Building Science

The Physics of Thermal Inertia in Low-Slope Roof Design

By Thomas J Taylor

January 13, 2021

Commercial building with a masonry facade

What are the key material properties?

In a previous article the use of thermal inertia to slow down heat flux through a roof assembly was discussed. In buildings where air conditioning costs dominate and heating use is relatively low, higher thermal inertia assemblies can potentially improve energy efficiency. This is particularly the case of buildings such as offices that are only occupied during daylight hours. Thermal inertia could delay the transmission of heat into a building towards the end of the day, increasing thermal comfort and allowing facility managers to reduce cooling during the day.

While the previous article provided an introduction to thermal inertia and its potential benefits, it didn't discuss the origin of the property. Also, the related but different terms, thermal inertia and thermal mass, were used somewhat interchangeably.

This article describes the material properties that contribute to thermal inertia and provides a basis for material selection when increased thermal inertia is a goal.


A building enclosure with high thermal inertia will slow down the transmission of heat. This effect has traditionally been used in the Mediterranean and other temperate climates to improve thermal comfort during the summer. As the building exterior surface heated up during the early afternoon period, high thermal inertia reduced the heat transmission into the interior. This was advantageous in the days before air conditioning. Today, designing with higher thermal inertia, as described in part one of this series, could improve energy efficiency in certain situations:

  • Buildings located in areas where energy costs are dominated by air conditioning.
  • Buildings only used during the day and not on a 24 hour basis. Thermal inertia can push heat loads into the evening, allowing for either temperature settings to be raised or HVAC fans speeds to be reduced.
  • For high thermal inertia within the roof assembly to have a significant effect, low to moderate rise buildings with larger footprints would be best.

Thermal Inertia Effects

There are two key characteristics of thermal inertia; the decrement factor and time delay, both of which can be readily modeled and experimentally verified. A schematic showing these is shown below:

The time delay is calculated as:

Φ = t[Tout(max)] - t[Tin(max)]

Where t[Tout(max)] and t[Tin(max)] are the time of day when the inside and outside surface temperatures reach maximum. The decrement factor, DF, is calculated from:

DF = (Tin(max) – Tin(min)) / (Tout(max) – Tout(min))

  • The time delay and decrement factor could be used by building designers and operators to better optimize thermostat specification, HVAC use, and temperature schedules. As noted earlier, a large time delay could significantly reduce daily AC cooling demands for office buildings.
  • Larger decrement factors can improve occupants' thermal comfort. Temperature swings are reduced, which in turn reduces HVAC cycling.
  • Importantly, high thermal inertia will not reduce the energy reaching the interior, it only delays the transmission. This can make increased thermal inertia part of a strategy to improve energy efficiency in buildings occupied during the day but not necessarily for those occupied on a 24-hour basis.

Roof Configurations and Thermal Properties

Building designers and construction professionals are familiar with the property of thermal resistance, which is a measure of the extent to which a material blocks or resists heat transfer. It is expressed as R-value or U-value, which are numerical descriptions of the extent to which a material can resist heat flow.

However, there is far less familiarity with the time delay of heat transfer, or the extent to which a material slows down or delays heat transfer. As will be seen, a material can have low thermal resistance but still delay heat transfer. This is the crux of the underlying properties "thermal diffusivity", "thermal mass" and "thermal inertia".

Fundamental Thermo-Physical Properties

There are three fundamental thermo-physical properties of materials that are the components of thermal diffusivity, thermal inertia, and thermal mass. These are thermal conductivity, density, and specific heat capacity.

Thermal Conductivity

Building design professionals are very familiar with thermal conductivity, k, measured as watts per meter per Kelvin (W/(m.K)). It is normally used to characterize individual materials, for example polyiso foam, and is a measure of the heat flow through a material when a temperature gradient of 1K (i.e 1°C) is applied.

A related term, the u-factor, is used to describe the thermal conductivity of a system. This could be a window, i.e. a combination of glass, air space, and frame etc.

Thermal conductivity is measured when heat flow has equilibrated and it doesn't include any time delay.


Density is a measure of the mass per unit volume, ρ=m/v. While this is straightforward for most materials, products such as polyiso can be harder to define. There are the facers and a small density gradient within the foam. Later, as values are listed, the facers will be ignored and the foam's density considered as an average.

Specific Heat Capacity

Specific heat capacity is defined as the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 kelvin, or Cp = J/(kg.K). It is worth considering the simple diagram above, showing the measurement of thermal conductivity. At the onset, heat flow through the material is delayed by its specific heat capacity. It takes energy to raise its temperature, an action required before heat can then transmit.

Derived Thermo-Physical Properties

As noted, the fundamental properties described earlier are all measured at equilibrium and do not include any time lag or delay. For that, the following derived properties need to be considered.

Thermal Diffusivity

Thermal diffusivity is a measure of the rate at which a temperature propagates from one point to another point in a material. It's the rate of transfer of heat from a hot side to a cold side and is calculated as:

In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'. In a sense, thermal diffusivity is what is meant when the topic of thermal inertia is discussed casually.

Thermal Inertia

Thermal inertia is the slowness with which the temperature of a material approaches that of its surroundings. It is a product of thermal conductivity, density, and specific heat capacity. From a building enclosure perspective, it could be considered as the rate at which the interior surface can supply heat into the interior, assuming a temperate climate.

It is arguable that thermal inertia is not the best property to use to characterize a building enclosure component in terms of thermal lag.

Thermal Mass

It is often broadly thought that thermal mass is essentially equivalent to gravimetric mass. Conceptually, this gives rise to the view that the more massive a construction the better. However, consider two blocks - one of steel and one of concrete - each having the same gravimetric mass. The two materials have different specific heat capacities and are not equivalent in terms of thermal properties. In addition, steel has a significantly higher thermal conductivity versus concrete.

Thermal mass is a property of a material that enables it to store heat and is the product of density and specific heat capacity:

Importantly, thermal mass doesn't fully describe thermal lag. High thermal mass would change the decrement factor, dampening out heat transmission but is only indirectly linked to thermal delay.

Roof Component Thermal Properties

Two deck types are predominant in North American construction of big-box type architecture; steel and concrete. Two possible idealized roof assemblies are shown below, based on the two roof deck types:

  • Both systems have most roof assembly layers adhered. The steel deck system has a first layer of mechanically attached gypsum board to act as a substrate for the adhered first layer of polyiso.
  • Thermal bridging is either minimal in the steel deck based system or absent in the concrete deck system (ignoring any real world penetrations).
  • The first layer of gypsum board in the steel deck case could be used as a substrate for a vapor retarder.

The membrane, adhesive layers, and steel deck are relatively thin and have no significant insulating properties. The following table shows the fundamental and derived thermo-physical properties of the other components:

thermal inertia chart

  • Polyiso and HD Polyiso specific heat values are estimates.
  • Concrete properties are very dependent on aggregate type and moisture level. Data shown represents average values for dry concrete.

Unsurprisingly, the data shows that concrete has significantly higher thermal mass and inertia versus the other materials compared in the table. As discussed in the first part of this series, insulation is best placed closest to the building exterior, and thermally massive materials placed closest to the interior. The southeast region tends to use concrete decks more than many other regions of the US, largely for improving the strength of the roof deck. This could also mean that, especially for those buildings occupied only during the day, such as offices, schools, and the like, have better opportunity for energy-efficiency benefits with well-designed roof insulation systems.


  • Thermal property data could be used in modeling exercises to better understand how to design and optimize energy-efficient buildings.
  • Clearly, concrete has a far higher thermal mass and inertia than other materials commonly used in roof assemblies.
  • Very lightweight concrete and gypsum board have very similar thermal mass, thermal inertia, and density, but have notably different properties for thermal diffusivity and conductivity.

Thermal property data is fundamental to the materials used in low slope roof assemblies. However, it needs to be converted into values specific for the thickness and weight of actual roof products. That will be a topic for the next part of this series.

Sources Used

  1. Verbeke, S., Thermal inertia in dwellings. Quantifying the relative effects of building thermal mass on energy use and overheating risk in a temperate climate. PhD Thesis, University of Antwerp, 2017.
  2. Balaji, N. C., Mani, M., and Venkatarama, R. B. V., Thermal performance of building walls. 1st IBPSA Italy Conference, Building Simulation, 2013, pp. 151 – 159.

About the Author

Thomas J Taylor, PhD is the Building & Roofing Science Advisor for GAF. Tom has over 20 year’s experience in the building products industry, all working for manufacturing organizations. He received his PhD in chemistry from the University of Salford, England, and holds approximately 35 patents. Tom’s main focus at GAF is roofing system design and building energy use reduction. Under Tom’s guidance GAF has developed TPO with unmatched weathering resistance.

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By Authors Thomas J Taylor

June 17, 2021

Building Science

Vapor Retarder Frequently Asked Questions

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The colder the climate, the higher the risk of condensation within the roof assembly. So, buildings located in northerly regions will generally have a higher risk of condensation forming in the building enclosure. The higher the anticipated interior moisture load, the higher the risk. Office buildings occupied during daytime only are likely to have a lower risk versus a building that includes a swimming pool. A building closed up during construction while a concrete slab floor is still drying will likely have a higher risk. The roof assembly design is also a factor. High wind events can cause mechanically attached single-ply membranes to billow which causes air to be drawn up into the assembly, which can increase the risk of condensation. To minimize condensation risk, roof designers should first consider adhering the roof membrane and upper layer of insulation, making it harder for interior air and moisture to be drawn up into the assembly. If a cover board is being used, it should also be adhered. Conclusions Vapor retarders can be used to reduce the movement of vapor within a roof assembly. They need to be positioned as low as practical within the assembly and any penetrations should be sealed. Vapor retarders in the roof assembly may be beneficial in buildings with large temperature differences from interior to exterior throughout the year, and occupancies with higher than normal interior moisture levels, either from use or during construction. Important Considerations The purpose of this article is to provide some background information and design considerations for roofing assemblies using vapor retarders. GAF manufactures and sells roof materials but is not responsible for building design and construction. Design responsibility remains with the architect, engineer, roofing contractor, or owner. This information should not be construed as being all-inclusive, nor should it be considered as a substitute for good application practices. Please consult your design professional for more information.

By Authors Thomas J Taylor

June 08, 2021

Polyiso installation
Building Science

Designing with Polyiso

Thermal insulation is an important part of commercial roofing assemblies. As with anything, there are ways to design with and install polyiso insulation — a better way, a best way, and many variations in-between! What may be best in terms of lowest up-front costs, may prove only good or worse over the long-term life of the building.As discussed later, important points to remember about polyiso and its use include:Due to polyiso's very low air permeability, good design and installation practices can result in low risks of condensation, even for buildings with somewhat higher than normal humidity levels.Building designers can use the label R-value, stated at a mean temperature of 75°F, for projects in most ASHRAE climate zones. However, for climate zones 6 and 7, it may be appropriate to use published values at 40°F.Electricity is four times as expensive as gas, on an equivalent Btu basis. Therefore, polyiso's greatest value is seen during summer months when air conditioning usage is at its highest.IntroductionPolyiso has become the go-to insulation for commercial roofing with about 75% market share. The reasons include:Lowest cost per R-value.High R-value per inch, meaning it doesn't require as much thickness as other types of rigid insulation to achieve the same insulation performance.Good fire resistance. Being a thermoset unlike polystyrene foams, it doesn't melt during a fire. Melting of thermoplastic foams and subsequent flowing down of molten material through the deck into a building can be hazardous for occupants and fire crews.Solvent compatibility — adhesives used in adhered systems don't adversely affect polyiso. This is not the case with polystyrene foams.Reduced condensation — When installed correctly in a properly designed system, polyiso helps to resist interior air from reaching the underside of the membrane, thereby reducing condensation risks.However, just because polyiso is specified and used doesn't mean that the ideal outcome is reached. There are installation details that need to be considered.Single-ply membrane combined with polyiso can make for a good roof, but additional factors can improve performance:The BasicsPolyiso boards have straight cut edges (the boards are not tongue and grooved). These butt joints between boards can allow for vertical air movement.Polyiso was often installed as a single layer:As shown in the figure above, a single layer of butt-jointed insulation is generally a bad idea and is no longer allowed by the International Building Code (IBC) in the 2018 and newer versions. For roofs with a single layer of butt-jointed insulation boards:There is little restriction for air flow and so, during wind events, wind uplift forces result in membrane billowing for attached systems.Membrane billowing draws interior conditioned air up to the underside of the membrane and may create a risk of condensation within the assembly.Billowing may place additional stress on membrane fasteners, a factor recognized by membrane manufacturers by the issuance of shorter guarantees or warranties for mechanically attached versus adhered membrane.Essentially unrestricted air flow up into the assembly diminishes the insulation value and lowers energy efficiency.In contrast, two layers of polyiso restrict the free flow of air into the roof assembly. Care must be taken to seal between roof penetrations and the polyiso, or air is still free to move up into the assembly as shown here:Spray foam is a good choice for achieving a seal between the polyiso and the penetrations.Two layers of polyiso with staggered joints and sealed penetrations is a good system, but two of its features still reduce its insulation efficacy. These are shown in the following magnified view of a roof assembly cross-section.This cross-section illustrates lower energy efficiency resulting from:Insulation and membrane fasteners both act as thermal bridges, conducting heat through the assembly.Gaps between insulation boards that allow thermal convection to occurWhen both the insulation and membrane are attached and fastener densities are at their highest, R-value reductions of up to 29% have been predicted.Adhered versus AttachedThe alternative to mechanical attachment is to adhere the insulation with adhesive. Typically, low rise foam is the adhesive used for both insulation and cover board installation. The original method of application was as a ribbon but for labor savings it is often sprayed in a spatter-pattern as shown in the following picture of a typical installation in progress using one of GAF's low rise foamsUsually, when polyiso is adhered, the roof membrane is also adhered. For a steel deck substrate, fasteners are typically only used for the first layer of insulation, and then the adhesive is used on the subsequent layers of insulation and membrane. While it may be possible to adhere directly to a steel deck and eliminate fasteners totally, this approach is more common with concrete decks, as shown in the schematic here:Key features of systems with adhered insulation are:Air flow up through the assembly is limited and the risk of condensation in cold climates is low. Similarly, membrane billowing is minimized due to the restricted air flow up through adhered insulation layers.Thermal bridging is minimized since only the first layer of insulation might be mechanically attached. With concrete decks, the first layer of polyiso can be adhered thereby eliminating the use of fasteners totally.Wind uplift resistance is uniformly distributed across the roof deck. A system with adhered membrane and insulation can act as a monolithic system with excellent wind uplift resistance.When combined with an adhered membrane the finished roof appearance is usually aesthetically pleasing. When applied in accordance with manufacturer's instructions, the membrane can be very flat and there will not be any insulation fasteners to telegraph through and mar the appearance.Induction WeldedInduction welded fasteners are another type of roof attachment, the largest type being the Drill-Tec™ RhinoBond® system. By definition this is a mechanical attachment method but it has many of the features of adhered systems. The technique fastens TPO and PVC membranes to the substrate below using a microprocessor controlled induction welding machine. The thermoplastic roof membrane is welded directly to specially coated fastening plates used to attach the insulation. The picture below shows such a system being used:The induction machine is placed above each plate in turn and activated for approximately 10 seconds. As the machine is moved to the next position, a weighted magnet is placed over the plate and acts to squeeze the membrane down onto the hot fastener plate causing it to weld to that plate's surface coating.For typical mechanical attachment of single-ply membranes with fasteners along the seam lines, the insulation boards are simply secured with five fasteners per 4 x 8 ft. board to keep them flat. When using a Drill-Tec™ RhinoBond® system, the combined insulation and membrane fasteners resist wind uplift forces as shown in this picture during a test of wind uplift resistance:This means that wind loads are more uniformly distributed versus a conventionally attached system.Key features of systems with induction welded membrane attachment are:Performance is very similar to adhered in terms of the distribution of loads.Thermal bridging is reduced compared to traditional mechanically attached membrane systems.There are no application temperature restrictions and so this approach can be used in place of adhesive attachment regardless of how cold it might be.Drill-Tec™ RhinoBond® systems can be cost competitive due to the speed of installation as compared with traditional bucket and roller adhesives.Dew Point CalculationsThe dew point is the temperature at which moisture vapor forms condensation. It's a function of the relative humidity and the ambient temperature. The evaluation of a roof assembly where the dew point might be reached is an important step towards designing a roof with minimized condensation risks. The topic has been covered in greater depth elsewhere, but this section summarizes the key steps. Examine the chart below (this is a simplified form of what is used by HVAC engineers).Locating 40% relative humidity in the first column and then going across to the 70°F, design dry bulb temperature shows a dew point of 45°F. This means that in an environment that is 70°F and 40% relative humidity (RH), water in the air will condense at a temperature of 45°F. A roof assembly separates the interior conditioned environment from the outside and the insulation layer in the roofing system resists heat loss or gain to/from the outside, depending on the season. Within the insulation layer the temperature has a gradient between the hot and cold side, i.e. between inside and outside.As an example, consider a building in the winter to illustrate the point. The interior is 70 °F with 40% RH, like the example on the chart above. The temperature gradually drops from the innermost part of the insulation until at the outermost part it will be at the exterior, cold temperature. The plotting of temperature through the insulation thickness is referred to as the temperature gradient of that system. Using the example, if the temperature gets to the dew point of 45°F at any point in that system then water would be expected to condense on the nearest surface. This is shown in the following diagram:Summarizing, in this example the interior air has 40% of the total water vapor that it can support. But as the air migrates up through the roof system, it gets cooler until the point where it can no longer hold onto the water vapor and condensation occurs. In the example shown above, that's at 45°F and just inside the insulation layer.As will be discussed later, dew point calculations can be used to inform the placement of a vapor retarder layer when used.When a dedicated vapor retarder layer is not used, it is good practice to ensure that the dew point is in the upper layer of polyiso insulation. This will lower the risk of interior air migrating up through the roof assembly and condensing on a surface below its dew point.Using Vapor Retarders with PolyisoVapor retarders can be used to limit humidity ingress to the roof assembly. Under certain circumstances, depending on the building use and location, condensation can occur as discussed in the previous dew point discussion. In general there are four basic building conditions that can be considered:1. Buildings with Standard Amounts of Occupancy-Generated MoistureThese are the most common situations covering for example, office, retail, and warehouse spaces. The risk of having a condensation issue is low and good roofing practices such as sealing around penetrations may likely suffice.2. Buildings with Larger Amounts of Occupancy-Generated MoistureThis category includes apartments and other multiple residency buildings, paper mills, laundries, buildings with indoor swimming pools, and the like. In fact, anything that doesn't fit into category 1 above should be evaluated to determine humidity levels. The building's air handling and ventilation systems should be carefully specified to take into account the moisture loading.3. Construction–Related MoistureMost construction practices release some amount of moisture into the building space. These can be relatively short term such as drywall installation and painting. However, some practices can release large amounts of water over a considerable time frame into the building. These include poured in place concrete floors and roof decks.4. Concrete Roof DecksThese can present a challenge for roof system designers especially in new construction. Regardless of the type of concrete, significant amounts of water remain after curing is completed. Allowing concrete to thoroughly dry is most appropriate; however, it is often reasonably impractical. Dealing with potential moisture in concrete decks is beyond the scope of this article, but guidance can be found elsewhere.It is recommended that a building science professional experienced in designs for Categories 2, 3, and 4 be involved to determine whether a vapor retarder should be used and what type.Specification of R-ValuePolyiso is manufactured to meet the ASTM C1289 Standard Specification for Faced Rigid Cellular Polyisocyanurate Thermal Insulation Board. ASTM C1289 specifies the thermal resistance at a mean temperature of 75°F for various product thicknesses and requires that the values at 40 and 110°F be made available upon request.Important features of manufacturer's published R-values are:The values are an average across a temperature range. The test methods need the insulation specimen to have a hot and a cold side at least 40°F apart. Most reputable test labs use a difference of 50°F for accuracy. A published value at 75°F is actually an average R-value across the range of 50 to 100°F.To take into account the diffusion of gas out of, and air into the polyiso foam, the values are based on projected "Long Term Thermal Resistance" or LTTR, obtained by rapidly aging thin slices of the foam.The Polyisocyanurate Insulation Manufacturers Association, PIMA, conducts a third-party certification program to independently validate LTTR values. This is referred to as the PIMA QualityMark™ program. The LTTR values are considered as "labelled R-values" to be used by building design professionals.Label R-values represent a 15-year time-weighted average value. They can help a design professional estimate a building's energy efficiency without having to be concerned about long-term loss of performance, which is already factored into the value.Building design professionals designing roofs for ASHRAE climate zones 6 and 7 may need to use the R-value reported for a mean temperature of 40°F.Attachment PatternsThe various fastener patterns for polyiso have been mentioned in the previous sections. However, due to the impact of fasteners on thermal bridging and wind uplift resistance, the key points are summarized here:For systems that have both mechanically attached membrane and insulation, the membrane attachment provides the wind uplift resistance. The polyiso insulation fasteners are simply there to hold the insulation flat during the roof installation and to resist long term lateral movement.Typical fastener patterns are shown here:For systems with adhered single-ply membrane and mechanically attached polyiso boards, the insulation fasteners provide the wind uplift load resistance. This is the case whether both layers of polyiso are mechanically attached or only the bottom layer (in which case the upper layer would be adhered).Manufacturers have tested the fasteners per board required to meet wind uplift resistance requirements for these combined mechanically attached and adhered systems. The number of fasteners needed depends on the board size and thickness. For common systems, the numbers are shown in the table below:For each of these combinations above, manufacturers' handbooks provide fastener patterns.The number of fasteners for these combined mechanically attached and adhered systems is very large, for example a 125,000 s.f. big box type roof could require around 50,000 fasteners, resulting in significant thermal bridging.When installing over a steel deck, to reduce thermal bridging and to make for a more robust system with reduced condensation risk, it is advisable to only attach the first layer of polyiso and to adhere all subsequent layers and the membrane.If the first layer of polyiso is attached and the rest of the system adhered, then using a 1.5" thickness for that first layer would help to bury the thermal bridging fasteners. It could also put the dividing line between first and second polyiso layers below the dew point, which is advisable.ConclusionsPolyiso is a cost-effective roof insulation and has the advantage that its permeability is low. Good design and installation practices can result in low risks of condensation even for buildings with higher than normal humidity levels.When designed correctly, mechanically attached components with two layers of polyiso having staggered and offset joints can be part of a successful roof system.Adhered insulation and membrane roof systems have advantages including reduced or eliminated thermal bridging, lowered condensation risks, and better wind uplift resistance.In cases where building use anticipates higher interior humidity levels and/or the local climate suggests higher condensation risk, then a building science professional should be consulted as to vapor retarder use and specification.Building designers and specifiers are advised to use the labelled R-values shown for a mean temperature of 75°F. For projects in ASHRAE climate zones 5 and 6, values at 40°F could be used depending on the building's geometry and local energy costs.

By Authors Thomas J Taylor

March 17, 2021

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