ASHRAE Journal - March 2011 - 72

solar NZEB projEct
0 330 –0.05 τ = 110 h ln[T–Ta)/(Ti–Ta)] –0.1 τ = –1/Bestf it Slope temperature (K) 320 320 – 330 310 – 320 300 – 310 Ambient Temperature

–0.15 τ = 22 h

310 12 cm

–0.2

Old Newell House Washburne House Equinox Oct. 16, 2010 0 1 2 3

τ = 33 h 4 Hours 5 6 7 8

300

8 cm 0 12 Hours 24 4 cm Surface

–0.25

Figure 2: Plots of the logarithmic temperature parameter versus time. The negative reciprocal of the slope is for the thermal time constant, which is shown on the plot in hours for each house. Ta = outside average ambient temperature Conducting a coast test during a time when a building has a small internal energy source term, G, is helpful. To coast indicates no thermostat or other controller is actively trying to maintain a setpoint condition, allowing the house to move toward equilibrium with its surrounding influences. The energy source term does not have to be zero as long as it is either known, or at least known to be small relative to other factors. The impact of the internal loading, which can be either positive or negative in value (e.g., an air conditioner versus a furnace), is an adjustment to the apparent outside ambient temperature as seen in the grouping of terms in the temperature parameter. For Equinox House, with a UA value of approximately 100 W/K (190 Btu/h·°F), a 100 W (341 Btu/h) internal load is a change of 1°C (1.8°F) of the effective outside temperature. The data from Figure 1 can be plotted using the logarithmic relation between temperature and time as shown in Figure 2. Because the logarithmic relation between the temperature parameter and time is ideally linear with zero intercept, the slope of a linear curve fit of the data will give us the value of the parameter (UA/mc) for the house. The negative reciprocal of the slope is the thermal time constant, τ, of the house. τ = (mc/UA) = thermal time constant of house The thermal time constant is a measure of the time for the house to drop exp–1 (0.368) of the difference from the initial inside temperature to the outside temperature. Figure 2 shows the best fit lines through the data sets for each house along with the negative reciprocal of the line slopes in hours. If the outside temperature stayed fixed at –3°C (27°F), our old house would drop to 11.3°C (52.3°F) after 33 hours. Notice that the Washburne house has a time constant of 22 hours for the data shown, and Equinox House has a time constant of 110 hours. So why does the Washburne house, a purported energy-efficient solar house, have such a low time constant? The Washburne house is very typical of 1980s-era passive solar homes (and probably many of today’s) designed with a “shoot from the hip” approach
72 ASHRAE Journal

Figure 3: Temperature variations in a 120 mm (4.7 in.) thick, bare concrete slab with insulated bottom and a cyclically varying ambient temperature above the concrete surface (330 K [57°C or 135°F] from 0 to 12 hours and 300 K [27°C or 81°F] from 12 to 24 hours). without engineering analyses. It has 70 m2 (750 ft2) of windows with 52 m2 (560 ft2) on the south side. The house was designed to be very “massive,” with concrete slab floor, water storage tanks in the greenhouse area, a massive two-story stone fireplace and an area with trays of some proprietary phase change storage material. The estimated window UA for the Washburne house was 197 W/K (375 Btu/h·°F). With today’s window technology, this loss coefficient could be reduced to less than half. The two story house (approximately 130 m2 or 1,400 ft2 floor plan with loft/ bedroom area) is similar to Equinox House in total floor area of 195 m2 (2,100 ft2). The walls and roof were R-24 and R-39, quite respectable for the early 1980s. Infiltration was found to be on the poor side with an estimated infiltration rate of 155 L/s (330 cfm), mostly caused by the internal combustion air supplied to the furnace. The active greenhouse had a humidification impact on the house that was a significant load. Overall, the Washburne house required 35,600 kWh (1,200 therm) of thermal energy just for its annual heating load (compared to Equinox House’s estimated total annual requirement of 8,000 kWh-electric for all house energy needs). A thermally “massive” house has a long time constant. As seen in the relation for the time constant, house massiveness is dependent on the building’s loss coefficient as well as the mass. If someone leaves a window open, for example, drastically increasing the house overall loss coefficient, the time constant and massiveness of the house are reduced. Unfortunately, many building designers are under the mistaken idea that adding mass is the only way to increase the thermal massiveness of a structure. So how does one predict, design or calculate the thermal mass of a house? Following the guidelines we’ve given for walls, roof, windows, and infiltration in previous columns can result in a house design that is inherently massive. As we discussed in December’s article, judicious selection of windows is very important. The time constant of a 0.3 m (12 in.) thick SIP wall with interior drywall is 20 hours, while a super window (U=0.57
ashrae.org March 2011

ASHRAE Journal - March 2011

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