07.05 Daylight factor

Categories: Lighting

Introduction
There are a number of formulae which can be used to calculate the approximate average daylight factor in a room. They should be used in slightly different circumstances, but they all may be used at the sketch design stage to indicate the area of glazing required to achieve a desired level of daylight factor.

There follows the derivation of the basic formula.
 

Formulae: Average daylight factor
The average daylight factor in a room is given by,

DF_av  =  E_av / E_sky  x  100%    ......    (1)

Previously it has been shown using energy methods that the average illuminance over all the surfaces in a room can be calculated from the light flux entering into the space. In this case it is the light flux entering through the window which is of interest and therefore the average illuminance resulting from the daylight is given by,

E_av  =  F_w / [ A_t ( 1 - r_av ) ]    ......    (2)
 

Where the light flux entering through the window will be,

F_w  =  E_w  A_wt  MF  GBC    ......    (3)
 

The illuminance on the window will vary, with the top of the window receiving a higher illuminance than the bottom of the window. However this is usually ignored and the illuminance at the mid-height of the window is taken as being equivalent to the average illuminance over the face of the whole window. This illuminance will be related to the horizontal illuminance from an unobstructed sky by some constant value C,

E_w  =  C E_sky    ......    (4)

This ratio C depends upon the type of sky being considered, the angle of the glazing to the horizontal plane and the degree to which the glazing is shadowed by obstructions, image. It may be calculated exactly, but in most cases it is sufficiently accurate to assume that C is related to the angle of unobstructed sky subtended at the mid-height of the window,

C  approxq / 200    ......    (5)

Substituting the approximate value of C into equation 4 gives a relationship for illuminance at the window,

E_wapprox  E_sky q / 200    ......    (6)

When this value is substituted into equation 3 the flux entering through the window will be given as,

F_wapprox  E_sky q A_w t MF GBC / 200    ......    (7)

and when in turn this relationship is substituted into equation 2, the average illuminance over the surfaces of the room from the daylight coming through the window will be,

E_avapprox  E_sky q A_w t MF GBC / [ 200 A_t ( 1 - r_av ) ]   ......    (8)

For the glazing bar correction (GBC), image,
 

Using this in the definition of daylight factor given in equation 1 leads to the formula for the average daylight factor within a room,

DF_avapprox  q A_w t MF GBC / [ 200 A_t ( 1 - r_av ) ] x 100%   ......    (9)

Which simplifies to,

DF_avapprox  q A_w t MF GBC / [ 2 A_t ( 1 - r_av ) ]  %   ......    (10)

Rearranging the formula enables one to find the window area which will achieve a given level of daylight factor,

A_w  approx  2 A_t ( 1 - r_av ) DF_av / qt MF GBC    ......    (11)

Where an accurate estimate of C is made then equation 10 will be slightly modified,

DF_av  =  C A_w t MF GBC / [ A_t ( 1 - r_av ) ] x 100%    ......    (12)

A further modification leads to a formula which gives the average daylight factor over the working plane, (cannot be easily shown)

DF_av  =  2 C A_w t MF GBC / [ A_t ( 1 - r_av² ) ] x 100%    ......    (13)

A more accurate estimate of daylight factor on the working plane is given by separately considering the direct light and reflected light, image,

DF_av  =  A_w t MF GBC [ C / A_l + ( C r_l + 0.05 r_u ) / A_t (1 - r_av ) ] x 100%    ......    (14)