The Impact of the Shape Factor on Final Energy Demand in Residential Buildings in Nordic Climates

Abstract

The shape factor of a building is the ratio between its envelope area and its volume. Buildings with a higher shape factor have a larger surface area in proportion to their volume, which results in larger heat losses in cold climates. This study analyzes the impact of the shape factor on the final energy demand by using five existing apartment buildings with different values of shape factor. Each building was simulated for twelve different scenarios: three thermal envelope scenarios and four climate zones. The differences in shape factor between the buildings were found to have a large impact and accounted for 10%-20% of their final energy demand. The impact of the shape factor was reduced with warmer climates and ceased with average outdoor temperature 11ºC-14ºC depending on the thermal envelope performance of the buildings.

Full text

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THE IMPACT OF THE SHAPE FACTOR ON FINAL ENERGY DEMAND IN
RESIDENTIAL BUILDINGS IN NORDIC CLIMATES
Itai Danielski
Mid Sweden University
Akademikgatan 1
Östersund SE 836 31
Itai.danielski@miun.se
Morgan Fröling
Mid Sweden University
Akademikgatan 1
Östersund SE 836 31
morgan.froling@miun.se
Anna Joelsson
SWECO
Västra Norrlandsgatan 10 B
Box 110, Umeå SE 901 03
Anna.Joelsson@sweco.se
ABSTRACT
The shape factor of a building is the ratio between its
envelope area and its volume. Buildings with a higher
shape factor have a larger surface area in proportion to
their volume, which results in larger heat losses in cold
climates. This study analyzes the impact of the shape
factor on the final energy demand by using five existing
apartment buildings with different values of shape factor.
Each building was simulated for twelve different
scenarios: three thermal envelope scenarios and four
climate zones. The differences in shape factor between
the buildings were found to have a large impact and
accounted for 10%-20% of their final energy demand.
The impact of the shape factor was reduced with warmer
climates and ceased with average outdoor temperature
11ºC-14ºC depending on the thermal envelope
performance of the buildings.
1 INTRODUCTION
The shape factor of a building is a measure of the
building’s compactness and expresses the ratio between
the building’s thermal envelope area and its volume. The
thermal envelope area is the area that separates between
the conditioned and unconditioned areas or alternatively,
the indoor and the outdoor environment. As a result, the
heat losses through the thermal envelope account for large
percentage of the total final energy use of a building in
cold climates. Buildings with a higher shape factor are
less compact and therefore have a larger thermal envelope
area in proportion to their volume and therefore larger
heat losses.
The value of the shape factor depends on the shape of the
building for a given volume as illustrated by building A
and B in Fig. 1. Both buildings have similar volume but
different thermal envelope areas, which results in
different shape factors. The size of the building also
influences the shape. A larger building with similar shape
will have lower shape factor as illustrated by building A
and building C in Fig. 1. Irregular façades with trenches
and bulges, e.g. heated balconies that extend beyond the
façade, may also increase the shape factor as illustrated by
buildings A and D in Fig. 1.
Fig. 1: The shape factor of buildings with different sizes
and shapes. The parameter ‘a’ symbolizes a unit of length.
Energy simulations done by Depecker et al.[1] showed
that in colder climates the correlation between the final
energy use and the shape factor is strong. Ourghi at el.[2]
found strong correlations between the shape factor and
final energy use in office buildings [2]. Ratti at el.
[3]calculated a 10% difference in specific final energy use
between Toulouse and Berlin due only to differences in
their buildings’ morphology. The study also suggested
that cold climate may increase the impact of the results.
As a measure to limit specific final energy use, China has
integrated the shape factor of buildings into its design
standard for energy efficiency of public buildings.
The standard applies strict values for new buildings in
cold climates [4]. The aim of this study is to quantify the
impact of the shape factor on the specific final energy use
in residential buildings with different thermal envelope
properties and different Nordic climate zones.

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TABLE 1: DESCRIPTION OF THE CASE STUDIES BY SLECTED PARAMETERS
Floor
area External
walls1 Windows1 Ground
floor Roof Shape
factor1 Window-to-floor-
area ratio1
Building A 2197 m2 1088-1154 m2 363-385 m2 389 m2 389 m2 1.01-1.08 16.5%-17.5%
Building B 1711 m2 909-970 m2 303-323 m2 401 m2 401 m2 1.18-1.25 17.7%-18.8%
Building C 975 m2 530-564 m2 177-188 m2 289 m2 289 m2 1.32-1.41 18.1%-19.3%
Building D 1069 m2 713-767 m2 238-256 m2 304 m2 304 m2 1.46-1.57 22.3%-23.9%
Building E 567 m2 385-426 m2 128-142 m2 201 m2 201 m2 1.61-1.8 22.6%-25.0%
1 The values vary because of the different thermal envelope scenarios as listed in Table 2.
2 METHEDOLOGY
The definition for the shape factor used hereinafter is the
ratio of thermal-envelope-area-to-the-total-floor-area of
the building. This definition differs from the definition
mentioned in Section 1 by the size of the floor height.
However, since all studied buildings have similar floor
height the two definitions are equivalent.
2.1 The Impact Of The Shape Factor
Five newly built apartment buildings with different shape
factors, ranging from 1 to 1.7, were used as case studies
(Table 1). The specific heat demand of each building was
calculated by the VIP-Energy simulation program under
different scenarios. Three thermal envelope scenarios
were used representing low energy efficiency thermal
envelop scenario, common practice scenario and passive
house standard scenario (Table 2). The buildings were
simulated in four different cities: Malmö, Karlstad,
Östersund and Kiruna, which represent four different
Nordic climate conditions, covering most climate zones in
Sweden and in other Nordic countries. The specific heat
demand is the heat energy needed to be supplied in order
to maintain an indoor temperature of 22°C.
The VIP-Energy simulation software [5] is a commercial
dynamic energy balance simulation program that
calculates the energy performance of buildings hour by
hour. VIP-Energy has been validated by IEABESTEST,
ASHRAE-BESTEST and CEN-15265. Monitored data for
wind, solar radiation and humidity from the NOAA Earth
System Research Laboratory was extracted by the VIP-
Energy Climate data creator for year 2010 [6]. Monitored
temperature data was imported from [7] for year 2010.
Table 3 lists yearly climate values for each city.
This study analyses the energy efficiency of the buildings
and therefore excludes the effects of tenants’ activities,
for example final energy use for domestic water heating
and household electricity are not included. Final energy
use from residents’ behavior is difficult to predict [8] and
may vary considerably between different households. In
all simulations the area of the windows was set to be 25%
of the total façade area and distributed evenly in all
directions. Each building was simulated with the largest
façade facing the south direction. The reason is to have
similar conditions of solar energy gains for all the case
studies. All the buildings are equipped with forced
ventilation with air flow of 0.35 l/(s m2).
TABLE 2: THERMAL ENVELOPE SCENARIOS
Insulation thickness mm
Thermal envelope scenario: Low Medium High
External wall 120 180 420
Roof 120 190 400
Ground floor 100 160 350
U-value W/(m2 K)
Thermal envelope scenario: Low Medium High
External wall 0.331 0.229 0.103
Roof 0.304 0.202 0.1
Ground floor 0.318 0.208 0.099
Windows 1.7 1.2 0.7
2.2 Sensitivity Analysis: The Effect Of Different
Relative Size Of Window Areas
The energy balance of a building is largely determined by
the thermal properties of its different surfaces. Roof,
ground floor and external walls have relatively similar
thermal properties in comparison to the thermal properties
of windows, in particular regarding thermal resistance and
solar transmissions. Therefore it is important to study how
the effect of the shape factor on the final energy demand
will change for different shares of window areas.
The energy performance of building B (Table 1) was
analyzed with different ratio of windows-to-floor-area
that ranges from 0.2 to 0.25. The windows were
distributed evenly around the building to have similar
window area in each facade direction to reduce variations
in energy performance because of differences in solar
radiations from different directions. The effect of different
windows-to-floor-area ratios was studied with the three
thermal envelope scenarios in Table 2 and four different
Nordic climate zones scenarios as described in Table 3.
The specific heat demand was simulated by the VIP-
Energy software.

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TABLE 3: THE CLIMATE SCENARIOS
Location (city): Malmö Karlstad Östersund Kiruna
Latitude 55°36'N 59°23'N 63°10'N 67°52'N
Average outdoor temperature 7.7°C 4.8°C 1.8°C -1.7°C
Yearly global solar radiation [kWh/m2] 1,411 1,340 1,292 1,189
Average wind speed [m/s] 5.7 3.4 3.7 3.6
3 RESULTS
3.1 The Impact Of The Shape Factor
The impact of the shape factor on the specific heat
demand is illustrated in Fig. 2-4 for buildings with
different thermal envelope scenarios as listed in Table 2.
In each of the figures, five building with different shape
factors are compared in four different Nordic climate
conditions resulting in 20 different scenarios. The results
from the energy simulations show that the specific heat
demand increases linearly with increasing shape factor
irrespective of the climate conditions and thermal
envelope properties. The slope of each linear line signifies
the impact of the shape factor on the specific heat
demand, that is to say the change in specific heat demand
due to one unit change in the shape factor of the building.
Fig. 2: The specific heat demand vs. the shape factor of
the five buildings with thermal envelope scenario called
Low in Table 2, and different annual average outdoor
temperatures. The characters ‘A’ to ‘E’ signify the case
study buildings listed in Table 1.
Fig.5 illustrates the values of the slopes of the different
scenarios. The impact of the shape factor found to be
higher in buildings with lower thermal envelope
properties. The impact of the shape factor also reduces
linearly with higher average outdoor temperatures.
However the values in the Malmö climate scenario, with
average outdoor temperature of 7.7°C, are higher than
what can be expected by the trend-line. Malmö is the only
coastline city among the four different cities listed in
Table 3. It is subjected to stronger winds and has 60%
higher average wind speed in comparison to the climates
in the other three cities. The stronger winds were found to
increase the impact of the shape factor on the specific heat
demand by about 7 kWh/(m2 year). This was confirmed
by energy simulations with the wind speed as the only
variable parameter.
Fig. 3: The specific heat demand vs. the shape factor of
the five buildings with thermal envelope scenario called
Medium in Table 2, and different annual average outdoor
temperatures. The characters ‘A’ to ‘E’ signify the case
study buildings listed in Table 1.
Fig. 4: The specific heat demand vs. the shape factor of
the five buildings with thermal envelope scenario called
High in Table 2, and different annual average outdoor
temperatures. The characters ‘A’ to ‘E’ signify the case
study buildings listed in Table 1.
By extending the trend-line in Fig.5, the impact of the
shape factor is expected to be nullified with outdoor
temperatures of 14.2ºC, 12.6ºC and 10.8ºC for the
respective low medium and high thermal envelope
properties. In climates with higher average wind speed, as
in Malmö city, the nullification of the impact of the shape
factor is expected to occur at higher temperatures.
0
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160
180
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
kWh/(m2year)
Theshapefactor
‐1.7°C 1.8°C 4.8°C 7.7°C
ABCDE
0
20
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60
80
100
120
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160
180
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
kWh/(m2year)
Theshapefactor
‐1.7°C 1.8°C 4.8°C 7.7°C
AB CDE
0
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40
60
80
100
120
140
160
180
0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8
kWh/(m2year)
Theshapefactor
‐1.7
°
C1.8
°
C4.8°C 7.7
°
C
ABCDE

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Fig. 5: The specific heat demand per unit difference in the
shape factor (SF) for different scenarios of thermal
envelope and outdoor temperatures. The calculation of the
trend-line does not include buildings in the Malmö
climate zone (7.7ºC).
Fig.6 illustrates the differences in yearly Energy demand,
for each thermal envelope and climate scenarios, between
the buildings with the highest and lowest shape factor.
The highest differences in heat demand, 18%-20%, were
found for buildings with lower thermal properties. 11%-
14% differences in energy demand were found for
buildings with high thermal properties. The lower values
relate to climates scenarios with higher average outdoor
temperature. The stronger winds in Malmö results with
higher differences in heat demand among buildings with
different shape factors. The shape factors of the different
case studies ranged between 1 and 1.7; but buildings can
be design with higher and lower shape factors that may
results with larger differences.
Fig. 6: The difference in heat demand between the
buildings with the highest and lowest shape factor for the
different scenarios of thermal envelope and climate
conditions.
3.2 Sensitivity Analysis: The Effect Of Different
Relative Size Of Window Areas
The specific heat demand was found to increase or
decrease with higher relative window area depending on
the climate conditions and the thermal envelope
properties of the buildings as illustrated in Fig.7-9.
Positive slopes indicate that the difference in conductive
heat losses between windows and external wall is higher
than the heat gains from solar radiations and v.v. Positive
slopes will intensify the impact of the shape factor while
negative slopes will decrease it.
The values of the slopes in Fig.7-9 ranges between 0-0.6
kWh/(m2 year) per 1% change in window-to-floor-area
ratio among buildings with different thermal envelope and
climate conditions. The effect of the relative window size
was calculated by multiplying the value of the slop by the
percent difference in the window-to-floor-area ratio. That
was done for each thermal envelope and climate scenario.
Fig.10 illustrates the impact of the shape factor on the
specific heat demand with correction to the differences in
window-to-floor-area ratio.
Comparison between Fig.10 and Fig.5 reveal only minor
changes to the specific heat demand caused by differences
in window-to-floor-area ratio. Persson at el. [9] showed
that the size of energy efficient windows does not have a
major effect on the heating demand in the winter. This
study expend Persson’s conclusion to windows with
lower energy efficiency. The conclusions apply to
windows and walls with thermal properties according to
Table 2.
Fig. 7: The effect of the relative window size on the
specific heat demand of buildings with Low thermal
envelope scenarios and different climate scenarios.

Fig. 8: The effect of the relative window size on the
specific heat demand of buildings with Medium thermal
envelope scenarios and different climate scenarios.
y=‐3.4702x+49.126
R²=0.9942
y=‐2.5995x+32.875
R²=0.9943
y=‐1.6922x+18.203
R²=0.9952
0
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30
40
50
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80
‐3‐113579111315
kWh/[(m2year·SF)
Annualaverageoutdoortemperature
Lowthermalenvelope
Mediumthermalenvelope
Highthermalenvelope
0%
4%
8%
12%
16%
20%
24%
‐3‐2‐10123456789
%differenceinheatsupply
Annualaverageoutdoortemperature
Lowthermalenvelope
Mediumthermalenvelope
Highthermalenvelope
0
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160
5% 10% 15% 20% 25% 30%
kWh/(m2year)
Windowarea‐to‐floor‐arearatio
7.7°C 4.8°C 1.8°C ‐1.7°C
0
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160
5% 10% 15% 20% 25% 30%
kWh/(m2year)
Windowarea‐to‐floorarearatio
7.7
°
C4.8
°
C1.8°C ‐1.7
°
C

5
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Fig. 9: The effect of the relative window size on the
specific heat demand of buildings with high thermal
envelope scenarios and different climate scenarios.

Fig. 10: The specific heat demand per unit difference in
the shape factor (SF) of buildings with different scenarios
of thermal envelope and climate conditions with
correction to differences in window-to-floor-area ratio.
4 DISCUSSION AND CONCLUSIONS
This study investigates the impact of the shape factor on
the specific heat demand in residential buildings located
in different Nordic climates. Designing new residential
buildings with lower shape factor will result in lower
specific heat demand. However the impact of the shape
factor varies considerably for buildings with different
thermal envelope properties and for different climate
conditions. For the scenarios used in this study the change
in specific heat demand for a unit change of shape factor
in the design of the building varied from 12 to 52
kWh/(m2 year). The shape factor has higher impact on the
specific heat demand in buildings with lower thermal
envelope properties and buildings that are located in
colder climates. The impact of the shape factor found to
increase in regions with higher average wind speed as
well. Sensitivity analysis found minor changes in specific
heat demand caused by differences in window-to-floor-
area ratio.
The span of shape factors among the investigated
buildings in this study is 0.7. This difference was found to
reduce the specific heat demand by 18%-21% for
buildings with low thermal envelope properties, by 15%-
19% for buildings with medium thermal envelope
properties and by 11%-16% for buildings with high
thermal envelope properties. The difference in shape
factor between buildings could in other cases be even
higher resulting in larger differences in specific heat
demand. The impact of the shape factor on the specific
heat demand was found to diminish in climates with
annual average outdoor temperatures above 14°C for
buildings with low thermal envelope properties and above
11ºC for buildings with high thermal envelope properties.
The above temperatures are expected to be higher with
higher average wind speed conditions.
The conclusion from this study is that the shape factor of
buildings should be considered as an important energy
efficiency measure in Nordic climates because of its large
impact on final energy use in buildings. It would be
advisable from an energy point of view to define limits
for shape factors to reduce final energy use in new
designed building, as was done in China [4].
5 ACKNOWLEDGMENTS
We gratefully acknowledge the financial support of the
European Union Regional Development Fund
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(1) Depecker, P., et al., Design of buildings shape and
energetic consumption. Building and Environment, 2001.
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analysis method to predict the impact of shape on annual
energy use for office buildings. Energy Conversion and
Management, 2007. 48(1): p. 300-305.
(3) Ratti, C., N. Baker, and K. Steemers, Energy
consumption and urban texture. Energy and Buildings,
2005. 37(7): p. 762-776.
(4) Tianzhen, H., A close look at the China Design
Standard for Energy Efficiency of Public Buildings.
Energy and Buildings, 2009. 41(4): p. 426-435.
(5) Strusoft, VIP-Energy simulation program. 2011.
(6) Strusoft, VIP-Energy Climate data creator.
(7) Temperatur.nu. [cited March 2012; Available from:
www.temperatur.nu.
(8) Itai, D., Large variations in specific final energy use
in Swedish apartment buildings: Causes and solutions.
Energy and Buildings, (0).
(9) Persson, M.-L., A. Roos, and M. Wall, Influence of
window size on the energy balance of low energy houses.
Energy and Buildings, 2006. 38(3): p. 181-188
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‐3‐1 1 3 5 7 9 11 13 15
kWh/(m2year)
Averageoutdoortemperature
Lowthermalenvelope
Mediumthermalenvelope
Highthermalenvelope