The term Insolation is derived from Incident Solar Radiation and refers to the amount of solar energy falling on a planar surface. It is a measure only of the radiation actually striking the surface so it is not affected in any way by surface properties or by reflective or refractive effects. Material properties only affect what happens next - the transmission or absorbed of energy by the surface.
Calculation ProcessThe total insolation (Gincident) at any instant is therefore affected only by:
- The angle of incidence of the solar radiation (A);
- The shading of the surface by surrounding geometry (Fshad), and;
- The diffuse sky radiation actually visible to the surface (Fsky);
These factors affect the direct (Gdirect) and diffuse sky (Gdiffuse) radiation components differently, such that:
For more information on this, refer to the Solar Components topic.
Direct Angle of Incidence
When radiation from the sun strikes the surface of an object from directly front-on, the energy density per unit area will be much higher than if the radiation struck from a much greater angle. This effect can be calculated using the cosine law, where the radiant energy from the sun is simply multiplied by the cosine of the incidence angle.
The incidence angle is always calculated relative to the surface normal of each plane. Radiant energy density is at its maximum at normal incidence when the incidence angle approaches 0°. It is at its minimum at grazing incidence when the incidence angle approaches 90°.
In the examples shown above, when the radiation strikes at 75° it imparts only 26% of its energy to the surface. At 15° it imparts 96% of its energy. Obviously at 0° it would impart 100% and at 90° it would impart 0% as it no longer actually strikes the surface.
This is a relatively simple calculation for the direct beam component as it can be considered as originating from a very distant point source (the Sun) whose position at any date and time is known or can be quickly calculated (Szokolay, 2004). Thus incidence is determined by the 3-dimensional angle between the surface normal (a line from the centre of the object directly outwards at 90° to the surface) and a line from the object centre running out towards the sun. This is illustrated in Figure 2 below.
This is an important concept as diurnal and seasonal changes in sun position will affect surfaces at various orientations quite differently, especially at mid-latitudes. For example, if a vertical equator-facing window is compared to a flat roof, at noon in winter the Sun is lower in the sky - thus closer to normal incidence for the window but closer to grazing incidence for the roof. In summer when the Sun is much higher in the sky, at noon it is closer to grazing incidence on the window and closer to normal incidence on the roof, as shown in Figure 3 below.
This is only a simple example, however it does illustrate that surfaces at different angles will be more sensitive to some parts of the sky than others.
Diffuse Angles of Incidence
Unlike direct radiation, which comes from a very specific part of the sky, diffuse radiation arrives from the whole sky. As shown in Figure 3, the angle of the surface will mean that, irrespective of the distribution of radiation over the sky dome, some parts of the sky will contribute more than others simply due to incidence effects.
For a horizontal surface under a uniform sky, the diffuse radiation arriving from a segment at the zenith of the sky will impart greater energy than a segment of equal area at the horizon. This is simply because the light from the zenith arrives close to normal incidence on a horizontal surface whereas that from the horizon is closer to grazing incidence.
Whilst it is possible to generate a calculus equation for any given surface for the continuous integral of the diffuse contribution from each part of the sky, it is usually much quicker to simply break the sky up into a large number of small segments, and then calculate the sum of their individual effect. This is known as sky subdivision and is a widely used technique as it has a range of other benefits which will also be explained.
Once the sky has been subdivided, the orientation and tilt angle of any surface can be used to determine which parts of the sky it is actually exposed to. For example a vertical surface, no matter which way it faces, will only ever 'see' at best one half of the sky dome - meaning that it will only ever receive a maximum of one half of the available diffuse component. A horizontal surface that faces upwards, however, could see it all.
However for a horizontal surface, any light from the zenith of the sky arrives normal to that surface whilst light from the horizon arrives at grazing incidence. For a vertical surface the reverse is true - light from the zenith arrives at grazing incidence whilst light from the horizon arrives along its normal. This means that the area of the sky that contributes most to any surface depends greatly on its tilt angle.
Figure 4 below shows a surface at different inclinations and its corresponding incidence angle effect mapped over a mask. This is simply the cosine of the incidence angle the geometric centre of each sky segment makes with the surface normal.
Thus, for horizontal surfaces the zenith is of most significance whereas for vertical surfaces it is those sky segments closer to the horizon and directly in front.