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13FORM FACTOR LIMITS DEPENDING ON THE BUILDING SHAPES
Chobanov Pl.
Assoc. Prof. Dr. Eng.
Department of Building Materials and Insulations University of Architecture, Civil Engineering and Geodesy
Sofia, Bulgaria
Abstract: The form factor (ratio of compactness) is the main criterion for assessing the building shape solutions in terms of their energy efficiency. Its values give a general idea of the future performance of the building envelope and determine to a great extent all subsequent actions and measures on energy saving in the operation of the building. His crucial role in energy savings is caused by the fact, that it defines one of the multipliers in calculating the heat loss through the surrounding structures. In case ofpoor building shape (with bad form factor) the requirements to the heat transfer coefficient U should raise to achieve certain (usually required) energy consumption in kWh/m2 per year.
Based on an analysis of different building shapes of a specified volume, there are proposed formulas to receive the limits of variability of f according a given volume. These limits of f can
serve as a quantitative criterion for the quality of project building shape in relation to the energy efficiency.
Keywords: Shape factor, Compactness, Energy efficiency, Thermal Insulations
1. Introduction
The form factor is a key criterion for assessing the building shapes in terms of their energy efficiency. Its values give a general idea of the future performance of the building envelope and determine to a great extent all subsequent actions and measures on energy saving in the operation of the building.
The form factor f is the ratio of the envelope surface A to the required volume of the building V by design: A
f =--form factor, m-1, where:
o v
A - envelope surface, m2;
V - volume of the building, m3.
According to the chosen approach the floor area of the surrounding structure can be included or not to the envelope surface. In this particular case the entire surrounding area of building shape will be taken into account and because of that the analysis will be performed with the added area of the floor surrounding structure.
In some sources, such as [1, Art. 6.3.2] the form factor is named "ratio of the compactness".
The crucial role of the form factor f in energy savings is caused by the fact, that it defines
one of the multipliers in calculating the heat loss through the surrounding structures [2]. In case of poor building shape (with bad form factor) the requirements to the heat transfer coefficient U should raise to achieve certain (usually required) energy consumption per year in kWh/m2a [3].
2. Case 1 - calculations and analysis
An analysis of change in the f at different volumes V and some typical planning solutions is
made. As a unit base volume was taken a cube with side a = 1 m (geometric minimum) or the base volume in this case is equal to 1 m3. For these assumptions a volume V is formed, for which the following parameters are set or calculated:
n - set number of base volumes on one side of the cube;
N - calculated number of all base volumes in the cube;
V - calculated volume of the cube (subsequently, with this volume are analyzed different planning solutions), m3.
There are considered typical planning solutions that differentiate the next schemes:
0 - Sphere. The ideal theoretical solution (geometric body with a best ^). It is calculated with such a radius that the volume is equal to V .
1 - Cube. The ideal practical solution (after the sphere with the best value for ^). This
solution fits the prerequisites for a basic volume.
2 - Area. All basic volumes are arranged in a rectangle on one floor.
3 - Wall. There forms a wall with thickness - 1, width - n and height - nn base volumes.
4 - Line. There forms a shape with a thickness - 1, width - nnn and height - 1 basic volume.
5 - Tower. There forms a shape with a thickness - 1, width - 1 and height - nnn base volumes. Practically, this is the worst planning decision for the agreed base volume, therefore the highest value for ^ .
6 - Module. There are formed nnn independent spaces of the individual base volumes. It does not depend on the total volume V , but depends on the assumed base volume in that case - 1 m3.
The input data, diagrams and the calculated values fQ for the relevant volumes are grouped in
table 1.
Table 1. Input data, diagrams and values of ^ for each scheme with a=1
Graphics of the calculated values of fo for each scheme and volume are displayed in fig. 1.
Fig. 1. Interdependence between n and f for each scheme with a=1
It is clear that for each volume (on the X axis) is differentiated limits amendment for the f
(on Y axis). These values for the minimum are between schemes 0 or 1, and for the maximum are schemes 4 and 5, or exceptionally 6 (fig. 2).
Assuming a = 1 m and set volume V = 1,500 m3 (~ 550 m2), the range for amendment of f
yields the following specific values for practical and theoretical extremes:
• Theoretical minimum - scheme 0: 0,422 m-1;
• Practical minimum - scheme 1: 0,524 m-1;
• Practical maximum - schemes 4 and 5: 4,001 m-1 For the possible range of practical change of ^ is obtained:
A f 1m = 4,001 - 0,524 = 3,477 m-1.
4,500 4,000 3,500 3,000 2,500 2,000 1,500 1,000 0,500 0,000
1
t
V
500
1000
1500
2000
■Max
■Min - практично •Min - теоретично
V, m;
Fig. 2. Interdependence between n and f for each scheme with a=1 3. Case 2 - calculations and analysis
In the second case again an analysis of change in the f at given volumes V for a base unit
volume is made, which is taken with the size of a room, consider cube with a side a = 3 m, or the base volume is equal to 27 m3. For these assumptions a volume V is formed, for which the following parameters are set or calculated:
n - set number of base volumes on one side of the cube; N - calculated number of all base volumes in the cube;
V - calculated volume of the cube (subsequently, with this volume are analyzed different planning solutions), m3.
Discussed are the same typical planning solutions, subject to the mentioned principles, which form the above schemes: Sphere, Cube, Area, Wall, Line, Tower and Module (the adopted base volume in this case - 27 m3).
The input data, diagrams and calculated f for the relevant volumes are grouped in the
following table 2.
Table 2. Input data, diagrams and values of ^ for each scheme with a=3
Graphics of the calculated values of fo for each scheme and volume are displayed in fig. 3.
Fig. 3. Interdependence between n and f for each scheme with a=3
It is obvious that the values of the individual schemes are subject to similar relationships with those in the first case. And here also the minimum is between schemes 0 and 1 and the maximum is at a schemes 4 and 5 or exceptionally at 6 (fig. 4).
3,500 3,000 2,500 2,000 1,500 1,000 0,500 0,000
500
1000
1500
2000
■Max
■Min - практично ■Min - теоретично
V, nv
Fig. 4. Interdependence between n and f for each scheme with a=3
Assuming a = 3 m and set volume V = 1500 m3 (~ 550 m2), the range for amendment of ^
yields the following specific values for practical and theoretical extremes:
• Theoretical minimum - scheme 0: 0,422 m-1 (coincides with the value of the first case);
• Practical minimum - scheme 1: 0,524 m-1 (coincides with the value of the first case);
• Practical maximum - schemes 4 and 5: 4,001 m-1 (the value is significantly lower than in the first case)
For the possible range of practical change of ^ is obtained:
A f 3m = 1,345 - 0,524 = 0,821 m-1.
It is obvious that the range of variation when a = 3 m are significantly closer than those for a = 1 m, or A f 3m < A f 1m and the increase of the base rate a reduces the potential range of
variation of A f .
o
4. Formulas proposed
On the basis of these analyzes the following formulas to obtain any limits amendment of fo at a predetermined volume can be applied. The expected minimums of fo are offered:
Minimum under ideal theoretical solution:
o,min
4,835 •
3v '
g
• Minimum under ideal practical solution: f . =-.
p o,min 3V
For the expected minimum of fo as function of the base size a, the following equation is
? r2 4
suggested: f = 2a + 4 o'max V a
The curves obtained on the basis of the above formulas (with adopted in advance a -recommended is 3 m) clearly outline the possible range of variation of f at a predetermined volume.
These limits of fo can serve as a quantitative criterion for the quality of project building shape
in relation to the energy efficiency.
5. Formulas check
For the considered volume V = 1500 m3 (~ 550 m2) and assuming a = 3 m, could check the values obtained for the range of variation of fo :
2
fo,min = 31=00 = °>524 m1, fo,max = ^ + 4 = >>345 m'.
These values perfectly match the calculated on conventional approaches. They should be used as borders for the evaluation of the actual form factor fQ. On this basis conclusions about the
behaviour of the building in relation to energy efficiency can be deducted.
6. Conclusions
The recommended basic size is a = 3 m (normal room - 27 m3). The increasing of the base size a significantly reduces the range of variation for f . The proposed formulas give a quantitative
assessment of building shapes in terms of their form factor as an indirect indicator for energy efficiency.
REFERENCES
1. Energy performance of buildings - Methods for expressing energy performance and for energy certification of buildings - BDS EN 15217:2007
2. Milkov S. , Chobanov Pl., Penev B. (2009) Opportunities for thermal insulating capability evaluation of building envelopes by the total thermal transmittance coefficient, International Conference UACEG2009: Science & Practice, Sofia, Bulgaria
3. Nikolovski P. (2012) Thermal bridges in buildings, Institut za standardi za cijana Republika Makedonija - ISRM
