Integrated Methods of Passive Solar Building Design

Integrated Methods of Passive Solar Building Design

A Proposition For a Solar Design-Support System

Margit Rudy

Acknowledgements

Research funded by the FWF (Austrian Science Fund),

in association with the Technical University of Vienna,

Institut für Hochbau für Architekten –

Abteilung Bauphysik und Humanökologische Grundlagen

(former dept. head and project coordinator: a.o.Univ.Prof. 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.

Vienna, March 1999

Table of Contents

Introduction...............................................................................1

Context ..........................................................................2

Aim & Objectives...........................................................3

Approach & Results.......................................................4

Part 1: The Solar Profiling Method .........................................7

1-1 Solar Geometry...............................................11

1-2 Solar Energy Potential....................................14

1-3 Solar Access ...................................................18

1-4 Site & Building Model ....................................22

1-5 Building Model Details ..................................26

1-6 Solar Gain through Apertures........................29

1-7 Surface Conditions.........................................32

1-8 Basic Thermal Envelope.................................35

1-9 Transition to Thermal Simulation.................38

Part 2: The Calculation Models .............................................40

2-1 Solar Position .................................................44

2-2 Solar Flux through Atmosphere ....................47

2-3 Local Solar Flux .............................................50

2-4 Shading & Resultant Flux ..............................54

2-5 Net Flux through Glazing...............................58

2-6 Spectral Solar Flux.........................................62

2-7 Climate Profiles ..............................................65

2-8 Resultant Air Temperature ............................67

2-9 Preliminary Performance Assessment ...........70

References ...................................................................73

Part 3: The Solar Toolbox ......................................................75

3-1 Solar Site Analysis .........................................77

3-2 Geometric Modeling.......................................83

3-3 Solar Gain Analysis........................................90

Summary & Prospects .............................................................99

Appendix................................................................................100

A: Parameter Studies.........................................102

B: Case Studies .................................................130

C: Glossary of Terms.........................................176

Introduction

1

Introduction

The last two decades have been marked by an increasing pub-

lic awareness of the need for environmentally sensitive solu-

tions in the realm of building design. Given the simple fact

that a major purpose of a built environment is to provide shel-

ter 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 sup-

plying a working building with the needed energy are tradi-

tionally the domain of engineering specialists, so-called pas-

sive 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 utili-

zation and, therefore, a core concern of architectural practice.

In order to effectively reduce the negative environmental

impact of erecting and operating buildings – without compro-

mising 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. Con-

cretely, 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 increas-

ingly sophisticated calculations to be performed for building

project permits.

Meeting more complex and stringent thermal quality stan-

dards 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 strate-

gies throughout the entire design process.

Context

2

Context

A wealth of quantitative methods and techniques for estimat-

ing 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 sim-

plified 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 tech-

niques, the architect must first familiarize him/herself with a

varied (and often inconsistent) array of characterizing parame-

ters – 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 con-

venient 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 & Obejctives

3

Aim & Objectives

Designing effective solar design tools entails establishing an

accessible bridge between the information needs of the build-

ing designer and the information provided by building phys-

ics. 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 consid-

erations: the optimization of thermal comfort and the economy

of means (Anderson 1990). Beyond this, solar design issues

also directly influence lighting options and, ultimately, psy-

chological 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 con-

cepts.

Approach & Results

4

Approach & Results

The crux of the difficulty in developing reasonably convenient

solar design methods which are also adequately comprehen-

sive in application lies in the fact that solar/thermal and archi-

tectural models are the product of diameterically opposite

approaches in integrating factors and, therefore, address con-

cerns according to very different priorities. Whereas architec-

tural 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 objec-

tives associated with the building project, such as architec-

tural 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 geo-

graphic 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 inter-

action 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 use-

fully 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

Approach & Results

5

extensive parameter and case studies (see Appendix for

details). The types of renderings and other graphic representa-

tions which most readily support accurate qualitative interpre-

tation 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 assess-

ments of environmentally responsive design are highly sensi-

tive to preliminary assumptions made about solar/climate fac-

tors. 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 stud-

ies 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 rec-

ommended which inform such key decisions in a schematic

manner that is both flexibly specific and immediately inter-

pretable. 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 imple-

mentation of the parametric radiation model can immediately

be used – without much further ado and with minimal compu-

tation time – to generate plausible solar geometry and radia-

tion data for building sites situated anywhere on the globe.

The second, less conspicuous, but equally important advan-

tage lies in the manageability and, therefore, interpretability of

preliminary results. Instead of handling unwieldy tables of

numeric values, which are generally impenetrable for anyone

Approach & Results

6

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 custom-

ized 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

described in Part 3: The Solar Toolbox.

Part 1

7

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):

1. Conceptual phase, which covers programming,

site/situation analysis, and an assessment of basic options

for building shape and placement.

2. Schematic phase, which entails the commitment to a basic

design strategy and certain key functional, structural, and

architectural aspects of a preliminary design concept.

3. Developmental phase, in which the design concept evolves

in increasing depth and detail, ideally in a manner which

progressively verifies the chosen strategy.

4. 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 relat-

ing thermal considerations in general – and solar parameters

in particular – to more or less equivalent levels of design

information (figure 1.1).

Fig. 1.1

Correlation of typical building design phases with

solar/climate profile levels.

Part 1

8

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 visu-

alizations 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 Appendix C: Glossary of

Terms.

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 (criti-

cal/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.

Part 1

9

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 poten-

tial. Typical scenarios, which are necessary to reliably esti-

mate the performance of a given building design under actu-

ally 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.

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).

Part 1

10

However, results based on such high resolution data can be

deceiving if used to ascertain the impact of a particular design

parameter (e.g., tilting a façade, enlarging an aperture, etc.),

since the raw data may 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 radia-

tion 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 influ-

ence of design-relevant parameters in a consistent manner

throughout various levels of analysis.

1-1 Solar Geometry

11

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.

1-1 Solar Geometry

12

Fig. 1.3

Solar path diagram for summer and winter dates:

Honolulu, USA – Vienna, Austria – Narvik, Norway.

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 Appendix B: Case Studies).

The first step of solar site analysis is to define a set of season-

ally characteristic dates of the year, depending on the basic

properties of the climate zone as well as the focus of the proj-

ect’s solar energy-related objectives. These dates are estab-

lished at the beginning of the profiling method and main-

tained 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 recom-

mended 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 unmanage-

able, with an increased likelihood of losing sight of meaning-

ful 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 equi-

nox as transition. In such locations, design decisions are pri-

marily directed by the the handling of solar geometry for year-

round shading and optimized energy collection systems (pas-

sive or active), while thermal performance issues are of secon-

dary importance.

1-1 Solar Geometry

13

Fig. 1.4

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

1.3.

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 sea-

sons: 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 Posi-

tion 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 hemi-

sphere 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.

1-2 Solar Energy Potential

14


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 defini-

tion 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).


15

Fig. 1.5

Profile of the day sums of solar flux on a tracking surface:

clear skies (A) and overcast (B) – summer/winter, Vienna.

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 informa-

tion 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 geome-

try 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 hori-

zon elevations (e.g., mountains). Since the direct component

of the calculated flux envelope is blocked at low solar eleva-

tions 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).


16

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.


17

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

18

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 geome-

try of such a surface plane in terms of azimuth and tilt deter-

mines its specific solar flux (see also in 2-3 Local Solar Flux).

This quantity will always be less than or equal to the momen-

tary 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 rela-

tion to the flux envelope show the magnitude of these con-

straints (figure 1.9, 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.

1-3 Solar Access

19

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).

The question of how to optimally harvest incident energy is a

special focus when the design objective includes the integra-

tion 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 pos-

sible orientations could most effectively contain apertures for

collecting solar gain, while at the same time giving a first indi-

cation of the potential for overheating (figure 1.14). Further-

more, 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.

1-3 Solar Access

20

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 [deg] of direct beams from fig. 1.10.

Figure 1.12

Photovoltaic panels integrated in the south façade of a power

station in Rieden, Austria, design: stromaufwärts, H. Wirt.

1-3 Solar Access

21

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

22


Existing buildings surrounding or on the site constitute sig-

nificant middle-field obstructions, especially in an urban con-

text. A complete picture of the site situation with respect to

overall solar access can be gained by analyzing a three-dimen-

sional 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 rela-

tive reductions in overall insolation due to existing or

designed obstructions provides a valuable measure for work-

ing 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 descrip-

tion of the handling of geometric surface models in conjunc-

tion with radiation data, see 2-4 Shading & Resultant Flux).


23

Fig. 1.15

Shading pattern on model ground plane:

site situation with existing and projected buildings.

As illustrated in figures 1.16 and 1.17, two and three-dimen-

sional 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 sur-

face 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 perform-

ance ranges based on a minimum of specific design informa-

tion. On the basis of such assessments, the schematic design

concept may then reflect the reasoned commitment to a par-

ticular solar design strategy in the further development of the

overall building design.


24

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).


25

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

26


As other constraints weigh into the developing design, com-

mitted 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 over-

heating 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-dimen-

sional renderings of the flux on detailed areas of a façade (fig-

ure 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.


27

Fig. 1.20

Flux/shading pattern on glazed apertures/surface areas:

façade detail of projected building (SSE).

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 pri-

mary solar systems may be implemented most effectively in

further design stages (e.g., buffer spaces, Trombe walls, pas-

sive cooling ventilation configurations, wind-sheltered collec-

tors, insulating shutters, etc.). Daylighting considerations are

initially treated in connection with the next level of design

focus profiles, 1-6 Solar Gain.


28

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:

glazing structure on a tilted façade.

1-6 Solar Gain through Apertures

29


First considerations about glazing options typically go hand-

in-hand with the more detailed design of the projected build-

ing. In combination with a parametric model for solar-optical

glazing properties, such givens allow a first look at the quanti-

ties 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.


30

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.

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 build-

ings, 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 actu-

ally save energy effectively, artificial lighting systems and

their controls must be integrated well in further design

development.


31

Fig. 1.24

Diurnal plot of solar gain [W] through a glazed aperture –

net flux after obstruction and solar-optical glazing properties.

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).

1-7 Surface Conditions

32


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 mod-

eled 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 (absorp-

tance, air temperature, and solar radiation) result in an effec-

tive temperature pattern at the surfaces of the building model

as illustrated in figure 1.25.


33

Fig. 1.25

Temperature pattern on incident surfaces of model:

aperture and room details of projected building.

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 proper-

ties (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 Cli-

mate Profiles). Plausible values for this basic type of mete-

orological data are commonly available for most sites.


34

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

35


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 spe-

cifically characteristic of design options already decided upon.

As the available amount and stringency of the design informa-

tion grows, calculations requiring increasingly detailed infor-

mation 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 concep-

tual design phase.

Whether explicitly or implicitly, the demand for thermal com-

fort lies at the heart of virtually all the building design objec-

tives that concern energy. The definitive quantification of this

objective, however, is hardly possible since it is part physio-

logical, 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.).


36

Fig. 1.27

Profile of mean resultant temperature [°C] in rooms of model:

summer date, free-running.

Usually only one aspect, the interior air temperature, is evalu-

ated as a basic measure of thermal comfort. Under free-run-

ning 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 simula-

tion, the resulting mean interior temperature can be estimated

if periodically stable conditions are assumed (see also 2-9 Pre-

liminary 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 unac-

ceptable, 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 condi-

tions 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.


37

Given the essential boundary conditions as already defined up

to this stage – net flux through glazing and resultant air tem-

perature at the surface components – diurnal mean tempera-

ture 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 surface elements

comprise the thermal envelope, and then assigning U-values

to the opaque areas and glazed apertures of these exterior sur-

faces. An overall U-value is then easily calculated for the basic

thermal envelope model (without thermal bridges and compo-

nents in contact with the ground) to provide an initial meas-

ure for the thermal quality of the building’s design geometry.

1-9 Transition to Thermal Simulation

38


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 cli-

mate 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 sum-

mer 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


39

for the site. Such base data are commonly monthly mean

quantities applied to mid-month dates (as with the air tem-

perature 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 plau-

sible reference year data from available sources or to generate

annual data sets synthetically (see also 2-9 Preliminary

Performance Assessment).

Part 2

40

Part 2: The Calculation Models

The predominantly visual method of solar profiling as out-

lined 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 paramet-

ric 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.

Fig. 2.1

The principal components of a simulation model for the

thermal behavior of buildings.

Thermal models for building simulation typically represent

the building envelope in the context of its internal and exter-

nal 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 tempera-

ture, 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 com-

ponents to a strictly linear system of equations.

Part 2

41

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 char-

acteristics of the building envelope are by and large independ-

ent of solar gains, many types of meaningful solar evaluations

can be performed without generating an envelope model.

Embedded in a seamless application method, such prelimi-

nary evaluations can then be efficiently done as input calcula-

tions for more comprehensive thermal simulations (see also

Appendix B: 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 func-

tional 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 charac-

terizing a building’s solar potential from its inception (figure

2.2).

Fig. 2.2

Components of the solar gain model.

Part 2

42

Generally stated, the intensity of solar irradiation on a speci-

fied 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. Tra-

ditional methods for generating time-dependent descriptions

of this “solar dimension” typically model the strictly geometric

aspects (in particular, solar position relative to incident sur-

face orientation) in a fairly exact and situation-specific man-

ner.

The meteorological basis, on the other hand, is usually pro-

vided in the form of daily total solar irradiation on a horizon-

tal 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 parame-

ters that clearly distinguish meteorological and terrain condi-

tions 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 “atmos-

pheric 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 conjunc-

tion with tabulated monthly values for the extraterrestrial

solar radiation intensity A, the atmospheric extinction coeffi-

cient B (together with a regional “clearness number”), and the

diffuse radiation factor C.

An alternative and, in certain respects, more flexibly analyti-

cal 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 nomencla-

ture to this particular context as well as to translate any spe-

cial terms into English.

Part 2

43

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 com-

parison of the two methods is not a core concern in the pre-

sented 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 devel-

oped building design is ready for simulation analysis.

2-1 Solar Position

44

2-1 Solar Position

The mathematical equations for calculating solar position rela-

tive 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 posi-

tion, 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 subse-

quent equations:

d M M D

d T

= ⋅ + − − +

= +

int . .30 0 6 3 305

31

c h if

if =

M

M

≠ 2

2

,

. (1)

The ecliptic longitude can be approximated as:

Fig. 2.3

Angles of the earth’s orbit around the sun.

2-1 Solar Position

45

ϕ = ⋅ − + ⋅ ⋅ − +a d d b a d d c0 0b g b gsin . (2)

d

a

b

c

0 28749

098630 [day

1 9137

10206

=

===

.

.

.

.

-1]

With the obliquity of the earth’s axis (23.45°), the solar decli-

nation δ is then given by:

sin sin . sin . sin .δ ϕ ϕ= − ⋅ = − ⋅2345 03979 (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]):

z = ⋅ − ⋅ − ⋅ −− ⋅ − ⋅ − − ⋅0008 0122 0052 2

0157 2 0001 3 0 005 3

. cos . sin . cos

. sin . cos sin ,

ϑ ϑ ϑϑ ϑ ϑ

(4)

whereby

ϑ = ⋅360365

d (in degrees).

Solar positions at a given terrestrial location are generally cal-

culated for mean solar time t (in hours). The shift between

conventional local time t 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:

t t z= + − ⋅ −115 0Φ Φb g. (5)

A transformation of the unit vector directed at the sun’s posi-

tion to an earth-based coordinate system (figure 2.4) yields the

expressions for solar azimuth α and elevation β at a given geo-

graphic latitude Ω :

α = −tan 1 2

1

ee

: − °< ≤ + °180 180α , (6)

β = −sin 13e : 0 90°≤ ≤ °β , (7)

with variables from the transformed vector matrix:

e t

e t

e t

1

2

3

15

15

15

= − ⋅ ⋅ ⋅ − ⋅

= − ⋅ ⋅

= − ⋅ ⋅ ⋅ + ⋅

cos sin cos sin cos ,

cos sin ,

cos cos cos sin sin .

δ δ

δ

δ δ

Ω Ω

Ω Ω

b gb gb g

2-1 Solar Position

46

Unlike in the ASHRAE method, a means for correcting the

apparent solar elevation ′β to account for direct beam refrac-

tion through the atmosphere is also incorporated by Heindl

and Koch:

′ = ++

−β ββ

KK

K1

23. (8)

with

K

K

K

1

2

3

14705

30427

00158

= °= °= °

. ,

. ,

. ,

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 ele-

vation that has not been corrected for refraction yields thor-

oughly misleading results as to whether the sun rises or sets at

all on dates near the solstices.

Fig. 2.4

Angles of the sun’s position relative to a terrestrial location.

2-2 Solar Flux through Atmosphere

47


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 “syn-

thetic” 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 nor-

mal 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). How-

ever, 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, parenthe-

ses 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, I. This equa-

tion involves the time-varying distance between sun and

orbiting earth to account for significant irradiation fluctua-

tions (± 3.34 %) owing to the eccentricity of the solar ecliptic.

It defines extraterrestrial radiation as a diurnal function of the


48

ecliptic longitude (instead of a tabular value of A for a given

month [ASHRAE 1989 p. 27.2]):

I I= ⋅ − ⋅ + °02

1 77 94ε ϕcos . ,b g (9)

with

I0 ===

solar constant (e.g., 1370 W / m

eccentricity of earth's orbit,

ecliptic longitude of the earth

(calculated angular distance

from spring equinox).

2 ),

εϕ

As related by Nehring (1962), the degree to which direct beam

radiation is mitigated due to atmospheric attenuation can be

adequately approximated with a combination of two parame-

ters, Γ and Q, reflecting meteorological haziness and the

inverse effect of the optical air mass at a particular altitude:

I I eND Q= ⋅ −Γ / . (10)

The atmospheric parameter Q is a function of the optical air

mass mA , which is in turn a function of site altitude a and the

calculated solar elevation ′β (refraction-corrected – see the

previous chapter):

Qc

mc

A

= +12, (11)

with c1 = 9.38076, c2 = 0.912018, and

ma

A =⋅ − ⋅

′ + + ′

−2 0015 1 10

0 003

4

2

.

sin . sin.

e jβ β

(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 num-

bers” to correct the average conditions assumed in the atmos-

pheric extinction coefficient B (as well as to account for high

altitudes), only two relatively clear-cut parameters need be

specified (Γ and a).

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 Π 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


49

ASHRAE, which varies strongly from month to month, does

not possess such convenient characteristics for two reasons:

1. The expression for diffuse sky radiation leaves the

inherent dependency on solar elevation embedded in the

value C.

2. 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

I I IHS

ND= ⋅ − ⋅ ′Π e j sin .β (13)

Using the Lambert cosine formula, the direct beam flux com-

ponent incident on a horizontal surface is given by

I I eHD Q= ⋅ ⋅ ′−Γ / sin .β (14)

Consequently, two further equations can be derived for corre-

lating 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 lev-

els, 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

50


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 cal-

culated.

The magnitude of the direct component I iD depends on the

angle of incidence θ i , which is best expressed as follows:

coscos cos sin cos sin sin

sin,θ

α β α β β β

βi

i i i i ie e

e e=

⋅ ⋅ + ⋅ ⋅ + ′ ⋅

+ + ′1 2

12

22 2

(15)

with

α i = azimuth angle of incident plane i,

β i = tilt angle of incident plane i,

e1 , e2 from equation (6), ′β from equation (8),

such that the Lambert cosine formula may be applied:

I I

I

iD

ND

i

iD

= ⋅

=

cosθ

0

if

if

cos ,

cos .

θθ

i

i

>≤

0

0 (16)

With respect to the diffuse sky component I iS , 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 hori-

zontal surface IHS from equation (13), the generally accepted

formula for calculating this component on a plane i tilted at an

angle β i from the vertical is:

I IiS

i HS= ⋅ω , (17)

whereby the view coefficient ω i (equivalent to the angle

factor Fss [ASHRAE 1989 p. 27.14]) is defined as

ω βi i= ⋅ +12

1 sin .b g (18)

Fig. 2.5

Angles of an incident surface plane at a terrestrial location.


51

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. None-

theless, a plausible expression for the diffuse ground-reflected

radiation component I iR 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 i is exposed only to sky and ground:

I I IiR

i G ND

HS= − ⋅ ⋅ ⋅ ′ +1 ω ρ βb g e jsin , (19)

with

ρG = reflectance of ground plane,

ω i 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,

I I I Ii iD

iS

iR= + + (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 nec-

essary 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 eleva-

tions (e.g., a mountainous horizon or other distant-field

obstructions) have on the “flux mix” incident on a given sur-

face 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 meth-

ods 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.


52

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 coef-

ficient of an incident surface plane i (ωG i, ) is thus reduced in

comparison to the case of a horizontal ground plane:

ω βπ

θ β αθ

G i i G i G G, ,sin cos sin .= ⋅ + − ⋅ ⋅ ⋅>

∑12

11

0

b g Δfor all cos G,i

(21)

whereby the angle of incidence expressed in relation to each

tilted ground segment θG i, is given by:

cos cos cos cos cos

sin cos sin cos sin sin

,θ αβ

α β

αβ

α ββ

β

G i GG

i i

GG

i iG

i

= ⋅ ⋅ ⋅ +

+ ⋅ ⋅ ⋅ + ⋅

2

2 2

(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 hori-

zontal, since this orientation is treated in the same manner as

an incident surface of arbitrary orientation.

Fig. 2.6

Angles of an elevated horizon around an incident plane and

coordinate system of the view coefficient.

A final detail should also be pointed out regarding the general

treatment of solar elevation ′β at sunrise and sunset in con-

junction 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 pur-

pose 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 radia-

tion associated with a fictitious full appearance of the sun. Of


53

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. 2.7

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

2-4 Shading & Resultant Flux

54


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 deline-

ated 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 pre-

simulative in nature, that is, an additive compilation of

sequential input information. Coupling a geometric surface

model with radiation results constitutes a basic (yet poten-

tially 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), orienta-

tions, 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 avail-

able 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 gener-

ate 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: con-

structing 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 hori-

zontally limited by a pre-defined base area (ground plane).


55

In accordance with the input metaphor for affixing model

pieces (either to a base or to each other), the position of a sur-

face 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 trans-

formed 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 defini-

tion 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 3-2 Geometric

Modeling and 3-3 Solar Gain Analysis).

Fig. 2.8

Positioning of a surface element in the model space.

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 triangula-

tion with the previously determined diurnal solar positions,

i.e. solar azimuth α and apparent elevation ′β at local time t

(as described in 2-1 Solar Position).


56

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 sim-

plifications 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

J A I B Ij j i j iD= ⋅ − ⋅ , (23)

with

Aj = total area of incident surface plane,

B j = momentarily shaded area,

I i from equation (20),

I iD 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:

J A B IjD

j j iD= − ⋅d i (24)

and

J A I IjS R

j iS

iR+ = ⋅ +e j, (25)

with

Aj , B j , I iD as in equation (23),

I iS from equation (17),

I iR from equation (19).


57

Solar apertures and near-field obstructions (e.g., façade shad-

ing 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 aper-

tures, is that of the room contour. This is specified in basically

the same fashion as an aperture, but without associated shad-

ing elements.

Fig. 2.9

Aperture definition in a planar surface element.

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 meaning-

fully combined output of calculation results for related aper-

tures and other surface sub-areas of the building model (see

also 2-9 Preliminary Performance Assessment).

2-5 Net Flux through Glazing

58


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 inte-

rior 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 θb g . The first of these, total solar energy transmittance, is an estab-

lished glazing parameter (European Standard 410) that speci-

fies 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:

G g J G Gj j jP

jS= ⋅ = + , (26)

with

J j from equation (23),

GjP = primary gain (directly transmitted),

GjS = 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 characteris-

tics, this factor can also be determined computationally (e.g.,

according to EN 410). However, for the purpose informing ini-

tial 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 spe-

cific 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: “Fenestra-

tion”). Thus an appropriate value for the total solar energy


59

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:

G g JJS

j= − ⋅( ) .τ (27)

This is taken as constant for all angles of incidence, meaning

that variations in transmittance τ θb g are assumed to be chiefly

compensated for by the complementary directional reflectance

ρ θb g together with variations in the absorbed radiation that is

emitted outward (figure 2.10). Since the directional distribu-

tion 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 radia-

tion is reflected as such and may potentially contribute to the

direct component incident on a nearby surface (Balcombe

1992 p. 87) – is considered 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 over-

all geometric model (2-4 Shading & Resultant 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 (D) glass. Sources: ASHRAE 1989,

Balcomb 1992.


60

In comparison to the proportionately small quantity of secon-

dary 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 radia-

tion, such that

G J JjP

jD

jS R= ⋅ + ⋅ +τ τ1 2 , (28)

where τ 1 and τ 2 represent the expressions for direct beam

and diffuse transmittance, respectively, with

J jD from equation (24),

J jS R+ from equation (25).

The direct beam transmittance τ 1 is equivalent to the

dependence on the angle of incidence τ θ( ) , which is a further

characteristic of the glazing:

τ τ θ1 = b g, (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 θb g ; 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 com-

plexities 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 fol-

lowing formula quite precisely describes the curves of manu-

facturer data for the incident angle response of glazing trans-

mittance in a generalized form:

τ θ τ θ κb g b g= ⋅ − −[ cos ].1 1 (30)

Hereby the exponent κ represents the sole parameter for

defining the directional profile of the glazing type, independ-

ently 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 con-

veniently characterizes standard categories of glazing assem-

blies 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.


61

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 stan-

dard 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

functionτ θb g for different values of κ.

Since it is assumed that the directional distribution of the dif-

fuse radiation J jS R+ is uniform, the diffuse transmittance τ 2 is

obtained by integrating the directionally dependent transmit-

tance over the half-sphere of all angles of incidence:

τπ

τ θ θ θ θ φπ

2 0

2

0

21= ⋅ ⋅ ⋅ ⋅zz b g cos sin .

/d d

r (31)

Solving this integral with the function τ θb g from the previous

equation yields the following simple expression (Heindl,

Sigmund, and Tschegg 1984 p. 186):

τ τκ κ

κ κ23

1 2= ⋅

⋅ ++ ⋅ +b g

b g b g . (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 character-

ized by a different combination of solar direct transmittance τ and exponent κ.

Fig. 2.11

Transmittance as a function of the angle of incidence for

various exponents: κ parameter of τ θb g .

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 chap-

ter: Spectral Solar Flux).

2-6 Spectral Solar Flux

62


Up to this point, the solar gain model has worked with com-

bined 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 inte-

grated 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):

1. a reduction in the global solar flux, as conveyed in

equations (10) through (12);

2. a shift in the bulk of spectrally distributed flux to longer

wavelengths (λ).

Fig. 2.12

Spectral variation of solar radiation at the earth’s surface for

different values of optical air mass mA. Source: Balcomb 1992.


63

Given a spectral description of extraterrestrial radiation I λb g and equations (10) through (12), a wavelength-dependent

expression for normal direct beam flux IND λb g could be devel-

oped with a spectral air mass mA λb g and haziness factor

Γ λb g . Theoretically, the wavelength dependence of these

parameters could be derived by means of correlation analysis

with reliable meteorological data; unfortunately, such radia-

tion 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 expres-

sion for this parameter, Π λb g , 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 calcu-

lating the spectral distribution of net flux through glazing

based on the spectral resultant flux J λb g 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, chap-

ter 11), the spectral expressions for these solar-optical proper-

ties are still lacking: τ λb g , ρ λb g , and α λb g .

Especially a function for the spectral transmittance τ λb g would be of interest (figure 2.13), since this would allow pro-

files of daylight conditions to be generated practically as a by-

product of the calculation models.

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.


64

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 τ vis (0.38 – 0.77 μm), and

solar infrared transmittance τ IR (> 0.77 μm).

A corresponding expression for at least the visible component

of resultant flux ( J vis ) would thus enable the integrated

assessment of luminous flux in conjunction with its direc-

tional 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.

2-7 Climate Profiles

65


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 defi-

nition 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 perform-

ance of a building design (1-7 Surface Conditions and 1-8

Basic Thermal Envelope).

For this purpose, a parametric description of ambient air tem-

perature is needed which adequately characterizes the applied

boundary condition as a diurnal profile, analogously to the

solar flux profiles. Such an analytical expression for generat-

ing 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 fig-

ure 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 meteoro-

logical 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

f x x x x( ) sin . .= ⋅ ⋅ − ⋅ − ⋅ +RSTUVW

2

21 2 0 4 1

π b g b g (33)


66

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 :

g x x x( ) cos . sin .= ⋅ + ⋅ ⋅RSTUVW

2 2

20 07

ππb g (34)

Calibrating these curves to fit a given temperature swing

between T tmin minb g and T tmax maxb g yields

T t T T T gt L t

t L tt t( ) min max min

max

min maxmin= + − ⋅

+ −+ −

FHG

IKJ ≤ <b g for ,0

T t T T T ft t

t tt t t( ) min max min

min

min maxmin max= + − ⋅

−−

FHG

IKJ ≤ <b g for , (35)

T t T T T gt t

t L tt t L( ) min max min

max

min maxmax= + − ⋅

−+ −

FHG

IKJ ≤ ≤b g for .

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 sun-

rise and corrected differently for clear sky and cloudy

conditions.

Fig. 2.14

Ambient air temperature as a periodic function over the

course of a day. Source: Fuchs, Haferland, and Heindl 1977.

It should be noted that the handling of characteristic climate

data in general – and the reduction of temperature data in par-

ticular – poses a much more complex problem in the climate-

sensitive context of thermal simulation than related here (Feist

1994). Though mathematical descriptions of boundary condi-

tions 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).

2-8 Resultant Air Temperature

67


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 lin-

ear 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 cor-

rect 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 trans-

lated form (with adapted nomenclature).

At a given point on an exposed surface i, the radiant air tem-

perature Ti is defined by the energy balance at the surface:

h T t T W p Tc i i i⋅ − + − =b ge j e j 0, (36)

whereby

hc = convective heat transfer coefficient,

T tb g = ambient air (sky) temperature from

equation (34),

Wi = solar and longwave radiation absorbed

by surface i,

p Tie j = radiation emitted by surface i.

The function p Tie j represents the Stefan-Boltzmann law for

blackbody radiation such that

p T CT

i i rie j = ⋅ ⋅FHGIKJε

100

4

. (37)

The full expression for Wi includes the absorbed quantities of

incident solar radiation and longwave radiation from the sur-

roundings (sky and terrain):

W I C

T t T

i i i i r

G i S G i GG

= ⋅ + ⋅ ⋅

⋅ ⋅ ⋅FHGIKJ + − ⋅ ⋅ FHG

IKJ

L

NMM

O

QPP

α ε

ω ε ω ε, , .b g c h

1001

100

4 4 (38)

Hence the defining equation can be rewritten as:

h T t T I C

T t T

CT

c i i i i r

G i S G i GG

i ri

⋅ − + ⋅ + ⋅ ⋅

⋅ ⋅ ⋅FHGIKJ + − ⋅ ⋅ FHG

IKJ

L

NMM

O

QPP −

− ⋅ ⋅FHGIKJ =

b ge jb g c h

α ε

ω ε ω ε

ε

, ,

,

1001

100

1000

4 4

4

(39)


68

with

α i = solar absorptance of surface i,

I i from equation (20) (less direct beam

component for shaded region),

Cr = blackbody radiation coefficient,

ε i = longwave emittance of surface i,

ωG i, from equation (21),

ε S = emittance of sky/atmosphere,

εG = emittance of surrounding terrain,

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 tb g in the practical application

of these formulae.)

Numerically, equation (39) is solved for the radiant air tem-

perature by applying the Newton iteration method (Koch and

Pechinger 1977). With the starting value taken as the mean

ambient air temperature T , this method yields in the first

approximation

T Th T t T W p T

h p Ti

c i

c

1 = +⋅ − + −

+ ′

b gd i d id i

, (40)

where Wi is from equation (38), p Td i is given by the Stefan-

Boltzmann law applied to T as in equation (37), and

′ = ⋅ ⋅ ⋅FHGIKJp T C

Ti rd i ε

4100 100

3

. (41)

Since the radiative heat transfer coefficient hr can be ade-

quately approximated as the derivative of the emission func-

tion (Haferland and Heindl 1970), the total heat transfer coef-

ficient is expressed in terms of radiant air temperature as

h h p Tc i= + ′e j. (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 nec-

essary differentiation of the thermal network for applying

exterior driving functions. Since this distinction also generally


69

corresponds to different assumed absorptances (wall and

glazing) for calculating the effective boundary condition of

temperature, the specification of surface elements with aper-

tures can be readily used to distinguish the geometric compo-

nents 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 aper-

ture) and orientation i is defined as

TA B T B T

Akres k k k

Ak k

B

k

=− ⋅ + ⋅b g

, (43)

with

Ak = total area of surface,

Bk = momentarily shaded area,

TkA = radiant air temperature calculated for

specific global flux ( I I IiD

iS

iR+ + ),

TkB = radiant air temperature calculated for

specific diffuse flux only ( I IiS

iR+ ).

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 assess-

ments (see next chapter) and as input data for thermal simula-

tion (Fuchs, Haferland, and Heindl 1977; Krec and Rudy

1996).

2-9 Preliminary Performance Assessment

70


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 sur-

faces 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. Appro-

priate U-values can be individually assigned to all of the com-

ponents 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:

U

A

A U

A

Ares

j

k kk

kk

j

jj

=

⋅⋅F

HGGG

I

KJJJ

∑∑∑

∑, (44)

with

Aj = total area of surface element,

Ak = component sub-area of surface,

U k = 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:

G A U T Tjj

k k kres

k∑ ∑− ⋅ ⋅ − =0 0e j , (45)

whereby

Gj = diurnal mean of net flux through

aperture j from equation (26),

T0 = diurnal mean of interior air

temperature (free-running),

Tkres = diurnal mean of resultant air

temperature at surface component k

from equation (43).


71

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 tem-

perature – can be obtained by rewriting equation (45) with the

sums expanded for the room’s enveloping components (aper-

tures j and surface sub-areas k) and solving for T0 .

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 tempera-

ture. A rough estimation of the building’s performance under

winter conditions can be obtained by setting T0 to a fixed

temperature and using equation (45) to calculate the resulting

mean heat flow. Multiplied by 24 hours, this result corre-

sponds 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 para-

metric impact of design decisions on solar gain, the profiles of

radiation and temperature would in general have been calcu-

lated for clear skies, that is, sunny conditions, which empha-

size geometric considerations involving direct beam radiation.

In the summer, this constitutes the critical case and is there-

fore 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 his-

torical 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 behav-

ior 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:


72

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 nomo-

graphs, 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 diur-

nal heat capacity method (DHC), as well as a methodology for

determining the optimum allocation of resources for conserva-

tion and passive solar strategies (Balcomb et al. 1980).

References

73

References

Anderson, B. Ed. (1990) Solar Building Architecture. Cam-

bridge, MA: The MIT Press.

ASHRAE (1989) Handbook: Fundamentals – SI Edition.

Atlanta: American Society of Heating, Refrigerating, and Air-

Conditioning Engineers.

Balcombe, J.D. et al. (1980) Passive Solar Design Handbook,

Vol. 2: Passive Solar Design Analysis. Washington, D.C.: U.S.

Dept. of Energy, DOE/CS-0127/2.

Balcombe, J.D. Ed. (1992) Passive Solar Buildings. Cambridge,

MA: The MIT Press.

Bundesministerium für Bauten und Technik – BMBT (1979)

Katalog für empfohlene Wärmeschutzrechenwerte von Bau-

stoffen und Baukonstruktionen. Vienna: Kommissionsverlag,

Österr. Ingenieur- und Architekten-Verein.

Feist, W. (1994) Thermische Gebäudesimulation. Heidelberg

Verlag C.F. Müller.

Fuchs, H., Haferland, F., and Heindl, W. (1975) Ein Verfahren

zur Ermittlung des wärmetechnischen Verhaltens ganzer

Gebäude unter periodisch wechselnder Wärmeeinwirkung.

Vienna: Berichte aus der Bauforschung 99.

Fuchs, H., Haferland, F., and Heindl, W. (1977) Entwicklung

eines einfach anzuwendenden Rechenprogrammes zur Ermitt-

lung von Luft- und Bauteiltemperaturen sowie Heiz- und Kühl-

leistungen. Vienna: Bundesministerium für Raumordnung,

Bauwesen und Städtebau.

Goulding, J. et al. (1993) Energy in Architecture: The European

Passive Solar Handbook. London: Batsford for the EC.

Haferland, F. and Heindl, W. (1970) “Der Einfluß des Schicht-

aufbaus von Außenwänden auf den Temperaturverlauf unter

periodischen Aufheizungs- und Abkühlungsvorgängen infolge

Sonneneinstrahlung und Heizunterbrechung.” Wärme-Klima-

Sanitärtechnik, 11/1969, 1/1970, 2/1970.

Heindl, W. and Koch, H.A. (1976) “Die Berechnung von Son-

nenstrahlungsintensitäten für wärmetechnische Untersuchun-

gen im Bauwesen.” Gesundheits-Ingenieur 97 12/1976, pp.

301-314.

Heindl, W., Krec, K., Panzhauser, E., Sigmund, A. (1987)

Wärmebrücken. Vienna: Springer-Verlag.

Heindl, W., Krec, K., and Sigmund, A. (1984), Klimadatenka-

talog des Bundesministeriums für Bauten und Technik. Vienna:

Kommissionsverlag, Österr. Ingenieur- und Architekten-

Verein.

Heindl, W., Sigmund, A., and Tschegg, E. (1984) Grundzüge

der Bauphysik. Vienna: Springer-Verlag.

References

74

Hittle, D.C. (1977) BLAST – The Building Loads Analysis and

System Thermodynamics Program. Washington, D.C.: U.S.

Army Construction Engineering Laboratory.

Hunn, B. Ed. (1996) Fundamentals of Building Energy Dynam-

ics. Cambridge, MA: The MIT Press.

Koch, A. and Pechinger, U. (1977) “Möglichkeiten zur Berück-

sichtigung von Sonnen- und Wärmestrahlungseinflüssen auf

Gebäudeoberflächen.” Gesundheits-Ingenieur 98 10/1977, pp.

265-280.

Kossecka, E. (1996) “Stochastic Modelling of Heat Transfer

through Building Walls.” Proceedings of International Sympo-

sium of CIB W67, Energy and Mass Flow in the Life Cycle of

Buildings, Vienna: CIB, pp. 581-586.

Krec, K. (1994) RAUM Benutzerhandbuch. Vienna: Technical

University, Dept. of Building Physics.

Krec, K. and Rudy, M. (1996) “Thermal Building Simulation

for Design Practice.” Proceedings of International Symposium

of CIB W67, Energy and Mass Flow in the Life Cycle of Build-

ings, Vienna: CIB, pp. 519-525.

Lechner, N. (1991) Heating, Cooling, Lighting: Design Methods

for Architects. New York: John Wiley & Sons.

Lemoine, M. et al. (1994) CEC European Solar Radiation Atlas,

Vol. I. Rheinland: TUV for the CEC Renewable Energy

Division.

Linke, F. and Boda, K. (1922) “Vorschläge zur Berechnung des

Trübungsgrades der Atmosphäre.” Meteorolog. Zeitschrift.

39/1922.

Moore, F. (1985) Concepts and Practice of Architectural Day-

lighting. New York: Van Nostrand Reinhold.

Nehring, G. (1962) “Über den Wärmefluß durch Außenwände

und Dächer in klimatisierte Räume infolge der periodischen

Tagesgänge der bestimmenden meteorologischen Elemente.”

Gesundheits-Ingenieur 83 7, 8, 9/1962.

Preuveneers, G. et al. (1994) CEC European Solar Radiation

Atlas, Vol. II. Rheinland: TUV for the CEC Renewable Energy

Division.

Reitz, G. (1939) “Pyranometrische Untersuchungen.” Gerl.

Beitr. z. Geoph. 55/1939.

Schempp, D., Krampen, M., and Mölling, F. (1992) Solares

Bauen: Stadtplanung – Bauplanung. Cologne: R. Müller.

Solar Energy Laboratory (1994) TRNSYS/TRNSHELL User

Manual. Madison, WI: University of Wisconsin.

TU-Wien (1989) SOLRAD/SOLFEN Benutzerhandbuch. Vienna:

Technical University, Dept. of Building Physics.

TU-Wien (1995) WAEBED Benutzerhandbuch. Vienna: Techni-

cal University, Dept. of Building Physics.

Threlkeld, J.L. (1970) Thermal Environmental Engineering. 2nd

ed. Chap. 13, Englewood Cliffs, NJ: Prentice Hall.

Part 3

75

Part 3: The Solar Toolbox

The solar toolbox application is structured closely along the

lines of the solar profiling method outlined in Part 1, 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 con-

ceived to contain the following sequence of modules:

1. solar geometry (geographic site specification – solar

position),

2. solar energy potential (atmosphere and terrain, distant-

field obstructions – solar flux envelope),

3. solar access (incident surface orientations – specific flux),

4. site/building model (full incident surface geometry,

middle-field obstructions – resultant flux),

5. building details (incident surfaces: aperture and room

geometry – resultant flux),

6. solar gain (apertures: solar-optical glazing properties – net

flux).

Consistently comparable results are supported by pre-defined

input sets for standard application cases. In particular, the

selection of standard query dates for seasonal comparison

helps in managing competing design options.

For the more advanced profiling levels (those that go beyond

solar gain modeling), the following tools are tentatively

planned as future extensions:

7. surface conditions (absorptance, ambient air temperature

– resultant temperature),

8. thermal envelope (envelope surface components: U-values

– preliminary performance check),

9. 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

the three chapters of this part (3-1 Solar Site Analysis, 3-2

Geometric Modeling, 3-3 Solar Gain Analysis). In lieu of

lengthy textual descriptions, these chapters contain mainly

graphic depictions of the basic layouts for primary compo-

nents of the user-interface. While the following is clearly not a

user manual, the intended functionality is partially implied by

symbolic conventions for such standard controls as buttons,

input fields, list boxes, and so on. Most of the examples are

shown in the so-called initial state, that is, directly upon

“opening” before user input or editing. Additional comments

are included wherever the operational scheme is not largely

self-explanatory (based on the application background pro-

vided by the previous two parts of this document).

Part 3

76

Fig. 3.1

Screenshot of the online solar workshop.

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.

3-1 Solar Site Analysis

77


The components depicted in this chapter are for generating

basic solar profiles aimed at site and situation analysis prior to

3D modeling.

A general navigation toolbar is located at the bottom of the

main panel for each input level. Buttons for the following

functions are symbolically included in the layout of all the

main panels:

to previous input level

to first input level (1)

this input level done

clear input for this level

generate tabular document of results

for this level (#)

to next input level (when this one

“done”)

to highest input level that is

currently “done”


78

Solar Geometry >>

Input panel >>

>> Solar Position

Output options –

>> solar paths:

>> tracking surfaces: same as for solar paths


79

Solar Energy Potential >>

Input panel >>

>> Flux Envelope

Output options –

>> irradiation profile:

>> solar flux plots:

>> site situation:


80

Horizon elevation edit:


81

Solar Access >>

Input panel >>

>> Specific Flux

Output options –



82

>> solar flux plots:

>> incident angles:

3-2 Geometric Modeling

83


The components presented in this chapter are for generating

building design profiles aimed at schematic analysis of a 3D

surface model. In preparation for modeling with these compo-

nents of the solar toolbox, it is recommended that the user

physically construct an analogous sketch model of the build-

ing design (using thin cardboard, for example) and keep it at

hand during input. This should serve

to help the user get a sure grasp of the necessary geometric

input (numbers and types of elements, their dimensions

and spatial relation to one another);

as an interpretation aid, both for input (comparison with

model control view) and output (orientations, attached

groups, etc. – see components of the modeling area);

to better tie solar profiling procedures into the “regular”

building design process (assuming, of course, that the

designer is relatively accustomed to working with such

sketch models).

From this level on it becomes necessary to graphically support

input, whereby two different types of views are distinguished:

input view – for graphic input, in particular positioning of

points, generally 2D;

control/selection view – overview of the current state of

the entire site and building model (3D in most instances),

also to be used to graphically select existing elements

(contextual functionality).

Buttons representing the following view controls are included

in a number of panels with graphic views (2D/3D):

zoom in (x2)

zoom out (1/2)

top view of model space (north

justified)

front view of current surface

orientation

cut off view at current surface plane

to wireframe options dialogue

(contextual)


84

The input views furthermore contain various tools to

graphically support the positioning of points in the model

space (anchors) and in a plane (line endpoints):

snap to existing anchor points

snap to contour corners/line

endpoints

snap to line intersections

snap to grid nodes (double click:

grid setup)

measure angle between 3 points

measure distance between 2 points

The general navigation toolbar at this level also includes an

additional button:

generate tabular document of

site/bldg model (surface element

data)

For contour input, the necessary tools for drawing and shaping

surface elements are grouped in a separate toolbar:

draw line between 2 points

create rectangle (4 lines) between 2

points

copy lines from existing contour

move selected point (line end or

contour corner)

define contour from sequence of

points

move selected anchor point of

contour

flip contour (invert front to back)

remove selected corner point

add corner point to selected line

segment


85

Site /Building Model >>

Input panel for surface elements >>

>> Resultant Flux on Surfaces

Output options –


86

Contour new/edit:

Orientation new/edit:


87

Blocked areas edit (group base surface):

>> surface model (documentation):


88


>> solar flux detail:


89

>> model insolation (24 hrs.):

>> surface insolation (24 hrs.):

3-3 Solar Gain Analysis

90


The last components of the solar toolbox are for developing

the 3D building model in further detail. The supplemental

geometric information and associated parameters modeled

here enhance the calculation of solar energy dimensions to

focus on more advanced issues of building design.

Some view control buttons are adapted to better support the

input of surface-related details:

3D/2D toggle

(model space / surface plane)

3D: top view of model (as before)

2D: top view perp. to current surface

2D only: front view of current

surface

2D only: right side view perp. to

current surface

2D only: left side view perp. to

current surface

The general navigation toolbar at these levels includes the

following additional button:

generate tabular document of bldg

model details (aperture and room

data, aperture glazing properties)


91

Building Details >>

Input panel for surface details (aperture new/edit) >>

>> Resultant Flux on Details

Output options –


92

Shading element new/edit:

Room new/edit:

same as aperture input (without shading elements)

>> surface model (documentation):


93


>> solar flux detail:


94

>> model insolation (24 hrs.):


95

>> surface insolation (24 hrs.):


96

Solar Gain >>

Input panel >>

>> Net Flux through Apertures

Output options –

>> solar gain detail:


97

>> transmission profile:


98

>> solar gain plots:

99

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 influ-

ential 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, “fin-

ished” 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.

Appendix

100

Appendix

A: Parameter Studies ....................................................102

A-1 Solar Energy Potential..................................102

A-2 Solar Access .................................................110

A-3 Solar Obstruction .........................................119

A-4 Solar Gain.....................................................124

B: Case Studies..............................................................130

B-1 Housing Retrofit ...........................................130

B-2 Office Building Facade.................................157

B-3 Sunspace Design ..........................................160

C: Glossary of Terms.....................................................176

Parts A and B of this appendix contain excerpted results from

a selection of parameter and case studies that were performed.

The final part – Glossary of Terms – is a compilation of defini-

tions, symbols, and units used throughout Part 2: The Calcu-

lation Models. For reference, commonly used synonyms and

related term,s have also been included, in addition to their

generally accepted translation in German. The chapter refer-

ences point to the terms’ main occurrences in parts 1 and 2 of

this document (as well as relevant case studies in some

instances), thus allowing the glossary to furthermore be used

as an index.

As mentioned in the introduction (Approach & Results), the

solar profiling method, which is also the application concept

behind the solar toolbox, was developed on the basis of exten-

sive parameter and case studies. A methodology of scenario-

based design questions was staked out initially, which in turn

motivated a system of output options targeting applicable

answers. Thus the application model itself essentially evolved

“backwards” in that the main criteria for the input procedures

was that they support reaching the targeted output options as

clearly as possible.

Appendix

101

Program Information

Renderings and other forms of documentation were produced

using standard CAD and graphic software to visualize data

generated with existing calculation tools. The following pri-

mary computer programs work with suitable parametric algo-

rithms and were therefore used in the course of investigating

parameter variations for this design tool application:

SOLRAD (SOLFEN): calculation programs for predicting

solar positions and incident radiation on planes tilted at

any given orientation at any geographic location (shading

of incident plane calculated with orthogonal flanking

planes), © K. Krec and E. Panzhauser.

GEBA, GebaControl: program package for dynamically

simulating the thermal behavior of coupled interior spaces

and entire buildings under periodic conditions at any

geographic location, © K. Krec and A.C. Rahn.

For the case studies that went beyond strictly diurnal evalua-

tions, two further thermal calculation programs were

employed:

WAEBED (EuroWAEBED): program package for predicting

annual heating loads and net heating energy requirements

of buildings, with climate data for sites in Austria,

© Technical University of Vienna.

WAEBRU: program package for calculating multi-

dimensional heat flows and temperature distributions

(“thermal bridges”) under constant conditions,

© K. Krec and E. Panzhauser.

A: Parameter Studies

102


A-1 Solar Energy Potential

seasonal profiles:

critical months for cooling, heating (July 15, January 15);

solstices for summer, winter (June 21, December 21).

geographic locations:

Vienna @ 48°15'N/16°22'E/ 200 m;

Honolulu @ 21°2'N/158°0'W/ 0 m;

Narvik @ 68°25'N/17°23'W/ 40 m;

… winter-summer times in respective time zones (15-30°E,

150-135°W).

atmosphere and terrain conditions:

Linke haziness factors 4.5 (clear), 45 (overcast)

… Reitz scatter factor 0.333 (standard)

… diffuse ground reflectance 0.2 (standard).

incident planes:

azimuth/tilt tracking the solar path;

azimuths/tilts ±90°/0° (east/west vertical), 0°/90°

(horizontal).


103


104


105


106

SOLSTICE, tracking surface

date location: meteo. ΣI D ΣI S R+ ΣI

Jun-21 Honolulu: clear 8273 1550 9823

overcast 77 3336 3413

Vienna: clear 9250 1710 10960

overcast 63 3401 3463

Dec-21 Honolulu: clear 5957 1131 7088

overcast 13 1909 1923

Vienna: clear 2442 455 2897

overcast 0 554 554

CRITICAL MONTH, tracking surface


Jul-15 Honolulu: clear 8213 1539 9751

overcast 77 3315 3392

Vienna: clear 8995 1664 10659

overcast 58 3275 3333

Jan-15 Honolulu: clear 6168 1171 7339

overcast 17 2022 2039


overcast 0 659 659


107

CRITICAL MONTH, tracking surface


Jul-15 Narvik: clear 9675 1827 11502

overcast 16 2928 2944

Vienna: clear 8995 1664 10659

overcast 58 3275 3333

Jan-15 Narvik: clear 81 6 87

overcast 0 6 6


overcast 0 659 659


108

SOLSTICE, clear skies, east/west surface

date location: orient. ΣI D ΣI S R+ ΣI

Jun-21 Honolulu: horiz. 6185 1621 7806

E/W vert. 2178 1591 3769

Vienna: horiz. 6230 1805 8034

E/W vert. 2648 1706 4353

Dec-21 Honolulu: horiz. 3264 1231 4495

E/W vert. 1329 1065 2394

Vienna: horiz. 607 589 1196

E/W vert. 419 414 833

CRITICAL MONTH, clear skies, east/west surface


Jul-15 Honolulu: horiz. 6148 1609 7757

E/W vert. 2180 1580 3760

Vienna: horiz. 5982 1758 7740

E/W vert. 2581 1653 4234

Jan-15 Honolulu: horiz. 3498 1266 4764

E/W vert. 1414 1109 2523


E/W vert. 517 478 994


109

CRITICAL MONTH, clear skies, east/west surface


Jul-15 Narvik: horiz. 4787 2047 6834

E/W vert. 2947 1707 4654

Vienna: horiz. 5982 1758 7740

E/W vert. 2581 1653 4234

Jan-15 Narvik: horiz. 1 9 10

E/W vert. 5 6 11


E/W vert. 517 478 994


110

A-2 Solar Access

seasonal profiles:




Vienna @ 48°15'N/16°22'E/ 200 m;

Honolulu @ 21°2'N/158°0'W/ 0 m;

Narvik @ 68°25'N/17°23'W/ 40 m;


150-135°W).


Linke haziness factor 4.5 (clear) … Reitz scatter factor

0.333 (standard) … ground reflectance 0.2 (standard).

ground reflectance 0.2 (20%), 0.5 (additional 30%).

incident planes:


azimuths 0° (south), ±45° (SW/SE), ±90° (west/east), 180°

(north) /tilt 0°;

azimuth 0° / tilts +20° (to sky), -20° (to ground).

shading geometry of incident planes:

minimal orthogonal dimensions to shade a surface

(aperture) area from the peak direct beam.


111

Vienna SOLSTICE: clear skies, vertical surface

date orient. ΣI D ΣI S R+ ΣI peak α /β θ

south 1940 1706 3646 512 0/65 65

SE/SW 2580 1706 4286 600 70/48 53

E/W 2648 1706 4353 655 84/38 37

Jun-

21

north 492 1706 2198 174 105/18 76

south 2135 414 2549 503 0/18 18

SE/SW 1513 414 1928 420 14/17 35

E/W 419 414 833 215 28/14 63

Dec-

21

north 0 414 414 75 0/18 -- Vienna CRITICAL MONTH: clear skies, vertical surface


south 2108 1653 3761 531 0/63 63

SE/SW 2652 1653 4305 607 70/46 51

E/W 2581 1653 4234 649 83/36 37

Jul-

15

north 387 1653 2040 163 0/63 --

south 2414 478 2892 545 0/21 21

SE/SW 1716 478 2194 463 16/19 34

E/W 517 478 994 248 30/15 61

Jan-

15

north 0 478 478 82 0/21 --


112


113

Honolulu SOLSTICE: clear skies, vertical surface


south 0 1591 1591 176 180/88 --

SE/SW 1136 1591 2727 413 102/41 66

E/W 2178 1591 3769 642 103/41 43

Jun-

21

north 1149 1591 2740 250 103/41 80

south 3792 1065 4857 693 0/46 46

SE/SW 2807 1065 3872 686 35/37 38

E/W 1329 1065 2394 493 47/28 53

Dec-

21

north 0 1065 1065 146 0/46 --

Honolulu CRITICAL MONTH: clear skies, vertical surface


south 0 1580 1580 179 180/89 --

SE/SW 1231 1580 2811 432 99/48 67

E/W 2180 1580 3760 646 101/40 41

Jul-

15

north 879 1580 2459 228 101/40 82

south 3737 1109 4847 686 0/48 48

SE/SW 2810 1109 3919 693 37/38 39

E/W 1414 1109 2523 516 49/29 49

Jan-

15

north 0 1109 1109 150 0/48 --


114

Narvik SOLSTICE: clear skies, vertical surface

date orientation ΣI D ΣI S R+ ΣI

south 3375 1835 5210

SE/SW 3466 1835 5301

E/W 3106 1835 4942

Jun-21

north 1343 1835 3178

south 0 0 0

SE/SW 0 0 0

E/W 0 0 0

Dec-21

north 0 0 0

Narvik CRITICAL MONTH: clear skies, vertical surface

date orientation ΣI D ΣI S R+ ΣI

south 3436 1707 5143

SE/SW 3459 1707 5166

E/W 2947 1707 11502

Jul-15

north 1044 1707 11502

south 80 6 86

SE/SW 57 6 63

E/W 5 6 11

Jan-15

north 0 6 6


115


116


117

Vienna: shading devised for peak SUMMER beam

date orientation θ ΣI shaded ΣI

south 65 3646 1702

SW 53 4286 2045

W 37 4353 2255

Jun-21

north 76 2198 1805

south 2549 2270

SW 1927 1452

W 833 592

Dec-21

north 414 412

Honolulu: shading devised for peak WINTER beam

date orientation θ ΣI shaded ΣI

south 46 4857 1676

SW 38 3872 1559

W 53 2394 1205

Dec-21

north -- 1063 1063

south 1591 1590

SW 2727 1630

W 3772 3772

Jun-21

north 2740 2740


118

Vienna: south tilted surface (±20°)

date orient.: ρG ΣI D ΣI S R+ ΣI peak θ

to sky: 0.2 3876 1689 5565 756 43

0.5 3876 2708 6583 872

to ground: 0.2 348 1617 1966 262 83

Jul-

15

0.5 348 3395 4043 500

to sky: 0.2 2536 542 3078 585 1

0.5 2536 732 3269 622

to ground: 0.2 2000 413 2414 449 41

Jan-

15

0.5 2000 802 2803 524

Honolulu: south tilted surface (±20°)

date orient.: ρG ΣI D ΣI S R+ ΣI peak θ

to sky: 0.2 1483 1590 3073 455 71

0.5 1483 2611 4093 588

to ground: 0.2 0 1570 1570 187 --

Jul-

15

0.5 0 3652 3652 458

to sky: 0.2 4709 1163 5872 856 28

0.5 4709 1790 6498 953

to ground: 0.2 2316 1056 3372 451 68

Jan-

15

0.5 2316 2334 4651 650


119

A-3 Solar Obstruction

seasonal profiles:




Vienna @ 48°15'N/16°22'E/ 200 m;

Honolulu @ 21°2'N/158°0'W/ 0 m;

Narvik @ 68°25'N/17°23'W/ 40 m;


150-135°W).




incident planes:

unit areas of building surfaces (see diagrams for

placement) …


(north) /tilt 0°.

shading configurations (see associated diagrams):

middle-field – SW façade area freestanding (none), across

from a building front of the same height at a distance of

10m (vis-à-vis), at right angles to equivalent building

tracts at either end (to NW, to SE);

near-field – aperture area (1m2 glazing + 5cm frame)

recessed 30cm into wall.


120

Vienna: unit aperture area of SW facade

date obstruction ΣJ D ΣJ S R+ ΣJ

none 2652 1653 4305

bldg. vis-à-vis 2097 1653 3750

bldg. tract to NW 1672 1653 3325

Jul-15

bldg. tract to SE 2652 1653 4305

none 1716 478 2194

bldg. vis-à-vis 104 478 582


Jan-15



121


122

Honolulu: unit aperture area of SW facade


none 1231 1580 2811

bldg. vis-à-vis 1042 1580 2622


Jul-15


none 2810 1109 3919

bldg. vis-à-vis 1360 1109 2469


Jan-15


Narvik: unit aperture area of SW facade


none 3459 1707 5166

bldg. vis-à-vis 1700 1707 3407


Jul-15


none 57 6 63

bldg. vis-à-vis 0 6 6


Jan-15



123

Vienna: unit glazed area recessed in aperture

date orientation ΣI ΣJ

south 3761 2180

SE/SW 4305 2967

E/W 4234 3454

Jul-15

north 2040 1701

south 2892 2564

SE/SW 2184 1738

E/W 709 995

Jan-15

north 478 478 Honolulu: unit glazed area recessed in aperture

date orientation ΣI ΣJ

south 1593 1584

SE/SW 2863 1909

E/W 3781 3057

Jul-15

north 2373 1606

south 4847 3367

SE/SW 3021 3920

E/W 1899 2524

Jan-15

north 1111 1111


124

A-4 Solar Gain

seasonal profiles:



geographic location:

Vienna @ 48°15'N/16°22'E/ 200 m … winter-summer time

(15-30°E).




ambient air (sky) temperatures:

diurnal minima~maxima …

extremes in Vienna 16~30 (summer), -7.5~1.5 °C (winter).

incident planes:

unit areas of building surfaces (see diagrams for

placement) …


(north) /tilt 0°;

shading configurations (see associated diagrams):

middle-field – SW façade area freestanding (none), across

from a building front of the same height at a distance of

10m (vis-à-vis), at right angles to equivalent building

tracts at either end (to NW, to SE).

near-field – orthogonal flanking element minimally

dimensioned to shade an aperture area from the peak

direct beam.

solar-optical properties:

glazing types with direct transmittances 0.65 (double: air-

filled, U=3.0), 0,47 (improved: Ar-filled, U=1.3), 0.29

(triple: Kr-filled, coated, U=0.7), 0.17 (reflecting: Ar-filled,

U=1.3).

surface conditions:

solar absorptances 0.5 (light wall), 0.9 (dark wall), 0.1

(glazing).


125

Vienna: unit glazed area in SOUTH façade, unobstructed

date glazing type ΣJ ΣGP ΣGS ΣG

double (air-filled) 3778 1611 209 1910

improved (Ar) 1162 613 1775

triple (Kr) 631 665 1296

Jul-15

reflecting film (Ar) 398 222 620


improved (Ar) 1227 472 1699

triple (Kr) 727 512 1238

Jan-15


Vienna: unit glazed area in WEST façade, unobstructed

date glazing type ΣJ ΣGP ΣGS ΣG


improved (Ar) 1623 686 2309

triple (Kr) 933 744 1677

Jul-15



improved (Ar) 343 160 503

triple (Kr) 191 173 364

Jan-15



126

Vienna: unit glazed area in SW façade with improved

double glazing (Ar-filled, coated, U=1.3, t=0.47)

date obstruction ΣJ ΣGP ΣGS ΣG

none 4322 1519 701 2220

bldg. vis-à-vis 3812 1350 590 1940

bldg. tract to NW 3423 1195 507 1702

Jul-15

bldg. tract to SE 4322 1519 601 2220

none 2194 861 357 1218

bldg. vis-à-vis 612 203 92 295

bldg. tract to NW 2194 861 357 1218

Jan-15

bldg. tract to SE 1225 509 166 675

Vienna: glazed area with improved double glazing (Ar-filled,

coated, U=1.3, t=0.47), unobstructed

date orientation ΣJ ΣGP ΣGS ΣG

south 3778 1162 613 1775

SE/SW 4322 1519 701 2220

E/W 4240 1623 686 2309

north 2058 700 327 1027

Jul-15

horizontal 7742 3058 1261 4319

south 2896 1227 472 1699

SE/SW 2194 861 357 1218

E/W 994 343 160 503

north 478 178 78 256

Jan-15

horizontal 1451 424 236 660


127

Vienna: aperture with improved double glazing, shading

devised for peak SUMMER beam (see A-2 Solar Access)

date orientation ΣI ΣGP ΣGS ΣG

south 3660 1112 593 1705

shaded 1704 633 277 910

SE/SW 4299 1490 698 2188

shaded 2053 752 332 1084

E/W 4355 1665 704 2369

shaded 2268 881 364 1245

north 2210 747 354 1101

shaded 1813 665 292 957

Jun-21

horizontal 8032 3184 1309 4493

south 2556 1089 417 1506

shaded 2270 964 370 1334

SE/SW 1935 759 315 1074

shaded 1450 583 236 819

E/W 837 285 135 420

shaded 601 223 93 316

north 414 154 67 221

shaded 414 154 67 221

Dec 21

horizontal 1196 344 194 538


128

Vienna: surface conditions, unobstructed

radiant air temperature

date orientation: surface min. mean max.

Jul-15 air (sky) temperature 15.62 22.96 29.64

south vert.: glazed 11.54 19.52 27.75

light wall 11.58 22.94 39.04

dark wall 11.54 26.38 50.53

SW vert.: glazed 11.53 19.66 28.88

light wall 11.57 23.55 42.15

dark wall 11.54 27.45 55.29

west vert.: glazed 11.56 19.64 28.97

light wall 11.70 23.44 42.76

dark wall 11.72 27.25 56.40

north vert.: glazed 11.60 19.06 25.82

light wall 11.51 20.94 29.12

dark wall 11.34 22.88 32.62

horizontal: glazed 8.97 17.81 27.10

light wall 8.97 24.79 45.84

dark wall 8.92 31.66 64.23


129

Vienna: surface conditions, unobstructed


date orientation: surface min. mean max.

Jan-15 air (sky) temperature -7.53 -4.02 -0.50

south vert.: glazed -9.74 -5.71 -0.47

light wall -9.84 -3.70 8.40

dark wall -9.94 -1.66 17.54

SW vert.: glazed -9.72 -5.85 -0.63

light wall -9.73 -4.33 7.07

dark wall -9.74 -2.77 14.90

west vert.: glazed -9.72 -6.10 -1.63

light wall -9.72 -5.41 2.68

dark wall -9.72 -4.70 7.10

north vert.: glazed -9.72 -6.20 -2.55

light wall -9.74 -5.87 -1.29

dark wall -9.76 -5.52 0.06

horizontal: glazed -11.09 -7.43 -3.20

light wall -11.14 -6.42 1.33

dark wall -11.20 -5.38 6.10

B: Case Studies

130

B: Case Studies

B-1 Housing Retrofit

“Living in the City” design competition

SITUATION ...

The default site in Pécs, Hungary, is composed of three L-

shaped complexes of the same orientation. Each L-complex

consists of two triple-unit blocks which are currently identical

except for the orientation of the main (entrance) facades:

southeast by south and southwest by west. Extreme repeti-

tiveness and a highly dominant modular system dictate a rigid

orthogonal structure. A single standard building unit is

repeated throughout, combined in blocks and placed with lit-

tle regard for orientation and situation relative to other blocks,

resulting in “dead” end walls and corner areas as well as an

unpleasantly “leftover” exterior.

B: Case Studies

131

DESIGN STRATEGY ...

The proposed redesign encompasses the entire building site,

whereby the architectural problem zones (interior and exte-

rior) have been treated mainly by

re-organizing circulation to activate “dead” areas and

engendering variety out of inherent differences in

orientation and situation.

With a few minor exceptions, the primary load-bearing walls

(exterior and center) and the overall structural system of pre-

fabricated concrete panels have been fully maintained, that is,

not radically remodelled. The need to renovate the roofs

afforded the opportunity to extend the south-oriented blocks

by an additional floor so that this somewhat more attractive

orientation could be better utilised, without obstructing solar

access to other parts of the building complex.

The parking areas (of which there is an apparent shortage)

have been extended and partially buried at basement level to

preserve and structure the court-like, semi-public outdoor

areas.

The circulation system has been reorganised such that the

three stairwells of the predominantly south-oriented blocks as

well as one stairwell each of the west-oriented blocks have

been consolidated in two replacement stairwells with eleva-

tors. The remaining two stairwells in the west-oriented blocks

have been adapted to include elevators as well.

The new vertical circulation units are located as additions at

the west ends of the south-oriented blocks and in the corner

areas formed by the two perpendicular blocks where they abut

towards the northeast. Both allow through-circulation to and

building access from the adjacent street and bus stop flanking

the site towards the north.

All of the apartment floor plans have been remodeled to gen-

erate a broad mix of types ranging from single-room studios to

double-floor “maisonettes”, including small, middle, and fam-

ily size apartments, as well as wheelchair-accessible units.

Nearly all the apartments are augmented by a sunspace,

whereby two different types have been designed according to

the different conditions of the two main facade orientations.

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THERMAL PERFORMANCE & ECONOMIC

CONSIDERATIONS ...

The measures proposed to improve thermal quality include

renewal of all windows (replacement: insulating double light,

U-value=1.3), as well as overcladding of exterior walls and

roof renewal with 10 cm insulation (separated roof build up).

Furthermore, buffer spaces which function as a hybrid

between isolated and direct gain systems were designed for

maximum usability in winter and summer (insulating double

light glazing, separating wall of existing concrete panels unin-

sulated). Two variations of the same standard system – corre-

sponding to two main facade orientations – were developed:

broad and shallow, single-sided toward SSE;

deep, two-sided “sun scoops” on WSW facades, spaced to

avoid solar obstruction.

Selection and development of the thermal performance

improvements were based on computer-aided solar-climatic

analysis and thermal simulations, whereby the focus was on

optimizing relatively simple (affordable) options rather than

on implementing more sophisticated (costly) systems. As

buffer spaces provide only minor savings in overall energy

requirements in this context, their expense is only justified if

they represent more than simply a glazed-over balcony, that is,

if they provide a comfortably usable extension to living spaces

year-round.

NET ANNUAL HEATING ENERGY [kWh/m2]

simulation results:

proposal:base case = 24% | net savings p.a. = 82 kWh/m2

GROSS ANNUAL HEATING ENERGY [kWh/m2]

heating system

efficiency:

base case proposed

improvement

40 % 268 (63)

80 % (134) 32

proposal:base case = 12% | gross savings p.a. = 236 kWh/m2

B: Case Studies

133

B: Case Studies

134

BUILDING & SITE REDESIGN

apartment sizes* &

numbers of units:

base case proposal

35 m2 90 35 m2 36

50 m2 120 65 m2 60

75 m2 36

90 m2 18

100 m2 18

125 m2 3

140 m2 12

TOTAL 210 units

(18 stairwells)

parking for 62

183 units (12

stairwells with

elevators) parki

ng for 102

* not including sunspaces

B: Case Studies

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B: Case Studies

136

B: Case Studies

137

SOLAR/THERMAL EVALUATIONS …

I. SITE PROFILE – SOLAR ACCESS

diurnal solar path, site shading (sunrise–sunset):

1. clear-sky winter day (mid-January) + clear-sky

summer day (mid-July)

radiation curves, day sums (SOLRAD):

2. 4 main facade orientations

II. BASE CASE PROFILE –

for comparing generic system options: standard base case unit

= one central floor (3 of 5) of one centrally located stair unit

(incl. flanking appartments)

A. THERMAL BEHAVIOR (GEBA)

diurnal characterization of standard building unit, periodic

simulation:

1. 2 standard orientations (corresponding to

otherwise identical existing buildings)

2. x 2 seasonal conditions: clear skies/overcast

winter (resultant heating load w./w.o solar gain)

+ summer (comfort: resultant interior temp.)

B. ANNUAL HEATING ENERGY (WAEBED)

overall building unit (base case all floors incl. roof +

basement), time-step simulation:

– 2 standard orientations (corresponding to

otherwise identical existing buildings)

C. THERMAL BRIDGING DETAILS (WAEBRU)

thermal conductance (temperature distribution, heat flow

pattern):

– exterior wall/floor joint

– exterior wall/roof joint

– window frame

III. SCHEMATIC/DEVELOP. DESIGN PROFILES –

A. THERMAL BEHAVIOR

resultant heating load w. solar gain (winter characterizations):

1. refurbished windows, sealed overcladding

insulation -- all exterior walls

2. 1 + sunspace towards south, ventilation directly

to exterior

(2a. 1 + sunspace towards north)

3. 2 without overcladding of separating wall areas

4. 3 + heating ventilation via sunspace

resultant temperatures w. solar gain (summer

characterization):

– necessary measures to attain acceptable comfort

levels

B. ANNUAL HEATING ENERGY

optimum version as determined in A for overall building unit:

– analogous to base case

C. THERMAL BRIDGING DETAILS

where base case proved critical,

optimum version as determined in A:

– analogous to base case

IV. FINAL DESIGN PROFILE

B: Case Studies

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B: Case Studies

139

B: Case Studies

140

B: Case Studies

141

B: Case Studies

142

B: Case Studies

143

B: Case Studies

144

SOLAR DETAILS …

VERTICAL SHADING ANGLES (at irradiation peaks)

in section: WSW SSE

January 19.4 22.6

July 45.9 58.2

SSE-facing sunspace:

CLIMATE PROFILE

average daily temp. [°C]

high low clear skies

January 2.4 -3.7 25 %

July 27.5 15.8 65 %

WSW-facing sunspace:

B: Case Studies

145

DIURNAL THERMAL ANALYSIS…

summer (Jul-15): 17.2°~32.1° C, clear skies

winter (Jan-15): -7.5°~-0.5° C, clear skies/overcast

SIMULATION MODELS OF CENTRAL BAY UNITS:

middle stairwell + 2 flanking apartments on floor 2 of existing

building tracts; model versions for each main orientation

(entrance façade) –

SSE-facing unit

WSW-facing unit

full input documentation separately includes:

thermal properties of building materials, building

component assemblies & dimensions, glazing properties &

dimensions, radiation data, air changes & infiltration,

heat transfer & other coefficients …

B: Case Studies

146

space description

1 BACK ROOMS (north zone, across entire unit):

77.76 m2 (221.6 m3), bounded by –

exterior wall > NNW or ENE,

separating walls > spaces 2 & 3,

interior wall > space 5,

apt. unit sep. walls > eq. neighboring spaces (X),

floor & ceiling > eq. spaces above & below (X).

Heated in some cases (20° C).

Internal gains: 2 daytime occupants.

Heating ventilation in some cases.

2 E-FRONT ROOM (south zone to right of stairwell):

15.39 m2 (92.3 m3), bounded by –

exterior wall > SSE or WSW,

separating wall > space 1,

interior wall > space 5,

apt. unit sep. wall > eq. neighboring space (X),



Internal gains: 2 occupants.

3 W-FRONT ROOM (south zone to left of stairwell):

base cases same as space 2,

design cases (with sunspace) bounded by –

exterior wall = separating wall > space 4,

otherwise same as space 2.

Heating vent. source for space 1 in some cases.

space description

4 SUNSPACE (buffer added to W-front of base case):

8.40 m2 (23.9 m3), bounded by –

exterior glazed wall > SSE or WSW,

ext. flanking walls > ENE/WSW or NNW/SSE,

separating wall > space 3,


No heating (free-running).

Internal gains: 1 daytime occupant.

Shades employed in some cases.

Force ventilated in some cases.

Heating vent. source for space 1 in some cases.

(5) STAIRWELL (between spaces 2&3):

12.96 m2 (36.9 m3), bounded by –

interior walls > spaces 1, 2 & 3,


No heating (free-running).

Internal gains: 1 daytime occupant.

(X) ADJACENT INTERIOR SPACES:

model boundary > all spaces (apt. sep. walls, floor

& ceiling)

Interior air temp. assumed same as adjacent space.

MODEL CONFIGURATIONS & RESULTS …

B: Case Studies

147

base cases:

existing building units (no sunspaces)

existing double fitted windows

no exterior insulation

case distinguishing mean temp. [°C]

label parameters (min~max.)

S Jul-15, clear skies ext. 25.0

(17.2~32.1)

a-S-0 SSE-facing 1: 25.7

(24.1~27.1)

2/3: 26.6

(24.9~27.5)

b-S-0 WSW-facing 1: 27.1

(25.2~28.2)

2/3: 27.4

(25.7~28.8)

case distinguishing 20°: mean load [W]


W Jan-15

ext. temp.: –4.0 (-7.5~-0.5)

a-W-0 SSE-facing, clear skies 1: 2347

(1969~2893)

2/3: 677

(434~878)

b-W-0 WSW-facing, clear skies 1: 2336

(1971~2770)

2/3: 775

(554~1093)

a-W-0/o SSE-facing, overcast 1: 2321

(1932~2828)

2/3: 820

(663~1039)

B: Case Studies

148

basic upgrade options:

new windows with double light, coated glazing (gas fill,

U=1.3/t=0.47/g=0.61)

overcladding insulation of exterior walls (12cm)



a-W SSE, Jan-15, clear skies

ext. temp.: –4.0 (-7.5~-0.5)

a-W-0 – base case 1: 2347

existing windows (1969~2893)

no ext. insulation 2/3: 677

(434~878)

a-W-0+ 1: 1877

new windows (1496~2384)


(354~746)

a-W-1 1: 1159

new windows + (821~1633)

overcladding insulation 2/3: 219

(-48~441)



b-W WSW, Jan-15, clear skies

ext. temp.: –4.0 (-7.5~-0.5)

b-W-0 – base case 1: 2336

existing windows (1971~2770)


(554~1093)

b-W-1 1: 1150

new windows + (827~1543)

overcladding insulation 2/3: 291

(57~563)

B: Case Studies

149

basic design options:

simple sunspace addition (4) to the W-front room (3)

leaving the overcladding insulation off of the separating

wall between the W-front (3) and the sunspace (4)




ext. temp.: –4.0 (-7.5~-0.5)

a-W-1 – see upgrade 1: 1159

no sunspace (821~1633)

2/3: 219

(-48~441)

a-WS-1 1: 1156

sunspace 4 added (817~1640)

insulation on sep. wall 2: 218

(-49~439)

3: -252

temperature in 4: (-729~9)

18.4 (12.7~27.9) °C 4: 0

a-WS-2 1: 1156


no sep. wall insulation 3: -242


18.8 (14.2~26.0) °C 4: 0

question 1 (1a):

How useful are sunspaces that are not oriented due south for

harvesting solar gain? (How comfortable are they in winter?)

sunspaces oriented SSE and WSW



b-W WSW, Jan-15, clear skies

ext. temp.: –4.0 (-7.5~-0.5)

b-W-1 – see upgrade 1: 1150

no sunspace (827~1543)

2/3: 291

(57~563)

b-WS-1 1: 1148


insulation on sep. wall 2: 291

(57~565)

3: -84


12.8 (9.0~21.0) °C 4: 0

b-WS-2 1: 1148


no sep. wall insulation 3: -32


14.5 (11.5~20.7) °C 4: 0

B: Case Studies

150

question 2:

How well does the sunspace perform on a cloudy day?

overcast conditions



a-W SSE, Jan-15

ext. temp.: –4.0 (-7.5~-0.5)

a-WS-2 – see previous 1: 1156

clear skies (817~1640)

2: 218

(-49~439)

3: -242


18.8 (14.2~26.0) °C 4: 0

a-WS-2/o 1: 1177

overcast (825~1614)

2: 364

(219~578)

3: 197

temperature in 4: (44~427)

9.8 (8.1~12.7) °C 4: 0

question 3:

Could anything be gained – energy or space that is partially

usable in winter – by applying a sunspace to the mainly east

oriented “back side”?

unit reversed such that the sunspace (4) is oriented ENE



W Jan-15, clear skies

ext. temp.: –4.0 (-7.5~-0.5)

b-WS-2 WSW-facing – see previous 1: 1148

(824~1538)

2: 291

(57~565)

3: -32


14.5 (11.5~20.7) °C 4: 0

c-WS-2 ENE-facing 1: 838

(space 1: WSW-facing) (-335~1600)

2: 389

(237~563)

3: 256

temperature in 4: (95~433)

8.3 (6.7~9.9) °C 4: 0

B: Case Studies

151

question 4:

What combination of heating and internal ventilation best

distributes the excess energy gained in the south zone?

sunspace as remote source for heating ventilation to back

rooms (1) during peak hours

W-front room (3) as free-running heat source to adjacent

back rooms (1) through additional internal air circulation




ext. temp.: –4.0 (-7.5~-0.5)

a-WS-2 – see previous 1: 1156

no heating vent. (817~1640)

(no exchange betw. 3 & 1) 3: -242


18.8 (14.2~26.0) °C 4: 0

a-WS-3

sunspace 4 as source to 1

circulation betw. 3 & 1 1: 1148

space 3 set at 20°C (818~1632)

3: -240


18.7 (16.3~21.5) °C 4: 0

a-WS-4

sunspace 4 as source to 1

circulation betw. 3 & 1 1: 946

free-running temp. in 3: (617~1453)

21.2 (20.9~21.8) 3: 0

temperature in 4:

19.1 (16.7~22.0) °C 4: 0

B: Case Studies

152

question 5 (5a):

What measures are necessary to control the overheating

tendency of the sunspace? (How effective are they in

maintaining an acceptable level of thermal comfort during a

hot summer spell?)

internal air circulation between the overheated W-front

(3) and the cooler back rooms (1)



a-S SSE, Jul-15, clear skies ext. 25.0

(17.2~32.1)

a-SS-2 – see basic design options 1: 26.4

(no exchange betw. 3 & 1) (24.8~27.9)

2: 27.0

(25.3~27.8)

3: 30.0

(28.1~31.2)

4: 39.9

(32.5~48.1)

a-SS-3 1: 27.0

circulation betw. 3 & 1 (25.3~28.6)

2: 27.1

(25.4~27.9)

3: 28.5

(26.8~29.6)

4: 39.4

(32.1~47.6)

B: Case Studies

153

shading devices used to cut out the direct beam on all

south-facing glazing (2 and 4)

mechanically forced night ventilation of the sunspace (4)



a-S SSE, Jul-15, clear skies ext. 25.0

(17.2~32.1)

a-SS-3 – see previous 1: 27.0

shades not used (25.3~28.6)

no forced night vent. 2: 27.1

(25.4~27.9)

3: 28.5

(26.8~29.6)

4: 39.4

(32.1~47.6)

a-SS-3+ 1: 25.6

shades in use: 7:00 – 14:00 (24.1~27.0)

no forced night vent. 2: 25.2

(24.0~26.0)

3: 26.1

(24.9~26.9)

4: 29.4

(25.7~32.5)

a-SS-4+ 1: 25.6

shades in use: 7:00 – 14:00 (24.0~27.0)

forced night vent. in 4 3: 25.8

(24.6~26.6)

4: 27.7

(23.3~31.2)

B: Case Studies

154

day: external movable shutters louvered to block direct

radiation

night: cooling ventilation to exterior (mechanically forced in

sunspace), net losses in longwave radiation exchange

with sky

B: Case Studies

155

day: predominantly isolated gain sunspace, partial direct

gain to south zone, heating ventilation to north zone

night: thermal masses give off stored heat, improved insulation

& airtightness, closed shutters cut long wave radiation

losses to sky

AUXILIARY HEATING LOAD [W/m2]

min.~max. output to maintain 20 °C

B: Case Studies

156

CONSTRUCTION DETAILS & THERMAL BRIDGES …

B: Case Studies

157

B-2 Office Building Façade

Sintex Pacific Hard Metals Corporation,

Forest Grove, Oregon, U.S.A.

geographic location: 67°0'E/15°30'N

solstices (Jun-21, Dec-21), clear skies …

B: Case Studies

158

question 1 (1a):

How does tilting the foyer façade affect the specific summer

quantities of solar flux? (How do these quantities compare to

the solar flux envelope?)


azimuth -90° (east) / tilts 0°, -18°55'

azimuth 0° (south) / tilts 0°, -18°55'

date orientation ΣI D ΣI S ΣI R ΣI

tracking 9865 1372 217 11454

east vert. 2834 825 836 4495

east tilted 1764 558 1107 3429

south vert. 1785 825 836 3446

Jun-21

south tilted 126 558 1107 1790

B: Case Studies

159

question 2:

What are the minimal overhang dimensions needed to

completely shade the south-tilted façade of the foyer from the

peak direct beam (glare) in summer?

depth of an orthogonal flanking element at the top of a

2.00m height of aperture area, with 2.5cm deep elements

spaced apart 1.15m horizontally (representing the

modular framing structure of the glazed façade)

date depth (orient.) ΣI D shaded ΣI

0 cm (south vertical) 1785 3446

0 cm (south tilted) 126 1790


Jun-21


question 3:

How much of the winter gain is obstructed by this minimal

shading geometry?

date depth (orient.) shaded ΣI

0 cm (south vertical) 3289

0 cm (south tilted) 2784

Dec-21

10 cm (south tilted) 2656

B: Case Studies

160

B-3 Sunspace Design

Haus Felber (design: Mihály Táksas), Himberg, Austria

SITE & SIMULATION MODEL …

geographic longitude/latitude/altitude: 48°15'N/16°22'E/200m

diurnal climate profiles –

summer (Jul-15): 16°~30° C, clear skies

spring (Apr-15): 4°~16° C, clear skies

winter (Jan-15): -6.5°~0.5° C, clear skies/overcast

full input documentation separately includes:

thermal properties of building materials, building

component assemblies & dimensions, glazing properties &

dimensions, radiation data, air changes & infiltration,

heat transfer & other coefficients …

B: Case Studies

161

space description

1 BUFFERSPACE (between structural glue lam.):

11.83 m3, bounded by –

main glazing area (south tilted 0°/45°) > exterior,

shades > space 2,

ventilation flaps > S-intake & N-exhaust (roof),

glue lam. timber > E-wall, space 3, W-attica.

No heating or other internal gains.

Force ventilated in some cases.

2 SUNSPACE (main focus):


shades > space 1,

roof glazing > W-attica & N-roof/-attica,

ext. wall > NE-attica & E-wall (part. glazed),

entrance “box” > E-wall (glazed),

sep. wall/ceiling > spaces 3 & “X” (part. glazed),

floor > basement,

planter & floor edge > S-exterior (“underside”).


Minimally heated in some cases (10°~17° C).

Ventilated directly to exterior in some cases

(intake from basement, exhaust to N-roof).

Shades employed in some cases.

space description

3 ROOM (workshop between sunspace & garage):


sep. wall > spaces 1+2 & “X”,

ext- wall > SW-firewall & E-wall (part. glazed),

ceiling > SW-roof,

floor > basement.



Reference space for the behavior of “X” – see

below (same diurnal temp. assumed at

boundaries).

(TZ) BASEMENT:

temperature zone > spaces 2 & 3 (floors).

Interior air temp. assumed constant: 18° C in

summer, otherwise 16° C.

Ventilation air source for space 2 in some cases.

(X) EXISTING BLDG:

model boundary > spaces 2&3 (sep. walls/ceiling)

Interior air temp. assumed same as space 3.

SUNSPACE CONFIGURATIONS & RESULTS …

B: Case Studies

162

base cases:

shades not used

no forced ventilation of buffer

3cm add. insulation in floor (> basement)

no insulation on separating wall (> existing bldg)

double glazing in sep. wall (> existing bldg)

main glazing area (tilted S): double light, coated (air fill,

U=1.5/t=0.48/g=0.61)




(16.0~30.0)

S-0 1: 45.8

basement: 18° C (27.0~72.3)

2: 46.7

(29.6~69.7)

space 3 free-running 3: 32.7

(27.9~36.1)

B: Case Studies

163

base cases:

shades not used

no forced ventilation of buffer

3cm add. insulation in floor (> basement)

no insulation on separating wall (> existing bldg)

double glazing in sep. wall (> existing bldg)

main glazing area (tilted S): double light, coated (air fill,

U=1.5/t=0.48/g=0.61)



T Apr-15, clear skies ext. 10.0

(4.0~16.0)

T-0a 1: 33.1

basement: 16° C (20.1~54.1)

2: 34.3

(23.4~50.8)


(22.7~25.7)

T-0b 1: 32

basement: 16°C (19.0~53.0)

2: 33.0

heating/cooling load in 3: (22.1~49.5)

-335 (-917~239) W 3: 20



W Jan-15 ext. -3.0

(-6.5~0.5)

W-0a

clear skies 1: 12.6

basement: 16° C (6.1~26.1)

sunspace 2 free-running 2: 14.4

heating load in 3: (8.9~25.1)

658 (416~873) W 3: 20

W-0b Jan-15

overcast 1: 7.5

basement: 16° C (4.5~12.2)



785 (592~950) W 3: 20

W-0c

overcast

basement: 16° C 1: 15.6


1214 (224~2655) W 2: 14.1


706 (519~874) W 3: 20

B: Case Studies

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B: Case Studies

165

question 1:

How effective are basic measures in reducing the extreme

overheating tendency?

shades between buffer (1) and sunspace (2)




(16.0~30.0)

S-0 – base case 1: 45.8


2: 46.7

(29.6~69.7)

3: 32.7

(27.9~36.1)

S0+ 1: 46.1

shades in use: 9:00 – 19:00 (23.9~84.2)

2: 39.7

(26.1~57.2)

3: 31.3

(26.7~34.4)

force ventilating the sunspace (2) via the buffer (1)



S-0 – base case 1: 45.8


no ventilation through 1 2: 46.7

(29.6~69.7)

3: 32.7

(27.9~36.1)

S-01 1: 31.2

shades not used ((18.9~46.9)

2 ventilated through 1 2: 41.4

(27.6~59.2)

3: 31.7

(27.0~34.9)

S-01+ 1: 49.8

shades in use: 9:00 – 19:00 (11.7~30.9)

2 ventilated through 1 2: 33.6

(23.9~44.3)

3: 30.2

(25.7~33.0)

B: Case Studies

166

shades between buffer (1) and sunspace (2)



T Apr-15, clear skies ext. 10.0

(4.0~16.0)

T-0a – base case (a) 1: 33.1


2: 34.3

(23.4~50.8)


(22.7~25.7)

T-0a+ 1: 32.7

shades in use: 9:00 – 19:00 (15.9~66.4)

2: 27.5

(18.6~39.8)


(20.9~24.1)



T-0b – base case (b) 1: 32


2: 33.0


-335 (-917~239) W 3: 20

T-0b+ 1: 32.1

shades in use: 9:00 – 19:00 (15.2~65.8)

2: 26.7


-217 (-815~345) 3: 20

B: Case Studies

167

question 2:

Is there anything to be gained through such measures that

influence the thermal coupling of the sunspace with the

existing building?

leaving out the additional 3cm layer of insulation in the

floor of the sunspace (2) over the existing basement (TZ)



W-a Jan-15, clear skies ext. -3.0

(-6.5~0.5)

W-0a – base case (a)

add. ins. in floor of 2 1: 12.6

sep. wall: base config. (6.1~26.1)



658 (416~873) W 3: 20

W-1a

no add. ins. in floor of 2 1: 12.4




661 (420~877) W 3: 20




(16.0~30.0)

S-01+ – see question 1 1: 49.8

add. ins. in floor of 2 (11.7~30.9)

no add. ventilation of 2 2: 33.6


3: 30.2

(25.7~33.0)

S-11+ 1: 30.3

no add. ins. in floor of 2 (17.2~49.6)



3: 29.8

(25.4~32.6)

B: Case Studies

168

leaving out the additional 3cm layer of insulation in the

floor of the sunspace (2) over the existing basement (TZ)



W-c Jan-15, overcast ext. -3.0

(-6.5~0.5)

W-0c – base case (c)

add. ins. in floor of 2

sep. wall: base config. 1: 15.6


1214 (224~2655) W 2: 14.1


706 (519~874) W 3: 20

W-1c

no add. ins. in floor of 2

sep. wall: base config. 1: 12.6


298 (-692~1786) W 2: 14.1


529 (319~694) W 3: 20

additionally ventilating the sunspace (2) with air drawn

from the basement (TZ) and exhausted directly to the

exterior (> N-roof)




(16.0~30.0)

S-11+ – see previous 1: 30.3

no add. ins. in floor of 2 (17.2~49.6

no add. vent. of space 2 2: 31.4


3: 29.8

(25.4~32.6)

S-12+ 1: 29.0

no add. ins. in floor of 2 (16.7~46.8)

add. vent. (TZ > 2 > ext.) 2: 26.9


3: 29.0

(24.7~31.6)

B: Case Studies

169

shielding the existing building (X) from the sunspace (2)

by insulating the separating wall



W Jan-15, clear skies ext. -3.0

(-6.5~0.5)



no ins. of sep. wall (6.1~26.1)



658 (416~873) W 3: 20

W-2a


sep. wall insulated (5.1~27.6)



632 (371~844) W 3: 20




(16.0~30.0)




no ins. of sep. wall (23.9~44.3)

3: 30.2

(25.7~33.0)

S-21+ 1: 31.1



sep. wall insulated (23.1~46.6)

3: 29.9

(25.5~32.8)

B: Case Studies

170

using single-light rather than double-light (insulating)

glazing in the separating wall



W Jan-15, overcast ext. -3.0

(-6.5~0.5)


double glazing in sep. wall

heating load in 2: 2: 14.1

1214 (224~2655) W (10.0~17.0)

W-3c

single glazing in sep. wall

heating load in 2: 2: 14.1

1115 (54~2587) W (10.0~17.0)




(16.0~30.0)




double glazing in sep. wall (23.9~44.3)

S-31+ 1: 30.9



single glazing in sep. wall (23.9~43.8)

B: Case Studies

171

question 3:

What type of main glazing would be best for the sunspace,

both in winter and in summer?

thermal-insulating glazing properties (standard or high-

performance gas-filled)




(-6.5~0.5)


double, ins. (air fill) 1: 12.6

U=1.5/t=0.48/g=0.61 (6.1~26.1)



658 (416~873) W 3: 20

W-0a-hg

triple, high ins. (Kr fill) 1: 14.3

U=0.7/t=0.29/g=0.48 (8.4~27.1)



549 (349~716) W 3: 20




(-6.5~0.5)

W-0b – base case (b)


U=1.5/t=0.48/g=0.61 (4.5~12.2)



785 (592~950) W 3: 20

W-0b-hg

triple, high ins. (Kr fill) 1: 9.1

U=0.7/t=0.29/g=0.48 (6.6~13.4)



663 (516~799) W 3: 20

B: Case Studies

172

thermal-insulating glazing properties (standard or high-

performance gas-filled)




(-6.5~0.5)


double, ins. (air fill)

U=1.5/t=0.48/g=0.61 1: 15.6


1214 (224~2655) W 2: 14.1


706 (519~874) W 3: 20

W-0c-hg

triple, high ins. (Kr fill)

U=0.7/t=0.29/g=0.48 1: 13.2


96 (-1063~1388) W 2: 14.1


453 (287~593) W 3: 20




(16.0~30.0)


double, ins. (air fill) (11.7~30.9)

U=1.5/t=0.48/g=0.61 2: 33.6

(23.9~44.3)

3: 30.2

(25.7~33.0)

S-01+hg 1: 30.5

triple, high ins. (Kr fill) (18.0~48.1)

U=0.7/t=0.29/g=0.48 2: 31.6

(23.2~40.7)

3: 31.4

(28.8~25.0)

B: Case Studies

173

solar-protective glazing properties (with or without light-

reflecting film + gas-filled)




(-6.5~0.5)



U=1.5/t=0.48/g=0.61 (6.1~26.1)



658 (416~873) W 3: 20

W-0a-rf

double, refl. film (Ar fill) 1: 9.0

U=1.4/t=0.27/g=0.33 (4.8~16.9)



721 (473~922) W 3: 20




(16.0~30.0)


double, ins. (air fill) (11.7~30.9)

U=1.5/t=0.48/g=0.61 2: 33.6

(23.9~44.3)

3: 30.2

(25.7~33.0)

S-01+rf 1: 27.9

double, refl. film (Ar fill) (17.5~41.1)

U=1.4/t=0.27/g=0.33 2: 31.1

(22.9~39.4)

3: 29.7

(25.3~32.4)

B: Case Studies

174

questions 1 & 2:

B: Case Studies

175

question 3:

C: Glossary of Terms

176


TERM

DEFINITION {chapter reference}

CHAPTER

REFERENCE

SYMBOL

[UNIT]

DEUTSCH

(GERMAN)

absorptance

ratio of absorbed to incident radiation on a surface (a.k.a. absorption

factor)

1-7 / 2-5, 2-8 α [--] Absorptionsgrad

absorption factor – see absorptance

albedo – see ground-reflectance Albedo

altitude

distance above (or below) sea level of a geographic location

1-2 / 2-2 a [m] Seehöhe

ambient air temperature

design temperature of the air in the space surrounding any object

being considered (e.g., a building, a thermal energy storage device,

or a solar collector)

1-7, 1-8, 1-9 /

2-7, 2-8, 2-9

T tb g [°C] Außenlufttemperatur

angle factor – see view coefficient Fss

angle of incidence

angle between the line joining the center of the solar disk to a point

on an irradiated surface and the outward normal to the irradiated

surface (a.k.a. incidence angle, incident angle)

1-3, 1-5, 1-6 /

2-3, 2-5

θ i [deg] Einfallswinkel


177

(glazed) aperture

opening in an exterior wall surface (solar collector), through which

unconcentrated solar radiation is admitted

1-5, 1-6, 1-7,

1-8 / 2-4, 2-5,

2-8, 2-9

(verglaste) Öffnung

aperture area

area of a transparent component of a building surface (the

maximum projected area through which unconcentrated solar

radiation enters a collector)

1-5, 1-6, 1-7,

1-8 / 2-4, 2-5,

2-8, 2-9

Ak [m2] Verglasungsfläche

(Öffnungsfläche)

atmospheric attenuation

decrease in the irradiance (and shift in its spectral distribution) of

solar flux while propagating through the atmosphere due to

absorption and scattering by the atmospheric constituents

1-2 / 2-2, 2-6 Abschwächung durch die

Atmosphäre

atmospheric radiation

longwave radiation emitted by and propagated through the

atmosphere (a.k.a. sky radiation)

1-7 / 2-8 Gegenstrahlung der

Atmosphäre

auxiliary heat source

source of heat (other than solar) used to supplement the output

provided by the solar energy system

1-8 / 2-9 (Zusatz-)Wärmequelle

bzw. Beheizung

auxiliary heating energy demand

load applied to the auxiliary heat source

1-8, 1-9 / 2-9 Q aux [Wh] (Zusatz-)Heizwärmebedarf

azimuth

angle between due south and the horizontal projection of the

normal vector of a surface plane

1-3 / 2-3, 2-4 α i [deg] Flächenazimut


178

beam radiation – see direct radiation direkte Strahlung

conduction

transfer of energy (heat) from a warmer to a colder region in a

material medium, whereby kinetic energy is transmitted between

particles without material displacement

1-8 / 2, 2-8,

2-9

Wärmeleitung

convection

heat transfer between a surface and an adjacent fluid medium

(usually air or water) as well as by fluid displacement

1-9 / 2, 2-8 Konvektion

date (day)

day of year

1-1, 1-9 / 2-1,

2-9

M/D

[mo./day]

d [day #]

Datum (Tag)

daylight – see visible solar radiation 1-6 Tageslicht

diffuse (solar) radiation

combined quantity of diffuse sky and (ground-)reflected solar

radiation received on a plane surface

1-2, 1-3, 1-4,

1-5 / 2-3, 2-4,

2-5

I iS R+ [W/m2]

J jS R+ [W]

diffuse Strahlung

diffuse (ground-)reflected radiation

solar radiation received on a plane surface that is diffusely reflected

by surrounding surfaces (terrain)

1-2, 1-3 / 2-3 I iR [W/m2]

J jR [W]

diffuse Reflexstrahlung

(der terrestrischen

Umgebung)

diffuse sky radiation

solar radiation received on a plane surface that is scattered in the

atmosphere

1-2, 1-3 / 2-2,

2-3 I i

S [W/m2]

J jS [W]

diffuse Himmelsstrahlung


179

direct (beam) radiation

radiation received on a plane surface i from a small solid angle

centered on the sun’s disk (a.k.a. beam radiation)

1-2, 1-3, 1-4,

1-5, 1-6 / 2-2,

2-3, 2-4, 2-5

I iD [W/m2]

J jD [W]

direkte Strahlung

directional transmittance

transmittance per unit interval of incident angle (a.k.a. incident

angle response)

1-6 / 2-5 τ θb g [--/deg] einfallswinkelabhängiger

Transmissionsgrad

ecliptic longitude

angular position of the earth in its orbit around the sun (measured

from the spring equinox position)

2-1, 2-2 ϕ [deg] ekliptische Länge

emission

radiant exitance of a body at a given temperature

1-6, 1-7 / 2-8 Abstrahlung

emissivity – see emittance

emittance

ratio of radiation emitted by a body to the emission of a full radiator

(blackbody) at the same temperature (a.k.a. emissivity)

2-8 ε [--] Emissionsgrad

Equation of Time

time adjustment applied to local and mean solar time to account for

certain irregularities in the daily rotation of the earth about its axis

over the course of the year.

2-1 z [--] Zeitgleichung

extraterrestrial solar radiation

solar radiation received at the limit of the earth’s atmosphere

2-2, 2-6 I [W/m2] extraterrestrische

Strahlungsintensität


180

geographic location

terrestrial position on the globe, expressed as latitude/longitude

1-1 / 2-1 Ω /Φ [deg] geographische Lage

(Breite/Länge)

global (solar) radiation

combined quantity of direct, diffuse sky, and diffuse reflected solar

radiation received on a plane surface from a solid angle of 2π sr,

integrated over all wavelengths (a.k.a. total incident radiation)

1-2, 1-3, 1-4,

1-5 / 2-3, 2-4,

2-5

I i [W/m2]

J j [W]

globale Sonnenstrahlung

Greenwich mean time

international reference time scale, based on the time zone meridian

at longitude 0° (Greenwich meridian)

1-1 / 2-1 GMT Greenwich-Zeit

ground-reflectance

average reflectance of the terrestrial surroundings at a given

geographic location (a.k.a. albedo)

1-2, 1-3 / 2-3 ρG [--] Reflexionszahl der

terrestrischen Umgebung

haziness factor

atmospheric parameter (Linke), used together with site altitude to

describe the effect of local meteorological conditions on the

quantity of direct solar flux passing through the atmosphere

1-2, 1-9 / 2-2,

2-6, 2-9

Γ [--] Trübungsfaktor (Linke)

heat flow

energy transfer through various materials and structures (usually

refers to conduction, convection, and radiation combined)

1-8, 1-9 / 2,

2-9

Q [W] Wärmefluß


181

heat transfer coefficient

any one of a number of coefficients used in calculating heat flow (in

this document: total, conductive, and radiative heat transfer coeff.)

1-8 / 2, 2-8 h [--]

hc , hr

Wärmeübergangszahl

(Gesamt- bzw. für

Konvektion und Strahlung)

horizon elevation

effective extent of a distant-field obstruction, expressed as the

angular elevation of the horizon at an azimuth measured from the

center of a site location (assumed for an azimuth interval)

1-2 / 2-3 αG / βG -

ΔαG

[deg]

Horizontüberhöhung

incident angle – see angle of incidence 1-3

incident angle response – see directional transmittance 1-6 / 2-5 einfallswinkelabhängiger

Transmissionsgrad

infrared radiation (IR)

radiation of wavelengths between 780 nm and app. 1 mm

1-6 / 2-6 I IR [W/m2] infrarot Strahlung

infrared transmittance

ratio of the infrared radiation transmitted through a body to the

incident radiation in the same range

2-6 τ IR [--] Infrarottransmissionsgrad

internal gains

energy dissipated as heat inside a space by occupants (body heat)

and appliances (lighting, electrical equipment, etc.)

2 / B-1, B-3 [W] [Wh] Innenwärmen

(Wärmequellen)

irradiance – see specific flux Bestrahlungsdichte


182

irradiation

incident energy per unit area of incident surface, found by

integration of irradiance over a specified time interval (usually an

hour or a day)

1-2, 1-3 / 2-3 ΣI i

[Wh/m2]

[MJ/m2]

Bestrahlung

light – see visible radiation 1-6 Licht

light transmittance – see visible transmittance

Lichttransmissionsgrad

load

heat supplied to the user (positive value: heating load; negative

value: cooling load)

1-6, 1-8, 1-9 /

2, 2-9

Ql

[Wh] [MJ]

Bedarf

local time

hour of day as determined by the time zone convention of the

geographic location

1-1 / 2-1 t [h] Zonenzeit

longwave radiation (LW)

radiation at wavelengths greater than 3 μm, typically originating

from sources at terrestrial temperatures (e.g., ground and other

terrestrial objects)

1-6, 1-7 / 2-8 I LW [W/m2] langwellige Strahlung

(Wärmestrahlung)

luminous flux – see visible radiation 1-6 / 2-6 sichtbare Strahlung (Licht)

mean solar time

hour of day as determined by the apparent angular motion of the

sun across the sky, with solar noon as the reference point for 12

o’clock

2-1 t [h] wahre Ortszeit


183

natural light – see visible solar radiation 1-6 natürliches Licht

(solar) obstruction

anything outside a building which prevents the direct view of part

of the sky (in this document: distant-, middle-, and near-field

obstructions treated separately)

1-2, 1-3, 1-4,

1-5, 1-6 / 2-3,

2-4

beschattender Gegenstand

optical air mass

measure of the length of the path through the atmosphere to the

earth’s surface traversed by extraterrestrial solar radiation,

expressed with reference to the path length in the vertical (varies

with the declination of the sun and site altitude, as well as local

barometric pressure – to be distinguished from meteorological air

mass)

1-2 / 2-2, 2-6 mA [--] relative Luftmasse

orientation

direction that a surface plane faces, expressed as the azimuth and

tilt angles of the plane’s normal vector

1-3, 1-4 / 2-3,

2-4, 2-8

α i / β i [deg] Orientierung

overall U-value

resultant average U-value over the extent of a thermal envelope

1-8 / 2-9 U res

[W/m2K]

mittlerer Wärmedurch-

gangskoeffizient (k-Wert)

perihelion

point in the earth’s orbit when it is closest to the sun (at ∼147 x 106

km)

2-1 Perihel

primary gain

solar radiation transmitted directly through a glazed aperture

1-6 / 2-5 GjP [W]

ΣGjP [Wh]

primäre Strahlungs-

transmission (durch

Verglasung)


184

pyranometer

radiometer designed for measuring the irradiance on a plane

receiver surface which results from the radiant flux incident from

the hemisphere above (within the shortwave range 0.3 – 3 μm) –

see also solar radiation

(References) Pyranometer


hypothetical temperature at an exposed surface, calculated to

account for solar absorptance of shortwave radiation, exchange of

longwave emission with the sky and ground, as well as forced

convection due to wind at a given ambient air temperature (similar

to sol-air temperature)

1-7 / 2-8 Ti [°C ] Strahlungslufttemperatur

radiant flux

quantity of energy transferred by radiation

1 / 2 ΣJ j , ΣGj

[Wh] [MJ]

Strahlungsenergie

radiation

transfer of energy in the form of electromagnetic waves or

associated photons

1 / 2, 2-8 Strahlung

reflectance

ratio of the radiant flux reflected from a surface to the incident

radiation (a.k.a. reflection factor)

2-3, 2-5 ρ [--] Reflexionsgrad

reflection factor – see reflectance


185

resultant air temperature

average radiant air temperature over the extent of a surface area of

uniform orientation and solar absorptance, calculated to account for

(partial) obstruction of direct beam radiation

1-7, 1-9 / 2-8,

2-9

Tjres [°C] resultierende (Strahlungs-)

Lufttemperatur

resultant (solar) flux

incident radiation on the extent of a surface area, calculated to

account for (partial) obstruction of the direct beam

1-4, 1-5 / 2-4,

2-5

J j [W]

ΣJ j [Wh]

resultierende

Strahlungsleistung

(Strahlungswärmestrom)

scatter factor

atmospheric parameter (Reitz), used together with the haziness

factor (Linke) to describe the effect of local meteorological

conditions on the diffuse sky component of solar flux passing

through the atmosphere

1-2, 1-9 / 2-2,

2-6, 2-9

Π [--] Faktor der diffusen

Himmelsstrahlung (Reitz)

scattering

interaction of radiation with matter where its direction is changed,

but the total energy and wavelength remain unaltered

1-2 / 2-2, 2-6 Streuung

secondary gain

solar radiation absorbed and re-emitted to the interior through a

glazed aperture

1-6 / 2-5 GjS [W]

ΣGjS [Wh]

sekundäre Wärmeabgabe

(durch Verglasung)

selective surface

surface of which the properties of reflectance, absorptance,

transmittance, and emittance vary with the wavelength of incident

radiation

2-6 selektive Oberfläche


186

shading coefficient (SC)

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 (related to total solar energy

transmittance)

2-5

shortwave radiation (SW)

radiation with wavelengths less than 3 μm (includes ranges of

ultraviolet and visible radiation)

2-6 I SW [W/m2] kurzwellige Strahlung

sky radiation – see atmospheric radiation 1-7 / 2-8

sky temperature

equivalent blackbody radiation temperature of the atmospheric

longwave radiation received at a horizontal surface

1-7 / 2-8 T tb g [°C] Gegenstrahlungs-

temperatur der

Atmosphäre

sol-air temperature – see radiant air temperature 1-7 / 2-8 “Sonnenlufttemperatur"

solar absorptance – see absorptance 1-7 / 2-8 Absorptionsgrad für

Sonnenstrahlung

solar altitude – see solar elevation Sonnenhöhe

solar azimuth

projected angle between a straight line from the apparent position of

the sun to the point of observation and due south (west positive)

1-1 / 2-1 α [deg] Sonnenazimut


187

solar (thermal) collector

building component or device designed to absorb solar radiation

and to transfer thermal energy so gained to an interior space or a

fluid passing through it

1-3, 1-5, 1-6 /

B-3

Solarkollektor

solar constant

solar irradiance outside the earth’s atmosphere on a plane normal to

the direction of this radiation when the earth is at its mean distance

from the sun (149.5 x 106) – defined as 1367 W/m2 (but may be

revised within ±7 W/m2)

2-2 I0

[W/m2]

Solarkonstante

solar contribution

heat supplied by the solar part of a system

2-9 Qsol

[Wh] [MJ]

solarer Beitrag

solar declination

angle subtended between the earth-sun line and the plane of the

equator (north positive, 0° on equinox dates, varying between

±23.45° on solstice dates)

2-1 δ [deg] Sonnendeklination

solar direct transmittance – see transmittance 1-6 / 2-5 direkter Sonnenenergie-

transmissionsgrad

solar elevation

angle between the line joining the center of the solar disk to the

point of observation and the horizontal plane through the point of

observation, corrected for refraction through the earth’s atmosphere

(a.k.a. solar altitude – the term elevation is preferred here in order

to distinguish this angular dimension from the linear distance of

site altitude)

1-1 / 2-1 ′β [deg] Sonnenhöhe


188

solar energy

energy emitted by the sun in the form of electromagnetic energy or

any energy made available by the reception and conversion of solar

radiation

1, 1-2, 1-4 /

2, 2-9

[Wh] [MJ] Sonnenenergie

solar flux

radiation emitted by, transferred or received from the sun

1 / 2 I [W/m2]

ΣI [Wh/m2]

Sonnenbestrahlung bzw.

-einstrahlung

solar flux envelope

specific flux on (or irradiation of) an ideal tracking surface, i.e.

global flux at a normal angle of incidence

1-2, 1-3 / 2-3 IN [W/m2]

ΣIN [Wh/m2]

Strahlung auf eine

nachgeführte Fläche

solar (savings) fraction

energy supplied by the solar part of a system divided by the total

system load

2-9 f [--] solarer Beitragsanteil am

Gesamtenergiebedarf

(direct) solar gain

net solar flux that passes into the interior through transparent

components of a building’s thermal envelope (e.g., glazed apertures)

1-4, 1-5, 1-6 /

2-5, 2-9

Gj [W]

ΣGj [Wh]

solare Gewinne

solar gain factor – see total solar energy transmittance Gesamtenergiedurchlaß-

grad

solar heat gain factor (SHGF)

specified condition for calculating solar gain through a glazing

system using shading coefficients (SC)

2-5

solar noon

local time of day when the sun crosses the observer’s meridian

tnoon [h] wahrer Mittag


189

solar path diagram

graphic representation of solar elevation versus solar azimuth,

showing the position of the sun as a function of time for various

dates of the year (a.k.a. sun-path diagram)

1-1 Polardiagramm

(Sonnenbahndiagramm)

solar position

location of the sun in the sky hemisphere, expressed as solar

azimuth and elevation angles

1-1 / 2-1 α / β [deg] Sonnenstand

solar radiation– see also solar flux

radiant flux emitted by the sun (primarily in the shortwave range

0.3 – 3.0 μm)

1 / 2, 2-6 [W] [Wh]

[MJ]

Sonnenstrahlung

solar spectrum

distribution by wavelength (or frequency) of solar radiation

2-6 Sonnenstrahlungs-

spektrum

solar time – see mean solar time wahre Ortszeit

solar zenith angle

angular distance of the sun from the vertical, i.e. the angle

subtended by a vertical line to the zenith and the line of sight to the

sun (90° complement of solar elevation)

′β z [deg] Zenitwinkel

specific (solar) flux

power or energy density of solar radiation incident on a surface, i.e.

the rate or quantity at which radiant flux is incident on a surface

per unit area of that surface (a.k.a. irradiance)

1-3 / 2-3, 2-4,

2-8

I i [W/m2]

ΣI i [Wh/m2]

Bestrahlungsdichte


190

spectral (solar) flux

solar radiation per unit interval of wavelength

2-6 I λb g [W/m2.μm]

spektrale

Strahlungsleistung

spectral irradiance – see spectral flux

spectral transmittance

transmittance per unit interval of wavelength

2-6 τ λb g [--/μm]

wellenlängenabhängiger

Transmissionsgrad

specular surface

surface with reflective properites where the angle of visible

incidence is equal to the angle of reflection (in this document: all

surfaces assumed to be uniformly diffuse-reflecting)

2-5 spiegelnde Oberfläche

sun-path diagram – see solar path diagram Polardiagramm

sunspace

solar collector that shares at least one common wall with the

associated building and doubles as useful building space

1-3, 1-5, 1-8,

1-9 / B-1, B-3

Wintergarten

surrounding air speed

air speed (velocity) measured in a specified location near an

exposed surface (e.g., a solar collector or system) – primarily

influences convection (heat transfer coefficient)

1-8 / 2-8 υ [m/s] Wind- bzw.

Luftgeschwindigkeit

temperature

thermal state of matter with reference to its tendency to

communicate energy (heat) to other matter by radiation exchange,

conduction, or convection

1-8 / 2, 2-7,

2-8, 2-9

T [°C] [K] Temperatur


191

temperature zone

space thermally distinguished by the assumed air temperature

(boundary condition node of the thermal network model)

1-8 / 2, 2-7,

2-8, 2-9 /

B-1, B-3

(Temperatur-)Raum

thermal conductance

time rate of heat transferred through a composite structure

separating two temperature zones (for planar components: product

of U-value and area)

1-8 / 2-9 Ck [W/K] (Wärme-)Leitwert

thermal (building) envelope

composite structure of building elements that separate an interior

temperature zone from the exterior

1-8 / 2-9 thermische Gebäudehülle

tilt

angle between the horizontal plane and the normal vector of a

surface plane

1-3, 1-4 / 2-3,

2-4

β i [deg] Flächenneigung

time zone meridian

reference longitude for adjusting mean solar to local time

1-1 / 2-1 Φ0 [deg] Bezugsmeridian der

Zeitzone

total incident radiation – see global solar radiation globale Sonnenstrahlung

total solar energy transmittance

ratio of the total solar energy transmitted through glazing (including

longwave re-radiation to interior) to the incident radiation (a.k.a.

solar gain factor, also related to shading coefficient)

1-6 / 2-5 g [--] Gesamtenergiedurchlaß-

grad


192

tracking collector

solar collector that moves so as to follow the apparent motion of the

sun during the day, rotating about one or two axes (single- or

double-axis tracking)

1-2 nachgeführter Sonnen-

kollektor

tracking surface

theoretical irradiated surface that ideally follows the path of the sun

such that it is always oriented normally to the direct beam

(coordinates of movement are the solar elevation and azimuth

angles, angle of incidence always 0°)

1-1, 1-2 / 2-3 nachgeführte Fläche

transmission factor – see transmittance

transmittance

ratio of the radiant flux passing through a body to the incident

radiation (a.k.a. transmission factor)

1-6 / 2-5, 2-6 τ [--] Transmissionsgrad

(Durchlaßgrad)

ultraviolet radiation (UV)

electromagnetic radiation with wavelengths shorter than visible

light (< 380 nm) and longer than X-rays

2-6 IUV [W/m2] UV-Strahlung

ultraviolet transmittance

ratio of the ultraviolet radiation transmitted through a body to the

incident radiation in the same range

2-6 τUV [--] UV-Transmissionsgrad

U-value

heat flow through unit area of a planar component of the thermal

envelope under steady conditions per unit temperature gradient

maintained in the direction perpendicular to the area

1-8 / 2-9 U k [W/m2K] Wärmedurchgangs-

koeffizient (k-Wert bzw.

flächenbezogener Leitwert)


193

view coefficient

angular portion of the sky hemisphere to which a surface is exposed

(similar to angle factor)

2-3 ω i , ωG i,

[--]

Einstrahlzahl

visible (solar) radiation

radiation in the wavelength range that stimulates the human optic

nerves, i.e. 380 - 780 nm (a.k.a. light, luminous flux)

1-6 / 2-6 I vis

[W/m2]

sichtbare Strahlung (Licht)

visible transmittance

ratio of the visible radiation transmitted through a body to the

incident radiation in the same range (a.k.a. light transmittance)

2-6 τ vis [--] Lichttransmissionsgrad

wind speed – see also surrounding air speed

air speed in meteorology

υ [m/s] Windgeschwindigkeit

zenith

highest point of the sky hemisphere, i.e. the point vertically above

the observer

Zenit

Integrated Methods of Passive Solar Building Design

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