ABSTRACT
There is a fundamental relationship between the concentration ratio and the angular field of view that places the entire subject of solar energy concentration in context. It addresses such basic issues as whether a solar collector will need to be tracked continuously or merely seasonally adjusted or may remain absolutely fixed. There are a variety of demonstrations of this relation (Welford and Winston, 1989), one of which is as follows (Figure 7.1). Imagine the Sun itself as a spherically symmetric source of radiant energy. The flux falls off as the inverse square of the distance R from the centre, as follows from the conservation or power through successive spheres of area 4πR 2. Therefore the flux on the Earth’s surface, say, is smaller than the solar surface flux by a factor (r/R)2 where r is the radius of the sun, and R the distance from the Earth to the Sun. By simple geometry, r/R = sin θ where θ is the angular subtense (half angle) of the Sun. If we accept the premise that no terrestrial device can boost the flux above its solar surface value (to do so would lead to a variety of perpetual motion machines) then the limit to the concentration is just (1/sin2θ). We will call this limit the sine law of concentration. This relation may be reminiscent of the well-known Abbe’ sine condition of optics, but the resemblance is only superficial. The Abbe’ condition applies to well-corrected optical systems and is first order in the transverse dimensions of the image. There are no such limitations to the sine law of concentration which is correct and rigorous for any sized receiver. There is an exception to this when the target is immersed in a medium with index of refraction, n, for then the limit is n 2/sin2θ. We shall demonstrate a real example later in this chapter. For the time being we accept this limit for the case most frequently encountered, n = 1. Of course the limit we have derived is for concentration in both transverse dimensions, which we will refer to as three-dimensional concentration (or 3D concentration for short). This would be appropriate <italic>The flux from a spherically symmetric sun falls of (r/R)<sup>2</sup> = (1/sinθ)<sup>2</sup>.</italic> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315074412/feb3d8c8-9146-4af7-a5ce-b80347ae78a3/content/fig00486_B.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
