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1 Lawrence Berkeley National Laboratory Lawrence Berkeley National Laboratory Title QUICKLITE 1: A DAYLIGHTING PROGRAM FOR THE TI-59 CALCULATOR Permalink Author Bryan, Harvey Publication Date escholarship.org Powered by the California Digital Library University of California

2 1 I CA IFORNIA NVIR LBL Preprint <' ry To be published in Lighting Design and Application QUICKLITE 1: A DAYLIGHTING PROGRAM FOR THE TI-59 CALCULATOR Harvey Bryan, Robert Clear, James Rosen, and Stephen Selkowitz April 1981 TWO-WEEK loan COPY This is a Library Circulating Copy which may be borr()wed for two weeks. For a personal retention copy, call Tech. Info. Diu is ion, Ext I.~ Prepared for the U.S. Department of Energy under Contract W-7405-ENG-48

3 DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California.

4 LBL W-80 EEB-W To be Published in Lighting Design and Application QUICKLITE 1: A DAYLIGHTING PROGRAM FOR THE TI-59 CALCULATOR Harvey Bryan ** Robert Clear * James Rosen** Stephen Selkowitz* April 1981 * Lawrence Berkeley Laboratory University of California Berkeley, California ** Department of Architecture Massachusetts Institute of Technology Cambridge, Massachusetts The work described in this paper was funded by the Assistant Secretary for Conservation and Solar Energy, Office of Buildings and Community Systems, Buildings Division of the U.S. Department of Energy under Contract No. W-7405-ENG-48. This manuscript was printed from originals provided by the author,

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6 ; ; ; Quickl ite I ABSTRACT This paper presents a set of daylighting programs that can be run on a TI-59 hand calculator. The paper gives the program listings, the step-by-step procedures for using the programs, worksheets, and a worked sample problem. The programs calculate interior horizontal illumination levels or daylight factors from a window. The user can specify the location of the calculation point, or, if a printer is available, the locations of a grid of points. Calculations can be performed for both CIE clear and overcast sky conditions. The direct sky component calculation uses Rivero's approximation for window transmission. The interreflected component calculation uses a split-flux approximation.

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8 INTRODUCTION Daylighting is now considered one of the most promising energy conservation strategies for nonresidential buildings. Although substantial savings in both electrical energy and peak power demand are possible, potential savings may not be achieved given the present state of daylighting design procedures. A major obstacle to the effective utilization of daylighting is the lack of accurate and simple procedures for daylighting design and analysis. Three types of design tools have been used to predict interior daylight illumination: scale models, graphic techniques, and calculations. A detailed discussion of the strengths and limitations of each is beyond the scope of this paper; we focus here on computational approaches. Calculations can provide a fast and accurate assessment of illumination levels for typical room and glazing design. Present procedures for calculating daylight illumination can be divided into two categories: simplified procedures, which often make simplifications and assumptions that may reduce flexibility and accuracy, and large-scale computer programs, which, although they may be more flexible and accurate, require the preparation of detailed input data and access to computers or time-sharing computer facilities. There is a need for a calculation procedure that combines the speed, low cost, and ease of the simplified methods with the flexibility and accuracy of the large computer models. This paper describes a calculation procedure, using a programmable hand calculator, that is a major step toward 'that goal. QUICKLITE 1 PROGRAM DESCRIPTION Quicklite 1 will predict daylight illumination at any point within a room. The methodology and algorithms used in the development of this program are documented in a previous paper. 1 Further details and additional program capabilities will be described in a later publication. 2 The program utilizes the CIE sky luminance distribution functions

9 for the overcast and clear skies. 3 ' 4 The light reaching the interior point being considered is separated into two components. Light arriving directly from the sky (Sky Component or SC) is calculated using a source area formula. Light reflected from external and internal surfaces (Reflected Component or RC) is calculated using the split flux approach. The total for these two components is given as either the daylight factor (the ratio of illumination at the reference point to illumination on a horizontal surface from the unobstructed sky) or illumination (in footcandles) for the point(s) being considered. This paper describes the use of the program to calculate daylight illumination for a simple window without obstructions or sun-control devices. The program can also be used to solve more complex daylighting problems; however, the length of this paper limits their inclusion. Solutions to these problems are described in reference 2. Quicklite 1 has been designed to be accurate, simple, and relatively fast-running. The output compares well with other daylighting calculation procedures as well as with a series of physical scale-model measurements. However, it must be remembered that no calculation procedure, no matter how accurate, can duplicate all the complexities that daylighting poses. In most cases we seek comparative performance levels rather than absolute quantitative results. We must also remember that the non-quantifiable aspects of lighting design are equally important and that nothing can substitute for good design judgment. I: SKY COMPONENT PROGRAM: This program uses the TI-59's master library.,if multiple point calculations are desired for a single program execution, the PC-100 printer must be used. Step 1: Repartition the calculator memory by entering 5 and then pressing 2nd OP 17. Step 2: Determine if sky condition is clear or overcast, then read appropriate program into calculator. The clear sky program will require reading sides 1, 2, and 3, while the overcast sky program requires reading only sides 1 and 2. Step 3: a) Enter window transmission at normal incidence (90 to the plane of the window). -2-

10 NOTE: Steps (3b-3e) should be executed only for the clear sky program. b) Enter the normalization factor (N ) which is the ratio of sc illumination on a horizontal plane to the luminance at the zenith. given as follows: This factor is a function of solar altitude and is Solar Altitude N sc c) Enter window azimuth angle (in degrees), which is the angle that a line normal to a vertical window makes with south (which is taken to be 0 ). Clockwise rotation from south is measured as positive while counter-clockwise rotation is measured as negative. (See Figure 1) d) Enter solar azimuth angle (in degrees), which is the azimuthal angle of the sun from south. Here again clockwise rotation from south is measured as positive while counterclockwise rotation is measured as negative. (See Figure 1) NOTE: This program does not compute the effect of direct sun in the room. There will be direct sun at some point in the room for an obstructed window if the absolute value of the difference between the window azimuth and solar azimuth is less than 90. e) Enter solar altitude (in degrees from horizontal). (See Figure 1.) -3-

11 Step 4: Enter the location and size of the window and the workplane height at which illumination is to be calculated. A rectangular coordinate system is used to locate the window as well as the calculation point{s) (see :Figure 2). The origin of this coordinate system should be placed at the lower left-hand corner of the window-wall's interior face. When facing the window from the interior of the room, the X-axis will run along the floor perpendicular to the window-wall. The Y-axis will run to the right, along the intersection of the floor and the window-wall. The Z-axis will point straight up. The location and size of the window is described by four values: Yleft and Yright represent the respective distances of the left- and right-hand sides of the window from the Z-axis, Z and Z represent the respective distances of the bottom top bottom and top of the window from the floor. Finally, the height of the calculation point(s) above the floor (Z ) must p be determined. For most office tasks Z p is assumed to be 2.5 feet. Figure 2 illustrates these relationships. Step 5: Determine if the output is to be calculated in units of daylight factor or illumination. To calculate the daylight factor, the number 1 must be stored in register 35. calculate illumination, the appropriate horizontal illumination from the sky (Esky) must be stored in register 35. To This value can be found in Figure 36A, B, C, or D in the IES Recommended Practice of Daylighting, 5 in reference 2, or can be taken from any other source of measured or calculated illumination data. NOTE: To calculate values for a single point, proceed to steps 6a and 7a. If a printer is available, multiple points on a rectangular grid may be calculated and printed by proceeding to steps 6b and 7b. -4-

12 Single Point Procedure: Step 6a: Step 7a: Enter the location of the point at which the daylight factor or illumination calculation is to be made. Y is the p distance from the measurement point to the wall to the left of the window. X is the distance from the measurement point p to the window-wall. (See Figure 2) Calculate the sky component by pressing 2nd B'. Multiple Point Procedure: Step 6b: and the farthest columns of calculation points. X. and m1.n X are, respectively, the distances from the window-wall max to the closest and the farthest rows of calculation points. (See Figure 2) Finally, the number of calculation points for they-column (N ), and X-row (N ), must be determined. y X N and N include the corner points and thus must be greater y X than or equal to two. Setting N or N to one will result y X in a "divide by zero" error. Step 7b: Calculate the sky component values by pressing 2nd D'. Run time for this option is approximately 1.2 minutes per point for overcast sky and 3 minutes per point for the clear sky. General Notes: Sky Component Program 1) It is unnecessary to re-enter all the input data for repeated calculations. Only those input values entered in step 6a or 6b must be re-entered to rerun the program. All other input values need to be changed only if their new values differ from those used in the previous run. 2) All inputs that relate to distance (such as width of the window) may be entered in any unit, English or metric, so long as the user is consistent. Enter the corner locations of the rectangular grid of calculation points. Y. and Y are, respectively, the disml.n max tances from the wall at the left of the window to the closest -5-

13 3) If a printer is being used, it is highly advisable to make a list of the register contents before running the program. To obtain a permanent list of the data registers, enter 30 and then press INV LST before executing step 7a or 7b..6.) (For register assignments see Figure 4) Figure 4 summarizes the steps required to enter and run the Sky Component program. REFLECTED COMPONENT PROGRAM: library. The PC-100 printer is optional. This program uses the TI-59's master Step 1: Repartition the calculator memory by entering 3 and then pressing 2nd OP 17. Step 2: The reflected component requires reading sides 1 and 2. Step 3: Step 4:. Step 5: Step 6: Enter window width and height. Enter room width, depth, and height plus the height of the window sill above the floor. Enter normal incidence window transmission. Enter reflectance of ceiling, floor, glass and walls as well as exterior ground. NOTE: There are four options for output from this program. The appropriate option must be chosen from steps 7a, b, c, or d. Step 7a: To calculate the daylight factor from the reflected component under an overcast sky, enter the window factor (f ). The s window factor is the ratio of the light flux entering the window from the sky to the light flux on an exterior horizontal plane. For an unobstructed sky f =.39. s Step 7b: To calculate the illumination level from the reflected component under an overcast sky, enter the window factor (f ) as s in step 7a and the horizontal illumination from the sky (E k ), which can be found from Figure 36A in reference 5. s y Step 7c: To calculate the daylight factor from the reflected component.tal illumination from the sky (E k) from Figure 36B, C, or D s y in reference 5, and the horizontal illumination from the sun under a clear sky, enter the window factor (fs)' the horizon -6-

14 (E ) from Figure 37A in sun reference 5. The window factor for a clear sky is a function of solar altitude as well as of window azimuth from the sun and is given below. Solar Window Azimuth from Sun Altitude oo so<> Step 7d: To calculate the illumination level from the reflected component under a clear sky, proceed as in step 7c, but a different label is pressed for the resulting answer. General Notes: Reflected Component 1) A single average value for the reflected component is computed for the entire room. 2) It is unnecessary to re-enter all the input data for repeated calculations. Change only those values entered in steps 3 through 6 that differ from the previous run. at step 7. Then execute the program beginning 3) If a printer is being used, it is highly advisable to make a list of the register contents before running the program. To obtain a permanent record of the data registers, enter 15 and then press INV LST before executing step 7. (For register assignments see Figure 7.) 4) Figure 5 summarizes the steps required to enter and run the Reflected Component program. SAMPLE PROBLEM Calculate the illumination for the room shown in Figure 3, which is -7-

15 30 feet wide, 20 feet deep, and 8.67 feet high and which has one large window, 5 feet high by 28 feet wide. floor and centered on a wall facing due west. The window is 2 feet above the Glazing consists of two layers of 1/4 inch clear glass having a combined normal daylight transmission of 78%. The ceiling has a reflectance of 80%, the floor 20%, the wall 50%, and the glass 14%. Illumination is to be calculated under both clear and overcast conditions. The sun is assumed to be due south at an altitude of 40. The horizontal illumination from the sky (E k ) is 1400 footcandles s y under overcast sky conditions (from Figure 36A in reference 5) and 1200 footcandles under clear sky conditions (from Figure 36C in reference 5). The horizontal illumination from the sun (E ) is 4800 sun footcandles (from Figure 37A in reference 5). Finally, a three-bythree calculation grid (9 calculation points) was selected, each edge of the grid being five feet from the nearest wall. (See Figure 3) The sky component program for both clear and overcast skies was run first. Figure 6 shows the sample input and output from this example in which both the data register contents and results are identified. The reflected component program for both sky conditions were then run. Figure 7 shows the sample input and output from this run; here again data register contents and results have been identified. Finally, the sky component and reflected component values were added to determine overall illumination values. shown in Figure 8. center line of the room as expected. are given in Figure 9. Results from the overcast sky example are Notice that the illumination is symmetric about the Results for the clear sky example Here the change in sky luminance with azimuth results in an asymmetrical illumination distribution across the room. In each case the reflected component is calculated as an average value throughout the room. This approximation will generally result in an overestimate of daylight illumination in the back of the room. Comparison between reflected component results from the average value approach described here, and a more detailed calculation is given in reference

16 CONCLUSION A relatively accurate, simple, and fast procedure for calculating interior daylight illumination has been presented. It is hoped that the application of this procedure will encourage the use of daylighting, placing it in a proper relationship to other design considerations. A lengthier version of this paper that includes a detailed program description, user instructions, and several worked examples (which include external obstructions, overhangs, direct sun in room, etc.) will be available from the authors at the address below. This calculation procedure is one of several daylighting design tools now under development as part of the LBL/DOE Daylighting Program. For information on the availability of other daylighting design tools, write to: Windows and Daylighting Program, Lawrence Berkeley Laboratory, Building 90, Room 3111, Berkeley, California ACKNOWLEDGEMENTS The work described in this paper was funded by the Assistant Secretary for Conservation and Solar Energy, Office of Buildings and Community Systems, Buildings Division of the U.S. Department of Energy under Contract No. W-7405-ENG-48. REFERENCES 1. Bryan, H. J., and Clear, R. C., "Calculating Interior Daylight Illumination with a Programmable Hand Calculator," presented at the 1980 IES Annual Technical Conference, Dallas, Texas, August 24-28, (To be published in the Journal of the IES). 2. Bryan, H.J., Clear, R.C., Rosen, J., and Selkowitz, S., Quicklite 1 Users Manual." (To be published as an LBL report.) 3. CIE Technical Committee E-3.2~ "Daylight: International Recommendations for the Calculation of Natural Daylight," CIE PUBLICATION No. 16, Commission Internationale d'eclairage, Paris, CIE Technical Committee 4.2, "Standardization of Luminance Distribution on Clear Skies," CIE PUBLICATION No. 22, Commission Internationale de l'eclairage, Paris, IES Daylighting Committee, "Recommended Practice of Daylighting," LIGHTING DESIGN & APPLICATION, Vol. 9, No. 2, February 1979, p. 45 &

17 Solar altitude angle Solar azimuth angle /./"' W(+) / / I I I Window azimuth angle FIGURE 1. SITE COORDINATE SYSTEM FOR PROGRAM ~10-

18 Origin of coordinate system Measurement.... f;.: o.! Oi... FIGURE 2. ROOM COORDINATE SYSTEM FOR PROGRAM

19 .::: Z axis FIGURE 3, EXAMPLE ROOM -12-

20 ~ PROCEDURE ENTER PRESS DISPLAY 1 Repartition calculator 2 Clear Sky: Read sides 1, 2 & 3 Overcast Sky: Read sides l & 2 5 1,2,3 1,2 2nd OP nd INV WRITE 1,2,3 2nd INV WRITE 1,2 3a Enter Window Transmission A Note: Steps 3b-3e should be executed for clear sky only 3b Enter Normalization Factor R/S 3c Enter Window Azimuth (in degrees) AZ.,indow R/S AZ.,;Lndow 3d Enter Solar Azimuth (in degrees) AZsolar R/S 3e Enter Solar Altitude (in degrees) R/S 4 Enter Yleft Enter Yright Enter zbottom Enter ztop STO 3(3 STO 31 STO 32 STO 33 5 To calculate Daylight Factor: Enter 1 1 or Esky To calculate Illumination: Enter Esky z p STO 34 STO 35 1 or Esky Note: For Single Point Calculation: 6a STO 36 7a Note: 6b Enter XP Run Program For Multiple Point Calculations: Enter Ymin STO 37 2nd B' STO 38 STO 39 Enter X,.in X,. in STO 4(.! X,.in Enter~ STO 41 Enter number of points along Y axis Enter number of points along X axis STO 42 N. ' STO 43 7b Run Program 2nd D' S.C. FIGURE 4. SKY COMPONENT PROGRAM WORKSHEET -13-

21 STEP PROCEDURE PRESS I DISPLAY 1 Repartition calculator 3 2nd OP 17 1: Read sides 1 & 2 1,2 2nd INV WRITE 1,2 3 Enter Window Width Widthwin STO 15 Widthwin Enter Window Height Heigh twin STO 16 Heigh twin 4 Enter Room Width Widthrm STO 17 Widthrm Enter Room Depth Depthrm STO 18 Depthrm Enter Room Height Heightrm STO 19 Heightrm Enter Window Sill Height Height 8111 STO 20 Height sill 5 Enter Window Transmission To STO 21 To 6 Enter Ceiling Reflectance ceiling STO 22 ceiling Enter Floor Reflectance floor STO 23 floor Enter Glass Reflectance glass STO 24 glass Enter Wall Reflectance wall STO 25 wall Enter Ground Reflectance ground STO 26 ground 7a Daylight Factor for an overcast sky: Enter Window Factor fs ST') 27 fs Run Program - A. R.C. 7b Illumination for an overcast sky: Enter Window Factor fs STO 27 fs Enter Illumination from sky Esky STO 28 Esky Run Program - B R.C. 7c Daylight Factor for a clear sky: Enter Window Factor fs STO 27 fs Enter Illumination from sky Esky STO -28 Esky Enter Illumination from sun E STO 29 Esun sun Run Program - c R.C. 7d Illumination for a clear sky: Enter Window Factor fs STO 27 fs Enter Illumination from sky Esky STO 28 Esky Enter Illumination from sun Esun STO 29 Esun Run Program - D R.C. FIGURE 5. REFLECTED COMPONENT PROGRAM WORKSHEET -14-

22 OVERCAST SKY CLEAR SKY VARIABLE INPUT MEMORY II INPUT MEMORY II :left r:l.ght ZbottGm Ztop Zp ilmky o. 36 o. 36 o. 37 o. 37 ~ ~ Ymax l!,ain ~ ~ ' 0 o !llilC j o AZ.window o. 47 o. 47 AZaolar o ALTeolar o. 49 o. 49 OUTPUT OUTPUT 5. X 5. X 5. v 5. v sc 77. SSE sc 5. X 5. X 15. v 15. '( sc sc 5. X 5a X 25. '( 25. v es sc sc 10. X 10. X 5. '( s. '( sc SE:3 sc 10. X 10. X 15. '( 15a '( sc sc 10. X 10. X 25. v 25. y sc sc 15. X 15. X 5. v 5. '( e sc ~:9. sc 15. X 15. X 15. v 15. v sc sc 15. X 15. X 25. v 25. y sc sc FIGURE 6. INPUT AND OUTPUT FOR SKY COMPONENT PROGRAM -15-

23 OVERCAST SKY CLEAR SKY VARIABLE INPUT MEMORY II INPUT MEMORY II WIDT~lwin,..., {;,. C a C.. : a HEIGHTwin 5. 1 t 5s 16 WIDTHrm ~:0. 17 ~:o. 17 DEPTHrm ::: : HEIGHTrm... C - f.""' C a t { 19 HEIGHT sill.:::. "". 20 2a 20 To o....,.-. ( 0: ::: 21 I' ceiling o. i""'t -t = 0. ::: "': :r - c...:: ~'-- Pfloor o. 2 2:~: o. 2 ""') :!glass ,r;:-!wall o. - C'.:::.._. o. :" 0-.s:::.::;.._.!ground (1.,.., 2E :::..:::. 2E~ FS 0. : =t._r , 0. c:: 2~' t:..l - Esky ,-. &.. :,:::;,.:. Esun o. 2' '3,;_ - OUTPUT OUTPUT R.C. 27 a RC 61. RC FIGURE 7. INPUT AND OUTPUT FOR REFLECTED COMPONENT PROGRAM -16--

24 + 89 sc 27 RC ~ s' 1s' 2s' Y coordinates FIGURE 8. OVERCAST SKY ILLUMINATION VALUES (fc) FOR EXAMPLE ROOM -17-

25 . : : :.. :: : : s' 15' Y coordinates FIGURE. 9. CLEAR SKY IL~UMINATION VALUES (fc) FOR EXAMPLE ROOM -18-

26 SKY COMPONENT PROGRAM: OVERCAST SKY :)(i J. C!Ci2 c~c14 CiC!5 00(. ('i,-i..., :... : :_:! 16 AJ: 42 :::3TD co:::; 42 STD ,.-,.. ':.:.:.:.:,...,r... 5:3 ( i...,.:. f i7 Cili E=5 ::< Ci l C~ 4:3 F.:C:L~ 12 Ctl4 ~::5 + C! ~ ~! 4:3 F~C:L Ct55 1::: 1 i:: -~) CtE. ~34 f->:: Ci57 i]~t::: c~ ~~ :? Ci ) 65 ::-:: 4:::: F.~CL i ~ J.! 4:3 F.:C:L 1 ~-. o::: o:::: , c Tn '"tt::.._t! w E, LE:t~ 5::: F I;:.:; :,r j ' LBL Ci:3 C!:::i E~ ~:; t ~ D Fl 1 E: ::; 4:3 F: c: L. 1 E=' ~ i 7Ct :44 ~:;!Jr= t 171 i Ci 1 Ci Ci ' '3 4 2 ::; T [J 1 ;:_;!] Ci ;:; C! ;:; Ci ) Ci7'2 '3:3 " Ci7':3 CIS 5... :...,. ' f...,: 1 C! 1 Ci C~2i] C~21 :-,...,.-1!_! ::.:. ~)!)24 Ci ;~:!::! Ci~~::; Cl2'3 ( ( ( 5:3 ( 4:3 F.~ c: L.. 1.-,.:.: '? 43 F.~CL C!::i 1 14 i 4 Ci::;2 54 ).. ".!. l. A ' Ci:::Ci.-!:" t -' Ci i [if; 1 '~:3 1 Ci ::; :~: Ci i 1 C!::=;4 C!;:: qt:::;... - :::: ct;:;f, 42 ::;ro ij ;:; ~-' Ci ;~; [; =:=t 1 F.~...- ::; C! ~:; '?- 7 E: L E~ L Ci'~iCi 1 :::; c: Ci'~l 1 4:3 F~C:L. i Ci.: :3 ~:i ::; I f l.-,.-, :.. -:.:,:..) {,L.. i~2 ~:;T[J ' ;::;:. ::.: 4 4 ::; ti!' i:!. t:~5 Ci4 4 1 I~ C! 4 :3 F~ c: L.. 21,-,-:; ~-~~!_i t ~-~ : 1'?-;:; 5;:; F I;:.: 1 '?- ~3 7 1:: L. E; L. 2 Ci!J 5 :3 X f ~ T !]4.:3 54 ) C!44 E=5 ::<!:".-. Ci45... ).;) ' ::.. i]47 65 ::-:: Ci4::: 4:3 F.:C:L O~iO 43 F.:CL PCL c~!:i 1 t-1 r:: :t ~-= - =,:.~ i] :?- 7 4 :::: F.: c: L Cf'?-::: ::no 1 o::.: 0'3 0'3 104 '35 :::: 1 CJ5 42!:;ro -r -: -~ -; 1 C!E, ~.::. ;::.~ i (!::: 42 ~:;T[l 1 (19 1 q ~ :3EI C!l3 ~- - F=l:-;t:1 [I'~ 14. Ii 52: E:5 >=: 5 :::; 4 :::: F.~ c L. 11 i 1 5::: E~5 ::< ~-; ~:~ 4 :3 F.~ c: L r:t t:; =:.. - 2Ci5 2CiE: 2Ci :3 F~ c: L o:::: 3

27 OV~RCAST SKY (cont.) Ci :3:~:Ct : ::.:; :;; :;; 1. '3 1 F.:... :::; :3;::;5 :3::;t, 7E~ LEi. 22 I r ~ ' 04 4:3 f:c:l E:5 ::< 2~:~7 4 :;; F.:C:L. 2 ::: ~=; 2 ~~~ =:_:?. 4 4 Ez 5 4 Li ::{ 27::: ' ) 2::;2 =3J5 = 2i:~:3 42 ::~TO 2f: ::.:5 7E~ LE:L l -1.::..).::.: :3:35 :::;:~:6 12 E: 70 PAD :.::t c p b... _. - ; :3 ::; ~:;t 4:3 F~ c: L. :34CI :34 :34 3f:9 3'?-Ct :3 ~:.i 1 :3' :::; F.: c: L.. 2::;~:;.-,. :z-: :::..~: :7 2~ Ci 2~1 2==~ 2 Ci = E='3 OF; C!E: CIE.: ~3 2 F.:T t ~ 7E= LEiL. 14 I! 2"~~ 5 4:3 F.:C:L. 42 ; ::;T[J 2:::;.::: CiC! [;(I 1 ::::: : ::-.: 2~~! 1 7'E~ LE;L~ 2=?-2 24 c:e 2=:~5 7E= LEiL 2':~E~ 44 ::;Lit=1 2'~i=j :3!]Ci :3CJ:~: ; := r l. -' - 22 It ~'~/ '37 I!::;z 4:3 ~:c:l :3C!4 :3'3 :3'3 :3Ci5 44 ::;!Jt= l 306 :3C~7 :3Ci::: E= 1 c~ rci 24 C:E :3Ci:3 7E= LE:L_ :31 c~ :34 r::-:: -:.-:...,.:: ';:::.-,.-!.-1.;! bf.:.: :3~-4 ' : It ~\' :34E: 77 C;E: :~: ~- 7 2 :;: L t ~ ;:.:: : ::;ro : :3 L t i := :: :3 5 ;:; 4 :3 F.: c: L :~!5'3 :~;? :3E:C! 55 :3(: 1 :362 :3E::3 :3E:4 4 :3 f.:~ c: L.. ni -.l 4 c~ 1 4 :3 F.~ c: L. 4Ci5 4C~ t 4:3 F:C:L. :=t c:; ::: :3 F:C:L. 42 ::no :3t~ :3f= ) '35 = :31: :::; l 5 4 :;; F:: c: L~ :::~ 1 E= :::; ::;ro :31::: ::::?o :~:~/4 :3 ~ ; ~.5 4:~: ~:C:L. ::7 :: -:;t - 1 i - 1 i 55 c: : -'.. } ( 4:3 F~C:L. 42~:3 E: 1 C;T[1 4:::4 12 B 427 1'3 Ii = 22 I! i\! ;:; t~ ::; T F. 01 4:3 F~ c: L. :~~ E= 7 4 :~: F.~ c: L 26::; 4i 41 7t:: i -' 4:3 F.~C: L. 4Ci 4C! 42 ::;T[] 271 -: _.,.-, t::.!'~ 2~'4 54 ) :::~ 2.~ :3 4 :::; F.: c: L : ~j :3C~5 44 ::;ijff :17 :, :."1._1!._1 l :t :,..,.,...1 b.~! 61 GTO...,...,,-,.;.r &.:. C: 4:3 F.:CL ::: 2 2 l t 1 ':/ :3C! TAt ~ 42 ::;ro 4:;:2 42 ::;1'[1 4 :;; :3 C! t= C! C: 4:~:;4 4:: ;s 14 I! -20-

28 SKY COMPONENT: CLEAR SKY 000 oc:::: 7E: LBL 15 1 c:- J.._! c~c~4 :3'31 c:o::; cnj5 42 ~:;ro C!CtE: 1 E; 1 E~ CiC}7 CiCl~:; ( CI1CI 17 1(:' Ol1 65 ::< Ci l 2 4 :;; F.: c: L [1]:3 12 i~~ C):;. 4 ;::5 + 4:3 F.:C:L Ci j_ E~ 1 :3 1 ::: Ci1.7 54) :] 1 ::; 42 ::;ro i] Oc:O t::" -._!.::.: ( ( 4:3 t?c:l. O.!:i? 43 F.:CL. Cl E: Ct 4 :~: F.: c: L [if, ?' Ci E= :3 4:3 F.: c: L. C~E~ ~ Cif~5 54 ) Ci f: 7 4 :;: F.~ c: L. () (: ;;:: i ::: 1 ::; Oi'5 01.oi t:" '. '"t -' ';'.. c:: i J..;.. J. -i,...-, l.l::4. -! ~.-, l j,.;t (.-,.:::. 114 '34 "!"/ 115 E~5 ::< 1~.' ~Ct 4:~; F~C:L. 1:?i li ij J.- l tl 1 2~ E, 22 It ~\~ 127 2:3 Lt ~>: 54 ) 1 :::o 1 -:.: i.:..... : J. of.- :...,.i.~:..:::. 1 ;:: ~~ 1 f; ::; E; F- ~ 2~:; LOCi ~ 1 ;:; 5 1 ;: ;f: C~25 CIZ:::: i]2:'3 i]::;ci Ci:;; 1 65 ::< 4 :::; F.:C:Lw -:1-1 -; L:,!_l,::.:.,i 65 ::< ( 4 :;; F.: c: L.. i 15 c:: J.._; :::5 + 4:3 F:~C:L Ci:::? 4:3 F.:C:L.. Ci:~::::: 11 1 J OC1 01 o:::4 Of:5 C! ;~~ E: 5:3 c~ ::.:~ 7 Ct : n - (.-,..:: 1:::::5 1 ::..:;:: 1 ::; '? ~l ~- C! l L ~ :3 1::1-4 5:3 ( Ci '32 f;:tt ~ -a.~! r:t ( tz LC)L. 1 ~ 7 2;:; LOC; 1 ~! ::~ E= 5 ~=< 2C!Ci :25 2(! 1 Ci4Ci Ci41 C!~-2 4:3 F.:C:L. C~4.:3 4 :;: F.~ c: L.. Ci44 16 d. l t Ct45 54 ) C~4E: 55 C!47 [i4::: Ciz:t'3 Cf~:!CI Ci~:; 1 o~;2 O~i:;: (1~!4 43 F.:CL. i :=: H::.-,.of r'.:.l"t ":, 54 ) Ci::~5 22 It ~\~ Ci ~~1 E: 2 :3 L t ~ ::< + c~ ~::~ ::: =;t ::i. ~ C!'~i'3 Ct (J1 Et5 ::-:: 1 Ci2 1 (J :::: 1 ()4 1 Ci5 1 CJEI 107 t::"...._l'"t 65!::' -...J.;z lob '3 '"l'j::' (.,) ) 1 1 : 5 '32 PH ~ 1 ~!E: 7E~ LEiL. i i J..!. A 65 >:: Ci ~:i'3 1 f,o t~ [1::: '? ::.-,.::,: ::: 2 '3 i ::.l._:,-. ;_. -21-

29 CLEAR SKY (cont.) + 2l 2?f. o ;::t 09 -:""":T"'"':' ::::.. :' ;.' 14 II 2? r:: t~ 5 ::< 2 7 '3 4 1 :~; F.~ c: l_ :.: 2;:; 1 E~5 ::-:: 2f;2 4:3 F.:C:L -:,"': -: ::::.::::.:.= 1 1 i 1 2f:;5 2f;t, 4:3 F.:C:L :;;:::o 69 OF' :;::::: ::::::::4 E-9 OF' : ::::::: :::; :3 ::: E~ '3 0 Ft 3:::9 o4 o.::j. 340 :34 2 E:'3 OF= :3t::j.:3 t]e= C~f~ :3::: :3 ';.i 7 :3 E~ :3 t ~ :::; ~:~~ ~=; 5 4 ) :3:~i:3 75 :::: :;:~ ;:> Ci 5 ;:; F I :: : ~:~ :::;. 1 (! :3 :3 2 =::i :3 t, ;:: t ~ 0 FJ 2=:~!4 4:3 F.~C:L.-,.-,.-,.- 1 ~z:::. ~:::. 2'}5 :345 Cit, E~ :34E, Ci i 1 :3~-7 CJ5 5 :3~!=~ t1:3 DFI :::; ~- '3 Ct4 Cl :::t. 4:3 ~:C:L :~;~i1 1:3 i:~ :3~ ;2 Er5 ::< ::.::;~:;:::; 4:3 pc:l ::.lc!c~ 4Ci 1 4C.!5 75 :3(.1:::: :3C! :::. 43 FCL. 414 Cit: (: 1 1 C! 1 Ct 2(:2 i. i J.f 27'1 (14 4 :::~CP3 7E= LE:L. :3 i!] t, ;:~ t ~ 0 F' :3 21 ;:: =;.t i! -t ~.-, r:; c:;.::.:.. ~ ,.:::. :;; ), 5 :32 :: ::%,- :3 j t, 4:3 F.:C:L ::;TO :;; :9 1 Ci 10 :3;~:Ct ::;~: i :;: ~~~ 2 '3 7 I! ::; ~~ :32:3 Ci7 Ct~? :324 5::; F I;:. :...,,... i lti!" C: Ll:! :3 2: E= 5 '3 I t 11. :~: C~ 7 ~3 ::~ A I! i=l :32::: (14 4 :32'3 1]4 4.-,... -:..::t::::.:. :3t::3 :3(~4 4:3 F.:C:L 366 '35 ::: :3f~7 E~'~ OF' CiE: Cit": ~32 F.:Tt 1 :3 '? ;:; Ci E~ Cit~ :37:,3 7E, LE:L.. 14 I! :::;;:;:3 42 STD :::;::: ~ 1 7 t~ Lri E: L~ 4 2~ 2 4 :;; F~ c: L. 4:3Ci 4 :~::; 1 22 It ~\'?E, L.E;L~ 4::;4 1:3 c: 4:::5 ~22-

30 CLEAR SKY (cont.) 4 ~;. (! :3 1 3 :3 r:,i 4::.; ~:;tjf:1 4::; CE q.:::j.5 7E~ LE!L 4 ::i. t~ :3 4 r :: :: 4 ~~ I t 1 \= 1 4 :::~. ::; '3 7 I! ::; Z 4:::;.'3 C!E: C!E~ 4 ::51J : ::.:: 42 4 ::!5?EI LE:L 4 '3 f, 2 :3 L t ~ ;: ::. 4~~ 1? 4:3 f~c:l 5C)CJ 4::: F.~C:L 1:.~ f i i -....: c..:;: :::..:;. 51J2 '35 = 5Ci:3 22 It ~\~' 5Ci4 :3C! TAt ~ 5Ci5 42 ~:;TO 5C!E~ 21 2l 5C~? 7'6 LBL. 55 C) 22 It ~\' 30 TAH s:; l 5:: 2 42 ::;T[l ~~ ::; :::: 5::i4 5~!5!]1!] :3 c 5 ~! (~ :3 2 F.: T t 1 4(:() E: l 4 4 ::; ~J t:1 :37 E= 1 C~T[l 4:3 F.:C:L 4 (: ::i 7 E= L E: L 4f:f: :35 i...-::.:; 4E~'3 17 Ei s 4 -;., C'.i ::; E= ::; T F~ 4 i':3 4 ~:-, ~ 12 B 2 t3 c: Fl 4?~) 4:3 F~C:L 4 ('(, 51 Ci t:: 1 1._: J...:. 51~~ t::; ::.._:.:.OM>~ ~:CL 52fJ 22 It ~~:/ 521 ::::Ci TAt~ 52:2 42 ::;T[! 52:::~ 52:4 7E= LE:L.. 52:5 22 I t ~\ 1 52E= 4:3 F.:C:L 52:~? :3Ci :3Ci 5:::;2 5:3:3 43 ~:CL rf.-,.:::. 5:3f, 22 I f i\: 1 5:3~-=- :3Ct TAt-~ 5:3;:: 42 ~:;ro 5:3~~ C! i Cll 5~ 1] 4:3 r::c:l~ 541 : :3 544 c:;:::;,t::; -. - '7&:;! - I:. c:;

31 REFLECTED COMPONENT PROGRAM ~:;un l !:;T[J C!7 Cl?' Ci()4 55 CiCi5 CiCii:= :-1 -:.-, i_ii:, :::.. ::: Cl():3 ':?.2 F~Tt 1 Ci l i] 7E= LE:L. c~ 1 1 :-:-!.-. ;_::. :::. 44 sur 1 4:3 F~C:L 2=3 2;3 ::;5 + i] 15 4:3 F.:C:L Ci5'3 Cl4 4 Cif:Ci 42 ::;T[] 12 i.-,. C!(~;2 E= i i~td Ci t= :3 2 :3 L t ~ :: ::!]E~4 7E~ LE:L. Clt.5 14 II C!E~E~ Clf.7 Cit: ::~ C!t:=3!]7C! 1 -;7 i '' ' Ci7-~2 -;.-, ' ' ":.:: -~),,,_ 4:3 F~C:L 42 ::;T[l i] ~:.: :~: (! 2 l] ~:~ C!'i"j4 CiCi Ci ::; i_i t:'f 115 Ct::; Ctf; ::-:: i.; 1:1.-1 -~:.L.L r_:..:::...:: 11'3 '?-5 = 1 ~~~Ci 42 ::;T[J '! ~: :: J. ~- ;.;_ 124.;,.~:::.i ::::.. i.; -=..- l,;:.c: 1 :;:: ~=; ti t:"j Ci:3 Ct:~:; 4:3 F.~ c: L.. 4:3 F.~ c: L.. i 71 i ~ :r J.!.,_1 4:3 PCL. 55 1~ 7 4 Ci2 2 1~~5 1:?-::t =.t _.,..'"1 l ( ( i 7::: 17'3 1 ::; 1 i (> t::.!. 1,.:._: >:: C!C~5 7E= LE:L.. CI~:t, i 1 A Ct 27 7 l ::; En~~~ C!i:: :3 4 :::; ~: c: L. CifiCi 27 2~= Cif; 1 42"~ ::;T[l 1::::5 1::; 1::; 1 :;.;(= t~5 ::< 1 :;; 7 4 :3 ~: c: L.. 1 :~-; ~=; =:~ 1 =?- Ct ;;:; ~~~ 1 4:3 F~C:L.. 1 ~:~2 Ci4 Ci~;. 1'~3 '35 = Cl::_;:::; 1 42 ::;TO C!:~:4 C!2 CiZ~ Ci:35 E= l C;T[J Ci :3 E= 2 :3 L t ~ ;:.:;!J f:; 5 E: 5 ::<!);::t= 4:3 F:C:L.. "....I. l tr l t:: CI;::::: '35 = [I :~3 :3 4 2 ::; T [1 Ci:31) 1 Ci 1 tj i] ~:.4 1 E~ 5 >:: 4:3 F.~ c: L ::; tj r: c~ ::; c~ ;::; i 4 E: 4 :::; F:: c: L. 1 '?- 5 4 :~.; F.~ c: L. 1 =:~;:; 4=3 F=F~Ii i=~=3 Cti Ctl 2CiC! Ct 1 1 2Ci :3 F.~ c: L.. 14 Ci4E~ 047 Ci4::: Ci4'3 Ci51 C!52 05:3 054 i :r i...,.l::....!.~ 61 GTD 23 Lt i>:: 13 c 03 1 Ci4 65 ::-:: 1 C! 5 4 ::; F.~ c: L ::..:::...._: ::: 1 (1!:: 42 ::;T[l 1 c19 o5 o::; 42 :3Tll Ci44 Ci2 CiL~.-. "'r-!j Lt ::! ~~;1 4:3 ~~C:L.. i "? L! 1 E~ 1 1 t~;2 ::-:: i -= l.. ) 4 4 ::; i_i f:'i Ci::: C!::_; 4:3 F.~C:L..., &::'.-. t:: ~._! :;:._i 2 Ci 2~ 1 2~ 2 2 :3 2 4 Ci7 Ci.? 4:3 F~C:L. 4:3 ~~C:L. 55 2!:i 4::~ F:c:. 2 '3 ~J7 C! I

32 REFLECTED COMPONENT PROGRAM (cont.) 22 ~: 09 [i'=~ 22:4 :::5 + 22:5 4:3 F.:C:L_ 01 <:Jt:" -._1 :::: :.. :: :s :l -i,..., ~._.1 _, l i,) ~; F:~ c: L. 2;:.~5 Ci:~ Ci~.~ 24rS '?-::i = 251 Cj5 252 Ci ::t 4 E= =3 5 D F= 2 ~.i 5 Ci 4 C! ~l 2 ~~ ~3 4 Ct I t ~ IJ 2t,C! 12 1 ~: 2 f.: ~ 1 E~ =3 0 Fl ;?t=2 Cit= Cit= ~~t=4 5::; F I:: : 2 (: 5 =3 ::; A Ii \ 1 2 t : r:l '?- 1 F.:... ::; -25-

33