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Development of a cold climate severity index
Energy and Buildings, 4 ( 1 9 8 2 ) 277 - 283
277
Development of a Cold Climate Severity Index T H O M A S A. M A R K U S
Department of Architecture and Building Science, University of Strathclyde, 131 Rottenrow, Glasgow G40NG (Gt. Britain)
For several purposes connected with planning, economic, and building policy, it is necessary to be able to define the climatic severity o f a region, zone or building site. In housing this is required in order to make more rational decisions on the partition o f fixed capital resources in retro-fit; to assess the housing potential o f alternative regions and sites; to draft better regulations and codes, and to distribute fuel subsidies in a way which is socially just. The index should take into account, at least, air temperature, useful radiation, and wind. It has to be related to assumed, standard house constructions, and the paper develops ideas for how this might be done. It concludes with a form o f multiple regression equation in which three coefficients define the mass/insulation, solar 'admittance', and wind permeability characteristics o f houses, and the index (proportional to annual heat loss) is derived from air temperatures, radiation and wind data.
INTRODUCTION
This paper describes an approach to the development of a Climatic Severity Index (CSI) for use in cold climates. In principle, there is no reason why the techniques proposed, once developed, should not be equally well used in warm climates. The need for such an index is argued; its nature is described; techniques for its development are proposed; finally, its use and future application are also described.
THE NATURE OF A CLIMATIC SEVERITY INDEX
(csi) In some ways a CSI resembles a thermal comfort index. The former would perform for the building an analogous task to that 0378-7788/82/0000-0000/$02.75
achieved for the human b o d y by the latter. It would indicate by a single, meaningful number, the stress placed upon a building's energy systems (analogous to the metabolic rate and the autonomous thermoregulatory systems of the body} by any given environment. As is the case in the physiological systems, this involves making certain assumptions a b o u t the state of the building organism - - i t s 'deep b o d y temperature' and the degree to which the control mechanisms were stressed. It has, of course, been found that no single index which combines the main environmental variables which affect c o m f o r t - air temperature, radiation, air velocity and h u m i d i t y - - c a n adequately express the quality of the environment in the absence of a definition of the two main human variables of clothing (insulation} and activity level (heat generation}. Even for physiologically-based, b o d y thermal comfort indices there has been a traditional problem of different methods used for indoor and o u t d o o r comfort. The normal indices have been developed for indoor use; out of doors "windchill" and other methods have been used. The Author has resolved this problem elsewhere [ 1 ] and applied a c o m m o n index of thermal c o m f o r t (Gagge's DISC} to all conditions. Figure 1 shows how an outd o o r location can have air temperature, sun, and wind all taken into account in terms of DISC, using an assumed level of clothing and activity. In this sense, therefore, a CSI already exists, but it is for the body, and not for the building. Figure 2 shows the DISC iso-curves in a specific tropical climate for the entire day and year. For buildings in cold climates the four main environmental variables which will determine climatic severity are air temperature, wind velocity, solar radiation, and rainfall. The first three are obvious, and relatively well studied; rainfall has often been ignored. Its © Elsevier S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
278
2
(a)
4
6
8
10
12
14
16
18
20
Distance (m)
2
4
6
8
10
12
14
(b)
16
18
20
Distance Ira)
Fig. 1. (a) Velocity isopleths; (b) DISC isopleths in wind o n the sunny and shady sides of a shelter wall. Clothing, 2.4 clo; activity, 1.0 met (= 58 W m-2); t a = --5.0 C, t o (in sun) = +5.0 C, t O (in shade) = t a. (After Markus.) o
000~_!~ :~
00
---
#
9.ool-
{-~a;
~s.ooI2 T0 ~
"PO J
F
M
A
M
J
J
A
S
O
N
D Months
Fig. 2. DISC values based on a specific set of tropical meteorological conditions.
N.B., DISC lines do n o t follow exactly the shapes of SET lines in Fig. 4. 11, as wind velocity, V, varies. (After Markus.)
,
o
effect is to saturate porous external wall materials, and thus reduce the theoretical, or 'dry' insulation values often found in calculations. However, as insulation standards have increased, the effect is marginal, and in this paper it is ignored. With lower insulation standards, however, this would not be safe. The combined effect of the other three variables is such that an infinite set of combinations could produce the same stress, i.e., required energy consumption, to give a stated internal environment. Any sets which give the same stress should be signified by an identical CSI. However, this is clearly impossible to achieve in the absence of assumptions about the building i t s e l f - and in particular about those properties which critically determine its response to air temperature, wind and radia-
279 tion. These are: insulation and mass; fenestration and air leakage. The effect of air temperature is less p o t e n t in a well-insulated building than in a poorlyinsulated one, and in one with infinite insulation it would be of no significance. Wind is only significant insofar as air can enter a building through designed or fortuitous openings; in a tightly-sealed structure wind exposure is of little significance. Radiation, to be a useful source of heat gain, requires transmitting areas of adequate size, of the correct orientation, with suitable glazing properties, unshaded by obstructions, and with a building structure which has the mass (storage) characteristics which enable it to absorb and later release the energy at a suitable rate. Buildings with small, northfacing windows (in Northern latitudes) and lightweight structures are unable to utilise radiation, even if plenty is available. There are other analogies with thermal comfort indices. The size and shape of a building will affect the ratio of envelope to volume. All the building variables are a function of envelope area, and since the thermal stress must be measured against a uniform q u a n t i t y - - s a y unit volume of controlled s p a c e - - a known ratio of envelope to volume has to be used. In the case of the human b o d y this is the Dubois surface area, whereby all heat gain and loss processes are given for a unit surface area of body. The Dubois area allows for variations in b o d y shape and size. A similar surface or volume unit has to be found for b u i l d i n g s - - t h e POP and VOLM ratios developed by the Building Performance Research Unit will do admirably [2]. Clearly, therefore, the CSI has to relate to a building of a certain shape and size and, hence, volume to envelope ratio, and with a specified combination of thermal characteristics. In fact it is directly proportional to the energy consumption for that building in that climate. It might be argued that this is an unnecessarily complex, and possibly inaccurate predictive tool, when the designer has several choices: sophisticated, mathematical models (such as the Response Factor) [3] ; analogue methods; and computer-based simulations using, say, finite difference methods. But all these are design tools, requiring an initial statement of design intention and then yielding energy predictions. The CSI is a decision tool for other
uses, as the following section describes, and its purpose is to state something a b o u t the climatic variations in a region, country, zone or site, prior to specific design solutions being proposed and tested.
THE NEED FOR AN INDEX Many decisions on housing and building require the comparison of one location with another from the point of view of climate and likely energy demands to maintain stated internal environments. In the case of housing this need is particularly clear, as often a wide range of options is available. Specifically, the following problems require such an index for a rational solution; some of these have been developed b y the Author in an earlier paper [4].
Design-location decisions National and regional, as well as urban agencies usually have a range of sites which can be developed for housing. Many factors will affect the decision, b u t one, for a particular choice, should be the energy consumption consequences for the individual household, the local authority and the country. This will have to be predicted at the strategic stage, before individual designers have been appointed or individual designs are available for detailed energy appraisals. For this purpose the sites must be compared on a standard (energy-related) severity i n d e x - and this involves making assumptions of a general kind regarding the thermal properties of the proposed housing. The index, therefore, will be house-specific, b u t it can be based on a range of 'model' or standard houses.
Building control As far as energy building legislation is concerned, the aim is to achieve a defined level of thermal comfort at a reasonable (or practically 'minimised') expenditure of fuel. Since labour mobility, wage rates, tax legislation, social security benefits, etc., are normally all factors operating as uniform systems within national boundaries, it is reasonable to aim for fuel expenditures which are similarly uniform, irrespective of the location of a family. This is especially important as an issue of social justice, where labour has to move from one part
280 of a country to another as a result of economic policies. Therefore, thermal standards have to be modulated, to become proportionately more stringent as the climate becomes more severe. The aim is to keep fuel consumption, say, per unit volume, identical for identical house types, irrespective of location. To achieve such a modulated and varied set of prescriptive standards, an index of climatic severity is needed. This will probably be used on average regional data, although even these will give rise to anomalies, since local and micro-climatic variations within a region can be substantial. It may be better to accommodate these by careful design based on nonmandatory design guides and Codes, than by legislation of too complex a kind. Optimum distribution o f scarce resources In many countries a substantial portion of the resources being invested in buildings, especially housing, is in the form of improvement to the existing stock, rather than new building. The total is limited by a capital budget; how much should be invested in a particular region, city or individual building scheme is usually determined by some measure of the defectiveness of the existing s t r u c t u r e - - i n terms of space, services, fabric or amenities. An important factor is the upgrading of inadequate insulation, heating systems, ventilation, etc., and to determine this, existing houses will have to be assessed in terms of the climate in which they are located and their thermal properties. It would be possible to carry out individual thermal (or annual fuel expenditure) appraisals for each house; but it is unlikely that a political framework for resource allocation can be found within which the outcome of such exercises could be utilised. The alternative is to work by a CSI, which takes into account the range of house types actually existing in (say) a region by matching them in various proportions against a range of standard or 'model' types. Justice in distribution of social security assistance In North America and m a n y Western European countries, social security payments ..... supplementary benefit, u n e m p l o y m e n t benefit, fuel subsidies -- are available. Generally, they try to take into account social factors, such as family size, the number and ages of children,
the presence of elderly, sick or disabled people in the household, and some crude physical factors, such as the age and size of the house and the type of heating. They generally fail to take into account the climate, or the real thermal properties of the dwelling, even to such an elementary extent that a house at the end of a terrace, or in mid-block, is rated as being in similar need to one in mid-terrace, or at the extremity of a block; even though this single variable could cause fuel consumption differences of the order of 20 - 40%. The administration of such payments precludes the detailed survey and appraisal of each applicant's house and site climate, but it is possible for relatively unskilled personnel to assess, from a range of standard house types, that which approximates most closely to the specific one, and to select from a standard CSI map the appropriate value, upon which the benefit payments would be based. Economic planning Long-term industrial development, job location, transport planning and land-use policy require a building, and specifically, housing, energy forecasting tool. The CSI should be used for this purpose.
SPECIFIC DEVELOPMENT OF A CSI There are two ways of proceeding in the development of the CSI. The first is by s y n t h e s i s - that is, by establishing the form of the relations between each of the three climatic variables and heat loss or gain for each of the three building variables, making the assumption that each variable, in its set of three, is independent of the other two; establishing a form of multiple relation between heat loss/gain and the three climatic variables in which the coefficients are functions of the three building variables; and finally assuming that the CSI is directly proportional to the annual heat loss. The form of the relationship will be Q = a T - - - b R +cW where Q is the annual heat loss (kW h/m3), T a selected value of o u t d o o r air temperature (°C), R a selected value of total radiation (W/m2), W a selected value of wind velocity (m/s), and a, b and c are appropriate coef-
281
ficients for specific types of construction. CSI = K X Q, where K = a constant. If the three individual relationships are non-linear, then a non-linear multiple relationship will apply. It seems worthwhile, therefore, to make the assumption of linearity as a first step. The second method for the development of the CSI is by actual measurement, either in the field or in accurate analogues or in detailed simulations based, say, on finite difference techniques, e.g., ESP [ 5 ] . On the assumption that each of these three, carried o u t with sufficient care, yields the same, and 'true', result, they can then be obtained for a very large number of combinations of the three climatic variables. Analysis of the results would enable a generalised multiple relationship to be obtained, linear or not, in which the coefficients would, again, be functions of the three building variables. The correspondence between the values of the coefficients obtained in this way, and those resulting from the first method, is a measure of the accuracy of the first method. The mass/insulation and air temperature relation The first problem in this relation is the combination of mass and insulation into a single characteristic. At one end of the scale is the lightweight, insulated structure, and the heavy, uninsulated structure; at the other end the light, uninsulated structure of low mass. In between lie the combinations of mass and insulation giving intermediate values of annual heat loss. Muncey's Response Factor technique
y
5
[6] could be used to construct a combined mass/insulation scale (M/I). Assuming that a single index, linearly related, can be used, the relations are as in Fig. 3. The temperature scale on the X axis is one that represents the o u t d o o r temperatures such that, at a particular value, the annual heat loss through all structures is equal; this will be a temperature lower than the indoor temperature, where natural heat gain from solar radiation exactly compensates for the loss due to temperature difference. This is analogous to the 'base' temperature concept of the Degree Day method, and to Dupagne 'temperature without heating' [7]. The coefficient a represents the slope for a unique construction, i.e., a unique combination of mass and insulation. The radiation 'admittance'and solar radiation relationship In this instance again, the property of the building which determines its ability to utilise any available solar radiation is a combination of a number of individual properties; we shall call it solar 'admittance'. It will be a function of window size and orientation; the nature of the glass/blind materials used in the windows; and the mass of the structure, particularly o f the floor, upon which the radiation falls, is absorbed and released over a period of time, as long-wave radiation and sensible heat. Davies [8] has developed an appropriate technique for defining the window's characteristics. Assuming, again, linearity between annual heat gain and solar 'admittance', the relation is as shown in Fig. 4. There is a level of radia-
c; 2
=
o c
.E
Air temperature, T
Fig. 3. Air temperature (T) and annual heat loss per unit volume (Qa/m 3) for three values of mass/insulation (M/I).
Radiation, R
Fig. 4. Radiation (R) and annual heat gain per unit volume (Qa/m 3) for three values of radiation 'Admittance' (A).
282
tion at which differences between admittances no longer have any significance--this is probably at such low levels of direct radiation that almost all available radiation is in diffuse form, hence obliterating the orientation effect and also, to a large extent, the effect of window size, since this diffuse radiation is continuously available to opaque surfaces and will ultimately have effects through absorption and transmission similar to that of the diffuse radiation transmitted through transparent areas and absorbed by internal surfaces. The coefficient b represents the solar admittance of a particular combination of characteristics. The p e r m e a b i l i t y and w i n d relation
In many ways this is the least understood of the three relations. Knowledge of what aspects of construction cause variations in air change is, as yet, relatively primitive. It is, of course, some type of 'permeability' which is involved, including the effects of gaps and cracks around windows and doors, construction joints, the effect of flues, ventilators, and other designed or fortuitous openings. In combination each of these responds not only to variations in wind pressure between inside and out, but also to the effect of 'stack' ventilation caused by differences in air temperature between inside and out. So, if the climatic variable of wind speed alone is to be used, standard assumptions about stack ventilation have to be made. Warren [9] has shown that linear relations between wind velocity and air change are a reasonable assumption. The combined effect of wind speed and stack effect is expressed as a relation between heat loss and wind permeability;with a speed at which all buildings have zero loss, equivalent to a such low pressure differential that permeability no longer has any significance. Figure 5 shows the assumed linear relation between velocity and air change rate for a range of permeabilities. The coefficient c measures the slope of the permeability line. Synthetic combination
The combined annual heat loss Qa will be represented by the multiple equation
J
r
<
Wind velocity, W
Fig. 5. Wind velocity (W) and annual heat loss per unit volume (Qa/m 3 ) for three values of wind permeability (P).
is represented by an appropriate coefficient and each of the climatic variables is accounted for. Of course, the solution has many assumptions, approximations, and relatively unkown features. Its advantages, if these features can be studied and resolved, are that individual characteristics of the construction can be studied in isolation; the information required for any given house type is minimal; and all the important aspects of climate are accounted for. 'Real' m e a s u r e m e n t
The validity of the synthetic approach can only be established by comparing the results with those obtained from accurate field measurements in real houses, or equally accurate analogue or digital simulations. In the programme of work referred to under the section headed "Current Work", the finite difference techniques of the ESP program are used and it is intended, initially, to establish the coefficients a, b and c for 4 out of a combinatorial set of 27. This is for 3 values of each of M/I, A and P. The multivariate data can be analysed to yield a multiple linear, or non-linear regression, and the correspondence between the two sets of coefficients established.
QUESTIONS AND APPLICATION
Qa = a T - - bR + c W
The paper has already indicated the questions which have to be resolved for the CSI to
in which each of the three building properties
be fully operational.
283 (i) The three sets of relations have to be analytically verified. (ii) The values of T, R and W for a particular location have to be determined. They will clearly depend on the meteorological data for the region; but they will have to be further modified for some uses by local and site data, including microclimatic effects of sun or wind shading, frost hollows, funnelling, etc. (iii) The selection of the most useful range of values for each of the three properties of mass/insulation, solar 'admittance', and permeability is critical; in combination, they should represent all feasible and recommended forms of house construction. (iv) The correction for shape and size, to allow all indices to be in terms of unit volume, requires further analysis. One solution is to use a standard envelope to volume ratio and apply correction factors for deviations from it. (v) Once the CSI is calculated it will be necessary to map it on a regional basis -- so (say), 27 maps would be available for any particular region, composed of the 3 X 3 X 3 combinatorial range of house types. For decisionmaking it would only be necessary to assess which of the 27 types most closely represented the house(s) in question, and this selects the map to be used. (vi) Finally, if the CSI concept was to be applied to other building types, all three of the analytical relations would have to be specifically determined for that type of building. CURRENT WORK This paper represents ideas relevant to a current research project sponsored by the
Scottish Development Department, and being carried out by the A u t h o r with his colleagues, Dr J. Clarke and Mr E. N. Morris. The paper is, however, his own, and does not commit either his colleagues or the SDD to these views.
REFERENCES 1 T. A. Markus and E. N. Morris, Buildings, Climate and Energy, Pitman, London, 1979, Ch. 3. 2 Building Performance Research Unit, Building Performance, Applied Science Publ., London, Chap. 6, 1979. 3 R. W. R. Muncey, Heat Transfer Calculations for Buildings, Applied Science Publ., London, 1979. 4 T. A. Markus, Fuel poverty in Scottish homes, A r c h i t e c t s ' J . 23 May, 1979, pp. 1077 - 1082. 5 J. A. Clarke, Energy implications in building design : a thermal simulation design model, Proc. 3rd Int. Symp. on the Use o f Computers for Environmental Engineering Related to Buildings, Banff, Canada, May, 1978, National Research Council of Canada,
Ottawa, 1978. 6 R. W. R. Muncey, Heat Transfer Calculations for Buildings, Applied Science Publ., London, 1979. 7 A. Dupagne, Methodology for low-cost housing design including new energy-saving concepts, Int. Conf. on Energy Resources and Conservation Related to Built Environment, Miami Beach, Florida, October 26 - 31, 1980. 8 M. G. Davis, Useful solar gains through a glazed
Southfacing wall in the U.K. climate, to be published in Built Environment. 9 P. R. Warren, Natural infiltration routes and their magnitude in houses -- Part 1 -- Preliminary studies of domestic ventilation, Building Research Establishment, Garston, U.K., 1976, Rep. No. ES 4/74.
277
Development of a Cold Climate Severity Index T H O M A S A. M A R K U S
Department of Architecture and Building Science, University of Strathclyde, 131 Rottenrow, Glasgow G40NG (Gt. Britain)
For several purposes connected with planning, economic, and building policy, it is necessary to be able to define the climatic severity o f a region, zone or building site. In housing this is required in order to make more rational decisions on the partition o f fixed capital resources in retro-fit; to assess the housing potential o f alternative regions and sites; to draft better regulations and codes, and to distribute fuel subsidies in a way which is socially just. The index should take into account, at least, air temperature, useful radiation, and wind. It has to be related to assumed, standard house constructions, and the paper develops ideas for how this might be done. It concludes with a form o f multiple regression equation in which three coefficients define the mass/insulation, solar 'admittance', and wind permeability characteristics o f houses, and the index (proportional to annual heat loss) is derived from air temperatures, radiation and wind data.
INTRODUCTION
This paper describes an approach to the development of a Climatic Severity Index (CSI) for use in cold climates. In principle, there is no reason why the techniques proposed, once developed, should not be equally well used in warm climates. The need for such an index is argued; its nature is described; techniques for its development are proposed; finally, its use and future application are also described.
THE NATURE OF A CLIMATIC SEVERITY INDEX
(csi) In some ways a CSI resembles a thermal comfort index. The former would perform for the building an analogous task to that 0378-7788/82/0000-0000/$02.75
achieved for the human b o d y by the latter. It would indicate by a single, meaningful number, the stress placed upon a building's energy systems (analogous to the metabolic rate and the autonomous thermoregulatory systems of the body} by any given environment. As is the case in the physiological systems, this involves making certain assumptions a b o u t the state of the building organism - - i t s 'deep b o d y temperature' and the degree to which the control mechanisms were stressed. It has, of course, been found that no single index which combines the main environmental variables which affect c o m f o r t - air temperature, radiation, air velocity and h u m i d i t y - - c a n adequately express the quality of the environment in the absence of a definition of the two main human variables of clothing (insulation} and activity level (heat generation}. Even for physiologically-based, b o d y thermal comfort indices there has been a traditional problem of different methods used for indoor and o u t d o o r comfort. The normal indices have been developed for indoor use; out of doors "windchill" and other methods have been used. The Author has resolved this problem elsewhere [ 1 ] and applied a c o m m o n index of thermal c o m f o r t (Gagge's DISC} to all conditions. Figure 1 shows how an outd o o r location can have air temperature, sun, and wind all taken into account in terms of DISC, using an assumed level of clothing and activity. In this sense, therefore, a CSI already exists, but it is for the body, and not for the building. Figure 2 shows the DISC iso-curves in a specific tropical climate for the entire day and year. For buildings in cold climates the four main environmental variables which will determine climatic severity are air temperature, wind velocity, solar radiation, and rainfall. The first three are obvious, and relatively well studied; rainfall has often been ignored. Its © Elsevier S e q u o i a / P r i n t e d in T h e N e t h e r l a n d s
278
2
(a)
4
6
8
10
12
14
16
18
20
Distance (m)
2
4
6
8
10
12
14
(b)
16
18
20
Distance Ira)
Fig. 1. (a) Velocity isopleths; (b) DISC isopleths in wind o n the sunny and shady sides of a shelter wall. Clothing, 2.4 clo; activity, 1.0 met (= 58 W m-2); t a = --5.0 C, t o (in sun) = +5.0 C, t O (in shade) = t a. (After Markus.) o
000~_!~ :~
00
---
#
9.ool-
{-~a;
~s.ooI2 T0 ~
"PO J
F
M
A
M
J
J
A
S
O
N
D Months
Fig. 2. DISC values based on a specific set of tropical meteorological conditions.
N.B., DISC lines do n o t follow exactly the shapes of SET lines in Fig. 4. 11, as wind velocity, V, varies. (After Markus.)
,
o
effect is to saturate porous external wall materials, and thus reduce the theoretical, or 'dry' insulation values often found in calculations. However, as insulation standards have increased, the effect is marginal, and in this paper it is ignored. With lower insulation standards, however, this would not be safe. The combined effect of the other three variables is such that an infinite set of combinations could produce the same stress, i.e., required energy consumption, to give a stated internal environment. Any sets which give the same stress should be signified by an identical CSI. However, this is clearly impossible to achieve in the absence of assumptions about the building i t s e l f - and in particular about those properties which critically determine its response to air temperature, wind and radia-
279 tion. These are: insulation and mass; fenestration and air leakage. The effect of air temperature is less p o t e n t in a well-insulated building than in a poorlyinsulated one, and in one with infinite insulation it would be of no significance. Wind is only significant insofar as air can enter a building through designed or fortuitous openings; in a tightly-sealed structure wind exposure is of little significance. Radiation, to be a useful source of heat gain, requires transmitting areas of adequate size, of the correct orientation, with suitable glazing properties, unshaded by obstructions, and with a building structure which has the mass (storage) characteristics which enable it to absorb and later release the energy at a suitable rate. Buildings with small, northfacing windows (in Northern latitudes) and lightweight structures are unable to utilise radiation, even if plenty is available. There are other analogies with thermal comfort indices. The size and shape of a building will affect the ratio of envelope to volume. All the building variables are a function of envelope area, and since the thermal stress must be measured against a uniform q u a n t i t y - - s a y unit volume of controlled s p a c e - - a known ratio of envelope to volume has to be used. In the case of the human b o d y this is the Dubois surface area, whereby all heat gain and loss processes are given for a unit surface area of body. The Dubois area allows for variations in b o d y shape and size. A similar surface or volume unit has to be found for b u i l d i n g s - - t h e POP and VOLM ratios developed by the Building Performance Research Unit will do admirably [2]. Clearly, therefore, the CSI has to relate to a building of a certain shape and size and, hence, volume to envelope ratio, and with a specified combination of thermal characteristics. In fact it is directly proportional to the energy consumption for that building in that climate. It might be argued that this is an unnecessarily complex, and possibly inaccurate predictive tool, when the designer has several choices: sophisticated, mathematical models (such as the Response Factor) [3] ; analogue methods; and computer-based simulations using, say, finite difference methods. But all these are design tools, requiring an initial statement of design intention and then yielding energy predictions. The CSI is a decision tool for other
uses, as the following section describes, and its purpose is to state something a b o u t the climatic variations in a region, country, zone or site, prior to specific design solutions being proposed and tested.
THE NEED FOR AN INDEX Many decisions on housing and building require the comparison of one location with another from the point of view of climate and likely energy demands to maintain stated internal environments. In the case of housing this need is particularly clear, as often a wide range of options is available. Specifically, the following problems require such an index for a rational solution; some of these have been developed b y the Author in an earlier paper [4].
Design-location decisions National and regional, as well as urban agencies usually have a range of sites which can be developed for housing. Many factors will affect the decision, b u t one, for a particular choice, should be the energy consumption consequences for the individual household, the local authority and the country. This will have to be predicted at the strategic stage, before individual designers have been appointed or individual designs are available for detailed energy appraisals. For this purpose the sites must be compared on a standard (energy-related) severity i n d e x - and this involves making assumptions of a general kind regarding the thermal properties of the proposed housing. The index, therefore, will be house-specific, b u t it can be based on a range of 'model' or standard houses.
Building control As far as energy building legislation is concerned, the aim is to achieve a defined level of thermal comfort at a reasonable (or practically 'minimised') expenditure of fuel. Since labour mobility, wage rates, tax legislation, social security benefits, etc., are normally all factors operating as uniform systems within national boundaries, it is reasonable to aim for fuel expenditures which are similarly uniform, irrespective of the location of a family. This is especially important as an issue of social justice, where labour has to move from one part
280 of a country to another as a result of economic policies. Therefore, thermal standards have to be modulated, to become proportionately more stringent as the climate becomes more severe. The aim is to keep fuel consumption, say, per unit volume, identical for identical house types, irrespective of location. To achieve such a modulated and varied set of prescriptive standards, an index of climatic severity is needed. This will probably be used on average regional data, although even these will give rise to anomalies, since local and micro-climatic variations within a region can be substantial. It may be better to accommodate these by careful design based on nonmandatory design guides and Codes, than by legislation of too complex a kind. Optimum distribution o f scarce resources In many countries a substantial portion of the resources being invested in buildings, especially housing, is in the form of improvement to the existing stock, rather than new building. The total is limited by a capital budget; how much should be invested in a particular region, city or individual building scheme is usually determined by some measure of the defectiveness of the existing s t r u c t u r e - - i n terms of space, services, fabric or amenities. An important factor is the upgrading of inadequate insulation, heating systems, ventilation, etc., and to determine this, existing houses will have to be assessed in terms of the climate in which they are located and their thermal properties. It would be possible to carry out individual thermal (or annual fuel expenditure) appraisals for each house; but it is unlikely that a political framework for resource allocation can be found within which the outcome of such exercises could be utilised. The alternative is to work by a CSI, which takes into account the range of house types actually existing in (say) a region by matching them in various proportions against a range of standard or 'model' types. Justice in distribution of social security assistance In North America and m a n y Western European countries, social security payments ..... supplementary benefit, u n e m p l o y m e n t benefit, fuel subsidies -- are available. Generally, they try to take into account social factors, such as family size, the number and ages of children,
the presence of elderly, sick or disabled people in the household, and some crude physical factors, such as the age and size of the house and the type of heating. They generally fail to take into account the climate, or the real thermal properties of the dwelling, even to such an elementary extent that a house at the end of a terrace, or in mid-block, is rated as being in similar need to one in mid-terrace, or at the extremity of a block; even though this single variable could cause fuel consumption differences of the order of 20 - 40%. The administration of such payments precludes the detailed survey and appraisal of each applicant's house and site climate, but it is possible for relatively unskilled personnel to assess, from a range of standard house types, that which approximates most closely to the specific one, and to select from a standard CSI map the appropriate value, upon which the benefit payments would be based. Economic planning Long-term industrial development, job location, transport planning and land-use policy require a building, and specifically, housing, energy forecasting tool. The CSI should be used for this purpose.
SPECIFIC DEVELOPMENT OF A CSI There are two ways of proceeding in the development of the CSI. The first is by s y n t h e s i s - that is, by establishing the form of the relations between each of the three climatic variables and heat loss or gain for each of the three building variables, making the assumption that each variable, in its set of three, is independent of the other two; establishing a form of multiple relation between heat loss/gain and the three climatic variables in which the coefficients are functions of the three building variables; and finally assuming that the CSI is directly proportional to the annual heat loss. The form of the relationship will be Q = a T - - - b R +cW where Q is the annual heat loss (kW h/m3), T a selected value of o u t d o o r air temperature (°C), R a selected value of total radiation (W/m2), W a selected value of wind velocity (m/s), and a, b and c are appropriate coef-
281
ficients for specific types of construction. CSI = K X Q, where K = a constant. If the three individual relationships are non-linear, then a non-linear multiple relationship will apply. It seems worthwhile, therefore, to make the assumption of linearity as a first step. The second method for the development of the CSI is by actual measurement, either in the field or in accurate analogues or in detailed simulations based, say, on finite difference techniques, e.g., ESP [ 5 ] . On the assumption that each of these three, carried o u t with sufficient care, yields the same, and 'true', result, they can then be obtained for a very large number of combinations of the three climatic variables. Analysis of the results would enable a generalised multiple relationship to be obtained, linear or not, in which the coefficients would, again, be functions of the three building variables. The correspondence between the values of the coefficients obtained in this way, and those resulting from the first method, is a measure of the accuracy of the first method. The mass/insulation and air temperature relation The first problem in this relation is the combination of mass and insulation into a single characteristic. At one end of the scale is the lightweight, insulated structure, and the heavy, uninsulated structure; at the other end the light, uninsulated structure of low mass. In between lie the combinations of mass and insulation giving intermediate values of annual heat loss. Muncey's Response Factor technique
y
5
[6] could be used to construct a combined mass/insulation scale (M/I). Assuming that a single index, linearly related, can be used, the relations are as in Fig. 3. The temperature scale on the X axis is one that represents the o u t d o o r temperatures such that, at a particular value, the annual heat loss through all structures is equal; this will be a temperature lower than the indoor temperature, where natural heat gain from solar radiation exactly compensates for the loss due to temperature difference. This is analogous to the 'base' temperature concept of the Degree Day method, and to Dupagne 'temperature without heating' [7]. The coefficient a represents the slope for a unique construction, i.e., a unique combination of mass and insulation. The radiation 'admittance'and solar radiation relationship In this instance again, the property of the building which determines its ability to utilise any available solar radiation is a combination of a number of individual properties; we shall call it solar 'admittance'. It will be a function of window size and orientation; the nature of the glass/blind materials used in the windows; and the mass of the structure, particularly o f the floor, upon which the radiation falls, is absorbed and released over a period of time, as long-wave radiation and sensible heat. Davies [8] has developed an appropriate technique for defining the window's characteristics. Assuming, again, linearity between annual heat gain and solar 'admittance', the relation is as shown in Fig. 4. There is a level of radia-
c; 2
=
o c
.E
Air temperature, T
Fig. 3. Air temperature (T) and annual heat loss per unit volume (Qa/m 3) for three values of mass/insulation (M/I).
Radiation, R
Fig. 4. Radiation (R) and annual heat gain per unit volume (Qa/m 3) for three values of radiation 'Admittance' (A).
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tion at which differences between admittances no longer have any significance--this is probably at such low levels of direct radiation that almost all available radiation is in diffuse form, hence obliterating the orientation effect and also, to a large extent, the effect of window size, since this diffuse radiation is continuously available to opaque surfaces and will ultimately have effects through absorption and transmission similar to that of the diffuse radiation transmitted through transparent areas and absorbed by internal surfaces. The coefficient b represents the solar admittance of a particular combination of characteristics. The p e r m e a b i l i t y and w i n d relation
In many ways this is the least understood of the three relations. Knowledge of what aspects of construction cause variations in air change is, as yet, relatively primitive. It is, of course, some type of 'permeability' which is involved, including the effects of gaps and cracks around windows and doors, construction joints, the effect of flues, ventilators, and other designed or fortuitous openings. In combination each of these responds not only to variations in wind pressure between inside and out, but also to the effect of 'stack' ventilation caused by differences in air temperature between inside and out. So, if the climatic variable of wind speed alone is to be used, standard assumptions about stack ventilation have to be made. Warren [9] has shown that linear relations between wind velocity and air change are a reasonable assumption. The combined effect of wind speed and stack effect is expressed as a relation between heat loss and wind permeability;with a speed at which all buildings have zero loss, equivalent to a such low pressure differential that permeability no longer has any significance. Figure 5 shows the assumed linear relation between velocity and air change rate for a range of permeabilities. The coefficient c measures the slope of the permeability line. Synthetic combination
The combined annual heat loss Qa will be represented by the multiple equation
J
r
<
Wind velocity, W
Fig. 5. Wind velocity (W) and annual heat loss per unit volume (Qa/m 3 ) for three values of wind permeability (P).
is represented by an appropriate coefficient and each of the climatic variables is accounted for. Of course, the solution has many assumptions, approximations, and relatively unkown features. Its advantages, if these features can be studied and resolved, are that individual characteristics of the construction can be studied in isolation; the information required for any given house type is minimal; and all the important aspects of climate are accounted for. 'Real' m e a s u r e m e n t
The validity of the synthetic approach can only be established by comparing the results with those obtained from accurate field measurements in real houses, or equally accurate analogue or digital simulations. In the programme of work referred to under the section headed "Current Work", the finite difference techniques of the ESP program are used and it is intended, initially, to establish the coefficients a, b and c for 4 out of a combinatorial set of 27. This is for 3 values of each of M/I, A and P. The multivariate data can be analysed to yield a multiple linear, or non-linear regression, and the correspondence between the two sets of coefficients established.
QUESTIONS AND APPLICATION
Qa = a T - - bR + c W
The paper has already indicated the questions which have to be resolved for the CSI to
in which each of the three building properties
be fully operational.
283 (i) The three sets of relations have to be analytically verified. (ii) The values of T, R and W for a particular location have to be determined. They will clearly depend on the meteorological data for the region; but they will have to be further modified for some uses by local and site data, including microclimatic effects of sun or wind shading, frost hollows, funnelling, etc. (iii) The selection of the most useful range of values for each of the three properties of mass/insulation, solar 'admittance', and permeability is critical; in combination, they should represent all feasible and recommended forms of house construction. (iv) The correction for shape and size, to allow all indices to be in terms of unit volume, requires further analysis. One solution is to use a standard envelope to volume ratio and apply correction factors for deviations from it. (v) Once the CSI is calculated it will be necessary to map it on a regional basis -- so (say), 27 maps would be available for any particular region, composed of the 3 X 3 X 3 combinatorial range of house types. For decisionmaking it would only be necessary to assess which of the 27 types most closely represented the house(s) in question, and this selects the map to be used. (vi) Finally, if the CSI concept was to be applied to other building types, all three of the analytical relations would have to be specifically determined for that type of building. CURRENT WORK This paper represents ideas relevant to a current research project sponsored by the
Scottish Development Department, and being carried out by the A u t h o r with his colleagues, Dr J. Clarke and Mr E. N. Morris. The paper is, however, his own, and does not commit either his colleagues or the SDD to these views.
REFERENCES 1 T. A. Markus and E. N. Morris, Buildings, Climate and Energy, Pitman, London, 1979, Ch. 3. 2 Building Performance Research Unit, Building Performance, Applied Science Publ., London, Chap. 6, 1979. 3 R. W. R. Muncey, Heat Transfer Calculations for Buildings, Applied Science Publ., London, 1979. 4 T. A. Markus, Fuel poverty in Scottish homes, A r c h i t e c t s ' J . 23 May, 1979, pp. 1077 - 1082. 5 J. A. Clarke, Energy implications in building design : a thermal simulation design model, Proc. 3rd Int. Symp. on the Use o f Computers for Environmental Engineering Related to Buildings, Banff, Canada, May, 1978, National Research Council of Canada,
Ottawa, 1978. 6 R. W. R. Muncey, Heat Transfer Calculations for Buildings, Applied Science Publ., London, 1979. 7 A. Dupagne, Methodology for low-cost housing design including new energy-saving concepts, Int. Conf. on Energy Resources and Conservation Related to Built Environment, Miami Beach, Florida, October 26 - 31, 1980. 8 M. G. Davis, Useful solar gains through a glazed
Southfacing wall in the U.K. climate, to be published in Built Environment. 9 P. R. Warren, Natural infiltration routes and their magnitude in houses -- Part 1 -- Preliminary studies of domestic ventilation, Building Research Establishment, Garston, U.K., 1976, Rep. No. ES 4/74.