Introduction to solar motion geometry on the basis of a simple model

Abstract

By means of a simple mathematical model developed by the authors, the apparent movement of the Sun can be studied for arbitrary latitudes. Using this model, it is easy to gain insight into various phenomena, such as the passage of the seasons, dependences of position and time of sunrise or sunset on a specific day of year, day duration for different latitudes and seasons, and time dependence of the solar altitude reckoned from the horizontal plane. We present simulations of the Sun path alongside animated data. We show that the model adopted can also be used to explain the principle of a horizontal sundial and to determine shadow areas. We give recommendations as regards how to build energy-effective houses and how to optimize solar cell positions.

The Sun’s position in the sky

“…(which agrees with the expression obtained in [6]). Figure 6 shows plots of H as a function of the day of the year d, at the latitudes of Cartagena de Indias (Colombia), Boston (USA), Stockholm (Sweden), and the Arctic Circle, all in the northern hemisphere.…”

“…V, expressed in terms of the angle θ , require only planar geometry and can be used independently of the linear algebra of Sec. II (which is the approach taken in [6]).…”

“…I thank Take Okui for calling my attention to the effect of atmospheric refraction on the duration of daylight, and Felice Kuan and Graeme Smith for hospitality during the expedition to observe the second Manhattanhenge of 2012. I thank an anonymous referee for pointing out to me [6] and other pedagogical articles related to this subject, and for suggestions on improving this manuscript.…”

“…Almanacs such as [3] also provide accurate values and formulas. The Sun's position in the sky has recently been treated analytically in [4][5][6], but these discussions make several approximations that we will avoid, and the overlap with the material covered here is only partial. In spherical coordinates, a three-dimensional vector r is expressed in terms of a radial distance r, a polar angle θ, and an azimuthal angle φ.…”

Application of Carbon Nanotubes Directly Grown on Aluminum Foils as Electric Double Layer Capacitor Electrodes

“…[1][2][3] Renewable sources of energy, especially solar energy, can serve as inexhaustible and natural resources of energy which can mitigate the effect of human activities on the environment, [2][3][4][5] however a serious disadvantage of such sources lies in the inconstancy of their energy generation. [4][5][6] Thus, there is a need for the development of cost-effective and portable electrical energy storage devices. Supercapacitors or, more specifically, EDLCs have attracted much attention because they satisfy desirable requirements for energy accumulation and they also have high specific power, a long life time, and are of simple construction.…”