Daylighting Design And Analysis

What is Daylighting?

Daylighting is defined as the practice of optimizing the placement and construction of windows, skylights, and reflective surfaces so that direct & indirect sunlight (direct or indirect) can provide effective internal lighting.

Particular attention is given to daylighting while designing a building when the aim is to maximize visual comfort or to reduce energy use. Huge energy savings can be achieved from the reduced use of electric lighting.

A modest amount of analytical based work had been performed in the daylighting. But the major use of the daylight was by architects. They allowed the daylighting to spill into interior spaces to create visual effects – not to provide quality lighting for doing visual work.

Conventionally, two sky conditions have been considered, they are overcast and clear sky conditions. Recently interest has been arisen in providing data for a third sky condition i.e. the partly cloudy sky.

The designer calculates external illuminance considering vertical, horizontal or sloped on the fenestration (window, skylight etc). This is not only direct radiation from the sun and sky but also reflected radiation from the ground and adjacent structures.

The important component of the daylight design process is to ascertain the visual transmission characteristics of the fenestration material.

Generally, there are two types of transmittance to consider namely direct transmittance of sunlight and diffuse transmittance of the clear or overcast skylight. The transmittance of the fenestration for these two types of input may indeed be different and the former may be opened on solar altitude. Another important step to daylight calculations is to process the luminous flux which enters the interior space.

Daylighting Advantages

The advantages of the daylighting are:

  • Energy savings
  • Reduced carbon footprint
  • Health benefits (increased Vitamin D)

Along with these advantages, there are some disadvantages as well:

  • The sun is the variable source considering its position (Longitude and Latitude wise)
  • It is not a fixed source of light or its light depends on the atmospheric conditions
  • Its CCT (Correlated Color Temperature) and CRI (Color Rendering Index) varies throughout the day
  • Discomfort from potentially high levels of glare

These disadvantages aren’t always present through. To overcome these advantages, you can:

  • Supplement daylighting with artificial lighting (i.e. electrical lighting)
  • Take special care in design to restrict glare

Natural Sources of Light

The sun is the main source of light. But whenever we calculate the daylight we should also take the sky also as the indirect source of the light. The dust particles in the atmosphere help the sunlight to get scattered to reach on the ground. Based on different condition of the sky, like cloudy sky condition, partly cloudy or clear sky condition, we have two sources (a) the sun for a direct light source and (b) the sky for an indirect source of light.

We can compare the sun and the sky as a light source.
day light source

Measuring Illuminance and Solar Irradiation

We use a pyrometer to measure solar irradiation. Irradiance means radiated energy per unit area. Its unit is W/m2.

Lux meter is used to measure the global illuminance in lm/m2.

Now we have to measure global irradiance without blocking the sun position by a baffle over this meter. Here global means the sun and the sky both together. By Lux meter the global Illuminance is measured without blocking the sun position.

Then we block the sun position by a baffle such that direct light never falls on the pyrometer or Lux meter. In this manner, pyrometer shows the sky irradiance and the Lux meter shows the sky Illuminance.
Now, the Solar Irradiance = Global Irradiance – Sky Irradiance
And the Solar Illuminance = Global Illuminance – Sky Illuminance

Day Lighting Design

Three important factors must be considered when considering daylighting in the design or construction of a building:

  • Day Light Factor
  • Sky Luminous Distribution
  • Overcast Sky Luminance

Day Light Factor

Day light factor is defined as the ratio between external illuminance levels to the room inside illuminance level at a particular point inside the room.

Day light factor (DF) is expressed in percentage.

Eext is the external horizontal Illuminance at a particular height.
EP is the room inside Illuminance at point P at the same height.
day light factor computation
Here, ESky = Illuminance due to light received from the sky at point P.
EObstruction = Illuminance due to light received from the obstruction at point P.
Einterflected = Illuminance due to light received after room inside internal reflection at point P.
It can be said that DF method is the relative method of Day Light Prediction.

Daylight Factor Calculation

To better understand the way daylight factor is calculated, let’s walk through a case study.

Let us consider AS = area of total room surface
AF = area of total floor surface,
AC = area of total ceiling surface,
AW = area of total wall surface.
Ag = the area of the window opening.
Eg = window plane Illuminance measured at width height of the window opening.
τ = transmittance of the window element.
Day Light Luminous Flux incident on window plane =
Transmitted Luminous Flux into the room =
Area weighted reflectance of the room

Thus the day light flux absorbed by the inside room surface

As the average Illuminance for the inside room surface is

and DF is the average day light factor for the room.
The day light flux or luminous flux received by the room surface

Let, EWF is the window factor that is the ratio of window plane Illuminance to external Illuminance, i.e.

From the conservation of the day light we can write that, day light flux transmitted from the window opening is equal to the day light flux observed by room surface.
So, we can write,

Again from the experimental observation it was found that the numerical value of EWF is approximately equal to the half of the vertical angle θ in degree.
So, a correction factor improves the predicted value of DF.
So, the corrected

estimation of average day light factor in a room

Sky Luminous Distribution

sky luminous distribution
Here ɣ is the altitude angle, and α is the azimuth angle.
Now we can calculate the Illuminance at point P due to considered elementary sky patch dA.
Let us assume IP is the luminous intensity due to dA sky patch towards P point.
So, Illuminance at point P is

Let, Lɣα be the luminance of the sky patch specified by the angle α and ɣ angles.
We know that luminance is the luminous intensity per unit area, hence we can write,

From this above equation we can say that horizontal point specific Illuminance at any point created by the sky patch is

From α1 to α2 – azimuth angle and from ɣ1 to ɣ2 — altitude angle
Horizontal Illuminance due to entire sky vault is

Lɣα is the sky patch luminance specified by the angle α and ɣ angles.
Now consider a patch viewed by a person standing on the ground. This person will see the sky patch with α1 to α2 azimuth acceptance angle and ɣ1 to ɣ2 altitude acceptance angle.
sky luminous distribution

Overcast Sky Luminance

Overcast sky model is the simplest model and it is used for artificial light model.
In this overcast sky model ɣ is variable but α is not variable, α is independent and α = 360o or 2ᴫ
Lɣ is the luminance due to angle ɣ.
LZ is the zenith luminance when ɣ = 90o
The CIE published an empirical formula for only overcast sky,

overcast sky luminance

Again when the sky is covered with uniformly thick cloud, then the sun is invisible.
So, we can calculate Illuminance at point P.

But for sky component of the daylight factor due to any element at dɣ, dα at ɣ and α,

This method of calculation is applied to measure luminance and Illuminance for a window at any point.
overcast sky luminance
The CIE standard general sky model:
Up to the year 2001, the CIE recommended the empirical formula related to clear sky and over cast sky. But after 2001, the CIE has categorized the sky in different 15 types. Out of these five types are different clear sky, five types are different intermediate sky and rest five types are different intermediate sky.
As per the CIE standard general sky model, the modified equation is given by

Where φ (z) is the luminance gradation function and it depends on angle of altitude ɣ and z is the angle of altitude measured from the zenith, hence z + ɣ = 90o.
f(Zs) and f(χ) are the scattering indicatrix functions that are related to the relative luminance of the sky element. The function f(χ) depends on the sun’s position (αs, ɣs) and χ is the sun’s angular distance from the sky. And the function f(Zs) depends on the angle of altitude of the sun Zs measured from zenith.
Computation of Inter Reflected Luminous Quantity in a Room
computation of inter reflected Luminous quantity in a room
Eg is the window plane illumination at any instance.
Ag is the average area of the window.
Total luminous flux incident on the window

Let us consider τ is the transmittance of the window material.
So average luminous flux inside the room

Amount of total first internal reflected flux

Due to multiple internal reflections, total flux effectively

Now the effective Illuminance level inside the room at any instance is

Where, AR is the effective room area.

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