R-value (insulation)
In the context of construction,[2] the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive[3] flow of heat. R-value is the temperature difference per unit of heat flux needed to sustain one unit of heat flux between the warmer surface and colder surface of a barrier under steady-state conditions. The measure is therefore equally relevant for lowering energy bills for heating in the winter, for cooling in the summer, and for general comfort.
The R-value is the building industry term[2] for thermal resistance "per unit area."[4] It is sometimes denoted RSI-value if the SI units are used.[5] An R-value can be given for a material (e.g. for polyethylene foam), or for an assembly of materials (e.g. a wall or a window). In the case of materials, it is often expressed in terms of R-value per metre. R-values are additive for layers of materials, and the higher the R-value the better the performance.
The U-factor or U-value is the overall heat transfer coefficient and can be found by taking the inverse of the R-value. It is a property that describes how well building elements conduct heat per unit area across a temperature gradient. [6] The elements are commonly assemblies of many layers of materials, such as those that make up the building envelope. It is expressed in watts per square metre kelvin: W/(m2⋅K). The higher the U-value, the lower the ability of the building envelope to resist heat transfer. A low U-value, or conversely a high R-Value usually indicates high levels of insulation. They are useful as it is a way of predicting the composite behaviour of an entire building element rather than relying on the properties of individual materials.
This relates to the technical/constructional value.
where:
The R-value per unit of a barrier's exposed surface area measures the absolute thermal resistance of the barrier.[7]
where:
Absolute thermal resistance, , quantifies the temperature difference per unit of heat flow rate needed to sustain one unit of heat flow rate. Confusion sometimes arises because some publications use the term thermal resistance for the temperature difference per unit of heat flux, but other publications use the term thermal resistance for the temperature difference per unit of heat flow rate. Further confusion arises because some publications use the character R to denote the temperature difference per unit of heat flux, but other publications use the character R to denote the temperature difference per unit of heat flow rate. This article uses the term absolute thermal resistance for the temperature difference per unit of heat flow rate and uses the term R-value for the temperature difference per unit of heat flux.
In any event, the greater the R-value, the greater the resistance, and so the better the thermal insulating properties of the barrier. R-values are used in describing the effectiveness of insulating material and in analysis of heat flow across assemblies (such as walls, roofs, and windows) under steady-state conditions.[7] Heat flow through a barrier is driven by temperature difference between two sides of the barrier, and the R-value quantifies how effectively the object resists this drive:[8][9] The temperature difference divided by the R-value and then multiplied by the exposed surface area of the barrier gives the total rate of heat flow through the barrier, as measured in watts or in BTUs per hour.
where:
As long as the materials involved are dense solids in direct mutual contact,[10] R-values are additive; for example, the total R-value of a barrier composed of several layers of material is the sum of the R-values of the individual layers.[7][11]
For example, in winter it might be 2 °C outside and 20 °C inside, making a temperature difference of 18 °C or 18 K. If the material has an R-value of 4, it will lose 0.25 W/(°C⋅m2). With an area of 100 m2, the heat energy being lost is 0.25 W/(K⋅m2) × 18 °C × 100 m2 = 450 W. There will be other losses through the floor, windows, ventilation slots, etc. But for that material alone, 450 W is going out, and can be replaced with a 450 W heater inside, to maintain the inside temperature.
Usage, units[edit]
Note that the R-value is the building industry term[2] for what is in other contexts called "thermal resistance" "for a unit area."[4] It is sometimes denoted RSI-value if the SI (metric) units are used.[5][12]
An R-value can be given for a material (e.g. for polyethylene foam), or for an assembly of materials (e.g. a wall or a window). In the case of materials, it is often expressed in terms of R-value per unit length (e.g. per inch of thickness). The latter can be misleading in the case of low-density building thermal insulations, for which R-values are not additive: their R-value per inch is not constant as the material gets thicker, but rather usually decreases.[10]
The units of an R-value (see below) are usually not explicitly stated, and so it is important to determine from context which units are being used: an R-value expressed in I-P (inch-pound) units[13] is about 5.68 times larger than when expressed in SI units,[14] so that, for example, a window that is R-2 in I-P units has an RSI of 0.35 (since 2/5.68 = 0.35). For R-values there is no difference between US customary units and imperial units.
All of the following mean the same thing: "this is an R-2 window";[15] "this is an R2 window";[16][5] "this window has an R-value of 2";[15] "this is a window with R = 2"[17] (and similarly with RSI-values, which also include the possibility "this window provides RSI 0.35 of resistance to heat flow"[18][5]).
is the thickness () of the sample (measured on a path parallel to the heat flow),
m
The more a material is intrinsically able to conduct heat, as given by its thermal conductivity, the lower its R-value. On the other hand, the thicker the material, the higher its R-value. Sometimes heat transfer processes other than conduction (namely, convection and radiation) significantly contribute to heat transfer within the material. In such cases, it is useful to introduce an "apparent thermal conductivity", which captures the effects of all three kinds of processes, and to define the R-value more generally as the thickness of a sample divided by its apparent thermal conductivity. Some equations relating this generalized R-value, also known as the apparent R-value, to other quantities are:
where:
An apparent R-value quantifies the physical quantity called thermal insulance.
However, this generalization comes at a price because R-values that include non-conductive processes may no longer be additive and may have significant temperature dependence. In particular, for a loose or porous material, the R-value per inch generally depends on the thickness, almost always so that it decreases with increasing thickness[10] (polyisocyanurate (colloquially, polyiso) being an exception; its R-value/inch increases with thickness[19]). For similar reasons, the R-value per inch also depends on the temperature of the material, usually increasing with decreasing temperature (polyisocyanurate again being an exception); a nominally R-13 fiberglass batt may be R-14 at −12 °C (10 °F) and R-12 at 43 °C (109 °F).[20] Nevertheless, in construction it is common to treat R-values as independent of temperature.[21] Note that an R-value may not account for radiative or convective processes at the material's surface, which may be an important factor for some applications.
The R-value is the reciprocal of the thermal transmittance (U-factor) of a material or assembly. The U.S. construction industry prefers to use R-values, however, because they are additive and because bigger values mean better insulation, neither of which is true for U-factors.[2]
Units: metric (SI) vs. inch-pound (I-P)[edit]
The SI (metric) unit of R-value is
kelvin square-metre per watt (K⋅m2/W or, equally, °C⋅m2/W),
whereas the I-P (inch-pound) unit is
degree Fahrenheit square-foot hour per British thermal unit (°F⋅ft2⋅h/BTU).[13]
For R-values there is no difference between U.S. and Imperial units, so the same I-P unit is used in both.
Some sources use "RSI" when referring to R-values in SI units.[5][12]
R-values expressed in I-P units are approximately 5.68 times as large as R-values expressed in SI units.[14] For example, a window that is R-2 in the I-P system is about RSI 0.35, since 2/5.68 ≈ 0.35.
In countries where the SI system is generally in use, the R-values will also normally be given in SI units. This includes the United Kingdom, Australia, and New Zealand.
I-P values are commonly given in the United States and Canada, though in Canada normally both I-P and RSI values are listed.[28]
Because the units are usually not explicitly stated, one must decide from context which units are being used. In this regard, it helps to keep in mind that I-P R-values are 5.68 times larger than the corresponding SI R-values.
More precisely,[29][30]
R-value (in I-P) ≈ RSI-value (in SI) × 5.678263
RSI-value (in SI) ≈ R-value (in I-P) × 0.1761102
Different insulation types[edit]
The Australian Government explains that the required total R-values for the building fabric vary depending on climate zone. "Such materials include aerated concrete blocks, hollow expanded polystyrene blocks, straw bales and rendered extruded polystyrene sheets."[31]
In Germany, after the law Energieeinsparverordnung (EnEv) introduced in 2009 (October 10) regarding energy savings, all new buildings must demonstrate an ability to remain within certain boundaries of the U-value for each particular building material. Further, the EnEv describes the maximum coefficient for each new material if parts are replaced or added to standing structures.[32]
The U.S. Department of Energy has recommended R-values for given areas of the USA based on the general local energy costs for heating and cooling, as well as the climate of an area. There are four types of insulation: rolls and batts, loose-fill, rigid foam, and foam-in-place. Rolls and batts are typically flexible insulators that come in fibers, like fiberglass. Loose-fill insulation comes in loose fibers or pellets and should be blown into a space. Rigid foam is more expensive than fiber, but generally has a higher R-value per unit of thickness. Foam-in-place insulation can be blown into small areas to control air leaks, like those around windows, or can be used to insulate an entire house.[33]
Thickness[edit]
Increasing the thickness of an insulating layer increases the thermal resistance. For example, doubling the thickness of fiberglass batting will double its R-value, perhaps from 2.0 m2⋅K/W for 110 mm of thickness, up to 4.0 m2⋅K/W for 220 mm of thickness. Heat transfer through an insulating layer is analogous to adding resistance to a series circuit with a fixed voltage. However, this holds only approximately because the effective thermal conductivity of some insulating materials depends on thickness. The addition of materials to enclose the insulation such as drywall and siding provides additional but typically much smaller R-value.
Factors[edit]
There are many factors that come into play when using R-values to compute heat loss for a particular wall. Manufacturer R-values apply only to properly installed insulation. Squashing two layers of batting into the thickness intended for one layer will increase but not double the R-value. (In other words, compressing a fiberglass batt decreases the R-value of the batt but increases the R-value per inch.) Another important factor to consider is that studs and windows provide a parallel heat conduction path that is unaffected by the insulation's R-value. The practical implication of this is that one could double the R-value of insulation installed between framing members and realize substantially less than a 50 percent reduction in heat loss. When installed between wall studs, even perfect wall insulation only eliminates conduction through the insulation but leaves unaffected the conductive heat loss through such materials as glass windows and studs. Insulation installed between the studs may reduce, but usually does not eliminate, heat losses due to air leakage through the building envelope. Installing a continuous layer of rigid foam insulation on the exterior side of the wall sheathing will interrupt thermal bridging through the studs while also reducing the rate of air leakage.
Primary role[edit]
The R-value is a measure of an insulation sample's ability to reduce the rate of heat flow under specified test conditions. The primary mode of heat transfer impeded by insulation is conduction, but insulation also reduces heat loss by all three heat transfer modes: conduction, convection, and radiation. The primary heat loss across an uninsulated air-filled space is natural convection, which occurs because of changes in air density with temperature. Insulation greatly retards natural convection making conduction the primary mode of heat transfer. Porous insulations accomplish this by trapping air so that significant convective heat loss is eliminated, leaving only conduction and minor radiation transfer. The primary role of such insulation is to make the thermal conductivity of the insulation that of trapped, stagnant air. However this cannot be realized fully because the glass wool or foam needed to prevent convection increases the heat conduction compared to that of still air. The minor radiative heat transfer is obtained by having many surfaces interrupting a "clear view" between the inner and outer surfaces of the insulation such as visible light is interrupted from passing through porous materials. Such multiple surfaces are abundant in batting and porous foam. Radiation is also minimized by low emissivity (highly reflective) exterior surfaces such as aluminum foil. Lower thermal conductivity, or higher R-values, can be achieved by replacing air with argon when practical such as within special closed-pore foam insulation because argon has a lower thermal conductivity than air.
General[edit]
Heat transfer through an insulating layer is analogous to electrical resistance. The heat transfers can be worked out by thinking of resistance in series with a fixed potential, except the resistances are thermal resistances and the potential is the difference in temperature from one side of the material to the other. The resistance of each material to heat transfer depends on the specific thermal resistance [R-value]/[unit thickness], which is a property of the material (see table below) and the thickness of that layer. A thermal barrier that is composed of several layers will have several thermal resistors in the analogous with circuits, each in series. Analogous to a set of resistors in parallel, a well insulated wall with a poorly insulated window will allow proportionally more of the heat to go through the (low-R) window, and additional insulation in the wall will only minimally improve the overall R-value. As such, the least well insulated section of a wall will play the largest role in heat transfer relative to its size, similar to the way most current flows through the lowest resistance resistor in a parallel array. Hence ensuring that windows, service breaks (around wires/pipes), doors, and other breaks in a wall are well sealed and insulated is often the most cost effective way to improve the insulation of a structure, once the walls are sufficiently insulated.
Like resistance in electrical circuits, increasing the physical length (for insulation, thickness) of a resistive element, such as graphite for example, increases the resistance linearly; double the thickness of a layer means double the R-value and half the heat transfer; quadruple, quarters; etc. In practice, this linear relationship does not always hold for compressible materials such as glass wool and cotton batting whose thermal properties change when compressed. So, for example, if one layer of fiberglass insulation in an attic provides R-20 thermal resistance, adding on a second layer will not necessarily double the thermal resistance because the first layer will be compressed by the weight of the second.
Calculating heat loss[edit]
To find the average heat loss per unit area, simply divide the temperature difference by the R-value for the layer.
If the interior of a home is at 20 °C and the roof cavity is at 10 °C then the temperature difference is 10 °C (or 10 K). Assuming a ceiling insulated to RSI 2.0 (R = 2 m2⋅K/W), energy will be lost at a rate of 10 K / (2 K⋅m2/W) = 5 watts for every square meter (W/m2) of ceiling. The RSI-value used here is for the actual insulating layer (and not per unit thickness of insulation).
Relationships[edit]
Thickness[edit]
R-value should not be confused with the intrinsic property of thermal resistivity and its inverse, thermal conductivity. The SI unit of thermal resistivity is K⋅m/W. Thermal conductivity assumes that the heat transfer of the material is linearly related to its thickness.
Multiple layers[edit]
In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added:[34]
R-value(outside air film) + R-value(brick) + R-value(sheathing) + R-value(insulation) + R-value(plasterboard) + R-value(inside air film) = R-value(total).
To account for other components in a wall such as framing, first calculate the U-value (= 1/R-value) of each component, then the area-weighted average U-value. An average R-value is 1/(average U-value). For example, if 10% of the area is 4 inches of softwood (R-value 5.6) and 90% is 2 inches of silica aerogel (R-value 20), the area-weighted U-value is 0.1/5.6 + 0.9/20 ≈ 0.0629 and the weighted R-value is 1/0.0629 ≈ 15.9.
Deterioration[edit]
Insulation aging[edit]
While research is lacking on the long-term degradation of R-value in insulation, recent research indicates that the R-values of products may deteriorate over time. For instance, the compaction of loose-fill cellulose creates voids that reduce overall performance; this may be avoided by densely packing at initial installation. Some types of foam insulation, such as polyurethane and polyisocyanurate are blown into form with heavy gases such as chlorofluorocarbons (CFC) or hydrochlorofluorocarbons (HFCs). However, over time these gases diffuse out of the foam and are replaced by air, thus reducing the effective R-value of the product. There are other foams which do not change significantly with aging because they are blown with water or are open-cell and contain no trapped CFCs or HFCs (e.g., half-pound low-density foams). On certain brands, twenty-year tests have shown no shrinkage or reduction in insulating value.
This has led to controversy as how to rate the insulation of these products. Many manufacturers will rate the R-value at the time of manufacture; critics argue that a more fair assessment would be its settled value. The foam industry adopted the long-term thermal resistance (LTTR) method,[38] which rates the R-value based on a 15-year weighted average. However, the LTTR effectively provides only an eight-year aged R-value, short in the scale of a building that may have a lifespan of 50 to 100 years.
Research has been conducted by the U.S. Army Engineer Research and Development Center on the long-term degradation of insulating materials. Values on the degradation were obtained from short-term laboratory testing on materials exposed to various temperature and humidity conditions. Results indicate that moisture absorption and loss of blowing agent (in closed-cell spray polyurethane foam) were major causes of R-Value loss. Fiberglass and extruded polystyrene retained over 97% of their initial R-values while, aerogels and closed-cell polyurethane saw a reduction of 15% and 27.5%, respectively. Results suggest an exponential decay law over time applies to R-values for closed-cell polyurethanes and aerogel blankets.[39]
Infiltration[edit]
Correct attention to air sealing measures and consideration of vapor transfer mechanisms are important for the optimal function of bulk insulators. Air infiltration can allow convective heat transfer or condensation formation, both of which may degrade the performance of an insulation.
One of the primary values of spray-foam insulation is its ability to create an airtight (and in some cases, watertight) seal directly against the substrate to reduce the undesirable effects of air leakage. Other construction technologies are also used to reduce or eliminate infiltration such as air sealing techniques.