The room temperature has evident effect on heating costs
but night setback won't give appreciable savings.
For every degree celsius increased room temperature throughout whole day you have to expect additional 5% heating cost.
It's easy to recalculate.
The temperature difference between inside and outside is proportional to heat emission. This dissipation causes heating costs.
Room temperature is assumed to 20°C. It's a nice even number. And outside?
The medium temperature in winter is 0°C. (Temperatures lower then -15°C are truely possible in Central Europe, but rarely. Children are looking forward to snow - long times because ist's seldom. About zero degree celsius is a usable assumption. In winter 2000/2001 here it has snowed one time - at easter!):
|1961 to 1990||°C||sunshine |
Weather in Warnemünde
(Source: Deutscher Wetterdienst, showcase)
But if keeping 20°C inside living rooms then the temperature difference is only 20 degrees.
21 degr ------- = 1.05 = 105% = 100% + 5% 20 degrThe heat dissipation at 21°C would be 5% higher then at 20°C.
To relingquish only one degree room temperature enables 5% energy saving and therefore cost saving.
The connection between changes in temperature (symbol /\T) and thermal energy is given by the base equation of thermodynamics:
Q = m · c · /\T
The heat surrendered at the surface of a home has to be replaced by heating to keep the room temperature stable. The result is a balance: While the room temperature doesn't changes we can be sure the heating supplies exact as much heat as is surrendered. Otherwise the temperature would raise or fall depending on supplied versus surrendered thermal energy, i.e. if there is more heating power then loss thru walls, windows, ventilation or waste water or if there is less heating power.
To determine the cost-saving by night set-back we only have to calculate the heat dissipation because the heat supply is exact equal.
"keeping off the heating is saving energy" - that's the mistake, a fallacy.Even while the heating pauses at night - the surrendering of thermal energy is continued. The heat transfer ist proportional to the difference of temperatures. As long as inside it's still warmer than outside as long thermal energy is surrendered. As bigger as the temperature gradient is it happens faster.
This idea suggests itself. if heating ist turned off at night then it doesn't consume fuel all night.
But, is it actually possible to save a third of fuel, if during 8 of 24 hours heating is off? In a tent, a wooden site trailer, a green house or an old barrack that actually nearly applies, because there the temperature sinks almost down to outside temperature, At night there it's inside just as cold as outside. And where no temperature gradient can be found, there is no loss of thermal energy.
But inside a well isolated house the warmth is kept excellently.
If the heating is broken during two frosty days,
the room temperature falls down to 12°C or perhaps 8 or 6°C.
In any case temperature will sink during 8 hours only around a few degree.
It's worth it to recalculate.
If the room temperature is lowered on 16°C at night, the heating suspends, until the temperature sank down from 20°C to 16 °C. That can last for a long time, if solid inner walls and heavy furnishings stored the warmth from the day like a tiled stove an now slowly deliver (in physics it's named a high termal capacity).
At the beginnig of the night as long as still 20°C happen it's still warm inside. There is no saving, 0%
At the end of the night-time heating reduction the temperature difference amounts to only 16°C. The heat emission is decreased from 100% to
16 -- = 0.8 = 80% = 100% - 20% 20Apparently 20% saving!
But this is correct only in the morning, at the end of the night-time heating reduction, after the room temperature really already sank to 16°C. As average value over the whole night results a saving of 10%.
evenig+morning 0% + 20% -------------- = -------- = 10% 2 2
However only eight out of 24 hours are night. Saving only by night-time heating reduction thus becomes
8h 10% · --- = 3.3% 24hnot exceeded.
Altogether this example results in merely 3.3% energy saving round 24 hours.
In this example we (with otherwise same conditions as in example 2) calculate whith an outside temperature of -10°C (thus 30°C temperature difference). Also in this very cold night the heating pauses. Then the room temperature sinks over night just like in example 2 around 20%. But that is no longer only 4°. It's a third more.
20% · 30°C = 6°CDuring 8 hours of night set-back the room temperature is falling continuosly from +20°C to 16°C. The temperature difference decreases from 30°C to only 22°C, As in example 1 the heat emission has lowered to:
24 -- = 0.8 = 80% = 100% - 20% 30Averaged over the whole night again results in a saving of 10% through the night. And a third over 24 hours.
Also in this example only 3,3% energy conservation remain over 24 hours. And that only if at the end of the night +14°C is tolerated as room temperature!
The room temperature from during the day 20°C may sink during the night-time heating reduction at the most down to 16°C (the 14°C as in example 3 is too cold). After 8 hours without heating the temperature (as in example 3) would be around 20% that is 6°C fallen. The granted 4°C is already reached after 5.3 hours.
6° 4° --- = ----- 8 h 5.3 hAt the end of these 5.3 hours the heat emission is sunken to
26 -- = 0.867 = 86.7% = 100% - 13.3% 30on the average only half of it, thus during 5.3 hours 6.7% saving. From that time the heating maintains 16°C room temperature by supply of thermal energy. The continuous temperature difference of 26°C causes during 8 - 5.3 = 2.7 hours a heat emission from again
26 -- = 0.867 = 86.7 % = 100% - 13.3% 30By way of calculation saving during the whole night results as the weighted means to
5.3 · 6.7% + 2.7 · 13.3% ------------------------ = 8.9% 5.3 + 2.7And during 24 hours on the average again only one third of it, only 3%.
On cold days possible saving by night-time heating reduction is proportionally much smaller than on less cold days Although on cold days a saving would be extra desirable and effective. By night-time heating reduction of acceptable 4°C it's arithmetically possible to reach heating cost savings from at the most 3% to 3.3%.
How rapidly the 3% night time saving is wasted!
That doesn't happen at the same time on the entire surface. In places, which are perhaps purely coincidentally somewhat more coldly, the self accelerating effect begins first and leads to spotting.
November 2010, A. Hok.
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