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#867276 - 05/06/2010 18:22 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Indoor versus Outdoor Temperatures
Scatter-plot of daily max and min temperatures for the Manilla solar-passive house


Data in this graph are taken from two thermometers; one in a Gill-type thermometer screen seven meters from the house (photo in previous post), and one on a wall in a core room of the house. The data are for the first three years of good screen readings.

The graph shows that indoor temperatures vary only 42% as much as outdoor temperatures. The outdoor temperature range is 45.9 deg (from -4.4 deg to 41.5 deg), but the indoor temperature range is only 19.4 deg (from 13.4 deg to 32.8 deg). Most indoor temperatures are within the “comfort zone”. Average temperatures are 17.8 deg outdoors and 22.3 deg indoors. The house raises the indoor average by 4.5 deg to near the ideal for comfort.

There is a similar three-year scatter plot for a solar-passive house at Bonnyrigg, near Liverpool, Sydney in "Energy Efficient Housing for New South Wales" by Ballinger, Prasad and Cassell.

Very likely the data is in this paper by John Ballinger:


I think Ballinger's scatter-plot for a house near Liverpool must include daily maxima and minima as mine does. His extreme outdoor points are 40 deg and +1 deg (range 41 deg) and extreme indoor points 32 deg and 12 deg (range 20 deg). In broad terms these two houses seem to yield similar levels of comfort, but the Manilla house does it in a more extreme climate. Manilla's daily temperature range is 15.5 deg, while Prospect Reservoir, near Bonnyrigg, has only 10.9 deg.
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#867456 - 07/06/2010 00:14 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Indoor versus Outdoor Temperatures
Manilla solar-passive house

Scatter-plot of daily minimum temperatures with regression line


This scatter-plot shows only daily minimum temperatures, indoors and outdoors, and displays the average values. The Manilla average outdoor minimum of 10.1 deg is far too cold for comfort. Solar-passive design has raised the indoor minimum by 10.6 deg without applied heating. The indoor average minimum of 20.7 deg is near the middle of the comfort zone.
The slope of the linear regression line shows that indoor minima vary only 34% as much as outdoor minima.
A dashed line in the lower right shows that nearly all points have indoor minima warmer than outdoor minima. This is a disadvantage only on nights warmer than about 20 deg.
A dashed line in the upper left shows that many cold mornings have indoor minima nearly 20 deg warmer than outdoors.
One morning (9/5/06) the indoor temperature was 21.8 deg warmer than outdoors. I think this may be a record for an unheated house. (Note: Screen temps have been corrected.)
Such large over-temperatures come with very dry air in autumn.
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#867498 - 07/06/2010 16:07 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Indoor versus Outdoor Temperatures
Manilla solar-passive house
Scatter-plot of daily MAXIMUM temperatures with regression line


This scatter-plot shows only daily maximum temperatures, indoors and outdoors, and displays the average values. The Manilla average outdoor maximum of 25.5 deg is already comfortable, if a little on the warm side. The average indoor maximum of 23.8 deg is closer to the ideal.

While this solar-passive house scarcely changes the average maximum daily temperature, it drastically reduces the extremes. The slope of the linear regression line implies that indoor maxima vary only 38% as much as outdoor maxima.

Dashed lines to the left and right show that, without applied heating or cooling, the indoor temperature on the hottest days is reduced by up to 10 degrees, while on the coldest days it is increased by up to 8 degrees.


Edited by Surly Bond (07/06/2010 16:09)
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#867857 - 09/06/2010 22:49 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Indoor versus Outdoor Temperatures
Manilla solar-passive house
Regression lines for daily maxima and minima, showing daily temperature ranges


This graph shows the two regression lines for daily maximum (purple) and daily minimum (green) temperatures, taken from previous graphs. I have marked three points on each line: the mean temperature point and points at the extreme ends of the lines, one for a very hot day and one for a very cold day.

The interest of this graph is in the space between the regression lines. It represents the daily temperature range. I have linked each pair of points by two lines like the tread and riser of a stair. The tread (red) is the outdoor daily temperature range; the riser (blue) is the indoor daily temperature range.

The mean outdoor temperature range here is 15.4 deg. and the mean indoor temperature range of the house is 3.1 deg. By this measure, the indoor temperature range is one fifth of that outdoors.
It happens that, in Manilla, the outdoor temperature ranges in the hottest and coldest parts of the year are, as shown, slightly less than for the year as a whole. Indoor temperature ranges show a clear gradient, from 3.7 deg on a very hot day through 3.1 deg at the mean, to only 2.3 deg on a very cold day.

For comfort, we do not need indoor temperature ranges as narrow as these. If the mean temperature on a given day is at the neutrality temperature , a range of 5 deg, or even 7 deg, would do.
Very narrow temperature ranges result from the way the high thermal mass dispersed within the house allows heat to be absorbed and radiated at room temperature, eliminating extremes. Hot spots and cold spots are few and do not last long.
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#868562 - 16/06/2010 12:43 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Conventional versus Solar-passive in winter

These graphs are like those of Post #864613 (23 May 2010). Autumn data are replaced by mid-winter data. For background, see that Post and Post #866648.


Daily temperature ranges, indoors and outdoors, are not much narrower or wider than they were in autumn.
In winter the unheated conventional house is uncomfortably cold nearly all the time. Relative to the minimum line for 80% adaptive comfort, the house is often nine degrees too cold.
The solar-passive house stays mainly within the 80% adaptive comfort zone. It seldom falls more than one degree below the minimum. Once again, there are many days when the coolest time inside the solar-passive house is warmer than the warmest time outdoors.

Both houses are built on concrete slabs on the ground. Such houses exchange heat daily with about a hundred tonnes of mass materials in and under the slab. These graphs suggest that the mean temperature inside each of these two houses takes up the temperature of the under-floor mass, shown by red lines on the graphs.
For the solar-passive house, this temperature was read by a probe 750 mm under the slab surface in the middle of the insulated area. The estimate for the conventional house is less direct. Not only is the estimate (750 mm depth) for a garden area away from both houses, but the sensor was down at the time, and remote readings had to be adapted. The values seem right, and fluctuations in the red line are plausible.

The mean values of indoor temperatures and under-slab temperatures during these observations agree very well:

Solar-passive house:
Mean indoor temperature: 18.9 degrees;
Mean under-slab temperature: 18.7 degrees.

Conventional house:
Mean indoor temperature: 13.4 degrees;
Mean under-slab temperature (remote estimate): 13.9 degrees.

The red line for the conventional house slopes slightly upwards, while that for the solar-passive house slopes down. Soil temperatures here have their minimum in mid-July. The edge-insulated heat-bank under the solar-passive house, however, carries summer heat, boosted by winter solar gain, for longer. It is still cooling during these observations.

While the mean temperature in the conventional house (13.4 degrees) is colder than in the solar-passive house, it is warmer than in a house without a floor slab. The mean temperature in such a house (unheated) would hover around the mean outdoor temperature of 10.1 degrees. Without heat storage in a slab, the indoor daily minimums would be too cold for comfort by fifteen degrees or more, rather than just nine.
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#869050 - 21/06/2010 21:44 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Conventional versus Solar-passive in spring

Regrettably, these graphs show that the solar-passive house, as designed and initially operated, was less comfortable in spring than a conventional house built on a slab.


Mean temperatures for this period
The Adaptive Comfort zone is from 20 degrees to 27 degrees.
For outdoor temperatures, the mean max (25.7) is comfortable but the mean min (9.7) is 10.3 degrees too cold.
For the conventional house, the mean max (25.0) is comfortable, but the mean min (16.9) is 3.1 degrees too cold.
For the solar-passive house, the mean max (21.1) is barely warm enough, and the mean min is 2.7 degrees too cold.

When I plotted these results, I did not know what to expect. The design of the solar-passive house had not been analysed for its expected performance. Nor had I plannned how I might measure its success. The aim was to achieve "comfort" thoughout the year, but I was not then aware of the "Adaptive Comfort" (Post #864290) that is now plotted on these graphs. By this standard, the house is remarkably comfortable in autumn and winter, but uncomfortably cold in spring.

I could feel that the house was too cold. The early morning temperature of 11.5 degrees on 22-Oct-2001 is the coldest ever recorded in the house. On 1-Oct-2001, on schedule, I had changed the regimen of house management from "Winter" to Summer". Details of the change are in Post #42328 of 1-Nov-2005.
The intention was to use the cool night air of October to cool the heat bank to protect the house from summer heat later. Unfortunately, that made the house too cold for comfort.
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#869056 - 21/06/2010 22:45 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Effect of changed management of Solar-passive house in spring

This graph is the temperature log for the Solar-passive house in spring 2009, for the same dates as in the spring 2001 graphs.


The house is intended to need attention only rarely. The north windows need none. By their design, they achieve solar gain from mid-March to mid-October and solar exclusion at other times. Other items were scheduled to be re-set twice a year: on April 1 for a winter (heating) regimen and on October 1 for a summer (cooling) regimen.

By spring 2009, only some of the summer (cooling) regimen re-sets were done on October 1:
Curtains and sun-porch shutter switched to be closed by day and opened by night;
Clear-story fans (thermostatically recirculating hot air) turned off;
Awnings set to form shaded breeze-ways instead of sun-traps.

Other re-sets were postponed to November 1:
Clear-story windows opened for stack-effect cooling;
Clear-story fans to assist stack effect from 01:00 to 05:00;
Outer doors, air-lock doors and some windows open at night.

As a result, most indoor temperatures for spring 2009 have risen into the comfort zone. Some are still too cold, but it is hard to say whether it will happen in future spring seasons. The heat bank is a degree warmer than before, very likely because cool night air is not let in during October. A warmed heat bank will tend to make the house warmer in summer. This is a pity, but some of the unwanted heat may have leaked away by then.
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#869629 - 26/06/2010 18:40 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Conventional versus Solar-passive in summer

These graphs are temperature logs for 50 days in mid-summer 2001-02, showing the relative thermal performance of two adjacent houses in Manilla NSW. They complete a set of graphs for all four seasons, in Posts #864613 (autumn), #868562 (winter), #869050 (spring) and #869056 (spring, updated).

In Manilla's mid-summer, days are uncomfortably hot, and nights are uncomfortably cold. The conventional house, on its concrete slab, succeeds in keeping out the cold at night (which blankets would do just as well) but hardly protects at all against the heat of the day.
The solar-passive house stays within the comfort zone nearly all the time. In this record, it was never too hot, but sometimes too cold. In my experience through eleven summers, cold has never been a problem, but some days, and even nights, have been too warm, even with fans running.

Mean temperatures over this fifty-day sample period are listed in the following table, together with those of the winter period logged in Post #868562.



In winter, the solar-passive house achieves comfort by raising the mean indoor temperature 8.6 degrees above the mean outdoor temperature.
In summer, the mean outdoor temperature (25.3 degrees) is comfortable enough already, but a house must protect people against daily extremes. The conventional house does reduce the extremes, but at an increased mean temperature: 28.1 degrees.
The solar-passive house, with its effective shading, draft-proofing, mass and insulation, brings the daily temperature range down to 4.2 degrees. That is not as narrow as the mid-winter range of 3.1 degrees. In mid-winter the house is closed up, except for the sunshine let in through the north windows and absorbed in the floor and brick walls near room temperature. In mid-summer, cooling is done mainly by admitting night air, no matter how cold, so the indoor temperature range is wider.
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#870563 - 01/07/2010 22:24 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Last night's minimum in the bedroom (15.4 degrees) was the coldest in 22 months. The minimum in the screen was -1.4 degrees, so the bedroom was 16.8 degrees warmer. I used two blankets and closed interior doors to stop heat leaking towards defects in the insulating shell of the house.

The previous night screen temperature was lower: -3.1 degrees, but the house was still carrying heat from the day before and the bedroom minimum was 15.9 degrees: 19.0 degrees warmer.
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#870587 - 02/07/2010 07:01 Re: Indoor Climate [Re: Surly Bond]
UK Steve Offline
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Registered: 05/05/2006
Posts: 2470
Loc: Birmingham, England
It was mentioned on one of the weather forums in the UK that Sydney had it's coldest June night in 61 years recently.

Am I correct that most homes in Australia do not have central heating as they are built to keep heat out, not in?

The reverse is true here, especially in houses with insulated roofs and double glazed windows. After a hot day homes here can retain heat overnight making it feel quite uncomfortable, even if the outside temp is only about 12-15ºC.


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#870614 - 02/07/2010 09:42 Re: Indoor Climate [Re: UK Steve]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Originally Posted By: UK Steve
Am I correct that most homes in Australia do not have central heating as they are built to keep heat out, not in?


Australia has quite a wide range of climates, Steve, but I am fairly sure that is not correct.
In my region my house is the only one that does not have built-in heating. People think I am crazy.

Sydney's weather gets a lot of news coverage, because many people have to live there.
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#870852 - 03/07/2010 14:05 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Here is a recent conference paper "'Passive Building Design and Active Inhabitants: The Potential od Frugal Hedonism?" by Deborah White of The University of Adelaide:
Quoting M. Kordjamshidi, she is scathing about the way a typical house energy rating scheme "under-rates the effectiveness of buildings designed, on ‘passive’ principles, to dispense with energy-consuming heating and cooling plant".

She mentions a few well-managed solar-passive houses (in Italy) with energy use on heating and cooling as low as 3 kWh/m^2a.
My House in inland NSW ("Zone 14") was assessed in 1999 by Max Mosher, using NatHERS V2.11 as follows:
For 127 m^2 of a 147 m^2 house to be heated and cooled: 18 kWh/m^2a.

In practice, my energy use for heating and cooling during 11 years has been about 10% of the NatHERS assessment.
I have been living alone in the 100 m^2 part of the house that is most efficient, excluding the 2-storeyed west wing (for visitors).

Annual energy use for heating and cooling has been:
Fans for moving warm and cool air: 100W for 1800 hours = 180 kWh;
Electic blower heaters: 1kW for 20 hours = 20 kWh;
Total heating and cooling: 200 kWh;
Total heating and cooling per square metre: 2 kWh/m^2a

Approximate annual cost of heating and cooling the house (all electric): $40.00.
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#870913 - 04/07/2010 09:59 Re: Indoor Climate [Re: Surly Bond]
avalon Offline
Weatherzone Addict

Registered: 18/07/2007
Posts: 1547
Loc: Mt Macedon Vic 870m elev
I was up at Mt Macedon yesterday morning, the temp inside my cabin was 3.2C and outside was 5.5C , hadnt been there for a few weeks,neither of the fires have been lit this June, things have got mould on them. It was weird to walk inside and feel colder!

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#874144 - 29/07/2010 18:11 Re: Indoor Climate [Re: avalon]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Midwinter2010
Modelling indoor temperatures of the house
1. Weather and house temperature logs

The first graph is the weather log for Manilla NSW in the mid-winter period from 16th June to 16th July 2010. It shows daily 9 am readings of rainfall in mm, and cloud amount in Octas, using the scale on the right. Temperatures, to be read on the left scale, include the daily maximum, mean and minimum, and the mean temperatures (at a depth of 750 mm) of the outdoor subsoil and the heat-bank under the house. Dashed lines mark the normal maximum, mean and minimum temperatures for the time of year.
The trend of the weather can be seen by comparing the mean daily temperature trace (open circles) against the dashed line showing the normal mean. The weather was warmer than normal except for a severe cold spell in the middle. One day (2/07/10), when the maximum was only 9.1 degrees, was the third coldest day in 12 years.


The second graph logs the indoor temperatures: maximum, mean and minimum, using an expanded scale. Temperatures are taken both at head-height on an interior framed wall and on the concrete slab floor. Mean temperatures of the subsoil and the heat-bank under the house are shown again. Purple curves show the 80% limits for adaptive comfort. (See Post #864290 in this thread.)
Indoor daily minima were below the comfort zone for twelve days, and indoor daily maxima below it for three days. I slept in comfort under two blankets in light pyjamas thoughout the period. During some evenings I used a blower heater to keep warm, as shown at the bottom of the graph. This heater consumed 25kWh of power in total, costing $5.00. It cannot have warmed the fabric of the house much, and it was turned off at least six hours before the time of indoor minimum temperature.

These readings provide data for study of how indoor climate relates to that outdoors.
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#877256 - 15/08/2010 20:00 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Midwinter2010
Modelling indoor temperatures of the Manilla solar-passive house
2. Modelling daily Indoor wall maximum temperature

These graphs are based on those in Post #874144, above.


The first graph shows (in red) the log of daily Indoor max temp taken at head height on an interior framed wall. It is set against the logs of both Outdoor max temp and Outdoor min temp. To get the best match, the indoor data are plotted with a larger scale and a changed zero.
Many details of the Indoor wall max temp log match those of the Outdoor max temp log. However, the largest feature, the sudden fall from high to low values, mimics the Outdoor min temp log, but with a lag.
To find relationships between the logs, I did scatter plots and regressions of Indoor wall max temp, as dependent variable, against both Outdoor max temp and Outdoor min temp on the same day, and Outdoor temps lagged by one, two, and three days.
(To get complete data for lagged plots I included some days before the 16th of June.)
Results are expressed as linear equations, with slope (A) times the Independent Variable (X), an Intercept (B), and a Coefficient of Determination (R^2):
A = 0.36; X = OutMax(--); B = 14.3; R^2 = 0.45
A = 0.26; X = OutMax(-1); B = 15.8; R^2 = 0.25
A = 0.27; X = OutMax(-2); B = 15.8; R^2 = 0.25
A = 0.26; X = OutMax(-3); B = 15.9; R^2 = 0.25
A = 0.04; X = OutMin(--); B = 20.1; R^2 = 0.01
A = 0.14; X = OutMin(-1); B = 19.6; R^2 = 0.13
A = 0.20; X = OutMin(-2); B = 19.4; R^2 = 0.25
A = 0.17; X = OutMin(-3); B = 19.6; R^2 = 0.16
The highest R^2 is for the first equation, relating the Indoor wall max temp to Outdoor max temp the same day, but there are also relatively high values of R^2 for Outdoor max temps lagged one, two and three days, and for Outdoor min temp lagged two days.
I modelled (green trace) the response of the Indoor max temp to the independent variables by trial and error, guided by the size of the Slope (A) and the Coefficient of Determination (R^2). For each trial, I calculated, and displayed, the remaining discrepancies between the model and the actual value. I also calculated the Standard Deviation of these discrepancies. I judged the success of the exercise by reduction in the Standard Deviation, and by the removal of individual large discrepancies.


The second graph shows (green) the First Model of Indoor max temp using the first regression equation alone. The model resembles actual values (red), but not closely. Discepancies are shown in yellow. Their Standard Deviation is 1.23 degrees.


The next graph applies a Second Model, using an equation including the Outdoor min temp of two days earlier as a predictor, as:
Y = 0.45*(0.6*(OutMax(--)) + 0.4*(OutMin(-2))) + 15
This model reduced the residual S.D. to 1.13 degrees.


The Third Model includes all regressions with an R^2 of 0.25 or more:
Y = 0.45*(0.6*(OutMax(--)) + 0.1*(OutMax(-1)) + 0.1*(OutMax(-2)) + 0.1*(Outmax(-3)) + 0.1*(OutMin(-2))) + 11.7
(Let us cut this expression down to: Y = 0.45*(Outdoor temps) + 11.7)
The match is clearly better, and the S.D. of the discrepancy has fallen to 1.05 degrees. However, the model still shows two systematic errors, which can be attributed to the neglect of the falling temperature of the Heat Bank and the occurrence of cloudy days.


The Fourth Model achieves a better fit at the ends of the time interval, with an S.D. of only 0.92 degrees, by giving full weight to the relative temperature of the under-floor rubble Heat Bank:
Y = 0.55*(Outdoor temps) + (Heat Bank temp) - 6.9

Some of the remaining discrepancies seem to relate to the amount of cloud in the sky. The relation is cryptic, however, so I regressed the discrepancies on unlagged and lagged observations of morning cloud in Octas:
A = -0.12; X = Octas(--); B = +0.54; R^2 = 0.16
A = +0.01; X = Octas(-1); B = -0.03; R^2 = 0.00
A = +0.07; X = Octas(-2); B = -0.27; R^2 = 0.06
A = +0.10; X = Octas(-3); B = -0.38; R^2 = 0.13
A = +0.01; X = Octas(-4); B = -0.02; R^2 = 0.00
Clearly only the equations for unlagged and for 3-day lagged cloud are of interest. I have included them both in the Fifth (and final) Model, with a residual Standard Deviation now reduced to 0.83 degrees:
Y = 0.55*(Outdoor temps) + (Heat Bank temp) - 0.12*(Cloud(--)) + 0.10*(Cloud(-3))- 6.8




Edited by Surly Bond (15/08/2010 20:05)
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#878964 - 25/08/2010 22:29 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Midwinter2010
Modelling indoor temperatures of the Manilla solar-passive house
3. Modelling daily Indoor wall MINIMUM temperature

In this post I apply the modelling of the previous post to Indoor wall minimum temperatures, rather than maximum temperatures. As before, the graphs are based on those in Post #874144, above.


The first graph shows (in red) the log of daily Indoor min temp taken at head height on an interior framed wall. It is set against the logs of both Outdoor max temp and Outdoor min temp. Surprisingly, the Indoor minimum temperature seems to relate to the outdoor maximum rather than the outdoor minimum.

Again, I did scatter plots and regressions of Indoor wall min temp, as dependent variable, against both Outdoor max temp and Outdoor min temp on the same day, and Outdoor temps lagged by one, two, and three days.
As previously, results are expressed as linear equations, with slope (A) times the Independent Variable (X), an Intercept (B) and a Coefficient of Determination (R^2):
A = 0.20; X = OutMax(--); B = 14.1; R^2 = 0.21
A = 0.33; X = OutMax(-1); B = 11.8; R^2 = 0.60
A = 0.36; X = OutMax(-2); B = 11.3; R^2 = 0.70
A = 0.29; X = OutMax(-3); B = 12.6; R^2 = 0.45
A = 0.16; X = OutMin(--); B = 16.7; R^2 = 0.26
A = 0.12; X = OutMin(-1); B = 16.9; R^2 = 0.14
A = 0.09; X = OutMin(-2); B = 17.1; R^2 = 0.07
A = 0.09; X = OutMin(-3); B = 17.1; R^2 = 0.08
The highest R^2 (0.70: much higher than any found for wall max temps) is for the third equation, relating the Indoor wall min temp to Outdoor max temp two days earlier.There are also high values of R^2 for Outdoor max temps lagged one day and three days. Outdoor min temps seem to affect Indoor wall min temps very little.
(Note: A daily minimum temperature value cannot be physically affected by a maximum temperature value read on the same day, as in Equation 1. Temperature maxima occur some seven hours after temperature minima.)

I modelled the response of the Indoor wall min temp to the independent variables as described in the previous post.


The second graph shows (green) the First Model of Indoor wall max temp using the third regression equation alone:

Y + 0.36*(OutMax(-2) + 11.3

This model is already a better fit than the Final Model for Indoor wall max temps. The Standard Deviation of the residual is 0.74 degrees.

I improved the model in steps as in the case of the Indoor wall max temps.


The third graph shows the final model. It gives an excellent visual fit and a Standard Deviation of the residual of only 0.44 degrees. The equation is:

Y = 0.45*(0.35*(OutMax(-1)) + 0.55*(OutMax(-2)) + 0.1*(OutMax(-3))) + (Heat Bank temp) + 0.07*(Cloud(-2))- 9.1
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#879315 - 26/08/2010 23:07 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
12,000 views!

It is a total mystery to me. The first 1000 views took 5 years to accumulate. Now each extra thousand comes in five days. Only the case of getting from 8000 to 9000 took the 25 days from July 11 to August 9.

The surfing thread has had 134,763 views, but I can find only 28 threads that have had more views than this one.
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#882793 - 12/09/2010 22:40 Re: Indoor Climate [Re: Surly Bond]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Midwinter2010
Modelling indoor temperatures of the Manilla solar-passive house
3. Inferences from models of Indoor wall temperatures
In Posts #877256 and #878964 (above) I was able to model Indoor wall max and min temperatures fairly closely as functions of Outdoor max and min temperatures, morning cloudiness, and the slowly-changing temperature of the under-floor Heat Bank.
Indoor wall max temp:
Y = 0.55*(0.6*(OutMax(--)) + 0.1*(OutMax(-1)) + 0.1*(OutMax(-2)) + 0.1*(Outmax(-3)) + 0.1*(OutMin(-2))) + (Heat Bank temp) - 0.12*(Cloud(--)) + 0.10*(Cloud(-3))- 6.8
Indoor wall min temp:
Y = 0.45*(0.35*(OutMax(-1)) + 0.55*(OutMax(-2)) + 0.1*(OutMax(-3))) + (Heat Bank temp) + 0.07*(Cloud(-2))- 9.1

(Key: "(OutMax(--))" means the value of the Outdoor maximum temperature of the same day; "(OutMax(-1))" means the value of the Outdoor maximum temperature one day earlier; etc.)

The relationships are shown in the graphs below. As an example, I have chosen the coldest day and night indoors, and I have marked the inputs to those results.


I will try to interpret these equations.

1. The house is heated by solar radiation. Most heating is done by radiation entering the windows and falling on indoor brick and tile surfaces. Similarly, much of the heat loss is by radiation to the sky at night. Since I do not have an instrument (pyranometer) to measure radiation, I use values of Outdoor max and min temperature as indexes of the daytime and night-time radiation balance.
In this mid-winter data set, the Indoor temperature is higher than the Outdoor temperature for every reading but one. Thus, the insulation, double-glazing, curtains and draft-sealing operate entirely to prevent heat from leaking out.

2. Effect of Outdoor temperatures.
Each equation includes a weighted sum of Outdoor temperature maximum and minimum values extending back up to three days.
The Indoor wall maximum responds most to the Outdoor maximum of the same day. A high Outdoor maximum temperature relates to high solar radiation entering the windows, and also reduces heat losses through the walls and roof.
The thermal mass (perhaps 200 tonnes) retains the heat received in each of the previous three days. The Outdoor minimum temperature two days earlier (actually 2.3 days earlier) also has an effect, by changing the rate of loss of stored heat.
The Indoor wall (early morning) minimum responds strongly to the Outdoor maximum of the previous day and even more strongly to the day before that.

3. Outdoor temperature variations from day to day are reflected in smaller temperature variations indoors. The damping factor (output/input ratio) for Indoor wall maxima is 0.55, and that for Indoor wall minima is 0.45.

4. The temperature deep in the Heat Bank, measured 750 mm below the surface of the floor slab, is a slowly-varying very effective control on mean wall temperatures.

5. Cloudy skies affect the house temperatures. In the model for Indoor wall max temperatures, cloud on the same day reduces the indoor temperature. Total overcast (eight octas) results in one degree of cooling indoors. However, eight octas of cloud three days earlier results in almost one degree of warming (not cooling) indoors.
In the model for Indoor wall min temperatures, the only cloud effect is a warming of half a degree for a total overcast two days earlier.
This apparent warming by cloud cover may be by reduced night-time radiation loss. It could also be that day-time cloud generally causes low values of Outdoor max temperature, and is effectively being counted twice.


The Intercept (the constant at the end of the equation) which was an arbitrary-seeming +14.3 degrees at first, is now seen as due mainly to the heat stored from month to month deep in the Heat Bank. The much smaller negative value remaining, -6.9 degrees by day and -9.1 degrees by night, can be thought of as a loss from the house due to imperfect insulation.
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#882903 - 13/09/2010 15:49 Re: Indoor Climate [Re: TOM1111]
StormTiggy Offline
Weather Freak

Registered: 11/09/2010
Posts: 98
I love cold rooms. especially in the summer!
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#890247 - 12/10/2010 11:16 Re: Indoor Climate [Re: StormTiggy]
Surly Bond Offline
Weatherzone Addict

Registered: 23/08/2003
Posts: 2193
Loc: Manilla, near Tamworth NSW
Midwinter2010
Modelling indoor temperatures of the Manilla solar-passive house
4a. Modelling max/min temperatures on the surface of the concrete floor slab: The Models

In Posts above I was able to model Indoor wall max and min temperatures fairly closely as functions of Outdoor max and min temperatures, morning cloudiness, and the slowly-changing temperature of the under-floor Heat Bank.
Here I do the same for the daily maximum and minimum temperatures of the air in contact with the surface of the tiled concrete floor slab.
The sensor is several metres away from surfaces that are heated directly by the sun. The sensor for the temperature of the Heat Bank is deep in the solid material 750 mm directly below.

Data points are shown in this graph, along with outdoor data plotted using a coarser scale.


The data were modeled by regression and trial-and-error as described above. The best models are compared with actual data in these graphs:


The best predictive equations are given below, using this Key:
"(OutMax(--))" means the value of the Outdoor maximum temperature of the same day; "(OutMax(-1))" means the value of the Outdoor maximum temperature one day earlier; etc.

Indoor slab max temp:
Y = 0.50*(0.27*(OutMax(--)) + 0.15*(OutMax(-1)) + 0.16*(OutMax(-2)) + 0.15*(Outmax(-3)) + 0.15*(OutMax(-4))+ 0.12*(Outmax(-5))) + (Heat Bank (-2)) + 0.05*(Cloud(-3)) - 8.2
The Standard Deviation of the discrepancy of the model from data points is only 0.25 degrees.

Indoor slab min temp:
Y = 0.43*(0.20*(OutMax(-1)) + 0.45*(OutMax(-2)) + 0.25*(OutMax(-3)) + 0.10*(OutMax(-4))) + (Heat Bank(-2)) + 0.1*(Cloud(-5))- 7.6
The Standard Deviation of the discrepancy of the model from data points is 0.34 degrees.
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