Calculations made on my house in december 1995
The heating installation is provided with a flowmetter, a thermometer on the hot water arrival and on the tepid water return and an electricity meter.
With a min/max thermometer, I noted the temperature mornings and evenings:
Measurement summary:
| Date | Tmin | Tmax | m3 | kWH |
|---|---|---|---|---|
| 1276.4 | 44 | |||
| 30/11/1995 | 5.0 | 8.0 | 1286.8 | 72 |
| 01/12/1995 | 5.0 | 11.0 | 1294.5 | 93 |
| 02/12/1995 | 8.0 | 13.0 | 1298.3 | 103 |
| 03/12/1995 | 10.0 | 13.0 | 1298.3 | 103 |
| 04/12/1995 | 7.5 | 9.0 | 1302.4 | 114 |
| 05/12/1995 | -4.5 | 3.0 | 1310.4 | 136 |
| 06/12/1995 | -6.0 | -2.0 | 1314.0 | 146 |
| 07/12/1995 | -8.0 | 0.0 | 1321.5 | 166 |
| 08/12/1995 | -8.0 | 0.0 | 1328.2 | 186 |
| 09/12/1995 | -3.0 | 4.0 | 1335.8 | 211 |
| 10/12/1995 | 3.0 | 5.0 | 1346.3 | 230 |
| 11/12/1995 | 0.0 | 2.0 | 1352.4 | 246 |
| 12/12/1995 | -1.0 | 2.0 | 1354.3 | 251 |
| 13/12/1995 | 0.0 | 4.0 | 1366.3 | 282 |
| 14/12/1995 | -1.0 | 2.0 | 1377.1 | 310 |
| 15/12/1995 | -2.0 | 2.0 | 1383.6 | 327 |
| 16/12/1995 | -3.0 | 4.0 | 1391.3 | 349 |
| 17/12/1995 | 0.0 | 8.0 | 1394.3 | 355 |
| 18/12/1995 | 1.0 | 5.0 | 1398.2 | 367 |
| 19/12/1995 | 1.0 | 6.0 | 1402.4 | 376 |
| 20/12/1995 | 2.0 | 6.0 | 1407.8 | 390 |
| 21/12/1995 | 3.0 | 6.0 | 1411.9 | 401 |
| 22/12/1995 | 6.0 | 12.0 | 1416.8 | 414 |
Sum of minimal temperatures : 15
Sum of maximal temperature : 123
Average temperature :(15+123)/23/2 = 3,00
Gap between hot water and tepid water temperature : 8 to 9, that is to say Δ = 8,5
Amount of m3 of water : 140,40
Amount of kWH : 370
Amount of heat brought into the house : Qa = m3×Δ×1,16 = 1384,34 kWH
Compressor efficienty coefficient : Cp = Qa/kWH = 3,74
Amount of degree.day :Dn = N×(21-Tmoy) = 414
Volume of the house : 146×2,6 = 379,60 m3
Volumic coefficient of losses : G = Qa×1000/(24×Dn×vol) = 0,367
Average heating power = 676,29 Watt (in december with several freezing days)
Consumed power on the coldest day (Second day at -8°C): 1041,67 Watt
(The compressor has a power of 1,5 kW)
Yield of the compressor without the pump: Qa/KWH×(1-5%) = 3,94
The consumption of the heating installation is, to within few kWh from one year to another, of 2500 kWh.
The coefficient G measured is better by 3/100 than the coefficient G calculated previously because the house on which it has been measured is not the same. It has been measured on a house built in 1995, while the one calculated is being built. The difference is in the construction and the insulation of the tile of the bottom floor. The current tile is a tile on raised platform insulated with 12 cm of polystyrene, while the tile of the first house is a load-bearing tile on 20 cm of close crawl space, not ventilated, with furthermore a layer of 6 cm of polystyrene coated with a triflex canvas to stop humidity. This canvas allow perhaps also to reflect the infra-red rays emited by the tile ?
In the crawl space limited to 20 cm, the air heated is at the top, and the cooled air is at the bottom, so that there can't be any convection and we profit of an insulating layer of dry and still air.
The conductivity of dry air being 0.02, this gives a resistance Rair = 0,2/0,02 = 10
Plus the resistance of the polystyrene and the styrodur Rpoly =(0,06+0,05)/0,04 = 2,75 °C.m2/W
hence a total resistance of 12.75 and a conductivity λ= 0,0784 W/m2.°C
If we calculate the losses through the florr of hour second house in these conditions,
we obtain p = 129,36×21×0,0784 = 213,06 Watt
if we apply this corrective term on G this gives : (3617,46-543,31+213,06)/(27×336,34) = 0,362
we are 5/1000 under the measured coefficient, which is normal considreing the losses which are not taken into account, such as for instance the small wall of the timbers wrapped in 20cm of glass wool.
If we take this second corrective term into account, we obtain
p = 49,20×0,20×0,04/0,2×30 = 59,04 Watt, thus Gcor = (3617,46-543,31+213,06+59,04)/(27×336,34) = 0,368
Equals the value measured to within a 1/1000, on a house with a different size and a different disposition
We didn't use this options on the second house because, apparently, norms forbid not ventilated crawl space, it is better worth refreshing in winter and humidify in summer, it is good for oil seller. Once filled with polystyrene, it is no more a crawl space, polystyrene sellers unerdstood it rather well !!