NBSIR 77-1303

A Simplified Procedure for

Calculating the Direct

Components of Contrast

Rendition Factor and

Equivalent Sphere Illumination

Joseph B. Murdoch (IPA)

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

November 1977

Prepared for Division of Buildings and Community Systems

Energy Research and Development Administration

Washington, D.C. 20545

NBSIR 77-1303 - A Simplified Procedure for Calculating the Direct Components

of Contrast Rendition Factor and Equivalent Sphere Illumination

by Joseph B. Murdoch

ERRATUM SHEET

The following legends for the

be interchanged:

Figures

Figures

Figures

Figures

Figures

figures are reversed and should

3 and 4

5 and 6

7 and 8

9 and 10

11 and 12

NBSIR 77-1303

A SIMPLIFIED PROCEDURE FOR

CALCULATING THE DIRECT

COMPONENTS OF CONTRAST

RENDITION FACTOR AND

EQUIVALENT SPHERE ILLUMINATION

Joseph B. Murdoch (IPA)

Center for Building Technology

Institute for Applied Technology

National Bureau of Standards

Washington, D C. 20234

November 1977

Prepared for Division of Buildings and Community Systems

Energy Research and Development Administration

Washington, D.C. 20545

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

Contents

Page

I. Introduction 1

II. CRF and ESI — Theory and Equations 3

III. Four Precalculation Matters

A. Body Shadow 8

B. Intensity Distribution Curve Interpolations 9

C. Approximating Equations for Bidirectional Luminance

Factor 12

D. Inverse Square Law Approximations 15

IV. Calculation Procedure 18

V. Calculator Program and User Instruction 30

VI. Three Design Examples

A. Point Luminaire 43

B. Strip Luminaire 47

C. Square Luminaire 47

References 58
.

-
Abstract

A procedure is presented which enables the user to compute the

direct components of contrast rendition factor (CRF) and equivalent

sphere illumination (ESI) for an interior lighting design with the aid

of a card-programmable hand calculator. The underlying theory and

equations of CRF and ESI are discussed, including a consideration of

body shadow, intensity distribution curve interpolations, bidirectional

luminance factor approximating equations and Inverse Square approximations.

The procedure is designed so that the user is a participant in

the computations as they progress and thus is able to modify a lighting

design in "midstream" to improve CRF or ESI. A set of user instructions

is included with the calculator programs.

Key Words: Body shadow; contrast rendition; hand calculator;

Illuminating Engineering; light design; luminaire

effectiveness; luminance factor; office lighting;

sphere illumination

A SIMPLIFIED PROCEDURE FOR CALCULATING

THE DIRECT COMPONENTS OF CONTRAST

RENDITION FACTOR AND EQUIVALENT

SPHERE ILLUMINATION

Joseph B. Murdoch

I. Introduction

The subjects of contrast rendition factor (CRF) and equivalent

sphere illumination (ESI) have received considerable attention in the

lighting literature in recent years.'*' ^ More specifically, there has

been great interest in developing methods of predicting CRF and ESI

prior to the installation of a lighting system, rather than simply trying

to measure these quantities after the installation is completed.

Perhaps the best known of the prediction methods is the Lumen 2

procedure developed by D. DiLaura (4). This technique relies on an

extensive computer program which discretizes luminaires into source

elements, formulates the luminances and illuminances produced by these

elements at a task location through the Inverse Square Law, and uses a

double Fourier series approximation to replace the discrete functions by

continuous ones for calculation purposes. Utilization of the technique

requires obtaining the Lumen 2 program and access to a computer or the

services of a central computer facility.

The procedure described herein enables the user to compute the direct

components of CRF and ESI quickly and simply with the aid of an inexpensive

card-programmable hand calculator. Because the user is a participant in the

computations as they progress, he is able to determine easily which

luminaires are having the greatest effect, either positively or negatively,

on CRF and ESI, and thus he is able to try different luminaire locations and

orientations in "midstream". Also, again because he and the calculator are

1
working together, he is able to understand the evaluation procedure and

calculations being made — he is more truly a "designer". And lastly,

because the procedure is a simple step-by-step one, a great deal of the

mystique that has unfortunately surrounded CRF and ESI in recent years is

swept away.

In Section II of this report, the theoretical considerations underlying CRF and ESI are reviewed and the equations necessary for

calculating each quantity are presented. In Section III four topics

relating to the CRF and ESI calculations are discussed. These are

body shadow, intensity distribution curve interpolations, approximating

equations for bidirectional luminance factors, and Inverse Square Law

approximations. In Section IV, the programmable hand calculator

procedure is presented in detail, followed by the calculator programs and

user instructions in Section V. The report concludes with three sample

designs in Section VI.

Only the direct components of CRF and ESI are considered in this

report. Development of an extension to the procedure for computing the

reflected components of CRF and ESI will be the subject of future work,

as well as an extension to permit the inclusion of daylighting . Also

a critical comparison of the author's procedure, Lumen 2, and other

procedures for calculating CRF and ESI needs to be made, and this will be

dealt with in the future. Lastly, and perhaps most important of all, the

issue of whether CRF, ESI or some other metric or combination of metrics,

is the best measure of one's ability to perform visual work needs to be

explored. It is anticipated that the procedure developed herein, the

extension of the procedure to include reflected components, and the

2
comparison with other predictive procedures will assist in answering

this question.

II. CRF and ESI — Theory and Equations

The geometry which will be used in this section and throughout the

report is shown in Figure 1. The task is located at the origin of an x

y coordinate system such that the +y direction is always the direction

of viewing. A typical source element is shown, whose center is at x ,

y . It is also useful to describe its location in terms of the azimuth

e angle (f> and the polar angle 0. (j) is 0° in the direction of viewing and

positive (f) is measured clockwise from that direction. Thus (j) can range

from 0° to + 180° . 0 is 0° when the source element center is directly

over the task and its range is from 0° to +90°

Contrast rendition factor (CRF) is defined as the contrast produced

by the actual lighting system divided by the contrast produced by the

standard reference lighting system — an illuminated sphere providing

equal luminous intensity from all directions. Thus CRF is clearly a

measure of the effects caused by the geometric distribution of the light

flux from the actual lighting system.

CRF is always defined for a specific task. The only task for which

published complete reflectance data as a function of both (p and 0 are

available is the concentric ring pencil task (5) . Hence the procedure

developed in this report is currently limited to this task, although

there is nothing inherent in either procedure that precludes other tasks

once the appropriate reflectance data become available.

To obtain CRF, one must first obtain contrast, or, more correctly,

luminance contrast^, defined as the difference between the luminance of

the object (task detail) and its immediate background divided by the

3
background luminance. Generally the magnitude of this quantity is taken,

so that contrast is positive. In equation form

h>

“ L

t

where "b" denotes background and "t" task. Then

C actual

C sphere

( 1 )

( 2 )

C sphere has been calculated as .1675 for the concentric ring

pencil task when viewed at 25° from the vertical, the standard viewing

angle^. Thus, the problem of predicting CRF reduces to the problem of

predicting values of and under the proposed lighting system for

the pencil task.

Luminances are obtained as products of illuminances and reflectances.

As mentioned previously, reflectance data for the pencil task are

available. ^ These data are in the form of tables of bidirectional

luminance factors (B) for both the pencil task and its background.

Luminance factor is defined as the luminance of a surface at a certain

viewing angle and illuminance divided by the luminance of a perfectly

reflecting and diffusing surface under the same conditions of viewing

and illuminance. Bidirectional simply means that a given B factor is

for a particular pair of azimuth and polar angles. We can write

B = L , E

rd

(3)

where "a" refers to the actual surface and "rd" to the perfectly reflecting

and diffusing surface. The second form of Equation 3 arises because the

luminance in footlamberts of a perfectly reflecting and diffusing surface

is identical to the illuminance in footcandles on that surface.

4
To obtain measured values of luminance factors as functions of

source and viewer locations (with respect to a task location), it is

necessary to place a collimated source of light at location 0, §

with respect to the task and place a receiver (photometer) at the chosen

25° task polar viewing angle and at 0 = 180°. Then Equation 3 can be

rewritten in the forms

Bti (4>, 6)

L

ti (4>, 0)

E.

x (4)

\

,

0 ) Bbi (*’ e) =

(5)

l

If we know B . and B, . (which, as mentioned earlier, we do), then we can

calculate L

^ and L if we know E^ . Thus, the problem of calculating

CRF has now been further reduced to the problem of calculating E ,

the horizontal illuminance at the task location produced by the ith

source element. (If we were including the reflected component as well,

we would also need the illuminance at the task from the jth reflective

surface element)

To obtain the horizontal illuminance produced by each source element

we use the Inverse Square Law:

*

E.

x

I (4>,0) cos 0_^

( 6 )

where I is the intensity of the ith source element in the direction

of the task, 9^ is its angle of incidence (angle with the vertical)

at the task and d. is the distance from the center of the ith element

x to the task. Recognizing that

Equation (6) is

E. =

x

h = d . cos0 .

x x’

I . (4) ,0) cos'

X

a more convenient form of

0 .x (7)

5
where h is the mounting height of the luminaire above the task.

To use Equation (7), we must first separate each luminaire into

elements, such that the largest dimension of each element is small compared

with the distance from the element to the task. This is necessary

because the Inverse Square Law holds exactly only for point sources and

thus we must choose small enough source elements so that each can be

treated as a point source.

Having done this, we compute E_. for each source element, using

Equation (7)

.

M With the known values of B . and B, . , we use

ti bi’

Equations (4) and (5) to compute L

^ and L^, again for each source

element. Next we sum to obtain L = EL . and L, = ZL, . and use

t ti b bx

Equation (1) to obtain C. Then Equation (2) yields the direct component

of CRF, since C sphere is known for the pencil task. If we desire the

total direct illuminance on the task (the "raw" lux or f ootcandles) , we

sum the values of E^ from Equation (7)

.

We turn now to the calculation of Equivalent Sphere Illumination

(ESI), defined as the illuminance from a uniform intensity sphere which

would produce a task visibility equivalent to that produced by the

actual lighting system.

With CRF in hand, it is not difficult to compute ESI. First, it is

1 2 necessary to determine relative contrast sensitivity (RCS) . *

RCS is the normalized inverse of the VL1 (threshold) Visibility Reference

Function and is obtained from the latter by writing

RCS 5.74

( 8 )

where C

1 luminance

is task contrast at threshold. For each value of background

, a value of C^ may be obtained from the VL1 curve. This has

6
been done, and values of RCS as a function of background luminance are

presented in tabular form in Figure 3-32 of (1) and Table 1 of (2)

From these tabular values, an empirical equation for RCS has been

developed :

RCS =

10 L

2.195721

1 + 1

2.25 N)

.2

_

(9)

Equation (9) is accurate within one percent for background luminance

values between 10 and 1600 footlamberts (35 and 5500 candelas per square

meter)

With RCS and CRF known, the next step is to obtain effective

contrast sensitivity, defined by

RCS = CRF x RCS

e

( 10 )

RCS is the relative contrast sensitivity the task would have under

e sphere lighting. Corresponding to RCS^ is an effective background

luminance L in the sphere, which may be obtained by reentering

Figure 3-32 of (1) or Table 1 of (2) with the known value of RCS^.

Or L, may be calculated, within the same range of background luminances

be

as before, from the inverse of Equation (9).

Lbe

2.25

1 2.195721

Log RCS

g

(ID

The illumination in the sphere corresponding to L^

e is found by

dividing by the overall luminance factor B for the 25° viewing angle.

The latter is obtained from Equation (3), with L = EL, . and E = EE.. Then

a bi l

7
L

E

be

( 12 ) e B,b

E is, by definition, equivalent sphere illumination (ESI) . It is

the illuminance under sphere lighting which produces the same task

visibility as is provided by the illuminance E from the actual lighting

system.

The ratio of the two illuminances, sphere and actual, is defined

as the lighting effectiveness factor (LEF) . It is simply a measure

of how closely the actual lighting system approximates sphere lighting

.

In equation form

Although a general procedure for calculating the direct components

of CRF and ESI has now been described, there are four matters which need

to be addressed before actual calculations can begin.

A. Body Shadow

The effect of the viewer's head and body is to shield certain

source elements from the task. Body shadow has been investigated at

3 7 length in the literature. ’ An "average" head size, upper body size,

head tilt and head and body location with respect to the task have been

postulated for the 25° viewing angle. These "average" conditions may be

summarized in terms of 0 and 9 by noting that a source element will be

shielded from the task by the viewer if

e

E

(13)

III. Four Precalculation Matters

8
145° < |cf>| < 165° and 0 > 52

or 165° < | <|)

| < 180° and 0 > 18

( 14 )

Any source element whose center lies in the shadow defined by these

angles is neglected in the calculations of luminance and illuminance. A

diagram of body shadow projection onto the luminaire plane for three

values of h is shown in Figure 2

One final point should be made about body shadow. The viewer is

assumed to be "zero reflective", so that no luminous flux reaches the

task after reflecting from the viewer's head and body. This assumption

is certainly questionable, especially for viewers wearing lightcolored

clothing

B. Intensity Distribution Curve Interpolations

Luminaire manufacturers generally present intensity distribution

data in 5° or 10° increments in polar angle 9 for three values of luminaire

azimuth angle ^-parallel (0°) perpendicular (90°) and at 45° to the

luminaire axis. It is thus necessary to develop interpolation procedures

for obtaining intensity values at other 9 and ip angles.

First degree polynomial interpolations, while easy to perform, are

quite inaccurate. Second and third degree polynomial interpolations, on

the other hand, have been widely used with good results. In this report

we will use a second degree polynomial for ip interpolations (since

only three values of intensity are available for each 0) and a third

degree polynomial for those in 9. For the iJj interpolation, we have

*(J) and \p are not necessarily the same angles. <p is the azimuth angle

at the task with respect to the viewing direction whereas ij; is the

azimuth angle at the luminaire with respect to the luminaire axis.

See Figure 1.

9
(15)

where

he)

= a

o + h* + V

a = I

o o

a, = -31 + 41., - I Qn o 45 90

90

a, =

I - 21., + I

Q

_ o _ 45 90

4050 (16)

For each value of 0, this interpolation passes a parabola through

the intensity values at 1* = 0°, 45° and 90°, resulting in three

coefficients which are then used to calculate 1(0) for the given value

of T. This interpolation is done prior to the 0 interpolation, and

must be repeated four times for each intensity determination, yielding

intensity values labeled I,, I„, I„ and I. at four consecutive 0

1 Z 3 4

angles, each A0 apart with two on each side of the given 0 value. The

procedure is illustrated in Table 1 where it is desired to obtain the

intensity at T = 56.9° and 0 = 43.9°. Here A0 = 5° and it is necessary

to perform the T interpolation at 0 = 35°, 40°, 45° and 50°. The

resulting intensity values are 1^ = 947cd, = 857cd, 1^ = 699cd and

I . = 505cd

.

4 For the 0 interpolation we have two cases, namely A0 = 5° and

A0 = 10°. The pertinent equations are:

for A0 = 5°

I (i|>,0) = A

q + A

i

0' + A

2 0

2 + A

3

0'

3

(17)

10
Table 1: Illustrating Double Interpolation to Obtain I(\fj t d)

e I

° o

I

° 45

I 56.9° I 90°

35° 290 860 (I

1 )947 1050

40° 260 780 (I

2 )857 940

43.9° (I) 738

45° 220 650 (I

3 )699 690

50° 180 490 (I

4

)505 400

First Interpolation: ip = 56.9°

0 a

o al a

2 35° 290 16.89 -.09383 I

1 = 947

O O 260 15.56 -.08889 I

2 = 857

45° 220 13.89 -.09630 I

3 = 699

Ln O

0 180 11.33 -.09877 I, = 505

4

Second Interpolation: 0 = 43.9°, 0' = 8.9°

0 A

o A1

A

2 A

3 43.9° 947 -9.067 -2.000 .0427

I

738

11
A

0

A

A

A

1

2

3

-111, + 18T - 9I„ + 21

1 2 3 4

30

2I

1 - 5I2 + 4I

3 - V

50

- 1

! + 3I2 * 3I3 + T 4

750

and for A0 = 10°

I (\p, 6) = A^ + A|0 ' + A^0

2 + A^03

where A' = A , A' = 1/2 A

o o 1 1 A^ = 1/4 A

2

, A^ = 1/8 A

3

( 18 )

(19)

( 20 )

The use of 0' requires explanation. To avoid large numbers in the

calculation of I(T, 0), it is necessary to shift the 0=0° axis to the

value of 0 at 1^. Thus in the example, 0' = 0 at 0 = 35q

. This yields

values of 0' between 5° and 10° for A0 = 5° and between 10° and 20° for

A0 = 10° in Equations 17 and 19, respectively. Referring again to Table

1, for 0 = 43.9°, 0' = 8.9° (43.9 - 35).

C. Approximating Equations for Bidirectional Luminance Factors

There is a confusion in the literature over what the visual task

actually is in the definition of contrast. The Illuminating Engineering

Society Handbook (1) uses the word "object" and defines luminance contrast

in terms of object and background luminances. RQQ5(3), on the other

hand, chooses to use flux contrast, and defines this quantity in terms

of "target" and background luminances. One might logically assume that

the words "object" and "target" mean the same thing, and thus conclude

that luminance contrast and flux contrast are identical. Such is not

the case however, for by "target", RQQ5 states that it means the task

detail and its very immediate background.

12
The bidirectional luminance factors for the concentric ring

pencil task'* are based on flux contrast, rather than luminance contrast.

Specifically the authors (5) state "... task detail consisting of

concentric pencil rings and paper spaces . . . ". The same general

statement appears in RQQ5

It is not our purpose here to debate the merits of the two definitions

of contrast, although they should be debated. Rather it is our purpose

to inform the reader that the only bidirectional luminance factors

available are for the pencil task under the conditions stated, that

these are being used by others in calculating CRF and ESI, and that they

will be used in the computational procedure presented in this report

Values of B and B , including polarization effects, are available

t b

3 5 in the literature in tabular form *

. The perpendicular and parallel

polarized values have been averaged and plotted for the 25° viewing

angle and are shown in Figures 3 and 4.

In order to permit calculations of CRF on a programmable hand

calculator, it was necessary to develop approximating equations for

B and B, .* Several mathematical models were tried and evaluated for

t b a least squares fit to the data. Ultimately a third degree polynomial

in Jin 0, including a <j) variation proportional to Sty, was chosen.

B = k + (a + a, /j)) Jln0 o 1

+ (b + b./F) (Jln0)

2 (21)

o I

+ (c + c /^) (Jln©)^

o 1

*These were derived by J. R. Rosenblatt and D. M. Maxwell of the

Statistical Engineering Section, National Bureau of Standards.

13
Values of the constants in this equation were derived for the

standard concentric ring pencil task and its background, using a least

squares curve fitting computer program. The results are:

Task Background

k .73586

a -.21398

o a .014979

b .18815

o b -.013542

c -.030878

o

c .0020351

.85206

-.12521

.0059725

.10455

-.0053031

-.014888

.000524257

Equation (21) and the coefficients above are used to obtain and

B^ values for each source element location. They yield B values within

a magnitude of .05 of the published data for all values of 0 and <J)

except the following:

Task

<j) = 0° and 10° < 0 < 15°, 45° < 0 < 90°

0 = 30° and 10° < <J> < 20° (22)

Background

4> = 0° and 0 = 15°, 45° < 0 < 90°

0 = 85° and 110° < <j> < 135°

The maximum error in B is .07; in B .10, the latter occurring

t b

at 0 = 85° (a relatively unimportant angle)

.

14
D. Inverse Square Law Approximations

If Equation (7) is multiplied by the appropriate bidirectional

luminance factor, we obtain the luminance of the task or its background

I.((J>,0) B.(cf>,0) cos^ 0.

L = -i — i (23)

h

where B . is used if task luminance L . is desired and B, . for L, .

ti ti bi bx

In using Equation (23) it is important to choose luminaire element

size small enough so that 1^, B^ and 0^ do not vary significantly over

the element surface. RQQ5(3) suggests that to accomplish this the angles

6^ and 6^ in Figure 5 should not exceed 10°.

The angles used in this study to describe the location of a source

element are not taken in the planes of 6^ and 6^. Rather, as previously

discussed, (p and 0 are used, as shown in Figure 1. The reasons for

* choosing <p and 0 are several:

1) They are more physically meaningful.

2) Luminaire intensity distributions are given in terms of these

angles

3) Bidirectional luminance factors are given in terms of these angles.

4) Cosine correction of the Inverse Square Law is done in terms of

one of these angles (0)

The choice of angles having been made, the next problem is to

determine acceptable luminaire element sizes and relate them to the

chosen angles. Luminaires can be placed in three general categories,

namely points, strips and rectangles. A point luminaire is one whose

largest source dimension may be considered small with respect to the

distance of the source from the task. As a practical matter, in offices

and schools, sources 18 inches (45 cm) or less in maximum source

15
dimension may be considered as points, permitting the entire source to

be considered as a single element.

A strip luminaire is one having one dimension small (less than

18 inches) with respect to the distance from source to task, but not the

other. Rows of fluorescent lamps fall into this category. For a strip

luminaire, it is necessary to divide the luminaire into elemental

lengths such that each element may be considered a point luminaire.

Figures 6 and 7 illustrate how this should be done for a typical mounting

height above the work plane of h = 7 ft (2.13 m) . Figure 6 presents the

situation when the rows of luminaires are parallel to the viewing

direction; Figure 7 when they are perpendicular.

Before describing the rationale behind Figures 6 and 7 , let us

discuss how to use them. Assume a row of fluorescent luminaires parallel

to the viewing direction and located at x = 0 (directly over the task) .

Figure 6 shows the luminaire element lengths that would be used. The

first element in the + y direction is 1.2 ft (.37 m) in length. Successive

elements are 1.3 ft (.40 m) , 1.5 ft (.46 m) , 1.8 ft (.55 m) , 2.2 ft (.67 m)

,

4 ft (1.22 m) and 8 ft (2.44 m) long. In the -y direction, the sizes

are the same but we stop at y

= -2.5 ft (-.76 m) because the body shadow

blocks elements beyond that point. If we now consider a row at x = 8 ft

(2.44 m) , longer elements can be used because the row is farther from

the task. Thus less elements are needed - two 4-ft (1.22-m) elements

and one 8-ft (2.44-m) element in the +y direction and three 4-ft (1.22-m)

elements in the -y direction. If there were a row at x = 5 ft

(1.52 m) , we could use the element lengths for either x = 4 ft (1.22 m)

or 6 ft (1.83 m) but would probably choose the former to be a bit more

accurate

.

16
Next let us turn 90° so that we are facing the rows. Figure 7 applies

and we again read off the element lengths for each row of luminaires

present. The element lengths are symmetrical about the y axis; therefore

we need consider only those for +x and eventually weight each of them by

a factor of 2.

Figures 6 and 7 were developed from the following guidelines:

First, element lengths were chosen to fit the customary 4-ft (1.22-m)

luminaire (there is no element extending between, say, y

= 6 ft (1.83 m)

and y

= 10 ft (3.05 m) . Second a row was placed directly over the task

and parallel to the direction of viewing . The elements in such a row

have no variation with <J), except in switching from cj) = 0° in front of

the task to <J) = 180° behind it. Element lengths in this row were chosen

so that A0 ** 10° for each element when h = 7 ft (2.13 m) . For example,

the element between y

= 4 ft (1.22 m) and y

= 5.8 ft (1.77 m) has 0

values of 29.7° and 39.6°, giving A0 = 9.9°.* Third, it was decided

that the change in B in traversing an element should be no more than

.10 (the change in B^_ is greater than the change in B^ for the same change

in 0 or (J>) . An examination of the overhead row, with the element lengths

chosen as indicated, shows that AB^ meets this criterion (when the overhead

row is turned 90°, changes in B are less and the criterion is easily met).

Fourth, rows displaced at intervals of 2 ft (.61 m) from the overhead row

were examined. For each row, the A0 and AB criteria were imposed in

selecting element lengths. In addition, A(J> (the change in azimuth angle)

was limited to 555 22.5°.** This seems justifiable when it is realized that

*7 ft (2.13 m) was chosen as an "average" mounting height above the work

plane for offices. For a given element size and location, as h increases,

A0 decreases.

**0ne value of A(f> for d = 2 ft (.61 m) exceeds this limit, but A0 and AB^_ are very small for this particular element

17
published intensity distribution curves are generally given in only three

azimuth planes separated by 45°.

We turn now to the rectangular luminaire and define it as one in

which neither luminaire dimension is small compared with the distance

from luminaire to task. Such a luminaire must be broken into rectangular

elements, in much the same fashion and using the same criteria as in

the strip luminaire case. The results, for a 3 ft (.91 m) by 3 ft (.91 m)

luminaire are shown in Figure 8, again based on a 7-ft (2.1 m) mounting

height. In that figure, each square luminaire is divided into 1, 2, 4 or

6 parts, depending on its distance from the task. For example, a 3 x 3

square luminaire centered at x = 4 ft (1.22 m) and y

= 5 ft. (1.52 m)

should be represented by four square elements, each 1.5 ft (.46 m) on a

side. A luminaire centered at x = 2 ft (.61 m) and y

= o should be

represented by six rectangular elements, each 1 ft (.30 m) by 1.5 ft (.46 m)

.

IV. Calculation Procedure

In this section, a systematic procedure for computing the direct

components of CRF and ESI for the concentric ring pencil task using a cardprogrammable hand calculator is presented. The procedure may be outlined

as follows : First , the room layout is drawn and task and luminaire

location are noted on an xy grid. Second, each luminaire is divided into

one or more elements, according to the guidelines in Section IV and

Figures 6 through 8. Third, the angular locations (polar and azimuth)

of the center of each element are calculated and, from these, the luminous

intensity of each element in the direction of the task is obtained. Fourth,

bidirectional luminance factors are calculated for the task and its

background for each element. Fifth, the illuminance on the task produced

by each element is calculated and the results summed to obtain overall

18
illuminance. Sixth, task and background luminances produced by each

element are obtained, and these are summed to obtain overall task

luminance and background luminance. Seventh, the direct components of

contrast rendition factor (CRF) and equivalent sphere illumination (ESI)

for the pencil task are calculated.

The procedure will now be presented in a step-by-step manner in six

parts, a preliminary part and a part for each of the five program cards

necessary for its execution. The actual programs and user instructions

will be presented in Section V.

A. Preliminary Steps

1) Sketch a top view of the room layout to approximate scale,

showing luminaire and task locations (an example of a typical

room and luminaire layout is shown in Figure 9) . Orient the

diagram so that the viewing direction is toward the top of the

page. Draw an xy coordinate system on the layout, with +y in the

direction of viewing, +x to the right, and the task at the

origin (o, o) .

2) Divide each strip and square luminaire into elements according

to Figures 6 through 8. Give each element a number designation

and each strip and square luminaire a letter designation. Refer

to Figure 9 for an example of dividing, lettering and numbering.

For example, in that figure, elements 1 through 7 are 2.5 ft

(.76 m) , 1.5 ft (.46 m) , 1.8 ft (.55 m) , 2.2 ft (.67 m)

4 ft (1.22 m) and 8 ft (2.44 m) long, respectively, as obtained

from Figure 6. Note symmetry about the viewing direction and

identify those elements, and entire luminaires, that will produce

equal luminances at the task. For example, corresponding elements

19
Table 2

Intensity Worksheet

Symmetric Asymmetric

0 in deg.

A0 = 5°

0 in deg.

A0 = 10

0 row

No . n L

°r Wo Intensity Format

I o

I 45

X 90

5 15 1

0 5 2

5 5 3

10 15 4

15 25 5

20 35 6

25 45 7

30 55 8

35 65 9

AO 75 10

45 85 11

50 95 12

55 105 13

60 14

65 15

70 16

75 17

Luminaire Description:

20
in rows A and A' in Figure 9 produce identical luminances in

the calculations and the luminances it produces doubled.

Also, use Figure 2 or Figures 6 through 8 to ascertain those

elements shielded from the task by the viewer. Omit such

elements from further consideration.

3) Use the luminaire manufacturer's intensity data to fill out the

Intensity Worksheet in Table 2. In that table, I is the intensity

distribution in a vertical plane along the luminaire axis, I

perpendicular to the luminaire axis, and I midway between.

If the luminaire is symmetric (no variation of intensity with azimuth

angle), it is necessary to fill in only one I value for each 0. The

symmetric column in Table 2 is used for this purpose. For an asymmetric

luminaire, the intensity format column must be completed. The only

exception to this latter statement is when a row of asymmetric luminaires

passes directly over the task location so that the intensity is always

either I or Then I values are inserted into the symmetric column

o 90 o

if the row is parallel to the direction of viewing and I values if

y (j it is perpendicular to it.

Manufacturer's intensity data is given in either 5° or 10° increments

in polar angle 0, and the appropriate A0 column should be noted in Table 2.

Each row of intensity data is given a row number n so that it may be

readily identified by the calculator.

There are 17 entries* for each intensity distribution curve (some

entries appear twice in each column because of the manner in which

interpolations are done for small values of 0) . Each entry in the intensity

*Because of calculator storage limitations, intensity data for 0 > 75°

(A0 =5°) are excluded. This limitation is minor.

21
format column must be of the form xxx.xxxxxx so that all intensity data may be

stored at one time in the calculator. Also each intensity value must be

less than 10,000c. The first three x's represent the value of I /10 rounded

o to the nearest 10 candelas. Thus, an intensity of 4876 candelas would be

entered as 488; an intensity of 876 candelas as 088. Next, a decimal

point is inserted, followed by three x's representing the value of

1^/10 to the nearest 10 candelas and, lastly, by three x's representing

I../10 to the nearest 10 candelas. No decimal point is used between

yu

these last two entries.

As an example, suppose I = 37 56cd , I,_ = 97 6cd and = 85cd for

o 45 90

a particular value of 0. Then the entry in the intensity format column

is 376.098009.

The reader should note that the 3-digit representation of intensity

is used only when completing the intensity format column for asymmetric

luminaires. Actual values of intensity should be used when completing

the symmetric luminaire column.

4) Complete the top portion of the CRF-ESI Work Sheet for the Direct

Component in Table 3. As before, h is the mounting height of the

luminaires above the work plane, the latter being generally

30 inches above the floor. A0 is either 5° or 10°. Viewing

direction can be indicated by a compass direction. Row

orientation (p) , if rows are present, is either parallel or

perpendicular to the viewing direction.*

Row or luminaire letters are inserted according to the labeling

in Step 2. For example, if the first six elements are in a square

*The procedure does not accommodate oblique viewing of rows.

22
'-ESI

Work

Sheet

for

Direct

Component

il ,g

II CD<

G

O

*H

4-1 CJ

<UG

•HQ

boC

&

a) H

>

G0

1

pi

s

G

O

rHP

G

O

O

PIe

oo

Pi

<uG

•HG

G

•HIP

!

p

G

o

•H

4-1 G

O

op

p

COG

H

Source

Element

Number

Row

or

Luminaire

Letter

Quantity Xe CD CD Element Scaling

m

Factor -S- 0

Row

Number

n

CD

rH M

CD

CNJ M

CD

co M

CD

'•w

Kf M

Scaled

I(<M)

Step

No.

Ol co LO cO CO <J\ 10 11 CM

rH

Program r—i CM CO

23
I

I

24
Table 4

Centers and Lengths of Strip Elements in ft (m)

If a Strip Element Its Center

Lies Between Its Length is is Located at

0 and 1 ,.2 (.37) 1 ,.2 (.37) .6 (.18)

1 ,.2 (.37) and 2,.5 (.76) 1 ,.3 (.40) 1 ,.85 (.56)

2,.5 (.76) and 4 (1 .22) 1 ..5 (.46) 3,.25 (.99)

4 (1 .22) and 5,.8 (1.77) 1 ..8 (.55) 4 .9 (1.49)

5,.8 (1.77) and 8 (2 .44) 2,,2 (.67) 6,.9 (2.10)

8 (2 .44) and 12 (3 .66) 4 (1 .22) 10 (3 .05)

12 (3 .66) and 20 (6 .10) 8 (2 .44) 16 (4 .88)

25
or strip luminaire A, insert the letter A in the rectangular

space above elements 1-6, and place a vertical line in the space

between elements 6 and 7.

B . Program 1

1) Using the luminaire location layout from Step Al, enter an x

e and value in Table 3, rows 1 and 2, for each luminaire element,

where x^ (y

e

) is the distance perpendicular (parallel) to the

viewing direction from the task to the center of the luminaire

element. In entering x^ and y^, be sure to include the sign of

each. Centers and lengths of elements for strip luminaires are

presented in Table 4 to assist in making these entries.

2) Program Card 1 is read into the calculator, the value of h is

entered, and the values of x and y for each luminaire element

e e are inserted. The program computes values for | <J> | , 6, m, and ip

for each luminaire element, prints these (if a printer is used)

and shows them in the calculator display. These values should

be inserted in Table 3 in rows 3 through 6. (J) ranges from

0° to + 180° but because of symmetry, only the magnitude of <p

(|(j)|) is required, and this is calculated from

hi - WO - | tan

1

for y- (24)

W = Itan”

1

||

for y+ (25)

is obtained from

i / 2 A 2

_ -1 / x + y

0 = tan / —-

1—

h

(26)

The parameter m is the element scaling factor, and is required

because manufacturers' intensity distribution curves are given for

26
entire luminaires. There are three situations to consider. In the

rectangular luminaire case, the user inserts the number of subdivisions

(1, 2, 4 or 6) into the calculator and obtains an element scaling factor

of 1, .5, .25 or .167. For rows, the basic unit is 4 ft (1.22 m) . The

user inserts Ail, the luminaire element length, in ft and obtains the

scaling factor as Ail/4. For point sources, the entire luminaire is

always used and m = 1

The fourth quantity computed is \p, the angle at the source. As

stated earlier, V and <j) are not necessarily the same, the former being

related to the source and the latter to the task. (Refer again to

Figure 1 and the diagram in Table 2) . It is necessary to calculate ifj

only when the source is asymmetric. The following cases exist:

The calculator program makes these distinctions after it is given

a value for "p", the row orientation factor (p=o if the rows are

parallel to the viewing direction and p=l if they are perpendicular to it) .

A final feature of Program Card 1 is that it permits a calculation

of body shadow factor if the user so desires. If the user has any doubt

after consulting Figure 2 as to whether or not a certain luminaire element

is shielded, he can ask the calculator to check. A 1 will appear if the

center of the luminaire element is not shielded from the task, a 0 if it is

U1 < 90° 1<H >90°

Luminaire axis parallel

to viewing direction $ " hi $

- 180° - |$|

$

- 90° — | <|>

| l|> = I Luminaire axis perpen- $1-90°

dicular to viewing

direction

27
C . Program 2

In Programs 2 and 3, intensity as a function of the angles (\p } 0) is

computed for each luminaire element. This is done through a single interpolation in 0 if the luminaire is symmetric or if ijj = 0° or 90° and

through a double interpolation in \p and 0 for all other conditions.

In the former case, the user omits Program Card 2 and goes directly to

Program Card 3. In the latter case. Program Card 2 must be used first.

As mentioned earlier, interpolation in the ifj dimension is done by

passing a parabola through the intensity values at ip = 0° , 45° and 90°

and calculating 1(0) for each of four consecutive values of 0. The

user first places the appropriate 0 row number n, obtained from Table 2,

into row 7 of Table 3. n is the number of the row in which the first

intensity interpolation (1^) is done (in the example in Table 1, n is 9,

corresponding to 0 = 35°) . He then reads Program Card 2 into the calculator

and inserts the intensity data from the format column in Table 2 and the

values of ip and n from Table 3. With these values in storage, the

calculator computes 1^, I^, I^ and 1^, the intensities for the four

consecutive 0 values. These values are either available from the printer

or may be observed directly in the calculator display. In either case,

the user should place the four intensities in rows 8 through 11 in Table 3

.

When Program 2 is omitted (for symmetric luminaires and overhead

rows of asymmetric luminaires) , the appropriate values of 1^ or I

from the symmetric column in Table 2 should be inserted in rows 8 through

11 of Table 3.

D . Program 3

Program 3 completes the double interpolation begun in Program 2 for

asymmetric luminaires or conducts the single interpolation required for

28
symmetric luminaires.

After reading Program Card 3 into the calculator, the user inserts

a 0 or a 1 to indicate that the increment in 0 is either 5° or 10° . He

then inserts 0, m, n,* 1^, I^, and 1^ , in that order, and the calculator

computes I((J>, 0) scaled by the element scaling factor m. This value is

printed and also appears in the calculator display. It should be inserted

in row 12 of Table 3. The unsealed value of l((J), 0) is also printed, to

provide a check for the user that his I value is reasonable in terms of the

values of 1^ through 1^ . The procedure is then repeated for each luminaire

element

E . Program 4

In Program 4, bidirectional luminance factors for the concentric

ring pencil task and its background are calculated using the log cubic

Equation (22). The user reads in Program Card 4, inserts the values of

| (p | and 0 from Table 3, and the calculator computes and B^ for each

luminaire element, printing and displaying each.

It should be stressed that Program 4 is applicable only to the

concentric ring pencil task. However, if bidirectional luminance factor

data for other tasks should become available, the program could be altered

easily to accommodate them.

F. Program 5

All factors necessary for the calculation of the direct components

of CRF and ESI have now been assembled except the duplicate element multiplying factor, d. Recall that in Step A2 the user was instructed to observe

symmetry and note those luminaires and luminaire elements which produce

*If Program 2 was skipped, values of n should be inserted in row 7 of

Table 3 prior to this step.

29
identical luminances at the task. In row 15 of Table 3, the user should

now insert a 2 if that element's contribution is to be doubled and a 0

if it is not, making that wherever a 2 is inserted, that element's mate

is not included in the calculations. Then Program Card 5 is read into

the calculator, h is inserted, and 0 , I, B , B, and d for each luminaire

t b

element are entered, one set at a time. The calculator then computes

and displays a running total of task illuminance (EE.), task luminance

(AL .) and background luminance (EL. .). EE. is also printed. These

values are entered in rows 16, 17 and 18 in Table 3. Thus, the entries

in column k of these rows in Table 3 give the total illuminance and

luminances produced by the first k luminaire elements. If it is desired

to know the contribution of luminaire element k to the illuminance and

luminances, the values of these quantities in column k-1 are subtracted

from those in column k.

The entries in rows, 16, 17 and 18 for the last luminaire element

give the direct components of illuminance and luminances for the entire

installation. Then the calculator computes and displays the direct

components of CRF, ESI and LEF . It also prints these quantities, as well

as the values of C, RCS, and RCS . e V. Calculator Program and User Instructions

A. Introduction

A Texas Instruments' SR-52 card programmable hand calculator was

used in this study, but any other similar calculator would also suffice.

This calculator has 224 program storage locations, 20 data storage

locations and 10 user-defined labels. It is not our purpose here to

describe in detail the SR-52 or any other calculator. Rather our aim is

to provide sufficient information about the SR-52 so that the user can

30
execute the five programs described in Section IV. For further details

about this or other calculators, the user should consult the appropriate

instruction manual.

B. Reading a Card

At Step Bl in Section V, the first program card must be read into

the calculator. To do this, first press the CLR button; then press the

2ND button and the READ button and insert the program card into the lower

slot on the right side of the calculator, with end A towards the calculator.

The calculator motor should carry the card through to the opposite side.

Next press 2ND and READ again and insert the card with end B towards the

calculator. Again it should pass through. The program is now in the

calculator memory and the card may be returned to its case.

C. User-Defined Labels

In order for the user to enter data into the calculator, he must be

able to tell the calculator not only the data to be entered but where to

go in the program to do the entering. The 10 user-defined labels, A

through E and A' through E' provide this latter feature. The second set

of these (primed letters) requires the user to press the 2ND button and

then the letter button, much as the shift key on a typewriter causes the

upper characters to be printed. Generally, an asterisk (*) is used in

place of 2ND in programming instructions.

Suppose a quantity 17.6 is to be entered using label A. The user

would press five buttons, namely 1, 7, ., 6, A to accomplish this. To

place the entry in *A* requires six presses — 1, 7, .,6, 2ND, A.

Quite often labels are used to start a calculation, rather than to

insert data. If so, only the buttons A or *A ’

for example, are pressed.

31
D

.

Readout

There are two means by which readout is accomplished, namely through

the display register and through an auxiliary printer. Halt statements

occur throughout the programs so that the final result of a calculation

appears in the display register. The auxiliary printer, if used, will

also provide the final answer, in printed form. In addition, it will

provide certain intermediate answers which the calculator and its display

pass by in traveling to the final answer. These printed intermediate

answers are not essential to have but are useful in checking results.

To repeat, the printer is not essential in carrying out the calculations,

but it is convenient to have.

E. Initialization

Each of the five programs begins with an initialization instruction

which is executed simply by pressing the E button. The purpose of this

is to insure that the data storage and display locations (registers) are

cleared before new calculations begin. Pressing E does not affect the program

storage locations.

F. Inserting a Minus Number

A negative number is inserted into the calculator by first inserting

the positive value of the number and then pressing the +/- button.

G. Instructions and Programs

User instructions for the five programs are given in Table 5.

The instructions must be carried out in the order given, unless otherwise

indicated. After entering an instruction, the user must wait until the

calculator stops, as indicated by a steady display, before entering the

next instruction.

32
Table 5 - User Instructions

Program 1

Entry Label Display Print

E 0

h *A' h

X A X

y B y e

C iff 1*1

D 6 e 6,4,2 or 1 *B ' m m

Ail *C ' m m

p(0 or 1) *D

* <1* *E ’ S 1 or 0

Comments

1. Pressing E clears display and data storage registers.

2. h need only be inserted once at the outset.

3. In computing m, *B ' is used for square luminaires, *C ' for strip

luminaires

4. In computing \p, a 0 is inserted if luminaires are parallel to the

viewing direction, a 1 if they are perpendicular, ip need not be

computed for symmetric luminaires.

5. S is an optional calculation, but cannot be done until | <f> | and 0 are calculated. A 0 is displayed if the viewer shields the center of the

luminaire element from the task, a 1 if he does not.

33
Table 5 (Cont.)

Program 2

Entry Label Display Print

E 1 XXX . xxxxxx A 2 first I entry

XXX . xxxxxx A 3 second I entry

•

XXX . xxxxxx A 18 last I entry

$ B 4 n C n

D 1 1,(0), M0),

i,(0), i.(0)

*A

1,(6)

*B ’ ii(0)

*C ' nee)

*D

14(e)

Comments

1. Pressing E clears the display register but not the data storage

register

.

Do not press E again after the first initialization

again after the I entries have been inserted.

2. If an error is made in an I entry prior to pressing A, press CLR and

redo the I entry. If an error is made in an I entry and A has been

pressed, press k ST098, where k is one less than the number in the

display and then redo the I entry and push A.

3. *A' , *B', *C '

,

and *D' need not be pressed if a printer is used.

Correct keying sequence in this case is EABCDBCD . . . .

34
Table 5 (Cont.)

Entry

A0 (0 or 1)

6m

n

I, (6)

1 ,( 0 ) 1 ,( 0 ) rj(0)

Program 3

Label

E

A

BB

B

B

BB

B

C

Display Print

1

0 or 1 1

1

1

1

1

11

scaled I (<p, 0) 0', I(4>, 0),

scaled I (cf> , 0)

Comments

1. Pressing E clears display and data storage registers.

2. Entry at A is 0 if A0 = 5° and 1 if A0 = 10°. This is done only once.

3. Entry at B is seven items, in the order given, for each luminaire

element. If an error is made in an entry prior to pressing B, press

CLR and redo the entry. If an error is made in an entry and B is

pressed, press k ST019 where k is the number (1-7) of the incorrect

entry. Then redo the entry and press B.

3. Printer shows 0' (the transformed value of 0 for calculation

purposes) , the unsealed value of I after multiplication by m.

(<P, 6 ) and the value of I

( 0 , 0 )

35
Table 5 (Cont .

)

Program 4

Entry

Comments

Label Display

E

A

B

C

D

B

B

tb

1. Pressing E clears display and data storage reg

Print

isters .

36

w

w
Table 5 (Cont.)

Entry Label

Program 5

Display Print

h

E

*E

0

h

0 A 1

I(<f>, 0) A 1 B A 1

B

b

A 1

d (B or 2) A 1 B EE. EE.

C el

1

. i

D

*A’

EL

11

cii 1 C, CRF

*BESI RCS , RCS , *C

LEF

e LEF

Comments

1. Pressing E clears display and data storage registers.

2. h should be entered once at the outset.

3. 0, 6), B , B^ and d must be entered in order. If an error is made

in an entry before A is pressed, press CLR and redo the entry. If an error is made in an entry and A is pressed, press k ST019 , where k is

the number (0-4) of the incorrect entry. Then redo the entry.

4. d is 0 if the luminaire element under consideration at x, y does

not have a counterpart at -x, y. It is 2 if it does.

5. EL anc* may not computed until EE_^ is found.

6. Normally, calculations of EE_^, EL

^ and EL^ are completed before

*A' is pressed to obtain CRF

1 Thin *B ' may1be pressed to obtain ESI and

*C’ to obtain LEF, if desired. However, if the user wishes, intermediate values of CRF and ESI may be obtained by pressing *A ’ and

*B' earlier. This allows the user to obtain the CRF due to a single row of luminaires, for example.

7. After calculations of overall CRF and ESI are completed, intermediate

values of EE., EL

^ and EL^ may be stored by the user and then used

to calculate1 inte&mediate values of CRF and ESI. For EE., enter its

value and then press ST007 . For EL enter its value and press

ST009; for EL enter its value and press ST011.

37
Table 6 Program 1 0 0 0 H* ’T, ij 5 0 0 3 0 G 1 16 0 5 1 0 0

___

u

_

n ? cr

U

U Li ul

V

M i* 0 0 3 o o 053 43 0 0 4 01 054 01 0 0 5 31 0 5 5 0 0 0 0 6 - 46 0 56 95 0 0 7 i i 057 42 _ _ _ _ u u a til. V 058 01 0 0 9 0 0 0 5 9 0 1 0 1 0 0 3 0 6 0 9 3 o i 1 3 1 0 6 1 3 1 0 1 2 4 6 0 6 2 4 6 0 1 3 12 u o J y 7 0 1 4 a j Li 64 4 3 0 1 5 0 0 0 6 5 0 1 0 1 6

04 066 "00 0 1 7 3 1 0 67 42 0 1 3 46 0 6 3 0 i 0 1 9

13 0 6 9 0 1 0 2 0 A •"« 0 7 0 9 3

021 i D 0 071 31

022 0 3 0 72 46 0 2 3 c c . J 073 14

024

C ”i .J . *i 074 43

LO 1

C'J 111 43 075 00 0 2 6 0 0 076 04

027 04 077 40 0 2 8 35 073 35 0 3 2 54 0 3 2 40 0 3 3 95 0 3 3 95

034 • j o 034 3 0 0 3 5 34 035 ET ET .J .J 0 3 6 3 0 0 3 6 fi 7 A •“« *-+« U 3 7 |J |j 0 3 3

i' i 94 0 8 3 01 0 3 9 46 0 8 9 95 0 4 0 f r 0 9 0 22

04 1 42 091 3 4

042 01 0 9 2

-~i

*-+ ^1. 043 0 0 093 0 0

044 43 0 9 4 05

045 0 0 095 93 0 4 6 04 0 9 6 O i 047 3 0 0 9 7 46

043

O j' ij y

y 1 7 0 4 9 01 0 9 9 20

38 1 0 0 9 8 150 05 1 0 1 3 1

151 f •J 102 46 152 01

103 IS 153 03

104 5 5 154 95 1 0 5 0 4 155 8 0 1 0 6 9 5 156 6 3

107 93 157 01

103 81 158 81 1 0 9 4 6 159 46

110 1 0

160

yy

111 43 161 00

112 01 162 31 1 1 3 0 1

163 46

114 75 164 15

115 01 1 6 5

"« ET 116 06 166 47

117 05 167 31

113 95 1 63 46

119 30 169 19

120 73 1 7'0 90

121 85 171 69

122 02 •172 0 9 1 2 3 0 0 1 l J 0 0

124 95 174 75

125 SO 175 43 1 2 6 79 176 01

127 01 177 0 0

123 31 173 95 1 2 9 4 6 179 93

130 79 1 3 0 9 9

131 43 131 si 1 3 2 0 0 i C1 "«

J. «-> iL. 46

133 05 1 OO i. 69

134 75 134

A “i *+ . 135 05 185 01

136 02 136 0 0

137 95 1 8 7 93

133 SO i y

y 99

139 67' 139 81

140 01 190 00

141 3 1 * 191 0 0 j 21 jJ. {—, 192 0 1 j i 4 3 7 S 193 00

144 00 194 0 0

145 81 195 i j 0

146 4 6 1 9 6 i0 0

147 78 1 9 7 i0 0

143 43 1 9 8 i3 0

149 00 199 i30
TABLE 6

Program 2

000 46

oo i 1 

002 9 8

003 36

004 42 0 0 5 09 0 0 6 08 0 0 7 01

008 44 0 0 9 09 0 1 

08

01 

43

012 09 0 1 

0 8

014 81 0 1 

46 0 1 

12 0 1 

dv 0 1 

01 0 1 

08

020 06

021 06

022 42

023 09

024

M

O

025 04

026 i

•" •r£ 027 00

028 00

029 99 0 3 0 O 1

i. 031 46

032 13

033 42

034 01

035 09 ' 036 8 

037 46

038 14

039 4 6

040

a

r 04 

36

042 43

043 01

044 09

045 75 0 4 6

‘4 .“I 047 G5 H ki ft q

cr 049 cr -7 •J i

050 00

f! cr -j ET

J .J

052 “i 0 5 3

ET j • J il 054

055 06 0 5 6 09

059 i 94

060 r. cr

r“i .J 061 36

062 43

063 01 0 6 4 09 0 6 5 95

066 65

067 0 

068 0 0

069 0 0

070 00

07 

95

072 42

073 09

074 09

075 “7 cr f J 076 93

077 05

078 95

079 57 0 8 2 2 2

083 cr

•" •J lL fj O .4 085 06

086 02

087 2 2 0 8 8 57

089 94

090 85

091 4 3 0 9 2 09

093 09

094 95 0 9 5 65 0 9 6 0 

0 9 7 0 0

098 0 1 j 0 9 9 00 1 0 0 95

101 42

102 0 6

103 0 3 1 04 01

105 44

106 01

107 09

108 04 1 0 9 65

110 43 1 1 

06 1 12 02

113 75

114 03 1 15 65

116 43

117 06 1 1 

09 1 19 75

120 43

121 06

122 03

123 95

124 55

125 09

126 95

127 42 i j q 06

129 04

130 43 1 3 

132 H “i i o o

06

09

-? cr i J 134 02

135 65

136 43

137

138

139

06f1 85

140 43

141 06

142 0 3

143 95

144 55

145 04

146 00

147 05

148 95

149 4- j!

150 06

151 05

152 43

153 06

154 09 1 55 65

156 01

157

n

n 158 85

159 43

160 06

161 04

162 65 1 6 3 43

164 01

165 08 1 66 85

167 43

168 06 1 69 05

170 65

171 43

172 01

173 08

174 40

175 9 Pi 176 93

177 36

178

179 09 i a u 1 8 

u y

01

132 44 i 8 3 09

134 0 8

185 58

186

O i 187 81

188 46

139 16

190 43

191 06

192 06

193 81

194 46

195 17

196 43

197 06

198 07

199 81 2 0 0 46

201 18 2 0 2 43

203 06

204 0 8

205

O 1

j. 206 46

207 19

208 43

209 06

210 09

211 r. * O i 212 46

213 15

214 25

215 01

216 j 217 2 1 

219

090 8

81

i“l i"« £ c. u 221

L'

U

00

lL 00

39
TABLE 6

Program 3 0 0 0

.•1 oo i 15 0 0 2

•*! ET

ill •J 0 0 3 47 0 0 4 01 0 0 5 42 0 0 6 01

007 09

008 81

009 46 0 1 0 1 1 Oil 42 0 1 2 0 0 0 1 3 0 3

014 81

015 46 0 1 6

12

017 36 0 1 8

42 0 1 9

01 0 2 0 09

021 0 1 022 44

023 01

024 0 9

025 81

026 46

027 1 3 0 2 8 0 1

029 42

030 01

031 0 9 U 3 2

033

02

65

034 10 0 3 5

-? cr i -J 036 09

037 65

038 19

039 i-. cr o 040

04 1 042

01M O

65

043 18

044 75

045 01 0 4 6 01

047 65 0 4 8 17 0 4 9 95 0 5 0

cr cr

._! .J 051 03 0 5 2 i j 0

053 95

054 42 0 5 5 0 U

056 09

057 02

058 65

059 17 0 6 0 75

061 05 0 6 2 65 0 6 3 is

064 ”| cr C* -J 0 6 5 04 0 6 6 65

067 19

068 “? cr r -j 069 10 0 7 0 q cr 07 1

cr cr •J J

ft "7

J fi cr

U i c_

fi

M

U i •_« 074

M I_1 95

075 42

076 01

077 0 0

078 10

079 75 0 8 0

081 0 3

65 0 8 2 19 0 8 3 I-, cr O •J 0 8 4 0 3

085 65 0 8 6 i 8

087 75 0 8 8 17 0 8 9 95 0 9 0 55

091 07 0 9 2 05 0 9 3 0 o 094 95 0 9 5 42

ij 9 6 .01

097 01 0 9 8 43 0 9 9 0 0

100 08 150 43 200 46 1 ij 1 9 0 151 00 201 17

102 87 152 03 202 4 3

103 02 153 75 2 0 3 0 0

104 2 2 154 02 2 0 4 0 4

105 49 155 54 205 5 6 1 0 6 0 0 156 95 2 0 6 4 6 1 0 7 0 9 157 98 207 18

108 04 158 42 208 43

109 22 159 01 209 00

110 49 1 6 0 0 2 210 05

111 01 161 46 211 56

112 00 162 8 3 212 46

113 08 163 45 213 19

114 22 164 03 214 43

115 49 165 65 215 00 1 1 6 0 1 166 4 3 2 1 6 ij 6

117 01 1 6 7 0 1

217 56

118 43 168 01 2 1 8 4 6

119 00 169 85 219 1 1j

120 01 170 43 220 43

121 75 171 01 221 0 0

122 01 172 02 222 07 1 2 3 0 0 173 40 2 2 3 5 6

124 65 174 65

125 53 175 43

126 43 176 01

127 00 177 00

128 03 173 85

129 75 179 4 3

130 02 180 01

131 93 181 02

132 05 182 65

133 54 133 43

134 95 1 8 4 0 0

135 98 185 09

136 42 186 85

138 02 188 ij ij

139 41 139 04

140 8 8 190 95

141 46 191 93

142

O f* 192 65 1 4 3 43 193 43

144 ij 0 1 94 0 1j

145 01 195 02

146 75 1 96 95

147 05 197 93

148 65 198 9 4

149 cr “i • J •“» 1 99 81

40
I

Table 6 Program 4 0 0 0 4 6 050 1 0 0 0 3 150 75 2 0 0 0 01 11 051 00

01

101 85 151 93 20 i 0 02 42 n s * -* 102 93 152 00 202 0 0 3 0 0

004 01

053 0 3 103 07

104 03

153 00 "j |“j

•“« 054 05 154 05 204 0 0 5 8 

055 04 105 05 155 03 2 0 5 0 0 6 4 6 056 02 1 0 6 0 8 156 0 0 2 0 6 0 07 12 057 65 1 0 7 0 6 157 03 207 0 0 8 4 2 0 5 8 43 108 95 158 01 0 0 9 0 0 0 5 9 00 1 0 9 9 9 159 65 2 0 9 0 1 0 0 2 0 6 0

061

01 110 98 160 43 210 0 11 81 3 0

C* ,-i 111 81 1 6 1 0 0 211

012 46

U 6 2 •J‘t 112 46 162 01

V 1 V

013 13 0 6 3 65 113 14 16.3 30 ? i 3

014 53 0 6 4 4 3 114 53 164 54 214

015 93 IJ

b 5 0 0 115 93 165 65 215

016 02 ij 6 6 ij 2 1 1 6 0 166 4 3 216 0 17 01 U 6 7

i“l 7 i“i •i 117 02 167 00 217 0 1 Q f

IJ h. o 4U 113 05 1 1 9 02 1 fjV 218 0 1 9 0 9 219 0 6 9

“i cr O •J

ET •” 169 23 0 2 0 0 8 U 7 U

071 .j . *i 93

120 01 170 40 220

021 94 121 94 171 85 221

022 85

U ( l2 IJ IJ 122 85 172 53 0 2 3 9 3 U ( 8 ij 3 123 93 173 93 777

024 00 074 GO 124 0 0 174 00

025 01 075 ij s 125 00 175 01 0 2 6 0 4 0 7 6 U7 126 05 176 04

027 09 077 0 8 127 09 177 08 0 2 8 0 7 078 94 128 07 178 08 0 2 9 0 9 079 O cr 129 02 179 08 0 3 0 6 5 080 93 130 05 180 94

031 43 08 1 0 0

fj |“i 131 65 181 85

032 00 “ *—

MM

|"”l •*! 132 43 132 93

033 01

U o o 1 3 3 0 0 1 8 3 0 0

034 30 084 00 134 01 184 00

035 54 085 0 3 M ^ 135 30 185 00 0 3 6 6 5 U 8 6 136 54 . 186 05

037 43 IJ t“i ;** 0 

£ cr 137 65 187 02 0 3 8 0 0 0 3 9 0 2 089 b J 43

138 43

139 00

188 04

189 05 0 4 0 2 3 090 00 140 02 190 07

041 85 0 9 

0 

141 23 191 65

042 53 0 9 2 3 0 142 85 192 43

043 93 0 9 3 54 143 53 193 00 0 44 01 0 9 4 65 144 93 194 01 0 4 5 0 8 095 43 145 01 195 30 0 4 6 0 8 0 9 6 0 0 146 00 196 54 0 47 01 097 02 147 0 4 197 6 5 0 4 8 0 5 0 9 8 23 148 05 198 43

049 75

U 9 9 45 149 05 1 9 9 0 0

02

450 3

cr

O -J 930 8

05

020 0

06

959 9

99

81

46

15V ^ 47

810 0

000 0 0 0

41
Table 6 Program 5 1 0 0 4 6 3 0 1 1 0 3 0 2 42 3 0 3 0 1 3 0 4 0 8

305 81 3 0 6 4 6

307 1 1 3 0 8 3 6 3 0 9 42

310 01 3 1 1 0 9

312 0 1

313 44 3 14 01

315 0 9

316 81

317 46 3 18 12 3 1 9 0 0 3 20 42

321 01 3 2 2 0 9

323 43 3 2 4 0 0

325 0 4

326 90

329 49 3 3 0 0 0

331 01

332 46

334 43 0 3 6 0 1

037 65

038 43 0 3 9 0 0 0 4 0 0 0

041 33

042 45 0 4 3 0 3

044 55

045 43

046 01

50 42 1 0 0 0 0 1 50 01 2 0 0 05 5 1 0 0 io i 09 151 02 20 1 55

Cj • j 06 102 cr cr J 152 95 202 43

53 44 103 43 153 9 3 2 0 3 0 0

54 0 0 104 01 154 41c! 204 07

cr cr •J • J 07 105 01 155 01 205 95

56 43 1 0 6 95 156 0 3 . 206 98

57 0 0 107 98 157 207 31

cr r« J O 07 108 55 153 04 2 0 8 46

59 98 1 0 9 93 159 55 2 0 9 O i 60 O 1i 1 1 0 01 160 09 • 210 02

61 46 1 i i 06 161 55 211 9 3

62 13 112 07 162 cr •“ . j . *i 212 oi 6 3 43 113 05 163 51 213 09

64 0 0 1 14 95 164

y

r 214 05 6 5 0 6 115 9 8 165 cr c .j .j 215 07

66 .•* cr O 1 16 42 166 43 216 i i v 67 •“ Lt O 117 01 167 01 217 01 6 3 0 0 118 02 163 0 3 2 1 8

56

69 02 1 19 81 169 •_i

y 219 46

70 95 120 46 170 cr ; .J 2 2 0 15

71 44 121 17 ' 171 01 22 1

•j cr i c. 0 0 122 0 1

172 95 •~i -*i 47 \ -Is 09 123 0 0 173 45 j • j j 81

74 .4 ~i •+ o 124 45 174 05

75 0 0 125 53 175 95 7 6 09 126 51 176 42 f r 81 127 O i 177 01 \ o 46 123 cr cr .j . j 178 04

79 14 129 53 179 43 8 0 43 130 01 180 0 0

81 0 0 1 3 1

85 181 07

06 132 01 182 55

!-! 3

65 133 cr cr • J •J 183 43

84 43 134 53 184 01

r, cr O J 0 0 135 02 185 01

36 0 3 136 93 186 65 0 7 q=r 137 02 187 43 8 8 44 138 05 138 01

39 0 1

139 65 189 04

90 01 1 40 43 190 95

91 43 141 oi 191 98 9 2 0 1

142 01 192 42 9 3 01 143 45 1 9:3 01

94 81 144 93 194 05

95 46 145 02 195 81

96 i 1 46 95 1 96 4 6 9 7 0 1

147 98 1 9 7 13

98 75 148 65 198 43 9 9 43 149 4 3 199 0i

42
The actual programs, as printed by the auxiliary printer, are given

in Table 6. In each program step, the left (3-digit) entry is the program

step number and the right (2-digit) number is the coded instruction.

VI. Three Design Examples

A. Point Luminaire

Consider the installation in Figure 10 and the associated intensity

and CRF-ESI worksheets in Tables 7 and 8. Four high pressure sodium

units are being used to .light a small lobby and two task locations have

been identified.

Proceeding through the steps of Section V, we first draw coordinate

systems on the room layout, one for each task, with +y in the direction

of viewing and each task located at the origin of its coordinate system.

We consider each luminaire as a point source in this case and thus do

not have to subdivide the luminaires into elements. Because the luminaires

are symmetrical, we need fill in only one column on the Intensity Worksheet,

noting that intensity values are given in 5 degree increments in 0.

Following this, we complete the top portion of the CRF-ESI Worksheet.

Because we are considering entire luminaires as elements, each element

number is a luminaire number also, and we can use the luminaire letter

row to designate which of the two tasks is being considered

We are now ready to carry out Programs 1 through 5. Element scaling

factors are 1 throughout, because each luminaire is a single element.

'f need not be calculated and Program 2 may be omitted because the

luminaires are symmetrical. The duplicate element multiplier is 2

for element 1 and task location 1 and 0 for all other elements. Thus

the column for element 2 under task location 1 is omitted.

A3
Table 7

Intensity Worksheet

/ Symmetric Asymmetric

0 in deg.

A0 = 5°

0 in deg.

A0 = 10°

0 row

No . n h

or ho Intensity Format

1 o: 45I 90

5 15 1 4857

0 5 2 4924

5 5 3 4857

10 15 4 4824

15 25 5 4765

20 35 6 4660

25 45 7 4516

30 55 8 4312

35 65 9 4003

40 75 10 3511

45 85 11 2823

50 95 12 2064

55 105 13 1396

60 14 826

65 15 448

70 16 235

75 17 175

Luminaire Description:

High Pressure Sodium Unit

44
rO

CTJ H

<!

qj r—

CLe

COXwI 4-» c0) co

CLco

CJ

4Ja

(D •HQHO

4-0UoM

C/3 bJI sU

4-4 CNno

II

CUM3

ti£) £oU

c0ao

hJgoo&

CD

<1

4-1 •H£63

•H"OO

C/1

QJH3

CO

CO

CDH

fHrCbD

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*H

c03

*HS3 Xu3o

C/1a

qjH

•HQ

003

*H£

qj •H> 3o

•H

4-1 CO

4-1 3

a) •H

J-4 o

pi

u

efl sI oLT|

CL. e

cO hJ

Co

•H

4-1 c0aoJ

cn

cO H

CNH

qj "e32

<u

qj •H

COc

*H§JO30

01 o ON 00 rH co <3* NO o • • • o rH CN NO ON <3- • m hi- 00 i—i rH m CO o co CN m 1 co

rH

<3* co CN CN rH CN o o in o NO NO 00 in NO • • • • ON CN nr CO CO o in nO rH rH CO co 00 <r CN r-. CO r—

i rH nO rH 1 rH o ON CN CO CO nO o • O • 00 rH o CN CO

CN

m 00 rH CO o in 00 NO

CO NT <r CO CN co c o <1* o * • • • NO NO co m NO o LO CO rH rH CO ON CN <3- co CO I—

rH nO nO rH co co nr CN 1 rH O o m o NO NO co m NO • • • • co ON CN co CO o m nO rH rH •—

co 00 nt CN f<

<1* rH I rH NO

rH o o ON 00 rH CO <r NO NT • • • • o rH CN NO ON <3* CO LO m <0* 00 rH rH in 00 o co CN 1 I CO

.. ..H. ht co CN CN rH CN o o ON 00 rH CO NT NO nr • • • • o rH CN NO ON 1—

m m <r 00 i—

rH

m co o CO CN I nr <r CO CN CN rH CN e 3

Pn 4-J 4-J 00

•H c c M

U

X3 ^ 4-1 a) QJ — QJ *H o 5 ai z-\ y-—

y—\

QJ CD

aX >>

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4-1 sO

J3 CD CD CD CD i—

cO

— <u 3 CJ pi e

V-/

n— v—V—' oj -e- 3 i—

a cd 3 rH CN CO <r u ^

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w co (H CD Z w

MM

M 00M

Oza rH CN co -*4* m NO 00 ON o rH CN

QJ rH rH rH

4-1 cns

cOLj00o rH CN co

P-.

45
I

<N| H 3

0)6323

OJ6

<u i—i w

a)u33O

on 3

<u

4-1

4-J (U h4

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•Ha3

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vD CO Ox CO 00 CO

rH • • • O* rH 04 v£) o m m CO • 00 • vO \o m vO • •

CO vO CTV rH i—I • • • rH vO o 00 m o co VO <r <r m * • CO CO CO CO <r • • • LO vo o vo <3* o\

04 CO o xd- <r <r

LO 04 04 in CO

CO <r o • • • rH v£> CO 04 rH rH • •

rH rH 04 00 x*d- rH vO o rH VO o • • • o • rH <r VO 04 VO • • * • m CO xd* rH in rH

rH o m

04vo o • • • CO vO Ox o m 04 • • m CO xd*

04

CO vO rH ON

LT) CO 04 • • • 1—1 r- 00 CO m CO • • CO 04 OJ

T3 3

pH 0) 0) u 4-J •H

•H (0 4-J rH *H •H u *H •H U 3 3- •H 4-J Ph

M P^ 3 4-J r-Q H 0) *H w r-4 pi CO w cd CQ P3 rH g 4-J w w w o w rJ 3 Cu 0) rH O' 3 i 1 3 Q W 2 oz

a, CO <d"

m v£5 O- CO CO o rH

ai rH <—l

t—i rH rH rH rH 04 04

U

COa

cd3

00 < m o Li

46
Following computation of illuminance and luminances, CRF , ESI and LEF

values are obtained for each task location. Note that this requires

Program 5 to be run essentially twice, once for Tl and again for T2.

B. Strip Luminaire

Only the dissimilarities between this example and the previous one

will be discussed. Refer to Figure 11 and the associated worksheets

in Tables 9 and 10. In this instance, the luminaires are strips,

fluorescent batwing units. Each row is given a letter label and elements

are selected from Figure 6 and numbered. Referring to the intensity

worksheet, the 1^ column is used for row A, because \jj is o for this row,

and Program 2 is omitted. However, for row B, the intensity format

column must be completed and Program 2 used to find the four intensities,

1^ through 1^, row A has no symmetrical counterpart, but row B does.

Hence d = o for row A and 2 for row B and elements in row B' are not

labeled or included in the calculations. The remainder of the calculations

proceed as in Example A.

C. Square Luminaire

This final example involves 3 ft x 3 ft (1.01 m x 1.01 m) cross lamp

fluorescent luminaires with prismatic lenses. Figure 12 and the associated

work sheets in Tables 11 and 12 apply. In this case, intensity data,

given in 10 degree increments, is inserted in the 1^ or I column

because the luminaire is symmetrical. Thus, Program 2 may be omitted.

Also ip need not be calculated. Each luminaire is subdivided into

elements according to Figure 8, and, because of the task location and

viewing direction, each element has a d factor of 2 and thus one-half

of the elements may be omitted from the calculations. The remainder of

the calculations are as in Example A.

47
Table 9

Intensity Worksheet

/ Symmetric Asymmetric

0 in deg.

A0 = 5°

0 in deg.

A0 = 10

0 row

No . n

I or ITM

o 90 Intensity Format

I oX 45T 90

5 15 1 349 035 . 037039

0 5 2 348 035 . 035035

5 5 3 349 035 . 037039

10 15 4 351 035 . 044053

15 25 5 351 035 . 055073

20 35 6 354 035 . 070094

25 45 7 326 033 . 081105

30 55 8 307 031 . 087109

35 65 9 285 029 . 086105

40 75 10 260 026 . 078094

45 85 11 217 022 . 065069

50 95 12 179 018 . 049040

55 105 13 159 016 . 034031

60 14 146 015 . 025028

65 15 127 013 . 019025

70 16 106 Oil . 016022

75 17 78 008 . 013019

Luminaire Description:

Batwing Fluorescent

48
CRF-ESI

Work

Sheet

for

Direct

Component

-Example

PQ

<U

r-1

<UU

•H

03Cs3

hJMO2o

02

>4

0) H32

a)a£o

co

UO

00 o vO in • CO • CM rH rH <r M0

m o rH rH vO CO o <3* m in m CM rH 1 rH • CO co co CO rH

UO

vO o • CO CO On rH rH

m

00 o • CO • o CM <rm

m

O 1 rH CO co co co rH

00

vO • CM vO vO CO CO

r*^ o rH o 00 o < CM o CM

vO rH rH rH rH CM

CN o • rH ON Ov VD rH vO o rH o CO o CNI m CM m m rH rH rH rH rH rH

rH in

On • in

O On On VC

m o • o 00 • o o vO rH

m o vO <* rH CM CM rH rH rH

CO in Ox • rm o c*. rH <r o • o 00 • o 00 o 00 vD rH CM CO CO CM CM CM rH

LOm

CNJ • <r VO r^»

m CO CO o • o CO o vO m CM o co rH CO CM • CO CO co CM rH m vO m

00 • CM rH rH <r VO

m CNJ o • o vO co o <r in m m CM rH

rH rH • CO co co CO rH

vO

m CO 00 ON rH rH

m i—

o • o • • o CM <r <r in m o m CO co CO co rH e C

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52
Table 11

Intensity Worksheet

/ Symmetric Asymmetric

0 in deg.

A0 = 5°

0 in deg.

A0 = 10

0 row

No . n

l 0 or ho Intensity Format

I o

T 45

T 90

5 15 1 1535 .

0 5 2 1575 •

5 5 3 1575

10 15 4 1535

15 25 5 1440

20 35 6 1270

25 45 7 995

30 55 8 600

35 65 9 370

40 75 10 210

45 85 11 70

50 95 12 0

55 105 13 0

60 14

65 15

70 16

75 17

Luminaire Description:

3x3 Crosslamp with Prismatic

Enclosure

V- HO

53
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55
CRF-ESI

Work

Sheet

for

Direct

Component

-

Example

CJ

Source

Element

Number

w 13 m 15 <r

CO

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68.6

1—1 009 370 210 70

307

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cn

00m

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vO 995 600 370 O

rHCN m

in

CN

Row

or

Luminaire

Letter

Quantity X

e 0J >> -& CD Element Scaling

m

Factor -3- 0

Row

Number

n

CD

rH M

CD

CN w

/•“N CD

cn M

/-\ CD

s-/ M

Scaled

Step

No.

f—

1

CN cn -4* m kO 00 G\ 10 11 12

Program «H CN cn

56
57
References

1. Illuminating Engineering Society, IES Lighting Handbook, 5th ed .

,

edited by Kaufman, J., 1972.

2. RQQ Report No. 4, A method of Evaluating the Visual Effectiveness

of Lighting Systems, Illuminating Engineering 65, 505-513 (1970).

3. RQQ Report No. 5, The Predetermination of Contrast Rendition Factors

for the Calculating of Equivalent Sphere Illumination, Journal of

IES 2, 149-166 (1973).

4. DiLaura, D. L., On the Computation of Equivalent Sphere Illumination,

Journal of IES 4, 129-149 (1975).

5. Blackwell, H. R. , and DiLaura, D. L., Application Procedures for

Evaluation of Veiling Reflections in Terms of ESI: II. Gonio Data

for Standard Pencil Task, Journal of IES 2, 254-283 (1973).

6. McNamara, A. C., The Potential of Location Within a Room in Producing

ESI, Journal of IES 5, 169-176 (1976).

7. Blackwell, H. R. , and Helms, R. N., Application Procedures for

Evaluation of Veiling Reflections in Terms of ESI; I. General

Principles, Journal of IES 2, 230-253 (1973).

58
> o

Figure 1. Geometrical Relationships Between x

£

, y h, <J) , ^ and
Y ft.

VIEWING

DIRECTION

-h 1 i

1 1 H

-9 -8 -7 -6 -5 -4 —

h

-3

h= MOUNTING HEIGHT

ABOVE WORK PLANE

IN FT. TASK LOCATION

I23456789 1 1 1 1 1 1 H

I' igurs 2. Body Shadow Diagram for 25° Viewing Angle.
AZIMUTH

ANGLE 0

IN

DEG.

8

O o o

0) 00 ^

o

q8 dOlOVd 30NVNIWni 1VN0I ±03810 18

o

<£>

Bidirectional Luminance Factors for Concentric Ring Pencil Task - 25° viewing angle.Figure 3.

POLAR

ANGLE

0

IN

DEG.
001

_ o

I o>

J.

Bidirectional Luminance Factors for Concentric Ring Pencil

Background - 25° Viewing Angle.

Figure 4. Task

POLAR

ANGLE

©

IN

DEG.
Figure 5. RQQ5(3) Source Element Angular Coordinates.
H

UJ 2 O LU

cr 2

Figure 6. Strip Luminaire - Element Length vs. Location for Parallel

Viewing. Dashed line denotes body shadow boundary for h = 7 ft

(2.1 m)

.

y axis numbers are locations of ends of elements.

TASK
o

<

z §

UJ CD 2 il

UJ z

-I o UJ o

roX

ro

tro

C\J

CD

Figure 7. Strip Luminaire - Element Length vs. Location for Perpendicular

Viewing. Dashed line denotes body shadow boundary for h=7 ft

(2.1 m)

x axis numbers are locations of ends of elements.
y

16

14

12

10

Figure 8. 3 ft (.91 m) x 3 ft ( . 91 m) Luminaire - Element Size and Number vs Location. Dashed line denotes body shadow boundary for h = 7 ft

(2.1 m)

.

Number pairs are x, y coordinates.
Figure 9 . Typical Room and Luminaire Layout.
y

Figure 10. Lighting Layout Diagram for High Pressure Sodium Installation

(Point Luminaire)

.
E

SOUTH

A

y

T

in

in

JL

in

y

10 .

V

5

'

13

10 9

1

8

-o—2-

5

'

B

Figure 11. Lighting Layout Diagram for Fluorescent Batwing Installation

(Strip Luminaire)
Figure 12. Lighting Layout Diagram for 3x3 Fluorescent Crosslamp Installation

(Square Luminaire)

.
NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 77-1303

2. Gov ’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

A Simplified Procedure for Calculating the Direct

Components of Contrast Rendition Factor and Equivalent

Sphere Illumination

5. Publication Date November 1977

6. Performing Organization Code

7. AUTHOR(S)

Joseph B. Murdoch

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Pro ject/Task/ Work Unit No.

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP) 13. Type of Report & Period Covered

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) A procedure is presented which enables the user to compute the direct components

of contrast rendition factor (CRF) and equivalent sphere illumination (ESI) for an interior lighting design with the aid of a card-programmable hand calculator. The

underlying theory and equations of CRF and ESI are discussed, including a consideration of body shadow, intensity distribution curve interpolations,

bidirectional luminance factor approximating equations and Inverse Square

approximations

The procedure is designed so that the user is a participant in the computations

as they progress and thus is able to modify a lighting design in "midstream" to

improve CRF or ESI. A set of user instructions is included with the calculator

programs

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Body shadow; contrast rendition; hand calculator; Illuminating Engineering; light

design; luminaire effectiveness; luminance factor; office lighting; sphere illumination

18. AVAILABILITY DTI Unlimited

| ! For Official Distribution. Do Not Release to NTIS

Order From Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. C 1 3

Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

74

22. Price

$5-24

USCOMM-DC 2 904 2- P 7 4
KS

-

.

.