 
6. Methods of Daylight
Factor (DF) Estimation
The above three components can be
determined by various approaches. Both SC and ERC can be found from the geometry of the
visible sky or external reflected surfaces, where as based on interreflection theory, IRC
can be found from formula, nomogram, or tables. Some common methods adopted in UK are:
(a) SC and ERC: Waldram diagram;
ERE protractors; BRE tables; and Pilkington 'pepper pot' diagrams.
(b) IRC: Formula; BRE tables; and
ERE nomograms.
The presentation and explanation
of all these methods are out of our scope. Hence selected methods are discussed as
follows:
6.1 The sky component (SC)
The sky component is usually
the greatest in magnitude among the three. Its magnitude depends on the area of sky
visible from the point considered, and in the case of CIE sky, also on the position of
this area at the sky dome.
(A) BRE protractors
The Building Research
Establishment BRE (formerly the Building Research Station BRS) developed a set of
protractors which give direct reading of the sky component in percentages. There are ten
nos. of such protractors, of which five are for the uniform sky and five for the CIE sky:

Uniform sky
(Protractor No.) 
CIE sky
(Protractor No.) 
Vertical windows 
1 
2 
Horizontal glazing 
3 
4 
30oC glazing 
5 
6 
60oC glazing 
7 
8 
Unglazed apertures 
9 
10 
The protractors No. 2 and No. 4 are given
in Figures 7 & 8 respectively.
The procedures to use BRE Protractor are as
follows:
Determine the initial sky component
(infinite length of window)
(a) Refer to the elevation view of a room
in Figure 9.
(b) Mark the work plane and the point
considered (A).
(c) Connect this point to the window
sill (AS) and the window head (AH).
(d) Make a tracing of protractor (Figure
7).
(e) Place the tracing with its centre on
point (A) and its base along the working plane, with scale 1 upright.
(f) Read the values where lines AS & AH
intersect the protractor scale.
(g) The difference between the two values
gives the initial sky component.
Figure 7 BRS Sky Component Protractor for
Vertical Glazing
(CIE Overcast Sky)
Figure 8 BRS Sky Component Protractor for
Horizontal Glazing
(CIE Overcast Sky)
Figure 9 Determining Initial Sky Component
Find the average altitude
(a) Read the angles of elevation of lines
AH and AS, on the inner degreescale.
(b) Add the two angles and divide the sum
by 2.
Determine the correction factor
(defined length of window)
(a) Refer to the plan view of the same room
in Figure 10.
(b) Mark on the plan the point considered
(A).
(c) Connect this point to the two sides of
the window opening (AL & AR).
(d) Place the protractor with its centre on
point (A), with the base parallel to the window and scale 2 towards the window.
(e) Interpolate an imaginary semicircle
between those designated 0o, 30o, 60o and 90o, corresponding to the average altitude
previously obtained.
(f) Read the values along the curves on the
inner scale. Interpolate if necessary.
(g) Find the sum of the two readings, if
they were taken on either side of the centre line.
(h) Find the difference of the two
readings, if they were both taken on the same side of the centre line.
The sky component is the product of the
initial sky component and the correction factor
(B) Tables
Table 1 is used for determining the sky
components for windows with clear, vertical, rectangular glazing in conjunction with a CIE
standard overcast sky. Other tables are available for other forms of glazing, e.g. roof
lights.
Figure 10 Determining Correction Factor
Table 1 Sky Component (CIE) Standard
Overcast Sky) for Vertical Glazed Rectangular Windows
The procedure for a measurement position on
the line of window and at sill level (Figure 11) is as follows:
(a) Establish H, the window head height
above the work plane level;
(b) Establish D, the distance from the
window to the point considered,
(c) Express D as a multiple of H (i.e., the
H/D ratio) and locate this at the head of the table;
(d) Establish W1 and
W2, i.e., the width of window to either side of the perpendicular (W1 + W2 = total width);
(e) Express both widths as a multiple of D
(i.e., ratios W1/D and W2/D) and locate these
in the first column of the table;
(f) Read the two values in the table. The
sky component for the point considered is the sum of the two values.
Figure 11 Sky Component for a Measurement
Position on the Line of the Window and at sill Level
For a position off the line of the
window, the sky component can be obtained by evaluating sky components for a series of
windows and obtaining the required sky component by a process of subtraction and addition.
(Figure 12)
6.2 The externally
reflected component (ERC)
(A) Charts
If there is an obstruction opposite the
window, then the lower limit for the sky component will be a line drawn from point (A) to
the top of this obstruction with reference to Figures 9 and 10. The sector between this
line and the sill (AS) line will give the ERC. Follow the same procedure as for the sky
component. Multiply the result by the reflectance of the obstruction (if known) or by 0.2
if the CIEsky protractors were used. Using the uniform sky protractors, take half of the
reflectance value or 0.1 as the multiplying factor.
Figure 12 Sky Component for a Measurement
Point that is off from the Window and below Sill Level
(B) Tables
ERC can also be done using Table 2. The
procedure is to treat the external obstruction visible from the reference point as a patch
of sky whose luminance is some fraction of the unobstructed sky luminance. In other words,
the SC for the obstructed area is first calculated as described above and is then
converted to the ERC by multiplying the ratio of the luminance of the obstructed area to
the sky luminance.
Table 2 The Minimum IRC of DF (percent)
6.3 The internally
reflected component (IRC)
(A) Formula
The average IRC can be determined quite
precisely from the BRS interreflection formula. The simplified form of this is:
(5)
where,
0.85 = transmittance of window glazing
assumed,
W = window area (m2),
A = total area (ceiling + floor + walls
including windows),
r = average reflectance of area A,
r fw = average reflectance of floor and the three walls below the plane
at the level midheight of the window (excluding the window wall),
r cw = average reflectance of ceiling and the upper (remaining) part of
the above three walls,
C = a coefficient depending on external
obstructions, as given below:
Angle of obstructions 
0o 
10o 
20o 
30o 
40o 
50o 
60o 
70o 
80o 
Coefficient C 
39 
35 
31 
25 
20 
14 
10 
7 
5 
The average IRC can be converted to minimum
IRC by the following factors:
Average ARC (%) 30 40 50 60
Conversion factor 0.54 0.67 0.78 0.85
Table 2 was formulated by the BRE to
give minimum internally reflected components of daylight factor, assuming a CIE standard
overcast sky and a known scheme of decoration. The table was primarily for rooms of the
following conditions:
(a) Dimensions : 6 m length x 6 m width x 3
m ceiling height. Floor area = 36 m2
(b) A window (glazed with ordinary glass)
on one side extending from a 1 m sill to the ceiling.
Minimum IRC for rooms of 10100 m2 floor area, with ceiling heights ranging from 2.5 to 4 m can be obtained
by multiplying the following conversion factors.
Floor 
Wall
reflection factor 
Area 
20% 
40% 
60% 
80% 
10 m2 
0.6 
0.7 
0.8 
0.9 
100 m2 
1.4 
1.2 
1.0 
0.9 
6.4 Additional
correction factors
The SC, ERC and IRC will be reduced by
the following factors:
(a) Maintenance factor, M, allowing for
dirt and other causes of deterioration of glazing (see Table 3);
(b) Glass factor, G, allowing for the type
of glazing if other than clear glass is used (see Table 4);
(c) Bars, or Framing Factor, B, which may
reduce the effective area of the window (see Table 5).
Location of 
Inclination of 
Maintenance Factor 
Building 
Glazing 
Nonindustrial or Clean
Industrial Work 
Dirty Industrial Work 
Nonindustrial or 
Vertical 
0.9 
0.8 
Clean Industrial 
Sloping 
0.8 
0.7 
Area 
Horizontal 
0.7 
0.6 
Dirty Industrial 
Vertical 
0.8 
0.7 
Area 
Sloping 
0.7 
0.6 

Horizontal 
0.6 
0.5 
Table 3 Maintenance Factors to be Applied to
the DF or to Each of its Three Components to Allow for Dirt on the Glazing
The IRC for dirt will also be reduced by
the maintenance factor, D, allowing on room surfaces (See Table 6)
