AN ELABORATION ON THE DESIGN PRINCIPLES OF A UNIVERSAL- SOLAR

International Journal on Architectural Science, Volume 4, Number 4, p.168-184, 2003

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AN ELABORATION ON THE DESIGN PRINCIPLES OF A UNIVERSAL-SOLAR-CHART SHADOW-PLOTTER K.P. Cheung Department of Architecture, The University of Hong Kong, Pokfulam Road, Hong Kong, China (Received 13 May 2003; Accepted 8 September 2003) ABSTRACT To comply with insolation requirements of some countries [1,2], recommendations have been made on several graphical methods for estimating the shadow of a building or its features cast by sunlight on other features or buildings on the drawing paper [3,4]. These methods use a series of graphs for estimating the solar shadow. To many architects, these methods are not easy to apprehend and are time-consuming for implementation. Furthermore, many projection lines will have to be drawn on the drawing paper, causing likely confusion and difficulty in identifying each line. Also, separate sheets of pre-drawn graphs have to be produced for different latitudes. There are now software developed for architects and students [5] to help them design for fenestration and obtain solar shading masks, and for obtaining solar shadows for buildings. In the learning process of a person, however, physical tools do maintain their contribution, and complement learning with the computer software. In pursuing this complementing contribution of the physical tools, a physical universal-solar-chart shadow-plotter has been invented. This tool performs as a universal solar chart [6] for relating the latitude, day, apparent solar time, solar azimuth angle, and solar altitude angle, for any latitude selected. Also it enables an efficient plotting of the shadow of an object, such as the corner of a house, cast by the sun light on the ground, when the solar azimuth angle and solar altitude angle are known. In fact, these angles can also be found by the tool. This paper reports on the principles of design and operation of this tool. This tool however is first seen in its patented form [7], which does not contain sufficiently illustration of the principles to the normal architectural science readers. Therefore this paper serves the elaboration purpose. 1. INTRODUCTION There are several graphical methods for estimating the shadow of a building/or its features cast by sunlight on other features/buildings on the drawing paper [3,4]. These methods include the use of horizontal and vertical shadow mast diagrams which were commonly produced for the variables of AST, d, A, L, (and L’), h based on a mast of variable length. These methods are [3,4]: • Horizontal shadow mast diagrams in which L,

the latitude, is fixed, for the shadow of the mast cast on a horizontal plane at various d, A, h, AST.

• Horizontal shadow mast diagrams in which L and d are fixed, for the shadow of the mast to be cast (i.e. for varying h) on a horizontal plane for various AST and A.

• Vertical shadow mast diagrams in which L and A are fixed, for the shadow of the mast to be cast on a vertical plane (i.e. for varying h), for various d and AST.

To many architects, these methods are not easy to apprehend and are time-consuming for implementation. Also there is an inherent defect with these diagrams that the shadow of the mast for low h (i.e. around the times of sunrise and sunset) cannot be shown on the diagrams. Furthermore, many projection lines will have to be drawn on the drawing paper, causing likely confusion and difficulty in identifying each line. A more commonly used method is to read off h for the concerned AST and A, (or AST and d) from solar charts which are commonly plotted by the equidistant-h method, or the stereographic-h method, for a fixed L [8]. h is then manipulated graphically, and by trigonometric calculations, and drafting for estimating the shadow of building features cast by direct sunlight. This process involves the conversion of h from an angle to a ratio of numerals by trigonometrical relationships for shadow calculation and subsequent plotting on the drawing paper with rulers and angle protractors. More the marking of the shadow points, more projection lines will

International Journal on Architectural Science

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appear on the paper. To overcome the confusion caused by the large number of projection lines, a shadow-plotter, requiring a small amount of projection lines to be drawn on the paper, has been developed. One of the two components of this plotter is, in fact, also a component of a universal solar chart [6]. Since it takes little additional effort to produce the remaining component of the universal solar chart, the chart is also produced. The package of tool produced and described here, is therefore a universal-solar-chart and a shadow-plotter. 2. THE EXISTING UNIVERSAL

SOLAR CHART Based on established principles [6], the universal solar chart comprises a hemispherical co-ordinate graph for A and h (Fig. 1), and a separate graph showing the solar path traversing in a segmental spherical surface (Fig. 2). When properly overlaying on each other, these graphs relate various L, (and L’), AST, d, h, A with respect to the observer point O which is the center point of the hemisphere [6] (Fig. 3). In constructing the diagrams (Figs. 1 to 3), it is assumed that there is practically no difference of topocentric observation (i.e. observing the sun at a spot on the surface of the earth) and geocentric observation (i.e. observing the sun fictionally at the center of the earth) of the sun in relating the parameters of the universal solar chart, viz. latitude, day (i.e. solar declination angle), time, solar azimuth angle, solar altitude angle. This is the assumption used by all solar charts [4-6,8-10]. For general purposes including general geographical and architectural applications, this assumption is acceptable because the distance between the sun and the earth far outweighs the diameter of the earth and the sun. With the dimensions of the graphics used (Figs. 1 to 3), the radius of the hemi-spherical co-ordinates (Fig. 1) and the radius of the spherical solar path segment (Fig. 2) is 75 mm. This is the scaled average distance of the sun from the earth drawn on a piece of paper. Based on this dimension, the diameter of the earth will be 0.0064 mm, and the diameter of the sun will be 0.7 mm (Table 2). The earth and the sun will be circular dots of 0.0064 mm diameter and 0.7 mm (Figs. 3 to 5). In the universal-solar-chart, the straight line(s) joining the position of the sun on the surface of the spherical segment of solar path and the center O of the segment (Fig. 5) (i.e. the center O of the hemispherical co-ordinates (Fig. 4)) above the geographical horizon shows the sunlight direction as observed from the earth (i.e. centre O). Since in

physical scales of the universal solar chart, the earth and the sun are practically small points (Figs. 1 to 5), therefore there is practically no difference in geocentric and topocentric observations of the solar path and sunlight direction. Such difference is not observable by our naked eyes when we look at the universal solar chart (Figs. 1 to 5). 3. THE UNIVERSAL-SOLAR-CHART

SHADOW-PLOTTER – THE BASIC COMPONENTS

The invented tool [7] consists of the following three components: • Component A – The hemispherical co-

ordinate of A and h, marked on the packing for the other two components (Fig. 4).

• Component B – A circular transparent plastic plate, with a straight hollow slot made at the central part of it, and marked with an orthogonal projection of the annual solar path on a segmental spherical surface (Fig. 5).

• Component C – A separate transparent hollow plastic plate, marked up with bearing angles and altitude angles (Fig. 6).

The radius of the transparent plastic circular Component B (Fig. 5) is equal to the radius of the hemispherical graphic (Fig. 4), and is slightly less than the radius of the circular hole of the plastic plate Component C (Fig. 6), allowing tight yet smooth rotation to occur between the transparent plastic circular Component B (Fig. 5) and the transparent hollow plastic plate (Fig. 6) – Component C. 4. USE OF THE UNIVERSAL-SOLAR-

CHART SHADOW-PLOTTER AS A UNIVERSAL CHART

When the transparent plastic Component B containing the solar path (Fig. 5) is properly overlayed onto Component A (Fig. 4) which is the paper packaging with the hemi-spherical coordinates marked on it, in accordance with an established method [6], (Fig. 3), the tool can be used as a solar chart for any latitude in the Northern Hemisphere (Fig. 3) and in the Southern Hemisphere (Fig. 8). Because it works for all latitudes, it is a universal solar chart. Since there are 5 parameters involved in the chart (Figs. 2, 4 and 5), the use of the chart depends on the number of parameters to be known first, and the complementing number of parameters then to be found.


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Fig. 1: Orthogonal projection of a hemispherical coordinating system for solar azimuth angle and solar altitude angle, with observer at center O

Notes: 1. Centre of hemisphere, is the location of the Earth. 2. The orthogonal projection is of reduced scale made from geographical West referring to the Earth geographical system,

at a distance of the Sun from the Earth. 3. Observation difference is insignificant for geocentric and topocentric observations of the related parameters – see text

Fig. 2: Orthogonal projection of spherical segment of sun path as seen from geographical West

Notes: 1. O, centre of segment, is the location of the Earth, and PP is centre line of segment passing through O. 2. The orthogonal projection is of reduced scale made form geographical West referring to the Earth geographic system, at a

distance of the Sun from the Earth. 3. Observation difference is insignificant for geocentric and topocentric observations of the related parameters – see text


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Fig. 3: A universal solar chart [4, with adaptation] Notes: 1. Illustration for use at 40 deg N, 5 May, 9 am (AST) is indicated. (Point I) 2. Line II’ is drawn parallel to the horizon of the said location. Point I’ at the semi-circle reads: solar altitude angle h = 44.5

deg. Line OB is making an angle of 44.5 deg with the horizon. 3. The curve II’’ follows the azimuth angle coordinate system, with Point I’’ cuts the azimuth coordinate circle at the

horizontal plan. Point I’’ reads: solar azimuth angle = 108.5 deg (i.e. The Sun is at 71.5 deg East of South). The normal use of a solar chart [4-6,8-10] is to know the latitude, day and time, and then to find solar azimuth angle and solar altitude angle. Adopting this approach of knowing three parameters and finding another two parameters (Table 3), the tool can perform 10 functions. Among these 10 functions, it is of particular interest to know the following particular cases: • A particular case of function 1.1 (Table 3):

when the latitude and the day are known, and apparent solar time = noon. (Note that solar azimuth angle = 180 degree, and t = 0):

- then for a fixed latitude, the solar altitude angle is related to solar declination angle corresponding to the day of interest by the following equation:

h = 180° - (90°+L) + d = 90° + d – L (Fig. 3), for Northern Hemisphere, with direct sunlight coming from South;

h = 180° - (90°+L’) - d = 90° - d - L’ (Fig. 8), for Southern Hemisphere, with direct sunlight coming from North (The –ve sign preceding d is needed to cope with the sign convention of d (Table 1) )


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A universal Solar-Chart Shadow-Plotter

Fig. 4: Component A of the invented tool - The basic content of the graphics shown on the packing of the invented tool

- also, for a given day at AST noon, the

more North one goes by one degree of latitude, the solar altitude is reduced by one degree, for Northern Hemisphere. The more South one goes by one degree of latitude, the solar altitude angle is reduced by one degree, for Southern Hemisphere.

Note that is this particular case, 0 ≤ h calculated ≤ 90°. If h is greater than 90°, subtract this calculated h from 180° to obtain the final correct altitude angle. Note that h cannot be negative of course, because sunlight cannot come below the horizon, except in sunrise and sunset which is explained below.

• A particular case of function 1.2 (Table 3):

when the latitude and the day are known, and solar azimuth angle = 180 degree (Note that apparent solar time = noon): This is identical to the particular case described above.

• A particular case of function 1.3 (Table 3). In which the latitude and the day are known, and solar altitude angle = zero, i.e. at sunrise and sunset: The apparent solar time and the solar azimuth angle(s) at sunrise and sunset can be found. However, due to the slanting path of sun movement at latitudes other than the equator,

atmospheric refraction of sunlight, and the definition of the times of sunrise and sunset regarding sitting of the solar disc, there exist a difference of several minutes between the estimated and actual times of sunrise and sunset [11-13]. Always consult the local meteorological station for the exact time for sunrise and sunset.

In the above functions, there are three parameters known first, then two other parameters are found. In fact, more functions can be performed by first knowing two parameters, then three other parameters are found. For example, if the latitude and the solar azimuth angle are known, then the combinations of day, time and solar altitude angle can be found. For example, this could be a case in which the sun is hidden behind a tall building as viewed from a strategic location of a park such as the entrance gate. The interest then would be to know when (i.e. which day/time) the sun will come round the tall building and shine at the entrance gate. The time parameter of the above functions and the universal solar chart are based on apparent solar time. With established methods of conversion from local standard time to apparent solar time [8,11]. the tool can be used to relate local standard time with latitude, day, solar azimuth angle and solar altitude angle. This conversion takes time in using the tool, making this application not convenient. That is, this tool is not convenient for use with local standard time.


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Fig. 5: Component B of the invented tool – The circular transparent plastic component of the invented

tool marked with the graphics of the solar path and related annotations (adapted from Fig. 1) and a straight slot on the 18 hour line

Note: The straight slot is made good for use with pencils having lead of less than 0.5 mm diameter. mm/cm scales are both marked along this slot and the equinox line, which is at right angle to the slot, reference to the centre of the circle.

Fig. 6: Component C of the invented tool – The hollow transparent plastic plate component of the invented tool marked with the graphics of bearing/azimuth angles and altitude angles


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Table 2: The prime sun-earth dimensions – actual and scaled on the tool

Actual dimension Scaled dimension in the components A, B, C (Figs. 4 to 6) Mean distance of the earth from the million

km 75 mm (Note 5)

Aphelion 152.5 million km (Note 2) 76.25 mm (Note 5) Perihelion 147.5 million km (Note 3) 73.75 mm (Note 5)

Diameter of the sun About 1.4 million km

0.7 mm (Note 4)

Mean diameter of the earth About 12,740 km

0.0064 mm (Note 4)

Notes: 1. Equatorial diameter of the earth is about 12,760 km, and polar diameter of the earth is about 12,720 km. 2. Aphelion: It is the point in the Earth’s orbit when it is farthest from the sun (152.5 million km).

Aphelion occurs on the 3rd or 4th of July. 3. Perihelion: The point on the Earth’s orbit which is nearest the sun (147.5 million km). Perihelion occurs

on the 3rd or 4th January. 4. With the actual dimensions of the Components A, B, C described, our naked eyes practically will regard

the scaled “sun” and “earth” as two small points, and give one value to any angle made by the line joining these two lines with other reference line. Note that a mechanical pencil of 0.5 mm diameter lead is recommended for drawing with the tool, and that the scaled diameter of the sun is 0.7 mm.

5. At aphelion and perihelion, the maximum and minimum distance of the sun from the earth differs respectively by 1.6% from the mean distance. This difference is 1.2 mm (which is 1.6% x 75 mm). A small error will exist in the tool due to the use of the mean distance throughout. When the sun-earth distance is close to the mean distance used, the error is certainly negligible, the error at other situations has to be reviewed later when the product is commercialized and used by many end users with 3 parameters known who will give values as read off by their naked eyes. The error is certainly is small.

Table 3: Functions of the tool as a universal solar chart-with Component A (Fig. 4) and Component B (Fig. 5) used together (Fig. 3, Fig. 7)

Functions Parameters involved

Latitude i.e. L, L’ Day (i.e. solar

declination angle, d)

Apparent solar time (i.e. AST)

Solar azimuth angle (i.e. A)

Solar altitude

angle (i.e. h)1.1 k k k f f 1.2 k k f k f 1.3 k k f f k 1.4 k f K k f 1.5 k f k f k 1.6 k f f k k 1.7 f k k k f 1.8 f k k f k 1.9 f k f k k

1.10 f f k k k Notes: 1. Any latitude in either hemisphere can be set by the tool. 2. k ＝ “known” means “parameters known” 3. f = “found” means “parameters that can be found by the tool. 4. Functions 1.1 to 1.10 are arbitrary numbers to record functions that can be performed based on knowing

3 parameters for finding another 2 parameters.


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5. USE OF THE UNIVERSAL-SOLAR-CHART SHADOW-PLOTTER AS A SOLAR-SHADOW-PLOTTER

It will be seen that Component B and Component C (Fig. 7) used together can perform efficient operations in drawing projections of points and objects when the altitude angle of projection is known. Note that altitude angles are marked on Component C. In this sense, it is an altitude projection plotter. However, Component C (Fig. 6) is also marked with bearing angles, enabling efficient drawing for solar azimuth. Then when the altitude angles are related with solar altitude, the tool can efficiently perform as a solar shadow plotter. Suppose there is a house in 40°N, drawn in 1:100 scale (Fig. 9), with the shadow of the house on its surroundings cast by sunlight at 7, 8, 9, 10 am, apparent solar time, 6 May, to be investigated. Elaborating from a flow chart [7], the steps to fulfill this task are as follows: Step 1 To obtain solar azimuth angle and solar

altitude angle by overlaying the circular transparent plastic Component – Component B (Fig. 5) onto Component A (Fig. 4) – i.e. the hemispherical co-ordinates and obtain the solar azimuth angle and solar altitude angle for 7 am, 8 am, 9 am, 10 am Apparent Solar Time of 5 May using the established principles of operating the universal solar chart (Fig. 3). Mark these solar angle values on the plan of the house (Table 4 in Fig. 9a).

Step 2 Rotate the circular transparent plastic

component – Component B (Fig. 5) about the circular hole of the hollow transparent plastic plate – Component C (Fig. 6) such that the slot of Component B (Fig. 5) is in line with the North-South orientation of Component C (Figs. 6 and 9a).

Step 3 With Components B and C maintaining in

this relative position, overlay and slide these 2 components onto the plan of the house (Fig 9a) such that the center of Component B (i.e. the center of the slot) meets the nearest edge of the house, with the slot in line with the North-South orientation of the house (Fig. 9a).

Step 4 Keeping Component C fixed relative to

the plan, rotate Component B such that its slot is in line with the edge of the house. Read off the azimuth angle of this edge and mark it on the plan (Fig. 9b). This

azimuth angle is 237 degree. Marking of this angle is optional, as far as construction of the shadow area is concerned.

Step 5 Keeping this relative position of

Component B and Component C, slide these two components together on the plan such that the center of the slot of Component B is at a corner of the roof the house (Figs. 9b and 9c), with the slot in line with one edge of the house.

Step 6 Keeping Component C stationary, but turn

Component B such that its slot of is at bearing angle (i.e. solar azimuth angle) of 86.5 degree 97 degree, 108 degree, and 124 degree, respectively for 7 am, 8 am, 9 am, 10 am, apparent solar time respectively. Draw a line for each azimuth angle, with the lines passing through the corner of the house (Fig. 9c).

Step 7 Now sunlight shines to this corner of the

house which is 3 m high, at an elevation angle at a particular time. The shadow of this corner on the ground is equal to the shadow cast by a pole of 3 m high on the ground along the solar azimuth direction. This step involves the construction of the related corner shadow on the ground.

Now rotate Component B such that its slot lies in the 90 degree altitude angle direction. (Fig. 9d). Then keeping the relative position of Component B and Component C, move these 2 components together such that the right-angle crossing line of the slot lie (i.e. the line pointing to zero altitude angle) lies or any azimuth line constructed earlier. Now let this crossing line lie on the 124 degree azimuth line (Fig. 9d). Note that the azimuth angle scale of Component C is not used in this step.

Step 8 From the center of the slot of Component B, red off the mark at 3 cm and draw a line from this center to this 3 cm mark. This line is at 90 degree to the 124 azimuth line (Fig. 9d). Note that the azimuth angle scale of Component C is not used in this step.

Step 9 Still keeping the relative position of Component B and Component C, move 2 components together such that the center of Component B is at the end of the 3 cm line, with the center of the slot in line with this 3 cm line (Fig. 9e).


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Step 10 Keeping Component C stationary, rotate Component B such that the centre of the slot rotates about the end of the 3 cm line. Let the slot of Component B point to the altitude angle scale of Component C at 54 degree, 44.5 degree, 33 degree and 25.5 degree which are actually solar altitude angles respectively relating to solar azimuth angles of 124 degree, 108 degree, 97 degree, 86.5 degree. As the slot of Component C points to the said altitude angles at one direction to the altitude angle scale of Component C, mark off the meeting point of the slot at the other direction as the slot meets the 124 degree azimuth line. In this way, 4 points are marked on the 124 azimuth line (Fig. 9e). The length along this line as measured from the corner of the house (i.e. from the center of the slot along the zero altitude line of Component B in this particular position) (Fig. 9e) to these 4 points respectively represent the true length of the shadow of the corner of the roof when the sun appears at these 4 altitude angles.

Step 11 Now mark off these true length of the 4 shadows on the respectively azimuth line (Fig. 9f).

Step 12 Repeat Steps 2 to 11 for the ridge end point, which is at 4 m above ground (Fig. 9f), for constructing the shadow of this ridge end cast by sunlight on ground.

Step 13 Copy the 4 end points of the shadow on

the ground for the 4 respective solar azimuth angles obtained from Step 2 to 11 for the other 2 corners of the house which are similarly at 3m above ground, using parallel line drawing techniques which is self-explanatory with Component B and Component C working together (Fig. 9e). Not that no illustration lines are shown for this step, because Components B and C are self-explanatory for drawing parallel lines.

Step 14 Connect all the relevant end points of the

shadows together to obtain the shaded area (Fig. 9g).

Note that the plotter in fact is a shadow-plotter. However, as illustrated for solar shadow plotting, it becomes a solar-shadow-plotter. Also when the user becomes familiar with the tool, the amount of lines drawn can be reduced.

Fig. 7: Components B & C put together for zero latitude i.e. Equator

Note that the diameter of the hollow part of Component C is slightly larger than the diameter of Component B.


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Fig. 8: A universal solar chart [4, with adaptation]

Notes: 1. Illustration for use at 40 deg N, 5 May, 9 am (AST) is indicated. (Point I) 2. Line II’ is drawn parallel to the horizon of the said location. Point I’ at the semi-circle reads: solar altitude angle h = 19.9

deg. Line OB is making an angle of 19.9 deg with the horizon. 3. The curve II’’ follows the azimuth angle coordinate system, with Point I’’ cuts the azimuth coordinate circle at the

horizontal plan. Point I’’ reads: solar azimuth angle = 46 deg (i.e. The Sun is at 46 deg East of North). 6. OTHER USES OF THE UNIVERSAL-

SOLAR-CHART SHADOW-PLOTTER

Based on the same operation principles illustrated above, the tool can be used to plot solar shadow lines on vertical walls and the roof of a building, and to efficiently construct solar shading/shadow masks together with the universal solar chart or other commonly used solar charts [8].

7. SHORTCOMINGS OF THE UNIVERSAL - SOLAR - CHART SHADOW-PLOTTER

Component B (Fig. 5) has regular mm divisions, and Component C (Fig. 6) has regular angular divisions for bearing/azimuth and altitude. These two components work together as the plotter with no apparent shortcomings. Except that perhaps they are limited by their size. This will make them not convenient to work with large drawings. This is a universal problem for physical tools.


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Fig. 9: Information about the house located at latitude 40 deg North and Step 1 of constructing the area on ground shaded by the house

Fig. 9a: Step 2 & 3 of constructing the area on ground shaded by the house


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Fig. 9b: Step 4 & 5 of constructing the area on ground shaded by the house

Fig. 9c: Step 6 of constructing the area on ground shaded by the house


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Fig. 9d: Step 7 & 8 of constructing the area on ground shaded by the house

Fig. 9e: Step 9 & 10 of constructing the area on ground shaded by the house


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Fig. 9f: Step 11 & 13 of constructing the area on ground shaded by the house

Fig. 9g: Shadow of the house cast by sunlight on ground at 40 deg North, 5 May at 7, 8, 9, 10 am of apparent solar time


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On performing as a Universal-Solar-Chart, both Components A and B have shortcomings at the spherical turning regions of the orthogonal projection. This effect makes azimuth lines very close together for Component A (Figs. 1 and 4) typically around true north and true south, and around the zenith region. These azimuth angle regions are practically about 160 to 200 degree, and 340 to 360 (i.e. 0) degree, and 0 to 20 degree. Also, this effect makes the hour curves around noon and midnight very close together. This hour curve regions are practically from the hour curves of 11 am, through noon to 1 pm, and from 11 pm through midnight to 1 am, apparent solar time (Figs. 2 and 5). This effect makes reading for the said regions of azimuth and hour curves very difficult. To help the user to overcome these shortcomings, special tables with suitable numbers have to be provided as well. Alternatively, traditional commonly used solar charts [4-6,8-10] can also be supplemented, but this will mean a lot of sheets will be needed to cover all latitudes. As internet is widely used now with availability of free interactive software for calculating the related parameters, and related software can also be downloaded, these short comings can be overcome. Of course a software can be provided with the tool as well. 8. CONCLUSION The tool is described and illustrated for 40°N. In fact it can be used for all latitudes on earth, and for the full range of day and time combinations. The tool is therefore a Universal-solar-chart shadow-plotter, plotting the shadow of an object cast by light, and in the illustration, by sunlight, on the plan. Also it performs the functions of a solar chart for all latitudes, without using many charts which is a common practice [8]. The tool has shortcomings when used as a Universal solar chart. But it works well as a shadow-plotter. Because the chart is constructed by scaled physical orthogonal projections of the mean spherical segment solar path with respect to an observer on the earth, the chart operation process serves as an ever reinforcing learning process on solar geometry to the user, every time he uses it. Likewise, because the plotter uses the principle of altitude projection of physically scaled true length with azimuth correlation, the user also will experience an ever reinforcing learning process, whenever he uses it.

The tool is a desirable tool for geographic and architecture students to understand and be acquainted with solar and shadow geometry, and for plotting shadows. It also serves as a handy tool for architects to obtain the related parameters quickly over a wide range of combinations of latitude, day, time, solar azimuth angle and solar altitude angle, with reasonable accuracy, except for the mentioned regions of projections where the spheres turn. For exact values of shadow length, solar altitude and solar azimuth, calculations with equations, or suitable computer software, have to be used. This physical tool therefore complements the learning process of physical happenings, rather than aims at obtaining exact numbers, which is the prerogative of computer software. NOMENCLATURE A Solar Azimuth angle, A = 0 deg for North

direction, A is 90, 180, 270 degree, when the sun is due East, South and West.

AST Apparent Solar Time, or true solar time.

d The declination angle of the sun with respect to the center of the earth, d = +23.5 deg at Summer Solstice and d = -23.5 deg at Winter Solstice. Different declination angles correspond to the different days of the year (Table 1).

h Solar altitude angle

L Geographical latitude of a place in the Northern Hemisphere

L’ Geographical latitude of a place in the Southern Hemisphere

T hour angle, t = 0 deg for solar noon (i.e. AST, apparent solar time = 12:00 noon), for one hour, the hour angle elapsed is 15 deg., t is positive for AST p.m. and negative for AST a.m. Some people define t with an exactly opposite sign convention.

REFERENCES 1. GB50180-93, Code of Urban Residential District

Planning & Design, Beijing, China, pp. 10-11 (1999) - in Chinese.

2. 田中授, 柳瀨正敏, 日照計畫的知識, 鹿島出版會,日本 . Knowledge of insolation design, ISBN 4-306-01096-1 C3052 P1854E, Kajima Publishing K K, Tokyo, Japan, pp. 43-62 (1992) - in Japanese.

3. 田中授, 柳瀨正敏, 日照計畫的知識, 鹿島出版會, 日本 . Knowledge of insolation design, ISBN 4-306-01096-1 C3052 P1854E, Kajima Publishing K K, Tokyo, Japan, pp. 15-42 (1992) - in Japanese.


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4. Beijing Industrial Architectural Design Institute, Architectural design handbook, Sinhua Publishers, China, Vol. pp. 71-83 (1980) - in Chinese.

5. Private communication. A. Marsh, School of Architecture and Fine Arts, University of Western Australia (1999).

6. E. Boa, Insolation design for buildings, Technology Publishers Limited, Taipei, Taiwan, pp. 51 (1979) - in Chinese.

7. Cheung Kwok Pun, US Patent No. US6449854, Universal solar chart shadow plotter and method for plotting a shadow, published on 17 September 2002. The patent can be read from http://l2.espacenet.com/espacenet/viewer?PN=US6449854&CY=gb&LG=en&DB=EPD

8. S.V. Szokolay, Solar geometry, PLEA note 1, c/o Department of Architecture, The University of Queensland, Australia.

9. K.P. Cheung, “An alternative solar chart and its use in a case study”, Architectural Science Review, Vol. 40, No. 1, pp. 23-25, March (1997).

10. Olgyay & Olgyay, Solar control & shading devices, Princeton University Press, New York, pp. 26, 27, 42, 43 (1957).

11. A.N. Strahler, Physical geography, 6th edition, John Wiley & Sons, New York, pp. 83-85 (1975).

12. The Nautical Almanac 1991, HM Stationery Office, London, pp. 10-253 (1990).

13. K.P. Cheung, “An alternative solar chart and its use in a case study”, Architectural Science Review, Vol. 40, No. 1, pp. 27, March (1997).

14. K.P. Cheung, “A 23-lamp heliodon”, Architectural Science Review, Vol. 42, No. 1, pp. 52-53, March (1999).

AN ELABORATION ON THE DESIGN PRINCIPLES OF A UNIVERSAL- SOLAR

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Transcript of AN ELABORATION ON THE DESIGN PRINCIPLES OF A UNIVERSAL- SOLAR