The Sun, Climate & Architecture:

Integrated Methods of Passive Solar Building Design

Acknowledgements

Margit Rudy, June 2000 Research funded by the FWF (Austrian Science Fund), in association with the Vienna University of Technology, Institut für Hochbau für Architekten – Abteilung Bauphysik und Humanökologische Grundlagen (former dept. head: a.o.Univ.Prof.em. Dr. Erich Panzhauser). The author would like to especially thank Dr. Klaus Krec for his contributions to, supervision and continued support of the work documented in the following.Margit Rudy, June 2000

Introduction  The last two decades have been marked by an increasing public awareness of the need for environmentally sensitive solutions in the realm of building design. Given the simple fact that a major purpose of a built environment is to provide shelter and comfort, the realization that this could and should be accomplished more intelligently so as to minimize the damage to the environment has gained acceptance as a strategic objective. Whereas active (mechanical and electrical) systems for supplying a working building with the needed energy are traditionally the domain of engineering specialists, so-called passive strategies seek to limit the need for auxiliary systems by designing the building envelope such that it inherently fulfills thermal tempering functions as extensively as possible under the given climatic conditions. In other words, passive energy-use strategies are by definition a matter of the entire building envelope together with its utilization and, therefore, a core concern of architectural practice. In order to effectively reduce the negative environmental impact of erecting and operating buildings -- without compromising thermal comfort or other functional and psychological priorities -- architectural design concepts should adequately reflect environmental concerns from their inception. Such an integrative approach implies a fundamental departure from the increasingly common practice of consulting specialists for energy arguments "after the fact" of architectural design. Since accounting for local climate is in large part a question of adequately modeling the influences of solar radiation on the overall thermal performance of a building, the meaning of the term passive solar has evolved to encompass nearly all major strategies of environmentally responsive building design: to provide comfortable and inexpensive heating in the winter, cooling in the summer, and daylighting all year round. Concretely, these objectives are also reflected in new building codes and thermal quality standards emerging in the European Union (as elsewhere in the world), which prescribe increasingly sophisticated calculations to be performed for building project permits.

Meeting more complex and stringent thermal quality standards poses a substantial addition to the tasks required of building designers. A positive challenge to the supporting field of building science lies in developing methods which not only yield the prescribed final calculations, but also serve to guide the consistent realization of passive energy-use strategies throughout the entire design process.

 context A wealth of quantitative methods and techniques for estimating solar influences on the thermal behavior of a building already exist. Nonetheless, the approaches behind these developments are either engineering-oriented and aimed at evaluation late in the architectural design process, or too simplified and individually limited in applicability to a single level of a specific design decision. The term "design tool" is generally used to encompass all design-support methods and aids, i.e. "forward-looking" guidelines as well as "backward-looking" simplified methods. Theoretically, a guidance tool would be used before each design step, followed by the use of an evaluation tool after the step to verify that the desired result was indeed obtained (Balcombe 1992). Practically, however, such an ideal usage sequence is only realistic if the individual procedures involve compatible tools. As it is, in order to effectively implement the entire range of currently available solar assessment techniques, the architect must first familiarize him/herself with a varied (and often inconsistent) array of characterizing parameters -- a time-comsuming, autodidactic process better left to specialists after all. The consequence, not surprisingly, is that very few of the many potentially valuable instruments in solar building physics have made their way into the training and practice of architecture. This may, in part, be due to the fact that most simplified methods which have been developed especially with architects in mind are highly derivative in nature, and thus tend to obscure rather than clarify underlying physical principles. Moreover, using such a diverse palette of methods means having to deal with incongruous models and sets of parameters for each type of evaluation, thus prohibiting the comparative interpretation of results spanning different design stages. In contrast, computer simulations of thermal performance -- which provide data for correlation analysis and thus constitute the source of many simplified methods -- are in some respects simpler to comprehend as they are much more closely linked to physical models. With the increasing availability and power of computer-based methods for simulating thermal behavior, simulation analysis appears to be gaining feasibility as a design guidance tool. There is, however, no doubt that full-scale simulation analysis is still far too unwieldy and data-intensive for immediate use during the course of building design, especially at early stages when key decisions are made. More importantly, even in the event that such tools should one day become sufficiently convenient for architects, the buiding design process in its earliest stages does not generally include enough thermally relevant detail information to make simulation results

truly indicative of performance quality. aim & objectives

Designing effective solar design tools entails establishing an accessible bridge between the information needs of the building designer and the information provided by building physics. It is commonly agreed that design-guidance methods in general -- and computer-based design tools in particular -- should be tailored specifically to the working methods of architects (rather than engineers) if the derived techniques are to gain full acceptance in actual design practice. From the architect's point of view, solar building physics is immediately relevant to two primary aspects of design considerations: the optimization of thermal comfort and the economy of means (Anderson 1990). Beyond this, solar design issues also directly influence lighting options and, ultimately, psychological and aesthetic qualities of the architecture itself. The relative importance of these design objectives varies according to the priorities specific to each project as well as to the designers and clients involved. Generally, however, it can be said that technical aspects demanding a high degree of pre-specification for assessment are only of peripheral interest to the architect at early design stages. Concretely stated, satisfying the needs described above calls for a system of design support tools that targets a number of goals in equal measure, such that it ▪ provides a means for generating custom information specific to the site, situation,

and overall project objectives; ▪ allows the architect to "gain a feel" for the physical parameters involved and how

the design is developing in these terms; ▪ requires only input that is horizontally consistent (in extent and level of detail)

with the building design in progress; ▪ yields answers to design questions as they arise in the decision-making process; ▪ emphasizes comparative interpretation (qualitities) - rather than absolute

numeric results (quantities); ▪ complements and enhances conventional methods of describing a building

design. To meet these goals, solar radiation information should ideally be modeled with the same level of detail and validity as the geometric information that architects are accustomed to working with. A tight coupling of solar radiation data and design geometry from the start of the design process serves to enhance intuitive understanding of solar influences, as well as to establish comparable design profiles for competing concepts.

 approach & results

The crux of the difficulty in developing reasonably convenient solar design methods which are also adequately comprehensive in application lies in the fact that solar/thermal and architectural models are the product of diameterically opposite approaches in integrating factors and, therefore, address concerns according to very different priorities. Whereas architectural design generally takes its point of departure from human-oriented purposes and thus works "from the inside out," the thermal model for simulation analysis focuses on bioclimatic conditions which are developed mainly "from the outside in." This means, for example, that an architect typically has the primary purpose of the building (e.g., to create interior spaces intended for a particular human use) in mind from the very beginning of the design process and develops the building envelope with material and geometric properties that satisfy the demands of this purpose in addition to any further objectives associated with the building project, such as architectural expression, use of exterior spaces, influence on the urban context, and so on out. The thermal performance of a building, on the other hand, can only be simulated effectively if first the global setting is clearly defined, that is, if the climatic conditions specific to the geographic location, independent of the thermal envelope, are adequately modeled. Together with a standardized description of internal conditions which, though purpose-oriented, is largely independent of the specific building as well, the interaction of these two "bounding environments" with a model of the given building envelope is what is ultimately simulated. In order to harmonize the development of a consistent thermal model with building design practice, workable premises needed to be staked out for the meaningful implementation of global criteria (i.e. solar/climate conditions) preliminary to full-scale thermal simulation. The progressive integration of such criteria entailed ▪ evaluating solar gain modeling approaches and parameters with respect to their

relevance at different stages of the design decision-making process, and ▪ extracting and rendering the applicable information that is implicitly yielded by

the generalized (parametric) methods proven to be most flexibly useful.

In this context, an analysis of architectural working methods and objectives meant first clarifying the information needs at each point of entry, i.e. which quantitative and qualitative parameters are meaningful and definable at various typified design levels. Subsequently, the processing of information within this framework was addressed, specifically: the form and level of precision that quantitative data could most usefully assume, as well as how the characterizing data is to be modeled

consistently from schematic to detailed design levels. Finally, appropriate visualization methods were developed in the form of "mockups" based on the calculation results of extensive parameter and case studies. The types of renderings and other graphic representations which most readily support accurate qualitative interpretation could thus be verified.

An important issue in this context was the decision to model conditions parametrically as extensively as possible from the base up and thereby avoid statistically derived factors in favor of more generally understandable physical dimensions. It is generally acknowledged that thermal performance assessments of environmentally responsive design are highly sensitive to preliminary assumptions made about solar/climate factors. Reliable assumptions are not only necessary for reliable simulation, but can also be used effectively for pre-simulation analysis of solar design potential. Systematic parameter studies allow key quantities -- and thus qualities -- to be pinpointed at the earliest stages such that their relative impact may be assessed for horizontal consistency with a given building design decision.

A rundown of the application model underlying the design guidance system presented here is given in Part 1: The Solar Profiling Method. Since it is in the early stages that the most significant decisions are made regarding sizing, placement, and orientation of the building volume, design tools are recommended which inform such key decisions in a schematic manner that is both flexibly specific and immediately interpretable. Furthermore, the energy information gained should remain consistently applicable through subsequent design stages and, ultimately, serve as part of an overall thermal model.

The desired flexibility is best obtained by basing the solar design guidance methods on a cohesive set of analytical descriptions, which are treated in Part 2: The Calculation Models. This proves especially useful for describing solar radiation -- as opposed to the standard method of relying on climate databases for relatively coarse and situationally unspecific radiation data. Though at first glance it may seem a more complicated proposition to work with custom calculated radiation data than to simply "plug in" a standardized sub-set from a reference climate database (or use tabulated monthly values for simplified parameters), this potential objection loses its validity upon closer scrutiny.

The first and most obvious advantage to an analytical model is the relative independence it affords the building designer, who typically has other concerns than that of drumming up, evaluating the consistency and analyzing the applicability of, for example, available climate data. A computer-based implementation of the parametric radiation model can immediately be used -- without much further ado and with minimal computation time -- to generate plausible solar geometry and radiation data for building sites situated anywhere on

the globe.

The second, less conspicuous, but equally important advantage lies in the manageability and, therefore, interpretability of preliminary results. Instead of handling unwieldy tables of numeric values, which are generally impenetrable for anyone but an expert, the parametric approach allows the development of the thermal simulation model in parallel with progressively detailed design stages. Thus each stage can be consistently characterized as well as documented with relatively manageable sets of parameters (profiles).

Above all, the parametric approach lets the designer extract valuable information to guide running decisions in a customized manner, that is, derive sketch assessments of parameter impact which are considerably more specific and secure than general "rules of thumb." The concept for a prototypical implementation of the necessary computational tools is briefly summarized in the conclusion (The Solar Toolbox).

                                                             

 

   

Part 1: The Solar Profiling Method

The entire extent of the building design process can be broken down into four main phases in order to roughly categorize the types of design decisions encountered and tools needed (Balcombe 1992, chapter 10): ▪ Conceptual phase, which covers programming, site/situation analysis, and an

assessment of basic options for building shape and placement. ▪ Schematic phase, which entails the commitment to a basic design strategy and

certain key functional, structural, and architectural aspects of a preliminary design concept.

▪ Developmental phase, in which the design concept evolves in increasing depth and detail, ideally in a manner which progressively verifies the chosen strategy.

▪ Final phase, which includes detailing and technical fine-tuning of building components as well as construction documentation.

The specific content of each phase is, of course, dependent on the concrete project, and especially on whether the design is for new or retrofit construction. Nonetheless, the four described stages do provide a theoretical framework for relating thermal considerations in general -- and solar parameters in particular -- to more or less equivalent levels of design information (figure 1.1).

The data required for the solar and climatic aspects of an overall thermal simulation model conveniently coincide with information that is available at the earliest stages of the building design process, i.e. during the conceptual phase of new construction. The objective of the solar profiling method is to utilize this information to reveal as much as possible about where the design stands in solar terms -- without making any premature assumptions as to the thermal properties of the building envelope. As the design model is developed through subsequent levels, it should yield further and increasingly specific profiles, and ultimately serve as the basis for more involved thermal performance assessments.

In order to facilitate the understanding of solar dimensions in a schematic yet consistent fashion, the profiling method on the whole works with physical dimensions of energy and geometry (e.g., W/m2). It aims to characterize a building's solar potential from the conceptual stage on; hence, the initial emphasis is not so much on computing absolute numeric quantities as it is on generating qualitatively comparable visualizations and renderings. Calculation results in numeric form may also be re-combined for the purpose of correlating solar/climate profiles with other simplified methods, since these often work with some form of

dimensionless ratios (Balcombe 1980, Moore 1985, ASHRAE 1989, Lechner 1991, Goulding 1993, see also 2-9 Preliminary Performance Assessment).

Regarding the choice of terminology, an effort has been made to select a concordant set of solar terms from the numerous synonyms stemming from different fields. Wherever possible without contradicting definitively established conventions, terms were chosen to underscore the characteristic quality of primary solar dimensions as defined in this particular context (e.g., "specific flux" instead of "irradiation density" or other available synonyms). The most commonly used equivalent terms are included for reference in the Glossary.

As mentioned in the Introduction, any prospective thermal simulation results are particularly sensitive to the description of solar and climate boundary conditions. With solar design considerations, assessing the impact of decisions on diurnal patterns is just as important as grasping the effect over an annual cycle. This makes it necessary to "sample" individual days of the year in order to obtain an informative picture of the relevant diurnal patterns.

The choice of which days of the year to sample is especially important if the results obtained are to bear relevance for later evaluations related to thermal performance. It essentially depends on whether the cases to be eventually considered later on in the design process are typical or extreme (critical/optimal) in thermal terms. This, in turn, is a question of the thrust of analysis beyond the strictly solar issues that can be addressed initially, and should be kept in mind from the very beginning in the course of developing design case models.

Another way of looking at it is in terms of design scenarios, which are best classified by the nature of the answers sought, in conjunction with the design model in progress. Generally speaking, extreme scenarios more readily point up the impact under either critical or "best case" conditions, making them most useful in the earliest stages, both for avoiding solar design mistakes as well as optimizing the use of solar potential. Typical scenarios, which are necessary to reliably estimate the performance of a given building design under actually expected conditions, come to bear mainly in later phases.

Thus initial solar/climate profiles are not only defined by the types of questions commonly asked during early design phases, but also implicitly targeted at future thermal profiles. Some examples of such questions, along with illustrations of the types of answers obtainable, are included in the following sections. These are structured with respect to the progressive levels of case model development, as well as the underlying architectural design issues.

In this context, it is important to distinguish between reference data and parametric profiles (figure 1.2). Reference type input (such as a standardized Test Reference Year of climate data [Solar Energy Laboratory 1994]) yields sample results aimed

at rendering a typical scenario as realistically as possible, and is therefore usually highly detailed.

However, results based on such high resolution data can be deceiving if used to ascertain the impact of a particular design parametr (e.g., tilting a facade, enlarging an aperture, etc.), since the raw data my be sampled inadvertently so as to mask criteria that are most critical to the diurnal behavior in question.

Extensive reference data sets that encompass a full year of diurnal solar/climate conditions in highly realistic form are appropriate for final evaluations or when concrete predictions are sought, but they lack the necessary abstraction to reveal characteristic information as needed for design guidance.

In contrast, a parametric profile characterizes temporal radiation data by means of parameterization in solar terms before sampling. This form of mathematical abstraction ensures that any diurnal samples retain the information about the influence of design-relevant parameters in a consistent manner throughout various levels of analysis.

Fig. 1.1

Correlation of typical building design phases with solar/climate profile levels.

Fig. 1.2 Parametric profiles vs. reference data: diurnal sample of incident solar flux [W/m2] on horizontal surface (and normal on theoretical tracking surface).

1-1: Solar Geometry

The task of programming a building project entails defining the primary project requirements and constraints (in terms of function, location, space, access, budget, etc.). Such program specifications can be extended to encompass target values for thermal performance, thermal comfort, daylighting, and other energy-related objectives. Together with the givens of the local climatic situation, these objectives dictate which days of the year would best be sampled for the purpose of developing a characteristic set of diurnal profiles. Programming is typically accompanied by a thorough site analysis for determining the range of basic design options given by the urban context, available space for building, pedestrian and vehicular access, building regulations. and so on. Analogously, a solar site analysis seeks to profile climate conditions and solar potential in such a manner that an initial assessment of promising solar design strategies can be made. In the case of retrofit design, programming and site analysis also require a complete description of the existing structure to be adapted. Energetically, the basic solar site analysis would be rounded out with evaluations of the current state of solar access, overall thermal performance, the thermal behavior of characteristic components, as well as the thermal quality of critical details. Set against such thermal base case profiles, comparative simulations of alternate concepts for remodeling the existing structure could then inform the choice of solar strategy and the combination of systems to be best integrated into the existing situation (see also Case Studies). The first step of solar site analysis is to define a set of seasonally characteristic dates of the year, depending on the basic properties of the climate zone as well as the focus of the project's solar energy-related objectives. These dates are established at the beginning of the profiling method and maintained throughout all levels of early analysis so that the profiles may be consistently interpreted and compared. Since the design model becomes very complex with the addition of geometric information at later stages, it is strongly recommended that the sampling of dates be reduced to a maximum of three at the start. Otherwise, the number of combinations for which profiles can be generated soon becomes unmanageable, with an increased likelihood of losing sight of meaningful information. For mild to tropical climates in which the annual and diurnal temperatures swings are minor in comparison to the variations in solar radiation, days that characterize solar seasons are most informative: winter and summer solstices, with an equinox as transition. In such locations, design decisions are primarily directed by the the

handling of solar geometry for year-round shading and optimized energy collection systems (passive or active), while thermal performance issues are of secondary importance. For locations in which the ambient mean temperatures vary significantly (thus requiring a fair degree of interior tempering most of the year), it is more useful to characterize climate seasons: mid-month days in January and July, with April as a transition month. Design issues here usually involve mixed passive strategies for optimally harvesting solar energy in cold weather and avoiding/exhausting excess solar gain in warm weather. Therefore, the thermal performance of the building envelope plays a dominant role in design development. Given just the basic information of site location -- geographic latitude and longitude, along with the applicable time zone meridian -- the diurnal paths of the sun associated with the seasonal dates can already be calculated (see 2-1 Solar Position for specifics on the calculation of these results). Alternately to a solar path diagram as shown in figure 1.3, a three-dimensional "terrestrial" rendering can be generated to visualize this characteristic solar geometry as a theoretical tracking surface, that is, a plane assumed to ideally follow the daily path of the sun from sunrise to sunset around the hemisphere of a pre-defined model space. By showing the tracking surface as discrete unit planes at hourly positions (as in figure 1.4), information about the local time in relation to the sun's path is also conveyed in such a rendering.

Fig. 1.3 Solar path diagram for summer and winter dates: Honolulu, USA -- Vienna, Austria -- Narvik, Norway.  

Fig. 1.4 Tracking surface rendering of the same solar paths as in fig. 1.3.  

1-2: Solar Energy Potential

The incident radiation on a tracking surface as illustrated in the previous section is, by definition, normal to the surface at all times during the day. Since this quantity represents the maximum possible solar flux that can be received at the given geographic location at any given time, it is a measure of the solar energy potential, or flux envelope, of the site. The calculation of a diurnal flux envelope requires the definition of some basic parameters to characterize the atmosphere and surrounding terrain: site altitude, haziness and scatter, and ground-reflectance (detailed descriptions in 2-2 Solar Flux through Atmosphere and 2-3 Local Solar Flux). These parameters are used to generate an irradiation profile that shows the day sums of the flux envelope on the given dates, whereby the global results can be broken down into solar flux components for direct, diffuse sky, and diffuse ground-reflected radiation (figure 1.5). The diurnal patterns of this quantity, i.e. global radiation or one of its components, are conveyed through a composite flux plot (figure 1.6). Site altitude can be viewed as an atmospheric parameter in that it determines the distance of atmosphere, or optical air mass, that solar flux passes through before reaching the earth's surface. This measure, in turn, affects the degree of atmos-pheric attenuation of the incoming radiation, especially at low solar elevations (when the distance is longest). The meteorological parameters for haziness and scatter can be derived from empirical data for direct/diffuse radiation on a horizontal surface -- in the unlikely event that such information is immediately available for the geographic location in question. Fortunately, it is not necessary (or even desirable) to work with measured meteorological data during initial site analysis, since the type of information sought generally focuses on the "best case" with respect to the site's solar energy potential. To this end, meaningful profiles can be obtained by simply applying standard parameters that describe the haziness and scatter on a cloudless day. The ground-reflectance of the surrounding terrain can also generally be assumed as standard without any loss in applicability. Such flux envelope profiles are entirely site-specific, as they are specially calculated for the given geographic location and altitude. These results may also be used to design the geometry of double-axis tracking collectors and subsequently gauge the amount of energy that could ideally be harvested (figure 1.7).

A further aspect of the site situation which should be modeled at this point are distant-field obstructions in the form of horizon elevations (e.g., mountains). Since the direct component of the calculated flux envelope is blocked at low solar elevations on days when the sun rises or sets "behind" an elevated portion of the horizon, this type of obstruction can have a noticeable impact on the given solar energy potential of the location (figure 1.8, defined in 2-3 Local Solar Flux).

Fig. 1.5 Profile of the day sums of solar flux on a tracking surface [Wh/m2]: clear skies (A) and overcast (B) -- summer/winter, Vienna.

 Fig. 1.6 Diurnal plots of the solar flux envelope in fig. 1.5, clear skies.

 Fig. 1.7 Photovoltaic collector tree ("Solarbaum") in Gleisdorf, Austria, design: H. Skerbisch & W. Schiefer.

 Fig. 1.8 Site situation with distant-field obstructions: solar path diagram and tracking surface rendering with a partially elevated horizon.      

 

1-3: Solar Access

For any surface plane with a fixed orientation, the incident radiation depends on the angle of incidence specific to the orientation at any given time. In other words, the local geometry of such a surface plane in terms of azimuth and tilt determines its specific solar flux (see also in 2-3 Local Solar Flux). This quantity will always be less than or equal to the momentary flux envelope, which is the normal radiation on an ideal tracking surface as defined in the previous chapter. A given site situation usually implies certain key orientations (e.g., street front, roof), which constrain the locally usable potential for receiving solar energy. Irradiation profiles and plots of the specific solar flux on such key orientations in relation to the flux envelope show the magnitude of these constraints (figures 1.9 and 1.10). Associated plots of the incident angles reveal the interrelationship between local and solar geometry (figure 1.11). By enabling a preliminary assessment of optimal (or critical) local geometry, these results inform initial decisions about building placement and sizing during the conceptual phase of design. Important design decisions to secure solar access should also account for future building developments as well as growing trees and other issues of general landscaping. If properly applied at the urban planning level (Schempp, Krampen, and Möllring 1992), such goals do not necessarily mean a loss in density and can be well-integrated in zoning restrictions. The question of how to optimally harvest incident energy is a special focus when the design objective includes the integration of active solar system components such as photovoltaic panels (figure 1.12). In certain situations, it may be useful to compare the effect of ground-reflectance in conjunction with decisions about tilting façade surfaces (figure 1.13). Specific flux and angles of incidence show which of the possible orientations could most effectively contain apertures for collecting solar gain, while at the same time giving a first indication of the potential for overheating (figure 1.14). Furthermore, knowing the relative position of the incident direct beam over the course of the day allows significant middle-field obstructions to be spotted already at this stage, before explicitly modeling them in the next level.  

 Fig. 1.9 Profile of the specific flux day sums [Wh/m2] set against respective flux envelopes: facades facing south (A), southwest (B), west (C), north (D) (summer/winter, Vienna, clear skies).

 Fig. 1.10 Diurnal plots of the global specific flux [W/m2] for one date in fig. 1.9: summer -- south (A), west (C), north (D).

 Fig. 1.11 Angles of incidence [°] of direct beams from fig. 1.10.

 Fig. 1.12 Photovoltaic panels integrated in the south façade of a power station in Rieden, Austria, design: stromaufwärts, H. Wirt.

 Fig. 1.13 Specific flux comparison: façade tilted towards sky (+20°) and ground (-20°) with different ground-reflectances.

 Fig. 1.14 Sunspace addition to a single family dwelling in Himberg, Austria, design: Mihály Táksás.

1-4: Site & Building Model

Existing buildings surrounding or on the site constitute significant middle-field obstructions, especially in an urban context. A complete picture of the site situation with respect to overall solar access can be gained by analyzing a three-dimensional site model for shading patterns over the course of the selected days (e.g. hourly "snapshots", figure 1.15). Beyond helping to avoid egregious misassumptions, gauging the relative reductions in overall insolation due to existing or designed obstructions provides a valuable measure for working with solar geometry consciously and effectively. During the schematic phase of design, modeling these middle-field obstructions together with the projected building entails specifying the positions and contours of main exterior surface planes (facades and other walls, roof surfaces), in addition to their orientations (azimuths and tilts). The surface planes that describe the projected building are the ones in question in terms of resultant solar flux, that is, the quantities of solar flux received over the extent of a surface after accounting for direct beam obstructions. Consequently, it is practical to treat only these planes as incident surfaces to the end of generating design-specific results (for a full description of the handling of geometric surface models in conjunction with radiation data, see 2-4 Shading & Resultant Flux). As illustrated in figures 1.16 and 1.17, two and three-dimensional renderings of the insolated model visualize resultant flux by coupling the shading patterns that result over the course of a day with specific solar flux information. Irradiation profiles of resultant flux convey the relative quantities of solar energy received on principal building surfaces, as well as the impact of any middle-field obstructions (figure 1.18). For surface areas that are the focus of further design development, a diurnal plot of the resultant flux also shows the time span during which the direct beam obstruction occurs (figure 1.19). In conjunction with the relative positions of the direct beam (angles of incidence obtained at the previous level), resultant flux profiles can be informative for successive design revisions aimed at both the utilization of solar energy during the heating season and the avoidance of interior solar gain during the cooling season. Generally speaking, solar profiles for guiding decisions up to this point focus on potential results mainly for identifying critical situations as well as staking out reasonable performance ranges based on a minimum of specific design information. On the basis of such assessments, the schematic design concept may then reflect the reasoned commitment to a particular solar design strategy in the further development of the overall building design.  

 Fig. 1.15 Shading pattern on model ground plane: site situation with existing and projected buildings.

 Fig. 1.16 Flux pattern on incident surfaces of model: existing and projected buildings.

 Fig. 1.17 Flux pattern on key incident surfaces of model: elevation of projected building (WSW).

 Fig. 1.18 Profile of the resultant flux day sums [Wh]: key surface areas of projected building (main façade orientations SSE and WSW), winter, clear skies.

 Fig. 1.19 Diurnal plot of global resultant flux [W] on an incident surface area: SW-facing, winter, clear skies.

1-5: Building Model Details

As other constraints weigh into the developing design, committed information about the projected building gains depth and detail. Central design issues that arise at this stage revolve around aperture placement and sizing for all manner of solar collection. The schematic building model is enhanced with details of aperture and room contours to enable evaluations of the resultant flux on such typically critical areas. Particular attention must be paid to the question of whether or not a given room is likely to overheat because of excess amounts of solar gain entering via the apertures. Overheating problems are usually caused by design errors, whereby overheating may even occur in the winter if, for example, the south glazing is oversized, or the thermal storage mass proves insufficient for the amount of direct gain. Such potential design errors can be anticipated with the aid of two-dimensional renderings of the flux on detailed areas of a façade (figure 1.20). Where a tendency to overheat has been identified, it can most likely be corrected at this stage by manipulating the aperture areas and/or adding shading elements. If the resultant flux on the areas under scrutiny remains critical, further reductions can be achieved by considering a re-design of the building model, especially with regard to the placement of surfaces which need to include large apertures. Near-field obstructions intended to protect an aperture from the direct beam are modeled in the simplified form of orthogonal shading elements (overhangs and wingwalls), whereby the minimum required design dimensions can be derived from the angle of incidence at the time of peak flux for the aperture in question (figure 1.21). In some cases, details of the glazing structure (framing) may already cause a significant reduction in resultant flux and, therefore, would also need to be modeled before making other changes (figure 1.22). A second focus of evaluation, both for profiles based on solar seasons and for the winter case of climate-based profiles (see 1-1 Solar Geometry) is the solar collection strategy, that is, the question of how to maximize use of the available solar energy within the geometric framework of the given building design. Comparative renderings of resultant flux allow the contextual analysis of generic options for deciding where and which primary solar systems may be implemented most effectively in further design stages (e.g., buffer spaces, Trombe walls, passive cooling ventilation configurations, wind-sheltered collectors, insulating shutters, etc.). Daylighting considerations are initially treated in connection with the next level of design focus profiles, 1-6 Solar Gain.  

 Fig. 1.20 Flux/shading pattern on glazed apertures/surface areas: façade detail of projected building (SSE).

 Fig. 1.21 Geometry of shading elements based on peak beam angles: placement and minimum sizing of an overhang.

 Fig. 1.22 Resultant shading effect of aperture details [W]: glazing structure on a tilted façade.

1-6: Solar Gain through Apertures

First considerations about glazing options typically go hand-in-hand with the more detailed design of the projected building. In combination with a parametric model for solar-optical glazing properties, such givens allow a first look at the quantities of direct solar gain, i.e. the net flux that can be expected to pass through transparent components to the building's interior spaces (see 2-5 Net Flux through Apertures). The transmission of solar flux through glazing transforms it such that the relevant components at this stage are primary gain (directly transmitted) and secondary gain (absorbed and emitted inwards as long-wave radiation). To calculate these quantities, the glazing is characterized by three key solar-optical properties: total solar energy transmittance, solar direct transmittance, and directional transmittance. Data for the directional response of a particular glazing type, that is, how the transmittance varies according to the angle of incidence, is generally not available from manufacturers. Fortunately, this parameter can be generically classified by the types of glazing commonly used in architectural design, e.g.: clear glass, translucent white glass, gray/bronze or green ("heat-absorbing") glass, light-reflecting film, glass block, etc. Solar gain profiles are most meaningfully generated for the combined net flux through all the apertures of a given room, which has been modeled as a building detail (figure 1.23). If the profiles at this level confirm an overheating tendency which cannot be remedied by appropriately specified glazing, then the apertures and associated shading elements (near-field obstructions) need to be modified. Beyond passive heating and cooling, a further passive strategy that becomes relevant at this stage is that of daylighting. This is especially effective in institutional and commercial buildings, which are used mostly during the daytime. Since the primary gain through glazing is largely in the visible range of the spectrum (luminous flux, see 2-6 Spectral Solar Flux), there is a natural synergy between daylighting and passive solar heating if the windows used for daylighting are also used to collect solar energy. It is also possible to reduce the cooling requirements of these buildings, since much of the cooling load in them is due to heat generated by artificial light (natural light contains more luminous flux in relation to the infrared). Of course, to actually save energy effectively, artificial lighting systems and their controls must be integrated well in further design development. The directly transmitted primary gain retains its directional distribution, so information about the angle of incidence can be used to control the quality of natural light and keep direct beam radiation from penetrating the building (figure 1.24). Glare can be avoided, for example, by keeping apertures that are used strictly for daylighting above eye level, as well as by strategically placing shading

elements (louvers or baffles) to diffusely reflect the direct component of resultant flux (1-5 Building Details).

 

 Fig. 1.23 Profile of solar gain day sums [Wh] through glazed apertures -- net flux after obstruction and solar-optical glazing properties: g=0.71/t =0.65/double (A) and g=0.48/t=0.29/triple (B) - standard clear glass.  

 Fig. 1.24 Diurnal plot of solar gain [W] through a glazed aperture -- net flux after obstruction and solar-optical glazing properties.

1-7: Surface Conditions

Radiation absorbed by opaque building components as well as the exchange of long-wave radiation with the sky have a strong influence on the momentarily effective temperatures at exposed surfaces and, therefore, on the indirect solar gain by means of conduction and convection. The calculation of these forms of heat transfer crosses over into the realm of thermal simulation. Nonetheless, a sense of the dimension of such effects can still be obtained as soon as design decisions about building materials and surface finishes become an issue and sufficient parameters are defined for calculating the sol-air temperature or, even better, the radiant air temperature at exposed surfaces (for a description of this approach, see 2-8 Resultant Air Temperature). Solar absorptances are separately defined for transparent and opaque building components, which correspond to the glazed apertures and remainder areas of the surface elements as modeled up to this point. Ambient air temperature is applied in the form of a diurnal profile analogous to the incident solar flux. Taken together with the resultant flux profiles that account for shading patterns, these three influences (absorptance, air temperature, and solar radiation) result in an effective temperature pattern at the surfaces of the building model as illustrated in figure 1.25. The resultant air temperature at any given moment is then the average radiant air temperature over the extent of a surface area (transparent or opaque), which is distinguished by the assumed solar absorptance in addition to its geometric properties (figure 1.26). As can generally be expected during the day, this value is very close to the ambient air temperature at surfaces receiving only diffuse radiation, and significantly higher than the surrounding temperature where direct beam radiation is incident on highly absorptive surfaces. At night, with cooler temperatures and in the absence of all solar flux, net losses in the exchange of long-wave radiation with the sky may result in radiant air temperatures that are noticeably below the ambient air temperature (especially under cloudless conditions). Depending on the overall design objectives, this latter effect may also be tapped as a night-time cooling resource during the overheated season. Profiles of resultant air temperature are primarily targeted at the next level (1-8 Basic Thermal Envelope), where they are applied as the boundary condition for performing preliminary assessments of thermal performance. Since such assessments are mainly relevant to the interseasonal analysis of climate extremes, i.e. mid-month dates for the warmest and coolest months of the year, the underlying diurnal profiles of ambient air temperature are best generated on the basis of monthly mean values for temperature minima and maxima (2-7 Climate

Profiles). Plausible values for this basic type of meteorological data are commonly available for most sites.  

 Fig. 1.25 Temperature pattern on incident surfaces of model: aperture and room details of projected building.

 Fig. 1.26 Diurnal plots of resultant (radiant) air temperature [°C] at glazed and opaque areas of a SW-facing surface.

 

1-8: Basic Thermal Envelope

The ramifications of running design decisions with respect to the solar strategy should be checked regularly by means of comparative target evaluations of competing solutions. This process is best supported by solar profiles which successively tighten the originally assessed potential to values more specifically characteristic of design options already decided upon. As the available amount and stringency of the design information grows, calculations requiring increasingly detailed information yield estimated results that ideally should provide a measure of the design's performance in terms of the energy-related objectives that were initially specified in the conceptual design phase. Whether explicitly or implicitly, the demand for thermal com-fort lies at the heart of virtually all the building design objectives that concern energy. The definitive quantification of this objective, however, is hardly possible since it is part physiological, part psychological, and depends on the unpredictable combination of a variety of factors (such as air temperature, surface temperature, air motion, relative humidity, as well as air quality, age, activity rate, clothing, season, cultural setting, etc.). Usually only one aspect, the interior air temperature, is evaluated as a basic measure of thermal comfort. Under free-running conditions, stable interior temperatures can only be ensured with effective thermal distribution, that is, if adequate thermal mass for heat storage is properly located in relation to major solar gain. Though the effect of heat storage on the temperature swing can only be calculated by means of dynamic thermal simulation, the resulting mean interior temperature can be estimated if periodically stable conditions are assumed (see also 2-9 Preliminary Performance Assessment). This is a reasonable basis for checking the overheating potential in the especially critical situation of a longer summer heat wave. Results that show a higher than tolerable mean temperatures are certainly unacceptable, whatever the dampening effect of thermal mass may be (figure 1.27). Time-dependent simulation is required to account for diurnal ventilation patterns (forced or natural), which are of special interest with respect to passive cooling strategies. A complementary question is that of how much energy is needed to maintain a specified interior temperature. The mean results for heat flow can be checked for critical summer conditions or optimal winter conditions based on the same steady-state assumption. Whereas inward flows correspond to the cooling load without ventilation, outward flows convey heat losses. Since ventilation strategies are not of primary concern in the winter, heat loss profiles give a reasonable estimate of

the auxiliary heating energy demand. Given the essential boundary conditions as already defined up to this stage -- net flux through glazing and resultant air temperature at the surface components -- diurnal mean temperature or heat flow can be calculated in a simplified fashion without extensive additional modeling. The building surface model need only be supplemented with basic information about the (one-dimensional) thermal conductance of exterior surface components. Concretely, this means first defining which sur-face elements comprise the thermal envelope, and then assigning U-values to the opaque areas and glazed apertures of these exterior surfaces. An overall U-value is then easily calculated for the basic thermal envelope model (without thermal bridges and components in contact with the ground) to provide an initial meas-ure for the thermal quality of the building's design geometry.  

 Fig. 1.27 Profile of mean resultant temperature [°C] in rooms of model: summer date, free-running.

 

1-9: Transition to Thermal Simulation

The emphasis of analysis shifts from comparison to prediction in the final stages of the design process, when the design has developed to the point where its thermal envelope, apertures, and mass size can be tightly defined. Generally stated, this means that the goal of numeric analysis is to predict the need for auxiliary heating, lighting, or cooling under average climate conditions. Once a set of results profiling the amount of solar energy that an overall design concept has to work with has been established, more complex design components such as thermal buffers -- which fully utilize the time-dependent nature of solar gain -- can be optimized with the help of small-scale dynamic simulations of their thermal behavior. Such simulation analysis allows comparisons between whole systems over a typical heating or cooling season in order to reliably distinguish between what is best for the particular building program and what is best for thermal performance. Diurnal simulations under periodically assumed conditions are most effective for profiling extreme situations of thermal performance, especially to anticipate overheating in the summer months and estimate critical cooling loads (as checked in a preliminary fashion for the basic thermal envelope). For estimating the impact on annual heating/cooling energy requirements, a longer-term solar profile must be applied. Since the focus is no longer solely on the impact of solar influences, typical solar profiles are established by calibrating the atmospheric parameters to meteorological radiation data for the site. Such base data are commonly monthly mean quantities applied to mid-month dates (as with the air temperature data described in 2-7 Climate Profiles). Summed over an annual cycle, the results that monthly diurnal simulations yield are sufficiently accurate for the purpose of comparative parameter studies. To this end, solar profiles generated within the geometric framework of the site and building model comprise a good portion of the input data necessary for thermal simulation up through final design, in particular: ▪ resultant flux on exterior surfaces (with distant, middle- and near-field

obstructions), ▪ net flux through glazed apertures (direct solar gain), and ▪ resultant air temperature at exterior surfaces (indirect solar gain).

For the purpose of full-scale thermal simulation over a typical year, annual base profiles of these monthly solar-climate dimensions can be used either to inform the selection of plausible reference year data from available sources or to generate annual data sets synthetically (see also 2-9 Preliminary Performance

Assessment).

 

Part 2: The Calculation Models

The predominantly visual method of solar profiling as outlined in the first part is intended to facilitate the meaningful interpretation of solar dimensions in a schematic fashion. The desired flexibility and reliability in application is ensured by basing the solar design guidance system on cohesive parametric models. Hereby the general direction is one that approaches thermal simulation by supporting the successive generation of a thermal model in stages that reflect the type of evaluation results called for at different stages of building design. Thermal models for building simulation typically represent the building envelope in the context of its internal and external environments (figure 2.1). Generally, the envelope itself is modeled independently in terms of its thermal characteristics (thermal conductivity, specific heat and density of materials and assemblies, solar absorptances of surfaces, etc.). The simulation then calculates the envelope's thermal response to applied environmental driving functions (ambient temperature, solar gains, internal gains, etc.). The applicability of simulation results is largely a question of how the various driving functions are modeled. If the overall thermal network is to be progressively built up in stages, then the superposition of thermal responses to separately applied boundary conditions must be permissible. The mathematical constraint of linearity limits the description of all model components to a strictly linear system of equations. The same tack of approaching simulation can be taken to treat individual components of such a thermal model, in particular, the parameters involved in solar gain. Since the thermal characteristics of the building envelope are by and large independent of solar gains, many types of meaningful solar evaluations can be performed without generating an envelope model. Embedded in a seamless application method, such preliminary evaluations can then be efficiently done as input calculations for more comprehensive thermal simulations (see also Case Studies). For calculating the transmission of solar gains to the interior, the thermal envelope must be at least partially incorporated into the solar gain model (solar-optical glazing properties, solar absorptances). Other types of solar evaluations, which go beyond the pre-simulative context of the solar profiling method, require simulation-type calculations based on more extensive information about related driving functions and thermal properties (Hittle 1977, Hunn 1996). This applies, for example, to the treatment of shading control involving functional conditions (e.g.,

diurnal operation of shutters or blinds) as well as passive solar system components (e.g., sunspaces, transparent insulation). Of particular importance for all levels of efficient model development is, therefore, the support of consistent transitions between components and information layers such that the data which has already been developed for preliminary evaluations need not be generated again for subsequent calculations. Fundamental to the solar profiling method are the aspects involved in modeling the solar dimensions of geometry and radiation on a daily basis for the express purpose of characterizing a building's solar potential from its inception (figure 2.2). Generally stated, the intensity of solar irradiation on a specified surface at any given point in time depends on the sun's position, meteorological conditions, as well as incident surface and obstructing geometry at the moment under scrutiny. Traditional methods for generating time-dependent descriptions of this "solar dimension" typically model the strictly geometric aspects (in particular, solar position relative to incident surface orientation) in a fairly exact and situation-specific manner. The meteorological basis, on the other hand, is usually provided in the form of daily total solar irradiation on a horizontal surface as measured at some (it is hoped nearby and well-funded) meteorological station. The specific geometric model is then applied to the most plausible climate data available for the site at hand in order to derive a synthetically enhanced description to be used as an ambient driving function for solar gain. Aside from the obvious uncertainties that arise whenever adequately detailed and typified climate data is not readily available, this type of reference data may only be used "as is:" the implied meteorological conditions can be neither adapted nor characteristically simplified for design-analytical purposes. One tenable way to compensate for these deficiencies is to implement a solar radiation model that incorporates parameters that clearly distinguish meteorological and terrain conditions from the geometric aspects, both solar and incident. A diurnal radiation profile generated synthetically by means of an appropriately selected parametric model has the particular advantage to architects of being inherently free of the "atmospheric noise" that gives historically based diurnal profiles their arbitrary character (even when "radiation smoothed" with an interpolation algorithm [Solar Energy Laboratory 1994] as in figure 1.2). As a result, a synthetic profile can be depicted to characterize primarily the directional distribution of solar radiation -- clearly the most significant characteristic for assessing the impact of predominantly geometric design decisions. A method for computing the three main components of solar radiation incident on a given surface (direct beam, diffuse sky and ground-reflected) has been made standard in

the ASHRAE Handbook of Fundamentals (1989 chapter 27: "Fenestration"). This involves a basic determination of solar angle in conjunction with tabulated monthly values for the extraterrestrial solar radiation intensity A, the atmospheric extinction coefficient B (together with a regional "clearness number"), and the diffuse radiation factor C. An alternative and, in certain respects, more flexibly analytical model was delineated by Heindl and Koch (1976), and is presented in detail in the first three chapters that follow (2-1 Solar Position, 2-2 Solar Flux through Atmosphere, 2-3 Local Solar Flux). The opportunity is taken to adapt the nomenclature to this particular context as well as to translate any special terms into English. The algorithms for generating synthetic radiation data based on this model were originally developed for use in a variety of stand-alone solar calculation programs (e.g., TU-Wien 1989), and also thoroughly tested within the framework of diurnal building simulation programs (Fuchs, Haferland, and Heindl 1977; Krec 1994). Qualitative differences between the ASHRAE "ABC" method and the formulae implemented here are pointed out but not related in detail, as a thorough comparison of the two methods is not a core concern in the presented concept of building design guidance. The remaining aspects of solar gain modeling -- geometric shading models and solar-optical glazing properties -- are treated in chapters four through six (2-4 Shading & Resultant Flux, 2-5 Net Flux through Glazing, 2-6 Spectral Solar Flux). The final chapters of this part focus on tangentially related components of the thermal model (2-7 Climate Profiles, 2-8 Resultant Air Temperature, 2-9 Preliminary Performance Assessment). Ultimately, if preliminary design evaluations are consistently modeled as described in the following, they yield customized input for solar/climate driving functions when a fully developed building design is ready for simulation analysis.  

 Fig. 2.1

The principal components of a simulation model for the thermal behavior of buildings.

 Fig. 2.2 Components of the solar gain model.

2-1: Solar Position

The mathematical equations for calculating solar position relative to the earth as related by Heindl and Koch (1976) are derived from a thoroughly "astronomical point of view" (figure 2.3). This allows the description of apparent solar position to fully account for annual deviations in the earth's ecliptic position, which are attributable to the eccentricity ε and obliquity of the solar ecliptic. The only significant simplifications made by Heindl and Koch lie in defining the unit of a day d as 1/365 part of a solar year and, furthermore, in assuming that the ecliptic position of the earth φ (and thus the solar declination δ ) remain constant throughout the course of one day. The maximum range of error that can result from these simplifications is proven quite negligible in comparison to other influences, especially when considered in the context of thermal simulations. It should furthermore be noted that all angles in the following equations are calculated in degrees (not radians). Given a date expressed as a day D of the month M, this must first be translated into a day of the year d for use in subsequent equations:

(1)

The ecliptic longitude can be approximated as:

(2) =2.8749 =0.98630 [day-1] =1.9137 =102.06

With the obliquity of the earth's axis (23.45°), the solar declination δ is then given by:

(3) The diurnal difference between apparent and mean solar time, which varies continuously with the earth's position on the ecliptic, is rectified by a special

corrective term z to represent the Equation of Time. In this description (Heindl and Koch 1976), z is expressed analytically as a function of the day of year d (rather than taken from a table of monthly values [ASHRAE 1989]):

(4)

whereby

(in degrees). Solar positions at a given terrestrial location are generally calculated for mean solar time t (in hours). The shift between conventional local time and mean solar time is determined by the geographic longitude Φ relative to an associated time zone meridian Φ0 (e.g., 15° for site locations with Central European Time) in a separate computational step:

(5)

A transformation of the unit vector directed at the sun's position to an earth-based coordinate system figure (2.4) yields the expressions for solar azimuth α and elevation β at a given geographic latitude Ω :

: (6)

: (7) with variables from the transformed vector matrix:

Unlike in the ASHRAE method, a means for correcting the apparent solar elevation β’ to account for direct beam refraction through the atmosphere is also incorporated by Heindl and Koch:

(8)

with =1.4705° =3.0427° =0.0158°

and β from equation (7).

 Though this effect is only significant at low solar elevations, it must be taken into account to accurately predict the time of sunrise and sunset, i.e. when the refraction-corrected solar elevation β’ = 0 (as viewed from the earth's surface). Accurate solar angle prediction is especially critical in the case of sites located beyond the arctic circle, where a calculated solar elevation that has not been corrected for refraction yields thoroughly misleading results as to whether the sun rises or sets at all on dates near the solstices.    

 Fig. 2.3 Angles of the earth's orbit around the sun.

 Fig. 2.4 Angles of the sun's position relative to a terrestrial location.

 

2-2: Solar Flux through Atmosphere

Most thermal simulation programs work with a climate input data base derived from empirical meteorological data (e.g., Heindl, Krec, and Sigmund 1984; Lemoine 1984; Preuveneers 1994). Typical limitations of such input data bases are due to the difficulty of obtaining timely access to correct climate data in the form needed, as well as to the inflexibility of working with such extensive data sets in general. Serious problems arise whenever ▪ the geographic coverage is either incomplete or too coarse for the case at hand

to be adequately modeled, or ▪ the data types are inappropriate for the simulation model or of incompatible

validity, or even if simply ▪ the form in which the data is provided requires extensive manual input to transfer

it to the data base.

Instead of maintaining a comprehensive input data base, solar conditions can be modeled as parametric functions with which the specific data is generated when needed. Such "synthetic" radiation data is sufficiently realistic for simulating thermal behavior and better manageable for the purpose of case comparisons, since it requires maintenance of only a few key parameters.

The trigonometric equations for translating quantities of normal direct beam flux to the radiation intensity that is incident on a surface plane of arbitrary orientation are well known (and recapitulated in the next section, 2-3 Local Solar Flux). However, as meteorological stations cannot implement ideal tracking and measuring devices for determining direct beam normal flux throughout the day, this theoretical base quantity is not directly available by empirical means and must be derived for all further calculations.

Heindl and Koch (1976) delineated a fundamental method for directly describing the insolation components on a normal surface in parametric terms, which -- due to key differences to the ASHRAE "ABC" parameters (1989 pp. 27.2-14) -- merits a more detailed re-introduction in this context (with adapted nomenclature). Because of the need to distinguish between the various components of solar radiation in this and subsequent chapters, the notation must employ indices in the superscript as well as the subscript. This requirement takes precedence over the usual exponential symbolism. Therefore, whenever a power of a variable quantity needs to be indicated, parentheses are used to bracket the quantity and set apart the exponent.

The first step is to determine with reasonable accuracy the amount of unmitigated solar radiation that reaches the earth, before passing through the earth's

atmosphere, . This equation involves the time-varying distance between sun and orbiting earth to account for significant irradiation fluctuations (± 3.34 %) owing to the eccentricity of the solar ecliptic. It defines extraterrestrial radiation as a diurnal function of the ecliptic longitude (instead of a tabular value of A for a given month [ASHRAE 1989 p. 27.2]):

(9) with

I0 = solar constant (e.g., 1370 W/m2), ε = eccentricity of earth's orbit, φ = ecliptic longitude of the earth (calculated angular distance from spring equinox).

As related by Nehring (1962), the degree to which direct beam radiation is mitigated due to atmospheric attenuation can be adequately approximated with a

(10) combination of two parameters, Γ and Q, reflecting meteorological haziness and the inverse effect of the optical air mass at a particular altitude: The atmospheric parameter Q is a function of the optical air mass mA , which is in turn a function of site altitude α and the calculated solar elevation β’ (refraction-corrected -- see the previous chapter):

(11)

with c1 = 9.38076, c2 = 0.912018, and

(12)

Given appropriate values for the total haziness factor Γ according to Linke and Boda (1922), assumed constant over the course of the day, the equations above are shown by Heindl and Koch to be sufficiently accurate for meteorological conditions from clear to partly cloudy skies. Typical clear sky values are, for example, Γ =4.3 for urban sites, Γ =3.5 for rural areas, and Γ =2.7 for mountain locations. By means of a time-dependent series of momentary values for the haziness factor, variably cloudy conditions can also be described with this equation. As compared with the ASHRAE formulae, this still constitutes a simplification from the point of view of the user: Instead of having to rely on regionally mapped data for "clearness numbers" to correct the average conditions assumed in the

atmospheric extinction coefficient B (as well as to account for high altitudes), only two relatively clear-cut parameters need be specified (Γ and α ). Part of the direct radiation filtered by the atmosphere still reaches the earth's surface in the form of diffuse sky radiation. The relative portion of this component, referred to here as the scatter factor P according to Reitz (1939), has been proven to be nearly constant at around 1/3 for fair sky conditions and, above all, generally independent of the haziness factor as well as solar elevation. The diffuse radiation factor C according to ASHRAE, which varies strongly from month to month, does not possess such convenient characteristics for two reasons: ▪ The expression for diffuse sky radiation leaves the inherent dependency on solar

elevation embedded in the value C. ▪ C is applied to the quantity of direct normal flux, rather than to the remainder of

extraterrestrial radiation that is scattered out of the direct beam.

With the Reitz scatter factor Π, the diffuse sky component of solar flux incident on a horizontal surface is expressed as

(13)

Using the Lambert cosine formula, the direct beam flux component incident on a horizontal surface is given by

(14) Consequently, two further equations can be derived for correlating the two main meteorological parameters with actual radiation data ("custom" Γ and Π), in the event that applicable data is or becomes available. However, such fine-tuning of the radiation model only becomes relevant at later evaluation levels, when estimates of thermal performance become an issue (as described in 2-9 Preliminary Performance Assessment). For the purpose of making initial assessments of the impact of primary design options, a model description that consistently works with standard values of Γ and Π is quite adequate, clear, and in most instances preferable during early stages of analysis.      

 

2-3: Local Solar Flux

At this point, given the atmospheric parameters and a locally assumed incident plane i of arbitrary orientation (illustrated in figure 2.5), both the direct beam and diffuse sky components of solar flux received by such a specified surface can be calculated. The magnitude of the direct component IID depends on the angle of incidence θi , which is best expressed as follows:

(15)

with αi= azimuth angle of incident plane i, βi= tilt angle of incident plane i ,

e1 and e2 from equation (6), β’ from equation(8), such that the Lambert cosine formula may be applied:

(16)

With respect to the diffuse sky component IIS , this is, of course, less than that incident upon a horizontal surface, since the inclined plane does not "see" the full extent of the sky hemisphere. Based on the diffuse sky flux incident on a horizontal surface IHS from equation (13), the generally accepted formula for calculating this component on a plane i tilted at an angle βi from the vertical is:

(17) whereby the view coefficient ωi (equivalent to the angle factor FSS [ASHRAE 1989 p. 27.14]) is defined as

(18)

Part of the total incoming radiation, direct and sky diffuse, is reflected by the surrounding ground and, to the extent that the incident plane is tilted into at least partial view of the ground plane, is also received by the inclined surface. Empirical radiation data that are limited to measurements made on a horizontal receiving plane do not include any information about the diffuse reflectance of the surrounding terrain. Nonetheless, a plausible expression for the diffuse ground-reflected radiation component IIR can be gained (Heindl and Koch 1976) by assuming ▪ isotropic sky radiation, ▪ a simplified surrounding terrain (ground plane G) that is horizontal and

homogeneously diffuse reflecting, and

▪ that the surface is exposed only to sky and ground:

(19) with

ρG= reflectance of ground plane, ωi from equation (18), β’ from equation (8), IND from equation (10), IHS from equation (13).

For most purposes, only the global solar flux specific to an incident surface, that is,

(20) will be of immediate interest to the building designer. This applies to planes of fixed orientation as well as to the ideal orientation normal to the direct beam (tracking surface), which yields the solar flux envelope IN for the locality. The full radiation component breakdown is nonetheless necessary for consistently calculating global specific flux while manipulating the parametric model. This makes it possible to account for, among other things, the effect that terrain elevations (e.g., a mountainous horizon or other distant-field obstructions) have on the "flux mix" incident on a given surface plane. Distant-field obstructions surrounding a geographic location are modeled as elevation angles βG for local azimuths αG , as measured from the center of the assumed horizontal ground plane G (origin of the model space as in figure 2.6, see also figure 1.8). This is essentially analogous to the familiar methods for constructing an obstruction angle overlay for a solar chart (Moore 1985 pp. 55-61, Goulding 1993 pp. 41-42). The direct beam component is effectively blocked when the solar position is such that the solar elevation β’ at azimuth α is less than the corresponding horizon elevation βG ; the calculated global flux at the location is reduced accordingly. When the sun is clearly above the elevated horizon, i.e. for β’ > βG , distant obstructions are treated as tilted segments of ground plane, with a mean tilt angle over respective intervals of angular width ΔαG (Heindl and Koch 1976). The view coefficient of an incident surface plane i (ωG,i) is thus reduced in comparison to the case of a horizontal ground plane:

(21)

whereby the angle of incidence expressed in relation to each tilted ground segment θG,i is given by:

(22)

The effect on the solar flux received by an incident surface that is in view of such horizon elevations is both ▪ a reduction of the diffuse sky component from equation (17) and ▪ an increase in the diffuse ground-reflected component from equation (19). It should be noted that the reflectance of an elevated ground plane also results in diffuse ground-reflected flux on the horizontal, since this orientation is treated in the same manner as an incident surface of arbitrary orientation.

A final detail should also be pointed out regarding the general treatment of solar elevation β’ at sunrise and sunset in conjunction with flux calculations using the equations above. The exact definition of this point in time varies from astronomical convention somewhat: It is here defined as the moment when the visible sun's center (rather than the top edge) passes the horizon. This allows a minor simplification in the radiation pattern that is convenient and sufficiently precise for the purpose at hand.

Solar flux is assumed to be null until the defined moment of sunrise and immediately after the moment of sunset. The points of dawn and dusk according to this description show a discontinuous jump from null to an initial quantity of radiation associated with a fictitious full appearance of the sun. Of course, the visible "disk" of the sun does not pass the horizon in a single moment with a sudden jump. The actual radiation pattern at sunrise and sunset instead reflects a gradual, albeit steep, transition from "sun still completely hidden" to "sun in full view" (figure 2.7).

 

 Fig. 2.5 Angles of an incident surface plane at a terrestrial location.

 Fig. 2.6 Angles of an elevated horizon around an incident plane and coordinate system of the view coefficient.

 Fig. 2.7 Solar flux at sunrise: actual vs. calculated radiation pattern.

 

2-4: Shading & Resultant Flux

In order to account for the impact of middle- and near-field solar obstructions on the amount of incident radiation, the projected building together with its immediate surroundings must be geometrically modeled. A graphical technique that is more or less equivalent to the computer-based method delineated in this chapter is that of using sun charts of available solar gain in conjunction with shading masks (Balcomb 1992 pp. 491-495). Up to this point, the solar gain model has been strictly presimulative in nature, that is, an additive compilation of sequential input information. Coupling a geometric surface model with radiation results constitutes a basic (yet potentially complex) simulation model in as much as the various components of calculation are spatially interdependent. It is in this connection that the intended integration of the proposed design-support system becomes indispensable for generating continued results that are truly meaningful to the building designer. The calculation of resultant radiation quantities on a building requires an exact description of the incident and obstructing surfaces in terms of their extents (areas and contours), orientations, and relative positions in a unified coordinate space. Due to the general lack of appropriate three-dimensional modeling standards in computer-aided design to date, the use of available CAD applications to facilitate model input is not feasible in a manner consistent with the constraints of computing solar gain. Therefore, a fundamental issue that must be addressed in conjunction with the proposed system is that of how to generate an integrated surface model via an understandable and reasonably user-friendly input procedure. This means, for example, avoiding the numeric input of absolute coordinates in favor of graphically supported input of relative positions (distance and direction between two elements), as the latter better corresponds to the visual-spatial mode of thinking during the building design process. The application concept presented here is based on an input metaphor that should be familiar to most architects: constructing a sketch model out of perfectly flat cardboard pieces, which are furthermore idealized to be infinitesimally thin. Analogous to the process of physically drafting, shaping, and finally gluing together the pieces of such a sketch model, input of the geometric calculation model entails specifying a set of surface elements with regard to the following two- and three-dimensional properties: ▪ A polygonal contour, which can be thought of as "drawn" and then "cut out" in an

assumed working plane. ▪ An implicit "front" side, to which the orientation is related and for which results

may also be calculated (incident surface). ▪ A fixed position in an implied model space, which is horizontally limited by a pre-

defined base area (ground plane).

In accordance with the input metaphor for affixing model pieces (either to a base or to each other), the position of a surface element is established firstly by

▪ positioning two so-called anchor points of a specified contour in the model space, in relation to either the ground plane or other existing surface elements,

and secondly by ▪ assigning an orientation, i.e. surface azimuth and tilt. The orientation is used solely as a geometric constraint when transforming the input data into definite coordinates for calculation. In detail, the unit vector defined by the anchor coordinates (together with the corner points of the planar polygon) is first rotated from an assumed initial position, and then transformed again with a rotational tensor derived from the applied orientation (figure 2.8). By thus having the exact positioning of the element anchors numerically take precedence over the user-specified orientation, a potentially contradictory definition of surface point locations is avoided and the notation of the orientation still remains recognizable for the purpose of selecting calculation results of interest (see also Summary & Prospects: The Solar Toolbox). Once a geometric description of the site and building design in question has been established, an overall shading pattern for the specified day d can be calculated by means of triangulation with the previously determined diurnal solar positions, i.e. solar azimuth α and apparent elevation β’ at local time (as described in 2-1 Solar Position). Given such a diurnal shading pattern, the solar flux resulting on any or all incident surfaces of the building model can be readily calculated based on the following simplification: ▪ Computationally, a solar obstruction serves only to cut out the direct radiation

component on the shaded area of the incident surface. ▪ It has no the effect on the total quantity of diffuse radiation (sky + reflected) that

ultimately reaches the surface in question, since any diffuse sky radiation that may be effectively blocked (reduced view coefficient) is uniformly assumed to be diffusely reflected by the surrounding surfaces.

This simplification is necessary since currently only very rough, intuitive approximations are available for handling the reflection of diffuse radiation parametrically with feasible computation time. Simulated parameter studies show that the conceivable effects of complicated reflection patterns are not necessarily negligible (Moore 1985), yet the empirical data necessary to verify and test the

sensitivity of acceptable simplifications is broadly lacking. Much more empirical research would still be required to develop a diffuse radiation model with the same level of validity as is available for describing direct beam radiation.

Within the framework of the solar gain model presented here, it follows that the resultant global flux on an incident surface area j of orientation i is given by

(23) with

Aj = total area of incident surface plane, Bj = momentarily shaded area, Ii from equation (20), IiD from equation (16). When developing solar apertures and shading configurations, a basic differentiation between direct beam and diffuse (sky + reflected) flux components may also be useful to the building designer, that is:

(24) and

(25) with

Aj, Bj, IiD as in equation (23) IiS from equation (17), IiR from equation (19).

Solar apertures and near-field obstructions (e.g., façade shading devices such as overhangs and wingwalls) are treated computationally in the same manner as the middle-field obstructions of the overall site and building model. From a modeling standpoint, however, such elements are handled separately as building details. More specifically, an aperture is defined as a sub-area of an incident surface and specified with the following properties (figure 2.9):

▪ A polygonal contour, which is "drawn and cut out" as well as positioned with one anchor point on the defined "front" side of an existing surface element.

▪ Optional shading elements, which are rectangular planes that are attached orthogonally to the incident surface element and positioned relative to the aperture contour.

The sub-areas defined as apertures are thus prepared for glazing in the next modeling stage (2-5 Net Flux through Apertures).

Another type of building detail which shall prove useful in later stages, especially in conjunction with groups of apertures, is that of the room contour. This is specified in basically the same fashion as an aperture, but without associated shading elements.

Furthermore, the delineation of a room may include multiple contours that extend over more than one surface element (e.g., around a building corner), without overlapping another room. Such an additional definition of rooms allows the meaningfully combined output of calculation results for related apertures and other surface sub-areas of the building model (see also 2-9 Preliminary Performance Assessment).  

 Fig. 2.8 Positioning of a surface element in the model space.

 Fig. 2.9 Aperture definition in a planar surface element.

 

2-5: Net Flux through Glazing

At any instant, the quantity of global solar flux falling on a glazed aperture equals the sum of radiation that is ▪ reflected back to the exterior, ▪ absorbed and emitted to the exterior, ▪ absorbed and emitted to the interior, and ▪ transmitted directly to the interior.

Of these components, only the quantities that reach the interior space are of interest for calculating solar gain as net flux through glazing. Specifically, the directly transmitted flux is referred to here as primary gain, while the portion of the absorbed component that is emitted inwards constitutes the so-called secondary gain. By concentrating on these two net flux components, the description of the solar-optical properties of glazing can be reduced to three characteristics:

▪ total solar energy transmittance g , ▪ solar direct transmittance τ, ▪ directional transmittance τ(θ) .

The first of these, total solar energy transmittance, is an established glazing parameter (European Standard 410) that specifies the overall fraction of incident radiation energy that passes through an aperture to the interior, i.e. the net solar flux through an aperture j with a given type of glazing:

(26) with

Jj from equation (23) Gj

P= primary gain (directly transmitted), Gj

S= secondary gain (absorbed/emitted).

In lieu of a standard value for g, or in the event that the desired glazing type is not documented with such characteristics, this factor can also be determined computationally (e.g., according to EN 410). However, for the purpose informing initial building design decisions, such a specific characterization of glazing properties is not applicable and, therefore, the description of this calculation procedure in detail lies beyond the scope of the solar profiling method at hand.

In North America, the more or less equivalent characteristic published by most glazing manufacturers is the so-called shading coefficient (SC), which is defined in ASHRAE as "the ratio of solar heat gain through a glazing system under a specific

set of conditions to solar gain through a single light of the reference glass under the same conditions." The net flux is then calculated by multiplying the shading coefficient with the solar heat gain factor (SHGF) for the given orientation and existing conditions (ASHRAE 1989, chapter 27: "Fenestration"). Thus an appropriate value for the total solar energy transmittance g can also be derived via this alternate route, if necessary.

By definition, the secondary gain through an aperture area j is equal to the difference between the total gain and the directly transmitted radiation:

(27) This is taken as constant for all angles of incidence, meaning that variations in transmittance τ(θ) are assumed to be chiefly compensated for by the complementary directional reflectance ρ(θ) together with variations in the absorbed radiation that is emitted outward (figure 2.10). Since the directional distribution of these quantities only applies immediately to exterior "gains," it is not of further interest here. The case of specular reflection -- in which direct beam radiation is reflected as such and may potentially contribute to the direct component incident on a nearby surface (Balcombe 1992 p. 87) -- is consid-ered to be of special interest only for certain detailed considerations of passive solar design. It has therefore not been incorporated in the framework of the overall geometric model (2-4 Shading & Resultant Flux). In comparison to the proportionately small quantity of secondary gain, the primary gain through aperture j is strongly dependent on the angle of incidence and is best calculated by first distinguishing transmittances for direct and diffuse radiation, such that

(28) where τ1 and τ2 represent the expressions for direct beam and diffuse transmittance, respectively, with Jj

D from equation (24) and JjS+R from equation

(25). The direct beam transmittance τ1 is equivalent to the dependence on the angle of incidence τ(θ) , which is a further characteristic of the glazing:

(29)

with θ equal to the momentary angle of incidence on a given orientation as yielded by equation (15).

Theoretically, the Fresnel equations could be used to derive an expression for the function τ(θ) ; however, this would only be applicable to ideal conditions, which are hardly given under the real circumstances of transparent building components. In order to arrive at a realistic yet simple description of the complexities involved in reflection, absorption, and transmission through multiple lights of glazing, it is necessary to resort to a more empirical approach (Fuchs, Haferland, and Heindl 1977 p. 46; Heindl, Sigmund, and Tschegg 1984 p. 185). The following formula quite precisely describes the curves of manufacturer data for the incident angle response of glazing transmittance in a generalized form:

(30) Hereby the exponent κ represents the sole parameter for defining the directional profile of the glazing type, independently of the specified direct transmittance τ . A realistically unclean state of the exposed glazed surface can be taken into account by applying a reduced design value for solar direct transmittance (e.g., 10% less than the ideal manufacturer-specified τ). The literature of technical data for typical glazing types (BMBT 1979, TU-Wien 1995) shows that the parameter κ conveniently characterizes standard categories of glazing assemblies used in construction, in particular those of the following materials: ▪ clear glass, ▪ translucent white glass, ▪ gray/bronze (absorptive) glass,

▪ green ("heat-absorbing") glass, ▪ light-reflecting film.

This means that characteristic exponents can be assigned in a standardized fashion to these basic glazing types for different numbers of lights (single, double, or triple), thus avoiding the need for detailed manufacturer specifications. Separate standard exponents are also available for skylight glazing and glass block (BMBT 1979). Figure 2.11 shows examples of such derived directional response profiles, that is, the characteristic function τ(θ) for different values of κ.

Since it is assumed that the directional distribution of the diffuse radiation JjS+R is

uniform, the diffuse transmittance τ2 is obtained by integrating the directionally dependent transmittance over the half-sphere of all angles of incidence:

(31)

Solving this integral with the function τ(θ) from the previous equation yields the following simple expression (Heindl, Sigmund, and Tschegg 1984 p. 186):

(32)

As opposed to the direct beam transmittance, the expression for the diffuse transmittance remains the same for the entire course of the calculated time period and, therefore, must only be determined once for each type of glazing that is characterized by a different combination of solar direct transmittance and exponent κ. Glass in general is opaque to all radiation beyond 4.5 µm (ASHRAE 1989 p. 27.21), so the incoming solar radiation that is absorbed and re-radiated in the infrared range by interior surfaces is effectively trapped as heat (see also the next chapter: Spectral Solar Flux).  

 

Fig. 2.10 Solar-optical properties as a function of the angle of incidence for double-strength sheet (A), 6-mm clear (B), and 6-mm grey, bronze, or green absorptive (C) glass. Sources: ASHRAE 1989, Balcomb 1992.

 Fig. 2.11 Transmittance as a function of the angle of incidence for various exponents: κ parameter of τ(θ) . 2-6: Spectral Solar Flux

Up to this point, the solar gain model has worked with combined radiation quantities for all wavelengths of the solar spectrum. Although this is sufficient for informing passive strategies with respect to the energy demands of heating and cooling (see 1-6 Solar Gain through Apertures), architectural daylighting requires information as to the spectral distribution of solar flux that enters a building. In particular, the quantity of luminous flux in the visible range (0.38 - 0.77 µm) is needed to guide this additional category of design decisions. Although the solar gain model as delineated in chapters 2-1 through 2-5 does provide a framework for addressing the issue of luminous flux, a suitable parameterization of spectral data is not (yet) possible in a form that could be consistently integrated in this solar profiling method. A complete spectral extension of the solar gain model would require the derivation of wavelength-dependent parameters at two separate levels: ▪ solar flux through the atmosphere (chapter 2-2) and ▪ net flux through glazing (chapter 2-5).

Regarding the attenuation effect of the atmosphere at the first level, the impact of increased optical air mass mA on terrestrial solar flux is apparently two-fold (figure

2.12):

▪ a reduction in the global solar flux, as conveyed in equations (10) through (12); ▪ a shift in the bulk of spectrally distributed flux to longer wavelengths (λ). Given a spectral description of extraterrestrial radiation I(λ) and equations (10) through (12), a wavelength-dependent expression for normal direct beam flux IND(λ) could be developed with a spectral air mass mA(λ) and haziness factor Γ(λ). Theoretically, the wavelength dependence of these parameters could be derived by means of correlation analysis with reliable meteorological data; unfortunately, such radiation data is currently not available in sufficient quantities.

Since the scatter factor according to Reitz (1939), which is used to estimate quantities of diffuse sky radiation, can be expected to vary strongly with wavelength, a spectral expression for this parameter, Π(λ), would be clearly necessary as well. Hence equation (13) may eventually be completed for further use in calculating the spectral solar flux components on an incident surface area (equations in 2-3 Local Solar Flux and 2-4 Shading & Resultant Flux).

With respect to the second level mentioned, that is, for calculating the spectral distribution of net flux through glazing based on the spectral resultant flux J(λ) incident on a given aperture, a parametric description of the spectral response of glazing in general would still need to be established. Although the relative transmittance, reflectance, and absorptance in the various wavelengths of the radiation spectrum are empirically understood and partially documented (e.g., Moore 1985, chapter 11), the spectral expressions for these solar-optical properties are still lacking: τ(λ), ρ(λ) , and α(λ) .

Especially a function for the spectral transmittance τ(λ) would be of interest (figure 2.13), since this would allow profiles of daylight conditions to be generated practically as a by-product of the calculation models.

As it is, however, the only spectrally relevant parameters that are occasionally published for glazing products are values for the overall transmittances in basic ranges of the solar spectrum, i.e.

▪ ultraviolet transmittance τUV (< 0.38 µm), ▪ visible transmittance τvis (0.38 - 0.77 µm), and ▪ solar infrared transmittance τIR (> 0.77 µm).

A corresponding expression for at least the visible component of resultant flux (Jvis) would thus enable the integrated assessment of luminous flux in conjunction with its directional distribution. This could be conceivably employed in a manner that is consistent with and naturally accompanies the general solar profiling method as outlined in part 1.

 

 Fig. 2.12 Spectral variation of solar radiation at the earth's surface for different values of optical air mass mA . Source: Balcomb 1992.

 Fig. 2.13 Transmittance as a function of wavelength for 3-mm regular sheet (A), 6-mm grey absorptive (B), and 6-mm green absorptive (C) glass. Source: ASHRAE 1989.

 

2-7: Climate Profiles

At the very beginning of the solar profiling method (1-1 Solar Geometry), a selection of characteristic dates was established for analyzing the solar situation and design issues consistently throughout subsequent levels. In particular, the characterization of climate seasons with a set of dates for the hottest and coldest months of the year (together with a transition month) implies that the consideration of ambient temperature takes precedence over solar radiation quantities for certain design-analytical purposes. The early focus on this aspect of the local climate is intended to generate supporting solar profiles that are ultimately aimed at thermal simulation (1-9 Transition to Simulation). Dynamic performance simulations of buildings located in climate zones with a strong seasonal variation in mean temperatures show that the results are most sensitive to the ambient temperature that is applied as a boundary condition in the thermal network model (see also 2-9 Preliminary Performance Assessment). Solar energy considerations on a diurnal basis are, therefore, most effective in connection with the climatic extremes of temperature. In other words, it is more important to know how much solar gain can be expected when the exterior conditions are hottest and coldest, than at the solstices defining the solar extremes (generally in the month prior to the temperature extreme). Although the parameter of ambient air temperature lies beyond the immediate scope of the solar gain model, its definition in this context allows the basic profiling method to be extended to include a number of supplemental evaluations, which can provide insight into the potential thermal performance of a building design (1-7 Surface Conditions and 1-8 Basic Thermal Envelope). For this purpose, a parametric description of ambient air temperature is needed which adequately characterizes the applied boundary condition as a diurnal profile, analogously to the solar flux profiles. Such an analytical expression for generating diurnal temperature curves was derived by Fuchs, Haferland, and Heindl (1977) on the basis of the standardized profile as established by Nehring (1962) and illustrated in figure 2.14. The following set of periodic functions for the air temperature at time t characterizes this curve in a generalized form, which also closely approximates the available meteorological data for varying seasonal temperature swings. The rising portion of the curve between the minimum and maximum temperature, i.e. for time t from tmin to tmax , is described by the function

(33)

Since periodicity is assumed, the first and last sections of the curve are considered as parts of a single continuous function from tmax to tmin :

(34)

Calibrating these curves to fit a given temperature swing between Tmin(tmin) and Tmax(tmax) yields

(35)

Herein L connotes the length of the time period (24 hours). Appropriate values for temperature maxima and minima can be taken from basic climate data available for most geographic locations. The time points at which these temperatures occur in the course of a day, however, are generally not included in the available data and must therefore be approximated. A realistic set of assumptions for these values is standardized on a seasonal basis (Fuchs, Haferland, and Heindl 1977 p. 33), whereby tmin is also tied to the calculated time point of sunrise and corrected differently for clear sky and cloudy conditions. It should be noted that the handling of characteristic climate data in general -- and the reduction of temperature data in particular -- poses a much more complex problem in the climate-sensitive context of thermal simulation than related here (Feist 1994). Though mathematical descriptions of boundary conditions have the advantage of enabling parametric analysis that is much more flexible than such based on historical data sets, the difficulty of obtaining calculation results that can be reliably interpreted over a range of potential conditions still remains. This concern is fundamentally one of underlying approach and has as yet not been satisfactorily resolved. Promising recent work in this direction seeks to incorporate random aspects of climate data in a stochastic model description (Kossecka 1996).    

 Fig. 2.14 Ambient air temperature as a periodic function over the course of a day. Source: Fuchs, Haferland, and Heindl 1977. 2-8: Resultant Air Temperature

In thermal evaluations of a building's performance, radiative heat transfer at exterior surfaces is usually accounted for by introducing a hypothetical ambient temperature (e.g. the sol-air temperature [Threlkeld 1970 pp. 279-311]) that explicitly includes the effects of solar radiative absorption and long-wave radiative emission. Together with a total heat transfer coefficient that combines both convection and radiation, a linear description of an equivalent thermal network can thus be constructed (Balcomb 1992 pp. 91-93). Koch and Pechinger (1977) demonstrated that the solution of a so-called "radiant air temperature" -- as established by Haferland and Heindl (1970) and further developed by Fuchs, Haferland, and Heindl (1975) -- exactly defines the boundary condition at an exposed building surface, provided that correct assumptions are made regarding the convective portion of the total heat transfer coefficient. Because of the exactness of this particular approach, as well as the fact that it has not yet been presented in English-language literature, the radiant air temperature ("Strahlungslufttemperatur") according to Haferland and Heindl shall be related briefly here in translated form (with adapted nomenclature). At a given point on an exposed surface i , the radiant air temperature Ťi is defined by the energy balance at the surface:

(36)

whereby hc= convective heat transfer coefficient, T(t)= ambient air (sky) temperature from equation (34), Wi= solar and longwave radiation absorbed by surface i p(Ťi)= radiation emitted by surface i.

The function p(Ťi) represents the Stefan-Boltzmann law for blackbody radiation such that

(37)

The full expression for Wi includes the absorbed quantities of incident solar radiation and longwave radiation from the surroundings (sky and terrain):

(38)

Hence the defining equation can be rewritten as:

(39)

with

αi = solar absorptance of surface i, Ii from equation (20) (less direct beam component for shaded region), Cr= blackbody radiation coefficient, εi = longwave emittance of surface i, ωG,i from equation (21), εS = emittance of sky/atmosphere, εG = emittance of surrounding terrain, T(t) = ambient air (sky) as in equation (36), TG = surface temperature of surrounding terrain.

(Note: For lack of a plausible description of the surface temperature of the

surrounding terrain, TG , is usually assumed to be the same as the ambient air temperature T(t) in the practical application of these formulae.) Numerically, equation (39) is solved for the radiant air temperature by applying the Newton iteration method (Koch and Pechinger 1977). With the starting value taken as the mean ambient air temperature , this method yields in the first approximation

(40)

Where Wi is from equation (38), is given by the Stefan-Boltzmann law applied to as in equation (37), and

(41)

Since the radiative heat transfer coefficient hr can be adequately approximated as the derivative of the emission function (Haferland and Heindl 1970), the total heat transfer coefficient is expressed in terms of radiant air temperature as

(42) In connection with the geometric model composed of planar surface elements (2-4 Shading and Resultant Flux), the shaded regions have an effective radiant air temperature that is, of course, considerably lower than the exposed areas receiving direct beam radiation. Though middle- and near-field obstructions should be accounted for in order to avoid overestimating the solar load on a building, it would be highly impractical to apply such a calculated boundary condition to the momentary shading pattern in a thermal network model. For this reason, the definition of a resultant air temperature that is analogous to the resultant flux on a given surface area of the geometric model needs to be introduced. Simply stated, the resultant air temperature (at any given moment) is the average radiant air temperature on a surface element over the extent of the area with the same specified solar absorptance. The basic distinction between opaque and transparent elements of a thermal envelope constitutes a necessary differentiation of the thermal network for applying exterior driving functions. Since this distinction also generally corresponds to different assumed absorptances (wall and glazing) for calculating the effective boundary condition of temperature, the specification of surface elements with apertures can be readily used to distinguish the geometric components as needed for incorporation in a detailed thermal model. Consequently, the resultant air temperature at surface area k with a given solar absorptance (wall surface or glazed aperture) and orientation i is defined as

(43)

with Ak = total area of surface, Bk = momentarily shaded area, Ťk

A = radiant air temperature calculated for specific global flux ( IiD+IiS+IiR), Ťk

B = radiant air temperature calculated for specific diffuse flux only (IiS+IiR).

Hereby the total area of the planar surface element as modeled in chapter 2-4 is broken down into transparent sub-areas for each of the specified apertures and the remainder, which is defined as opaque. Resultant air temperatures described in this manner provide a very close approximation of the diurnal surface conditions both for preliminary performance assessments (see next chapter) and as input data for thermal simulation (Fuchs, Haferland, and Heindl 1977; Krec and Rudy 1996).                                                            

                     

 

2-9: Preliminary Performance Assessment

In order to obtain preliminary information about the thermal performance of a building, the geometric building model (2-4 Shading & Resultant Flux) needs to be further enhanced by specifying which surface elements are to be considered part of the overall thermal envelope. This specification is best done in a separate step, since not necessarily all of the surface model may be of interest for evaluation. Sub-areas of envelope surfaces that are already defined as rooms (building details) remain as such for separate detail evaluations. Hence the basic thermal envelope is described as a model sub-set of opaque surface elements with glazed apertures. Appropriate U-values can be individually assigned to all of the components of each surface element (transparent aperture areas and opaque remainder area). A first look at the conductive thermal quality of the building design is then possible after calculating the overall U-value in the usual manner for all the components k of all the surface elements j included in the envelope:

(44)

with

Aj = total area of surface element, Ak = component sub-area of surface, Uk = component U-value.

The overall U-value for the exterior walls of a given room is calculated analogously.

Thermal capacitance is not included at this stage of the solar gain model, since the effects of thermal storage can only be accounted for by means of dynamic simulation (Hunn 1996, Krec and Rudy 1996). Nonetheless, based on the assumption of periodic steady-state conditions, the following basic energy balance is valid for constant mean values and includes the primary heat flows associated with a building's solar load:

(45)

whereby

= diurnal mean of net flux through aperture j from equation (26),

= diurnal mean of interior air temperature (free-running),

= diurnal mean of resultant air temperature at surface component k from equation (43).

Energy losses or gains due to infiltration and ventilation (forced or natural) are generally neglected for the purpose of simple preliminary assessments. With this in mind, a measure for determining the likelihood of overheating in a particular room of the building model -- the resulting mean interior temperature -- can be obtained by rewriting equation (45) with the sums expanded for the room's enveloping

components (apertures j and surface sub-areas k) and solving for .

When considering the entire building envelope, information as to the overall heat losses to be expected is generally of greater interest than the result for a free-running interior air temperature. A rough estimation of the building's performance

under winter conditions can be obtained by setting to a fixed temperature and using equation (45) to calculate the resulting mean heat flow. Multiplied by 24 hours, this result corresponds to the auxiliary heating energy demand for the given day under the applied conditions -- bearing in mind that the energy balance includes neither heat losses to the ground nor thermal bridging effects (Heindl et al. 1987).

Since the analysis up to this point has focused on the parametric impact of design decisions on solar gain, the profiles of radiation and temperature would in general have been calculated for clear skies, that is, sunny conditions, which emphasize geometric considerations involving direct beam radiation. In the summer, this constitutes the critical case and is therefore appropriate for assessing the summer situation, especially with regard to overheating and passive control of excess solar gain.

For the winter case, on the other hand, such profiles represent "best case" conditions for harvesting solar energy. In order to arrive at a reasonable annual estimate of auxiliary heating energy demand, the calculations would need to be based on typical -- rather than ideal -- winter conditions. To this end, a preliminary annual climate profile can be generated from historical data that is commonly available for most geographic locations: monthly mean values of air temperature and solar radiation on a horizontal surface. The latter data is used to derive typical values for the atmospheric parameters Γ and Π (2-2 Solar Flux through Atmosphere), such that corresponding solar profiles may be calculated for mid-month dates.

This type of annual climate profile could also provide a plausible foundation for the

development of synthetic climate data that is detailed enough for application in thermal simulations of annual heating energy demand (e.g., TU-Wien 1995, Krec and Rudy 1996).

Depending on the focus of analysis and the supplemental information required, other simplified methods may be useful for comparison before actually simulating the thermal behavior of a building design. Data extracted from the solar gain model as defined up to this stage may be appropriately used in a number of additional methods derived by correlation analysis (i.e. by determining relationships between variables numerically rather than from first principles). Simplified methods that are already developed include, for example:

▪ the degree-day method for estimating heat loss and the solar savings fraction (SSF or f ), i.e. the solar contribution to the building's overall heating load;

▪ the solar load ratio method (SLR), which correlates solar gain and heating load on a monthly basis;

▪ the unutilizability method for estimating the solar savings fraction based on solar load ratio, solar radiation incident on an aperture surface, and thermal storage characteristics (Balcomb 1992 pp. 182-189).

Multivariable methods generally work with sets of nomographs, whereby software has been developed for the most widespread ones to facilitate their application in practice. Other available applications include the LT method (lighting and thermal value of glazing, Goulding et al. 1993), the diurnal heat capacity method (DHC), as well as a methodology for determining the optimum allocation of resources for conservation and passive solar strategies (Balcomb et al. 1980).

   

Summary & Prospects

The traditionally engineering-oriented approach to thermal building simulation tends to leave such analysis tools out of the reach of general design practitioners, especially during the early stages of building design when many of the most influential decisions regarding the thermal envelope are made. An alternate approach is proposed for making a situation-specific component of the overall thermal simulation -- the ambient climate conditions -- accessible and informative at the level of schematic design considerations. Before and beyond simulation of a building's overall thermal behavior, solar radiation data can be made useful to inform qualitative design decisions if it is ▪ analytically modeled in parametric terms that consistently correlate geometry

with radiation, ▪ selectively implemented in diurnal profiles that capture meaningful seasonal

characteristics, and ▪ rendered to reveal the interdependence of solar dimensions to the building

designer.

By accompanying design phases with the development of a progressively concise solar/climate model, such information brings the added benefit of applicability as ambient boundary condition data for full-scale thermal simulations.

Unto themselves, the kinds of simulations required for the complete thermal evaluation of fully developed building designs do not represent design tools in the narrower sense of the word, since such final evaluations are generally intended to yield predicted results as proof of target fulfillment (includ-ing documentation mandated by standards) for a single, "finished" solution.

But if viewed in light of a seamless application model which allows energy-related information to be built up and extracted in layers corresponding to typical decision levels in the building design process, the strict distinction between design and evaluation tools disappears. By integrating further levels of complexity and details as need and available, a principle of progressive model generation -- applied to areas of solar gain modeling in the context of an overall thermal model -- forms the basis of an integrated solar design tool concept.

Though for new construction the building design process in its earliest stages does not generally include enough thermally relevant detail information to make simulation results truly meaningful, the design of retrofit construction poses an entirely different situation. To the end of evaluating measures for improving the energy efficiency in existing buildings, the application method presented here shall

be systematically extended to encompass the complexities of thermal simulation analysis.

   the solar toolbox The solar toolbox application is structured closely along the lines of the solar profiling method outlined in Part I, whereby each "tool" is a program module for processing the set of input parameters that is needed for a further level of output options. The individual output options are systematized to support the targeted manner of profiles for early building design guidance, i.e. site analysis and schematic building design development. Consequently, the principal solar toolbox prototype is conceived to contain the following sequence of modules: ▪ solar geometry (geographic site specification -- solar position), ▪ solar energy potential (atmosphere and terrain, distant-field obstructions --

solar flux envelope), ▪ solar access (incident surface orientations -- specific flux), ▪ site/building model (full incident surface geometry, middle-field obstructions --

resultant flux), ▪ building details (incident surfaces: aperture and room geometry -- resultant

flux), ▪ solar gain (apertures: solar-optical glazing properties -- net flux).

For the more advanced profiling levels (those that go beyond solar gain modeling), the following tools are tentatively planned as future extensions:

▪ surface conditions (absorptance, ambient air temperature -- resultant temperature),

▪ thermal envelope (envelope surface components: U-values -- preliminary performance check),

▪ transition to simulation (monthly radiation and ambient temperatures -- annual base profile of solar/climate data).

A preliminary concept for the principal toolbox is covered in a separate, three-part set of documents (1: Solar Site Analysis, 2: Geometric Modeling, 3: Solar Gain Analysis), available via the solar workshop presented in the next section.

   about the implementation The calculation modules of the solar toolbox prototype are currently programmed

as Java applets, which are flexibly embedded in an HTML user-interface referred to as the solar workshop (figure 3.1). Since both the solar profiling method and the algorithms behind it are globally applicable, the main objective of this Internet-based implementation is to open the development base and make the "work in progress" as widely accessible as possible to trial users -- without the usual hassles of physical media distribution, installation, and security risks on the users' part. The tools available in the online solar workshop are organized in separate main frames for input by level and an overview of associated output options, whereby the completion of each input level activates a further set of graphic output options. The opportunity to document input parameters and numeric results in tabular form (HTML) is also given in connection with each level. Two additional frames are incorporated for related "Help" information as well as project handling. Since the modeling sequence is intended to accompany the building design process in an on-going fashion, a general case manager tool allows for the saving, loading, and editing of previously entered project data. The author would like to extend a special thanks to the applet programmer, Tomasz Kornicki, without whom such an experimental implementation would not have been possible.  

 Fig. 3.1 Screenshot of the online solar workshop (2002).

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