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 inter-reflection 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 degree-scale.

(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 CIE-sky 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 inter-reflection 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 mid-height 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 10-100 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

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 Non-industrial or Clean Industrial Work Dirty Industrial Work Non-industrial 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)