Posted by: @rob-of-york

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The graph below shows exactly the same data points as used in the previous post, but now they are divided into individual months and 6 regression lines drawn, one for each month. It is apparent from the large variation in the slope and y-axis intercepts of these lines that 30 or so data points are simply not enough.

An excellent description of the problem with small data sets, and thanks for posting all this.

Posted by: @jamespa

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The positive intercept...

...suggests something is wrong, and it can't be explained by the data set being too small, because it isn't! As you said recently of my positive intercept, "IMHO its worth investigating"!

As @rob-of-york put it very succinctly (PM = power measured from the primary heat source, PO = power from other heat sources) :

"The equation can be rearranged to read: PM = HTC(IT - OT) - PO.

If we plot data for PM against (IT-OT) on a graph, then the equation is that of a straight line, with a slope of HTC that crosses the y-axis at a negative value equal to PO."

The only way the offset can be positive in the real world is by the other power sources, instead of contributing extra heat, act to suck heat out of the building. Aliens might be able to do that, but we humans can't, likewise the energy that comes out of a socket to boil a kettle goes into the kettle, and then the house, not the other way round. We both need to explain our positive intercepts.

I'm making progress tidying up my disorganised files, and am trying to find the cleanest and most adaptable way of getting 24h data for plots using daily data. At the moment I stuck trying to explain the albeit small discrepancies in the 24h totals and averages that arise when different methods are used. Since the underlying data is the same, the results should be the same.  

Posted by: @cathoderay

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Posted by: @jamespa

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The positive intercept...

 

 

...suggests something is wrong, and it can't be explained by the data set being too small, because it isn't! As you said recently of my positive intercept, "IMHO its worth investigating"!

Because the plot is against degrees days not OAT, with an assumed base of 15.5, this is most likely an indication that my house has a base a bit higher.  Eyeballing the intercept suggests 17.5.  Of course it could be something else but a base of 17.5 is very plausible.

@jamespa @cathoderay 

I'm inspired to try out the degree days approach using my data.

Gas only power

Going step by step, first I've taken the electricity usage out, so looking at gas-only power vs. temperature difference.

This changed HTC (the slope) by a tiny amount, now 269W/C rather than 268W/C, definitely in the noise, but increased the power from other sources from 455W to 755W, so 300W extra. It turns out my average electricity usage was 290W over the 6 month period, so that correction is pretty much spot on for what has been removed. The estimated heat loss from gas-only power vs. temperature difference is (269 x 24) + 755 - 180 = 6280W, only 20W different from before, again in the noise.

A useful conclusion from this is that if electricity usage is relatively low (our average is 6.9kWh per day) and follows a fairly steady weekly average, then including it is not necessary to obtain a good heat loss estimate. Our daily electricity consumption varied between 3.9 kWh and 13.8 kWh, but that variability does not seem to have impacted the results when a gas-only view is taken.

Degree days

Second, I switched to using degree-days on the x-axis, where the degree-day value is 15.5C minus the average outdoor temperature for the day.

Now the HTC value (the slope) has changed to 250W/C. The x-axis intercept is close to -1C, suggesting that no gas heating is required once the outdoor temperature reaches  16.5C. The overall average indoor temperature was 18.5C, hence a degree days value of -3C is the point at which the outdoor temperature matches the average indoor temperature. The regression line crosses the x = -3C vertical line at a value of -520W. Hence, the power from other sources is estimated at about 520W.

The estimated heat loss from gas-only power vs. degree days is (250 x 24) - 234 - 180 = 5820W, somewhat lower than before.

This graph is interesting because if the indoor temperatures were absolutely constant at the 18.5C average, then the points and the lines on the two graphs above would look identical, there would just be a 3-degree shift in the x-axis values. In fact, the daily average indoor temperatures varied from 17.6C to 20.0C, and there is a correlation between lower outdoor temperatures and lower indoor temperatures. This is mainly because we do not run the heating overnight, and so while the indoor temperature is relatively stable during the day, it drops by a variable amount at night depending on the outdoor temperature. (The 91 days with the lowest outdoor temperatures have an overall average for the indoor temperature of 18.3C, compared to 18.8C for the other 91 days with the highest outdoor temperatures). This small difference would appear to be enough to shift the slope of the regression line, which is reducing the estimated heat loss.

In conclusion, if indoor temperatures can be held very stable, for example by running the heating system 24/7, then good heat loss estimates could still be obtained without the need for indoor temperature information. However, if average indoor temperatures correlate with outdoor temperatures, for example because the heating system switches off over night, then the small differences will likely impact the quality of the heat loss estimate.

I would encourage anyone looking to make an accurate estimate of heat loss based on measurements over the 2026/27 heating season to invest a small amount of money in their own weather station, allowing indoor and outdoor temperatures to be recorded on a frequent basis (at least hourly).

@rob-of-york Hi Rob,

we paid ~£350 for an air leakage test and it was worth every penny. It gave our installer hard evidence to not use the MCS default values so saved us the 30% uplift in pump size we would have ‘needed’. Also the tester kept it running while we went round the house closing the doors to each room in turn to find where the residual leaks were.

In our case it was not the classic under-bath or kitchen work-top holes into the cavity or outside but where pipes used to go into the roof space. We had not filled the ‘whole of the hole’. With this guide we blocked more leaks.

I found the most unknown of heat loss values was air leakage and after the measurement at 50pA the next unknown was the de-rating based on wind exposure and protection from surrounding trees and houses. We live half way down a west-facing hill so we’re sheltered one direction but not the others. Wind-chill in driving south-westerly rain is very noticeable here.