Chapter 06
Sun-Earth Geometry
Abstract
Just like navigation for a naval ship or airplane, we observe that time and space relations are linked together, and can be represented and communicated as geographic information. In this chapter we describe how to manipulate that geographic information in terms of angles, and use key relations from spherical trigonometry to make time and space relations easy to calculate with a computer. For our purposes: angles are coordinates in space and time. We describe the spatial and temporal relationships of the Sun relative to the Earth and for an Observer on the surface of Earth relative to the Sun at any given time. These angular relationships are then used to describe in detail the relative orientation of a Solar Energy Conversion System (SECS) surface relative to the moving Sun, while identifying the times that local shadows might obscure our SECS.
Keywords
Declination; Hour angle; Analemma; Altitude angle; Tilt; Azimuth
[Harrisonās āequation of timeā] table enabled the clockās user to rectify the difference between solar, or ātrueā time (as shown on a sundial) with the artificial but more regular āmeanā time (as measured by clocks that strike noon every twenty-four hours). The disparity between solar noon and mean noon widens and narrows as the seasons change, on a sliding scale. We take no note of solar time today, relying solely on Greenwich mean time as our standard, but in Harrisonās era sundials still enjoyed wide use.
Dave Sobelās Longitude: The True Story of a Lone Genius Who Solved the Greatest Scientific Problem of His Time (2007).
Diunior et excellentior sit Triangulorum sphƦricorum cognitio, quam fas sit eius mysteria omnibus propalare.āThe nature of comprehending spherical triangles is so divine and elevated that it is not appropriate to share these mysteries with everyone.
Tycho Brahe De Nova Stella (1573)
THINK, before watches and computers were synchronizing time via satellite, in accordance with an international standard set by atomic clocks in national laboratories across the globe, our cultures had powerful thought and design invested in the linkage between astronomy, place, and time. We can surmise from an informal poll that our contemporaries in science and engineering (and science writing) no longer view solar time as relevant to āmodernā society, even though solar time is equivalent to the sequencing of diurnal events that we observe. In solar design we require that our concepts transition into a solar time frame of reference. For the solar design professional, it is far easier to just find solutions first in solar time, and then correct our answers back to mean time for the public.
After completing this chapter, we wish you congratulations and bid you welcome to the club of mysteries that Tycho Brahe referred to.
We have established that time and space are essential relations in solar resource assessment, and we have argued that in keeping with a sustainability ethic for design in SECS, the precepts of sustainability science should be in our minds to ensure that our solving for patterns are tied to critical self-reflection of our diverse scientific approaches and our underlying assumptions. Again, among other factors sustainability science is developed in reference to the locale and the local nature of solutions as well as coordinating our solutions for ecosystems services (like provisioning and regulating services) with respect to time. One cannot develop a strong design project for SECS without holding in mind the locale and the relative positioning of the Sun and Aperture with respect to time.
Sustainability in design and systems thinking has enormous potential to lift up society and our supporting ecosystems. You will likely spend your entire careers developing sustainability as an integral ethic to your design principles.
Now consider the topic of communication. As solar energy design is a part of sustainability science and environmental technology, we must communicate our work across many disciplines, and we must be able to bridge the communication among science and society.1 So how do we āorientā ourselves in both language and coordinates such that we can communicate across disciplines and audiences regarding:
ā¢ our position on Earth relative to others,
ā¢ the orientation of our SECS relative to the Sun,
ā¢ the time of day relative to the Prime Meridian,
ā¢ the times of shadowing from the beam irradiation relative to surrounding trees and buildings, and
ā¢ the animation and tracking of our SECS with respect to the Sun?
These are all relevant and challenging, and each is within our grasp to learn and then hone to become strong career skills as professionals in the solar industry.
Given the goal of solar design, we will have three tools that we can leverage to affect the solar utility for a client in a given locale:
1. Reduce the angle of incidence on ...