In our last blog post, I wrote about the thermal resistance (R-value) and transmittance (U-factor) of insulation and windows. The R-value represents how well a material prevents heat transfer through its thickness, and U-factor is its inverse, representing how much heat a material will conduct through. These values are fairly simple to calculate for most building materials materials like the bricks and panels in Figure 1, as they primarily experience only conductive heat transfer. Windows are a more challenging proposition, however, since the heat transfer through them includes radiation across the entire spectrum, not just the visible light we see and the infrared we feel. In addition, the combination of glass, frames, spacers, and dividers made of different materials makes the conductive thermal resistance calculations more complicated. In this post, I’ll be looking at how heat transfer through windows is quantified and rated.
You might have seen a window sticker like Figure 2 at some point. This label means the window is rated by the National Fenestration Research Council, a US non-profit that certifies windows, doors and skylights with regards to their energy efficiency. This gives architects and contractors a standard metric by which to compare the specifications of products with different construction, materials, and manufacturers. The NFRC provides rating guidelines for five different characteristics:
Thermal transmittance: This is the U-factor I wrote about previously, though determined by a more complicated method that I will explain in this post. Lower U-factor means less heat transfer through the material.
Solar Heat Gain Coefficient: SHGC represents the amount of solar energy transmitted through a window, taking into account not just the glass and coating, but any sashes, shading or screens as well. This ranges between 0 and 1, with lower values representing better heat gain prevention.
Visible transmittance: This represents the amount of visible light that the glazing allows through. This ranges from 0 to 1, with higher values indicating more daylight transfer.
Air leakage: This represents how much air leaks through a window in cfm/ft2. Since this air carries heat with it, the lower leakage value the better.
Condensation resistance: Represents how well a product resists condensation on its inner surface. Ranges from 1-100, where higher numbers mean better resistance.
Thermal Transmittance of Windows, Skylights and Doors
Calculating the U-factor for windows is not a simple process, due to the complexity of their construction and the energy transfer through them. Window and frame assemblies composed of multiple materials will conduct heat differently at different points, but buyers still need a single value that they can use to compare thermal transmittance of different products. This single value must account for the glazing, the frame, and the boundary between the two. The method given in NFRC 100 divides the window into separate areas, as illustrated in Figure 3. Besides the frame and glazing areas, the NFRC defines a 2.5”-thick “edge” area around the perimeter of each glazed pane. Once divided, the NFRC method then calculates an area-weighted-average of the U-factors for these areas using Equation 1.
Ut = total product U-factor
Uf = frame U-factor
Ud = divider U-factor
Ue = edge-of-glazing U-factor
Ude = edge-of-divider U-factor
Uc = center-of-glazing U-factor
Apf = projected fenestration product area
Af = frame area
Ad = divider area
Ae = edge-of-glazing area
Ade = edge-of-divider area
Ac = center-of-glazing area
Outside of the US, manufacturers use ISO 10077 to define an equivalent U-factor for a window assembly. It uses the same area-weighted-average method, but forgoes the edge areas in favor of multiplying the perimeter of each glazed panel by a “linear thermal transmittance” value, as shown in equation 2.
Ut = total window U-factor
Ug = glazing U-factor
Up = opaque panels U-factor
Uf = frame U-factor
Ψg = linear thermal transmittance due to the combined thermal effects of glazing, spacer and frame
Ψp = linear thermal transmittance for the opaque panels
Ag = glazing area
Ap = opaque panels area
Af = frame area
lg = glazing perimeter length
lp = opaque panel perimeter length
Both the NFRC 100 and ISO 10077 method can be reworked to calculate the equivalent U-factors for skylights and doors as well, by simply applying the area-weighted average of the various glazing, frame and panel components as appropriate.
Figure 4: Multi-chamber window frame cross-section By Kozuch [CC BY-SA 3.0], via Wikimedia Commons
Equations used in NFRC 100 and ISO 10077 rely on U-factors for the frames, glazing, and other components, but those components are too complex to rely on the simple U = k/L relation I provided in the last blog post. Each component on the window has its different heat transfer characteristics that must be accounted for in determining their U-factors.
Window glazing U-factor must take into account not just the thermal conduction, but also the transmittance of radiation through the window. Different windows use numerous types low-emissivity coatings, solar control films, or colored finishes, which all affect the amount of radiation passing through the window without noticeably changing the thermal conductance.
Window frames are opaque and transmit heat primarily through conduction, but their complex construction can preclude a simple conduction calculation. In order to lighten their weight and reduce thermal transmittance, modern window frames are often designed with numerous hollow chambers through their length, as visible in Figure 4. Furthermore, frames can be constructed of multiple materials, like combinations of wood, metal and plastic, in addition to rubber or polymer gaskets, spacers, and thermal breaks between separate components.
The boundaries between glazing and frame combine the complex factors for both window and frame, and thus would be even more difficult to calculate mathematically.
As such, both NFRC 100 and ISO 10077 require that the U-factors used in their equivalent U-factor calculations are determined experimentally or use previously tabulated experimental data.
Selecting Windows by U-Factor
Luckily, the complex method behind determining a window’s equivalent U-factor is not usually left to the consumer or contractor installing it. Companies that manufacture windows and frames will make these calculations in advance, according to ISO or NFRC standards. They should provide the thermal transmittance information along with the other window specifications and performance ratings, like solar heat gain coefficient (SHGC), visible transmittance, air leakage, and condensation resistance. It is up to the architect or contractor to determine the appropriate U-factor for a building’s windows, based on climate zone, heating or cooling requirements of the building, external shading by trees or awnings, and any mandatory energy efficiency standards for the location. I’ll discuss some of these considerations throughout the next blog posts as I cover SHGC and the other performance ratings in depth.
NFRC. 2004. NFRC 100-2004: Procedure for Determining Fenestration Product U-Factors
ISO. 2006. Thermal performance of windows, doors and shutters — Calculation of thermal transmittance — Part 1: General.