- Email: [email protected]
Shading Mask: a teaching tool for sun shading devices
ELSEVIER
Automation in Construction 5 (1996) 219-231
SHADINGMASK:a teaching tool for sun shading devices Karen Kensek University
*, Douglas
’
Noble, Marc Schiler, Effendi Setiadarma 2
ofSouthern California, School of Architecture, Watt Hall #204, Los Angeles, CA 90089-0291 USA
Abstract Sun shading devices provide an opportunity for the designer to control natural lighting, ventilation, and solar gain, all of which provide a benefit to the overall building performance. Through sun path diagrams and shading masks, some of the effects of these solar controls can be demonstrated graphically. This paper describes SHADINGMASK, a computer program written to help designers understand the basic theory of solar control; generate sun path diagrams; design overhead, side, and eggcrate shading devices; calculate solar angles and shading masks; and provide case studies of actual buildings. Keywords: Solar control; Sun path diagram; Shading mask
1. Introduction
Sun shading devices, either as part of a building or separately placed from a building’s facade, affect natural lighting and ventilation, solar gain, and overall building performance. The role of sun shading devices or solar radiation control systems is taught at every school of architecture. Yet, only few architecture students, architects, and designers have applied them as a useful tool to reduce glare, control light intensity, radiation, and minimize cooling load on their projects. Using a well-designed computer program to teach, and re-teach when necessary, the use of sun shading devices is more understandable, clearer, and more interesting than reading a book on the same topic.
* Corresponding author. ’ Discussion is open until March 1997 (please submit your discussion paper to the Editor of Architecture, Y.E. Kalay). ’ Master’s thesis.
Having a readily available tool would also encourage architects and designers to use shading devices as a method of conserving energy and lowering operating costs in the buildings that they design. In the Passive Solar Energy Book, Edward Mazira [ll provided multiple sun charts based on latitudes from 28 degrees north to 56 degrees north. The chart comes in the form of vertical elevations of the sun’s movements. The diagram shows one example of a rectangular sun chart. Any obstructions that are outside the windows of a building, either trees, other buildings nearby, walls, and shading devices can be added to the sun chart as shading masks. Fig. 1 shows a simple diagram explaining the shapes that overhangs and fins provide to a shading mask for a rectangular sun chart. SHADING MASK uses Edward Mazira’s rectangular sun path diagrams and shading masks as a conceptual basis. The program, written in VISUALBASIC 3.0, explains the basic theory of solar control; generates sun path diagrams; allows the design of overhead, side, and eggcrate shading devices; calculates solar
0926-5805/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO926-5805(96)00147-l
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K. Kensek et al./Automation
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Fig. 1. A simplediagramexplainingthe shapesthatoverhangsand fins provideto a shadingmaskfor a rectangular sun chart.
angles and shading masks; and provides case studies of actual buildings.
2. Description of the program SHADINGMASK can plot sun charts for any latitude, in one degree increments, for any time of the year. Users may display a specific daily sun path diagram or a collection of monthly paths which produce an annual sun path diagram. Various height to depth (h/d) ratios and width to length (w/l)
4
EAST
ratios may be input to produce different types of shading masks. Users can manipulate these ratios and plot lOO%, 50%, and 0% shading masks. SHADING MASK consists of two executable programs: SHADINGMASK and SHADINGMASK THEORY. Both of them can be run independently. In THEORY the user can choose from the following subjects: introduction, chart, shading mask, sun path diagram, sun shading devices, and references. This information can also be called from the main body of the program, SHADINGMASK. SHADINGMASK’S main screen allows the user to produce a daily or yearly sun path diagram by adjusting the latitude and date of the place being studied. Fig. 2 illustrates the six pull-down menus: File, Shading Mask, Examples, Explain, Tables, and Help. The File menu has options to print plots, masks, or case studies and to exit the program. The Shading Mask menu is used to input ratios of window height to overhang depth (h/d) and window width to fin length (w/l) in order to create a
4
4
SOUTH
Fig. 2. Menustructure of
WEST
SHADING
MASK.
K. Kensek et al. /Automation in Construction 5 (1996) 219-231
shading mask. There are three options: Instant Shading Mask, Novice Options, and Advanced Options. Essentially they provide the
user with increasing control over the specific ratios input. In the Instant Shading Mask, h/d and w/l are set to 1. In Novice Options a limited range of rations are: available for 0%, 50%, and 100% shading, while in the Advanced Options, the user can input any ratio. The user can also vary the window orientation. The Examples menu currently contains examples of eight existing buildings that use overhangs and/or fins. It also :has shading mask examples for specific latitude, window treatment, and window orientations. The Explain menu is intended to provide users with the general theory of shading devices and help users develop a deeper understanding of solar control devices. The sun path diagrams can also be depicted in tabular form. This is done through the Tables menu. In addition, the user can get charts of information about glazing, shading coefficients, shading effectiveness, and latitudes of major cities. The Help menu functions as a user’s guide. From this menu, a user can learn how to use the program. The user can choose form how to start, how to plot a sun path diagram, how to plot a shading mask, how to explore examples, how to print, how to read the theory, and how to use help.
Double click on SHADING MASK,click on “click here to continue”, and then on “click here if you are a Novice User”, as shown in Fig. 4. This puts you into the Help menu, also accessible within the main body of the program if you need to remember specific information. It is useful to read through the
choices and instructions for an overview of how to use the program. See Fig. 5. Fig. 6 details the help screen for “How to Start.” Click on Start. Fig. 7 depicts the main graphic window for display of the sun paths and shading masks. Set the sliders for latitude and date. If the latitude is unknown, use the menu choice Tables.. . Latitudes to look up the latitude of the city that you are interested in. After the latitude and date is set, click on Plot to display a sun path diagram for that date, Clear to clear the screen, and Option to plot a yearly sun path diagram. It is important to set a specific date again if you use Plot to display a
3. Sample session SHADINGMASK is a Windows application and although designed with the novice user in mind, basic familiarity with Windows and the mouse is assumed. This section will describe how a novice user might proceed through the program. In Windows, the user can choose between SHADING MASK THEORY and SHADING MASK.Double click on SHADING MASKTHEORY.Fig. 3 shows the opening menu. Click on introduction and continue through chart, shading mask, sun path diagram, sun shading devices, and references, to gain an understanding of exterior solar control principles. File. . . Exit. The information on theory is also available within the main body of the program.
221
Fig.3. Openingmenufor SHADING M.v.KTHEORY.
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K. Kensek et al./Automation
daily diagram, but the program will remind you of this if you forget. Fig. 8 and Fig. 9 show the daily (April 28th) and annual sun path diagrams for 34 degrees north latitude, respectively. Set a specific date and use the selection Tables.. . Tables of Sun Path to produce a numeric display of these values. See Fig. 10 for the table of values of the April 28th sun path diagram, 34 degrees north latitude. Next, make a simple sun mask. Use the menu selection Shading Mask.. . Instant Shading Mask to try the options for fins (w/l = l), overhang (h/d = 1) or eggcrate (both fins and overhang). Then click on Shading Mask on the main display to have it calculate and draw your selected shading mask. You will need to Clear the display before displaying a new shading mask. See Fig. 11. Shading Mask (in the menu bar). . . Novice Options (Fig. 12) lets you describe fins or an overhang with a limited range of options for the w/l and h/d ratios. Click on the desired height or depth dimensions (in gray). The program calculates the
in Construction 5 (19%) 219-231
ratios and partial shading angles. Click OK to return to the main page, and then click the Shading Mask button to see the mask of your particular shading device (Fig. 13). You can also change your window orientation. Shading Mask.. . Advanced Options (Fig. 14) is similar to the novice options but lets the user have more choice in the ratios selected for 0%, 50%, and 100% shading. Fig. 15 shows the result of the choices; note that the window orientation has been changed to east of south. Once the dimensions are set, you can try different solar path plots and then superimpose the shading mask over the plots. Click Options first to display the plots, then click the Shading Mask button. After each change of your latitude, date, or shading mask values, you should Clear the display. If you forget these steps or any others, use the Help menu for directions. See Fig. 16. Use File... Print to print out examples that you wish to take with you. You will probably want to go back to the menu
Fig. 4. Opening menu for SHADING MASK.
K. Kensek et al. /Automation
under Explain.. . Shading Mask (Fig. 17) and Explain.. . Sun Path to review what the display is showing you. Examples... Euilding Designs will help to show what these fins and overhangs look like on actual building designs. Fig. 18 shows one example. When finished, use File. . . Exit to leave the program. Hopefully you have learned more about the uses of fins and overhangs to shade windows.
4. Algorithms
and logic
There are two sets of equations required for the program. The first s,et deals with astronomical relationships between the earth’s orbit, polar tilt, and the sun’s position. The s,econd set deals with the trigonometric relationship between the overhang, fin, eggcrate, and window. The astronomical equations have been simplified to produce the sun’s, position relative to a tangent to the earth’s surface at the latitude in question (perceived as the horizontal plane) and the projection of the sun’s position onto that horizontal plane. The first angle is called the altitude angle and is measured up from the horizontal, and the second is the azimuth angle, measured in relationship to the compass coordinates. In order to calculate those angles, it is necessary to calculate several interim angles, including the declination (polar tilt compared to sun’s location) Julian dam, and hour angles. The orbital speed also varies slightly, since the earth does not orbit in a perfect circle around the sun. The declination for a particular date may be calculated by:
in Construction 5 (1996) 219-231
The azimuth angle may be calculated by the equation: azimuth = sin-’ [cos( S ) * sin( w ) /cos(
LY
)]
where azimuth is the azimuth angle (clockwise from north), 6 is the declination angle, o is the hour angle, and (Y is the altitude angle. These values could be plotted on a Cartesian graph of altitude versus azimuth values. Due south was chosen as the center. The net result is a rectangular graph which approximates the view of the sun’s path when looking south. Extending the graph past the 90 degree point in either direction results in wraparound (the equivalent of looking over your left or right shoulder) but is still fairly easy to understand. At first, the plot was continuous from point to point, but it was determined that plotting only the points gave an intuitive feel of how fast the sun was
S = 23.45 * sin( 360(284 + n) /365) where 6 is the declination angle (or the wobble), and IZis the number of days since January 1. The altitude angle for a particular hour on that date may be calculated by: (Y= sin- ’ [ sin( S) * sin( L) + cos( 6 ) * cos( L) * cos( w)] where (Yis the altitude angle, S is the declination, L is the latitude of the site, and w is the hour angle (each hour the sun moves 15 degrees).
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Fig. 5. Choices in the Help menu.
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K. Kensek et al. /Automation
moving at different portions of the path. The hour angle was varied in constant increments, and the wider the spacing between the dots, the more rapidly the sun seems to be moving, which corresponds to the actual perceived speed. The position of the sun “on the hour” was noted especially and identified by callout. Some logic was required to make adjustments in the charts. For latitudes below the equator, a north facing plot is far more useful. For latitude between the tropics, some of the plots go completely behind the observer, not just over his/her shoulder. The noon position at certain latitudes and times seemed to appear out of nowhere and was sometimes confusing. Data was never adjusted, but views were adjusted to provide the clearest information in each case. The equations dealing with the overhangs and side fins are actually straight forward trigonometry. The shadow depth from a fin is expressed by the equation: w= tan( Az’) Xx
in Construction 5 (1996) 219-231
where w is the shadow width, AZ’ is the angle between the solar azimuth and the wall azimuth (a normal to the wall surface), and x is the length that the fin extends from the wall. The shadow depth resultant from an overhang is expressed by: h = tan( alt)
X x/cos(
AZ’)
where h is the depth of the shadow from the base of overhang, alt is the altitude angle, x is the extension of the overhang from the wall surface, and AZ’ is the angle between the solar azimuth and the wall azimuth (a normal to the wall surface).
5. Evaluation The intent of the program was to explain the basic theory of solar control; generate sun path diagrams; allow the design of overhead, side, and eggcrate shading devices; calculate solar angles and shading masks; and provide case studies of actual buildings.
Fig. 6. The help screen for “How to Start”.
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K. Kensek et al. /Automation in Construction 5 (1996) 219-231
file
Shading Mask
Examples
Gqlaig...
Iables
Help The
Sun-path
t&gram
90
80 70 60 f 50 ;
t 40 ” d 30,
Fig. 7. The main graphic window for display of sun paths and shading masks.
5le
Shading Mask
Examples
Explain...
Lables
.Mp
The Sun-pathDiagram
90
20 10
EAST
SOUTH Bearing
WEST
Angle
Fig. 8. Sun path diagram for April 2&h, 34 degrees north latitude
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K. Kensek et al./Automation
shading Mask
bmples
in Construction 5 (1996) 219-231
Explain...
Tables
Yelp
The Sun-path
Diagram 90
60
f
50
; t
alI
30
d e
20
EAST
SOUTH Bearing
WEST Angle
Fig. 9. Annual sun path diagram for 34 degrees north latitude.
I -
Fig. 10. Table of values of the April 28th sun path diagram,
34 degrees north latitude.
K. Kensek et al./Automation in Construction 5 (1996) 219-231
Ble
Shading Mask
&les
Explain...
lablcs
&lp
Fig. 1 I. Instant eggcrate shading mask for the April 28th sun path diagram,
34 degrees north latitude.
The SHADIMGMASKPmgram Die
Shading Mask
Examples
Explain...
Iables
Help
Fig. 12. Menu selection Shading Mask. . . Novice Options dialogue box.
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K. Kensek et al. /Automation
228
file
Shading Mask
Examples
Explain...
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Iables
flelp
The Sun-mth Diaaram
a
WEST
SOUTH
EAST
Bearing
Angle
Fig. 13. Shading mask for the values selected in figure 12 for an annual sun path diagram,
Eile
shading Mask
BarnpIes
34 degrees north latitude.
The SHADING MASK Program Explain... Iables !&tip
Fig. 14. Menu selection Shading Mask..
Advanced Options dialogue box.
K. Kensek et al. /Automafion in Construction
Ble
Shading Mask
bmples
ExplaiB...
Iablcs
5 (1996) 219-231
229
Help
The Sun-path
Diagram 90 80 70 60 p 50
EAST
4
SOUTH Bearing
I
WEST Angle
Fig. 15. Shading mask for the values selected in figure 14 for an annual sun path diagram,
34 degrees north latitude.
Fig. 16. Sample screen from the Help menu, “How to Plot a Shading Mask”.
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Fig. 17. Menu selection Explain..
. Shading Mask screen.
Cargenter Center Cwstal Cathedral ‘Qharmala Building $Dw Energy Demo. Bldg. Menera Mesiniaga Qffice Bldg. Omaha ,&zynolds Metal Co Robie House Clear All Buildlnos
Fig. 18. Example from the Examples..
. Building Designs menu selection.
K. Kensek et al./Automation in Construction 5 (1996) 219-231
shading Mask Examples
4
EAST
a
4
WEST
SOUM Bearing
Fig. 19. Confusing
Help
Tables
Explsb.
231
Angle
annual sun chart for 10 degrees north latitude.
Overall, the program reaches this goal and runs well. It is surprisingly simple (one central page provides most of the data) and fairly easy to understand given the possible permutations. It is remains very flexible in allowing many different variables to change. Yet, still some sun charts are confusing. The worst problem remains when users choose latitudes less than 24 degrees (north or south) and plot annual sun charts as shown in Fig. 19. In those latitudes part of the sun path should be perhaps be plotted on a different chart. Similar problems occur when users want to plot a shading mask on those sun charts. The print command in this program is basically a built-in print method in VISUAL BASIC 3.0 [2]. The resolution of the print-out may be dependent upon screen or monitor resolution. There are also many imperfect pictures in >thisprogram caused by the low resolution from scanner images or other bitmap files. The examples section of the program is not yet as detailed as it should be, and an option might be added to provide Olgyay style sun diagrams (hemispherical projections) [3]. And, of course, one could add additional options to the overhang and fin design
including asymmetrical arrangements, tilted louvers (e.g. Venetian blinds), and light shelves.
6. Conclusions Sun shading devices are important options for designers to consider to minimize heat gain, control daylighting, and protect walls from rain. A better understanding of these devices will hopefully generate a desire to apply them on projects. SHADING MASK is a good demonstration of how to integrate theory into a teaching or simulation tool to make important solar control information easily accessible to designers, student, and architects.
References Dl Mazira, E., 1979. The Passive Solar Energy Book, Rodale Press, Emrnaus, PA (1979).
El Cornell, G., 1993. The Visual Basic 3 for Windows Handbook, McGraw-Hill, Berkeley, CA (1993). [31 Olgyay, O., 1957. Solar Control and Shading Devices, Princeton University Press, Princeton, NJ (1957).
Automation in Construction 5 (1996) 219-231
SHADINGMASK:a teaching tool for sun shading devices Karen Kensek University
*, Douglas
’
Noble, Marc Schiler, Effendi Setiadarma 2
ofSouthern California, School of Architecture, Watt Hall #204, Los Angeles, CA 90089-0291 USA
Abstract Sun shading devices provide an opportunity for the designer to control natural lighting, ventilation, and solar gain, all of which provide a benefit to the overall building performance. Through sun path diagrams and shading masks, some of the effects of these solar controls can be demonstrated graphically. This paper describes SHADINGMASK, a computer program written to help designers understand the basic theory of solar control; generate sun path diagrams; design overhead, side, and eggcrate shading devices; calculate solar angles and shading masks; and provide case studies of actual buildings. Keywords: Solar control; Sun path diagram; Shading mask
1. Introduction
Sun shading devices, either as part of a building or separately placed from a building’s facade, affect natural lighting and ventilation, solar gain, and overall building performance. The role of sun shading devices or solar radiation control systems is taught at every school of architecture. Yet, only few architecture students, architects, and designers have applied them as a useful tool to reduce glare, control light intensity, radiation, and minimize cooling load on their projects. Using a well-designed computer program to teach, and re-teach when necessary, the use of sun shading devices is more understandable, clearer, and more interesting than reading a book on the same topic.
* Corresponding author. ’ Discussion is open until March 1997 (please submit your discussion paper to the Editor of Architecture, Y.E. Kalay). ’ Master’s thesis.
Having a readily available tool would also encourage architects and designers to use shading devices as a method of conserving energy and lowering operating costs in the buildings that they design. In the Passive Solar Energy Book, Edward Mazira [ll provided multiple sun charts based on latitudes from 28 degrees north to 56 degrees north. The chart comes in the form of vertical elevations of the sun’s movements. The diagram shows one example of a rectangular sun chart. Any obstructions that are outside the windows of a building, either trees, other buildings nearby, walls, and shading devices can be added to the sun chart as shading masks. Fig. 1 shows a simple diagram explaining the shapes that overhangs and fins provide to a shading mask for a rectangular sun chart. SHADING MASK uses Edward Mazira’s rectangular sun path diagrams and shading masks as a conceptual basis. The program, written in VISUALBASIC 3.0, explains the basic theory of solar control; generates sun path diagrams; allows the design of overhead, side, and eggcrate shading devices; calculates solar
0926-5805/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved. PII SO926-5805(96)00147-l
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K. Kensek et al./Automation
in Construction 5 (1996) 219-231
Fig. 1. A simplediagramexplainingthe shapesthatoverhangsand fins provideto a shadingmaskfor a rectangular sun chart.
angles and shading masks; and provides case studies of actual buildings.
2. Description of the program SHADINGMASK can plot sun charts for any latitude, in one degree increments, for any time of the year. Users may display a specific daily sun path diagram or a collection of monthly paths which produce an annual sun path diagram. Various height to depth (h/d) ratios and width to length (w/l)
4
EAST
ratios may be input to produce different types of shading masks. Users can manipulate these ratios and plot lOO%, 50%, and 0% shading masks. SHADING MASK consists of two executable programs: SHADINGMASK and SHADINGMASK THEORY. Both of them can be run independently. In THEORY the user can choose from the following subjects: introduction, chart, shading mask, sun path diagram, sun shading devices, and references. This information can also be called from the main body of the program, SHADINGMASK. SHADINGMASK’S main screen allows the user to produce a daily or yearly sun path diagram by adjusting the latitude and date of the place being studied. Fig. 2 illustrates the six pull-down menus: File, Shading Mask, Examples, Explain, Tables, and Help. The File menu has options to print plots, masks, or case studies and to exit the program. The Shading Mask menu is used to input ratios of window height to overhang depth (h/d) and window width to fin length (w/l) in order to create a
4
4
SOUTH
Fig. 2. Menustructure of
WEST
SHADING
MASK.
K. Kensek et al. /Automation in Construction 5 (1996) 219-231
shading mask. There are three options: Instant Shading Mask, Novice Options, and Advanced Options. Essentially they provide the
user with increasing control over the specific ratios input. In the Instant Shading Mask, h/d and w/l are set to 1. In Novice Options a limited range of rations are: available for 0%, 50%, and 100% shading, while in the Advanced Options, the user can input any ratio. The user can also vary the window orientation. The Examples menu currently contains examples of eight existing buildings that use overhangs and/or fins. It also :has shading mask examples for specific latitude, window treatment, and window orientations. The Explain menu is intended to provide users with the general theory of shading devices and help users develop a deeper understanding of solar control devices. The sun path diagrams can also be depicted in tabular form. This is done through the Tables menu. In addition, the user can get charts of information about glazing, shading coefficients, shading effectiveness, and latitudes of major cities. The Help menu functions as a user’s guide. From this menu, a user can learn how to use the program. The user can choose form how to start, how to plot a sun path diagram, how to plot a shading mask, how to explore examples, how to print, how to read the theory, and how to use help.
Double click on SHADING MASK,click on “click here to continue”, and then on “click here if you are a Novice User”, as shown in Fig. 4. This puts you into the Help menu, also accessible within the main body of the program if you need to remember specific information. It is useful to read through the
choices and instructions for an overview of how to use the program. See Fig. 5. Fig. 6 details the help screen for “How to Start.” Click on Start. Fig. 7 depicts the main graphic window for display of the sun paths and shading masks. Set the sliders for latitude and date. If the latitude is unknown, use the menu choice Tables.. . Latitudes to look up the latitude of the city that you are interested in. After the latitude and date is set, click on Plot to display a sun path diagram for that date, Clear to clear the screen, and Option to plot a yearly sun path diagram. It is important to set a specific date again if you use Plot to display a
3. Sample session SHADINGMASK is a Windows application and although designed with the novice user in mind, basic familiarity with Windows and the mouse is assumed. This section will describe how a novice user might proceed through the program. In Windows, the user can choose between SHADING MASK THEORY and SHADING MASK.Double click on SHADING MASKTHEORY.Fig. 3 shows the opening menu. Click on introduction and continue through chart, shading mask, sun path diagram, sun shading devices, and references, to gain an understanding of exterior solar control principles. File. . . Exit. The information on theory is also available within the main body of the program.
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Fig.3. Openingmenufor SHADING M.v.KTHEORY.
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daily diagram, but the program will remind you of this if you forget. Fig. 8 and Fig. 9 show the daily (April 28th) and annual sun path diagrams for 34 degrees north latitude, respectively. Set a specific date and use the selection Tables.. . Tables of Sun Path to produce a numeric display of these values. See Fig. 10 for the table of values of the April 28th sun path diagram, 34 degrees north latitude. Next, make a simple sun mask. Use the menu selection Shading Mask.. . Instant Shading Mask to try the options for fins (w/l = l), overhang (h/d = 1) or eggcrate (both fins and overhang). Then click on Shading Mask on the main display to have it calculate and draw your selected shading mask. You will need to Clear the display before displaying a new shading mask. See Fig. 11. Shading Mask (in the menu bar). . . Novice Options (Fig. 12) lets you describe fins or an overhang with a limited range of options for the w/l and h/d ratios. Click on the desired height or depth dimensions (in gray). The program calculates the
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ratios and partial shading angles. Click OK to return to the main page, and then click the Shading Mask button to see the mask of your particular shading device (Fig. 13). You can also change your window orientation. Shading Mask.. . Advanced Options (Fig. 14) is similar to the novice options but lets the user have more choice in the ratios selected for 0%, 50%, and 100% shading. Fig. 15 shows the result of the choices; note that the window orientation has been changed to east of south. Once the dimensions are set, you can try different solar path plots and then superimpose the shading mask over the plots. Click Options first to display the plots, then click the Shading Mask button. After each change of your latitude, date, or shading mask values, you should Clear the display. If you forget these steps or any others, use the Help menu for directions. See Fig. 16. Use File... Print to print out examples that you wish to take with you. You will probably want to go back to the menu
Fig. 4. Opening menu for SHADING MASK.
K. Kensek et al. /Automation
under Explain.. . Shading Mask (Fig. 17) and Explain.. . Sun Path to review what the display is showing you. Examples... Euilding Designs will help to show what these fins and overhangs look like on actual building designs. Fig. 18 shows one example. When finished, use File. . . Exit to leave the program. Hopefully you have learned more about the uses of fins and overhangs to shade windows.
4. Algorithms
and logic
There are two sets of equations required for the program. The first s,et deals with astronomical relationships between the earth’s orbit, polar tilt, and the sun’s position. The s,econd set deals with the trigonometric relationship between the overhang, fin, eggcrate, and window. The astronomical equations have been simplified to produce the sun’s, position relative to a tangent to the earth’s surface at the latitude in question (perceived as the horizontal plane) and the projection of the sun’s position onto that horizontal plane. The first angle is called the altitude angle and is measured up from the horizontal, and the second is the azimuth angle, measured in relationship to the compass coordinates. In order to calculate those angles, it is necessary to calculate several interim angles, including the declination (polar tilt compared to sun’s location) Julian dam, and hour angles. The orbital speed also varies slightly, since the earth does not orbit in a perfect circle around the sun. The declination for a particular date may be calculated by:
in Construction 5 (1996) 219-231
The azimuth angle may be calculated by the equation: azimuth = sin-’ [cos( S ) * sin( w ) /cos(
LY
)]
where azimuth is the azimuth angle (clockwise from north), 6 is the declination angle, o is the hour angle, and (Y is the altitude angle. These values could be plotted on a Cartesian graph of altitude versus azimuth values. Due south was chosen as the center. The net result is a rectangular graph which approximates the view of the sun’s path when looking south. Extending the graph past the 90 degree point in either direction results in wraparound (the equivalent of looking over your left or right shoulder) but is still fairly easy to understand. At first, the plot was continuous from point to point, but it was determined that plotting only the points gave an intuitive feel of how fast the sun was
S = 23.45 * sin( 360(284 + n) /365) where 6 is the declination angle (or the wobble), and IZis the number of days since January 1. The altitude angle for a particular hour on that date may be calculated by: (Y= sin- ’ [ sin( S) * sin( L) + cos( 6 ) * cos( L) * cos( w)] where (Yis the altitude angle, S is the declination, L is the latitude of the site, and w is the hour angle (each hour the sun moves 15 degrees).
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Fig. 5. Choices in the Help menu.
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moving at different portions of the path. The hour angle was varied in constant increments, and the wider the spacing between the dots, the more rapidly the sun seems to be moving, which corresponds to the actual perceived speed. The position of the sun “on the hour” was noted especially and identified by callout. Some logic was required to make adjustments in the charts. For latitudes below the equator, a north facing plot is far more useful. For latitude between the tropics, some of the plots go completely behind the observer, not just over his/her shoulder. The noon position at certain latitudes and times seemed to appear out of nowhere and was sometimes confusing. Data was never adjusted, but views were adjusted to provide the clearest information in each case. The equations dealing with the overhangs and side fins are actually straight forward trigonometry. The shadow depth from a fin is expressed by the equation: w= tan( Az’) Xx
in Construction 5 (1996) 219-231
where w is the shadow width, AZ’ is the angle between the solar azimuth and the wall azimuth (a normal to the wall surface), and x is the length that the fin extends from the wall. The shadow depth resultant from an overhang is expressed by: h = tan( alt)
X x/cos(
AZ’)
where h is the depth of the shadow from the base of overhang, alt is the altitude angle, x is the extension of the overhang from the wall surface, and AZ’ is the angle between the solar azimuth and the wall azimuth (a normal to the wall surface).
5. Evaluation The intent of the program was to explain the basic theory of solar control; generate sun path diagrams; allow the design of overhead, side, and eggcrate shading devices; calculate solar angles and shading masks; and provide case studies of actual buildings.
Fig. 6. The help screen for “How to Start”.
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file
Shading Mask
Examples
Gqlaig...
Iables
Help The
Sun-path
t&gram
90
80 70 60 f 50 ;
t 40 ” d 30,
Fig. 7. The main graphic window for display of sun paths and shading masks.
5le
Shading Mask
Examples
Explain...
Lables
.Mp
The Sun-pathDiagram
90
20 10
EAST
SOUTH Bearing
WEST
Angle
Fig. 8. Sun path diagram for April 2&h, 34 degrees north latitude
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Explain...
Tables
Yelp
The Sun-path
Diagram 90
60
f
50
; t
alI
30
d e
20
EAST
SOUTH Bearing
WEST Angle
Fig. 9. Annual sun path diagram for 34 degrees north latitude.
I -
Fig. 10. Table of values of the April 28th sun path diagram,
34 degrees north latitude.
K. Kensek et al./Automation in Construction 5 (1996) 219-231
Ble
Shading Mask
&les
Explain...
lablcs
&lp
Fig. 1 I. Instant eggcrate shading mask for the April 28th sun path diagram,
34 degrees north latitude.
The SHADIMGMASKPmgram Die
Shading Mask
Examples
Explain...
Iables
Help
Fig. 12. Menu selection Shading Mask. . . Novice Options dialogue box.
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Iables
flelp
The Sun-mth Diaaram
a
WEST
SOUTH
EAST
Bearing
Angle
Fig. 13. Shading mask for the values selected in figure 12 for an annual sun path diagram,
Eile
shading Mask
BarnpIes
34 degrees north latitude.
The SHADING MASK Program Explain... Iables !&tip
Fig. 14. Menu selection Shading Mask..
Advanced Options dialogue box.
K. Kensek et al. /Automafion in Construction
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Help
The Sun-path
Diagram 90 80 70 60 p 50
EAST
4
SOUTH Bearing
I
WEST Angle
Fig. 15. Shading mask for the values selected in figure 14 for an annual sun path diagram,
34 degrees north latitude.
Fig. 16. Sample screen from the Help menu, “How to Plot a Shading Mask”.
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Fig. 17. Menu selection Explain..
. Shading Mask screen.
Cargenter Center Cwstal Cathedral ‘Qharmala Building $Dw Energy Demo. Bldg. Menera Mesiniaga Qffice Bldg. Omaha ,&zynolds Metal Co Robie House Clear All Buildlnos
Fig. 18. Example from the Examples..
. Building Designs menu selection.
K. Kensek et al./Automation in Construction 5 (1996) 219-231
shading Mask Examples
4
EAST
a
4
WEST
SOUM Bearing
Fig. 19. Confusing
Help
Tables
Explsb.
231
Angle
annual sun chart for 10 degrees north latitude.
Overall, the program reaches this goal and runs well. It is surprisingly simple (one central page provides most of the data) and fairly easy to understand given the possible permutations. It is remains very flexible in allowing many different variables to change. Yet, still some sun charts are confusing. The worst problem remains when users choose latitudes less than 24 degrees (north or south) and plot annual sun charts as shown in Fig. 19. In those latitudes part of the sun path should be perhaps be plotted on a different chart. Similar problems occur when users want to plot a shading mask on those sun charts. The print command in this program is basically a built-in print method in VISUAL BASIC 3.0 [2]. The resolution of the print-out may be dependent upon screen or monitor resolution. There are also many imperfect pictures in >thisprogram caused by the low resolution from scanner images or other bitmap files. The examples section of the program is not yet as detailed as it should be, and an option might be added to provide Olgyay style sun diagrams (hemispherical projections) [3]. And, of course, one could add additional options to the overhang and fin design
including asymmetrical arrangements, tilted louvers (e.g. Venetian blinds), and light shelves.
6. Conclusions Sun shading devices are important options for designers to consider to minimize heat gain, control daylighting, and protect walls from rain. A better understanding of these devices will hopefully generate a desire to apply them on projects. SHADING MASK is a good demonstration of how to integrate theory into a teaching or simulation tool to make important solar control information easily accessible to designers, student, and architects.
References Dl Mazira, E., 1979. The Passive Solar Energy Book, Rodale Press, Emrnaus, PA (1979).
El Cornell, G., 1993. The Visual Basic 3 for Windows Handbook, McGraw-Hill, Berkeley, CA (1993). [31 Olgyay, O., 1957. Solar Control and Shading Devices, Princeton University Press, Princeton, NJ (1957).