine. He was President of the Academy of Environmental Biology (2006-2009), Vice-President of the Indian Botanical Society (2003-2004), and International Society of Environmental Botanists (2013-18). He worked as Visiting Scientist at South Korea and Poland under the Scientists Exchange Program of Indian National Science Academy and as a Visiting Professor at King Saud University, Riyadh, Saudi Arabia He is an elected Fellow of 8 national and international scientific organizations, including the Linnean Society of London (FLS) and the National Academy of Sciences, India (FNASc).

Autoren/Hrsg.

Iqbal, Muhammad

Leseproben

Chapter 1

SUN–EARTH ASTRONOMICAL RELATIONSHIPS

Publisher Summary

This chapter discusses the motion of the earth around sun and around its polar axis, the angle between the earth’s equator and the plane containing the sun–earth orbital system. It presents the trigonometric equations relating the position of the sun to a horizontal or an inclined surface. The chapter focuses on the relevant astronomical relationships that do not require a prior knowledge of solar radiation. The earth revolves around the sun in an elliptical orbit with the sun at one of the foci. The amount of solar radiation reaching the earth is inversely proportional to the square of its distance from the sun. Solar time is based on the rotation of the earth about its polar axis and on its revolution around the sun. A solar day is the interval of time as the sun appears to complete one cycle about a stationary observer on earth. The solar day varies in length through the year. The chapter presents an overview of the calculation of the sun–earth distance, declination, and the equation of time.

1.1 Introduction

This book begins by considering the motion of the earth around the sun, the motion of the earth around its polar axis, and the angle between the earth’s equator and the plane containing the sun-earth orbital system. Trigonometric equations relating the position of the sun to a horizontal or an inclined surface are presented. The main objective, however, is to write down the relevant astronomical relationships that do not require knowledge of solar radiation.

1.2 Sun-Earth Distance

The earth revolves around the sun in an elliptical orbit with the sun at one of the foci (Fig. 1.2.1). The amount of solar radiation reaching the earth is inversely proportional to the square of its distance from the sun; an accurate value of the sun-earth distance is, therefore, important. The mean sun-earth distance o is called one astronomical unit:

Figure 1.2.1 Motion of the earth around the sun.

or, more accurately, 149 597 890 ± 500 km.1 The minimum sun-earth distance is about 0.983 AU, and the maximum approximately 1.017 AU. The earth is at its closest point to the sun (perihelion) on approximately 3 January and at its farthest point (aphelion) on approximately 4 July. The earth is at its mean distance from the sun on approximately 4 April and 5 October. In long-term cycles, these distances are influenced, however slightly, by other heavenly bodies and the leap year cycle. However, the sun-earth distance for any day of any year is known with considerable accuracy. For precise information on a particular year, an ephemeris should be consulted, such as the “American Ephemeris and Nautical Almanac,” published each year by the U.S. Naval Observatory.

It is more desirable, however, to have this distance expressed in a simple mathematical form: for this purpose, a number of mathematical expressions of varying complexities are available. Traditionally, the distance is expressed in terms of a Fourier series type of expansion with a number of coefficients. With a maximum error of 0.0001, Spencer [1] developed the following expression for the reciprocal of the square of the radius vector of the earth, here called the eccentricity correction factor of the earth’s orbit, 0:

(1.2.1)

In this equation, G, in radians, is called the day angle. It is represented by

(1.2.2)

where n is the day number of the year, ranging from 1 on 1 January to 365 on 31 December.2 February is always assumed to have 28 days; because of the leap year cycle, the accuracy of Eq. (1.2.1) will vary slightly. For most engineering and technological applications, however, a very simple expression,

(1.2.3)

used by Duffie and Beckman [2] may be employed. A comparison of Eq. (1.2.3) with the Almanac values has shown that this equation can be safely employed for most engineering calculations. For greater accuracy and for use in digital machines, Eq. (1.2.1) is preferred. For individual calculations, Table 1.2.1 lists the eccentricity correction factor 0 for all days of the calendar year.

Table 1.2.1

Eccentricity Correction Factor E0 = (r0/r)2for Each Day of the Yeara

aCalculated from Eq. (1.2.1).

EXAMPLE 1.2.1

Calculation of the sun-earth distance on 16 October.

Solution

On October 16 the day number n = 289 and the day angle G = 2p(288)/365 = 4.958 rad or G = 284.16°.

From Eq. (1.2.1)

Therefore, = 0.9968 AU.

From Eq. (1.2.3)

or

1.3 Solar Declination d

The plane of revolution of the earth around the sun is called the . The earth itself rotates around an axis called the polar axis, which is inclined at approximately 23½° from the normal to the ecliptic plane (Fig. 1.2.1. The earth’s rotation around its axis causes the diurnal changes in radiation income; the position of this axis relative to the sun causes seasonal changes in solar radiation. The angle between the polar axis and the normal to the ecliptic plane, however, remains unchanged. The same is true of the angle between the earth’s equatorial plane and the ecliptic plane. However, the angle between a line joining the centers of the sun and the earth to the equatorial plane changes every day, in fact, every instant. This angle is called the . It is zero at the and (literally, equal nights) and has a value of approximately + 23½° at the and about — 23½° at the . The four seasons pertain here to the northern hemisphere; the reverse is true in the southern hemisphere.

The actual dates of the equinoxes and solstices vary slightly from year to year. Because of this, one encounters slightly different dates for when the earth is in these four principal positions.

Another means of describing the solar declination is by drawing a celestial sphere with the earth at the center and the sun revolving around the earth (Fig. 1.3.1). In the celestial sphere, the celestial poles are the points at which the earth’s polar axis, when produced, cuts the celestial sphere. Similarly, the celestial equator is an outward projection of the earth’s equatorial plane on the celestial sphere. The intersection of the plane of the earth’s equator with the plane of the sun’s revolution, the ecliptic, makes an angle of approximately 23½°. At any given time, the position of the sun relative to the plane of the celestial equator describes the declination angle. The main variations in the declination are due to the leap year cycle: during this four-year period, the declination may vary from the order of ± 10' at the equinoxes to less than 1' at the solstices [1].

Figure 1.3.1 Celestial sphere showing apparent path of sun and sun’s declination angle.

In 24 h, the maximum change in declination (which occurs at the equinoxes) is less than ½°. Therefore, if the declination is assumed constant for 24 h, a maximum error of ½° may occur in calculating the solar azimuth and zenith angles (to be described later). To obtain an accurate value of solar declination, an ephermeris should again be consulted. Expressions giving the approximate values of solar declination with varying degrees of accuracy have been developed by a number of authors. Spencer [1] presented the following expression for d, in degrees:

(1.3.1)

This equation estimates d with a maximum error of 0.0006 rad (< 3') or, if the final two terms are omitted, with a maximum error of 0.0035 rad (12').

Two other simple and commonly used formulas for declination are

(1.3.2)

obtained from Perrin de Brichambaut [4] and

(1.3.3)

from Cooper [5].

The two simpler equations are in fact quite accurate. However, for greater accuracy and for use in digital machines, Eq. (1.3.1) is preferred. To facilitate rapid calculations for individual days, the values of the declination for all calendar days are given in Table 1.3.1.

Table 1.3.1

Declination for Each Day of the Yeara

aCalculated from Eq. (1.3.1).

EXAMPLE 1.3.1

Calculation of the solar declination on 16 October.

Solution

From Example 1.2.1, the day angle G = 284.16°.

From Eq. (1.3.1) the declination d...