ASHRAE Journal - March 2022 - 42

TECHNICAL FEATURE
FIGURE 5 Model.
FIGURE 6 Model result with no heating unit.
Conditioned Space
Heating
Inside Temperature
Heat Loss
Outside Temperature
Figure 6 shows that starting at an indoor temperature
of 68°F (20°C) it takes about 500 minutes for the model
to approach the outdoor temperature of 32°F (0°C). The
winter temperatures in Detroit are normally around
32°F (0°C).
Heat loss is nonlinear with time because the temperature
difference changes. However, over a short
time period where a heating unit is likely to cycle, on
this plotting scale the heat loss appears about constant.
Likewise, since the indoor temperature variation is
small, its effect on the air exchange rate won't be significant.
The plot of actual data would be a function of the
overall heat transfer coefficient (U) for the buildings.
The actual convergence to outside temperature wouldn't
be smooth because the exterior temperature varies over
the day. However, in the cloudy Detroit winters, the temperature
stays somewhat constant.
One factor in a model is the boiler capacity. Heating
systems tend to be overdesigned. First, they are designed
for peak hour, which occurs rarely over the life of the
system. Second, each engineer that touches a design
tends to add an additional 5% overdesign.4 Based on
Figures 2 through 4, it appears that it is common to have
boilers oversized compared to normal operating conditions.
However, if the normal operating condition is
defined as the average over the worst week, then Figures
2, 3 and 4 show that boilers use around 25% of capacity.
This influences the modeling because parameters
should be chosen so that the heat is on 25% of the time.
Therefore, in a model the heat production at full capacity
should be four times the rate of heat loss when operating
under normal conditions.
Figure 7 shows two cases from the model. Case A is an
indoor thermostat setting of 68°F (20°C) allowing for
minus 2°F (1.1°C) differential. Heat loss is defined as
0.004 times the temperature difference per minute, and
the boiler capacity is four times the heat loss. Outside
temperature is 32°F (°C). There is no modulation. Case B
42
ASHRAE JOURNAL ashrae.o rg M A R CH 2022
80
70
60
50
40
30
20
10
100
200
300
Time (Minutes)
FIGURE 7 Model results for thermostat at 68°F and 55°F (20°C and 13°C).
70
68
66
64
62
60
58
56
54
52
50
20
40
60
Time (Minutes)
is the same except that the thermostat setting is 55°F
(13°C).
See from Figure 7 that when the temperature difference
between inside and outside is smaller, 55°F (13°C) minus
32°F (°0), the heat loss is lower. It takes longer for the
thermostat to reach the minimum temperature when
the temperature difference is smaller.
Case C, with the thermostat at 68°F (20°C) and the
outside temperature at 45°F (7.2°C) is not shown; however,
it would look exactly the same as Case B if it were
included on the graph. The only factor in the heat loss is
the temperature difference.
In Figure 7, Case A, with the high thermostat setting
with low outdoor temperature, is the only situation
where the boiler is short cycling. Case B and Case C, with
lower temperature variations with the outside, have long
cycling. This violates conventional wisdom. Short cycling
is not a problem due to energy conservation measures
such as low setpoints and is not a seasonal efficiency
issue in the way it is normally portrayed. Instead, short
400
500
600
Case A (68°F)
Case B (55°F)
80
100
Air Temperature (°F)
Air Temperature (°F)
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ASHRAE Journal - March 2022

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