NBS BUILDING SCIENCE SERIES 152

A Daylighting Model for

^"ilding Energy Simulation

TA

152

1983

C.2

RTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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NBS BUILDING SCIENCE SERIES 152

Ui;.-- A Daylighting Model for

Building Energy Simulation

Gary Gillette

Research Associate

National Fenestration Council

in collaboration with

Thermal Analysis Group

Building Physics Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored by:

The National Fenestration Council

3310 Harrison Street

Topeka. KS 66611

The U.S. Department of Energy

Buildings Division

1000 Independence Ave., S.W.

Washington, DC 20585

and

«

00 Q

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued March 1983
Library of Congress Catalog Card Number: 83-600513

National Bureau of Standards Building Science Series 152

Natl. Bur. Stand. (U.S.), Bldg. Sci. Ser. 152, 136 pages (Mar. 1983)

CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1983

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $5.00

(Add 25 percent for other than U.S. mailing)
ABSTRACT

A computer model is outlined for estimating the annual energy performance of a daylighted building. The daylighting model is a system of FORTRAN subroutines

designed for inclusion into larger building energy simulation programs such

as DOE-2, BLAST, and NBSLD. Once incorporated into the main energy program,

these subroutines will allow the existing program to account for the energy

tradeoffs associated with natural illumination.

The daylighting model, DALITE , comprises three separate routines to do three

separate functions. The first routine generates hourly sky luminances and sky

illuminances as well as direct sun illuminance, taking solar radiation and sun position data as input. The second predicts interior daylight illumination

at various points within a room due to any number of windows, skylights or clerestories. The last routine adjusts the electric lighting load (via photoelectric controls) in response to the available daylight. Unlike most other

daylighting estimation techniques, this model is a dynamic model designed to

study how conditions change with time. It has a further advantage in that it can be easily installed into most existing energy models written in FORTRAN 77.

Key Words: building computer simulation, building energy performance,

clerestory performance, daylighting, lighting, skylight performance,

window performance.

Cover: Daylight admitted through sloped glazing

in a high-rise office complex.

iii
PREFACE

This report is one of a series documenting NBS research and analysis efforts in

developing energy and cost data to support the Department of Energy/National

Bureau of Standards Measurements Program, The work reported in this document

was performed under the Research Associate Program between the National Fenestration Council and the National Bureau of Standards. The Research Associate

Program was partially supported by the U.S. Department of Energy under the

Building Thermal Envelope Systems and Insulating Materials Program (contract

no. ORNL/PO-22201).

iv
ACKNOWLEDGMENTS

Don Vild, J. W. Griffith, and other members of the NFC Technical Committee

gave valuable direction to the project, as did Dr. Tamami Kusuda, Group Leader

of the Thermal Analysis Group, Buildiiig Physics Division, National Bureau of

Standards, who guided the technical details. The sky measurement assistance

of Stephen Treado, the computer assistance of John Bean, and the lighting

consulting of Ted Hattenburg and Gary Yonemura, all of NBS, contributed

significantly to the success of this project. To all, the author offers his

deepest thanks.

V
Conversion Factors from English to Metric (SI) Units

Physical

Quantity

To Convert From

Customary Units

To SI

Units

Multiply

By

Length ft m 0.3048

Area ft2 m2 0.0929

Energy Btu J 1055

Rt-ii JO U Ll //hrLI L w 0 7931

Illuminance fc Ix 10.76

Irradiance Btu/hr»f t2 W/m2 3.155

Luminance fL nit

(cd/m2)

3.426

vi
TABLE OF CONTENTS

Page

ABSTRACT iii

PREFACE iv

ACKNOWLEDGMENTS v CONVERSION FACTORS FROM ENGLISH TO METRIC (SI) UNITS vi

1. INTRODUCTION 1

2. THE DALITE SUBPROGRAM 3

2.1 CAPABILITIES 3 2.2 INCORPORATING THE SUBPROGRAM INTO AN ENERGY PROGRAM 4

2.2.1 Subprogram Structure 4

2.2.2 Input/Output 8

2.2.3 Reference and Coordinate System 8

2.3 LIMITATIONS 8

3. THE SKYLUM ROUTINE 13

3.1 CAPABILITIES 13

3.2 THE PHASING TECHNIQUE 14

3.3 THE ZENITH LUMINANCE AND LUMINANCE DISTRIBUTION 16

3.4 PREDICTING HORIZONTAL ILLUMINANCE 20

3.5 PREDICTING DIRECT BEAM ILLUMINANCE 20

4. THE RMLITE ROUTINE 25

4.1 CAPABILITIES 25

4.2 PREDICTING INTERIOR DAYLIGHT ILLUMINANCE 26

4.3 PREDICTING ILLUMINANCES FROM PRIMARY LIGHT SOURCES 26

4.3.1 Diffuse Light From Vertical Windows 26

4.3.2 Diffuse Light From Horizontal Skylights 28

4.3.3 Diffuse Light From Clerestories 28

4.4 PREDICTING ILLUMINANCES FROM SECONDARY LIGHT SOURCES 31

4.4.1 Light From External Obstructions 31

4.4.2 Light From Ground and Roof 31

4.4.3 Light Interref lected Within Room 31

4.5 PREDICTING DIRECT SUNLIGHT 34

4.6 MODELING GLAZING TRANSMITTANCE 34

4.7 MODELING OVERHANGS AND SIDE FINS 34

5. THE LLOAD ROUTINE 37

6. VALIDATION 41

6.1 VALIDATION OF THE SKY MODEL 42

6.1.1 Validation of Sky Luminance 42

6.1.2 Validation of Exterior Illuminance 43

6.1.3 Validation of Direct Beam Illuminance 43

6.2 VALIDATION OF THE ROOM ILLUMINANCE MODEL 43

7. CONCLUSIONS 59

vii
TABLE OF CONTENTS (Cont.)

Page

REFERENCES 61

APPENDIX A: DETERMINING EFFECTIVE SKYLIGHT TRANSMITTANCE A-1

APPENDIX B: DESCRIPTION OF VARIABLES B-1

APPENDIX C: SUBROUTINE INTERFACING C-1

APPENDIX D: SAMPLE RUN D-1

APPENDIX E: PROGRAM LISTING E-1

vlli
LIST OF FIGURES

Page

Figure 2.1 The DALITE program as a part of the total energy

analysis 5

Figure 2.2 DALITE subroutine structure 6

Figure 2.3 Building orientation coordinates 8

Figure 2.4 Room and fenestration coordinates 9

Figure 2.5 Fenestration coordinates for a clerestory 10

Figure 2.6 Surface coordinates 11

Figure 3.1 Curve used to obtain intermediate sky luminance as a function of cloud ratio 15

Figure 3.2 Sky dome with angles used in the sky luminance equations .. 17

Figure 3.3 Clear sky zenith luminance as a function of solar

altitude 19

Figure 3.4 Diffuse illuminance as a function of diffuse solar

radiation 21

Figure 3.5 Total illuminance as a function of total solar radiation .. 22

Figure 4.1 Predicting the interior illuminance Ep at point p 27

Figure 4.2 Geometric configurations for equations 4.2-4.4 29

Figure 4.3 Clerestory illuminance technique 30

Figure 4.4 Light from external obstructing buildings 32

Figure 4.5 Sunlight projection within room 35

Figure 5.1 Task/ ambient and general lighting layouts as viewed by

program 39

Figure 5.2 Dimming curve of luminare dimming system 40

ix
LIST OF FIGURES (Cont.)

Page

Figure 6,1 Measured sky luminance versus calculated luminance using

the clear sky distribution model 45

Figure 6.2 Measured sky luminance verses calculated luminance using

the overcast sky distribution model 46

Figure 6.3 Measured zenith sky luminance verses calculated luminance

using the clear sky zenith model 47

Figure 6.4 Measured zenith sky luminance verses calculated luminance

using the overcast sky zenith model 48

Figure 6.5 Measured horizontal illuminance verses calculated

illuminance using the sky Illuminance model for all sky

types 49

Figure 6.6 Comparison of measured sunlight illuminance with predicted

illuminance of direct sunlight > 50

Figure 6.7 Description of scale model test rooms 51

Figure 6.8 Description of full scale test rooms 52

Figure 6.9 Hourly Interior daylight illumination for an overcast day

in room no. 1 53

Figure 6.10 Hourly interior daylight illumination for a partly cloudy

day in room no. 1 >. 54

Figure 6.11 Hourly interior daylight illumination for a clear day in

room no. 2 55

Figure 6.12 Hourly interior daylight illumination for several sky

conditions in room no. 3 56

Figure 6.13 Collective plot of measured versus calculated interior

illumination in room no. 4 58

Figure A.l Well efficiency as a function of a well index and well

reflectance A-3

Figure B.l Input/output array B-7

Figure B.2 Room coordinates defined with respect to glazing surface

in IRL subroutine B-8

X
LIST OF FIGURES (cont.)

Page

Figure B.3 Wall surface variables used internally in the DALITE

program B-9

Figure B.4 Surface numbering sequence and clerestory reference

variables B-10

Figure B.5 Clerestory coordinates B-11

Figure B.6 Sun projection variables for skylights B-12

Figure C.l Program interfacing C-2

Figure C.2 Input variable specifications for room and sky data C-3

Figure C.3 Input variable specifications for fenestration data C-4

Figure C.4 Output variable specifications C-5

Figure D.l Sample building D-2

Figure D.2 Input from main energy simulation program D-3

Figure D.3 DALITE input snapshot for a specified hour D-4

Figure D.4 DALITE output snapshot for a specified hour D-5

Figure D.5 Main program output for a day showing the daylighting

impact on the building loads D-6

Figure E.l Block diagram for predicting hourly daylight E-2

Figure E.2 Block diagram for predicting sky conditions E-9

Figure E.3 Block diagram for predicting room daylight conditions E-16

Figure E.4 Block diagram for predicting elecf-.rtc lighting load E-30

xi
Facing page: Daylighting from continuous

skylights in an office mall

xii
1 . INTRODUCTION

With the renewed interest in energy conservation in general, and with

daylighting in particular, many in the building profession have become interested in how daylighting impacts the energy performance of a building over

time. This interest extends beyond simple daylighting design calculations by

including the impact of daylighting strategies on the building lighting,

heating, and cooling requirements. The goal has become annual energy consumption not illumination at one point in time. Only since the recent introduction

of computers into the building industry, has it been possible to perform an annual energy analyses with any substantial degree of certainty. Today many

computer programs exist for estimating energy use in buildings. Among the

1
best known public domain programs are DOE-2 [1], BLAST [2], and NBSLD [3]; not

to mention the host of proprietary programs currently in use [4]. These programs consider most of the major transient energy parameters in buildings.

Some are more rigorous than others, and each has its strengths and weaknesses,

but few have an integrated daylighting model sufficient for existing

daylighting practice.

While there are also computer programs developed exclusively for daylighting

analysis, these are designed for rigorous yet static design conditions and are normally too time consuming to be used repetitively for energy studies. In

this category are such lighting programs as LUMEN II [5], SUPERLIGHT [6], and

CEL-1 [7], which are useful programs for those interested in a careful evaluation of an illuminated space, but are much too rigorous for execution each

daylight hour of the year. They also share in a common weakness as far as building energy simulation programs are concerned in that they study only

standard sky conditions and are not designed to be responsive to changing

weather conditions.

In the following pages, a daylighting model is offered which is specifically

designed for use in large-scale building simulation programs. It has been

prepared as a set of subroutines that can be incorporated into existing programs with a minimum of effort. The subroutines are short, concise, and com- putationally fast (normally causing under ten percent of the total CPU time for

a full daylighting analysis). They should be compatible with most computer

programs currently written in FORTRAN 77, and with only slight modifications

could also be revised into FORTRAN IV. In fact, the daylighting algorithms are small enough to put into a micro-computer provided it has a FORTRAN compiler.

Facing page: The sky hemisphere under partly

cloudy conditions
2. THE DALITE SUBPROGRAM

2.1 CAPABILITIES

The DALITE subprogram is unique in that it comes as a package, a group» of small

subroutines, which can be incorporated into most existing building simulation

programs. Unlike most other daylighting models, its small packaged form

enables it to be fully integrated into a larger building simulation program

without requiring excessive computation time. In this way, hourly daylighting

analyses can be done simulataneously with the thermal calculations, allowing

an assessment of the overall energy impact of daylighting.

3
The DALITE package is streamlined to be computationally fast and computes only

those elements that contribute significantly to the energy performance of the

building. While being a simplified model, it is still flexible in its ability

to simulate a range of fenestration scenerios - windows, skylights, clerestories,

roof monitors, overhangs, sidefins, and almost any combination of these. The

subprogram is also fairly even-handed in that it does not concentrate computation time on a few noncritical calculations at the expense of others. For

instance, the interref lection model is flexible for use with both sidelighting

and toplighting, yet avoids rigorous interflux calculations.

The sky subroutine deals with a continuous range of sky conditions, not just

clear or overcast, and needs only the instantaneous solar radiation and sun position as input. From this internally generated availability data, another

subroutine estimates the reflected light from surrounding buildings, light from

the sky dome, reflected ground light, and internally reflected light. The

direct beam illuminance, as a rhomboidal patch of sunlight on the workplane, is

also simulated for each aperture that has sunlight falling on it. Thus, the

package is capable of performing all critical daylighting/energy calculations,

and utilizes information in the existing building simulation program to perform

the daylighting analysis.

2.2 INCORPORATING THE SUBPROGRAM INTO AN ENERGY PROGRAM

Although the DALITE subprogram is a complete package and can be prepared as a stand-alone program, its intended purpose is for use as a subroutine package in

other energy simulation programs. DALITE and its three subordinate subroutines

should be executed as a part of the hourly building load calculations as shown

in figure 2.1. From the programmer's point of view, incorporation requires

only input/output preparation through a single two-dimensional array (see

Appendix B) . The instantaneous electric light load and heat-of-lights given as output can be fed into the hourly load compilaton along with the other thermal

loads, which are totalled for each zone and sent on to the system and plant

compilations to give the total annual energy (see Appendix C)

.

2.2.1 Subprogram Structure

The DALITE subprogram comprises a sky model (SKYLUM), an interior daylight

model (RMLITE), and a lighting load model (LLOAD) , each as a separate subroutine. Figure 2.2 illustrates the subroutine structure. DALITE is the

master routine coordinating the data from the subroutines and prepares the

input/output information. It acts as an interface between the individual

components and the main energy program. DALITE is executed only once each

daytime hour for any given room but the SKYLUM and RMLITE subroutines are executed, respectively, for each fenestration aperture and for each sensor

position. LLOAD is executed once for each sensor each hour. To streamline

the program further, the repetitive calculations in the RMLITE model are suppressed once the geometry coefficients have been computed and these

coefficients are used each repeated hour, greatly increasing the speed of

the program.

4
INPUT:

WEATHER

4r

BUILDING

CO

CO

>-CO

g Solar gains

g Conduction gains/losses

-* Thermal mass

Infiltration

Ventilation

Equipment

People

^

Lighting

DALITE

Heat from lights

^OUTPUT:

ANNUAL ENERGY

Figure 2.1 The DALITE program as a part of the total

energy analysis process
TO

no ^o

CO o U- o

00

C/5 ^ Ll. U- o o

QQ OQ

O

TO

O o

00

CO

— o

>-00

COTOo E i o »^

it

.M 2 O

a» o

03 = TO

to c c: X

CO

0)3

j-i O3

»^

j-i w

<u •H

4-1 3O3

CO wH

CM

CM

<u

9-1 3

bO

•H 6
2.2.2 Input /Output

Input is requested by the main energy program internally at two points during

execution of the program: 1) during initialization when the main program is

defining building information that remains constant throughout the analysis,

and 2) during each repetitive execution when the sky and other conditions

change (see Appendix C) . A single array is used for storing input and output

(I/O) information. The array is sized through parameter statements in the main

program to accommodate an arbiturary number of fenestration apertures and

dimmer/switch controls. In this way, for a larger (or smaller) capacity of

either, adjustments can be made in the array size and the limits on the doloops. Details of array element assignments are delineated in Appendix C.

2.2.3 Reference and Coordinate Systems

The DALITE routine has its own reference and coordinate systems which positions

the building and the sun on the building site, positions the photo sensors in

the room, and positions the fenestration on the walls or ceiling. Each

reference system is briefly discussed below.

The coordinates of the building's orientation are shown in figure 2.3.

Buildings oriented off the north/south axis (as shown) have an azimuth angle

correction AZM, where AZM is in degrees clockwise from north. The sun angles

SUNAZ and SUNALT are also input in degrees, and are the solar azimuth clockwise

from north and solar altitude above the horizon, respectively.

Figures 2.4 and 2.5 illustrate the coordinates used to locate sensor positions

and the fenestration. The coordinates of the room and the coordinates of each

wall are always referenced to the lower left-hand corner of the plane. For

example, to locate a window on a wall, the lower left-hand corner of the window

is referenced to the lower left-hand corner of the wall as viewed externally.

Skylights and clerestories are located on the ceiling in a similar way. It is

important to note that coordinates of each surface, including the floor, are specified in either the height, width or length directions as represented in

figure 2.6.

2.3 LIMITATIONS

As is characteristic of any prediction procedure, the daylighting model has

limitations. Although the ceiling plane is allowed to be sloped, the room plan

is otherwise assumed to be rectangular, meaning that the program cannot simulate interref lections in L-shaped or other non-rectangular geometries. A

warning might be made here that when simulating room geometries with depth-toheight ratios greater than two or three to one, interref lected light should not

be computed, since the validity of the assumptions used to determine interf lected light is questionable at such room depths. There are also unique types

of fenestration designs that cannot be sufficiently represented such as light

shelves and domes. However, with wisdom in making the right assumptions these

too can be done by approximation and should not be considered a severe weakness; most thermal models do not accurately account for such configurations

either. When novel or complex fenestration designs are to be analyzed, a

7

WORK PLANE - 2.5 ft ^ ABOVE FLOOR

SENSOR

POSITION #1

SENSOR

POSITION

#2

RMW

Figure 2.4 Room and fenestration coordinates

9
(SOUTHWEST CORNER OF ROOM]

Figure 2.5 Fenestration coordinates for a clerestory

10
\AZM

o

i —J

t

i Wi

1—

>

1 . U|

-SKYLIGHT OR CLERESTORY

CAN ALSO REPRESENT THE

POSITION OF PHOTOCELL

WITHIN ROOM!

LENGTH DIRECTION

al FOR CEILINGS AND FLOORS

WINDOW

HiXZt

Wi

WIDTH DIRECTION*-

b] FOR WALL SURFACES

Figure 2.6 Surface coordinates
possible option Is to determine the geometric daylight coefficients (see

section 2.2.1) apart from the DALITE program using either physical models or manual calculations, and assuming these as constants, simulate the sky and

building load Interfacing using the remaining dayllghtlng algorithms. Great

flexibility can be achieved In this way, with the limits being only the extent

at which such coefficients can be obtained.

Glare Is not modeled explicitly, but this Is Intentional. DALITE seeks to

simulate the photoelectric control response to changing dayllghtlng conditions,

not the user response to those conditions. While It Is true that a relationship probably exists between the two, a valid correlation can only be assumed

If building occupants respond to a glare problem by applying or adjusting a glare or sun control device, which In turn adjusts the effective transmlttance

of the fenestration. Since such adjustments are normally modeled as a part of

the existing loads program. It Is necessary only to replace the specified

transmlttance with an hourly adjusted value before the call statement to the

DALITE subroutine Is given.

Another possible limitation may be found In the model's assumption that the rooms are empty. Internal obstructions such as furniture and occupants are

not considered as contrlbuters In the lighting calculations even though they

do contribute to the thermal latent and sensible loads. Since the dayllghtlng

model was developed as a streamlined program, such capabilities were not

considered essential.

Facing page: Measuring the sky luminance

at selected positions in

the sky.

12
3. THE SKYLUM ROUTINE

3.1 CAPABILITIES

Since the weather data normally used in building energy programs do not include

hourly exterior daylight, such values are generated internally from the available values of solar radiation and sun position. Total and diffuse solar

radiation incident upon a horizontal surface, values that are normally computed

within the larger existing programs, are used to determine the sky conditions.

From this hourly information the sky luminances as seen through each window

or skylight are calculated. The intensity of the direct sun and the total

illuminance on a horizontal plane is also determined.

13
Obtaining hourly solar data in any form is a complex issue. For the relatively

few locations in North America where hourly values of total horizontal and

direct normal solar radiation are recorded, such data can be easily accessed.

But for cities where only TRY (Test Reference Year) data are available, the

hourly solar radiation must be generated internally using a calculation procedure such as developed by Liu and Jordan [8], Stevenson and Kimura [9], or others [10]. When the more common TRY weather tapes are used, the only hourly

sky information provided is a visual (subjective) assessment of the cloud

conditions, specified in terms of a cloud cover value and the type of cloud in

four different layers. Even when TMY (Typical Meteorological Year) weather

tapes or other solar data are used the data itself is normally incomplete and

is interpolated for a complete hourly file. Therefore, due to the nature of

the input data alone, the sky model carries a degree of uncertainty. The

SKYLUM routine assumes that the following solar data are accessible by the

time the DALITE subroutine is called: 1) sun altitudes and azimuth, 2) total

horizontal solar radiation, and 3) the ratio of diffuse to total horizontal

solar radiation. .The instantaneous solar altitude and azimuth are used to

determine the zenith clear sky luminance; the horizontal solar radiation is

used to derive the horizontal illuminance and the overcast sky luminance; the

ratio of the diffuse to total radiation (denoted as the cloud ratio, CR hereafter) is used to determine intermediate partly cloudy sky condition. This

latter term is discussed in more detail below.

3.2 THE PHASING TECHNIQUE

To capture the variable nature of the sky as it changes with time, a continuous

phasing technique is employed. Since skies are often neither perfectly clear

nor perfectly overcast, a weighted averaging is done hourly between the two

extremes based on the cloud ratio CR described above. The process requires an initial determination of the sky luminance as seen through the fenestration

under the clear and overcast conditions, and a phasing technique is done

between the two conditions to get the intermediate value actually used as shown

in figure 3.1. The intermediate sky luminance at point P thus becomes,

~ ^clr^^p ) ^ovr (^p ) ovr ^ovr

or

Lp = Cclr(Lp ) + (l-Cclr)(Lp ) (3.1)

clr ovr

where,

^clr ~ clear sky fraction

Ko^/x = the overcast sky fraction

Lp = the clear sky luminance

clr

Lp = the overcast sky luminance,

' ovr

14
15
Due to the nature of the CR, a sinusoidal curve was used to interface between

sky luminance values. This curve gives expressions for ^cj^j- and ^ovr

r = 1 + COS (CR*tt) (3.2)

^clr 9

and

^ovr

= 1 - COS (CR*tt) (3.3)

which provides the slightly biased weighted average in favor of either of the

clear or overcast sky condition. It should be pointed out, however, that

equations 3.2 and 3.3 do not generate the percentage of the sky in clouds, but

rather estimate a weighted average luminance; the cosine curve is this weighting function. From sky measurements it has been noted that cloud ratios of

about 0.20 and below are effectively clear skies with possibly only a slight

haze present. Likewise, it appears that the blue sky is no longer present

after the cloud ratio exceeds about 0.80. The cosine function is simply an

•attempt at capturing this natural bias toward the extremes.

3.3 THE ZENITH LUMINANCE AND LUMINANCE DISTRIBUTION

For the clear sky luminance at point P in the sky, Kittler's luminance

distribution equation [11] is used,

T _ T (1-e " O-32/sin0) (q^^^ + lOe"^^ + 0.4 5cos^ if;) ,n ^p clr - clr — _o/'^/9_v,\ o ^ U.^;

0.274 (0.91 + lOe ^^^'"^ + 0.45 sin^ h)

where the radian angles 9, \\), and h are given in figure 3.2. The zenith sky

luminance L2 clr perfectly clear sky conditions is given by the equation

L2 ^-^j. ^ + h^ (k cd/m2) (3.5)

where

,

h = the solar altitude in degrees

aQ, ai = atmospheric coefficients as found in table 1.

The coefficients ag and a^ are from Dogniaux [12] with the coefficients for the

h^ term excluded since their contribution is insignificant for this type of

application. The values for the AngstrOm turbidity coefficient 3 and the

precipitable water u, while not normally available, can be approximated using

the classification shown in table 1 (also from Dogniaux). Reference is made

to Linke [13] and Nagel [14] for the relationship between p and o) and other

atmospheric factors.

Figure 3.3 shows a plot of the NBS sky measurements [15] of clear sky zenith

luminance along with curves for the upper and lower limits of equation 3.5.

16
Lp = SKY LUMINANCE AT POINT p

h - SOLAR ALTITUDE

e = ALTITUDE OF POINT IN THE SKY

^ = GREAT CIRCLE ANGLE BETWEEN

SUN AND POINT

Figure 3.2 Sky dome with angles used in the sky luminance equations

(angles in radians)

17
Table 1. Atmospheric Coefficients According to Dogniauxl^^]

(Excluding Term)

Dry Air

(Desert

Climate)

Humid Air

(Tropical

Climate)

Rural Region

B = 0.05

Urban Region

3 = 0.10

Industrial Region

6 = 0.20

^o ^1 ^o ^1 ao ^1

to - 0.5 0.9361 0.0020 1.0329 0.0024 1.1399 0.0030

0) = 1.0 0.9093 0.0018 1.0206 0.0022 1.1499 0.0028

(1) = 2.0 0.8727 0.0014 1.0074 0.0019 1.1698 0.0025

w

= 3.0 0.8547 0.0012 1.0019 0.0017 1.1833 0.0023

u

= 4.0 0.8460 0.0011 0.999 0.0016 1.1899 0.0022

0) = 5.0 0.8410 0.0011 0.998 0.0016 1.1968 0.0021

* w given in centimeters of water

The data is bias toward the lower curve, which is to be expected since the NBS

measurement station is in a semi-rural area where the air tends to be somewhat

humid. This is confirmed by measurements taken 60 years ago in the same area

[16].

The overcast luminance distribution model is based on the simplified Moon and

Spencer model [17],

= L ( 1+2 sin 9 ) ovr Z ovr q (3.6)

If this equation is integrated across the sky dome to obtain horizontal

illuminance Ey^ from the overcast hemisphere, the resultant integration can be

solved for the luminance at angle 6 as,

L„ = 3_ E (1+2 sin 9)

9 7^ vt (3.7)

for which the zenith luminance becomes.

L = ?_ E

z 7^ vt (3.8)

Equations 3.6 and 3.8 are, therefore, combined to provide Lp q^j- as a direct

function of E^^ under overcast conditions. This approach provides a substantially improved correlation with sky measurements (see chapter 6 on Validation)

when compared to methods proposed by others.

18
19
3.4 PREDICTING HORIZONTAL ILLUMINANCE

Total and diffuse horizontal illuminance is obtained directly from knowledge

of the total and diffuse solar radiation provided from the main program. Here

a luminous efficacy approach is taken. Two equations are used,

Evd = 111 Eed (3.9)

and

E^t = (93 + 18 CR)Eet (3.10)

where

Eyd = diffuse horizontal illuminance (lux);

Ey^ = total (global) horizontal illuminance (lux);

o Eg^ = diffuse horizontal solar radiation (W/m );

Egj. = total (global) horizontal solar radiation (W/m ); and

CR = !ed

Eet

Equations 3.9 and 3.10 were also developed from the NBS measurements shown in

figures 3.4 and 3.5. While it is possible to correlate Ey^ with Eg^ using

a single efficiacy value (figure 3.5), it is more useful to express E^^ also in

terms of the cloud ratio, which gives a smooth, continuous transition into

equation 3.8 for CR = 1.00 (where Ey^j = Ey^) while also covering more of the

range seen in figure 3.5.

3.5 PREDICTING DIRECT BEAM ILLUMINANCE

For predicting the intensity of the direct normal sunlight the following

equation is used.

^DN ^v SC

1 + 0.033COS f X J

(

360 j\

365

;

-a/sin h

e (3.11)

where

Epfj = the direct normal beam illuminance;

^v SC ~ solar illuminance constant;

J = the Julian date, from J=l to J=365;

a = the atmospheric extinction coefficient; and

h = solar altitude.

20
CO

l-i COO

C/3

•Hco

4-1 oc3

<4-i

CO3

bO

21
22
The value for the mean extraterrestrial illiamlnance , , was obtained by

integrating the ASTM [18] standard spectral irradiance as follows:

760

Ev SC = % / Egx dx (3.12)

380

where

K]yj = the lES standard maximum spectral luminous efficiency, 683 Im/W [19];

= the lES standard spectral photopic eye response; and

EeX ~ ASTM standard spectral irradiance for the wavelength band, d;^.

The resultant value,

Ev SC = 127.5 klx

can be thought of as the daylighting equivalent of the solar constant, 1353

w/m^. Measurements made both at NBS and elsewhere [20, 21] of the direct beam

illuminance (figure 3.8) have been used to determine an average extinction

coefficient for equation 3.7 of a == 0.210 for an unobstructed sun.

Others have measured the intensity of the direct beam with similar results [22].

Jones and Condit [20] extrapolated the Kimball and Hand data [16] to derive a zenith sun illuminance of 104.9 klx for the average condition between December

and June sun. Moon [23] has also proposed a zenith value, which, when revised

to agree with the currently recommended Kj^j, gives Eqj^ = 108.1 klx. From equation 3.7 the predicted mean illuminance is 105.3 klx, which agrees with Jones

and Condit by within one percent and with Moon by within three percent. Similarly, Elvegard and Sjbstedt [24] fit a curve through their Swedish and

Finnish data and reported a constant extinction coefficient of 0.231, a value

that would cause the direct" solar illuminance to be only slightly lower than

predicted for equation 3.10.

The final form of the equation, therefore, for the instantaneous sun illuminance

on a horizontal plane becomes,

Evs ^ Eqjj • sin h • (3.13)

where,

Eyg = the horizontal solar illuminance;

?clr ~ clear sky fraction (see Section 3.2).

The sin h term corrects for the flux on the horizontal plane, and C^lr corrects

for the loss in intensity due to partly cloudy conditions.

23
Facing page: Measuring the interior daylight

illuminance within a room.

24
4. THE RMLITE ROUTINE

4.1 CAPABILITIES

RMLITE computes the Interior illuminances on a horizontal workplane 0.76 m

(2.5 ft) above the floor. The cumulative effect of multiple windows o. skylights is recorded to give illuminances at user selected points within the

room. It should be noted, however, that this routine is room specific and

surface specific, meaning that the fenestration must be on one of the room

surfaces, and that the illuminance positions must be within a defined room configuration. In some energy programs this might cause problems. For cases where the main energy program is not room specific, simplifications are possible in the RMLITE routine. This is discussed further under Subroutine

Interfacing (Appendix C).

25
4.2 PREDICTING INTERIOR DAYLIGHT ILLUMINANCES

The interior daylight prediction technique is a simplified radiant flux

procedure. The fenestration, room surfaces, and exterior surroundings are divided into sufficiently small surface elements where each element is either

a primary or secondary source of light with a luminous exitance M*. In the

most general case, the expression is:

Ep = 1 / / M cos e cos ^ df dm (^-D

^ TT f m jj2

for the illuminance Ep from direct light sources above the workplane such as the portion of sky viewed through the fenestration (figure 4.1).

Equation 4.1 can also be used to compute the illuminances on the interior

surfaces, which then become sources of secondary or reflected light. The more

rigorous lighting computer programs generally make extensive use of radiant

transfer [25] to obtain a much more refined solution, but such rigor is not

necessary for this type of analysis.

Simplification can be done if the integration is made for generic types of

geometric configurations. Using the integrated equations of Higbie [26], and

more recently Pierpoint and Hopkins [27], a direct solution can be achieved for

equation 4.1 provided the luminance of the surface is assumed uniform. Furthermore, subdividing the room and fenestration surfaces into a minimum number of

surfaces further reduces the number of computations. Both strategies are used

by the RMLITE routine and, as will be shown, provide a fast, yet in most cases sufficiently accurate daylighting algorithm.

4.3 PREDICTING ILLUMINANCES FROM PRIMARY LIGHT SOURCES

4.3.1 Diffuse Light From Vertical Windows

For the diffuse illuminance from the sky on a horizontal surface due to a vertical window, Higbie 's perpendicular surface geometry equation is used.

Ep = L

^ 2 tan-1 m _ / a \ tan"! I ^ \ (4.2)

where,

Ep = workplane illuminance at point p;

L = centroid luminance of sky patch seen through opening mf; and

a,m,f = distances as shown in figure 4. 2. a.

* Luminous exitance can be assumed equal to source luminance if an approximate

lambertian surface is assumed; if so, M = tt L, where L is the source luminance.

26
Figure 4.1 Predicting the interior illuminance Ep at point p

27
Ep is given in lux when a, m, and f are in meters and L in nits (cd/m ); Ep is

in footcandles when a, m, and f are in feet and L in f ootlamberts . Lastly,

superposition is used to locate this surface element anywhere on the wall.

4.3.2 Diffuse Light From Horizontal Skylights

For the diffuse illuminance from the sky on a horizontal surface due to a horizontal skylight, Higbie's parallel surface geometry equation is used,

'

2 L/c^ -H (a-f)^ V/c^ + (a-f)^ jj

where the geometry is shown in figure 4.2.b.

The skylight luminance L deserves a special note. For the skylight units with

both transparent inner and outer glazing, L is the centroid sky luminance. However, when either outer or inner glazing is translucent, which is normally the

case, L becomes the total exterior horizontal exterior illuminance E^t (from

sun and sky) multiplied by the net transmittance. The net transmittance

includes the transmittance of both glazings, the dome effects, and the wall

effects; it can be obtained from Appendix A [28].

4.3.3 Diffuse Light From Clerestories

The direct skylight admitted through the vertical glazing in a clerestory is

treated as if coming from a remote vertical window (see 4.3.1), except that

checks are made for those illuminance points along the workplane that would be

obstructed from view of the clerestory fenestration (figure 4.3). The reflected

light from roof and the sky onto the sloped clerestory ceiling is modeled using

the Pierpoint and Hopkins equation.

Ep = L

^ 2

where

,

X tan

-1 m + z' x^ + y^ + z^

f cos ij^ - X

/x2 + z2 + f 2 + 2fG

tan

-1

ym

m A'^ + + f'^ + 2fG

:2 + y2 + z2 - ym + f 2 + 2fG

_Z_££|4 -1 f /y2 + H^ tan

/y^ + H2 y2 + h2 + g2 + fc

- Cy - m) cos tan"^ f /(y - m)^ + H^

/(y - m)^ + H'^ (y - m)2 + h2 + g2 + fG

(4.4)

and

G = z sin ij; - X cos ^

H = z cos il' + X sin

The geometry is illustrated in figure 4.2.c. The luminance in this case is the

centroid exitance of the surface, found by the product of the ceiling

reflectance and the illuminance at the ceiling centroid.

28
RIGNT ANGLED SURFACE GEOMETRY

(UNIFORM LUMINANCE)

Figure 4. 2.

a

PARALLa SURFACE GEOMETRY

(UNIFORM LUMINANCE)

Figure 4.2.b

Figure 4.2.c

Figure 4.2 Geometric configurations for equations 4.2 - 4.4

29
REFLECTED LIGHT

OF CLERESTORY

CEILING

LIGHT FROM

THE SKY

REFLECTED LIGHT

OFF ROOF

CLERESTORY

SENSOR VIEWING

THE SKY

i

L SKY VIEW CUT OFF LINE

SENSOR NOT

VIEWING THE SKY

<L WORK PLANE

^77777}

Figure 4.3 Clerestory illuminance technique

30
4.4 PREDICTING ILLUMINANCES FROM SECONDARY LIGHT SOURCES

4.4.1 Light From External Obstructions

External obstructions, such as surrounding buildings, are modeled as diffuse

light, sources with a uniform luminance. This luminance is obtained by multiplying the sky luminance for that obstructed region of the sky by the obstruction reflectance p^* Geometrically, the obstructions are assumed to be simple

vertical projections above the workplane running continuously in the horizontal

direction (figure 4.4). It is possible to simulate external obstructions in a more rigorous way, yet because actual size and surface reflectance are rarely

(if ever) known, it would be difficult to justify the increased complexity.

4.4.2 Light From the Ground

The ground reflected light is found by first obtaining the uniform ground

luminance, which is the product of the total horizontal illuminance, E^j- , and

the ground reflectance. Assuming that the ground surface is an infinite horizontal plane, the parallel surface equation is used to project ground light

onto interior horizontal surfaces (the ceiling for example); the perpendicular

surface equation is similarly used for vertical wall surfaces.

Light reflected off the roof onto the sloped clerestory ceiling surface is

treated in like manner. Here the Pierpoint and Hopkins equation is used to

obtain the illuminance at the center of the interior sloped surface due to the

sky and the roof, which in turn, is then reflected into the room.

4.4.3 Light Interreflected Within Room

The multiple reflections and interref lections of light flux within a room is

normally the most time consuming part of the most large lighting programs.

Analytically, it is the most complex. Not only must equation 4.1 be applied

for each incremental area within the room due to each source of light, but this

must be done repetitively as these areas illuminate to become themselves

sources of secondary light. Yet such an approach is necessary only if a rigorous solution is sought.

A simpler technique is to subdivide the room into only a few surfaces, such as the six enclosure surfaces. Obviously, averaging the luminance over these

larger surfaces will be a less exact procedure. However, the fraction of the

total illuminance due to interref lected light is normally quite low, thus,

minimizing the impact on the total illuminance at a given point. Furthermore,

due to uncertainties in the correct values for hemispherical-directional

reflectance, and noting that internal obstructions on the walls and within the

room normally exist, it is difficult to justify substantial time on the

interflected light calculation.

In some ways the interref lected model used in RMLITE is similar to the split

flux method [29, 30] which subdivides the room into two hemispherical elements,

but overcomes one of its weaknesses by being more general and applicable to rooms with fenestration other than windows. The six surface model should also

31
Px = OBSTRUCTION REFLECTANCE

Figure 4.4 Light from external obstructing buildings

32
be slightly more accurate. Once the initial light flux is determined on each

of the six surfaces, multiple interref lections are accounted for by assuming

the room acts as an Ulbricht integrating sphere, an assumption that is valid

for wall reflectances approaching the ceiling reflectance and room depths less

than twice the ceiling height.

Dressier [31] found that if the wall surfaces act as diffuse lambertian

reflectors, then the first reflected flux within the room can be expressed as,

SFi = Fipi + F2P2 + + FnPn (4.5)

where F^ is the initial flux on surface n, is its diffuse reflectance, and

EFj^ is the sum of the first reflected flux. The multiple reflected flux then

becomes

,

EF • ZFid + Pave + Pave^ + Pave^ + ) = jz—— " ^^'^^ ^ave

Since the illuminance of the Ulbricht sphere is total flux over the total area,

the interref lected illuminance becomes,

_ (F^Pi -h F2P2 + F3P3 + + F^p^) + F^pf

^ref 7~, T";: (4.7)

(1-Pave> \

where

Fj^ = En (for each room surface)

~ ^s

^ (for the projected sunlight)

pf = the reflectance of the floor

Pave ~ average reflectance of all surfaces

= the total area of all surfaces

Aj^ = the area of surface n

Ag = the area of the sun patch rhomboid

= the centroid illuminance of surface n

Eg = the sun patch illuminance from equation 3.13.

The initial centroid illuminance E^ for each surface is found by equations 4.2

through 4.4.

By letting n = 6 and solving equation 4.5, the inter-reflected daylight is

obtained in a fraction of the time it would require other more rigorous models

4.5 PREDICTING DIRECT SUNLIGHT

The model to determine the contribution of direct sunlight is fairly

straightforward. The rhomboidal projection of the fenestration on the workplane is first determined and a check is made whether an illuminance point is

within one of these patches of sunlight (figure 4.5). If so, the direct beam

illuminance Eg is added to the existing workplane illuminance, after being

corrected for glazing angle transmittance and cosine angle between the workplane and the sun.

33
4.6 MODELING GLAZING TRANSMITTANCE

There are two types of glazing transmit tance used, the angular dependent

transmittance , tj), for direct sunlight, and the hemispherical transmittance t^,

for diffuse sky light. For flat fenestration the latter is assumed constant.

The former, xj), varies with the angle between the surface normal and the sun

angle, \|;, according to the expression [32] ,

= 1.018 Tq cos il; (1 + sin^ ^\)) (4.8)

where Tq is the visible transmittance value normally obtained from manufacturer'

data.

For domed skylights, the curvature of the upper dome has been found to affect

the transmittance of both the direct and diffuse daylight [33]. Although the

aspect ratio of the dome, incident angle, and variations in thickness of the

glazing material will cause variations in the direct transmittance, td, the

range is within approximately 10 percent of Tq for solar altitudes above 20

degrees [28]. Thus, a single value is used for the direct transmittance. On

the other hand, requires correction for well losses, which combine to give a single effective transmittance, x^ff. While it is possible to incorporate all

the transmittance correction factors into the computer model, it is far easier

and probably more practical to allow this value to be computed externally (see

Appendix A)

.

4.7 MODELING OVERHANGS AND SIDE FINS

Overhangs and side fins are accounted for by adjusting the effective window

area according to the viewing obstruction angle. For overhangs, an effective

window height is computed and used as if this were the actual height. Similarly, side fins adjust the window width to provide an effective window size

as seen by point p. Since each correction is specific to the illuminance point

under consideration, these adjustments are done for each point.

34
SUNLIGHT PROJECTION

ON THE WORK PLANE

PLAN

VIEW

Figure 4.5 Sunlight projection within room

35
Facing page: Supplementing daylight ing with

incandescent sources to provide

a constant illuminance level.

36
5. THE LLOAD ROUTINE

Once the illuminance is obtained at a point within the room, it is the lighting

load routine LLOAD which developes an associated power load for use in the main

building energy program. But a note should be made here. The daylight illuminance at a position on the workplane means nothing in terms of energy unless

some type of control system recognizes this intensity and can respond by

changing the power requirement of the lighting system. This is usually accom- plished through the use of a photocell. The response strategy could be either

switching or dimming; and the lighting system sensitive to this point illuminance could be a single luminaire, a bank of luminal res , or all the luminaires

within the room. Since photocells are normally not located on the workplane.

37
it Is Important to explain that the lighting system must be balanced once installed to meet a specified workplane Illuminance and, therefore, the point

where balancing is done becomes the illuminance point.

The LLOAD subroutine is not a lighting design tool but an analysis tool.

Information must be supplied to the program stating the full lighting power load

controlled by each photocell. On so doing, a completely general model is provided for modeling almost any type of lighting layout. Figure 5.1 will help

explain this. Ambient and task lighting is shown where three illuminance points

control three banks of general illumination, and one controls a task luminaire.

As far as the daylighting model is concerned, the only important information

necessary is the position directly below the photocell, the full connected

power which will respond to the sensor, the setpoint illuminance, and the

dimming strategy.

Four dimming strategies are offered. A simple on/off strategy shuts the

connected power off once the setpoint illuminance is met by daylight. The

second strategy, half-on/half-of f step-down, shuts off half the connected power

at half the prescribed illuminance, and the remainder after this illuminance is

exceeded. The third strategy is a continuous dimming technique where the power

is proportionally adjusted to follow a typical performance curve [34,35], but

remains at the minimum power level when supplemental light is no longer necessary. The fourth is similar to the third except it allows the luminaires to

shut off completely once the minimum power is reached. The continuous dimming

strategies assume a simple linear relation between the percent supplemental

light, %Eg^p , and the percent power required, %Wj.gq

,

%Wreq = ^ (^Eg^p) + x (5.1)

where ^ and x ^re specified lighting control coefficients. If such

coefficients are not available, the following default values are assumed for a generic system.

? = 0.70

X = 0.30.

Equation 5.1 is a simplified expression representing the generic curve for the

dimming performance of a fluorescent ballast system (figure 5.2). For other

types of lamp systems, such as high pressure sodium, appropriate values for

5 and X can be substituted.

38
Figure 5.1 Task/ambient and general lighting layouts as viewed by

program

39
I

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CO COo

Q)

M

4J CO CO ?

>^

CO U-lo G CO •H 1) SB

•r-1 ,^

01

u

CO

CO rH

•H S i CO 3

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Caption: Validation measurements within a full scale room

6 . VALIDATIO^J

Inherent in any prediction technique is the need for validation against

real-case conditions. Although it is sometimes possible to show a sufficient

correlation by simply conducting a relative check with field measurements, such

simplification can be very misleading. The case is particularly true with the

validation of computer models. Some models simulate some conditions better

than others, and as with all prediction techniques, the accuracy of the assumptions in the model and the accuracy of the input variables can often remain

uncertain. Furthermore, daylighting measurements must be done with extreme care

and should be based on a series of like measurements in order to assess the

uncertainty of each measured quantity.

41
To control these characteric uncertainties, evaluating the accuracy of the

DALITE model was done in stages, by first carefully establishing the test

conditions for comparisons, and then by conducting step-by-step validation of

each of the major algorithms used within the program. The sky model was com- pared against hourly measurements of sky luminance, sky illuminance, and solar

radiation; the room illuminance model was compared against measurements made in

two full-scale test rooms and in mock-up models; and the lighting load model

was checked against laboratory tests of luminaire dimming and step-down performance. Where comparable measurements by others were available, a check with

their data was also done. The result is an overall validation, showing both

the strengths and weaknesses of the daylighting model.

6.1 VALIDATION OF THE SKY MODEL

SKYLUM, the subroutine that generates the hourly sky luminance, sky illuminance,

and direct sun illuminance, was validated against sky measurements made at the

National Bureau of Standards in Gaithersburg, MD (latitude 38° 5', longitude

77° 0'). The NBS data were from a series of days taken from more than two years

of sky measurements. The reference sky data were selected from measurements

known to be correct, and were chosen to provide good hourly data of clear skies,

overcast skies, partly cloudy skies, summer conditions, winter conditions, and

fall/spring conditions.

6.1.1 Validation of Sky Luminance

There are two basic parts to the sky luminance algorithm that need to be

validated: the sky luminance distribution and the zenith luminance. Also,

since a phasing technique is used to obtain intermediate sky condition based

on the mix between the clear and overcast sky, both the validity of the phasing

technique and the modeling of the clear and overcast skies must be substantiated.

The luminance distribution plots are illustrated in figures 6.1 and 6.2 of the

clear and overcast skies respectively. Figure 6.1 shows the validity of the

clear sky distribution model, particularly for sky regions away from the sun where the sky luminances are below 2,000 cd/m^. It should be noted, however,

that figure 6.1 is not a validation of the Kittler clear sky equation, but

rather a comparison showing the ability this equation has in estimating the

luminances in the real (not a standardized) clear sky. Likewise, figure 6.2

represents the correlation of the overcast luminance distribution with measured

luminances. The four different symbols represent the 42 degree luminance at

the four cardinal orientations. If the sky were perfectly uniform with respect

to orientations, the symbols would coincide; and if the distribution matched

the simulated distribution perfectly, the plot would fall on the solid line.

Given the variableness in instantaneous sky conditions, both distribution models

appear to perform reasonably well.

The zenith luminance correlations shown in figures 6.3 and 6.4 plot the sky

model's ability to predict the sky luminance at the zenith, which is normally

the reference value used to obtain absolute luminances once the luminance distribution is known. Figure 6.3 compares the validity of the clear sky zenith

equation while also revealing the stability in the sky conditions. In a

42
similar way, a general agreement is also illustrated in figure 6.4, but with an expected increase in scatter due in part to the variability of the overcast sky.

6.1.2 Validation of Exterior Horizontal Illuminance

A comparison of calculated exterior horizontal illuminance is shown against

comparable measurements in figure 6.5. The data represents a substantial set

of measurements for a wide range of sky conditions and cloud type and shows a good linear agreement. The correlation shows agreement both in the clear summer months (above 60,000 lux) as well as the winter months (below 60,000

lux)

.

6.1.3 Validation of Direct Beam Illuminance

Figure 6.6 is used to validate the direct beam illuminance algorithm. The

sunlight algorithm for the winter solstice (Julian date = 321) and summer solstice is compared against measurements made both at NBS and elsewhere within

the United States. [36]. Unfortunately, much of the data recorded elsewhere was not separated by season, and it appears as though there is a slight seasonal

dependence, but this is only a second order affect for lower solar angles. The

equation is seen to capture the seasonal variation and exhibits a good fit to

the measured data.

6.2 VALIDATION OF THE ROOM ILLUMINANCE MODEL

The interior daylight illuminance model was validated using measurements from

two full-scale test rooms and two scale-model test rooms. Because the interior

prediction routine incorporates all the other subroutines, this validation

represents the overall performance of the daylighting program. Furthermore,

since the collective set of subroutines can simulate many daylighting scenerios,

it was desirable to evaluate several room, fenestration, and sky conditions.

The physical characteristics of the four test rooms used in the validation work

are given in figures 6.7 and 6.8. The four rooms provide measurement data for rooms of different dimensions, wall reflectances, and fenestration types and

orientations. Although not all possible combinations were explored, the ones illustrated appear representative; scale model measurements facing east and

west and with different glazing areas show similar results. The two scalemodels (test room No. 1 and No. 2) and one of the full-scale rooms (test room

No. 3) had workplane illuminance recorded each hour along with the other hourly

measurements of sky luminance, sky illuminance, and horizontal solar radiation.

The fourth test room was instrumented in a slightly different way, with independent measurements taken every five minutes and catalogued according to depth

from the fenestration. These latter measurements could be compared to determine the amount of relative uncertainty in the daylighting measurements. Hourly

profiles of both calculated and measured illuminance in the scale models are shown in figures 6.9, 6.10, and 6.11 representing the overcast, partly cloudy,

and clear sky conditions respectively. All three figures show good agreement

for all sky conditions, particularly under the clear and overcast sky. Figure

6.11 also shows the successful modeling of the direct sunlight. In a similar

way, hourly values are compared for the full-scale room No. 3, but with a full

range of sky conditions (cloud ratios) in figure 6.12.

43
The measurements performed in test room No. 4 were done separately from the

others. Special care was taken to obtain precision measurements of instantaneous room and sky conditions and to provide exact input information for the

prediction routine. In this way a band of the uncertainty in the data can be

noted. Figure 6.13 is an overall comparison plot of all the measurements

(excluding the clerestory measurements) for room No. 4 and shows that, in

general, the daylight program tends to overpredict slightly at deeper room

depths and to underpredict slightly near the fenestration; however, given the

uncertainty of each measured quantity, the correlation is still quite good.

44
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57
Facing page: Sunlight penetration from an atrium in an office complex.

58
7 . CONCLUSIONS

A small computer model has been developed for inclusion into larger building

energy simulation programs for studying the hourly energy impact of daylighting

in buildings. The model is computationally fast in computer time, yet can accommodate a variety of fenestration designs and electric light dimming strategies. The model uses solar radiation and sun position data for estimating

outdoor daylighting conditions, and these data are currently available in the

existing hourly energy simulation programs. Although the model is streamlined

for its particular application, it still simulates field conditions reasonably

well, usually well within 30 percent including uncertainties in both the sky

and room prediction models. It should easily fit into most building energy

59
programs written in Fortran 77. With its modular structure, revisions and

expansions to the original model can be accomplished easily. Its modular

design also lends itself to micro and mini-computer applications either as part

of a small-scale energy simulation model, or as a stand alone daylighting

program.

Other strengths of the DALITE model include the streamlined simulation of

skylights, sloping clerestores, and vertical windows, and the capability to

simulate a full range of sky conditions. Validation efforts have shown the

program to perform well when compared against actual daylighting measurements

under real sky conditions for a variety of room and sky senerios.

The limits of the DALITE raodle include the restriction to rectangular room

geometries and simplified fenestration appendages such as overhangs and side

fins. While exterior louvers can be modeled as multiple minute overhangs, this

technique is not always best. Further research work is therefore suggested in

modeling exterior appendages, particularly with respect to specular reflections.

60
REFERENCES

1 . DOE-2 Program Manual; Vol. II , Lawrence Berkeley Laboratory and Los

Alamos Scientific Laboratory, Supported by the U.S. Department of Energy,

February 15, 1979.

2. Hittle, D., The Building Loads Analysis and System Thermo-dynamics (BLAST)

Program , Version 2.0, Users Manual, Vol. 1 and Vol. 2, Technical

Report E-153/ADA072272 and ADA72273, U.S. Army Construction Engineering

Research Laboratory, June 1979.

3. Kusuda, T. , NBSLD, The Computer Program for Heating and Cooling Loads in

Buildings , NBS Building Science Series 69, National Bureau of Standards,

1976.

4. Kusuda, T. , Review of Current Calculation Procedures for Building Energy

Analysis , NBSIR 80-2068, National Bureau of Standards, July 1980.

5. Dilaura, D. and Hauser, G. , "On the Effects of Daylighting in Interior

Spaces," Journal of the Illuminating Engineering Society , Vol. 8, No. 1,

p. 2-14, October 1978.

6. Modest, M. , "Daylighting Calculations for Non-rectangular Interior Spaces

with Shading Devices," presented at the Annual Technical Conference of

the Illuminating Engineering Society, Toronto, August 9-13, 1981.

7. Brackett, W. , CEL-1 Lighting Computer Program - User's Guide, CR81.026 , prepared for the Naval Civil Engineering Laboratory, Port Hueneme, CA,

September 1981.

8. Liu, B. and Jordan, R. , "The Interrelationship and Characteristic

Distribution of Direct Diffuse and Total Solar Radiation, Solar Energy , Vol. 4, No. 3, pp. 1-19, 1960.

9. Kimura, K. and Stevenson, D. , "Solar Radiation on Cloudy Days," ASHRAE

Transactions , Vol. 75, part I, pp. 227-233, 1969.

10. Ruberg, K. , Solar Availability in Cities and Towns: A Computer Model , NBSIR 82-2498, National Bureau of Standards, March 1982.

11. Kittler, R. , Standardization of Outdoor Conditions for the Calculation

of Daylight Factor with Clear Skies," proceedings of the CIE Intercessional

Conference on Sunlight in Buildings, Bauwcentrum, Amsterdam, pp. 273-285,

1967.

12. Dogniaux, R. , "Representations Analytiques des Composantes du Rayonnement

Lumineux Solaire," Institut Royal Meteorologique de Belgique, Publication - Seri A, No. 83 (in French).

13. Linke, F. , Handbuch der Geophysik (Gebr. Borntrager, Berlin) Vol. 8, No.

2, p. 284-307, 1942 (in German).

61
14. Nagel, M. , "Ground Illuminance from a Turbid Cloudless Sky," Applied

Optics , Vol. 14, No. 1, p. 68, January 1975.

15. Treado, S. and Gillette, G. , "Measurements of Sky Luminance, Illuminance,

and Horizontal Solar Radiation," to be published in the Journal of the

Illuminating Engineering Society , 1983.

16. Kimball, H. and Hand, I., "Daylight Illumination on Horizontal, Vertical,

and Sloping Surfaces," Monthly Weather Review , Vol. 50, No. 12, pp. 616-628,

December 1922.

17. Moon, P. and Spencer, D. , "Illumination from a Non-uniform Sky,"

Illuminating Engineering , Vol. 37, pp. 707-726, December 1942.

18. American Society for Testing and Materials, "Standard Solar Constant

and Air Mass Zero Solar Spectral Irradiance Tables," ASTM E490-73a,

ASTM (Philadelphia), November 1974.

19. "Proposed American National Standard Nomenclature and Definitions for

Illuminating Engineering (proposed revision of Z7 . 1-R1973) , " Journal of

the Illuminating Engineering Society , Vol. 9, No. 1, p. 7 and 35,

October 1979.

20. Jones, L. and Condit, H. , "Sunlight and Skylight as Determinants of

Photographic Exposure: I. Luminous Density as Determined by Solar

Altitude and Atmospheric Conditions," Journal of the Optical Society of

America , Vol. 38, No. 2, pp. 123-178, February 1948.

21. Kunerth, W. and Miller, R. , "Visible and Ultraviolet in the Light Obtained

from the Sun," lES. Transactions (New York), Vol. 28, pp. 347-353,

April 1933.

22. Lynes, J., Principles of Natural Lighting , Applied Science Publishers, Ltd.

(London), 1968.

23. Moon, P., "Proposed Standard Solar-Radiation Curves for Engineering Use,"

Journal of the Franklin Institute , Vol. 230, pp. 583-617, November 1940.

24. Elvegard, E and SjSstedt, G. , "The Calculation of Illumination from Sun

and Sky," Illuminating Engineering , Vol. 35, pp. 333-342, April 1940.

25. Dilaura, D. , "On Radiative Tansfer Calculations in Unempty Rooms,"

Journal of the Illuminating Engineering Society , Vol 10, No. 2, pp. 120-125,

January 1981.

26. Higbie, H. , Lighting Calculations , John Wiley & Sons (New York), 1934.

27. Pierpoint, W. and Hopkins, J., "The Derivation of a New Area-source

Equation," presented at the Annual Conference of the Illuminating Engineering Society, Atlanta, August 1982.

62
28. Illuminating Engineering Society, lES Lighting Handbook; Reference Volume , lES (New York), pp. 9.84-9.86, 1981.

29. Hopkinson, R. , Longmore, J., and Petherbridge , P., "An Empirical Formula

for the Computation of the Indirect Component of Daylight Factor," lES

Transactions (London), Vol. 19, No. 7, pp. 201-209, 1954.

30. Narasimhan, V., Saxena, B., and Maitreya, V., "The Internal Reflected

Component of Daylight: A Finite Approach to the Split Flux Method,"

Indian Journal of Applied Physics , Vol. 6, pp. 100-101, February 1968.

31. Dresler, A., "The Reflected Component in Daylighting Design," lES

Transactions (London), Vol. 19, No. 2, pp. 50-60, 1954.

32. Bryan, H. and Clear, R., "Calculating Interior Daylight Illumination with

a Programmable Hand Calculator," Journal of Illuminating Engineering

Society , Vol. 10, No. 4, pp. 219-226, July 1982.

33. Linforth, E., "Efficiency of Domed Acrylic Skylights," Illuminating

Engineering , Vol. 53, pp. 544-546, October 1958.

34. Treado, S. and Kusuda, T., Daylighting, Window Management Systems, and

Lighting Controls , NBSIR 80-2147, National Bureau of Standards, December

1980.

35. Verderber, R. , Selkowitz, S., Berman, S., "Energy Efficiency and

Performance of Solid-State Ballasts," Lighting Design and Application , Vol. 9, No. 4, pp. 23-28, April 1979.

36. Gillette, G., Pierpoint, W. , and Treado, S., "A General Illuminance Model

for Daylight Availability," presented at the Annual Conference of the

Illuminating Engineering Society, Atlanta, August 1982.

63

I

APPENDIX A: DETERMINING EFFECTIVE SKYLIGHT TRANSMITTANCE

To obtain a realistic estimate of the daylighting performance of a skylight, it

is necessary to provide an appropriate value for the effective (net) skylight

transmit tance. This effective transmittance is a composite correction for

doming effects, well losses, mullion factors and sun control devices. While

only an abbreviated discussion is provided here, further reference is made to

the Reference Volume of the lES Lighting Handbook. [28]

The effective direct transmittance xj) and diffuse transmittance of a horizontal skylight can both be expressed as.

Tc = T X Tlw X Tm X T( (A.l)

where

,

Tc

Tnw

Tm^m =

Xn =

the effective transmittance

the combined glazing transmittance

the well efficiency

the mullion correction factor

the correction factor for louvers or other solar control.

The combined transmittance of a double domed (two layer) skylight is found by.

T = l"PboPti

(A. 2)

where

,

Pbo

Pti

the transmittance of the outer dome

the transmittance of the inner dome

the reflectance of the bottom side of the outer dome

the reflectance of the top side of the inner dome.

To represent the effects of doming the skylight, which causes the thickness of

the skylight to vary across the domed surface, a third equation can be used. [28

Tdome = 1.25 ^fs ^'l^ - 0.416 xps) (A. 3)

where

Tdome ~ integrated glazing transmittance for the domed surface

TPS - the flat sheet transmittance of acrylic (as normally given by the

manufacturer)

.

The well efficiency is obtained by figure A.l

figure can be found by the equation.

The well index used in the

WI = (w + 1)

2 w 1

(A. 4)

A-1
where

,

h = the well height w = the well width

1 = the well length

By computing the appropriate factors and solving equation A.l, the effective

transmittances for diffuse and direct light can be provided for input into the

skylight algorithm.

A-2
1.00 0.90

0.80

0.70 0.60

0.50

0.40

0.35 0.30

0.25

0.20

^ 0.15

0.10

0.05

e X

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 WELL INDEX

1.8 2.0

Figure A. 1 Well efficiency a function of a well index

and well reflectance

(from the 1981 Reference Volume of the I.E.S.

Lighting Handbook, p. 9-86, used with permission)

A-3

APPENDIX B: DESCRIPTION OF VARIABLES

The following is a listing of all the important variables used within the

DALITE program, Including both I/O variables "seen" by the user and variables

used internally. It should be noted that although it is possible to adapt th

program for use in computer models that use SI units, the I/O is here given i English units for compatibility in most of the existing energy programs

currently available. A conversion table to SI unit is given on page vi.

A = total surface area of interior room surfaces (square feet)

AZM = azimuth angle of the building off the cardinal axis, clockwise from

north (degrees)

AZS = difference in azimuth angle between the surface perpendicular and th

azimuth of the sun (degrees)

ANG = solar profile angle from horizon (radians)

ANGLl = azimuth angle sensor makes with right edge of window (degrees)

ANGL2 = azimuth angle sensor makes with left edge of window (degrees)

ANGL3 = ANGLl referenced to true north (degrees)

ANGL4 = ANGL2 referenced to true north (degrees)

AW = distance from ceiling to top of window (feet)

BCF = Basic Configuration Factor - general sloping case

BCFS = Basic Configuration Factor - parallel surface (skylight) case

BCFW = Basic Configuration Factor - perpendicular window case

BETA = atmospheric turbidity coefficiency (3)

CC = length of sloped clerestory ceiling (feet)

CHI(x) = constant offset dimmer control coefficient (default is 0.30)

CR = cloud ratio; ration of diffuse to total horizontal solar radiation.

CRL = ceiling reflected light coefficient.

CNFLX = ceiling flux coefficient; for reflected light off clerestory

DAYLT = daylight illuminance array for "n" number of sensors (f ootcandles

)

DAYLTE = daylight illuminance of sensor under consideration (f ootcandles)

B-1
DILL = maintained design illuminance at the photocell (f ootcandles)

DIM = dimmer type:

1 - on/off switch or relay

2 - two level step-down; half off at half load, full off at full load.

3 - continuous dimming

4 - continuous dimming with shut-off

DP = depth of photocell from fenestration; for skylights & clerestories,

distance from bottom of fenestration to workplane (feet)

DSl = horizontal depth of sun's projection within room due to upper edge of

window - see figure B2 (feet)

DS2 = horizontal depth of sun's projection within room due to lower edge of

window - see figure B2 (feet)

DW = depth of skylight well (feet)

DX = distance of external obstructing building from fenestration surface

(feet)

EX = extraterrestrial illuminance of the sun (f ootcandles)

FLUXl = first reflected flux coefficient for surface containing the

fenestration

FLUX2 = first reflected flux coefficient for left surface with respect to

fenestration

FLUX3 = first reflected flux coefficient for surface opposite fenestration

FLUX4 = first reflected coefficient for right surface with respect to

fenestration

FLUX5 = first reflected flux coefficient for the ceiling

FP = fin projection from the fenestration (feet)jtwo fins are assumed on either side of fenestration

GAMMA = angular great circle distance between the sun and the specified point

in the sky (radians)

GRDLIT = exterior horizontal illuminance incident on the ground (f ootcandles

)

GRL = ground reflected coefficient

H = height of fenestration (feet)

HI = height distance from fenestration to bottom of wall surface (feet)

B-2
H2 = height distance as shown in figure B.3 (feet)

H3 = height distance as shown in figure B.3 (feet)

H4 = height distance as shown in figure B.3 (feet)

H5 = height distance as shown in figure B.3 (feet)

HH = height distance as shown in figure B.3 (feet)

HHl = height distance as shown in figure B.3 (feet)

HH2 = height distance as shown in figure B.3 (feet)

HH3 = height distance as shown in figure B.3 (feet)

HH4 = height . distance as shown in figure B.3 (feet)

HH5 = height distance as shown in figure B.3 (feet)

HX = height of external obstruction above the workplane (feet)

HC = height of clerestory projection above ceiling plane (feet)

HC is negative if clerestory is sloped, positive if roof monitor ((^0)

HHC = the distance from the top of the clerestory fenestration to the

clerestory ceiling (feet)

JUL = Julian date from 1 (January 1) to 365 (December 1)

L = length of skylight (feet)

LI = length distance from room reference to skylight reference (feet)

L2 = length distance as shown in figure B.4 (feet)

L3 = length distance as shown in figure B.4 (feet)

LC = distance from room reference to clerestory reference in length

direction (feet)

LLOAD = incremental instantaneous lighting load due to single phototcell and

single aperature (kilowatts)

LLOADN = the instantaneous lighting load associated with photocell "n"

(kilowatts)

LLOADX = the hourly sum of all photo-controlled lighting loads per room

(kilowatts)

B-3
LOAD = full connected lighting load associated with each photocell, including

ballast losses (kilowatts)

LSI = length distance from room reference to near edge of sunlight patch

from skylight on workplane (feet)

LS2 = length distance from room reference to far edge of sunlight patch from

skylight on workplane (feet)

M = mullion correction factor; the fractional loss in transmittance due to

mullions and glazing bars

NA = number of aperatures within room

NL = number of luminare switch /dimmers within room

OfffiGA = atmospheric water vapor content in centimeters of water (w)

OP = horizontal overhang projection from the fenestration (feet)

PHASE = percentage of clear sky luminance and sun illuminance available

PHI = in the SUNN subroutine the vertical profile angle of the sun-see

figure B.2 (radians); in the DL subroutine the slope of the clerestory

from the horizontal (radians)

PL = position of photocell along the length direction from the room reference

(feet)

PSI = complement angle of PHI; the slope of the clerestory from the zenith

(radians)

PSL = percentage of supplemental light necessary (decimal)

PW = position of photocell along the width direction from the room reference

(feet)

RAVE = average reflectance of all interior room services (decimal)

RCN = reflectance of the ceiling (decimal)

RFL = reflectance of the floor (decimal)

RG = reflectance of the ground immediately outside the fenestration

(decimal)

RL = apparent room length as seen by the particular fenestration (feet)

RHM = room height (feet)

RML = interior room size in length direction (feet)

B-4
RMN

RMW

RRF

RRL

RW

RWL

RX

SIDLIT

SKYLIT

SN

SNL

SRD

SRT

SUI4FLX

SUNALT

SUNAZ

SUNBM

SUNFLX

SUNLIT

SURFAZ

T

room number (just an identifier)

interior room size in width direction (feet)

roof reflectance immediately outside clerestory (decimal)

roof reflected light coefficient

apparent room width as seen by the particular fenestration (feet)

reflectance of the interior wall surfaces (decimal)

average reflectance of external obstruction (decimal)

total exterior vertical illuminance on window surface (f ootcandles

)

sky illuminance at fenestration centroid (f ootlamberts

)

surface number of fenestration:

1 - if north facing

2 - if east facing

3 - if south facing

4 - if west facing

5 - if ceiling/roof

6 - if clerestory north facing

7 - if clerestory east facing

8 - if clerestory south facing

9 - if clerestory west facing

sunlight coefficient

diffuse horizontal solar radiation (Btu/S .F-hr .

)

total horizontal solar radiation (Btu/S.F-hr.

)

sum of the interior surface flux coefficients

solar altitude above horizon (degrees)

solar azimuth clockwise from north (degrees)

solar beam illuminance direct normal (f ootcandles

)

sun flux coefficient

the horizontal illuminance due to beam sunlight (f ootcandles

)

azimuth angle from surface normal clockwise to true north (degrees)

average visible transmittance of glazing (including a maintenance

factor)

THETA = altitude angle between the window centroid and the photocell (degrees)

B-5
TNX = angular visible transraittance , accounting for angle of incidence

W = width of fenestration (feet)

Wl = width distance of window or skylight from surface reference (feet)

W2 = width distance as shown in figure B.3 (feet)

W3 = width distance as shown in figure B.3 (feet)

W4 = width distance as shown in figure B.3 (feet)

W5 = width distance as shown in figure B.3 (feet)

W6 = width distance as shown in figure B.3 (feet)

W7 = width distance as shown in figure B.3 (feet)

WA = window area (square feet)

WC = width of clerestory opening (feet)

WCl = width distance of clerestory opening from room reference (feet)

WINAZ = viewing azimuth angle between photocell position (at work plane) and

window/skylight centroid; clockwise from north (degrees)

WP = width distance of photocell with respect to surface reference - see figure B.3 (feet)

WSl = width distance of near edge of skylight sun projection from room

reference at workplane (feet)

WS2 = width distance of far edge of skylight sun projection

WX = depth of skylight well from ceiling to fenestration (feet)

XDL = direct skylight coefficient

XI(5) = linear dimmer control coefficient

XIRL = internally reflected light coefficient

XERL = externally reflected light coefficient

ZLUM = zenith sky luminance (f ootlamberts

)

B-6
XJ c c o o 3 00 (fl *H O •H tn r-H P T3 rH o (U .H « US C u <u e e -H » o 3 o <J

t-j 3 r-1 iJ O

a o o l-l u OM-t »u ki u 0) u <U M O o c M C O o o rH o CI. 0 x:

Oil-I C/21-1 fa o bu < (X

I

+ 1

C/2 [/)

3 3 3
RW2 RW2

RW

Figure B.2 Room coordinates defined with respect

to glasing surface in IRL subroutine

B-8
^ W2 ^ W4 —• »

»~ WP

Figure B.3 Wall surface dimensions used internally

in the DALITE program

B-9
North

B-10
Sloped Clerestory

Figure B.5 Clerestory coordinates

B-11
Direction

Figure B.6 Sun projection variables for skylights

B-12
APPENDIX C: SUBROUTINE INTERFACING

Interfacing the DALITE subroutines with an existing FORTRAN program is

accomplished by changes at two locations in the main program. The first is at

initialization. Here the common block for the two input/output arrays and the

dimensioning of the other internal arrays are assigned (figure C.l). Here

also READ statements are given, following the array declarations, where the

building and component characteristics are defined for the daylighting I/O

array along with the other building characteristic assignments. Such READ

statements may be provided either through a pre-processor or through various

statements within the main program. At this point the room, aperature, and

photocell information is assigned within the ZLITE array (see figure B.l)

where it will be called later by the various daylighting subroutines during

execution.

The second revision is done inside the hourly (or other time step) loop. Here

input assignments are given for each hourly set of sky conditions preceeding

the CALL statement for the daylighting analysis. Daylighting output information is then passed from the DALITE subroutine to the main program via the

ZLITE array, where it is used as a part of the hourly load compiliation.

The adjusted electric load (WLAMP) and the exterior horizontal illuminance

(FCDAY) are the normal output values. However, illuminance at each sensor position is also accessible from the array DAYLT (n) , n being the sensor number.

Further output information, such as wall luminances, luminance ratios, and the

like can also be obtained, but program revisions would be necessary; normally

such data would be too exhaustive to include in an energy simulation, and was therefore not specified as part of the normal output.

Since the daylighting interref lection routine is room-specific and models a rectangular room geometry, a few revisions may be necessary for programs that

do not prescribe set room dimensions or for cases where the assumption of a rectangular room is invalid* Two options are possible. The first is to

approximate an equivalent (or effective) room height, width, and depth for the

enclosed volume. The second option is to leave out the room geometry and surface reflections altogether, which would avoid the calculation of any interreflected light. This latter option is a good one when there is substantial

uncertainty in the room configuration; this option is conservative, yet not

excessively so since interref lected light is normally a small fraction of the

total.

C-1
Array declarations

PARAMETER NNN=30

PARAMETER LLL=10 PARAMETER MMM= LLL+NNN+2

DIMENSION COEF(NNN.LLL) .SURFAZO) . W I NAZ ( NNN . LLL ) THETACNNN, LLL) .WP(NNN. LLL) , DP (NNN. LLL)

COMMON /DD/ZLITE(MMM. 12) .DAYLT( LLL)

Hourly loop for thermal loads

Solar loads are done here within the|

main program

722

Hourly initialization of solar loads

Continuation of thermal loads

READ DAYLIGHTING INPUT DATA

READ( 5 ,1460) (ZLITEd . J) .0x5. 11 ) ITEST=0 READ (5. 1466)(ZLITE( II .K) ,K=1 .12)

LN=ZL1 TE( 1,11 )+32 READ (5. 1460) (

( ZL I TE ( I . d ) . d« 1 . 7 ) . 1=33. LN)

DAYLIGHTING CALCULATIONS

WLAMP=0 PINIT FOR NON-OAYLIGHT

.

ZLITE(33, 12)=0S0L(NK)*0.2931M11 . ©FC

DO 722 1=33.42

WLfiMP = WLAMP-t-ZLITE( I .5)

IF(0LITX(NK.JJ) .EO.O. ) GO TO 725

IF( SALT(NK) . LE.O. ) GO TO 725

IF( (2LITE(33.1) .EQ.O. ).0R.(ZLITE(33,4).E0.0. ))G0 TO 725

iPINIT FOR DAYLIGHTING CALCS

=HT

aL

= W

= IROT

WLAMP=0.

ZLITE( 1 . 1 ) ZLITE( 1,2)

ZL1TE( 1 ,3)

ZLITE( 1,4)

ZHTE( 1 . 12) = IJKLMN

ZLITE( 2. 1 )=SALT(NK)

ZLITE( 2,2 )= I80+SAZM(NK)PS0LAR AZIMUTH

ZLITE(2,3)=XIDFHC

ZLITE(2,4)=QS0L(NK)

ZLITE(2,8)=ND

ITEST=ITEST+1

NA =NNN

NL «LLL

S'ROOM NUMBER

^iSOLAR ALTITUDE (DEGREES)

(DEGREES)

©DIFFUSE SOLAR HORIZONTAL

©TOTAL SOLAR HORIZONTAL

©JULIAN DATE ©LOOP COUNTER TEST

©NUMBER OF APERTURES( MAX

)

©NUMBER OF LUMINAIRE CONTROLS(MAX)

CALL DALITE(COEF.SURFAZ.WINAZ.THETA.WP.OP.NA.NL.ITEST)

C DO 724 1=33.42

WL&MP=WLAMP+ZLITE( I . 1 1) ©ADJUSTED LIGHT LOAD (KW)

724 CONTINUF

FCDAY(NK)=ZLITE(33.12) ©EXTERIOR HORZ. ILLUMINANCE ( FC)

725 OLITE(NK)=( {0LITY*AG)+(WLAMP*1OO0) )*(0LlTX(NK.dJ)*3.412*NOFLR)

Figure C.l Program interfacing

C-2
Variable Variable*

Name Specification

Variable

Limits

RMH REAL None

RML REAL None

AZM REAL Minimum = 0 .

; Maximum = 360

.

RCN REAL Must be decimal fraction less then 1 .00

RWL REAL Must be decimal fraction less then 1.00

RFL REAL Must be decimal fraction less then 1 .00

RG REAL Must be decimal fraction less then 1.00

RX REAL Must be decimal fraction less then 1 .00

NA REAL (Assigned) Limit is number

statement

used in NNN parameter

NL REAL (Assigned) Limit is number

statement

used in LLL parameter

RMN REAL NONE

SUNALT REAL IF SUNALT < 5., SUNLIGHT = 0.

SUNAZ REAL NONE

SRD REAL SRD must be < SRT

SRT REAL NONE

BETA(3) REAL Allowable values for 3 are 0.05,0.10, & 0.20

OMEGA(a)) REAL Allowable values for w are 1.0, 2.0, 3.0

4.0, & 5.0

JUL REAL (Assigned) Minimum = 0.; Maximum = 365.

* Format is arbitrary and depends only on the format specified in the READ

statement of the main program.

Figure C.2 Input variable specifications for room and sky data

C-3
Variable Variable*

Name Specification

Variable

Limits

W REAL None

H REAL None

L REAL (Assigned) None

HI REAL None

LI REAL (Assigned) None

Wl REAL None

T REAL Must be decimal fraction less then 1.00

M REAL Must be decimal fraction less then 1.00

HX REAL None

WCl REAL None

DX REAL None

SN REAL Minimum = 1.; Maximum = 9.

OP REAL NONE

WC REAL Must be > W + Wl

AW - REAL NONE

LC REAL (Assigned) NONE

FP REAL NONE

HC REAL Must be > H + HI

PW REAL If PW = 0. , DAYLIGHT contribution is

assumed zero. PL REAL NONE

DILL REAL NONE

DIM REAL Allowable values are 1., 2., 3., & 4.

LOAD REAL (Assigned) NONE

XI REAL Must be decimal fraction less than 1.00

CHI REAL Must be decimal fraction less than 1.00

* Format is arbitrary and depends only on the format specified in the READ

statement of the main program.

Figure C.3 Input variable specifications for fenestration data

C-4
Variable

Name

Variable*

Specification

Variable

Limits

DAYLTE REAL None

LOADX REAL (Assigned) None

GRDLIT REAL None

DAYLT(n) REAL None

* Format is arbitrary and depends only on the format specified in the READ

and WRITE statements of the main program.

Figure C.4 Output variable specifications

C-5

APPENDIX D: SAMPLE RUN

SAMPLE RUN OF A BUILDING DAYLIGHTED WITH CLERESTORIES

D-1
Location : Washington, D.C. Latitute = 38° 5'N Longitude = 77° O'W

Fenestration : Three north facing clerestories

Lighting Control : Five banks of fluorescent luminaires at 1.25 KW each

continuous dimming (50 fc minimum illuminance)

Figure D.l Sample Building

D-2
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D-6
APPENDIX E: PROGRAM LISTING

A FORTRAN 77 listing of the DALITE program is given on the following pages

The listing is subdivided into four sections and includes a diagrammatic

representation preceding each. The code is the UNIVAC version of FORTRAN

E.l The DALITE subroutine

E.2 The SKYLUM subroutine

E.3 The RMLITE subroutine

E.4 The LLOAD subroutine

E-1
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E-2
Q$QSQ$*GARY{ 1 ).DALITE( 16)

12 CSUBROUTINE DALITE{COEF , SURFAZ ,WI NAZ , THETA , WP ,DP ,NA,NL , I TEST

3 C ANALIZES THE HOURLY DAYLIGHTING CONDITIONS AND

4 C CALCULATES HOURLY ELECTRIC LIGHTING ENERGY REQUIREMENTS.

5

6 Cc THESE DALIGMTING ALGORITHMS WERE DEVELOPFD BY GARY GILLETTE

78

9

c

c

c NOTE : ALL DISTANCES ARE IN FFFT AND Al 1 ANGI FS IN DFGRFFS

10

1 1 c

c ROOM VARIABLES'

1 2 c RMH =ROOM HFIGHT (FT>

1 3 c RML =ROOM LENGTH (FT)

1 4 c RMW =ROOM WIDTH (FT)

1 5 c AZM =CLOCKWISE AZIMUTH OF ROOM FROM NORTH

1 6 c RCN =CEILING REFLECTANCE

I 7 RWL =WALL REFLECTANCE

1 0 Q RFL =FLOOR REFLECTANCE

1 9 RRF =ROOF REFLECTANCE (IMMEDIATELY OUTSIDE CLERESTORY)

20 RG =GROUND REFLECTANCE

2 1 RX =EXTERNAL OBSTRUCTION REFLECTANCE

22 c NA =NUMBER OF APERTURES IN ROOM

23 c NL =NUMBER OF BANKS OF LUMINAIRES CONNECTED TO A

24 c LIGHTING CONTROL DEVICE

25 c RMN =ROOM NUMBER

2S

2 7 SKY VARIABLES:

28 Q

29 Q SUNALT=SUN ALTITUDE ABOVE THE HORIZONTAL

30 c SUNAZ =SUN AZIMUTH CLOCKWISE FROM NORTH

3 1 c SRD =SOLAR RADIATION DIFFUSE HORZ . ( BTU/SF-HR

)

3 2 c SRT =SOLAR RADIATION TOTAL ON HORZ . ( BTU /S F - HR

)

33 c CR =CLOUD RATIO, D I F F US E / TOTAL SOLAR RADIATION

34 c ZLUM =ZENITH SKY LUMINANCE

35 c 36 c WINDOW VARIABLES:

37 c 38 c W =WIDTH OF WINDOW

39 c H =HEIGTH OF WINDOW

40 c HI =HEIGTH OF WINDOW SILL FROM FLOOR

41 c Wl =WIDTH OF WINDOW'S LEFT EDGE FROM WALL'S LEFT EDGE

42 c T =VISIBLE TRANSMITTANCE

43 c M =CORRECTION FOR MULLIONS

44 c HX =HEIGHT OF EXTERNAL OBSTRUCTION

45 c DX =DISTANCE OF EXTERNAL OBSTRUCTION FROM ROOM

46 c SN =WALL SURFACE ASSOCIATED WITH APERTURE

47 c 1-NORTH SURFACE

d 8 r 2-EAST SURFACE

49 c 3-SOUTH SURFACE

50 c 4-WEST SURFACE

51 c OP =HORIZONTAL OVERHANG PROJECTION (FEET)

52 c AW =DISTANCE FROM CEILING TO TOP OF WINDOW (FEET)

53 c FP =FIN PROJECTION FROM FENESTRATION (FEET)

5 4 c 55 c SKYLIGHT VARIABLES:

56 c 57 c W =WIDTH OF SKYLIGHT

E-3
58 C L =LENGTH OF SKYLIGHT

59 C LI =DISTANCE (IN LENGHT DIRECTION) OF SKYLIGHT FROM

60 C ROOM REFERENCE

61 C Wl =DISTANCE (IN WIDTH DIRECTION) OF SKYLIGHT FROM

62 C ROOM REFERENCE

63 C T =EFFECTIVE VISIBLE TRANSMITTANCE OF SKYLIGHT W/ WELL

64 C (ENTER NEGATIVE VALUE IF TRANSLUCENT)

65 C M =CORRECTION FOR MULLIONS

66 C WX =WELL EXTENT I ON ( DEPTH OF SKYLIGHT WELL)

67 C RX =WELL REFLECTANCE

68 C SN =5 FOR CEILING SURFACE

69 C 70 C CLERESTORY (AND ROOF MONITOR) VARIABLES:

71 C WC =WIDTH OF CLERESTORY OPENING

72 C LC =LENGTH OF CLERESTORY OPENING

73 C HC{-) =TOTAL HEIGTH OF SLOPED CLERESTORY (ABOVE CEILING PLANE)

74 C HC(+) =TOTAL HEIGHT OF SQUARE MONITOR CLERESTORY (ABOVE CEILING PLANE)

75 C W =WIDTH OF WINDOW IN CLERESTORY

76 C H =HEIGHT OF WINDOW IN CLERESTORY

77 C HI =HEIGHT OF CLERESTORY WINDOW SILL FROM CEILING

78 C Wl =WIDTH OF CLERESTORY WINDOW'S LEFT EDGE FROM CLERESTORY

79 C WA L L 80 C LCI =DISTANCE{IN LENGTH DIRECTION) OF CLERESTORY

81 C FROM ROOM REFERENCE

82 C WCl =DISTANCE(IN WIDTH DIRECTION) OF CLERESTORY

83 C FROM ROOM REFERENCE

84 C T =VISIBLE TRANSMITTANCE OF GLAZING

85 C M =CORRECTION FOR MULLIONS

86 C SN =6 FOR CLERESTORY/MONITOR NORTH SURFACE

87 C 7 FOR CLERESTORY/MONITOR EAST SURFACE

88 C 8 FOR CLERESTORY/MONITOR SOUTH SURFACE

89 C 9 FOR CLERESTORY/MONITOR WEST SURFACE

90 C 91 C DIMMER VARIABLES:

92 C 93 C PW =WIDTH DISTANCE OF SENSOR POINT FROM SOUTH WALL (FT)

94 C PL =LENGTH DISTANCE OF SENSOR POINT FROM WEST WALL (FT)

95 C DILL =DESIGN ILLUMINANCE (FC)

96 C DIM =DIMMER SYSTEM ( ON/OF F = 1 , STEP -D0WN=2 , CONT DIMMING W/MIN=3,

97 C DIMMING W/0FF=4)

98 C LOAD =CONNECTED LIGHT LOAD ASSOCIATED WITH SENSOR (KW)

99 C CHI =CONSTANT (MIN) OFFSET DIM CONTROL COEFF ICIENT( DEFAULT=0.3flF)

100 C XI =LINEAR DIM CONTROL COEF F I C I ENT ( DEFAULT=0. 30

)

101 C 102 PARAMETER MMM=42

103 PARAMETER NNL=10

104 REAL L0AD,LL0AD,LL0ADX,LL0ADN,L,LC,L1 ,L2,M

105 COMMON /DD/ZLITE{MMM, 12) ,DAYLT(NNL ) 106 DIMENSION COEF ( NA , NL ) , SURFAZ ( * ) , Wl NAZ ( NA , NL )

, THETA( NA , NL )

,

107 *WP{NA,NL ) ,DP(NA,NL ) 108 PI=3. 14159

109 IF(ZLITE(2,4) .LE.0. )G0 TO 90 OCHECKS IF IT IS DAY OR NIGHT

110 RMH = ZL ITE{ 1 , 1 ) 111 RML=ZLITE{ 1 ,2)

112 RMW=ZLITE{ 1 ,3)

113 AZM = ZLITE{ 1 ,4)

114 DO 30 1=1, NL 115 DAYLT(I)=0.

E-4
116 30 CONTINUE

117 GRDLIT=0.

118 LLOADX=0.

119 NN-NA+3

120 NST = ZL ITE{ 1 , 11 ) + 3?

121 C 122 DO 70 K=NN,NST QFOR EACH OF NL POSSIBLE FIXTURE BANKS

123 C 124 IF{ZLITE{K. 1 ) .EQ,0. )G0 TO 70

125 PW =ZLITE{K,1)

12S PL =ZLITE<K,2)

127 DILL=ZLITE(K,3)

128 DIM =ZLITE(K.4)

129 L0AD=ZLITE(K,5)

130 N =K-32

131 MST=MMM-NNL

132 C 133 DO 60 0 = 3, MST (3F0R EACH OF NA POSSIBLE APERTURES

134 C 135 IF(ZLITE< J ,9) .LE.0. )G0 TO 60

136 T =ZLITE{ J ,5)

137 M =ZLITE<J.6)

138 SN=ZLITE(0,9>

139 ISN-SN

140 IF(SN.GE.6)SURFAZ{ I SN ) =90 . * ( SN-6 > +AZM

141 IF(SN.LT.6)SURFAZ( ISN)=90.*(SN-1 ) +AZM

142 IF ( ITEST.GT. 1 )G0 TO 50 (? I F COEFFICIENTS ALREADY OBTAINED

143 C 144 C CALCULATE DAYLIGHT GEOMETRY COEFFICIENTS

145 C THESE COEFICIENTS ARE CALCULATED INITIALLY AND STORED

146 C FOR HOURLY USE

147 C 148 IF { {ZLITE(0 , 9 > . EQ.0. ) .OR . (ZL ITE( 0 , 5 ) . EQ.0. ) )G0 TO 60

149 W =ZL ITE( 0 , 1

)

150 W1=ZLITE( J ,4)

151 C 152 C DEFINE LOCAL COORDINATES (THESE ARE DISTANCES AS SEEN BY

153 C THE FENESTRATION, OR ANGLES AS VIEWED THROUGH THE FENESTRATION)

154 C 155 C WINAZ(0,N> =F ENESTRAT I ON AZIMUTH ANGLE @ CENTRIOD

156 C THETA(J,N) = F ENESTRAT I ON ALTITUDE ANGLE (? CENTROID

157 C SURFAZ( ISN >=WALL SURFACE AZIMUTH (DEGREES FROM NORTH)

158 C 159 C COORDINATES FOR ROOM SURFACE 1 160 C

161 IF(SN.EQ. 1 )THEN

162 WP { J , N )=RML-PL

163 DP{0 ,N)=RMW-PW

164 RW=RMW

165 RL=RML

166 IF(W1.GE.WP(J,N) )WINAZ(0 , N )=SURFAZ{ ISN )-ATAN( (Wl-WP ( J , N )+ . 5*W)/

167 *DP(J,N) )*57.3

168 IF(W1.LT.WP{0,N) ) WI NAZ ( 0 , N ) =SURFAZ ( ISN)+ATAN( ( WP ( 0 , N

) -Wl - . 5*W )

/

159 *DP(0,N) )*57.3

170 C 171 C COORDINATES FOR ROOM SURFACE 2 172 C 173 ELSE IF (SN.EQ.2) THEN

E-5
174 WP(CI,N)=PW

175 DP{J,N)=RML-PL

176 RW=RML

177 RL=RMW

178 !F(W1.GE.WP<0.N) >WINAZ{0 , N )=SURFAZ{ ISN )-ATAN{ { Wl -WP ( J , N ) + . 5*W )

/

179 •DP<J,N> )*57.3

180 IF{W1 .LT.WP(0,N) )WINAZ{ J ,N)=SURFAZ{ ISN)+ATAN( ( WP ( 0 , N

) -Wl - , 5*W )

/

181 *DP(0,N) )*57.3

182 C 183 C COORDINATES FOR ROOM SURFACE 3 184 C 185 ELSE IF <SN.EQ.3) THEN

186 WP(J.N)=PL

187 DP(0,N)=PW

183 RW=RMW

189 RL=RML

190 IF { Wl .GE .WP ( J , N ) )"WINAZ(0,N>=SURFAZ( ISN)-ATAN{ ( W 1 -WP ( 0 , N ) + . 5*W } /

191 *DP{a .N) )*57.3

192 IF'.Wl.LT.WPCJ.N) )WINAZ{0 , N )=SURFAZ( ISN )+ATAN{ ( WP { J . N ) -W 1 - . 5 *W ) / 193 *DP { 0 , N ) )*57 . 3 194 C 195 C COORDINATES FOR ROOM SURFACE 4 196 C 197 ELSE IF {SN.EQ.4> THEN

198 WP(0,N>=RMW-PW

199 OP(J,N)=PL

200 RW=RML

201 RL=RMW

202 IF(W1.GE.WP<J,N) )WINAZ{ J , N )=SURFAZ( ISN >-ATAN{ (Wl-WP (0 , N ) + .5*W)/

203 *DP ( J , N ) >*57 . 3 204 IF(W1,LT.WP{J,N) )WINAZ{0 . N )=SURFAZ{ ISN >+ATAN( ( WP ( J , N

) -Wl - . 5*W )

/

205 *DP(J,N) )*57.3

206 C 207 C COORDINATES FOR CEILING SURFACE 5 208 C 209 ELSE IF (SN.EQ.5) THEN

210 L =ZLITE(J,2)

211 L1=ZLITE(0 ,3)

212 DP ( J , N )=RMH-2 .

5

213 L2=L1-PL

214 W2=W1-PW

215 IF { ( L2 .GT.0. ) .AND . {W2 .LT.0. ) )AZM=AZM + 90. (? I N DEGREES

216 IF{ (L2.LT.0. ) .AND. (W2.LT.0. ) )AZM=AZM+180. @IN DEGREES

217 IF{ (L2.LT.0. ) .AND. (W2.GT,0, ) )AZM=AZM+270. @IN DEGREES

218 IF{AZM.LE.360. )AZM=0.

219 IF{L1 .LT.PL )L2 = PL-L-L1

220 IF(W1 .LT.PW)W2=PW-W-W1

221 IF(W2+W/2.EQ.0. )THEN

222 WINAZ(0,N)-=AZM

223 ELSE

224 WINAZ( J,N)=ATAN{ {L2+L/2)/(W2+W/2) )*57.3+AZM PIN DEGREES

225 END IF 226 IF( {L2 + L/2.EQ.0. ) .AND. {W2+W/2.EQ.0. ) )THEN

227 THETA{ J , N )=90.

228 ELSE

229 THETA{0,N>=ATAN{DP(J,N)/SQRT{ {L2+L/2)**2+{W2+W/2)**2) )*57.3 ©IN DEGREES

230 END IF 231 C

E-6
232 c COORDINATES FOR CLERESTORY SURFACE 6 233 C 234 ELSE IF (SN.E0.6) THEN

235 H 1 =ZL ITE { 0 , 3 > 236 LC = ZL ITE( J ,11)

237 LC 1 =ZL ITE ( J , 8 ) 238 WC=ZL ITE(0 , 10)

239 WC 1 =ZL ITE ( J , 7 ) 240 DP { J , N / =RMH-2 . 5 + H 1 241 WP ( 0 , N ) =RML-PL

242 RW=RMW

243 RL=RML

244 I F { ( WC 1+WC ) . LT . PW>WI NAZ (J,N)=SURFAZ(ISN) @NOTE:DSF =0

.

245 IF(LC1 .GE.PL )WI NAZ (J,N)=SURFAZ<ISN) +ATAN { (LC1-PL+.5* LC ) / 246 * (WCl+WC-PW) >*57 . 3 247 IF(LC1 .LT.PL )WINAZ{J ,N)=SURFAZ{ ISN) -ATAN ({PL-LC1-.5* LC ) / 248 * { WCl +WC-PW ) ) *57 . 3 249 c

c COORDINATES FOR CLERESTORY SURFACE 7 25 1 c 252 ELSE IF (SN.EQ.7) THEN

253 H1=ZLITE( J ,3)

254 LC = ZL ITE( J ,11)

255 LC1=ZLITE( J .8)

256 WC=ZL ITE( 0 , 10)

257 WC1=ZLITE(0 ,7)

258 DP(J,N)=RMH-2.5+Hl

259 WP ( J , N )=PW

260 RW=RML

261 RL=RMW

262 IF(((LC1+LC).GE.PL).AND.{WC1.GE.PW) )WINAZ( J , N )=SURFAZ( ISN )-

263 * ATAN( (WC1-PW+.5*W)/{LC1+LC-PL ) )*57.3

264 1F(({LC1+LC).GE.PL).AND.{WC1.LT.PW) )WINAZ( 0 , N )=SURFAZ( ISN )+

265 * ATAN{ (PW-WC1-.5*W)/{LC1 + LC-PL > >*57.3

266 IF((LC1+LC>. LT.PL )WINAZ( J , N )=SURFAZ{ ISN > (3N0TE : DSF = 0.

257 c 268 c COORDINATES FOR CLERESTORY SURFACE 8 269 c 270 ELSE IF (SN.EQ.S) THEN

271 H1=ZLITE{0,3)

272 LC=ZL ITE{ J .11)

273 LC1=ZL ITEd , 8 ) 274 WC=ZLITE( J , 10)

275 WC1=ZLITE{J,7)

276 DP{ J , N )=RMH-2 . 5 + Hl

277 W?{0,N)=PL - 278 RW=RMW

279 RL=RML

280 IF (WCl .GT- PW)WINAZ( J ,N )=SURFAZ( ISN ) ©NOTE :DSF=0.

281 IF(LC1.GE.PL )WINAZ( J , N )=SURFAZ( ISN ) -ATAN ( (LC1-PL+.5* LC )/

282 * (WCl+WC-PW) )*57.

3

283 IF (LCI .LT.PL>WINAZ(0,N)=SURFAZ( ISN)+ATAN( (PL-LC1-.5* LC ) / 284 *(WC1+WC-PW) )*57.3

285 c 28S c COORDINATES FOR CLERESTORY SURFACE 9 237 c 288 ELSE IF (SN.EQ.9) THEN

289 H1=ZLIT£{ J,3)

fl

,11
290 LC=ZLITE( J , 1 1

)

291 LC1=ZLITE{0 ,8)

292 WC=ZLITE(0 , 10)

293 WC1=ZLITE(0,7>

294 DP { J , N )=RMH-2 . 5 + Hl

295 WP{0 ,N)=RMW-PW

296 RW=RML

297 RL=RMW

298 IF { (LCl+LC ) .LT. PL )WINAZ(0 ,N >=SURFAZ{ ISN ) ONOTE : DSF=0.

299 IF {({ LCl+LC ) .GE. PL > .AND. (WCl .GE .PW) ) WI NAZ < J , N ) =SURFAZ ( I SN ) + 300 * ATAN{ {WC1-PW+.5*W)/{LC1+LC-PL) )*57.3

301 IF({(LC1+LC).GE.PL).AND.(WC1.LT.PW) ) WI NAZ { J , N ) =SURFAZ { ISN )

302 * ATAN{ {PW-WC1-.5*W)/{LC1+LC-PL ) )*57.3

303 END IF 304 50 CONTINUE

305 C 306 C CALCULATE ANGULAR CORRECTION OF GLAZING TRANSMITTANCE

307 C (CORRECTS FOR SUNLIGHT GRAZING ANGLE)

308 C 309 SUNALT=ZLITE{2, 1 ) QIH DEGREES

310 SUNAZ =ZLITE(2,2) @IN DEGREES

311 IF { SUNAZ. GT. 360. )SUNAZ=SUNAZ-360.

312 AZ=ABS{SUNAZ-WINAZ{ J ,N)

)

313 IF (AZ.GT,90. )THEN

314 ANG=0.

315 ELSE

316 ANG=ATAN{SQRT{TAN(SUNALT*PI/180. ) **2+S I N {AZ*P I / 1 80. )*»2)

317 */COS(AZ*PI/180. )

)

318 END IF 319 TNX=1 .018*T*COS(ANG )*{ 1 . +S I N { ANG ) **3

)

320 C 321 C CALCULATE SKY LUMINANCE AS SEEN THROUGH THE FENESTRATION

322 C 323 CALL SKYLUM(SURFAZ{ ISN ) , WI NAZ ( 0 , N ) , THETA{ J , N ) , P L , PW , WP ( 0 , N )

,

324 *DP(0,N>,J ,SKYLIT,SUNLIT,GRDLIT,SIDLIT)

325 IF{ ITEST.GT. 1 )G0 TO 55

326 C 327 C CALCULATE ROOM ILLUMINANCE AT SENSOR LOCATION

328 C 329 CALL RML ITE(WP (0 ,N ) ,DP { J ,N ) ,PL ,PW,RW,RL ,0 ,SKYL IT,SUNLIT,

330 *GRDLIT,XLITE)

331 COEF(0 ,N)=XLITE

332 55 CONTINUE

333 IF{ {T.LT.0) .AND. { SN . EQ . 5 ) ) DAYLTE=COEF ( J , N

) *GRDL IT*ABS ( T) *M

334 - IF{ {T.LT.0) .AND. {SN.NE.5) )DAYLTE=COEF{J,N)*SIDLIT*ABS{T)*M

335 IF{T.GT.0)DAYLTE=SUNLIT*TNX*M+COEF{O ,N )*T*M*SKYLIT

336 IF(T.EQ.0)DAYLTE=0.

337 DAYLT( N )=DAYLT( N )+DAYLTE

333 60 CONTINUE

339 C 340 C CALCULATE ADJUSTED LIGHTING LOAD

341 C 342 DAYLTE = DAYLT{ N ) 343 XI=0.70

344 CHI =0.30

345 IF{ZLITE{K,6).GT.0. ) X I =ZL I TE ( K , 6 ) 346 IF(ZLITE{K,7) .GT.0. ) CH I =ZL I TE ( K , 7 ) 347 LLOADN=LLOAD( DAYLTE , DILL , DIM, LOAD ,XI ,CHI

)

348 ZLITE{K, 10)=DAYLTE

349 ZLITE{K, 1 1 )=LLOADN

350 ZL ITE( K, 12 )=GRDL IT 351 70 CONTINUE

352 90 RETURN

353 END

E-8

Q$Q$Q$*GARY{ 1 > .SKYLUM(31 ) 1 SUBROUTINE SKYL UM { S UR F AZ ,WI NAZ , THETA , PL ,PW,WP , DP , J ,SKYL IT,

2 *SUNLIT,GRDLIT.SIDLIT)

34

C

C TO CALCULATE THE SKY LUMINANCE AS SEEN THRU A WINDOW/SKYLIGHT

5

6 c

c SUNALT=SOLAR ALTITUDE ANGLE (DEGREES ABOVE HORIZON)

7 c SUNAZ =SOLAR AZIMUTH ANGLE (DEGREES CLOCKWISE FROM NORTH)

8 c BETA =HAZINESS F ACTOR : R URAL =0 . 05 URBAN=0.10 I N DUSTR I AL =0 . 20

9 c WINAZ =VEIWING WINDOW AZIMUTH ANGLE (? CENTER AS SEEN BY

10 c POINT ON WORK PLANE (DEGREES CLOCKWISE FROM NORTH)

1

1

c THETA =VEIWING WINDOW ALTITUDE ANGLE @ CENTER AS SEEN BY

12 c POINT ON WORK PLANE (INPUT IN DEGREES ABOVE HORIZON)

13 c CR =CLOUD RAT 1 0 , D I F F USE/TOTAL SOLAR RADIATION

14 c (CLOUD COVER/10. COULD BE USED IN LIU OF CR,BUT W/ SOME

15 c LOSS OF ACCRURACY)

16 c SRT =TOTAL SOLAR RAD I AT I ON , HOR I ZONTAL ( BTU/ HR /SF

)

17 c SRD =DIFFUSE SOLAR RAD I AT I ON , HOR I ZONTAL ( BTU/HR /SF ) 18 c SKYLUM=SKY LUMINANCE @ WINDOW CENTROID ( FOOTLAMBERTS

)

19 c CLRSKY=CLEAR SKY LUMINANCE @ WINDOW OR SKYLIGHT CENTROID

20 c OVRSKY=OVERCAST SKY LUMINANCE Q WINDOW OR SKYLIGHT CENTROID

21 c SUNL IT=DIRECT SUN ILLUMINANCE ON THE HORIZONTAL

22 c SUNBM =DIRECT BEAM ILLUMINANCE AT NORMAL INCIDENCE

23

24 COMMON /DD/ZL ITE( 42 , 12 ) , DAYLT( 10)

25 REAL L , L 1 , LC . LC

1

26 RMH =ZL ITE (1,1)

27 AZM =ZL ITE( 1 , 4 ) 28 SUNALT=ZL ITE( 2 . 1

)

29 SUNAZ =ZLITE(2,2)

30 SRD =ZLITE(2,3)

31 SRT =ZLITE(2,4)

32 BETA =ZLIT£(2,5)

33 OMEGA =ZLITE(2,6)

34 JUL =ZLITE(2.8)

35 SN =ZLITE{J,9)

36 PI =3.14159

37 IF ( SUNAZ .GT .360, )SUNAZ=SUNAZ-360.

38 IF(SN.EQ.5)THEN @FOR HORIZONTAL SKYLIGHTS

39 X=0.

40 H =0.

41 H1=0.

42 W =ZL ITE( J , 1 ) 43 L =ZLITE(J,2)

44 L1=ZLITE( J,3)

45 W1=ZLITE(0 ,4)

45 HX = ZL ITE ( J , 7 ) 47 DX = ZL ITE ( 0 , 8 ) 48 OP=ZL ITE(0 , 10)

49 THETA=THETA*P I /180.

50 HWP =0.

51 ELSE IF (SN . LT. 5 )THEN QFOR VERTICAL WINDOWS

52 X=0.

53 L =0.

54 L1=0.

55 W =ZLITE(0 , 1

)

56 H =ZLITE(0,2)

57 H1=ZL ITE(0 , 3

)

E-10
58 W1=ZLITE( J,4)

59 HX=ZLITE( J .7)

60 DX = ZL ITE ( J . 8 > 61 OP=ZL ITE( J , 10)

62 AW=ZL ITE( J ,11)

63 HWP=H+Hl-2.5

64 HH=HX*(DP/(DP+DX)

)

65 THETA=ATAN( {HWP-{HWP-HH)/2)/DP> (? I N RADIANS

66 ELSE IF{SN.GT.5>THEN @FOR CLERESTORIES

67 W =ZL ITE( J , 1 ) 68 H =ZLITE(0.2)

69 H1=ZLITE(0,3)

70 W1=ZLITE(J,4)

71 WC1=ZLITE( J ,7)

72 LC1=ZLITE( 0,8)

73 WC=ZLITE(0, 10)

74 LC = ZL ITE{ J ,11)

75 HC = ZL ITE( J , 12 ) 76 OP=0.

77 AW=DP

78 IF{SN.EQ.6 )X=WC+WC1-PW

79 IF(SN.EQ.7)X=LC+LC1-PL

80 IF{SN.EQ.8)X=PW-WC1

81 IF(SN.EQ.9)X=PL-LC1

82 HWP=RMH + Hl+H/2-2 . 5 83 THETA=ATAN{ HWP/X ) QIN RADIANS

84 END IF 85 IF{SRT.EQ.0, )G0 TO 20

86 IF{THETA.LT.0, )THETA=0.

87 C 88 C CALCULATE INTERMEDIATE CLOUD-MODIFIED SKY LUMINANCE

89 c 90 CR =SRD/SRT

91 PHASE =( 1 .+COS(PI*CR) )/2.

92 SKYL I T=CLRSKY{SUNALT,SUNAZ,WINAZ,THETA, BETA, OMEGA )*PHASE

93 *+OVRSKY{SRD,THETA)*( 1 .-PHASE)

94 c 95 c CALCULATE SUNLIGHT PRESENT AT SENSOR POSITION

96 c 97 IF(SUNALT.LT.5)THEN

98 SUNBM=0. ^CONTROLS PROBLEM DUE TO LOW SUN ANGLES

99 ELSE

100 SUNDM=SUNN(SUNALT,SUNAZ ,AZM, H ,H1 , W , Wl , L , L 1 , OP , AW , WP

,

101 *PL,PW,DP,DX,SN.JUL ,X )*PHASE

102 - SUNLIT=SUNBM*SIN(SUNALT*PI/180.

)

103 END IF 104 c 105 c CALCULATE OUTDOOR HORIZONTAL & VERTICAL ILLUMINATION

106 c 107 AZ=ABS(SURFAZ-SUNAZ

)

108 GRDLIT=(93.+18.*CR)*SRT*.2931 ^ILLUMINANCE ON GROUNDIFC)

109 IF{ AZ.GE. 90. )SIDLIT=. 5*111. *SRD*. 2931 (3(FC)

110 IF(AZ.LT.90.)SIDLIT={.5*111.*SRD*.2931)

1 1

*+(SUNBM*COTAN{SUNALT*PI/180. ) ) 0 I L L UM I NANCE ON VERTICAL(FC)

112 20 RETURN

113 END

E-11
Q$Q$Q$*GARY{ 1 > .SUNN{ 9

)

1 FUNCTION SUNN(SUNALT.SUNAZ ,AZM, H , HI ,W,V/1 , L , L 1 .OP ,AW,WP , 2 *PL , PW. DP . DX ,SN ,OUL ,X

)

3 C

4 C SUBROUTINE TO CALCULATE THE DIRECT SUN CONDITIONS

5 C

6 C SUNAZ =SUN'S AZIMUTH (DEGREES CLOCKWISE FROM NORTH)

7 C SUNALT=SUN'S ALTITUDE (DEGREES ABOVE HORIZON)

8 C JUL =JULIAN DATE(JAN 1 = 1, DEC 31=355 ) 9 C AZM =CLOCKWISE AZIMUTH COORDINATES OF WALL OFF N-S AXIS

10 C EX =EXTRATERRESTRIAL ILLUMINANCE NORMAL TO SUN (FOOT-CANDLES)

11 C SUNN =DIRECT SUNLIGHT ILLUMINANCE NORMAL TO SUN (FOOT-CANDLES)

12 C 13 REAL L,L1.LS1,LS2

14 PI =3.14159

15 SUNN =0.0

16 IF{SN.GT.5)DP=X

17 EX=11840.*( 1 .+.033*COS( .99*OUL*PI/180) ) (3EXTRATERRESTR I AL ILLUMINANCE (FC)

18 C 19 C ALGORITHM TO DETERMINE THE SOLAR DISC ILLUMINANCE

20 C PROJECTED ON THE WORKPLANE FROM A VERTICAL WINDOW OR CLERESTORY

21 C

2 2 ANGL 1=ABS(ATAN{ (W+Wl-WP >/DP)*180./PI)

2 3 ANGL2=ABS{ATAN( (Wl-WP )/DP)*180./PI)

24 IF<(SN.EQ.1).0R.{SN.EQ.6))THEN

25 GO TO 60

26 ELSE IF( (SN.EQ.2) .OR. (SN.EQ.7) )THEN

27 IF(SUNAZ.GT. ( 180.+AZM) )G0 TO 60

28 DS1={ H+H1+AW>/TAN( ( SUNAL T* P I / 1 80 . )/

29 * CQS(ABS(SUNAZ-90.-AZM)*PI/180. ) )-0P

30 ANGL3=90. +AZM-ANGL

1

31 ANGL4=S0. +AZM+ANGL2

32 ELSE IF{ (SN.E0.3) .OR. (SN.EQ.8) )THEN

33 IF ( (SUNAZ . LT. ( 90. +AZM) ) .OR . (SUNAZ .GT. (270. +AZM) ) )G0 TO 60

3 4 DS1=( H+H1+AW)/TAN( ( SUNALT*P I / 1 80. )/

35 * COS(ABS(SUNAZ-180.-AZM)*PI/180. ) )-0P

36 ANGL3=180.+AZM-ANGL1

37 ANGL4=180.+AZM+ANGL2

38 ELSE IF( (SN.EQ.4) .OR. (SN.EQ.9) )THEN

39 IF(SUNAZ.LT. ( 180.+AZM) )G0 TO 60

A0 DS1=(H+H1+AW)/TAN( ( SUNALT*P I / 1 80 . )/ 41 * COS{ABS(SUNAZ-270.-AZM)*PI/180. ) )-0P

42 ANGL3=270. +AZM-ANGL

1

43 ANGL4=270. +AZM+ANGL2

44 ELSE

45 GO TO 50 (3F0R(SN.EQ.5>

45 END IF 47 IF( (SUNAZ. LT.ANGL3) .OR . (SUNAZ. GT.ANGL4) )G0 TO 60

48 DS2=0. (3INITIALIZE

49 IF(SN.LT.5)DS2=(DS1+0P >*H1/(H1+H+AW)

50 IF ( SN .GT . 5 )DS2=DS1*( Hl+AW) /( H+Hl +AW)

51 IF( (DP .GT.DSl ) .OR. (DP .LT.DS2) )G0 TO 60

52 SUNN-EX*EXP(-.21/SIN{SUNALT*PI/180. )

)

53 GO TO 60

5 4 C 55 C ALGORITHM TO DETERMINE THE SOLAR DISC ILLUMINANCE

515 C PROJECTED ON THE WORKPLANE FROM A HORIZONTAL SKYLIGHT

57 C

E-12
58 50 SANGLl=SUNALT+{90.-SUNALT)*ABS(COS(SUNAZ*PI/18£r. ) ) 59 IF{ (SANGLl .IF:Q.9jef. ) .OR. (SANG LI . EQ . 2 7jer . ) ) TH E N G0 LS1=L1

61 ELSE

62 IF(SUNAZ.LE.180. ) L S 1 = L 1 - ( D P + DX ) / TAN ( SANG L 1 * P I / 1 . ) 63 I F { SUNAZ .GT .180. ) LS 1 = L 1 + ( DP +DX ) / TAN ( SANGL 1 *P I / 1 80 . ) 64 END IF 65 LS2=LS1+L

66 IF( (PL .LT.LSl ) .OR . (PL .GT.LS2) >G0 TO 60

67 SUNN=EX*EXP(-. 21 /SIN(SUNALT*P 1/180. )

)

68 SANGL2=SUNALT+(90.-SUNALT)*ABS(SIN(SUNAZ*P 1/180. )

)

69 IF(SANGL2.EQ.90. )WS1=W1

70 IF { SANGL2 . NE . 90. ) WS 1 =W 1 + ( DP + DX ) /TAN ( SANG L 2 * P I / 1 80 . ) 71 WS2=WS1+W

7 2 IF( (PW.LT.WSl ) .OR. {PW.GT.WS2) )SUNN=0.

73 60 CONTINUE

74 RETURN

75 END

E-13
Q$Q$Q$*GARY{ 1).CLRSKY{25>

1 FUNCTION CLRSKY{SUNALT,SUNAZ,WINAZ,THETA, BETA, OMEGA)

2 C

3 C SUBROUTINE TO CALCULATE THE CLEAR SKY LUMINANCE AT THE

4 C CENTROID OF THE WINDOW/SKYLIGHT

5 C

6 C (INPUT VALUES FOR CLRSKY ARE CONVERTED TO RADIANS BELOW)

7 C SUNALT=SOLAR ALTITUDE IN DEGREES ABOVE HORIZON •8 C ZLUM =ZENITH SKY LUMINANCE ( FOOTLAMBERTS

)

9 C AZ =AZIMUTH ANGLE BETWEEN SUN AND VIEW POINT OF GLAZING

10 C THETA =ALTITUDE ANGLE OF GLAZING VIEW POINT

11 C GAMA =SOLID ANGLE BETWEEN SUN AND GLAZING VIEW POINT

12 C OMEGA =ATMOSPHERIC MOISTURE COEFFICIENT

13 C BETA =ATMOSPHERIC TURBIDITY COEFFICIENT

14 C 15 DIMENSION A0{ 6 , 3 ) ,A1 ( 6 , 3 ) 16 DATA(A0{ J , 1 ) ,0 = 1 , 6 )/0. 9361 ,0, 9093 ,j0f. 8727 ,j0r. 8547 .0. 845fir,jEr. 8410/

17 DATA{A0{O , 2 ) ,0=1 , 6 )/l .0329 . 1 .0206 , 1 .0074 , 1 .0019 ,0. 9990,0, 9980/

18 DATA( A0{O , 3 ) ,0 = 1 ,6 )/l . 1399 , 1 . 1499 , 1 . 1698 , 1 . 1833 , 1 . 1899 , 1 . 1968/

19 DATA{A1 (0 , 1 ) ,0 = 1 , 6 )/0. 0020. 0.0018 ,0.0014 ,0.0012 ,0.001 1 ,0.001 1/

20 , DATA(A1 (0 , 2 ) ,0=1 , 6 >/0. 0024 ,0.0022 ,0.0019 ,0.0017 ,0.0016 ,0.0016/

21 DATAIAHO, 3) ,0 = 1 ,6)/0. 0030, 0.0028, 0.0025, 0.0023, 0.0022, 0.0021/

ZZ PI=3. 14159

23 IF{BETA.LE.0.05>IBETA=1

24 IF {( BETA .GT. 0.05 ) .AND .( BETA. LE .0. 10> > IBETA=2

25. IF(BETA.GT.0. 10)IBETA=3

26. IF(OMEGA.LE.0.5)IOMEGA=1

27 IF (( OMEGA. GT.0. 5 ) .AND . (OMEGA. LE . 1 .0) ) I0MEGA=2

28 IF{ (OMEGA. GT. 1 .0) .AND. (OMEGA. LE. 2.0) )I0MEGA=3

29 IF( (OMEGA. GT. 2.0) .AND. (OMEGA. LE. 3.0) )I0MEGA=4

30 IF{ ( OMEGA. GT. 3.0) .AND. ( OMEGA . L E . 4 . 0 > )I0MEGA=5

31 IF(OMEGA.GT.4.0)IOMEGA=6

32 SALT =SUNALT*PI/180. PIN RADIANS

33 ZLUM =(A0( IOMEGA, IBETA)+A1 { IOMEGA, IBETA)*SUNALT**2)*291 .9

34 AZ =ABS( (SUNAZ-WINAZ)*PI/180. ) QIH RADIANS

35 GAMA =ACOS(SIN{ THETA )*SIN( SALT )+COS( THETA )*COS( SALT )*COS(AZ)

>

36 CLRSKY=ZLUM*{0.910+10.*EXP( -3*GAMA) +0.45 *COS{ GAMA) *COS( GAMA) >* 37 *( 1

. -EXP (-0. 32 /SIN( THETA) >)/(0.27385*(0. 91+10. *EXP(-3*(1 .57-SALT))

38 *+0.45*SIN(SALT)*SIN(SALT) ) ) 39 RETURN

40 END

E-14
Q$Q$Q$*GARY( 1 ) .OVRSKY{ 17

)

1 FUNCTION OVRSKY(SRD,THETA)

2 C

3 C SUBROUTINE TO CALCULATE THE OVERCAST SKY LUMINANCE AT THE

4 C CENTROID OF THE WINDOW/SKYLIGHT

5 C

6 C ZLUM =ZENITH SKY LUMINANCE ( FOOTLAMBERTS

)

7 C OVRSKY=OVERCAST SKY LUMINANCE OF APERTURE MIDPOINT

8 C THETA =ALTITUDE ANGLE STUDY POINT MAKES WITH APERTURE MIDPOINT

9 C 10 PI=3. 14159

I 1 C 12 C CALCULATE ZENITH LUMINANCE

1 3 C 14 ZLUM={ 111 . *SRD*jer. 29 31 >*9/7

15 C IS C CALCULATE OVERCAST SKY LUMINANCE AT WINDOW VIEW ANGLE

17 OVRSKY=ZLUM*( ( 1 . + 2

. *S I N ( THE TA > ) / 3 .

)

18 RETURN

19 END

E-15
E-16
Q$Q$Q$*GARY( 1 ) .RMLITE(36)

1 SUBROUTINE RML I TE ( WP , DP , PL , PW, RW , RL , J

2 *SKYLIT, SUNLIT, GRDLIT,XLITE)

3 C

4 C THIS ROUTINE CALCULATES THE COMBINED ILLUMINANCE COEFFICIENTS

5 C USED TO OBTAIN TOTAL WORKPLANE ILLUMINANCE,

6 C

7 C DP =DEPTH OF THE REFERENCE POINT FROM THE APERTURE SURFACE ( FEET >

8 C T =TRASMISSION COEFFICIENT OF WINDOW OR SKYLIGHT

9 C (NEGATIVE IF TRANSLUCENT)

10 C WA =WINDOW OR SKYLIGHT AREA. SQ. FT.

11 OA =ROOM INTERNAL SURFACE AREA

12 C RX =REFLECTANCE OF EXTERNAL OBSTRUCTION OR SKYLIGHT WELL

13 C RFW =AVERAGE REFLECTANCE FACTOR OF THE LOWER HALF OF THE ROOM

14 C RCW =AVERAGE REFLECTANCE FACTOR OF THE UPPER HALF OF THE ROOM

15 C RAVE =AVERAGE REFLECTANCE OF THE ENTIRE ROOM

16 C W =WINDOW OR SKYLIGHT WIDTH, FT.

17 C L =SKYLIGHT LENGTH, FT,

18 C H =WINDOW HEIGHT, FT,

19 C ML =PROJECTED HEIGHT OF OBSTRUCTION ON WINDOW

20 C HX =HEIGHT OF OBSTRUCTION FROM WORK PLANE

21 C DX =DISTANCE OF OBSTRUCTION FROM WINDOW

22 C WX =SKYLIGHT WELL DEPTH

23 C RMH =ROOM HEIGHT

24 C RML =ROOM LENGTH

25 C RMW =ROOM WIDTH

26 C RW =APPARENT ROOM WIDTH (USED IN INTER-REFLECTION MODEL)

27 C RL =APPARENT ROOM LENGTH (USED IN INTER-REFLECTION MODEL)

28 C WP =DISTANCE FROM CORNER OF ROOM TO PERP. REFERENCE LINE

29 C HI =SILL HEIGHT ABOVE FLOOR

30 C Wl =DISTANCE FROM LEFT MOST CORNER OF WINDOW OR SKYLIGHT

31 C TO LEFT MOST CORNER OF WALL SURFACEdN "WIDTH" DIRECTION)

32 C LI =DISTANCE LEFT MOST CORNER OF SKYLIGHT TO LEFT MOST

33 C CORNER OF WALL SURFACE{IN LENGTH DIRECTION)

34 CM =CORRECTION FOR GLAZING MULLIONS

35 C T =COMBINED EFFECTIVE TRANSM 1 TTANCE OF THE GLAZING

36 C TNX =ANGULAR DEPENDENT TRANSMI TTANCE

37 C RG =GROUND REFLECTANCE

38 C JUL =JULIAN DATE

39 C DAYLTE=INTERIOR DAYLIGHT ILLUMINATION

40 C XDL =DIRECT LIGHT FROM THE SKY

41 C XERL =EXTERNALLY REFLECTED LIGHT (FROM OBSTRUCTING BUILDINGS)

42 C RRL =ROOF REFLECTED LIGHT ENTERING CLERISTORY

43 C XIRL =INTERNALLY REFLECTED LIGHT (FROM ROOM SURFACES)

44 C SKYLIT=SKY LUMINANCE @APERTURE CENTRO I D ( AVERAGE APERTURE LUMINANCE)

45 C SUNL IT=HORIZONTAL ILLUMINANCE FROM THE DIRECT SUN

46 C GRDLIT = TOTAL HORIZONTAL GROUND I L L UM I NAT I ON ( SKY&SUN

)

47 C SIDL IT=VERTICAL SURFACE ILLUMINANCE( SKY ONLY)

48 C GRL =GROUND REFLECTED LIGHT COEFFICIENT

49 C SNL =SUNLIGHT COEFFICIENT

50 C

51 COMMON/DD/ZL ITE( 42 , 12) ,DAYLT( 10)

52 REAL M,L,L1,LC,LC1

53 P 1=3 . 14159265

54 RMH =ZLITE(1,1)

55 RML =ZLITE(1,2)

56 RMW =ZLITE(1,3)

57 RCN =ZLITE(1,5)

E-17
11 : 58

59 1

60

61

62O vJ O 4

r.fi fi7 1

'!

DO

DJ / JO

r 7 1 4

•n 7 A

7^; f o 77

7R

79

80S 1

83

84

86

r 87

88

89

909 1

92

93

94

95

97

r 9nJ r 1 CCT 1 Qi 1 L JO c. 1 PfT 1L JO(HA 1 i^Il 1 Q'f^ 1 -o o 1I JOC?7/ 1 1 l?f 1 1 1 1 12

113 1 14 1 15 c

Dill RWL "7 1 T

T cr / 1 1 1 b. V 1 5 ) R F L = Z L I TE { 1 7 ) RG = ZL I TE ( 1 8 ) RX = Z L I TE { 1 9 ) SUNALT = Z L I TE { 2 1 > JUL = ZL ITE( 2 8 ) T = ZL ITE{ J 5 ) M = ZL ITE{ J 6 ) SN = ZL ITE{ J 9 ) OP = ZL ITE( J , 10)

AW = ZL ITE(J 1 1 ) FP = ZL ITE{0 , 12 ) FOR THE FOUR ROOM SURFACES

IF ( SN . LT. 5 )THEN

W=ZL ITE<J , 1 ) H=ZLITE(J,2)

H1=ZLITE(

J ,3)

W1=ZLITE(J,4)

HX=ZLITE<0,7)

DX = ZI. ITE(J,8)

V,'A = W*H

HH=HX*DP/ ( DP+DX )

HL=HH-Hl+2.b

HHl=H + Hl-2 . 5 IF(HL .GT.H)HH = H FOR CEILING SURFACE

ELSE IF{SN.EQ.5>THEN

W=ZL ITE(

J , 1 ) L=ZL ITE( J , 2 ) L 1=ZL ITE( J , 3 ) W1=ZLITE{ J,4)

HX=ZLITE(0,7)

DX=ZLITE{

J ,8)

H =L HL=0.

FOR CLERESTORY SURFACES

ELSE IF{SN.GT.5)THEN W =ZLITE<0 , 1 ) H =ZL ITE{ J , 2 )

H1=ZLITE{0,3)

W1=ZLITE^(J,4>

WC1=ZLITE{ 0,7)

LC1=ZLITE(0 ,8)

WC=ZL ITE(

J , 10)

LC=ZLITE{0 ,11)

HC=ZL ITE(0 , 12 )

HH=0.

HK1=0.

HL=0.

END IF XDL=0.

E-18
116 c PREPARF VARIARI F*s FOR TNTPRRFFI FTTTriN 1 1 p p nilT T N r 117 c 118 A = 2 . *( (RML*RMH ) + ( RML *RMW ) + ( RMH*R MU > ) 119 ACN= RMW*RML

1 20 AWL = (RL*RMH)+2*(RW*RMH)

121 RAVE={AWL*RWL+ACN*RFL+ACN*RCN+(W*H )* . 1 5+ ( RL *RMH-W*H ) *RWL

)

122 */(AV/L+ACN+ACN + RL*RMH ) 123 IF(SN.GT.4)G0 TO 10

124 c CALCULATE CORRECTION FOR EXTERIOR FINS & OVERHANGS

1 2S c 127 IF ( HL .GE . H )G0 TO 20

11 ?ft £~ O IF( (OP .GT.0. ) .AND. (ATAN( AW/OP ) . LT . ATAN ( HH 1 / DP ) ) ) HH 1 =DP * ( HH 1 +A\; ) /

*(OP+DP) ^CORRECTION FOR OVERHANG

1 ox/ IF{FP .GT.0. )W=W-{FP*W/2/(DP+FP ) ) OCORRECTION FOR SIDE FINS

1 T 1 ©ASSUMES WINDOW CENTRIOD REPRESENTATIVE

1 ICr ix) PHMTTMIIC LUril INUt

loo r

c LALLULAIt 1 nt UlKbLI LlbHI L UN h 1 G UR AT I ON COEFFICIENT BETWEEN THE

1 T=> r rtlxcolKAIiUN AI^U A rulNI IN Inb KUUM.

r

r UMLL ULVAUL ,Ut\L ,KKL ,nni ,nn,W,Wr »Ur ,rL ,rW,bKULl 1 ,J /

1 r

1 Aff PAI nil ATF TMF PyTFRNAI 1 V RFFI FPTirn 1 TPUT

1 il 1 r 14 2 143 7Cf T F f *s N 1 T ^ y F R 1 -FR! f U H Ul HI MH UP nP\*DV ISPVTPQNAI OFF 1 T r UT

14 4 145 PAI PHI ATF THF ^HNI Tt^HT TNTFN^TTV FNTFRTWr; ROnM

146 c H THF f;Rf)MNn 1 TCiHT PnFFFTPTFNT*s

147 c 148 TF(^HNAI T 1 T >THFN

149 SNL=0. ^CONTROLS PROBLEMS DUE TO LOW SUN ANGLES

1 50 ELSE

151 SNL=SUNL IT/ (ABS(T )*M*SKYL IT)

152 IF((SN.GE.6).AND.{XDL.EQ.CRL))SNL=SUNLIT/GRDLIT

153 END IF 154 GRL=GRDLIT/(ABS(T)*M*SKYLIT)

155 c 156 c CALCULATE INTERNALLY REFLECTED LIGHT

157 c 158 CALL IRL{J,HH,RL,RW.RAVE,A,GRL,SNL,CRL,XIRL) ©INTERNAL REF LIGHT

159 c

1 60 c CALCULATE DAYLIGHT ILLUMINANCE

161 c NOTE: NEGATIVE TRANSMITANCE MEANS TRANSLUCENT GLAZING

162

163 IF((SN.GE.6).AND.(XDL.EQ.CRL))T=1.0

154 XRRL=RRL/{T*M*SKYLIT)

165 IF{(T.LT.0>.AND.(SN.EQ.5))XLITE=XDL+XIRL

166 IF{{T.LT.0).AND.{SN.NE.5))XLITE=XDL+XIRL-XERL

167 IF{(SN,GE.6).AND,{XDL.EQ.CRL>)XLITE=XIRL

168 IF{(T. GT.0). AND. (T.NE.1))XLITE=XDL+XERL+XIRL+XRRL

1G9 • IF(T.EQ.J0f. )DAYLTE=0.

170 RETURN

171 END

E-19
OSQSQ$*GARY( 1 ) .DL(19>

1 SUBROUTINE DL ( XDL , CRL , RRL , HH 1 , HH , W , WP , DP , P L , PW , GRDL I T , 0

)

2 C

3 C DL =DIRECT LIGHT FROM SKY ON A POINT IN THE ROOM.

A C THIS ROUTINE CALCULATES POINT ILLUMINANCE COEFFICIENTS

5 C , OF THE DIRECT SKY COMPONENT FOR WI NDOWS , HOR I ZONTAL SKYLIGHTS,

6 C AND CLERESTORIES.

7 C

8 COMMON /DD/ZL ITE< 42 , 12 >

, DAYLT( 10)

9 REAL L,L1 ,L2,L3,LC,LC1 ,LC2

10 PI =3.14159265

11 PI2=PI/2

12 H =ZLITE{0,2)

13 HI =ZLITE(CI,3)

14 Wl =ZLITE{0,4)

15 SN =ZLITE{0,9)

16 RCN = ZLITE(1 ,5)

17 RG =ZLITE( 1,8)

18 XDL=JE2f. ^INITIALIZE

19 CRL=0. ©INITIALIZE

20 ZERO=0.

21 IF ( SN .GE . 5 )G0 TO 30

22 C 23 C WINDOW ROUTINE

24 C 25 H2 =2.5-Hl

26 H2A=ABS(H2)

27 W4 =WP-W1-W

28 W5 =WP-W1

29 IF{HH.GE.HH1 )G0 TO 40

30 IF{HH.EQ.0. )THEN

31 IF(H2.LE.0. )XDL=BCF(W,H,DP ,W5,H2A,PI2)

32 IF{H2.GT.0.)XDL=BCF<W,HH1 , DP , W5 , ZERO , P I 2

)

33 ELSE

34 HH4=H-HH

35 HH6=HH-H2

36 ' XDL=BCF (W, HH4 , DP ,W4 , HH6 , P 12

)

37 END IF 38 GO TO 40

39 30 CONTINUE

40 C 41 C MODEL DIRECT LIGHT FROM TOP L I GHT I NG { OVERHEAD FENESTRATION)

42 C 43 WCi=ZLITE{0 ,7)

44 LC1=ZLITE(0 ,8)

45 WC =ZL ITE( J , 10)

46 LC =ZLITE( J ,11)

47 HC =ZLITE(J, 12)

48 IF(HC.GT.0. )PSI = 90. (?ROOF MONITOR CHECK

49 HC=ABS(HC)

50 X =PL-LC1

51 Y =PW-WC1

52 ZZ =DP

53 IF(SN.EQ.5)THEN

54 C 55 C SKYLIGHT ROUTINE

56 C 57 C ASSUMES USE OF EFFECTIVE TRANS FOR LIGHT WELL EFFECTS

E-20
3 O

o y AA — cr — Ji^ • ox/ 1L —-Z.LlItV\J,/i/ 7ITTir/T 0\

c 1 11— 71TTC/10\

o ^ \jy WA —— 7l.cLlTTF/I !t\J,o/Q\

D O 7 7 — n P 4.\ IV O *f W ^ — W 1 r W 65 1L 7 =— 1L 1 - P 1 1 r L 66 irvw^.iati.Jc'. / int. 11 67 w o — W w 68 [. U o H 69 W-J— MDOxW^ / 70

7 1 Fc liM nu Ti Fr 72 TF(I? QF CT ^TMFN

73 L. O — L c. ~ L 7 A TrM7 Fn

7'i FIC L "^F o C 76

77

78 FC Nn nU TX Fr 79 T F ( IF U ^ THFN

w ^ — W wo

R 1 v4 •i — vJ no 9^ IF 1 ^T^FM

o o L <^ — L L o o ^ L o — L R K O u Vni— XUL-bLrb\Wo,LJ,ZZ.,A;+DUrc>\WJ,Ld,^Z,A/ DPCC/WO lO 77 A\ADr'CC/l/D lO 77 A\

O O R 7 t L o t: R O 11. 7 —— 1L*:i+ 7-i.A/\^v*i \ \VtA Li:://Ur/ o\/r»D\

£2 Q Vni— DPCC/V/tJ lO 77 A\_Dr'CC^\/'7 lO 77 A\

* j-DPrCM/'? lO 77 A\_DPrCM/7 17 77 A\

Q 1 3 Jl r- M n T c L ii U 1 r R9 F 1 F c. L o t. Q "J \/7— \/7j. / / V/ V*V/'7 \ / no \ Q A TFMQ IF I \TUCW

1 9 — 1 — 1 T QV e,D L O — L R7

t)R F J Q F

1 7 = 1 7 + M uy * 1 7 wn p ^ yni =RrF*^(UT l 77 A>-RrF<N/U7 l 77

1 fil 1 * -RPF^^IW^ 1 7 77 A^+RrF<;;fU7 1 7 77 A^

Fc wnll L/ T1 Fr

1 Fc Nll nu T1 Fr p

r riFRF*^TnRv pniiTTNF (TNTiiinTNt^ RnnF MnN T TrvR ^ >

1 (IP.

1 / FI*^F TFM^N'FO fi> OR (<sN Ffl PMTHFN

1i yj o yA yA =~ VT

1 fif^ 1 A/ >

1 10 YY =X-W1

1 1 ! IF{SN,EQ.8)YY=\>/+W1-X

112 CC =SQRT(WC**2+HC**2

)

113 IF ( PSI . EQ. 90. )CC=WC

114 CC2=CC/2

115 LC2=LC/2

E-21
lis WC2=WC/2

117 C 118 C CALCULATE ROOF REFLECTED LIGHT: RRL

113 C 120 IF(PSI .EQ.90. )THEN

121 PHI=0.

122 A =HC

123 ZZ =DP+HC

124 ELSE

125 A =WC2*SIN{ PHI ) 126 END IF 127 B1=CC2*SIN{ PHI ) 128 B2=H-81

129 C =SQRT(WC2**2-i-A**2 ) 130 RRL = BCF{LC,B2,C,LC2,A,PHI )*RG*GRDLIT

131 **BCF(LC,CC,XX,YY,ZZ,PHI )*RCN

132 IF<PSI .EQ.9;0f)GO TO 10

133 C 134 C CALCULATE CEILING REFLECTED LIGHT: CRL

135 C 136 XX =WC-Y

137 HHC=HC-H-H1

138 CRL=BCF<LC,CC,XX,YY,ZZ,PHI ) *BCF (W, H , CC2 , LC2 , HHC.PS I )*RCN

139 10 CONTINUE

140 C 141 C CALCULATE DIRECT LIGHT: XDL

142 C 143 XX =WC-Y

144 IF(SN.EQ.8)XX =Y

145 XDL=BCF(W,H,XX,YY,DP.PI2)+CRL

146 IF{ (SN.EQ.e) .AND. (Y.GT.WC) )XDL=CRL

147 IF({SN.EQ.8).AND.(Y.LT.J0f,) )XDL=CRL

148 C 149 ELSE IF( {SN.EQ.7) .OR. (SN.EQ.9) )THEN

150 XX =X

151 IF(SN.EQ.9)XX =LC-X

152 YY =Y

153 CC =SQRT{ LC**2 + HC**2 ) 154 IF ( PSI . EQ. 9af)CC = LC

155 CC2=CC/2

156 LC2=LC/2

157 WC2=WC/2

158 C 159 C CALCULATE ROOF REFLECTED LIGHT: RRL

15^ C 161 PHI=ATAN{ HC/LC ) 162 PSI=PI/2-PHI

163 IF(PSI .EQ.9j0f. )THEN

164 PHI =0.

165 . A =HC

166 ZZ =DP+HC

157 ELSE

163 - A=LC2*SIN{ PHI

>

169 END IF 170 B1=CC2*SIN(PHI ) 171 B2=H-B1

172 C =SQRT( LC2**2+A**2 ) 173 RRL=BCF(WC,B2,C,WC2,A,PHI )*RG*GRDLIT

E-22
174 **BCF(WC,CC,XX,YY,ZZ,PHI)*RCN

175 iF(PSi .EQ.gjer. )G0 to 20

176 C 177 C CALCULATE CEILING REFLECTED LIGHT: CRL

178 C 179 HHC=HC-H-H1

180 CRL = BCF(WC,CC,XX,YY,DP,PHI ) * BC F ( W , H , CC 2 , WC2 , H HC , PS I )*RCN

181 20 CONTINUE

182 C 183 C CALCULATE DIRECT LIGHT: XDL

184 XDL=BCF<W,H,XX,YY,Z,PI2)+CRL

185 XX =LC-X

186 IF(SN.EQ.9>XX =X

187 IF((SN.EQ.7).AND.(X.GT.LC) )XDL=CRL

188 IF((SN.EQ.8).AND.<X.LT.0.) )XDL=CRL

189 END IF 180 40 RETURN

191 END

E-23
Q$QSQ$*GARY{ 1 ) . IRL {5j0r)

1 SUBROUTINE IRL{0,HH,RL, Rw , RAVE ,A,GRL ,SNL,CRL ,XIRL

)

2

3 C

C COMPUTES THE INTER-REFLECTED LIGHT (FROM THE ROOM SURFACES)

4

5

c

c RMH =RO0M HEIGHT

6 c KW =ArrAKLlN] KUUn wlUIH v Ab bbbN dY Inh rtlNhblKAllUli;

7 c

8 c RWL =KbrLhCIAnLti Ur WA L L 9 c RCN =R LLL 1 ANLL Ur LtlLlIMb

lJ0f c RFL =Ktl" L tL 1 AMLL Uh hLUuR

1

1

c XIRL =ilNih.KNALL. Y KhrLhLlbL) Llbnl LUbrriClbril

12 c GRL =bKOUNU KbhLbLlbU Llbnl LubrrlLlbNl

13 c SNL =SUNLIGHT COEFFICIENT

14 c 15 REAL LC , LC

1

16 COMMON /DD/ZLnE(42, 12) ,uAYLT( Iw)

1

7

RMH =ZL I Tt ( 1 , 1 ) 18 RCN =ZL I Tt ( 1 , 5 ) 19 Rv/L =ZL n E { 1 , 6 ) 20 RFL =ZL I Ft ( 1 , 7 ) 21 RG =ZL I TE ( 1 , 8 ) 22 RX =ZL I TE ( 1 , 9 > 23 Oil MAI T" ^1 TTr/O 1 \ SUNALT = ZLITh{Z, 1 ) 24 SUNAZ =ZLnE{Z,Z)

25 W =ZLnE(J,l)

26 H =ZLITE(J,2)

27 111 ~TiTT'r"/T o\ HI =ZL I TE ( J , 3

)

28 wl =ZL I 1 E ( J , 4 ) 29 SN =ZL I TE ( J , y ) 30 PI=3. 14159

31 . PI2 =PI/Z

32 KOUNT=

1

33 ZLITE{42,12)=ZLITE(42,12)+KOUNi

34 c 35 c FOR I N 1 ER-R LbL riUMS FROri 1 Ur L 1 b H 1 1 iNb ( b K Y L 1 b n 1 S & L L bR bi> 1 UR 1 bb / 36 c 3 7 c NOTE:LIbHI V/bLL & LLbRbblURY LAVIIY RbFLbUlbU Llbnl

38 c IS COMrUTEu IN DL SUBROUFINE

39 G 40 IF(SN.EQ.5)SURFAZ=ZLITEv 1 ,4)

41 IF {SN.GT.5)SURI Az. = yw.'*vbN-b)+^Ll lb( 1,4)

42 c 43 G

TMT"r"ripiAi r^f"rI f"oTTi^R[o oiyv/i Toil T INTERNAL REFLECTIONS FROM SKYLIGHT

44 c 45 I F ( SN . tU . D ) 1 HhN

46 F L UX 1 =0

.

47 F L UX2 = 0

.

48 FLUX3=,ti.

49 f- L U a4 =jy

.

K Of rLUAD"-W n ut\L VyrLUA rixVJri oixYLlvani

51 SUNFLX = SNL*W*H*RFL (3FLUX FROM THE SUN

52 G 53 C

' INTERNAL REFLECTIONS FROM CLERESTORY

54 c 55 ELSE IF(SM.GT.5)THEN

56 WC1=ZLITE(J,7>

57 LC1=ZLITE{0,8)

E-24
C Q 3 O WC =ZLITE{O,10)

LC =ZLITE( J ,11)

faJW T C / C M 1 r \ S) IN . tU . b ; 1 HhlM

r 1 b i AA-WU 1 +WL

b <i YY = LCl+LC-Wl-W

b J ELSE IF(SN.EQ.7)THEN

b 4 XX = LCl+LC

b b YY = WCl+Wl

b b ELSE IF{SN.Ea.8)THEN

fa / XX = RW-WCl

b o YY = LCl+Wl

fay ELSE IF(SN.EQ.9)THEN

la XX = RW-LCl

/ 1 YY = WCl-Wl-W

/ <C END IF

7 i ZZ=RMH/2+Hl

/ 4 FLUXl =0.

/ b FLUX2 =0.

"7 r

1 b BCF3 = BCF{W,H.XX,YY,ZZ,PI2) (PFLUX FROM BACKCOPPOSITE

"7 "7 FLUX3 =BCF3*RL*RMH*RWL

"7 O

/ 8 FLUX4 = 0.

"7 Q 79 FLUX5 =0.

Oaa SUNFLX=SNL*W*H*RWL ©FLUX FROM THE SUN

Q 1 CNFLX =CRL*LC*WC*RCN

O ^ a c. U ELSE IF(SN.LT.5)THEN

o4 FP = ZLITE(CI, 10)

o b AW =ZLITE<0, 11

)

o b L- Q 7 O /

r* FOR INTER-REFLECTIONS FROM SIDELIGHTING

O QO L. Q Q RL2 =RL/2

via RH2 =RMH/2

Q 1 RW2 = RW/2

y ^ HHl =H+Hl-2.5

y o HH2 =RMH/2-HH-2.5

y 4 HH3 =RMH/2-Hl

y o HH4 =H-( HH3-HH2

)

y b HH5 =RMH/2-HH2

H2 =2.5-Hl

O Q y o H3 = H1+H

Q Q y y H4 =RMH-H1-H2

100 H5 =RMH-H1-H

101 H6 =RMH-H1

102 W2 =W1+W

103 W3 =RL2-W1

1 ly ji 104 W6 =RL-W2

1 ore 10b W7 =RL-W1

1 06 ZERO =0.

110 / SURAZ = 90.*{SN-1 )+ZLITE( 1,4)

108 c 109 c CALCULATE INTERNALLY REFLECTED FLUX FROM THE SUNLIGHT

1 10 c

1 1

1

AZS=ABS{SUNAZ -SURAZ ) 112 IF{AZS.GE.90. )THEN

113 SUNFLX=0.

114 ELSE

115 PHI =<SUNALT*PI/180. )/COS{AZS*PI/180.

)

E-25
lib IF{AW,LT.{FP*TAN(PHI ) ) ) DS 1 =RMH/TAN ( PH I )- FP

1 1 ~7 11/ IF(AW.GE. (FP*TAN{PHI ) ) ) DS 1 = ( RMH -AW ) /TAN { P H I

)

~r r lid DS2=H1/TAN{PHI

>

DS3 = F P* ( TAN (AZS*PI/180. )

)

1 20 IF{DS3.GT.w. >W=W-DS3

121 SUNF LX = SNL "W* ( DS 1 -DS2 ) *RF L @FLUX FROM THE SUN

122 END IF 12 3 C 12 4 c CALCULATE FLUX FROM CEILING

125 c 12 6 BCFCN = BCF { w , H , Rvy2 , w3 , h5 , P I 2 ) 12 7 CNhLX = BCFCrH'-RW'RL*RCN*RG*GRL

128 c 129 c CALCULATE FLUX FOR EACH WALL SURFACE

1 30 c lot 1 J 1 SUMFLX=ZLITE(33,9)

132 I F { ZL I TE ( 42 , 1 2 ) . GT . KOUNT ) GO TO 10

1 o o

113 4 c WINDOW WALL SURFACE 1 IOC 1 Jb L IOC lob FLUX1=JW (?SINCE WINDOW WALL HAS LITTLE REFLECTED LIGHT

1 O 7 C

1 o o loo LEFTSIDESURFACEZ

1 O Q

IFtRX.EQ.W. )BCF2=BCF{H,W, Rw2 ,HH3,W1 ,PI2)

14 1 IF{RX.GT.J0. )BCF2 = BCF(HH4,W, RW2 ,HH2,W1 ,PI2)

1 >l o * +BCF { HH 1 , W , RW2 , HH3 , Wl , P I 2

)

*RX

1 j< o 143 FL UX2 = BCF 2*RMH*RW*RWL

144 C 14a 1^L BACK WALL SURFACE 3 146 c 147 IF(RX.lQ.J0'. )BCF3 = BCF(W,H,HH3,W3,RW,ZER0)

1 jl o 14a IFlRX.GT.M. )BCF3=BCF{W,HH4,HH2 , W3 , RW , ZERO

)

1 4 y * + BCF { W , HH 1

,

HH3 , W3 , RW , ZERO

)

*RX

1 bJ^ F L UX3 = BCF 3*RMH*R L *RWL

1 C 1 1 b 1 152 c RIGHT SURFACE 4 ICO 1 b J

1 C jl 1 b4 IF{RX.EQ.F. )BCF4=BCF{H,W, RW2 ,HH3,WG,PI2)

155 IF{RX.GT.0.)BCF4=BCF(HH4,W,RW2,HH2,W6,PI2)

156 * +BCF { HH 1 , W , RW2 , HH3 , W6 , P I 2

)

*RX

157 FLUX«=BCF4*RMH*RW*RWL

158 c ICO 1 by FLOOR SURFACE 5

1 bjy c 161 IF<RX.EQ.0. )BCF5=BCF{W,H,RW2.W3,H1 ,PI2)

162 IF{RX.GT,0. )BCF5=BCF{W,HH4,RW2,W3,HH5,PI2>

163 * +BCF{W,HH1 ,RW2,W3,H1 ,PI2)* RX

164 FLUX5=BCF5*RW*RL*RFL

1 65 c

1 bo c

1 7 END IF 168 c 169 c COMPUTES MULTIPLE I NTER -REF L ECT I ONS (ASSUMING ULBRICHT SPHERE)

170 c 171 SUMFLX={ FLUX1+FLUX2+FLUX3+FLUX4+FLUX5)

172 */A/{ 1-RAVE

)

173 10 IF{SN.LT.5)ZLITE{33,9)=SUMFLX

E-26
174 XIRL=SUMFLX+( ( CNF LX + SUNF LX > /A/ ( 1-RAVE )

)

175 RETURN

176 END

E-27
Q$Q$Q$*GARY( 1 ) .ERL(31

)

1 FUNCTION ERL{W,H,W1 ,H1 ,HH,WP,DP>

2 C

3 C ERL = EXTERNALLY REFLECTED LIGHT FROM SURROUNDING BLDGS

4 C

5

lltfn 111 all HwP = H 1 +H

6 W4 =WP-W1

7 W5 =W4-W

8 H2 =Hl-2.5

9 H2A=ABS { H2

)

lj0f w5A=ABS ( Wb

11 w4A=AB5 { W4

)

1

2

I F V wb . G 1 . 0 ) GO TO 1 1

3

IFvwo.LI.jy) GO 10 d

1

4

ERL=BCFW(w,HH,DP )-BCFw(w,H2A,DP

)

15 GO TO 3 16 1 ERL = BCFW{W4 , HH , DP )-BCFW(Wl , HH , DP )-BCFW(W4 ,H2A,DP >+BCFW(Wl ,H2A, DP > 17 GO TO 3 18 2 IF{W4.LT.0. >ERL=BCFW(W5A,HH,DP ) -BCFW{ W5A , H2A , DP ) -BCFW( W4A , HH , DP

)

19 *:BCFW(W4A.H2A.DP ) 2.0 ERL = BCFW{W4,HH,DP ) +BCFW( W5A , HH , DP ) -BCFW( W4 , H2A , DP > 21 *-BCFW(W5A,H2A,DP

)

22 3 RETURN

23 END

END PRT

i3PRT,S GARY.BCF, .BCFS, .BCFW, .LLOAD

E-28
Q$Q$Q$*GARY{ 1 ) . BCF ( 5

)

1 FUNCTION BCF(M,F ,X,Y,Z,PHI

)

2

3 C

C BCF = BASIC CONFIGURATION FACTOR ( P I ER P 0 1 NT/HOP K I NS EQUATION)

4 C M F =SURFACE WIDTH & HEIGTH R ESP ECT I VEL Y ( I N FEET)

5 C XYZ =X,Y,&Z COORDINATES TO SURFACE'S LOWER LEFT CORNER(IN FEET)

6 C PHI =SURFACE DECLINATION ANGLE (IN RADIANS)

7

8 C REAL M

9 PI = 3 . 14159265

10 G = Z*SIN( PHI )-X*COS( PHI )

1 1 H = Z*COS( PHI )+X*SIN( PHI ) 12 A = SQRT(X**2 + Z**2 ) 13 Al =A**2+Y**2-Y*M

1 4 B = SQRT( X**2 + Z**2 + F**2 + 2*F*G ) 15 Bl = B* *2 + Y**2-Y*M

1 S C =SQRT( Y**2+H**2

)

1 7 D =SQRT{ (Y-M)**2+H**2>

18 El =0.0

19 E2 = 0.0

2F C DIVIDE CHECK

2 1 IFCAl .EQ.0. ) Al =0.0001

22 IF{B1 .EQ.JU. ) Bl =0.0001

23 IF (Al . LE .0. ) El =P

I

24 IF ( Bl . LE .i?. ) E2 =P I 25 c 26 BCF = (X/A*(ATAN(M*A/(A1 ) )+El)

27 * + {r *COS(PHI >-X )/B*(ATAN(M*B/{Bl ) )+E2)

28 * + Y* COS (PHI )/C*ATAN(F*C/(C**2+G**2+F*G)

)

29 *-{ Y -M)*COS(PHI )/D*ATAN(F*D/(D**2+G**2+F*G) ) >/2/PI

30 RETURN

31 END

E-29
E-30
Q$Q$Q$*GARY{ 1 ) .BCFSO)

1 FUNCTION BCFS{W,L ,DP ,A)

2 C

3 C BCFS =BASIC CONFIGURATION FACTOR BETWEEN A HORIZONTAL SKYLIGHT AND

4 C A HORIZONTAL WORKPLANE

5 C

6 C W =WIDTH OF SKYLIGHT

7 C L =LENGTH OF SKYLIGHT

8 OA =SHIFTED DISTANCE OF POINT ALONG REFERENCE EDGE

9 C (NOTE: LENGTHS ARE HORIZONTAL DISTANCES IN THE DIRECTION OF

10 C THE ROOM'S LENGTH{RML). THE WIDTHS ARE IN THE DIRECTION OF THE

11 C ROOM'S WIDTH{RMW) ) 12 C DP =DISTANCE FROM WORK PLANE TO BOTTOM OF SKYLIGHT

13 C

14 REAL L 15 PI=3. 14159265

16 B =SQRT{ DP*DP + L*L ) 17 C =SQRT(DP*DP+A*A)

18 D =SQRT{ DP*DP + (A-L )**2 ) 19 E =SQRT{ DP*DP+W*W)

20 C IF{A.GT.J0r. )BCFS={A/C*ATAN{W/C)+W/E*ATAN(L*E/

21 C *SQRT(A*A+DP*DP+W*W-A*L ) )+{L-A)/D*ATAN(W/D) )/2./PI

22 BCFS={ L/B*ATAN(W/B )+W/E*ATAN{ L/E ) )/2./PI

23 RETURN

24 END

E-31
QSQ$Q!B*GARY( 1 ) .BCFW{S>

1 FUNCTION BCFW{W,H,D)

2 C

3 C BCFW=BASIC CONFIGURATION FACTOR FOR A WINDOW

4 C (HIGBIE'S EQUATION FOR HORIZ. ILLUMINATION FROM VERTICAL WINDOW)

5 C

6 PI=3. 14159265

7 A=SQRT( D*D+H*H

>

8 BCFW=(ATAN{W/D)-D/A*ATAN{W/A) )/2./PI

9 RETURN

10 END

E-32
Q$QSQ$*GARY{ 1 ) . LLOAD( 8

)

1 FUNCTION LLOAD(DAYLTE, DILL , DIM, LOAD, XI , CHI

)

2 C

3 C LLOAD =LIGHTING L0AD(HOURLY KW

)

4 C

5 C DAYLTE=DAYL IGHT ILLUMINANCE AT SENSOR

6 C DILL =DESIGN I L L UM I NANCE ( FOOTCANDL ES ) REQUIRED AT SENSOR LOCATION

7 C DIM =DIMMING STRATEGY , E I THER 1( ON/OFF ), 2 ( STEP DOWN >

, 3 ( CONT I NOUS >

,

8 C OR 4(C0NTINU0US W/ OFF)

9 C LOAD =POWER LOAD{BEFORE DIMMING) ASSOCIATED WITH SENSOR LOCATION

10 C XI =LINEAR DIMMING COEFFICIENT

11 C CHI -CONSTANT DIMMING COEFFICIENT

12 C

13 REAL LOAD, LLOAD

14 PSL=( DILL-DAYLTE )/DILL ©DETERMINES PERCENT SUPPLEMENTAL LIGHT NEEDED

15 IF(PSL .GT .0,00) GO TO 1 16 IF(0IM.EQ.3)LLOAD=CHI*LOAD

17 LLOAD=0.0

18 GO TO 4 19 C 20 C ON/OFF SWITCHING

21 C 22 1 IF(DIM.GT.

1

.0) GO TO 2 23 LLOAD=LOAD

24 GO TO 4 25 0

26 C TWO LEVEL STEP-DOWN SWITCHING

27 C 28 2 IF(DIM.GT.2.J0r) GO TO 3 29 IF(PSL.GT.0.5) LLOAD=LOAD

30 IF(PSL.LE.0.5)LLOAD=LOAD*0.5

31 GO TO 4 32 C 33 C CONTINUOUS DIMMING

34 C (FLUORESCENT DIMMING IS DEFAULT)

35 C 36 3 LLOAD=( CHI+XI*PSL )*LOAD

37 4 RETURN

38 END

END PRT

?SEND IBM0J0ri

E-33
NBS-1I4A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS BSS 152

2. Performing Organ. Report No.| 3. Publication Date

^1arch 1983

4. TITLE AND SUBTITLE

A Daylighting Model for Building Energy Simulation

5. AUTHOR{S)

Gary Gillette

6. PERFORMING ORGANIZATION (If joint or other thon NBS. see instructions; 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered WASHINGTON, D.C. 20234 Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. Stote, 2/P; The National Fenestration Council - 3310 Harrison Street - Topeka, KS 66611

and The U.S. Dept. of Energy - Buildings Division - 1000 Independence Ave., S.W.

Washington, D.C. 20585

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 83-600513

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. 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 computer model is outlined for estimating the annual energy performance of a daylighted building. The daylighting model is a system of FORTRAN subroutines designed

for inclusion into larger building energy simulation programs such as DOE-2, BLAST,

and NBSLD. Once incorporated into the main energy program, these subroutines will

allow the existing program to account for the energy tradeoffs associated with

natural Illumination.

The daylighting model, DALITE, comprises three separate routines to do three separate

functions. The first routine generates hourly sky luminances and sky illuminances as well as direct sun illuminance, taking solar radiation and sun position data as input.

The second predicts interior daylight illumination at various points within a room due

to any number of windows, skylights or clerestories. The last routine adjusts the

electric lighting load (via photoelectric controls) in response to the available daylight. Unlike other daylighting estimation techniques, this model is a dynamic model

designed to study how conditions change with time. It has a further advantage in that

it can be easily installed into most existing models written in FORTRAN 77.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

building computer simulation; building energy performance; clerestory performance;

daylighting; skylight performance, window performance.

13. AVAILABILITY

Unlimited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

[^^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

135

15. Price

$5.00

USCOMM-DC 6043-P80

-A' U.S. GOVERNMENT PRINTING OFHCE : 1983 O—380-997 (504


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