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					Building Insulation
2040BIEN1003
December 2003




                      Insulation Theory




                             Insulate for life
                                                 1
                                                           Contents

                                                           Energy saving and economics of
                                                           insulation                         4-5

                                                           Insulation Economy                 6-8

                                                           Structural design                 9-12

Making Far-reaching Choices                                Heat                             13-18
Insulation makes good economic sense as it reduces
energy consumption in buildings. Insulation as a single    Moisture                         19-26
investment pays for itself many times over during the
life cycle of a building. Reduced energy consumption       Frost                            27-28

also benefits the environment.
                                                           Ground insulation                29-33
    This information is common knowledge in the EU.
The EU has already passed the Energy Performance
                                                           Fire                             34-43
Directive that requires the member states to adopt new
practices to improve the energy efficiency of buildings.   Acoustics                        44-57
    We are well prepared for the increasing
requirements. The unique properties of stone and the       CE marking                         58
extreme Nordic weather conditions have inspired us to
develop economically and ecologically rewarding, safe
and sound insulation solutions. Stone wool, made
from nature’s own stone, is extremely fire resistance,
durable and reliable choice for protecting lives and
property.
    We are happy to share our knowledge in this
Insulation theory, which has become something of an
institution and has already guided generations of
builders in the field.
    We hope that you find this material useful in
designing high quality insulation solutions, which will
meet the requirements in the years to come.




2
                    Insulation Theory
Designing safe and sound insulation structures requires knowledge from all fields
of building physics. Here the concepts and fundamental functions related to
insulation material are presented. The content is divided into the following:

                     Energy saving and economics of
                            insulation
Insulation is a powerful mean in reducing energy consumption. Economically
optimal insulation can be calculated and it is often much thicker than is stipulated
in the regulations.

                          Constructive design
Four principles to follow in carrying out the construction to avoid the risk of
unnecessarily high energy consumption and damp damage.

                                       Heat
Fundamental definitions of heat followed with the heat transfer mechanism of
insulation material and the calculation of thermal transmittance for building
components

                                    Moisture
Fundamental definitions and terms and a number of calculation examples in
addition to a list of practical tips in order to minimise the risk of moisture in
buildings.

                                       Frost
The occurrence of frost and how to reduce or prevent its build up by using
insulation.

                           Ground insulation
The use of stone wool as insulation of constructions to the ground with one side
warmed up. The chapter is referring to experiences from different follow up of
damages in buildings.

                                        Fire
Fundamental terms in addition to the classification system applied to the materials
and buildings. Finally, the section includes graphs, which facilitate the
establishment of dimensions for fire insulation in different types of constructions.

                                   Acoustics
This part gives a theoretical description of acoustics and the function of stone wool
for different usage in buildings. Typical values for stone wool are given. It also
refers to common European standards regarding absorption and sound reduction.

                                 CE marking
In this part a short description of the European regulations for marking of mineral
wool is given. What does it mean and what kind of quality control is promised?




                                                                                        3
s I N S U L A T I O N T H E O R Y – E N E R G Y S AV I N G




Energy saving and economics of insulation
Energy economising and thermal insulation make up the              energy saving and consequently to a good standard of
“Principal requirement” of the EU Building                         thermal insulation. This has been done after seeing the
Commodities Directive. The EU Commission has                       consequences of the escalating energy prices of recent
therefore chosen to set out the importance of                      years and with increased awareness of our global
constructing buildings with a view to the need for good            environmental problems.




Energy saving                                                      Even if a better insulation standard than that required by
National regulations stipulate the minimum requirements            the regulations were to increase costs, it is still a very
so as to limit the need for heating energy in buildings. The       inexpensive measure in relation to its efficiency. The extra
aim is to achieve good energy economy. But what is good            costs can be viewed as a very inexpensive insurance policy
energy economy? Who is it good for? For the homeowner?             against what will occur in the future. It makes good
For the tenant? For the community?                                 economic sense to bear in mind rising energy prices, so
    There is no conflict here. If the most personally              that making further investments in additional insulation in
favourable thickness is chosen (the thickness that in              the future can be avoided. It can be said that choosing a
common terms is called optimal thickness), it appears that         high insulation standard is a favourable insurance policy
it is generally thicker than is stipulated in the regulations.     against future rises in energy prices.
Furthermore it provides a more comfortable indoor climate
                                                                   Total environmental balance for stone wool
and above all is more energy efficient as seen from society’s
                                                                   insulation
perspective when environmental considerations are
increasingly being taken into account.                                    Positive contribution         Negative contribution
    The most favourable insulation must be calculated based
on a particular lifetime for the building. The insulation
does not wear out, does not require maintenance and does                                            >100
not require replacing. A lifetime of 50 years is normally
reckoned for insulation that is to match the estimated
working life for the building. However, this is much too
short. If the structure has been correctly designed, there
will be nothing to affect the insulation when it is in place.
It will have the intended insulating effect for as long as it is
in place and we do not know the age of a piece of
insulation. In practice, the lifetime is unlimited. Therefore,
the lifecycle analysis for stone wool insulated structure
proves that a significantly greater amount of insulation                               1

should be used than that which is stipulated in the                           Manufacture Usage stage      Demolition
regulations.                                                       Figure 1
    Therefore, it is important that proper insulation is fitted
with a view to the future when new construction or
renovation will be carried out. Seen over the lifetime of the
building, there are hardly any measures that increase energy
efficiency that are as favourable to the homeowner as
effective insulation.




4
Environmental concerns                                          Optimal insulation
How does insulation affect our environment?                     Traditionally we have calculated the economical optimal
Does the manufacture and transportation of insulation lead      thickness for different structures in a building. In this case,
to significant environmental damage?                            the fact that building costs will rise when insulation is
How is the insulation finally dealt with after demolition?      increased is taken into consideration. But at the same time
   The use of thermal insulation has a very positive effect     the annual energy consumption will decrease without there
on the environment. Manufacture, including the extraction       being any outlay for maintenance. A schematic example is
of raw materials, transportation and assembly have a            shown here for a traditional attic joist floor where the
negative environmental effect that is compensated for           economic thickness is normally around 0.50 m. This is
during the first year in which the insulation is used. It is    found where the curve has its minimum point, simply
usually said that the environmental usefulness is several       expressed as the lowest annual expenditure for building and
hundred times greater than the environmental stress.            energy costs.
   If the total lifetime of the building is considered,
                                                                Sacrifice
operation and maintenance equate to approx. 85 % of the
total environmental strain. Totally overwhelming is the
amount energy required for heat and hot water. Approx.
15 % comes from the manufacturing process and less than
1 % from the demolition. It is easy to show that investing
in extra insulation will pay for itself many times over when
taking into account the environmental strain over the                                              Environment
entire lifecycle. And this additional insulation is motivated
on purely personal economic grounds.                                         Economy


The total environmental strain of a building
                                                                0          0.5     1.0      1.5       2.0        2.5     3.0
       Normal insulation             Increased insulation
                                                                                                       Optimal thickness in m
                                                                Figure 3

                                                                The diagram also suggests the location of an
                                                                environmentally optimal insulation thickness. The curve
                                                                represents the sum of the environmental influences upon
                                                                construction and for annual operation. The
                                                                environmentally optimal insulation thickness for the attic
                                                                joist floor is an unrealistic 2.5 m.
                                                                   It is mainly due to the fact that the additional effects on
                                                                the environment when the thickness increases originate
                                                                almost entirely from the insulation itself. The calculation
                                                                shows that an investment in insulation thicknesses in excess
                                                                of normal thicknesses will also lead to an investment in our
                                                                environment.
           Manufacture Usage stage     Demolition
Figure 2
                                                                The house as an energy system
                                                                If we were to construct a house that satisfied the
                                                                requirements for optimal energy economising we should be
                                                                looking at the bigger picture and not just the individual
                                                                parts. It often proves to be the case that extra insulation
                                                                will allow a slightly simpler heating system to be chosen.
                                                                For example, it must be appreciated that the various
                                                                components in a building have different lifetimes. We
                                                                recommend that the effects that different insulation
                                                                standards have on the choice of heating system in the
                                                                house be examined at an early stage.

                                                                                                                                5
s I N S U L AT I O N T H E O RY – I N S U L AT I O N E C O N O MY




Insulation Economy
Heating and running of buildings contribute to                   show the association to the construction solutions in the
approximately 40 % of the total energy consumption in            table.
Europe. There is therefore great potential to reduce the             The SC method provides the insulation level that leads
energy consumption. Especially important is that at times        the lowest annual expense with the chosen calculation
of new construction adequate insulation standards are            prerequisites. The minimum point is fairly flat that means
used. Even when renovating, you should consider which            that the annual costs only increase marginally if you chose
constructions ought to be additionally insulated.                a slightly higher insulation standard. You can say that there
   The following includes a calculation to estimate the          is a low premium to ensure against future extreme energy
economical insulation thickness. This method is used for         price increase.
economically optimal insulation thickness in the tables that




The important condition                                          SC Method
By 2006 each Member State of the EU must implement               SC stands for saving costs. The SC method means that you
the Energy Performance Directive for Buildings into the          compare the costs of saving energy - the saving cost - with
national legislation. This significantly changes the way the     the current price of energy. Step by step, the thickness of
building regulations stipulate for the energy use in             the insulation is increased and you can calculate the
buildings. The new regulation will be based on the total         marginal saving cost. As long as it is lower than the current
energy consumption of a building taking into conside-            energy price, the insulation measure is profitable.
ration the thermal losses through the envelope, ventilation         The savings cost - SC – may be calculated using the
losses and heat recovery gains, solar and other gains as well    following formula:
as tap water generation, cooling by means of air                            ∆ I EUR/kWh
                                                                   SC =
conditioning systems etc.                                                   B·α
   However, reduced energy consumption in a private
building may only take place under the conditions of a           – ∆I = increased investment cost (EUR/m2)
properly insulated climate shield. Only then, it will be         – B = energy saving per year (kWh/m2)
possible to have full usage of efficient installations for the
production of energy.                                            The energy saving may be calculated
   A high insulation standard for floors, walls, roof and          B = ∆U · Q
windows does not only mean lower energy consumption. It
will also reduce the power need and makes the heating            where ∆U is the improvement of the U value and Q is the
period shorter. It improves the conservation of existing free    thermal consumption figure for the actual area in
energy and creates conditions for simpler heating systems.       approximately 1000 degree hours/year.
   A high insulation standard is an investment with very
good profitability for unlimited time. There is no               – α = is the correction figure, which takes into
requirement for running costs or maintenance.                      consideration the life span (n), the real energy price
                                                                   increase (q), desired real return on the investment (r)
                                                                   and is calculated using the following formula.
                                                                         1 – tn     1+q
                                                                    α=          ;t=
                                                                         1–t        1+r
                                                                 – n = life span (years)




6
Note that if the formula should be applied for a measure        Profitability
that demands maintenance, for example waste heat
                                                                Example. Below we indicate how to calculate economical
recovery, the ∆I also contains the current value of the
                                                                thermal insulation for a building. As an example, we have
annual expenses for maintenance.
                                                                chosen a detached house in the middle of Sweden with a
                                                                loft made of wood, insulated with Paroc loose wool. It is
Average and marginal saving                                     normally performed using an optimising calculation on the
costs                                                           computer.
The financial benefit of each extra centimetre of insulation
decreases with thickness. It is profitable to increase the
thickness of the insulation until the last centimetre fulfils
the return requirement. That is to say, until the savings
exceed the cost.
   Using the marginal saving cost – SCmarg – you can
calculate the consequences of gradual increases of thickness.
   For the maximum financial benefit, the SCmarg should
be the same as the current energy price. This determines        Figure 4: Wooden joists.

the financial optimal thickness of the insulation. Since the
optimal thickness is decided, you may find the total            Conditions for calculation:
profitability of the measure by calculating the average         – Current energy price                  0.60 SEK/kWh
saving cost - SCaverage.                                        – Real interest, r                      4%
                                                                – Real annual energy price increase     2%
NOTE! For profitable insulation measures, the SCaverage is      – Life span, n                          50 years
always lower than the SCmarg. This generally also applies to:   – Heat consumption figure, Q            110 · 103 K h/year
SCmarg dimensions the insulation thickness                      – Investment in order to increase the
SCaverage describes profitability.                                thickness of the insulation by 1 cm   3 SEK
                                                                – α, calculated using the above rate
                                                                  of interest energy price increase
                                                                  and life span                         32.4
                                                                – λD for insulation                     0.042 W/m K

                                                                The following thermal resistance may be applied in the
                                                                calculations

                                                                 Construction                                R m2 K/W

                                                                 Surface transfer resistance
                                                                 + outer roof + inner covering                   0.47

                                                                 d2 = 170 mm Loose wool, 5 % rule
                                                                 share                                           3.85
                                                                                                                  d1
                                                                 d1* Loose wool without wood frame
                                                                                                                0.042

                                                                * Increased successively until economical thickness is
                                                                  achieved.

                                                                We have chosen to start the calculation from an insulation
                                                                thickness of 170 + 50 mm. It provides an Up value of
                                                                0.205 W/m2 K. With an increase in insulation standard by
                                                                20 mm the investment increases by 6.00 SEK/m2. At the
                                                                same time, the U value drops by 0.018 W/m2 K.




                                                                                                                         7
s I N S U L AT I O N T H E O RY – I N S U L AT I O N E C O N O MY




The energy saving will be as follows:                                                           Temperature inside
                                                                                                      the house
B = ∆U · Q = 0.018 · 110 = 1.98 kWh/m2
                                                              Area (Sweden)                  18 °C       20 °C      22 °C

With the aid of the energy saving, the investment             Kiruna                          156         175         194
difference and other conditions, the above will be:           Arjeplog                        150         166         182
                                                              Piteå                           140         155         170
           ∆I · 100         6.0 · 100                         Lycksele                        131         146         161
SCmarg =               =                 = 0.0935 SEK/kWh
            B·α            1.98 · 32.4                        Östersund                       122         136         150
                                                              Härnösand                       111         123         135
The measure is profitable since the SCmarg < 0.60 SEK/kWh     Falun                           109         121         133
                                                              Gävle                           103         114         125
The corresponding calculation is completed for every
                                                              Örebro                           98         109         120
increase in insulation thickness for the SCmarg, until it
                                                              Nyköping                         95         106         117
exceeds the applicable energy price. The increase in
                                                              Visby                            89          99         109
thickness is chosen according to the standard thickness so
that the step will be 20 – 30 mm.                             Kalmar                           88          98         108
   According to this calculation, it will become apparent     Göteborg                         82          91         100
that the optimal insulation thickness today is                Malmö                            79          88          97
approximately 650 mm for the construction in question.       Table 5: Heat consumption figure Q at different temperatures
                                                             inside the house.
The average savings cost is determined by calculating the
total step from 220 to 650 mm insulation thickness.

B = ∆U · 110 = (0.205 – 0.093) · 110 = 12.3 kWh/m2


SCaverage = ∆I · 100   = 38 · 3 · 100    = 0.29 SEK/kWh
             B·α         12.3 · 32.4

The measures are very profitable since

SCaverage < 0.60 SEK/kWh.




8
s I N S U L AT I O N T H E O RY – S T R U C T U R A L D E S I G N




Structural design
When planning, it is important that the house is looked at       If the material and the construction are both perfect, there
in its entirety and not just by the performance of the           will be a certain safety margin in relation to the calculated
individual components.                                           value. But any errors in the execution of the work or faults
   Even if the calculation of the heat losses has been carried   in the finished structure can affect both the insulating
out correctly in theory, there is no guarantee that the result   efficiency and durability.
will agree with the actual outcome. Construction must be             The following points are particularly important to
carried out in a professional way. This means that the work      consider in order for the work to be performed correctly
must be performed both correctly and accurately.                 and accurately:




• Air and vapour barriers                                        It is important that these four principles are followed when
  The building must have an airtight layer, a so-called air      construction is carried out, otherwise there will be a risk of
  and vapour barrier, on the inside of the structure. The        unnecessarily high energy consumption and in the worst
  layer must not only prevent the transfer of moisture from      case damp damage may result. There now follows some
  the inside to the outside, but should above all make the       advice and tips for each of the points. If you follow the
  structure airtight. A structure that is not airtight will      recommendations the building will function correctly!
  result in higher energy consumption and there will be a
  risk of damage due to damp and mould within the                Air and vapour barriers
  structure. In addition, draughts can cause discomfort.         A modern house must be airtight in order for the ventila-
                                                                 tion to function as intended. Therefore, an air and vapour
• Installation of insulation                                     barrier is required, this will operate during the entirety of
  Thermal insulation must fill up the whole of its space.        the lifetime of the house. Normally a plastic sheeting is
  There must be no air gaps. It is particularly important        built into the structure, which is placed on the “warm side”
  to avoid air gaps on the “warm” side of the insulation. If     of the insulation. Other materials, such as concrete, can
  the insulation does not fill up the whole of its space, air    provide airtightness.
  can begin to circulate, a convection that can seriously
  decrease the intended insulation efficiency.

• Wind protection
  When the air moves behind the facade, it is important
  that it cannot penetrate the primary insulation or the
  gaps around the insulation. Therefore, there must be
  wind protection in place to prevent this. The wind
  protection must be adapted to the insulation material,
  the façade material and the entire structure.
                                                                                   Overpressure inside: Air is
                                                                                   forced out
• Ventilated air space
  There should normally be an air space that is ventilated
  by outdoor air behind a façade layer or under a large
  number of roof coverings. The air space allows the
  moisture that comes in from the outside to be ventilated
  away. It also functions as an extra safety device if any
  part of the inside of the structure has not been made
  airtight. Certain structures with totally airtight exteriors                     Underpressure inside: Air is
  - e.g. warm roofs and sandwich structures - do not                               taken in
  require an air space.




                                                                 Figure 6


                                                                                                                                 9
s I N S U L AT I O N T H E O RY – S T R U C T U R A L D E S I G N




A correctly functioning air and vapour barrier is
                                                                   THINK ABOUT THIS IN PARTICULAR:
particularly important when there is too much pressure             • Place an airtight layer, e.g. a 0.2 mm PE foil on the inside
indoors. This occurs nearly always at the top of the               of the insulation to prevent air leakage and vapour diffusion
building during the winter. If the attic joist floor is not
                                                                   • If possible place the installations on the inside of the plastic
airtight, heat and damp air can penetrate their way into the       foil
structure and condense.The consequences can be serious
                                                                   • Think about making all joins and routings airtight. Use
mould damage. In addition, if the insulation is not kept
                                                                   durable tape, adhesive, caulking compound or other special
dry, its insulating properties will be reduced.                    arrangements
   Moisture convection, moisture that accompanies air
                                                                   • Pack and seal large gaps
when it penetrates into a structural component, is much
more dangerous than moisture diffusion, that is moisture           • On roofs made of concrete or light concrete the barrier is
                                                                   to protect against building moisture.
which is transferred due to differences in vapour content.
   Airtightness is therefore very important. But the barrier       • Low-sloping unventilated roofs on supporting sheets should
should also prevent vapour diffusion into the structure.           always be constructed using an air and vapour barrier on the
                                                                   sheet. This becomes particularly important if the activity on the
Otherwise water vapour can condense and cause damage.
                                                                   premises markedly increases the moisture content of the air
The driving force for diffusion is highest during the winter
since moisture will flow into the building from people and         • Plastic foil must not be used in structural components that
                                                                   are in direct contact with the ground, e.g. basement outer
from activities. The barrier must then be placed on the
                                                                   walls, basement floors or slabs on the ground
inside in order to be effective. If it is placed on the outside,   The ground usually has higher moisture content than the
it will have almost the opposite effect to that intended. In       internal air. Therefore, the majority of the insulation should be
this case the moisture will condense on the barrier.               laid on the outside and the underside respectively. If insulation
   It is sometimes stated that a vapour barrier on the inside      is used on the inside, an effective vapour barrier should be
can cause damage during warm, rainy summer days when               placed under the insulation for slabs on the ground or
                                                                   basement floors. A vapour barrier is not to be used for an
the diffusion drives the moisture from the outside to the
                                                                   inverted insulated basement wall. Wood must not be in
inside of the structure. However a large number of                 contact with the supporting elements.
investigations show that these fears are exaggerated. It is the
driving forces during the winter that must be guarded
against.
   The air and vapour barrier is usually a 0.2 mm PE foil
that satisfies national standards for ageing resistance. Joints
must be kept to a minimum and be as well sealed as
possible.
   A lot of damage has been reported from buildings where
the construction has been made knowingly permeable in
order to allow it to “breathe”. Paroc would most definitely
warn against such solutions. Be careful when constructing
the air and vapour barrier. The most critical points are
– Connections between different building components
– Routings for pipes, electrical points or ventilation devices
– Joins in the barrier




10
Installation of insulation                                         THINK ABOUT THIS IN PARTICULAR:
The construction of an insulating material with cells or a         • Be careful to cut the insulation so that it fits. Be careful when
lattice of fibres causes the air to move and the heat transfer     assembling so that the insulation completely fills out the space
                                                                   for which it is intended.
will thereby be significantly reduced. Therefore, it is
important that the insulation completely fills out the             • Stone wool must be cut to be slightly larger in length and
intended space. Otherwise the air can begin to move                width. No air spaces between the insulation and the
                                                                   surrounding surfaces.
through the gaps and spaces.
    Since warm air is lighter than cool air, the air works         • Insulation in several layers must be assembled with offset
along an outer wall after rising along the warm side of the        joints where this is possible.

insulation and sinking down the cool exterior. These               • The air and vapour barrier and the insulation must lie close
driving forces increase as the temperature difference across       against each other. If there is a thin panel in the roof, for
the insulation increases. In a roof the air will move through      example, the barrier is to be placed on top of this.

the structure.
    It is therefore important to avoid spaces, cavities, gaps or
other imperfections in the insulation and in particular on
the warm side. If cool external air is allowed to reach the
inside of the insulation, the insulation has been short-
circuited.




Wind protection
                                                                   THINK ABOUT THIS IN PARTICULAR:
The wind protection must prevent air that moves behind a           • Wind protection must not be so airtight against vapour
façade or an external wall from ruining the thermal                diffusion that it prevents moisture that has come into the
insulation capabilities of the insulation. Therefore the air       structure from evaporating outwards.
that moves parallel to the insulation is to be protected           • Be particularly careful with wind protection at the corners of
against using the wind protection, the air and vapour              the building. There must be no unnecessary joins here.
barrier will deal with air movement through the structure.         • Follow the instructions in the recommendations, which can
   The requirement for wind protection depends on the              be gathered from the figures below. They are based on many
size of the air movements to be expected behind the façade         years’ experience and are a guarantee for correct functioning.
layer. A well-walled brick façade will provide significantly       If an alternative solution is chosen, this will be at your own
                                                                   risk. If this should be the case, consult the manufacturer or a
lower air movements than a wooden panel, for example.
                                                                   recognised expert.
High buildings provide greater air movements than low
buildings and buildings exposed to the wind provide
greater air movements than buildings protected against the
wind. Particularly exposed are the corners of the buildings
where the difference in wind pressure between both sides
can be great.




                                                                                                                                    11
s I N S U L AT I O N T H E O RY – C O N S T R U C T I V E D E S I G N




                                                              Light stone wool like PAROC UNS 37


                                                              Stone wool, minimum PAROC WAS 50


                                                              Stone wool, minimum PAROC WAS 25 (30 mm) or PAROC WAS
                                                              35 (50, 80 mm)



                                                              Optional façade material




                                                              Façade layer of facing stone, concrete, etc.




                                                              Wind protection of plaster, board, foil or paper




Figure 7




Ventilated air spaces                                          THINK ABOUT THIS IN PARTICULAR:
Behind the façade layer and under the roof coverings there     • If the façade material has a smooth rear side, nailing
                                                               battens or similar must not seal the air space.
should be a ventilated air space. The purpose of an air
space is to ventilate (and in walls also to drain) away any    • If the edge of the joist must be sealed in order to prevent
rain water that has penetrated and to prevent it from          the risk of fire spreading, air permeable stone wool should be
                                                               chosen
reaching other moisture sensitive construction
components. Furthermore, the space must ventilate away         • Ensure that you build in good ventilation at the eaves of the
any moisture that comes from within the building.              attic floor joist and supplement it with ridge ventilation or
                                                               gable ventilation.
   The air space should be at least 20 mm wide and must
not be packed with lath or mortar remains.                     • Follow the instructions in the recommendations. They are
   Sandwich structures, concrete elements or so-called         based on many years’ experience and are a guarantee for
                                                               correct functioning. If an alternative solution is chosen, this will
industrial roofs or low-sloping roofs do not normally
                                                               be at your own risk. If this should be the case, consult the
require an air space.                                          manufacturer or a recognised expert.




12
s I N S U L AT I O N T H E O RY – H E AT




Heat
Thermal transmission, or the transfer of heat from a           Thermal Conductivity
warmer body to a colder body may in principal take place
                                                               Thermal transmission may be theoretically calculated
in the following ways:
                                                               starting from the laws of physics, however in practice the
                                                               calculation is difficult to carry out. Therefore, the thermal
1) Conduction – transfer of heat through solid/liquid
                                                               conductivity is measured in the various materials. This is
   material.
                                                               defined as a heat amount in Wh per hour – h – passing
2) Convection – the moving of heat through moving fluid
                                                               through a 1 metre thick layer with an area of 1 m2 and the
   or gas.
                                                               difference in temperature across the material is 1 °C. Figure
3) Radiation – transfer of heat by means of
                                                               8 illustrates this definition and it may be written as a
   electromagnetic waves.
                                                               mathematical formula:
                                                                                           W·h·m
Thermal transmission through fixed opaque material only                                    h · m2 · K
takes place by conduction. Convection and radiation
transfer heat in liquids and gases. Thermal transmission in    this may be shortened to W/m K.
a vacuum is only possible by means of radiation.                  Using this formula, thermal conductivity can be
    The materials that are applied as thermal insulation are   expressed as a figure. This is signified by the Greek
all porous; part of the material is filled with gas and most   character λ (lambda).
often with air. Thermal transmission through traditional
insulation material takes place as a result of the             λ value
conduction, convection and radiation.                          λ may be used when calculating the amount of heat that
    The thermal insulation capacity of a material is           has been transported through a certain material over a
designated by thermal conductivity signified by λ.             certain period of time.

                                                               Example: If two bodies, both with an area of A and with
                                                               the temperatures t1 and t2 are separated by an insulated
                                                               material with the thermal conductivity of 1 and the
                                                               thickness of d, in the time of h, a heat amount of Q is
                                                               transported through the insulation material. See figure 9.

                                                                                 λ
                                                                            Q=     · (t2 – t1) · A · h
                                                                                 d

                                                               The lower the λ value, the better the insulation quality of
                                                               the material. Normal insulation materials carry a value of
                                                               approx. λ = 0.03 – 0.04 W/m K (measurements are taken
                                                               in laboratory conditions where the average temperature is
Figure 8                                                       approximately 10 °C).




                                                               Figure 9



                                                                                                                            13
s I N S U L AT I O N T H E O RY – H E AT




How the structure of the material influences                        Thermal transport
thermal conductivity                                                If an air gap separates two surfaces of different temperatu-
The insulation properties of a material depend on the               res, heat will transfer from the warmer surface to the
material density, which in turn is influenced by the                colder. The thermal flow through the air gap per m2 and
porosity of the material. Porosity can be achieved in               per hour may be expressed in the following way:
different ways.
   When cellular plastics such as XPS, Extruded polystyrene,                                  λ air
are used the spaces become sealed due to the porosity. The                               q=           (t2 – t1)
                                                                                                 d
basic material is entirely connected and rigid. Stone wool
has a completely different porosity. The pore volume is             λ air consists of three parts:
continuous and the basic material, the fibres, are in contact       λcd = the actual thermal conductivity of air
with each other only in certain points. In all the other            λcv = contribution from convection
porous materials, the porosity exists in the form somewhere         λra = contribution from radiation
between these two extremes.
                                                                    The value highlighted in Figure 10 applies to a 100 mm air
                                                                    column between wood surfaces or brickwork (not shiny
                                                                    metallic surfaces).




                                                                                              λconductivity

                                                                                              λconvection
                     λradiation


                       λconductivity                                                          λradiation




Figure 10: Composition of thermal conductivity in Paroc stone wool and the air column.




14
If a porous insulation material is placed in the air gap, the      The influence of density on the insulation
air gap is divided by either the cell walls or fibres. The         properties of Paroc stone wool
convection in the air gap stops almost completely as the air       The following five figures indicate the way in which the
movements are strongly inhibited by dividing the volume.           insulation properties of Paroc stone wool vary based on
Radiation contribution, which used to be the dominating            density with regard to the four abovementioned
transmission form, is significantly reduced and there are          contributions to the thermal transfer as well as the overall
now many small cells or fibres which transfer radiation at         thermal conductivity.
very small differences in temperature. If the insulation
material is filled with air, the actual thermal radiation          Convection
through the air does not change. In addition to the other          As a result of the temperature difference, convection may
factors present in the three aforementioned transmission           take place in stone wool insulation. It is clear from the
forms, there is now also a contribution to the thermal             figure that the influence of convection is marginal, when
transfer in the form of thermal conduction through the             the density is 20 kg/m3 or greater. All Paroc products on
basic insulation material – cell or fibre material.                the market are above this density.
    Similar to the case with the convection contribution, the
fewer fibres or cells that there are in the insulation material,    λ10 W/m K
the smaller the radiation contribution. In order to reduce
                                                                    0.04
the total thermal radiation, fibres or cells may be used. On
                                                                    0.03
the other hand, a large quantity of insulation material will
                                                                    0.02
lead to increased thermal conductivity through the basic
                                                                    0.01
material. Therefore, the more fibres there are per mass unit
                                                                    0.00
in the fibre material, the better.                                         0                100                    200 γ kg/m 3

                                                                   Figure 11: The effect of convection.
         Insulation W/m K               Air gap W/m K

  λcd:    0.028       (82 %)             0.025          (4%)       Thermal conduction through air
  λcv:    0.000         (0 %)            0.116        (19%)        Thermal conduction through stationary air makes the
  λra:    0.006       (18 %)             0.476        (77%)        largest contribution to the total thermal transfer through
                                                                   the insulation material and only varies very little according
          0.034      (100 %)             0.617      (100 %)
                                                                   to density. This is due to the fact that the fibrous material
                                                                   under all conditions represents only a small part of the
                                                                   total volume

                                                                    λ10 W/m K

                                                                    0.04
                                                                    0.03
                                                                    0.02
                                                                    0.01
                                                                    0.00
                                                                           0                100                    200 γ kg/m 3

                                                                   Figure 12: The effect of conductivity in air.




                                                                                                                                  15
s I N S U L AT I O N T H E O RY – H E AT




Radiation                                                       Total thermal transfer
The radiation contribution is strongly dependent on the         If you add the abovementioned contributions to a total
density of the stone wool and may at lower densities            thermal transfer, the result will be a graph that presents the
become dominant. Furthermore, it should be noted that a         thermal conductivity of Paroc stone wool as a function of
radiation contribution is also dependent on temperature         density. The graph illustrates that the thermal conductivity
and the radiation contribution increases in higher tempe-       is at its minimum when the density is approximately
ratures.                                                        80 kg/m3. However, the minimum level varies depending
                                                                on the temperature.
λ10 W/m K
                                                                    The above described connection between the thermal
0.04                                                            conductivity and the density applies to the majority of
0.03                                                            insulation materials, nevertheless, with different figures.
0.02                                                                It should be noted that this relation regarding stone
0.01                                                            wool can also vary, as the fibre orientation can be altered in
0.00                                                            order to obtain optimal properties for the installation and
       0                 100                200 γ kg/m 3        the compressive strength.

Figure 13: The effect of radiation.                              λ10 W/m K

                                                                0.04
Thermal conductivity through fibrous materials
                                                                0.03
As the amount of fibre grows proportionally with the
                                                                0.02
density (for the same fibre diameter), so does the fibre
                                                                0.01
conductivity contribution.
                                                                0.00
                                                                       0                100               200 γ kg/m 3
λ10 W/m K

0.04                                                            Figure 15: The relationship between thermal conductivity and
                                                                density.
0.03
0.02
                                                                λ value for calculation
0.01
                                                                It is the λ10 value, with statistical variations, that is used
0.00
       0                 100                200 γ kg/m 3        when calculating the thermal insulating status of a
                                                                construction. In EN-regulations it is called λD, where D
Figure 14: The effect of convection in the fibres.              stands for declared. EN 10456 describes the way of
                                                                calculating the λD in detail. There may also be national
The graph will look different if the fibre consistency of the   adding, depending on local constructions, for the λ
material changes.                                               calculation. Paroc always introduce current λD values for
                                                                the specific products.




16
Thermal conductivity’s dependence on temperature                λ W/m K                            Average temperature
                                                                                                                    °C
The thermal conductivity of stone wool increases in
accordance with the average temperature. The increase is        0.15
approximately 0.5 % per °C in relation to lighter products,
and approximately 0.3 % per °C in relation to heavier
products, within the temperature range of 0–100 °C.                                                                    450
   This depends on the fact that thermal transmission by        0.10                                                   400
means of radiation and thermal conductivity through                                                                    350
stationary air increase with raising temperature.                                                                      300
Convection and fibre conductivity are much less                                                                        250
                                                                                                                       200
dependent on temperature.                                                                                              150
                                                                0.05
   The dependence of thermal conductivity on tempera-
ture at different densities is illustrated in Figure 16.


λ W/m K                                PAROC UNS 37
                                                                0.00
                                                                       50           100              150             200 3
                                                                                                                    γ kg/m

                                                                Figure 17: λ value as the function of density and average
0.20                                                   PAROC
                                                       FPS 10   temperature.


                                                                Furthermore, it ought to be noted that the λ value should
0.10                                                            always be used in conjunction with a figure showing the
                                                                average temperature it is measured at. For building
                                                                insulation thermal conductivity λ10 is used, which means
0.00
                                                                that the λ value is measured at 10 °C.
       100   200       300      400      500       600
                                       Average temperature °C
                                                                The dependence of thermal conductivity on the
Figure 16: The dependence of thermal conductivity on            water content of the insulation material
temperature at different densities.                             If insulation material contains water, this will naturally
                                                                affect the thermal conductivity of the material. In the
Figure 17 shows thermal conductivity as a function of both      manufacturing of Paroc stone wool, water-repellent
density and average temperature. It is clear from the figure    properties are added to the wool and in practice this has a
that the λ-minimum is moved towards higher density              significant effect on how the stone wool absorbs water. The
when the thermal transfer takes place at a higher tempera-      material will only absorb water when it is pressed in.
ture. This means that it is advantageous to use the products    Experience shows that it is very difficult in any other way
with higher densities for insulation work in high tempera-      to reach a water content that exceeds 0.5 % volume.
ture applications.                                                  The amount of water absorbed is minimal. At 95 % of
                                                                relative air moisture there is hygroscopic water content in
                                                                stone wool of only 0.004 % volume.
                                                                    The material is open to diffusion and the value, water
                                                                vapour transfer coefficient is approximately 0.5 mg m/hN.
                                                                This low figure means that when vapour passes through the
                                                                insulation layer and cooles down, no condensation takes
                                                                place.
                                                                    The properties of Paroc stone wool mean that the
                                                                material may be used as a capillary breaking layer.




                                                                                                                             17
s I N S U L AT I O N T H E O RY – H E AT




                                                                     In order to calculate the thermal transmittance for a
     λ W/m K
                                                                     structural part (not a window), access to the following is
0.100                                                                required:

                                                                     • EN ISO 6946 “Building components and structural
                                                                     parts – Thermal resistance and thermal transmittance -
                                                                     Calculation methods”
0.050
                                                                     • EN 12524 “Building materials and building products –
                                                                     Moisture technical and thermal technical properties –
                                                                     Tables with calculated values.”
                                                                     • EN ISO 10456 “Building materials and building
                                                                     products – Procedures for the determination of declared
                 2         4         6          8        10
                                                                     and calculable thermal values.”
                                         Moisture content (vol.-%)
                                                                     • Material data from the manufacturer of the thermal
Figure 18: λ value as the function of water content                  insulating material. Note that these data are manufacturer
                                                                     specific.


Limiting heat losses                                                 The majority of manufacturers state the corrected thermal
                                                                     transmittance, Uc for the structures that are recommended.
Thermal resistance
                                                                     If it is decided to use these values, there is no need to carry
When the material property, λD is known, the thermal
                                                                     out your own calculation. However, you will need to check
resistance over the insulating layer can be determined. It is
                                                                     that the manufacturer refers to the correct standard.
calculated in accordance with EN 6946 from the formula:
                                                                         On the market there also are computerised calculation
                                                                     programmes that simplify the task of calculation for those
           R = d/ λD ;        m2 K/W,
                                                                     who wish to carry out their own calculations.
           d = insulation thickness in metres.
                                                                         When following EN ISO 6946, a U value in W/m2 K
                                                                     will be arrived at. Then a correction is carried out using
EN 6946 stipulates how the thermal resistance is calculated
                                                                     the three terms that are stated as ∆U values. Information
for different types of structures. Rsi and Rse, the inner and
                                                                     on these is to be found in Appendix D to the standard.
outer transition resistances in different directions, are also
given. Furthermore, the standard describes how different
                                                                     ∆Uf is a correction term for extra thermal flow caused by
air spaces and other specific details are dealt with.
                                                                     smaller metallic attachments in the structure. The term is
    The end result for a structural component is RT
                                                                     often insignificant especially in wooden structures.
The thermal transmittance can then be calculated from                ∆Ug is a correction term that takes account of normal
                                                                     construction errors incurred when assembly takes place.
           U = 1/RT ;           W/m2 K                               The standard is general and does not provide sufficient
                                                                     guidance for national structures.
Corrected thermal transmittance                                      ∆Ur is a correction for precipitation and wind that have an
for building components                                              additional influence on the heat losses for inverted roofs.
The corrected thermal transmittance, Uc, for a building
component is calculated according to the equation below:

           Uc = U + ∆Uf + ∆Ug + ∆Ur

To calculate Uc EN ISO 6946 is used.


                                                                      For further information of material properties and our
                                                                      products see www.paroc.com


18
s I N S U L AT I O N T H E O RY – M O I S T U R E




Moisture
This section firstly deals with a number of terms relating      Relative humidity
to moisture followed by the moisture properties of stone        The relative humidity (RH) is also referred to as the
wool. Moreover, an outline will be given of the different       relative moisture and is measured using the relationship
types of moisture that may appear in addition to moisture       between the actual moisture content (water vapour
transport.                                                      pressure) and saturated moisture content (saturated water
   A few special moisture problems will also be addressed       vapour pressure). RH is expressed as a percentage.
in this section including air tight housing, the relationship      The relative humidity is of great significance when
between insulation and ventilation, cellar outer wall as well   determining origins of moisture damage.
as slab on the ground floor.
   As much of the international research regarding              The moisture properties of stone
buildings relates of natural reasons to moisture problems,
                                                                wool
and hence there is a vast amount of information available
on the subject. Information may for example be found in         The water vapour permeability of stone wool is high in
the Moisture handbook from the Moisture group at Lund           comparison to other building materials. This means that
Institute of Technology in Sweden. There are also large         condensation does not take place inside an insulated layer
quantities of computer programs that facilitate moisture        of Paroc stone wool despite the possible drop in tempera-
calculations.                                                   ture across the insulation and even if the so-called dew
                                                                point falls inside the insulation.
Definitions
Moisture diffusion
The transportation of water vapour as a result of
compensation of steam content or steam pressure. Diffu-
sion is a relatively slow course of events.

Moisture convection
The transportation of water vapour as a result of air
movement is a result of differences in air pressure.
Convection is a relatively quick process.

Moisture content
The relationship between the total mass of steam and the
total volume of the gaseous mixture. Expressed in kg/m3.

Saturated water vapour pressure                                 Figure 19
The partial pressure for the water vapour in the air may at
a certain temperature amount to the certain highest value.
This is called the saturated steam pressure and may only be
varied by change of temperature. The higher the tempera-
ture, the higher the saturated steam pressure.

Saturated water vapour content
The steam content at a certain temperature corresponds to
the saturated steam pressure called the saturated steam
content. It is also the greatest amount of steam that air
may contain at a certain temperature.




                                                                                                                         19
s I N S U L AT I O N T H E O R Y – M O I S T U R E




Water repellents and hygroscopicity                           Water resistance and moisture stability
Every Paroc stone wool product is manufactured in such a      Paroc stone wool products have a very high resistance
way that makes it water repellent.                            towards water and moisture. They are made of fibrous
   The purpose of repelling water means that water will       material resistant against moisture and have a hardened
run off the outside of the Paroc slabs, water will not soak   binder – phenol resin, which displays very good moisture
the fibres and will not be absorbed in the wool either.       stability.
   Only if the water is exposed to pressure it may press in
the slabs. In this situation, the fibres do not absorb any    Corrosion
water. Therefore, drying will take place quickly, not least   Any insulation material that is in contact with metal may
because of the high water vapour permeability.                contribute both passively and actively towards corrosion if
   Paroc stone wool products do not absorb water in a         there is a presence of water or moisture.
capillary action. Furthermore, they do not absorb moisture        A passive contribution to corrosion provides insulation
from the air other than in small amounts at extreme           material if it binds the water against the exterior of the
humidity.                                                     metal. Since Paroc stone wool is water repellent and lacks
                                                              both hygroscopic and capillary absorbing tendencies, it is
                                                              possible to reduce the corrosion contribution to a mini-
                                                              mum. Therefore, the lowest diffusion resistance facilitates
                                                              drying when the conditions are favourable. Conversely, the
                                                              lower diffusion resistance leads to a situation in which the
                                                              stone wool cannot contribute towards preventing moisture
                                                              vaporisation from a cold surface. If there is air in the
                                                              insulation, corrosion may take place on corrosive material
                                                              if the moisture does not dry out.
                                                                  The insulation material that is water-soluble may
                                                              increase water’s electrolytic capacity or significantly alter
                                                              the water’s pH value and by that means contribute actively
                                                              towards corrosion. The high moisture resistance of Paroc
                                                              stone wool means that the solubility is very low. The
                                                              electrolytic capacity and pH value do not change.
                                                                  Certain other types of insulation material may contain
Figure 20                                                     materials that directly contribute to the events causing
                                                              corrosion, such as fire retardant salts. Paroc stone wool is
                                                              incombustible and contains no such materials.




20
Sources of moisture                                              Normally, the main sources of moisture are:
Part of a building may be subject to moisture through            – air moisture
precipitation, condensation of water vapour in the air,          – building moisture
absorption of ground moisture or leakage. Furthermore, all       – rain moisture
materials come into contact with the water vapour in the         – ground moisture (vapour content of 100 %)
air and absorb a certain amount of water. During the time        – running water
of building, the construction may also be subject to great
amounts of water, known as building moisture.



                                         Rain moisture




                                                                                      Building moisture

                                               Running
                                               water
            Air moisture




                                                                                      Ground moisture




Figure 21




Air moisture                                                     Building moisture
Air contains water vapour and the content level is denoted       Building moisture is moisture to which constructions are
by RH.                                                           subjected during the building stage or during the
    The relative humidity level outdoors may be assumed to       manufacturing of the building materials.
85 % during the winter and 70 % during the summer.                  After the building phase, building moisture should dry
    The relative humidity level of the air inside the house is   out in order that the construction comes into equilibrium
determined by the outside air temperature and the vapour         with the surrounding relative vapour content.
content, the inside air temperature, production of moisture
inside the house in addition to the ventilation intensity
below the stationary circumstances. That is to say, if there
is an even production of moisture and level ventilation
intensity, the correlation may be written as vapour content
inside the house = vapour content outside the house + the
moisture contribution. The full value of this moisture
contribution during the winter months may be; 3 g/m3 for
the office and 4 g/m3 for the normal dwellings.




                                                                                                                         21
s I N S U L AT I O N T H E O RY – M O I S T U R E




Ground moisture                                                 Moisture transport
The influence of ground moisture is largely dependant on
                                                                The most important moisture transport mechanisms are:
the level of the ground water, but also the type of land, the
                                                                – Diffusion
ground level, the cause of the water and the ground’s
                                                                – Convection (as water vapour)
drainage properties.
                                                                – Capillary absorption
                                                                – Force of gravity (as liquid)
Ground moisture may be divided into the following
categories:
                                                                Diffusion
– Surface water
                                                                Moisture diffusion strives to level out the differences in
– Infiltration water (i.e. surface water penetrating into
                                                                vapour content in the air through molecule movements.
   construction)
                                                                The moisture flows from an area with higher vapour
– Ground water
                                                                content to an area with lower vapour content. Diffusion
– Fracture water
                                                                may in practice be regarded nondependent of the tempera-
– Capillary absorbed water
                                                                ture.

Above the highest surface of the ground water (HSGW),           Temperature Saturation vapour           Saturation vapour
the ground moisture should always be assumed as 100 %              (°C)          content                     pressure
                                                                             cm (10–3 kg/m3)            Pm (Pa)   (mmHg)
RH.
                                                                    – 12                 1.81             217.3         1.63
Example                                                             – 10                 2.15             259.9         1.95
A building is heated to +20 oC and ventilated with 0.5 air           –8                  2.54             309.3         2.32
changes per hour (outside air). The volume of the building           –6                  3.00             367.9         2.76
                                                                     –4                  3.53             437.2         3.28
is 300 m3 and the moisture production inside the house as            –2                  4.15             517.2         3.88
a result of people, animals and plants etc is 0.6 kg/h.               0                  4.86             610.5         4.58
Outside the house, the air temperature is +- 0 oC and the              1                 5.18             657.2         4.93
relative humidity is 90 %, that is to say the vapour content           2                 5.57             705.2         5.29
is 0.0043 kg/m3. The saturation vapour content at +20 oC               3                 5.96             758.2         5.69
                                                                       4                 6.37             813.1         6.10
is 0.0173 kg/m3. The relative humidity within the house is:            5                 6.79             871.8         6.54

                                                                       6                 7.26             934.4         7.01
               vapour content                                          7                 7.74            1001.0         7.51
RH =
           saturation vapour content                                   8                 8.27            1073           8.05
                                                                       9                 8.83            1148           8.61
                                                                      10                 9.40            1228           9.21
The vapour content of the air inside the building =                   11                10.03            1312           9.84
                                                                      12                10.67            1402          10.52
              0.6                                                     13                11.38            1494          11.23
0.0043 +
           0.5 · 300                                                  14                12.05            1598          11.99
                                                                      15                12.83            1705          12.74

                                                                      16                13.66            1817          13.63
(The amount of vapour in the outside air per m3 plus a                17                14.45            1937          14.53
total vapour production inside the house through the                  18                15.36            2063          15.48
ventilation level).                                                   19                16.29            2197          16.48
                                                                      20                17.3             2338          17.54
                       0.6                                            21                18.3             2486          18.65
       0.0043 +
                    0.5 · 300                                         22                19.4             2643          19.83
RH =                            = 48 %                                23                20.6             2809          21.07
              0.0173                                                  24                21.8             2983          22.38
                                                                      25                23.0             3167          23.76

                                                                      26                24.4             3360          25.21
The reduced ventilation level inside the house increases the
                                                                      27                25.8             3564          26.74
relative humidity. This is a problem that may in some cases           28                27.2             3779          28.35
be acute in today’s well-insulated and air tight houses with          29                28.7             4004          30.04
                                                                      30                30.4             4242          31.82
poor ventilation.
                                                                Table 22: The correlation between temperature – saturation
                                                                vapour content and saturation vapour pressure.


22
                                                                 Capillary suction
                                                                 Capillary suction attempts to level out the moisture
                                                                 content in a material through moisture travel in the fluid
                                                                 phase.
                                                                    Capillary suction may normally be neglected on dry
                                                                 material but if certain critical moisture content is found,
                                                                 there will be a continuous water mass in the material and
                                                                 moisture transport through capillary suction will be
                                                                 significant. This type of capillary water transport rarely needs
                                                                 to be taken into consideration. However it occurs around
                                                                 insulation on the ground and by oncoming pelting rain.

         High –                       Low vapour content
                                                                 Convection predominant
                                                                 Moisture diffusion and moisture convection may exist
                                                                 simultaneously and either cooperate or counteract.
Figure 23: Diffusion from high to low vapour content.
                                                                 Previously, the importance of having a vapour barrier in the
                                                                 construction has always been noted. If you observe the
                                                                 amount of moisture that may be transported from one
                                                                 place to another during a certain amount of time as a result
                                                                 of diffusion, you will always find small in comparison with
Outside                               Inside
                                                                 the amount that is transported via convection. Therefore, a
temperature   +10 °C                  temperature   +20 °C       vapour barrier in an outer wall or roof is primarily effective
RH              50 %                  RH              40 %       as a convection or air barrier.
Vapour pressure 614 Pa                Vapour pressure 935 Pa
                                                                     The amount of moisture transported via convection is,
                                                                 in addition to the air pressure difference across the
                                                                 construction, dependent on the total area of perforation. It
                                                                 is important to be aware that one large hole permits a
                                                                 greater moisture transport than many small holes with
                                                                 exactly the same area. It is therefore most important to
                                                                 avoid larger leaks.

Figure 24: Diffusion through untreated walls.
                                                                      Transported                                    Convection
                                                                      amount of water
The outside temperature is +10     oC.The relative humidity
is 50 %. According to the table, this provides a vapour
pressure of 614 Pa.
    The temperature inside the house is +20 oC and the RH
40 %. This provides a vapour pressure of 935 Pa.
    Diffusion takes place from higher vapour pressure to a
lower vapour pressure i.e. inside to outside.

Convection
Moisture convection refers to the fact that the water vapour
content of the air follows the air travelling through a
construction. If the air travels from a warmer area to a
colder area, the water vapour in the air will condense on
the cold exterior. If the air travels from a cold to a warm
                                                                                                                    Diffusion
area, condensation will not take place; the air flow dries the
structure. Thus it is dangerous to have over pressure inside
the house for normal applications.
                                                                                                                      Void with
   Air movement and therefore convection is reduced if
there is an airtight layer anywhere in the construction.         Figure 25


                                                                                                                                23
s I N S U L AT I O N T H E O RY – M O I S T U R E




Air tight housing                                                content level of which may be described by the relative
                                                                 humidity. That is to say, the relative humidity is a quote
This applies to efficient building insulation in order to save
                                                                 between the actual vapour content and the saturation
energy. Simultaneously, the building has to be constructed
                                                                 vapour content of the actual inside air temperature.
air tight in order for the ventilation to be controllable. A
                                                                    A house equipped with furniture, walls etc tends to
good air tightness means that the air is transmitted to all
                                                                 moisture equilibrium with air in the house. With good
the largest parts via the ventilation system. The ventilation
                                                                 ventilation, the vapour content will remain at the normal
amount may be adjusted to the requirements of the
                                                                 level.
building irrespective of wind pressure and similar.
                                                                    On the other hand, with poor ventilation, the moisture
    The requirement for ventilation may exist for many
                                                                 enrichment will take place in any material that can absorb
reasons: to remove odours (from people, tobacco smoke,
                                                                 moisture. The concentration will proceed and the risk of
cooking etc), provide people with vital oxygen, avoid high
                                                                 the formation of mould will increase.
CO2 levels; prevent dangerous levels of radon gas and
                                                                    It is easy to see that as the level of ventilation is reduced,
formaldehyde, as well as to remove moisture (avoiding
                                                                 the relative air humidity increases.
condensation on windows and walls, mould etc).
                                                                    The risk of mould formation will increase. Even at a
Therefore, the requirement for ventilation significantly
                                                                 relative humidity of 75 %, certain types of mould fungus
varies between different types of buildings.
                                                                 thrive at average room temperature.
Reduced ventilation raises relative humidity
From the point of view of the moisture prevention, well
functioning ventilation is of great importance. The level of
ventilation affects the relative air humidity, which is the
main determinant on the existence of mould.
   In an average residence, a lot of moisture is generated.
The human being emits moisture even at temperatures
below +20 oC. At +20 oC, the average person emits 40 g
water per hour and this amount increases by 7 g/per ºC.
Cooking, washing, laundry and plants provide their own
contribution to this moisture load.
   The generated moisture transforms into water vapour
and is absorbed by the air inside the house, the moisture        Figure 26: The effect of low and high ventilation.




                                                                                  Mould fungus may form on wood
                                                                                  and other organic materials
                                                                                  Wood-based materials are subjected to
                                                                                  increased moisture movement

                                                                                  Wood rot




                                                                                  Adhesive on plastic flooring is broken down




                                                                                  Plastic based materials are subjected to
                                                                                  greater moisture movements



Figure 27: The effect of moisture content.


24
Cellar walls                                                     Slab on the ground and cellar
Cellar walls are susceptible to different sources of damp. In    floors
the cellar walls there is building moisture, gaps within the     Slab on the ground floor and cellar floors may be insulated
walls contain air moisture and in the ground outside the         above and below concrete. Many complaints in recent years
wall, there is ground moisture. Furthermore, the area may        have focused on the moisture problem of the slab on the
be subjected to obtaining local water pressure against the       ground foundations. Most cases refer to wood framed
wall as a result of rain, melted water or water currents in      flooring above the concrete slab. Therefore, this construction
the ground. Moisture may also be absorbed via capillary          solution is applied to hardly any constructions today.
action through the lower plate in walls.
   Therefore, damp in cellar constructions must be dried         Insulation above concrete
out. The design engineer has to presuppose that one is able      One reason in support of thermal insulation on top of the
to provide the interior with dense material for example,         slab is that it feels more comfortable to walk on than one
vinyl tape or tight acrylic paint. The scientific way is to      with plastic carpet fixed directly on the concrete. Another
prevent the moisture problem in cellar walls thus making it      reason is that the surface of the concrete slab requires less
possible for the construction to dry out from the outside.       accuracy.
   If the cellar wall is insulated from the outside with a          The disadvantage of having insulation above the slab is
capillary breaking, vapour permeable material must the           that the transport of moisture in the vapour phase up
outside forthcoming moisture be diverted. Building               through the slab must be stopped with a vapour barrier. If
moisture may dry out through the vapour permeable                this is not done, the floor may get damaged. Cellular
insulation. This means that it does the same irrespective of     plastics may not replace the vapour barrier since there will
the material on the inner jacket. It is also advised to have a   always be cracks between the plates. Cellular plastic is not
taut coating on the inner jacket as well.                        even sufficient to be used as diffusion seal.
                                                                    If you are at all unsure about achieving a lasting taut
                                                                 vapour barrier you should place the insulation below the
                                                                 concrete instead.



                                 isture
                             g mo
                      Buildin




                        re
                    istu
                  mo
              und
           Gro


                         e    Capillary
                     inag
                  Dra         breaking
                                                                                                   Moisture transport




                               layer




Figure 28: The capillary breaking insulation of cellar walls.    Figure 29: Insulation below the concrete slab.




                                                                                                                             25
s I N S U L AT I O N T H E O R Y – M O I S T U R E




Insulation below concrete
The best and safest way to build a slab on the ground floor
is to insulate the under side of it with open insulation. This
type of thermal insulation incorporates a moisture
mechanical advantage and allows moisture transport from
the slab to the ground instead of from the ground to the
slab. How is this possible?
    Well, the ground has 100 % RH in certain temperature,
say 17 oC. This provides a vapour pressure of 1937 Pa. The
insulation means that you receive a temperature on the
underside of the plate that is higher than in the ground, for
example 20 oC. The saturated vapour pressure in the plates,
i.e. at 100 % RH will be 2338 Pa at that temperature.




                                                                                                 Moisture transport
    Since the vapour pressure attempts equilibrium, it
results in vapour transport in a downward direction. This
continues until the vapour pressure is the same in the
ground and the plate. In the above example, the slab will
reach 83 % RH. The level of humidity will not influence
the plastic carpet or the adhesive.
                                                                 Figure 30: Floors without insulation.
    To ensure that the vapour transport is downwards, a
temperature difference of at least 2 oC is required, which
can be achieved by using 30 – 40 mm thick stone wool for         Floors without insulation
the slab widths up to 15 metres. From the energy efficient       What happens if you have laid a taut floor covering on a
point of view, people often choose a significantly thicker       concrete slab which already had time to dry to an average
insulation. This provides even better protection against         humidity of 90 % RH?
moisture damage.                                                    Beneath the slab lies a drained and capillary breaking
    Insulation must be laid under the entire floor. If the       layer. The humidity of the ground is 100 % RH. Since the
insulation is only placed on the edge, the inner parts of the    temperature of the slab will be the same as the ground, you
floor will not be protected against ground moisture.             will get vapour transport from the ground to the dry plate.
Insulation also has to be taken from beneath the edge            Vapour transport will continue until the vapour pressure
section, stiffening etc. It is advised that an insulation        reaches equilibrium i.e. 100 % RH.
material that may bear a higher load than the rest of the           The result will be saponification of the adhesive on the
insulation be used.                                              floor coating or mould growth on organic material.




                                                                   For further information of material properties and our
                                                                   products see www.paroc.com


26
s I N S U L AT I O N T H E O RY – F R O S T




Frost
When heat is transformed from the ground and the                 The conditions for the ice layer growing are that there
temperature is lower than 0 oC, it transforms the water          must be a capillary connection with the ground water. The
content in the ground to ice and the ground freezes. There       ice layer will appropriate the water molecules from the
are two types of frost: ice stripes frost (discontinuous) and    grains of earth that are nearest under the frost boundary.
homogenous frost. Only the ice stripes create the frost          The resolved grain of earth will in turn appropriate from
elevation.                                                       the nearest grain lying beneath and wave of thefts will
   One term of significant importance in connection with         continue in this way as long as the ice layer has capillaries
frost is capillaries. If you place a small pipe in a bowl with   connected to the ground water. In the event that the
water, the water will rise into the pipe. Exactly the same       connection is lost, there will be no more ice volume and
happens in the ground, i.e. a dry area of land has the ability   there will be no space for the frost elevation.
to absorb water provided there are small holes in the
ground which serve as pipes for transport by the ground          Different kinds of ground provide different
water from a lower level to a higher.                            types of frost
                                                                 The more fine-grained the area of land, the thicker the
The origin of frost                                              water holes resulting in the individual grain of earth will
Every type of land has a certain purpose to bind water. A        be. This means that the water molecules may be
water coating surrounds every grain of earth and its             transported easier and even quicker when the grain of earth
thickness depends on the size of the grain.                      is small and the transport route short. In a fine-grained
   When the heat leaves the ground, the grains of earth in       area of land however, the frost elevation will be easier since
the water coating are transformed to ice crystals – frost. If    the number of contact points between the ice sheets and
the frost now stops at a certain depth known as the frost        the amount of grains is significantly greater (the load at
boundary and the conditions are suitable for new water           each point is smaller). Clay is an exception since it has a
molecules to be transported there, they will also be trans-      low capillary path speed.
formed to ice and join the existing mass of ice crystals.            On an area of land with coarse particles, the water
With that, the ice layer receives an increase in volume that,    transport will be complicated because of a long transport
according to the smallest resistance layer, straightens out in   way and more narrow water holes. The load in the contact
an upward direction and consequently raises the layer of         points is so great that the ice crystals will not be able to
earth above.                                                     raise the layer above and instead fill the space of the hole
                                                                 between the grains. In order for the frost elevation to take
                                  Frost elevation                place, the following conditions must be met simultaneously.

                                  Directed resultant force       – The area of land needs to be prone to frost.
                                                                 – Water should be able to transport to the frost boundary.
                                  Frost boundary: ice crystal    – Enough significant amount of heat should disappear
                                  formation provides an            from the area of land.
                                  increase in volume             – The load on the ground must be less that the lifting
                                                                   power of the frost.
                                  Capillary moisture transport


                                  Ground water


Figure 31: The frost elevation mechanism.




                                                                                                                            27
s I N S U L AT I O N T H E O RY – F R O S T




Insulation in the ground prevents frost damage                 In order to obtain functioning ground insulation, the
Frost damage may be prevented in different ways. You can:      following requirements are also demanded in the insulation
                                                               material:
– Change the frost prone area of land for one less prone to
  frost.                                                       –   It must not rot
– Lower the ground water level in order that the earth         –   It must withstand acid found in the ground
  cannot absorb water.                                         –   It must have high pressure strength
– Foundations for frost free depth.                            –   It must have good thermal insulation power
– Lay a layer of thermal insulation in the ground.
                                                               Extruded cellular plastics fulfil these requirements.
From an economical point of view, the most interesting         Stone wool is not recommended as insulation against frost
alternative is to position a thermally insulated layer. The    in roads, railways or other cold constructions. In the long
advantage with ground insulation is that the thermal           time run stone wool will get wet and the thermal
current can be limited from the ground during insulation.      conductivity reduced. If one side of the construction is
As a result there is less frost depth since the temperature    warmed up, stone wool works very well.
beneath the insulation layer seldom falls short of 0 oC. The
reduced frost depth in turn:

– Much smaller risk for frost damage
– Less foundation depth for houses etc
– Less disposition depth for water and sewer




28
s I N S U L AT I O N T H E O RY – G R O U N D I N S U L AT I O N




Ground insulation
There are many different recommendations for insulation         Critical factors
materials that are to be used in the ground and for             – The structure shall be such that it prevents ground
structures on the ground.                                         water, capillary water or water seeping in from the
   The old tradition of observing natural geography is            outside from reaching the thermal insulation or flooring
unfortunately not always followed. Today, houses are built        material susceptible to moisture.
on old swamps or dried seabed or lakebeds, or on other          – The structure shall also reduce the relative humidity, i.e.
types of ground that are less suitable for the purpose. The       the thermal insulation function shall hold the RH so
conditions of the locality should be taken into conside-          low that flooring materials susceptible to moisture are
ration when deciding on a solution.                               protected.
   The various ground insulation solutions are more or less     – The structure must also be durable and non-deformable
resistant to moisture load. The functioning of the various        so as to bear moving loads.
materials and the major differences are presented below.        – The structure shall consist of materials that withstand
   Statements were obtained from The Swedish National             any moisture loads without being ruined or releasing
Testing and Research Institute (SP) and from Munthers             hazardous materials.
Torkteknik AB with regard to the structures presented
below. Both organisations have had to deal with multiple        Important details
difficulties and have thus learned how not to build. They       – The slab of concrete must be able to dry out upwards or
are called SP respectively MT in the following.                   downwards before tight flooring materials are laid.
                                                                  Thick parts of the slab may be particularly problematic
Ground Slab                                                       in this respect.
                                                                – The moisture barrier separates the moisture sensitive
General description
                                                                  material, e.g. wood on the slab, from the slab.
A ground slab supporting a heated building must always be
                                                                – When the insulation is underneath the slab, a moisture
provided with heat insulation. Its main purpose is to limit
                                                                  barrier is placed on the slab, if required.
relative humidity in the floor to a level that does not
                                                                – Diffusion-proof flooring with moisture sensitive glue
damage the flooring material. The insulation shall also
                                                                  requires a moisture barrier.
reduce heat losses along outer parts of the floor. If the
                                                                – When the insulation is above the slab, a moisture barrier
insulation of the slab is very thick, ground frost insulation
                                                                  is placed between the slab and the insulation. This
may be necessary on the outside.
                                                                  requires that the slab be carefully cleaned.
    Thermal insulation can be placed either underneath or
                                                                – The recommendations are generally valid for small
on top of the concrete slab.
                                                                  houses. Where larger slabs - width over 10 m - are used,
    In order for the ground slab to function properly, highly
                                                                  a special moisture solution is required, such as a
reliable capillary barrier and drainage between ground and
                                                                  moisture barrier between insulation and the slab.
the concrete slab is required. When a concrete ground slab
                                                                – When floor heating is used, the insulation should be
is used, the slab must be protected from contact with water
                                                                  completed with moisture barrier between the slab and
sucked up by capillary action. The insulation shall be dry
                                                                  the insulation underneath.
so as to ensure that excessive humidity does not reach the
floor.
    A correctly designed ground slab is theoretically safe
with regard to moisture, and it is also considerably less
expensive than other solutions.




                                                                                                                           29
s I N S U L AT I O N T H E O RY – G R O U N D I N S U L AT I O N




Slab on insulation                                                    Insulation above slab




Figure 32: The entire slab is always insulated. Minimum 100 mm        Figure 33: A PE vapour barrier or a moisture barrier is placed
draining material under insulation. Edges are insulated, if           between the insulation and the slab. The layer breaking down the
insulation of the slab is over 120 mm thick.                          capillary phenomenon should be at least 150 mm thick.


Insulation with Paroc stone wool under the slab is conside-           This solution gives a soft and warm floor. No problems
red to be a dry application; no extras when calculating the           with moisture from the structure, if the concrete surface is
thermal isolating capacity.                                           perfectly clean.
   The drying time for a slab with stone wool is                         Requires careful work. The structure is susceptible to
approximately 40 days. The slab continues drying                      moisture from above.
downwards even after installation of the flooring.                       Keeping the vapour barrier during building work can be
   If EPS or other plastic insulation is used, the drying             a problem.
time will be 60 days. Plastic insulation can give extra
protection against moisture from below.                               COMMENT:
                                                                      SP: Frequent damage above all on floor structures with studs.
COMMENT:                                                              Plastic foil does not guarantee freedom from damage. There
SP: Little damage on this floor. If stone wool is replaced with       will be moisture under the plastic sheets, and microorganisms
cell plastic insulation, drying will take longer after installation   will flourish. If smell occurs, a floating floor is more difficult to
of tight flooring. Before laying the flooring the slab will dry       fix. Vapour movement will make the slab moist in spite of a
mainly upwards irrespective of the insulation material.               layer stopping capillary action.
Adequate drying time is necessary. When the direction of
moisture movement is reversed, e.g. when turning off floor            MT: As for moisture, this structure should be avoided. The
heating, dense insulation is better than open stone wool.             insulation layer may not include organic material. Sills and
Moisture barrier is required in such cases.                           the like are placed above the upper edge of the insulation layer,
                                                                      in warm room air, and should be sufficiently insulated against
MT: With regard to protection against moisture this is the best       moisture. The vapour resistance of the insulation layer should
ground slab structure. Sills and the like should also be              be taken into consideration with regard to other layers
protected from concrete. The moisture content in the concrete         including the flooring.
slab will usually be so low that the surface layer can be selected
quite freely.




30
Insulation above and below the slab                                Basement wall
                                                                   General
                                                                   The basement is subject to various sources of moisture.
                                                                   The wall structure contains moisture that must be allowed
                                                                   to dry out. There is moisture from the ground outside the
                                                                   basement wall. Rain, water from melting snow and ice or
                                                                   water currents in the ground can also cause local water
                                                                   pressure against the basement wall. Capillary action can
                                                                   cause water to be sucked through the slab and up the wall.

                                                                   Moisture in structure
                                                                   The moisture in a basement structure must be allowed to
                                                                   dry out, either outwards or inwards. If the inside of the
                                                                   wall is coated with a non-breathable material, e.g. a vinyl
                                                                   wallpaper or plastic paint, the moisture can in practice dry
                                                                   out only outwards.
                                                                       A correctly constructed basement wall therefore allows
                                                                   diffusion on the outside.
                                                                       The moisture dries out over a period of several years,
Figure 34: Combination of insulation below and above the slab
                                                                   after which the inside of the wall can be sealed against
as per previous alternatives.                                      diffusion without a risk of damages, even if the outside wall
                                                                   is diffusion-proof.
The main insulation underneath the slab can be combined
with a thin layer of comfort insulation.                           Ground moisture
   If the slab is insulated on the underside with PAROC            Ground moisture is the main cause of problems. You
GRS 30, the slab can continue drying downwards after the           should count with a relative humidity (RH) of 100 % in
dense flooring has been laid.                                      the ground, even if the value is occasionally lower.
   A plastic foil is placed between concrete and stone wool           Ground moisture in the form of free water can be
on the topside.                                                    drained away. The wall should for the sake of safety have
   Optimal moisture protection and comfort:                        an anti-capillary layer so that the water current in the
PAROC GRS 30 under the slab and 17 or 25mm PAROC                   drainage does not damage the wall.
SSB 2 on the topside. Double floor sheets for even
compression on the topside. Plastic foil between the               Surface moisture
insulation and the slab.                                           Plan a slope leading away from the building.

COMMENT:                                                           Critical factors
SP: Good, comfortable floor. No damage. An alternative             – Moisture in the structure must be able to dry outwards
solution is ventilated sealing layer, moisture protection mat,       if the inside of the basement wall is sealed.
which allows the drying of moisture in the structure, and at       – The wall must be protected against moisture from the
the same time the floor is warm.                                     outside.

MT: With regard to moisture insulation this is only better
with insulation underneath. With regard to comfort the
footing should be separated from the concrete slab so that floor
surface temperature will not be too low. This can occasionally
be achieved with correct flooring material. The insulation
layer should never have a load-bearing frame made of organic
material. Place sill and the like above the top edge of the
insulation layer.




                                                                                                                               31
s I N S U L AT I O N T H E O RY – G R O U N D I N S U L AT I O N




Important details                                                 External insulation
– The concrete slab extends outside the basement wall,
  and a cove is poured on the edge. The cove must be
  poured carefully in order to cover the gap between the
  wall and the slab. To be on the safe side, the wall should
  be insulated against moisture by bitumen 0.5 m above
  the cove.
– One way to interrupt the capillary action is to set up a
  ground insulation slab, PAROC GRS 30, against the
  basement wall.
  Any water in the ground will flow parallel to the slab,
  as the flow resistance of the slab is usually higher than
  that of the ground. In dense ground the opposite is
  possible. To prevent water from running in through the
  slab into the wall there must be a drainage layer outside
  the slab made of suitable material. The slab is a part
  of the drainage system and must therefore contact with
  the part leading the water away.
– A grooved insulation slab or a moisture protection mat
  are open at the bottom and thus increase the risk of
  water penetration.                                              Figure 35: Down: Insulation contacting with drainage.
                                                                             Up: Plaster on insulation or base element.
– If there is a high risk of water pressure on the wall, fit an
                                                                             Wall: Bitumen coating approximately 0,5 m up.
  bitumen mat on the wall irrespective of type of
  insulation.
                                                                  A draining layer of a minimum thickness of 200 mm is
– Draining filler shall lead to the drainage line.
                                                                  placed closest to the insulation.
                                                                     Stone wool stops capillary action, but has an open
                                                                  structure that allows the wall to dry outwards. Water is led
                                                                  off along the insulation surface.
                                                                     Stone wool is sensitive to high pressure, but a flat layer
                                                                  underground is ok.
                                                                     The thermal resistance is reduced, as per instruction in
                                                                  the Swedish building codes, with 0.20 m2K/W when stone
                                                                  wool contacts with ground.

                                                                  COMMENT:
                                                                  SP: Good structure irrespective of insulation material. Water
                                                                  pressure in the ground, resulting from blocked drainage, causes
                                                                  problems. It is important to drain surface water away from the
                                                                  house.

                                                                  MT: Clearly the best alternative with regard to humidity.
                                                                  Paint the inside wall with a silicate or KC paint that will pass
                                                                  through vapour. You can also leave the wall untreated.




32
Internal insulation                                                External and internal insulation




Figure 36: N.B.! Wooden studs must not be placed inside the        Figure 37: Recommendations for external and internal insulation
wall – RISK OF ROTTING. Do not use a plastic sheet as vapour       can be combined. The insulation is placed mainly on the outside
barrier.                                                           of a wall.


If wooden studs are used, fit first a 20 mm stone wool             The external insulation is the main insulation and it
board directly on the entire wall.                                 completed with a thin insulation layer on the inside for
    The wall can to a degree dry inwards, when stone wool          increased comfort.
is used as insulation.
                                                                   COMMENT:
COMMENT:                                                           SP: The point is the external insulation. On the inside a
SP: Great risk of mildew on the wall. This is a risk               board, such as gypsum, is enough, since a wall is not touched
constructors should be aware of.                                   in the same way as the floor is.

MT: The basement wall will be colder and therefore moister         MT: With regard to moisture this version is worse than
than without insulation or with external insulation. The           insulation on the outside only. The moisture permeability
insulation layers should never have a frame of inorganic           characteristics of the insulation layer must be taken into
material. Pay attention to the vapour resistance of the            consideration when “closing in” parts of building. The
insulation layers with regard to other materials in the wall. In   insulation layers should never have a frame of organic
relation to comfort, the structure has the same benefits as        material. As for comfort, this alternative has benefits as
external and internal insulation.                                  compared with externally insulated walls. Counter radiation
                                                                   from the wall is reduced, and the basement is experienced as
                                                                   less ”raw”.




                                                                                                                                33
s I N S U L AT I O N T H E O RY – F I R E




Fire
Fire can be defined as a destructive thermal process which        Air
increases damage on its own until all combustible material        The oxygen required for combustion usually comes from
exposed to fire is burned out.                                    air. The intensity of the fire depends on the oxygen supply.
                                                                  A reduction in the amount of oxygen can therefore
The following are required for a fire to ignite and to sustain:   extinguish or dampen a fire.
– Combustible material
– Sufficient amount of oxygen                                     Heat
– Heat that causes a material to reach ignition temperature       When the temperature of combustible material reaches
                                                                  ignition temperature, rapid combustion will result. The
                                                                  heat required for ignition can be produced by:
                                                                  – open flame (e.g. match)
                   N



                                                                  – a heated body (e.g. welding spark)
             GE




                                                                  – optical phenomenon (e.g. burning lens)
                                         HE


                                                                  – electrical phenomenon (e.g. arc)
                                                                  – friction (e.g. over-heating of a bearing)
       XY




                                              AT



                                                                  The combustion temperature reached depends of several
                                                                  factors, such as the heat value of the burning materials
     O




                                                                  (MJ/kg), rate of combustion (depends on the
                                                                  pulverisation), air supply and the amount of flue gases
                                                                  generated.

                       FUEL                                       A fire in a room can be divided into three main
                                                                  phases: ignition, combustion and cooling down.

Figure 38: Fire triangle shows the requirements for a fire.             Temperature


Fuel
When combined with oxygen, combustible materials
generate more heat than is required for the chemical
reaction. Combustibility is graded as inflammability.
• Self-igniting materials
  Materials that can start burning without the influence of
                                                                    Ignition          Flame phase               Cooling down
  an external heat source, e.g. linseed oil soaked in cotton
  waste.
• Flammable materials
  Materials, which finely dispersed can be ignited with a                                                                      Time
  match and which continue burning in air, such as paper,         Figure 39: The various stages of fire on time/temperature curve.
  wood splinters and most textiles.
• Materials that do not ignite easily                             1. Ignition
  Material that will ignite when heated locally and will          Flammable interior material, such as textiles or other
  burn as long as heated, but which will not continue to          upholstery material, catch fire as a result of careless handling
  burn after the heat source has been removed. Some               of a heat source. A fire can be caused by cigarettes, matches,
  examples: wood-wool cement boards and certain                   radiators, welding equipment or something similar. Fault in
  plastics. Test methods exist for determining whether            electrical equipment and arson are other possible reasons.
  material is difficult to ignite.                                The ignition phase can be up to several hours long if the fire
                                                                  begins as glowing combustion. The process can, however, be
Non-combustible materials include the common building             extremely rapid if flammable materials, liquids or gases
materials such as cement, concrete, aerated concrete,             ignite. Smoke and gases are generated in a room when
gypsum, brick and stone wool. The non-combustibility is           glowing starts and the atmosphere can be life endangering
usually tested.                                                   long before the temperature in the room starts increasing.

34
2. Flame phase, fully developed fire
                                                                          Ignition protected
Ignition becomes a full fire with the so-called flashover.
                                                                          coating
This is a critical phase in the development of a fire. After
the flashover it is no longer possible to stay in the room
and constraining and extinguishing the fire will be
difficult. All combustible surfaces in the room are now on
fire, and the temperature rises rapidly. The maximum
temperature in a room during the fire phase is 800-
1,100 °C. The structure is subject to fire stress, and the fire
                                                                                                                 Wooden floor
can spread to other rooms and other parts of the building
through the spread of flames, heat radiation, thermal
conduction or convection of combustible gases. The
                                                                                               Conduction
generation of smoke and gases can be extreme.

3. Cooling down
                                                                           Ceiling                               Steel beam
During this phase the amount of combustible material
lessens and the temperature drops. The combustion process
ceases gradually.
   The most important factors determining the shape of
                                                                  Figure 40 B. Fire spread through conduction.
the time/temperature curve in Figure 39 are the amount
and distribution of combustible material, ventilation,
                                                                  Conduction
oxygen supply, and the characteristics of building
                                                                  Heat is conducted in a material (solid body, liquid or gas)
components (such as thermal capacity etc).
                                                                  or from one object being in direct contact with another.
                                                                  Metals are the best conductors of heat. Liquids conduct
                                                                  little heat, and gases even less.
                                                                      In case of a fire, heat can also be conducted through
Spreading of fire
                                                                  non-combustible materials and structures. A thin concrete
A fire is spread mainly through radiation, conduction and         wall, for example, is no sure obstacle to a spreading fire. As
convection.                                                       metals are good heat conductors, pipes and other such
                                                                  structures that penetrate walls can be a risk.


                                 Radiation


                                Radiation




Figure 40 A. Fire spread through radiation.


Radiation
Heat is radiated from warm bodies to cold ones. For the
main part, heat radiation is invisible infrared radiation.
The radiation intensity is reduced as a square of distance.




                                                                                                                                35
s I N S U L AT I O N T H E O RY – F I R E




                                                                Fire protection of buildings
                                                                The purpose of the national building code is to build
                                                                houses in a way that prevents fires. On the other hand, the
                                                                spreading of fire within a building or to other buildings
                             Convection
                                                                should be prevented. Here is a simple summary of the goals
                                                                of fire protection regulations

                                                                – To save lives
                                                                – To save property

                                                                This can also be expressed in the following way:

                                                                • Preventing fires
                                                                  Requirements concerning non-combustible material,
                                                                  sufficient distance to combustible materials, surface
                                                                  layers etc.
Figure 40 C. Fire spread through convection.
                                                                • Allowing a secure escape in case of fire
Convection                                                        Requirements concerning two exits or the maximum
The generated flue gases and the surrounding air are heated       length of escape routes etc.
in a fire. Since warm gases are lighter than cool ones, there
                                                                • Ensuring the durability of structures in case of fire
will be convection or thermal radiation of hot gas mixtures.
                                                                  The frame should consist of fire-engineered structures
   In case of an indoor fire, such convected heat can cause
                                                                  etc.
secondary fires at long distances from the main fire, partly
by heating combustible materials to ignition temperature,       • Reducing the risk of spreading fire
partly because gases that have not burned due to lack of          Requirements concerning surface materials, fire cells in
oxygen are ignited when sufficient oxygen is available.           attics etc.

                                                                • Facilitating the putting out of fires
                                                                  Requirements concerning ventilation, fire posts and
                                                                  accessibility for rescue vehicles etc.

                                                                These requirements are the basis for the fire engineering of
                                                                a building.




36
Fire insulation                                                     Type of building                 Fire load in kg
Fire insulation of buildings is designed to prevent the                                            Wood m2 floor area
commencement and spreading of fire as well as ensuring              House                                  25 – 45
that the potential fire can be restricted in such a way that is     Hospital                               20 – 40
beneficial for personal safety.                                     Hotel                                  15 – 25
   The construction performance and fire technique                  Office                                 20 – 95
assessments are in the majority of cases based on full-scale        School                                 15 – 30
                                                                    Library                               200 – 400
testing, type tests of all the constructions or testing of a        Storage premises                      30 – 125
particular construction. We are currently investing in the          Warehouse                              15 – 50
development of theories, which enable the dimensioning of
flammable constructions using calculations. It is therefore       Table 42: The table shows the results of an investigation of the
important to have knowledge regarding the characteristics         size of fire load in different buildings with mainly concrete
                                                                  constructions.
of materials at high temperatures.

                                                                  The table indicates that the fire load does not only vary
Fire load
                                                                  between different categories of buildings, but also within
The term fire load refers to the relationship between the
                                                                  the same category. This depends on the different types and
total amount of heat that is released on total combustion of
                                                                  extent of furniture.
the entire inflammable material in a building, inclusive of
                                                                     A broad knowledge of existing fire loads in different
goods in the warehouse, inventories etc and the total area of
                                                                  types of building will also provide a foundation for the
the building.
                                                                  requirements for the building constructions (bearing
    The fire load is expressed as MJ/m2, however in writing,
                                                                  constructions, outer walls, joists etc.) and for the fire
it is often referred to as kg wood/m2. This unit is
                                                                  technical dimensions of these.
internationally recognised and useful, as a significant
number of fires are related to wood. Other combustible
materials are calculated from wood in ratio with
combustion heat. The fire load may therefore be calculated
as a sum of the total combustion heat of the material,
divided by the combustion heat of one kg tree (pine) that is
19000 kJ/kg.
                                                                                             Fire load = kg wood/m2


                                                                  Figure 43


                                                                  Fire course
                                                                  The fire course – that is to say the temperature/length of
                                                                  time, largely depends on the fire load and the geometry of
                                                                  the firecells.
                                                                     A complete description of the fire course in a firecell is
                                                                  complicated due to the number of influencing factors.
                                                                  Therefore, it is advised to use the normal fire curve (refer
                                                                  to Figure 44) for all tests and calculations where there are
                                                                  no particular reasons to veer from it. Such a reason may
                                                                  pose a risk for petrol fires for which there is another curve,
                                                                  the hydrocarbon curve, which portrays another time and
                                                                  temperature course.
                                                                     The unique fire properties of stone wool are clear when
                                                                  compared to the normal fire curve.


Figure 41




                                                                                                                                     37
s I N S U L AT I O N T H E O R Y – F I R E




                    Fire temperature
                     1200



                                                                            Natural stone starts shrinking and the
                     1000
                                                                            strength of the concrete is significantly
                                                                            reduced (120 mins)
                      800


                                        Glass melts (approx 7 mins)
                      600
                                        Wood gas ignites (approx 5 mins)

                      400




                      200

                                        Rubber and plastic materials melt and ignite (approx 3 mins)

                        0
                            0      30       60      90     120        150       180       210       240      270        300


Figure 44: The normal fire curve                                                                          Length of fire - minutes




Firecell                                                                Fire technical building classes
A firecell may include a room or a group of rooms in a                  In national building codes it is common to devide the type
building and is designed in such a way that a fire may be               of buildings into classes. In Sweden, as an example,
prevented from spreading to another area of the building                buildings are divided into three different fire technical
within a time frame.                                                    classes. When dividing the classes, the attic should be
                                                                        calculated as a floor if it is used as a residence or main part
                                                                        of a home.

                                                                        Buildings in class Br1
                                                                        Buildings with three or more floor plans should be classified
                                                                        in class Br1.
                                                                           The following buildings with two floors should be
                                                                        classified in class Br1:
                                                                        – Buildings designated to be slept in by people, who are
                                                                           not expected to have good knowledge of the
                                                                           surroundings.
Figure 45: A building with two firecells.                               – Buildings designated for persons, who are not able to
                                                                           easily move to safety by themselves.
The time frame is determined in terms of the function of                – Buildings with assembly premises on other floors.
the building and the number of floors.
   In the final construction of the firecell, there are no              Buildings in Br2 class
building parts, such as windows and doors with less fire                The following buildings with two floor plans should be
resistance than that which corresponds to the firecell.                 classified as lowest in the class Br2:
Providing that the fire can still be prevented from                     – Buildings designated for more than two flats and where
spreading to these parts of the building, via intervention of              the living area or workroom is in the attic.
the fire defence within the normal effort time or in another            – Buildings with assembly premises on the ground level.
way.                                                                    – Buildings which have a building area greater than
                                                                           200 m2 and which are not divided by fire walls into
                                                                           units bigger in size than in the lowest class REI 60-M.




38
Buildings with a one floor plan with assembly premises in or       Class division of the coating
under the ground level should, as lowest, be grouped in the        The coating is decided upon in terms of smoke progression
class Br2.                                                         and fire spreading in a room during the fire’s preliminary
   Since other buildings may depend on a particular type           phase. Therefore, the fire exit requirements are very strict.
of usage, there are special guidelines to be followed. Other       The regulation divided the coating into three requirement
buildings, not mentioned above, are classified as Br 3.            levels: Euroclass B-s1, d0 (previously coating class I), C-s2,
   Detailed guidelines for different parts of a building and       d0 (previously class II) and D s2, d0 (previously class III).
different types of buildings may be found in provisions in         Coatings of a lesser quality D-s20, d0 are not utilised.
for example The Swedish National Board of Housing,
Building and Planning or the Swedish Insurance Sector.             Classification of the building sections
                                                                   The regulations set requirements for building sections
Euro classes                                                       depending on the function of the classes:
As part of the EU, a new common system for testing and             – R (load-bearing capacity)
classifying the fire properties of building materials has been     – E (integrity)
taken into use. This means that the number of fire testing         – I (insulation)
methods is reduced and replaced by a fewer number of               The term integrity refers to the constructional capacity to
harmonised measures. All earlier national classifications are      prevent the entire building burning. Insulation limits the
replaced by the new Euro classes A1, A2, B – F. A1 is the          temperature of the areas not exposed to the fire – normally
best class. During the transitional period, the old classes        a maximum temperature of 140 °C.
apply within parentheses. The Euro classes describe the               The class designations that are usually a combination of
building materials’ contribution to fire and the risk of over      two or three classes are connected to a time frame in
ignition. No over ignition takes place in classes A1, A2 and       minutes such as RE 30 or REI 60.
B. Classes A2-D should be combined with additional                    The classification may be combined with an additional
classes which describe the building material releasing             classification
smoke from itself (s1, s2, s3) or emits burning drops (d0,         – M with special consideration paid to mechanical
d1, d3) when affected by the fire. Class E may only be                damage
combined with the additional class d2. For the lowest class        – C for doors with locking device fitted
F, the performance has not been established or it means
that the product burns easily. The National Building
guidelines should outline how the different materials may
be used. Paroc stone wool without the outer coating or
covered by glass fibre tissue is classified in the top class A1.

Coatings
Ignition protected coating is a coating made from fire-
resistant or another suitable material, which is fixed safely
and which, when fire tested in accordance with standardi-
sed methods for a period of at least 10 minutes, prevents
the ignition of the flammable material it covers.
   In specific construction solutions, Paroc stone wool is
classified as an ignition protected coating.




                                                                                                                              39
s I N S U L AT I O N T H E O RY – F I R E




Fire resistant capacity of Paroc stone wool                    Efficiency of the insulation
Paroc stone wool is manufactured from Diabase stone that       The following factors conclude the efficiency of the fire
is heated to its melting point of approximately 1500 °C        insulation:
and is then transformed into fibre by a special process.       1) Thermo stability
    Paroc stone wool is therefore to a high degree an              Insulation material should be able to endure high
inorganic product, apart from a very small content of              temperatures that exist during a fire without melting or
binder and oil.                                                    shrinking significantly in size.

Resistance to temperature                                      2) Insulation power
Paroc stone wool is an insulation material with a high            The insulation power is dependant on the temperature.
melting point appropriate for constructions with high fire        The insulation material should have good thermal
requirements. Insulation does not increase the fire load and      insulation properties even at high temperatures.
the protected insulation capacity during a fire. The binder
in Paroc stone wool products melts at a temperature of         3) Thermal capacity
approx 200 °C. Stone wool fibres reach up to 1000 °C.             The thermal capacity of Paroc stone wool is somewhat
Paroc stone wool may therefore be used at temperatures            dependant on the low density. Concrete for example
higher than 200 °C – the fibres remain in tact and protect        has a high thermal capacity.
the underlying material from the effects of the flame.
Insulation should be placed in the construction so that the    Dimensioning
mechanical influence may not change form when the              The aim of fire technical dimensioning is to bring about a
binder leaves.                                                 construction that with safety withstands the influence of
   As a rule, only one side is exposed to high temperatures    fire it may be exposed to without collapsing. Furthermore,
followed by the breaking down of the binder. Paroc stone       it often applies to preventing the ignition of material on
wool has good thermal insulation properties even in the        the side not exposed to fire.
high temperatures that are incurred during fire. The               However, the calculations are complex. In many cases,
temperature drop of the outermost insulation layer is so       the dimensions that lead to tests have already been
great that the rest of the insulation remains intact.          conducted. For certain constructions, it is possible to
                                                               carryout data calculations such as fire insulation of steel
                                                               constructions with PAROC FPS 14. The Addition method
                                                               is adopted for divided wooden constructions. A summary
                                                               description may be found in the following.




40
Addition method                                                    A sample calculation.
                                                                   Here is an example of fire resistance (btot) calculated
General                                                            according to the Addition method (formula 1).
The following method is not 100 % exact and does not                                                12    mm   chip board
compensate real fire tests. There are still too many unsure                                         95    mm   timber stud
                                                                                                    95    mm   (A) air gap, (B) glass wool, (C) stone wool
parameters. The result of such a calculation can be used as                                         12    mm   chip board
complement to the testing or a reference test can complete
the calculation.
                                                                   (A) Air gap
                                                                   btot=(13.6 x 0.8)+(5.0 x 1.0)+(13.6 x 0.6)= 24.0 min
Divided Timber Structures
The addition method is a method for calculating the fire           (B) Glass wool
resistance of timber structures with wooden studs and the          btot=(13.6 x 0.78)+(10.0 x 1.0)+(13.6 x 0.67)=29.7 min
highest fire-engineering class of EI 60. By adding the fire
resistance of the structure’s various material layers it is        (C) Stone wool
possible to get an estimate of the entire structure’s fire         btot=(13.6 x 0.78)+(19.0 x 1.0)+(13.6 x 2.9)= 69.0 min
resistance (btot). The calculations are based on a large
number of fire tests. The starting point is the so-called base
value (bn). This is the fire resistance of a material layer. The
location of the layer in the structure can be established by
multiplying the base value with a position coefficient (kn).
The following formula can also be used.                            Position coefficient (kn) for various material layers in a wall
                                                                   with a single board layer.
btot = b1k1 + b2k2 + ... = Σbnkn        (formula 1)
                                                                    Type            Thick-                               Position coefficients
                                                                                    ness
                                                                                    (mm)     Exposed board                                   Non-exposed board
Examples of a material’s base value (b) and position                                         cover on rear with                             covered on front with
coefficient (k) are shown in the table below.
                                                                                             Glass wool/       Air    Ins/     *)1)Glass         Stone wool (mm)     2)3)
                                                                                             stone wool      gap     air gap    wool                                  Air

Base value (bn) of various materials                                                            (mm)                            (mm)                                 gap
                                                                                               45–195                          45–195       45    70     95   145


 Type                 Density        Thickness     Base value       Wood based       12         0.78         0.8      1.0       0.67       1.9   2.4    2.9    3.9 0.6
                      (kg/m3)          (mm)          (min)          board and        20         0.94         0.8      1.0       1.23       1.9   2.4    2.9    3.9 0.6**)
                                                                    all plywood
 Wood based boards    450–590            12           11.1
 and all plywood                         20           18.7          Chip and         12         0.78         0.8      1.0       0.67       1.9   2.2    2.9    3.9 0.6
                                                                    fibre boards     22         0.98         0.8      1.0       1.37       1.9   2.4    2.9    3.9 0.6**)
 Chip boards and      600–800            12           13.6
 fibre boards                            22           24.6          Gypsum board
                                                                        Normal       13        0.80          0.8     1.0        0.74       1.9   2.4    2.9    3.9   0.7
 Gypsum board                                                           Protect F    15        0.84          0.8     1.54)      0.88       1.9   2.4    2.9    3.9   0.7
          Normal      680–780            13           18.0
          Protect F    ≥830              15           22.0
                                                                   *) With regard to thickness of the exposed board.
 Glass wool             19               45            5.0         **) 0.8 when stud spacing is ≥ 70 mm.
                                         95           10.0
                                        120           12.0
                                        195           20.0         When Protect F or equivalent is used as the exposed board,
 Stone wool             28               45            9.0         i.e. the board resists fire ≥ 60 minutes, the following
                                         95           19.0
                                        120           24.0
                                                                   position coefficients can be applied:
                                        195           39.0         1) The same as for stone wool, however max. 2.9.
                                                                   2) 1.5 for wood-based boards.
 Air gap                               45–195          5.0
                                                                   3) 1.8 for gypsum board and fibre cement boards.
                                                                   4) 2.0 for glass wool




                                                                                                                                                                      41
s I N S U L AT I O N T H E O RY – F I R E




Position coefficients (kn) for various materials layers in                           Divided Timber Structures
walls with two board layers.
                                                                                     Addition method -
                               Exposed board       Isolation/   Non-exposed boards
 Structure2)                 board 1    board 2     air gap     board 3    board 4   Complementary data for Paroc stone wool
 Exposed/non-exposed board   exposed     closest                closest     non-
 + board closest to stud                 to stud                to stud    exposed
                                                                                     The base values for materials were obtained through an
 2 x wood-based board         1.0         0.6        1.0         0.5         0.7
 air gap                                                                             extensive test programme, in which samples were tested
 2 x gypsum board             1.0         1.0        1.0         1.0        0.73)    both in full and reduced scale. In order to complement the
 air gap
                                                                                     study and mainly to study the influence of stone wool
 Gypsum
 + wood-based board           1.0         1.0        1.0         0.8        0.73)    density we initiated a test project at the Swedish Institution
 air gap
                                                                                     for Technical Education in Norrköping. The methods used
 Wood-based board
 + gypsum                     1.0         0.6        1.0         1.0        0.73)    were the same as the first ones used by Trätek. Some tests
 air gap                                                                             were carried out in parallel, and they proved to be
 2 x wood-based board         1.0         0.6        1.0         1.01)      2.01)
 stone wool, 28 kg/m3
                                                                                     compatible. The results are shown in the tables below.
 2 x gypsum board             1.0         1.0        1.0         1.01)      3.51)
 stone wool, 28 kg/m3
                                                                                     Base values (bn) for various Paroc stone wool products and
 Gypsum
 + wood-based board           1.0         1.0        1.0         1.01)      2.01)
                                                                                     for Gyproc Normal gypsum board
 stone wool, 28 kg/m3
 Wood-based board                                                                     Product number               Density                       Thickness               Base value
 + gypsum                     1.0         0.6        1.0         1.01)      2.51)                                  (kg/m3)                         (mm)                    (min)
 stone wool, 28 kg/m3
                                                                                      Gypsum board                    730                              13                     18.7


1)                                                                                    PAROC UNS 37                       26                         45                        7.7
   The value is clearly on the safe side. To obtain higher                                                                                          70                        10.9
values more base layer is required.                                                                                                                 95                        11.6
                                                                                                                                                   145                        20.3
2) Total board thickness max 26 mm per side of wall.
3) 1.0 when stud spacing ≥ 70 mm.                                                     PAROC FPS 4                        45                            45                     10.4
                                                                                                                                                       70                     16.8
                                                                                                                                                       95                     20.2

                                                                                      PAROC COS 10                       80                         50                        12.6
                                                                                                                                                    80                        24.5
                                                                                                                                                   100                        32.3

                                                                                      PAROC FPS 14                    140                              30                     11.9
                                                                                                                                                       50                     23.5
                                                                                                                                                       70                     38.0
                                                                                                                                                       80                     43.7



                                                                                     Position coefficients (kn)

                                                                                                      Position coefficient    Stone                          Position coefficients
                                                                                      Type     Thick- Exposed lined           wool       Stone    Non-exposed lined board with
                                                                                               ness   board with stone        density    wool     stonewool on front side, thickness (mm)
                                                                                               (mm) wool on back side         (kg/m 3)             30   45     50    70 80 95 100 145


                                                                                      Gypsum   13            0.9               26        1.0       –    2.1 –        2.6 – 2.9 – 3.5
                                                                                      board                  0.9               45        1.0       –    2.3 –        2.7 – 3.3 –         –
                                                                                                             0.9               80        1.0       –    –      3.1 3.5 – 4.1 4.3 –
                                                                                                             0.9              140        1.0      2.6 –        3.6 4.1 4.3 –         –   –




                                                                                     NB. (-) = no data available.




42
                                                                Other Paroc information regarding fire
                      13   mm gypsum board
                      95   mm PAROC slab                        Instruction for how to insulate steel structure against fire
                      45   x 95 mm stud c 600 mm
                      13   mm gypsum board
                                                                are to be found on our web pages. There will also other
                                                                tested and approved constructions be found, depending on
A sample calculation.                                           how far the implementation of the EN-regulations have
Here are sample calculations of the structure described         gone in different countries.
above as per (formula 1) on page 41.

(D) PAROC UNS 37 (26 kg/m3)
btot = (18.7 x 0.9)+(11.6 x 1.0)+(18.7 x 2.9)= 82.7 min

(E) PAROC FPS 4 (45 kg/m3)
btot = (18.7 x 0.9)+(20.2 x 1.0)+(18.7 x 3.3)= 98.7 min




Addition method –
Fire resistance period over 60 mins
According to the above calculations long fire resistance
periods are obtained when using stone wool as insulation.
These periods are usually longer than the fire-engineering
classes given in other information material from Paroc.
Why? In a fire the inner lining either burns or falls down –
usually after the fire has been burning for 15 to 25
minutes. After that the studs and the isolation are exposed
to fire. Withstanding temperatures of over 1,000 °C stone
wool stays in place and protects the non-exposed skin
plate. The studs are charred at a rate of 0.7–1.0 mm per
minute, and will thus be consumed in about 100 minutes.
Oversized insulation units are commonly clamped between
the studs, but as the studs burn off, the insulation falls
down. After that the fire will penetrate the non-exposed
board. As this process can vary from case to case, it is
disregarded when calculating the fire resistance. This is
why certain care is required when making such
calculations. This is also the main reason why the Addition
method may not be used when the burning time exceeds
60 minutes.

Another reason for lower fire-engineering classes is that the
fire resistance period is rounded down to the closest value.
In example D above 82.7 minutes is reduced to 60
minutes.




                                                                 For further information of material properties and our
                                                                 products see www.paroc.com


                                                                                                                          43
s I N S U L AT I O N T H E O RY – A C O U S T I C S




Acoustics
Sound power and sound intensity                                           Sound pressure
Sound is energy and treating sound as energy can solve                    We are not able to hear the sound intensity directly, as our
many acoustic problems. This is a simple way of looking at                hearing experience is based on the perceived sound pressure
sound issues.                                                             in the sound wave. The relationship between the intensity
   A sound source may be considered as a power point                      and sound pressure may generally be written as follows:
source emitting P (watt). A point source emits equally in all
directions and at the distance r (m) the intensity I (watt/                    I = p2/(nZ) = p2/(n c) (3)
m2) may be calculated using the following formula. We
presume no reflective surfaces in the space.                              p = sound pressure, Pa
                                                                          Z = c = characteristic impedance of the medium = 400 for
      I = P/(4πr2)        (1)                                                 normal air
                                                                            = density of the medium, kg/m3
P = sound power, W                                                        c = speed of sound in the medium, m/s
r = distance, m                                                           n = a constant, varying between 1 and 4 depending on the
I = sound intensity, W/m2                                                     character of the sound field.

For hemispherical conditions, i.e. a sound source on the                  Free plane sound wave
ground, the result will be:                                               When the sound source is located at a great distance and in
                                                                          a space where there are no reflective surfaces, a free plane
      I = P/(2πr2)        (2)                                             sound wave is propagating.
                                                                          n = 1 in the formula (3). Formula (1) applies.

                                                                          Diffuse sound field
                                                                          In a diffuse sound field, the sound waves arrive from all
                                P                          I              possible directions.
                                                                          n = 4 in the formula (3).
                                            r
Figure 46: The distribution of sound from a point source on the ground.   In a reverberation room, a diffuse sound field prevails. If a
                                                                          sound source is placed in such a room, balance is achieved
NOTE! The intensity is inversely proportional to the                      when the supplied and emitted sound power are the same,
(distance)2 from the source (Reduced 6 dB every time the                  i.e. in the reverberant field:
distance is doubled).
 Source of sound                            Power, W           LW dB           P=I·A         (4)

 Whispering                                      10-9           30        P = supplied sound power, W
 Conversation                                    10   -5
                                                                70        I = intensity, W/m2
 Scream                                          10-3           90        A = absorption of the room, m2
 Lorry                                           10   -2
                                                               100
 Trumpet, grand piano                            10-1          110
 Compressed air, riveting hammer                 10   0
                                                               120
 Large orchestra                                 101           130
 4-engine propeller plane                        10   3
                                                               150
 Jet plane                                       104           160
 Rocket                                          10   7
                                                               190
Table 47: Sound power output of some sound sources.


Example 1: A crowded Ullevi Stadium in Gothenburg,
Sweden (40,000 people) shouts goal! What is the sound
power produced?

Answer: 40,000 · 10-3 W = 40 Watt

44
Example 2: The output of a machine is 0.1 W sound               Absorption
power. It is placed:                                            When a sound wave strikes a surface of a room, a propor-
a) Outdoors on a hard ground
                                                                tion of the sound will be reflected. The remaining sound
b) Indoors in a reverberation room with the absorption
                                                                will be absorbed.
   = 6 m2 .
What is the sound intensity and the sound pressure at
100 m distance outdoors and in the reverberant field              Iin
indoors?

Answer: a) I = P/(2πr2) = 0,1/2 · π · 1002 = 1,6 · 10-6 W/m2.
p2 = I · (n c) = 1,6 · 10-6 · 1 · 400.
p = 0,025 Pa.                                                                                                     Ia
b) I = P/A = 0,1/6 = 0,017 W/m2.
p2 = I · (n c) = 0,017 · 4 · 400.
                                                                                   Ir
p = 5,2 Pa.

Transmission                                                    Figure 49: Absorption of a surface.

When a sound wave is incident upon a partition separating               Iin = Ir + Ia   (8)
two spaces, some of it will be reflected and a small amount             α = Ia / Iin    (9)
will be transmitted through the partition. We disregard the             ρ = Ir / Iin    (10)
fact that the wall may absorb sound power.
                                                                Iin   = Incident sound intensity, W/m2
                                                                Ia    = Absorbed sound intensity, W/m2
                                                                Ir    = Reflected sound intensity, W/m2
Iin
                                                                α     = Absorption coefficient
                                                                ρ     = Reflections coefficient
                                                                Note: In reality, of course, absorption and transmission
                                                                occur at the same time in most cases.
                                               Itr
      Ir




Figure 48: Transmission through a partition.

           Iin = Itr + Ir (5)
           τ = Itr / Iin (6)
           ρ = Ir / Iin (7)

Iin   = Incident sound intensity, W/m2
Itr   = Transmitted sound intensity, W/m2
Ir    = Reflected sound intensity, W/m2
τ     = Transmission coefficient
ρ     = Reflection coefficient




                                                                                                                           45
s I N S U L AT I O N T H E O RY – A C O U S T I C S




dB – quantity                                                      Example 4: Express the answer for the above examples 1
                                                                   and 2 in dB!
The terms dB and Bel (=10 dB) are purely mathematical
terms and not special measures for sound. If you compare two
                                                                   Answer: 1) Lw = 10 · log(W/W0) dB = 10 · log(40/10-12)
magnitudes such as A and B, it can be said that A is a certain
                                                                   dB = 136 dB.
number of times greater (older, heavier etc.) than B, or a
                                                                   2 a) LI = 10 · log(I/I0) dB = 10 · (1,6 · 10-6/10-12) dB = 62 dB
certain number of dB in relation to B. If a great grandfather is
                                                                   Lp = 10 · log(p/p0)2 dB =
100 years old and his great granddaughter is 1 year old, he is
                                                                   = 10 · log(1,6 · 10-6 · 1 · 400/400 · 10-12) dB = 62 dB
100 times = 102 = 2 Bel older than her. To be precise, grand-
                                                                   (Lp similar to LI in a free plane sound wave)
father is 20 dB old (compared to his great granddaughter). Bel
                                                                   2 b) LI = 10 · log(I/I0) dB = 10 · (0,017/10-12) dB = 102 dB
is logarithmic to a relationship between two magnitudes.
                                                                   Lp = 10 · log(p/p0)2 dB =
    Within acoustics, we talk about a level (L), which is
                                                                   = 10 · log(0,017 · 4 · 400/400 · 10-12) dB = 108 dB
presented in dB, regarding the sound power as well as
                                                                   (Lp is 6 dB greater than LI in a diffuse sound field).
the sound intensity and the sound pressure (plus
vibrations etc.). Therefore, the different kinds of dB values
and their reference values must always be kept in mind.            Sound reduction index
Reference values:                                                  The term sound reduction index is actually the same as the
Sound power            W0 = 10-12 W                                transmission coefficient but expressed in dB. In order to
Sound intensity        I0 = 10-12 W/m2                             obtain a positive value of dB, you have to invert the
Sound pressure         p0 = 20 · 10-6 Pa                           coefficient.

                                                                        R = 10 · log(1/τ)        (11)
Levels:
Power level          Lw      = 10 · log(W/W0) dB                   R = Sound Reduction Index, dB
Intensity level      LI      = 10 · log(I/I0) dB                   τ = Transmission Coefficient
Sound pressure level Lp      = 10 · log(p/p0)2 dB
                                                                   Example 5: The transmission coefficient at a certain
The reference value for sound pressure corresponds to the          frequency is
hearing threshold (at 1000 Hz). The intensity level and            a) for 160 mm concrete = 0.000003
sound pressure level are about the same in free plane sound        b) 13 mm plasterboard = 0.001.
wave in “normal” air.                                              What is the Sound Reduction Index?

Adding dB                                                          Answer: a) R = 10 · log 1/(3 · 10-6) = 55 dB
dB is a logarithmic quantity. One has to revert to linear          b) R = 10 · log 1/0.001 = 30 dB
quantities in order to add or subtract and then go back to
the logarithm.                                                     The resultant sound reduction index
                                                                   If a wall consists of two or more elements (windows, doors
Example 3: Five different dB values are to be added: 43,           etc) with different sound reduction index, we may calculate
45, 33, 32 and 38 – what is the sum?                               the resultant sound reduction index for the entire wall by
                                                                   using the following formula:
Answer: Pass to the Bel values first: 4.3, 4.5, 3.3, 3.2 and
                                                                        τ0 · S0 = τ1 · S1 + τ2 · S2 + τ3 · S3 + ...    (12)
3.8 Bel are to be added. Now go to the linear figures and
add. 104.3 + 104.5 + 103.3 + 103.2 + 103.8 = 20000 + 30000
+ 2000 + 1600 + 6300 = 60000 = 104.8. So the sum will be
4.8 Bel = 48 dB.




46
or expressed in dB for two surfaces:                             Example 7: Practising a piano in the living room produces
                                                                 95 dB. There is a bedroom in an apartment next to the
      R0 = R1 - 10 · log[S1/S0 + S2/S0 · 100,1(R1-R2)]   (13)    living room with a common dividing area of 8 m2. Assume
                                                                 that the wall’s sound reduction index is 55 dB and that the
τ0   = resultant transmission coefficient                        absorption in the bedroom is 12 m2. What is the sound
R0   = resultant sound reduction index                           level in the bedroom?
S0   = total area
τn   = transmission coefficient of element n                     Answer: L2 = L1 - R - 10 · log(A2/S) =
Rn   = sound reduction index of element n                        = 95 - 55 - 10 · log(12/8) = 38 dB
Sn   = area of element n

Example 6: A door with R = 30 dB is placed in a wall with
R = 52 dB. The area of the door = 2 m 2 and the wall area
(including the door) = 25 m2. What is the resultant sound
reduction index?

Answer: R0 = R1 - 10 · log[S1/S0 + S2/S0 · 100,1(R1-R2)] =
= 52 - 10 · log[23/25 + 2/25 · 100,1(52-30)] = 52 - 11 = 41 dB


Measurement and calculation of the sound
reduction index

 L1                         S                       L2
                                                    A2

                            R




Figure 50: Sound insulation between two rooms.


If a wall with the area of S m2 divides two rooms, the
sound reduction index can be calculated using the
following formula:

      R = L1 - L2 - 10 · log(A2/S)        (14)

L1    = sound pressure level in the source room, dB
L2    = sound pressure level in the receiving room, dB
A2    = absorption of the receiving room
S     = area of the dividing partition, m2

The sound pressure levels L1 and L2 are measured directly,
whereas A2 is calculated using the formula (17), after
measuring the reverberation time T.

Note: R represents the sound reduction index of a partition
(measured in a lab).
R' represents the apparent sound reduction index between
two rooms (measured in the field).


                                                                                                                          47
s I N S U L AT I O N T H E O RY – A C O U S T I C S




Room acoustics                                                      The absorption of a room can be calculated as follows:
Sound propagation                                                        A = A1 + A2 + A3 +... =∑Sn · αn = S · αm       (18)
The sound pressure level from a point sound source with a           A = Total absorption of the room, m2
known output power may be achieved by:                              A1 = Absorption of the surface 1, m2
                                                                    S1 = Area of the surface 1, m2
     Lp = LW + 10 · log(1/4πr2 + 4(1-αm)/A)            (15)         α1 = Absorption coefficient for the surface 1
                                                                    Sn = Area of surface n, m2
Lp   = Sound pressure level at a distance of r, dB                  αn = Absorption coefficient for the surface n, m2
LW   = Sound power level from the point sound source, dB            αm = The room’s average absorption coefficient
r    = Distance, m                                                  S = The total area of the room, m2
αm   = Average absorption coefficient of the surfaces of the room
A    = Absorption of the room, m2                                   Example 8: The desired reverberation time in a classroom
                                                                    is max. 0.8 seconds. Assuming the dimensions of the
The first term describes the sound pressure level in the            classroom are 6 · 10 · 3 m and that you want to achieve the
direct field and the second term describes the sound                mentioned reverberation time with just an absorbent
pressure level in the reverberant field.                            ceiling. What is the absorption coefficient required for the
    A reduction of 6 dB in the sound pressure level in direct       absorbent ceiling?
field corresponds to a doubling of distance from a point
sound source. Compare with a linear sound source (for               Answer: A = 0.16 · V/T = 0.16 · 180/0.8 = 36 m2.
example, traffic on a road) that provides 3 dB/doubling of          α = A/S = 36/ 60 = 0.6
distance.
                                                                    Sound as a wave motion
Absorption
A fraction of the sound intensity is absorbed when the sound        In many cases, the sound cannot be treated in terms of
is incident to a surface. Each surface has a certain absorption.    energy but has to be considered as a wave motion. Air
                                                                    molecules move and vibrate around their equilibrium in a
     A=S·α           (16)
                                                                    sound wave. The distance between two particles in the
α = absorption coefficient                                          same motion phase constitutes a wavelength. The number
S = area of the surface, m2                                         of oscillations per second makes up the frequency. The
A = absorption of the surface, m2                                   following equation describes the relationship:

Reverberation time                                                       c=f·λ         (19)
The reverberation time is used to characterise the absorp-
                                                                    c = speed of sound, m/s
tion properties of a room. It is defined by the size and the
                                                                    f = frequency, Hz
absorption of the room.
                                                                    λ = wavelength, m
     T = 0.16 · V/A         (17)
T = Reverberation time, s                                           In air, the speed of sound is approximately 340 m/s
V = Volume of the room, m3                                          (depending on the temperature).
A = Absorption of the room, m2                                         In gases, there are only longitudinal waves and the speed
                                                                    does not depend on the frequency.
The reverberation time is defined as the time for the sound            In plates (sheet material such as plaster and chipboard)
pressure level to decay by 60 dB, after the sound from a            there are also bending waves. The speed of sound in
loudspeaker has been turned off or a gun has been fired. A          bending waves is dependant on the frequency and increases
straight line may generally approximate the decay of the            as the frequency increases.
sound pressure level.




48
Hearing and frequency weighting                                     Weighting dB


filters
The human ear responds differentially throughout the
audio frequency spectrum. Our hearing threshold is about
0 dB in the frequency bands of 1 – 4 kHz, but is much
higher at low frequencies. It is 40 dB at 50 Hz.
   As a rule of thumb, the lowest change in sound pressure level
that can be heard is 3 dB and a change of 10 dB is subjectively
heard as a doubling of the loudness. As highlighted in the
diagram showing curves representing equal loudness for pure
tones, these rules of thumb are very simplified.


                                                                   Figure 52: Standardised weighting curves.



                                                                        Octave Hz            A-filter                C-filter

                                                                            16                   -56,7                -8,5
                                                                            31                   -39,4                -3,0
                                                                            63                   -26,2                -0,8
                                                                           125                   -16,1                -0,2
                                                                           250                   -8,6                     0
                                                                           500                   -3,2                     0
                                                                           1000                   0                       0
                                                                           2000                  1,2                  -0,2
                                                                           4000                  1,0                  -0,8
                                                                           8000                  -1,1                 -3,0

                                                                   Table 53: Weighting values for filters A and C.
Figure 51: Equal loudness curves according to ISO 226.

                                                                   By noise control the sound is preferable measured in octave
Filter
                                                                   bands and by sound insulation problems the measurements
When measuring, attention must be taken to the sensitivity of
                                                                   are made in third octave bands (1/3 octaves). These bands
the ear by using a filter connected between the microphone
                                                                   have a constant relative bandwidth. The following applies:
and the measuring instrument. Usually, the measuring is done
using an A filter, dBA, when there is a risk of hearing damage
                                                                          B = fu - fl.   (20)
and discomfort.
   In apartments, C filters are often used in order to
                                                                   Octave band: fu = 2 · fl and fc = √2 · fl
estimate the low frequency noise annoyance.
                                                                   Third octave band: fu = 21/3 · fl and fc = 21/6 · fl

                                                                   B    = Bandwidth, Hz
                                                                   fu   = Upper band edge, Hz
                                                                   fl   = Lower band edge, Hz
                                                                   fc   = Centre frequency, Hz




                                                                                                                                49
s I N S U L AT I O N T H E O RY – A C O U S T I C S




Example 9: In a fan plant room, the sound pressure levels                  Ln = Li + 10 · log(A/10)       (21)
were measured in octave bands as shown in the table. The
fan plant room shares a partition with a bedroom with an             Li    = Impact sound pressure level in the receiving room, dB
area of 10 m2, and the absorption of the bedroom is10 m2.            A     = Absorption in the receiving room, m2
The sound reduction index of the wall in octave band is
shown in the table. What is the sound level in dBA in the            Ln    = Impact sound pressure level for a floor (lab.
fan plant room and in the bedroom?                                           measurements)
                                                                     L'n   = Impact sound pressure level (field measurements)
Answer:
                                                                     A low value for Ln or L'n means good insulation.
125    250     500   1000   2000    4000   Octave

 69       62    55     52     48      45   Sound pressure level
 -16      -9    -3      0     +1      +1   A-filter

 53       53    52     52     49      46   A-weighted level in fan
                                           room
 20       30    50     55     60      60   Sound reduction index
 33       23     2      -       -      -   A-weighted level in
                                           bedroom


The correction term 10 · log(A2/S)= 0, so L2 = L1 - R
   The total level in the fan plant room (logarithmic
addition of 53 + 53 + …) = 59 dBA
   The total level in the bedroom (logarithmic addition of
33 + 23 + 2) = 33 dBA

Sound insulation
There are two types of insulation related to buildings.

Airborne sound insulation
Airborne sound insulation is the expression used when the
sound is produced directly to the air, like speech, singing
and sound from the radio and TV.
   Airborne sound insulation is determined from
measurements of the sound reduction index (defined
earlier) in 21 third octave bands from 50 to 5000 Hz.
   A high R or R' indicates good insulation.

Impact sound insulation
Impact sound insulation stands for insulation against
sound created when someone walks on a floor close to the
flat.
    Impact sound insulation is determined from
measurements of the sound pressure level, when the floor is
mechanically worked on with a standardised hammer. The
level is measured in 21 third octave bands from 50 – 5000
Hz.




50
Calculation of Rw                                            C terms
                                                             The Rw concept is taken to pass the situation when the human
A sound insulation measurement is presented by a curve of
                                                             voice is the main source of sound. As we have noise sources
R or R' from 50 to 5000 Hz according to the figure. R and
                                                             such as stereos in flats today, the term is insufficient. When it
R' are given with one decimal.
                                                             comes to the insulation of outside walls where the source of
   When the weighted value Rw or R'w is to be calculated,
                                                             sound is made up by traffic, the Rw term is also unsuitable.
the curve has to be weighted in a suitable manner. The
                                                                Therefore, the ISO 717 standard incorporates the Rw
weighting performance means that the measured curve is
                                                             completed with the spectrum adoption terms or C terms.
compared with a standardised reference curve between 100
                                                             The complete single-number quantity reads:
and 3150 Hz. See figure 54.
                                                                  Rw (C; Ctr; C50-3150; Ctr,50-3150)
   Sound reduction index dB
                                                             C and Ctr include the frequency range 100 – 3150 Hz.

                                                             The single-number quantities

                                                             Rw + C and Rw + C50-3150

                                                             express the sound insulation in dBA for a noise spectrum
                                                             with identical levels in all third octave bands.

                                                             The single-number quantities

                                                             Rw + Ctr and Rw + Ctr,50-3150

                                                             express the sound insulation in dBA for a standardised
                                                             traffic noise spectrum.

                                                             Floor with wooden joists
                                                             Figure 54 and Table 56 show the results from a field
                                                             measurement of a floor with wooden joists according to
                                                             Figure 55. The floor covering consist of 14 mm parquet
                                                             flooring and 3 mm plastic foam.
                         Frequency Hz
Figure 54: Measured sound reduction index, R’, and the
reference curve.

The reference curve is moved in steps of 1 dB towards the
measured curve, until the sum of the deviations below the
reference curve is as large as possible, however, not
exceeding 32.0 dB.
   The value of the reference curve at 500 Hz after it has
been moved is defined as Rw or R'W for the measured curve.




                                                             Figure 55: Floor with wooden joists.




                                                                                                                            51
s I N S U L AT I O N T H E O RY – A C O U S T I C S




The complete single-number quantity for the airborne                  Calculation of Ln,w
sound insulation is as follows:
                                                                      Impact sound insulation is calculated from measurements
                                                                      of the sound pressure level that a standardised hammer
R'w = 58 (-2; -6; -3; -15) dB, so
                                                                      produces in the room below. The result can be presented as
                                                                      a curve of Ln or L'n from 50 – 5000 Hz. Ln and L'n are
R'w + C = 58-2 = 56 dB, and
                                                                      given with one decimal.
                                                                         When calculating the single-number quantity Ln,w or
R'w + C50-3150 = 58-3 = 55 dB
                                                                      L'n,w, you proceed in a similar way from the impact sound
                                                                      levels for the 16 frequencies 100 – 3150 Hz and compare
The result means that the single-number quantity will drop
                                                                      the curve with a standardised reference curve.
when care is taken to the poor insulation at lower
                                                                         The same conditions as for Rw apply regarding total
frequencies.
                                                                      deviations max. 32.0 dB in addition to the reading of the
                                                                      reference curve after moving at 500 Hz. Observe that the
   f      R'      Ref.     ∆R'      Pink A-filter    A-    L-R'       deviations this time lies above the reference curve. See
  Hz      dB     curve              noise         weighted
                                                    pink              figure 57.
                                                   noise L
  50     21,0                        -11   -30,2     -41     -61
  63     27,9                        -11   -26,2     -37    -64,9
                                                                          Impact sound pressure level dB
  80     29,8                        -11   -22,5     -34    -63,8
 100     37,5      39      1,5       -11   -19,1     -30    -67,5
 125     42,7      42       0        -11   -16,1     -27    -69,7
 160     43,4      45      1,6       -11   -13,4     -24    -67,4
 200     48,5      48       0        -11   -10,9     -22    -70,5
 250     45,4      51      5,6       -11   -8,6      -20    -65,4
 315     47,3      54      6,7       -11   -6,6      -18    -65,3
 400     50,5      57      6,5       -11   -4,8      -16    -66,5
 500     54,0      58       4        -11   -3,2      -14     -68
 630     57,3      59      1,7       -11   -1,9      -13    -70,3
 800     59,7      60      0,3       -11   -0,8      -12    -71,7
1000     62,6      61       0        -11    -0       -11    -73,6
1250     64,7      62       0        -11    0,6      -10    -74,7
1600      65       62       0        -11     1       -10     -75
2000     64,3      62       0        -11    1,2      -10    -74,3
2500     64,9      62       0        -11    1,3      -10    -74,9
3150     69,7      62       0        -11    1,2      -10    -79,7
                  R’w =   Σ∆R’ =                   logΣ =   logΣ =

                 58 dB    27,9 dB                   0 dB    -55 dB
                                                                                                Frequency Hz

Table 56: Calculation of R’w and C50-3100 for the floor in Figure     Figure 57: Measured impact sound pressure level, L’n and the
54. When the reference curve is moved as high as possible             reference curve.
without Σ∆R’ >32.0 dB, the R’w value will be read at 500 Hz.
The pink noise stands for similar levels in each third band. The
level is chosen so that the A-weighted level (logarithmic sum of L)
is 0 dB (normalised to 0 dB).
The logarithmic sum of L-R’ will be -55 dB that is to say the
construction insulates 0- (-55) = 55 dB for the selected pink noise
sound spectrum.
Therefore, C50-3100 will be 55-58 = -3 dB




52
C terms                                                                f                L' n        Reference             ∆L
The Ln,w concept does not provide a completely correct                Hz                dB             curve
picture of the impact sound insulation for different types            50              61,8
of floors, especially with wooden joists. Above all, you need         63              64,8
to pay attention to higher impact sound levels at
                                                                      80              59,7
frequencies below 100 Hz for light wood beams.
                                                                     100              56,4              54               2,4
Therefore, ISO-717 complements Ln and L'n with two
                                                                     125              58,0              54               4,0
spectrum adoption terms or C terms:
                                                                     160              60,0              54               6,0
     Ci,100-2500 and Ci,50-2500                                      200              58,0              54               4,0
                                                                     250              58,3              54               0,3
These terms take into consideration the measured sound               315              58,3              54               4,3
level from the hammer for the entire emitted frequency               400              54,6              53               1,6
range and the single-number quantity becomes:                        500              52,4              52               0,4
                                                                     630              47,6              51                 0
     Ln,w (C; Ci,50-2500)                                            800              44,6              50                 0
                                                                     1000             44,4              49                 0
                                                                     1250             41,4              46                 0
Flats separated by floor with wooden joists
                                                                     1600             40,2              43                 0
Figure 57 and Table 58 show the results from an impact
                                                                     2000             38,4              40                 0
sound level measurement (in the field) on the same light
                                                                     2500             35,1              37                 0
floor with wooden joists shown in Figure 55.
   The single-number quantity for the impact sound level is:         3150             28,6              34                 0
                                                                                      logΣ =          L'n,w =            Σ∆L
L'n,w = 52 (0; 3) dB, so                                                             70,1 dB          52 dB            27,0 dB


L'n,w + C = 52 + 0 = 52 dB, and                                 Table 58: Calculation of L’n,w and C50-2500 for the floor in Figure
                                                                55. When the reference curve is moved downwards as far as
                                                                possible without ∑∆L> 32.0 dB, L’n,w is read at 500 Hz.
L'n,w + Ci,50-2500 = 52 + 3 = 55 dB
                                                                L’n -values for the frequency range 50 – 2500 Hz are summarised
                                                                logarithmically and provide a total level of 70.1 dB from the
The result means that the single-number quantity increases      hammer.
(= poor impact insulation), when the impact sound levels        C50-2500 is calculated from C50-2500 = log∑L -15 - L’n,w = 70 - 15 -
below 100 Hz are taken into consideration.                      52 = 3 dB




                                                                                                                                 53
s I N S U L AT I O N T H E O RY – A C O U S T I C S




Façades                                                          Coincidence
If a wall or a window shall insulate against traffic noise       The speed of sound for free bending waves in the panel is
from the street, the single-number quantity for insulation       dependent on the frequency. At a critical frequency, the
against traffic noise needs to be as high as possible.           sound velocity in the panel will be the same as the speed of
    Typical value for a highly (thermal) insulated wooden        sound in air. At this coincidence frequency, the wave
façade is:                                                       pattern of the panel comes close to the sound waves in the
                                                                 air and the panel´s insulation capacities decrease.
Rw = 48 (-2; -7; -2; -12) dB                                         The coincidence frequency is defined by the stiffness of
                                                                 the sheets. In the coincidence area and at higher
The insulation against traffic noise for such a wooden           frequencies, the sound reduction index is affected by the
façade would be:                                                 panel’s internal damping.
                                                                     As an example it may be noted that the coincidence of
Rw + Ctr,50-3150 = 48 - 12 = 36 dB                               13 mm plaster occurs at approximately 3000 Hz. Therefore,
                                                                 if 26 mm plaster should be used, the coincidence frequency
                                                                 moves to lower frequencies, which is unfavourable. 2 times
Wall constructions insulated
                                                                 13 mm plaster is therefore a better solution.
against sound
Single leaf panel                                                Double leaf partitions and cavity walls
Single leaf partitions are one-layer constructions, one sheet    Cavity walls are a suitable alternative when high insulation
of plaster, glass, brick, concrete etc. The sound reduction      is required for a light construction. Cavity wall
index is described by the mass of the wall, the stiffness, the   constructions are defined due to their resonance frequency.
internal damping and interaction with flanking walls as          Below the resonance frequency, the wall behaves as a single
well as the area. Looking only at the mass of the wall panel     wall in terms of the wall mass, near the resonance
can make a good first approximation. The sound reduction         frequency the sound reduction curve dips and above the
index according to the mass law is as follows:                   resonance frequency the insulation will be very high.

     R = 20 · log m + 20 · log f - 49 dB      (22)

m = mass/area, kg/m2
f = frequency, Hz

Note: The sound reduction index increases by 6 dB when
the mass is doubled and with 6 dB when the frequency is
doubled, 6 dB/octave.

Example 10: Calculate the sound reduction index for 1 mm
steel plate at 500 Hz.

Answer: R = 20 · log m + 20 · log f - 49 =
= 20 · log 8 + 20 · log 500 - 49 = 23 dB




                                                                 Figure 59: Cavity wall with a steel studded frame.


54
Resonance frequency                                                  Sound insulated floors
The resonance frequency is calculated as follows:                    Floors should satisfy both the demand of high airborne
                                                                     sound insulation and low impact sound levels.
     fr = 60 · √(m1+m2)/(m1 · m2 · d)          (23)                     As a rule, it is more difficult to meet the impact sound
                                                                     requirement.
fr   = Resonance frequency, Hz
m1   = Mass of partition wall 1, kg/m2                               Airborne sound insulation
m2   = Mass of partition wall 2, kg/m2                               The principles for single leaf walls and cavity walls are also
d    = Distance between partition walls, m                           applicable to floors.
                                                                        A homogenous concrete solid floor of 16 cm can be
Example 11: A cavity wall with a panel of 13 mm plaster              expected to fill the demands of sound reduction index
(9 kg/m2) on both sides. If you want a resonance frequency           outlined for example in the Swedish regulation. Hollow
of 63 Hz, what distance would you need between the                   concrete floors should give the same effect when the weight
plaster panels?                                                      corresponds to 16 cm of homogenous concrete.
                                                                        Floors with wooden beams may not be expected to meet
Answer: fr = 60 · √(m1+m2)/(m1 · m2 · d) = 63 =                      the standard requirements. In order to achieve high
= 60 · √18/(81 · d).   d = (60/63)2 · (18/81) = 0.2 m                insulation with the wooden beams, the cavity wall principle
                                                                     needs to be applied, i.e. using a free hanging ceiling and a
                                                                     floating floor.
Absorber                                                                In practice you can achieve a good effect by hanging the
                                                                     ceiling (plaster sheets etc.) in resilient clips or studs.
When a highly absorbent material as stone wool is used in
                                                                        A so-called floating floor consisting of a board etc on a
the air cavity, the sound insulation increases. The greater
                                                                     resilient layer gives a very good effect.
the cavity, the greater the benefit obtained from the
absorber. Generally you can expect an increase of about 5 –
10 dB of R with a filled wall compared to an empty wall.             Absorber
                                                                     Like in cavity walls, stone wool absorbers are effective in
Rigid connections                                                    floors with wooden joist structure if the ceiling is
A rigid connection between two cavity walls may have a               suspended. But the effect is poor if the beams connect the
dreadful effect when the cavity wall panels consist of stiff         floor on the upper side with the ceiling on the lower side.
materials, such as concrete or light concrete. For resilient
panels such as plaster sheets, the deterioration is not so severe.   Impact sound insulation
                                                                     The impact sound requirement can be satisfied by using one
”Resilient Skin”                                                     of two main principles, floating floors or soft floor covering.
The radiation-decreasing resilient skin is a typical way to
improve the insulation of a heavy wall. It consists of a             Soft floor covering
resilient panel, for example 13 mm of plaster, which is              This solution to the impact sound insulation problem can
mounted to a heavy wall such as light concrete with stone            only be used when the floor itself satisfy the requirements
wool behind. The mounting may be carried out with                    for airborne sound insulation and it is the normal solution
ordinary studs, or according to special mounting methods             for concrete solid floors.
without direct contact to the existing wall. In order to                 The soft floor covering may consist of a soft fitted carpet
reach a good effect at lower frequencies, the thickness of           or linoleum with a soft underside. The Swedish National
the stone wool must be increased.                                    Testing and Research Institute (SP) have approved impact
                                                                     sound tested carpets.
                                                                         The carpets have been tested on a concrete floor and
                                                                     received a weighted reduction of impact sound pressure
                                                                     level, ∆Lw dB. If you assume that for a concrete floor Ln,w
                                                                     is about 75 dB, you must have a soft carpet with ∆Lw at
                                                                     least 17 dB in order to reach Ln,w = 58 dB.




                                                                                                                                   55
s I N S U L AT I O N T H E O RY – A C O U S T I C S




Floating floor                                                            Vibration isolation
A floating floor consists of a board, a slab, etc on a resilient layer.   A machine such as a fan placed directly on a floor may
   An effective floating floor should have as heavy sheets                transmit the vibration as sound throughout the entire
and as soft resilient layers as possible. If the board consists           building. In order to avoid this, the machine must be
of a concrete slab and the elastic layer of stone wool, the               placed on vibration isolators made of steel or rubber or a
effect will be excellent. It is extremely important that the              stone wool slab. In order to get an effective isolation, the
concrete slab has no contact to the basic floor. Therefore                floor under the springs must be heavy or solid. As a rule of
the resilient layer also must divide the concrete slab from               thumb, the weight of the ground floor should exceed that
the surrounding walls.                                                    of the machine by approximately 4 times. A wooden joist
                                                                          may have to be fitted with rigid steel joists in order to
                                                                          function as a ground.




Figure 60: Floating floor.


However, you can achieve a fairly good effect with a light
and dry floating floor made from chipboard and plaster on
layers of stone wool. The effect may be improved by laying
the floor on a sheet of sand above the resilient layer, which
will increase the mass.
   If you would try to achieve a high sound insulation, you
may need to use a floating floor system.The floating floor is             Figure 61: Vibration isolation.
used for both airborne and impact sound insulation.
                                                                          The advantage with a stone wool slab as an isolator is that
Sound insulation in buildings                                             the internal damping is high, for which reason the
                                                                          amplitude will not be great at resonance. It is important
In order to achieve the desired insulation in the building
                                                                          that the vibration insulation is correctly calculated. The
from the chosen constructions, all non-desired sound
                                                                          resonance frequency for the system(sometimes referred to
transport must be avoided. These are of two types:
                                                                          as natural frequency), fr, Hz should be much lower than
                                                                          the lowest disturbing frequency from the machine fs, Hz.
Flanking transmission
In a building, a fraction of the sound transmission between
two rooms may go by a flanking building element, such as
the outer wall or the ceiling. In order to avoid this, the
manufacturer’s instructions must be followed carefully.
There are often requirements for a safety margin on the
different sound data of the elements in order to avoid the
flanking transmission.

Leakage
Slits, ventilation channels, common tubes for the TV-
cables, are all examples of objects that may result in sound
leakage. This can be avoided by good planning and job
performance.




56
Elastic facilities of stone wool slabs                           Choice of slab/thickness
Paroc stone wool slabs are a heterogeneous material. This        When choosing the slab and the thickness, the following
means that the dynamic elasticity may not be deduced             factors need to be taken into consideration:
from the measured results of the static compression, but         • Compression of the slab under static load
must be measured separately.                                     • Recommended static maximum load of the slab
    The principal appearance of the dynamic stiffness sd         • The dynamic stiffness of the slab, sd according to Table 63.
related to the load, is presented in Figure 62. Observe that
sd is constant above a certain load of approximately             In floating floor constructions, the elastic layers should be as
500 kg/m2.                                                       soft as possible. According to the test standards, the dynamic
                                                                 stiffness of stone wool shall be presented by a load of
     sd MN/m3                                                    200 kg/m2, when the stone wool is used as a resilient layer
30
                                                                 under a concrete slab in a floating floor construction.
25
                                                                               Dynamic stiffness, MN/m3
20
                                                                  Thickness mm    17         25       30                   50
15                                                                Product
                                                                  PAROC SSB 1                                   12         10
10                                                                PAROC SSB 2t          20          15

 5                                                               Table 63. Dynamic stiffness, MN/m3 for Paroc slabs. The value
                                                                 at a load of 200 kg/m2 load shall be used in floating floor
 0
     0             500        1000          1500          2000   constructions with concrete slabs. The value at a load of
                         Load kg/m2                              > 500 kg/m2 in vibration isolation of machines etc. To these
                                                                 values, the dynamic stiffness of the enclosed air must be added.
Figure 62: The principal appearance of the dynamic stiffness
related to the load for Paroc stone wool slabs.                  Example 12: A machine weighs 100 kg and is to be placed
                                                                 on a concrete slab of 1 times 2 metres. It is then placed on
The resonance frequency for the vibration isolation system       a 100 mm stone wool slab with sd = 10 MN/m2 at a load
can be calculated from the following formula:                    > 500 kg/m2 on top of a concrete floor. If you need a
                                                                 resonance frequency of 30 Hz for the system, how thick
         fr = (1/2π) · √s/m Hz    (24)                           must the concrete slab be?

fr = Resonance frequency, Hz                                     Answer: fr = (1/2π) · √sd/m = 30 = (1/2π) · √10 · 106/m
s = Dynamic stiffness, N/m3                                      m =[1/(30 · 2π)]2 · 10 · 106 = 280 kg/m2. The machine
m = Load, kg/m2                                                  weighed 100/2 = 50 kg/m2, i.e. the concrete slab shall
                                                                 weigh 230 kg/m2 and should therefore be approximately
When stone wool and similar materials are used as                10 cm thick. (According to the diagram, sd and fr are
”springs” the dynamic stiffness, s, consists of two              probably lower at this lower load. This is only favourable
components - sd is the stiffness of the material and sa the      for the vibration isolation).
stiffness of the enclosed air. sa can be calculated for
different thickness to the following values.

            h mm                       sa MN/m3

              5                            22
              10                           11
              20                            6
              30                            4
              50                            2
             100                            1



                                                                  For further information of material properties and our
                                                                  products see www.paroc.com


                                                                                                                                  57
s I N S U L AT I O N T H E O RY – R E G U L AT I O N S




CE marking
                                                              values, but mostly in the form of classes. CE marking is the
                                                              way to ensure that the product properties are tested and
                                                              reported in the same way within the whole of the EU.

                                                              Standards for thermal insulation
                                                              products
                                                              The European standard EN13162 is applicable to mineral
                                                              wool that is intended to be used as thermal insulation in
                                                              buildings. It is called “Thermal insulation products for
                                                              buildings – Factory manufactured mineral wool products
                                                              (MW) – Statement of properties”.
Why CE marking?                                                   There are 11 materials included in the standard package
In order to facilitate trade within Europe, harmonized        for building insulation, all with lower declared thermal
standards have been produced for a number of goods to be      conductivity, λD, than 0.06 W/mK. Common property
freely sold within the whole EU without national              designations and class limits have now been introduced for
restrictions. The standards for thermal insulation products   all of these 11 materials. A minimum level of internal
contain relevant product properties. Reference is made to     testing routines has been introduced for manufacturers,
testing methods and the designations and levels of the        sometimes supplemented by external manufacture testing
properties are fixed, sometimes in the form of limiting       of certain properties.




58
59
PAROC GROUP is one of the leading manufacturers of mineral
wool insulation products and solutions in Europe. Paroc products
and solutions include building insulation, technical insulation,
marine insulation, structural stone wool sandwich panels and
acoustics products. We have production facilities in Finland,
Sweden, Lithuania, Poland and Great Britain. We have sales and
representative offices in 13 countries in Europe.

                                      Paroc building insulation is a wide
                                      range of products and solutions for all
                                      traditional building insulation. The
                                      building insulation is mainly used for the
                                      thermal, fire and sound insulation of
                                      exterior walls, roofs, floors and
                                      basement, intermediate floors and
                                      partitions.




                                      Paroc technical insulation is used
                                      for thermal, fire and sound insulation in
                                      building techniques, industrial processes
                                      and piping, industrial equipment and
                                      ship structures.




                                      Paroc Fire Proof Panels are steel-
                                      faced lightweiht panels with a core
                                      material of stone wool. Paroc Panels are
                                      used for façades, partition walls and
                                      ceilings in public, commercial and
                                      industrial buildings.


Warranty: Our recommendations are based on our most up-to-date knowledge and experience. As the
products are used outside our control we cannot take responsibility for any damage which may be caused
when using the product. This brochure replaces all earlier ones. Because of constant development all
information is subject to change without notice.




                                                                                                         PAROC OY AB
                                                                                                         Neilikkatie 17
                                                                                                         P.O.Box 294
                                                                                                         FIN-01301 VANTAA, Finland
                                                                                                         Tel. +358 204 55 4868
                                                                                                         Fax +358 204 55 4738
2040BIEN1003
                                                                                                         A M E M B E R O F PA R O C G R O U P



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