Archive for the ‘Environment’ Category

Gas and Gaslighting

January 1, 2023

Click on image for a larger version. BBC News stories detailing gas explosions this autumn: See end of article for links.

Friends, welcome to 2023.

I would have liked to start the year talking about something positive, but I can’t!

Over the Christmas break it struck me just how astonishing it is that we still allow homes to be heated by burning methane gas.

And we even build new homes incorporating this deadly and disgusting technology.

In case you didn’t know:

  • Over 100 people a year in the UK die from carbon monoxide poisoning, mainly arising from poorly-maintained gas-burning equipment.

Click on image for a larger version. Graph showing data from the Office for National Statistics on the number of people killed each year from carbon monoxide poisoning (link).

  • Even when gas-apparatus functions correctly, gas cookers emit toxic fumes into the homes of people who cook with gas. It is likely the highest exposure to mixed oxides of nitrogen (NOX) that you will experience anywhere in the UK is not by a roadside, but in a kitchen.

Click on image for a larger version. While cooking with gas in this US household, NO2 levels rose to almost 300 ppb. This figure is modified from the linked article.

  • And on top of it all, every year gas causes more than 300 explosions in the UK, killing or maiming around 100 people each year.

Click on image for a larger version. There are over 300 fires involving gas and an explosion every year. About 100 of these incidents result in a casualty or a fatality (Data Source).

  • And on top it all again, burning it emits tonnes of carbon dioxide, a gas which is destabilising the climate on which we depend.

So how is it that we tolerate such a technology? Why are we not outraged?


Friends, we are being ‘gaslighted‘ by the Gas Industry.

Gaslighting – as Wikipedia puts it – is a term that:

…”may also be used to describe a person (a “gaslighter”) who presents a false narrative to another group or person, thereby leading them to doubt their perceptions and become misled, disoriented or distressed. Often this is for the gaslighter’s own benefit.

The gas industry – and the media it influences – suggest that the deaths and appalling climate impacts of burning gas are in some way ‘normal’ and ‘acceptable’.

Because we are familiar with gas, they propagate a false narrative that ‘burning gas’ is somehow ‘safe’, ‘natural’, ‘warming’ and ‘friendly’.

To understand how shocking and deceitful this really is, try the following exercises:

  • Imagine that Wind Turbines killed more than 100 people a year.
  • Imagine that Heat Pumps killed more than 100 people a year.
  • Imagine that Solar Panels killed more than 100 people a year.

Do you think there would be media outrage? Of course there would! But with gas – these consequences are literally just ignored.

The Reality

The reality is this: gas is a filthy polluting technology and burning gas damages our climate, our health, and kills over 100 people a year in the UK alone, as well causing 300 explosive fires per year.

I urge you not to be misled into thinking that gas is anything other than a toxic mistake. If you can, I urge to eliminate gas appliances from your life.

BBC News Story Links


2022 to 1978: Looking Back and Looking Forwards

May 3, 2022

Friends, it’s been two years since I retired, and since leaving the chaos and bullying at NPL, retirement has felt like the gift of a new life.

I now devote myself to pastimes befitting a man of my advanced years:

  • Drinking coffee and eating Lebanese pastries for breakfast.
  • Frequenting Folk Clubs
  • Proselytising about the need for action on Climate Change
  • Properly disposing of the 99% of my possessions that will have no meaning to my children or my wife after I die.

It was while engaged in this latter activity, that I came across some old copies of Scientific American magazine.

Last year I abandoned my 40 year subscription to the magazine because it had become almost content free. But in its day, Scientific American occupied a unique niche that allowed enthusiasts in science and engineering to read detailed articles by authors at the forefront of their fields.

In the January Edition for 1978 there were a number of fascinating articles:

  • The Surgical Replacement of the Human Knee Joint
  • How Bacteria Stick
  • The Efficiency of Algorithms
  • Roman Carthage
  • The Visual Characteristics of Words


  • The Carbon Dioxide Question

You can read a scanned pdf copy of the article here.

This article was written by George M Woodwell a pioneer ecologist. The particular carbon dioxide question he asked was this:

Will enough carbon be stored in forests and the ocean to avert a major change in climate?

The article did not definitively answer this question. Instead it highlighted the uncertainties in our understanding of the some of the key processes required to answer the question.

In 1978 the use of satellite analysis to assess the rate of loss of forests was in its infancy. And there were large uncertainties in estimates of the difference in storage capacity between native forests, and managed forests and croplands.

The article drew up a global ‘balance sheet’ for carbon, and concluded that there were major uncertainties in our understanding of many of the physical processes by which carbon and carbon dioxide was captured (or cycled through) Earth’s systems.

Some uncertainty still remains in these areas, but the basic picture has become clearer in the subsequent 44 years of intense study.

So what can we learn from this ‘out of date’ paper?

Three things struck me.


Firstly, from a 2022 perspective, I noticed that there are important things missing from the article!

In considering likely future carbon dioxide emissions, the author viewed the choices as being simply between coal and nuclear power.

Elsewhere in the magazine, the Science and the Citizen column discusses electricity generation by coal with no mention of CO2 emissions. Instead the article simply laments that coal will be in short supply and concludes that:

“There is no question… coal will supply a large part of the nation’s energy future. The required trade-offs will be costly however, particularly in terms of human life and disease.

Neither article mentions generation of electricity by gas turbines. And neither makes any mention of either wind or solar power generation – now the cheapest and fastest growing sources of electricity generation.

From this I note that in it it’s specific details, the future is very hard to see.


Despite the difficulties, the author did make predictions and it is fascinating from the perspective of 2022 to look back and see how those predictions from 1978 have worked out!

The article included predictions for 

  • The atmospheric concentration of CO2
  • CO2 emissions from Fossil Fuels

Click on image for a larger version. Figure from the 1978 article by George Woodwell. The curves in green (to be read against the right-hand axis) shows two predictions for atmospheric concentration of CO2. The curves in black (to be read against the left-hand axis) shows two predictions for fossil fuel emissions of CO2. In each case, the difference between the two curves represents the uncertainty caused by changes in the way CO2 would be cycled through (or captured by) the oceans and forests. See the article for a detailed rubric.

The current atmospheric concentration of carbon dioxide is roughly 420 ppm and the lowest projection from 1978 is very close.

The fossil fuel emissions estimates are given in terms of the equivalent change in atmospheric CO2, and I am not exactly sure how to interpret this correctly.

Atmospheric concentration of CO2 is currently rising at approximately 2.5 ppm per year, and roughly 56% of fossil fuel emissions end up in the atmosphere. So the annual emissions predicted for 2022 are around 2.5/0.56 ~ 4.5 ppm /year, which is rather lower than the lowest prediction of around 6 ppm/year.

The article also predicts that this will be the peak in annual emissions, but that has yet to be seen.

The predictions did not cover the warming effect of carbon dioxide emissions, the science of which was in the process of being formulated. ‘Modern’ predictions can be dated to 1981, when James Hansen and colleagues published a landmark paper in Science (Climate Impact of Increasing Atmospheric Carbon Dioxide) which predicted:

A 2 °C global warming is exceeded in the 21st century in all the CO2 scenarios we considered, except no growth and coal phaseout.

This is the path we are still on.

From this I note that the worst predictions don’t always happen, but sometimes they do.


The final observation concerns the prescience of the author’s conclusion in spite of his ignorance of the details.

Click on the image for a larger version. This is the author’s final conclusion in 1978

His last two sentences could not be truer:

There is almost no aspect of national or international policy that can remain unaffected by the prospect of global climatic change.

Carbon dioxide, until now an apparently innocuous trace gas in the atmosphere may be moving rapidly toward a central role as a major threat to the present world order.


Heating Degree Days:4:Three numbers you need to know about your home

March 15, 2022

Friends, after the previous three posts (1, 2, 3) about Heating Degree Days, you may be wondering:

  • Is Michael OK? He seems to be obsessed with Heating Degree Days?
  • Hasn’t he been keeping an eye on the COVID figures?

Well, I have indeed been focussed on Heating Degree Days, and in this short (!) article I would like to summarise why.

The Heating Degree Day (HDD) concept enables two calculations for numbers you really should know about your dwelling:

  • It’s thermal leakiness: technically its heat transfer coefficient (HTC)
  • The size of heat pump your dwelling requires.

When combined with an estimate for how good the insulation is, you will be in a great position to make rational choices about improving the thermal performance of your dwelling.

Here are the three calculations:

#1:Heat Transfer Coefficient.

How much does heating power does it take to make your dwelling 1 °C warmer?

The answer to this question is known as the Heat Transfer Coefficient (HTC) for a dwelling.

A first estimate of your HTC can be made by dividing your annual gas consumption (in kWh) by 57.3:

Note: This formula was revised on 21/3/2022 due to a typo in the original text.

This assumes your dwelling (flat or house) is in the southern half of the UK (i.e. South of Manchester) and that you set your thermostat to 20 °C.

  • If you live between Manchester and Edinburgh, reduce your estimate of HTC by 10%.
  • For each 1 °C above 20 °C that you set your thermostat, reduce the first estimate of HTC by 10%.
  • For each 1 °C below 20 °C that you set your thermostat, increase the first estimate of HTC by 10%.

#2:Heat Pump Size.

How big a heat pump do I need?

It’s the question everyone wants an answer to!

A first estimate of the size of heat pump you require can be made by dividing your annual gas consumption (in kWh) by 2,900.

This assumes your dwelling (flat or house) is in the southern half of the UK (i.e. South of Manchester) and that you set your thermostat to 20 °C.

  • If you live between Manchester and Edinburgh, increase your estimate of heat pump power by 10%.
  • For each 1 °C above 20 °C that you set your thermostat, increase your estimate of heat pump power by 10%.


Do I need more insulation?

If your home is a house (rather than a flat), then you can assess how good your home is compared to the best possible as follows.

Divide your annual gas consumption (in kWh) by the floor area of all the floors in your home that live in i.e. include the loft if its part of the domestic space but not if it’s just used for storage.

  • The best possible is < 15 kWh/m^2/year: this is the Passivhaus standard
  • The best possible retrofit is < 25 kWh/m^2/year: this is the Enerphit retrofit standard
  • The AECB retrofit standard is < 50 kWh/m^2/year.

My house was ~ 90 kWh/m^2/year before external wall insulation and triple-glazing reduced it to around 45 kWh/m^2/year. The only way to significantly improve on this would be with underfloor insulation and air-tightness work.

If the figure for your home is very much above 100 kWh/m^2/year then I would suggest you consider insulation work.


If you know these numbers – even approximately – for your home, then you will be in a position to make reasonable choices about what to do next.

Please bear in mind that all the figures are approximate. I can see ways in which they could be wrong by 10%, but I would be surprised if they were 20% wrong.

Estimating Rates of Air Change in Homes

June 6, 2021

Air flow in modern homes

Modern homes are built with low air leakage rates and then mechanically ventilated to keep the air ‘fresh’. To prevent heat losses associated with this air exchange, the outgoing ‘stale’ air is flowed through a heat exchanger to warm the incoming ‘fresh’ air.

However this Mechanical Ventilation with Heat Recovery (MVHR) is not suitable for many older homes – such as mine – which are too leaky.

My home has gaps between floorboards on the ground floor and the air can flow in and out easily through the underfloor void.

To seal my home to modern standards would require re-building the entire ground floor – adding insulation as one worked. One would then add MVHR to the newly-sealed house. This would be very disruptive, and so I have instead chosen to remain married.

So in my old house and many like it, heat losses from air flow are highly uncertain.

Wouldn’t it be great if there were some way to measure air flow in older homes which was cheap and convenient!


Air flow through a building is commonly characterised by the number of air changes per hour – ACPH. But how can this be measured if one doesn’t know where the air is coming in or going out?

This building wiki suggests:

Tracer gas measurement can be used to determine the average air change rate for naturally’-‘ventilated spaces’ and to measure infiltration (air tightness)’. To do this, a detectable, non-toxic gas is released into the space and the reduction in its concentration within the internal atmosphere is monitored over a given time period.’

By ‘tracer gas measurement’ the wiki means that a gas is released into the air at a known rate, and its concentration measured versus time. If the rate of production of tracer gas is known, then the final stable concentration allows one to work out the number of air changes per hour (ACPH).

  • If the number of ACPH is small, the final concentration will be high.
  • If the number of ACPH is high, the final concentration will be low.

What this wiki frustratingly fails to point out is that carbon dioxide is an ideal tracer gas and has been used for years for this purpose.

This essential fact is pointed out in the first paragraph of an outstandingly clear and authoritative paper from Andrew Persily and Lillian de Jonge.

Carbon dioxide generation rates for building occupants Persily A, de Jonge L. Indoor Air. 2017;27:868–879. . It’s also available with alternate formatting here.

The first line of the abstract is:

Indoor carbon dioxide (CO2) concentrations have been used for decades to characterize building ventilation and indoor air quality.

This surprised me because in all my reading about this subject in the UK I have never seen it mentioned. But then, in the first line of the paper itself, Persily and de Jonge point out just how old the idea is:

Indoor CO2 concentrations have been prominent in discussions of building ventilation and indoor air quality (IAQ) since the 18th century when Lavoisier suggested that CO2 build-up rather than oxygen depletion was responsible for “bad air” indoors.

The gist of their paper is a thorough review and examination of the factors which affect the rates at which human beings emit carbon dioxide. I won’t deprive you of the pleasure of reading the paper but factors discussed include:

  • The ratios of fat, protein and carbohydrate in people’s diet.
  • Age, gender and ethnicity.
  • Body size and mass.
  • Levels of activity.

The paper is very readable and I recommend it in the highest terms.

A worked example: my bedroom.

At night my wife and I sleep in a room which is about 7 m long, 3.5 m wide and 2.2 m high. So it has a volume of 7 x 3.5 x 2.2 = 54 cubic metres, or 54,000 litres.

There are no obvious draughts and I had no idea how many air changes per hour there were.

But overnight, the concentration of carbon dioxide rises from about 450 parts per million (ppm) characteristic of fresh air, and stabilises around 1930 ppm.

I can work out the number of air changes per hour ACPH using the formula below.

In this formula:

  • The room volume in litres
    • In my case 54,000 litres
  • c is the measured stable CO2 concentration in ppm
    • In my case 1930 ppm
  • c0 is the concentration of CO2 in ‘fresh’ air in ppm
    • In my case around 450 ppm
  • 10-6 is the scientific way of saying “divide by a million”
    • 1/1,000,000
  • CO2 production rate is what Persily and de Jonge’s paper tells us:
    • For sleeping males over the age of 11, the answer is within 10% of 12.7 litres per hour.
    • For sleeping females over the age of 11, the answer is within 10% of 10.2 litres per hour.
    • So our joint CO2 production rate is about 23 litres per hour

Putting all those numbers in the formula……we find the rate of change of air is around 0.29 ACPH – with the answer probably being within 10% of that value.

Some other factors.

Persily and de Jonge’s paper is extraordinarily thorough and tackles some of the tricky problems about using this technique for estimating air flow in buildings.

Firstly, there is the question of the level of activity of the people in a particular space. The metabolic rate is generally measured in units of mets with 1 met being roughly the metabolic activity during sleep. Very roughly it corresponds to around 58 watts.

The paper has extensive tables showing the CO2 production rate in litres per second for different levels of activity of different sexes at different ages. (Remember to multiply these numbers by 3600 to convert them into CO2 production rate in litres per hour before using them in the formula above.)

Secondly, there is the wider question of which volume of air is relevant. My bedroom represents a small volume with well understood rates of CO2 production.

But is a CO2 meter placed in a ground floor room measuring the characteristic concentration of the room it is in, the whole ground floor, or the entire house? Resolving questions like this may take a few experiments, such as moving the meter around.

Additionally, the amount of CO2 generated in a house over a day may not be clear. For example, the number of occupants and their level of activity may be hard to determine.

Mi casa no es tu casa

The situations encountered in your home will be different from those in my home.

Nonetheless, if you are trying to assess air flow within your home, I would recommend that you consider using carbon dioxide measurements as part of your arsenal of measurement techniques.

I use two CO2 meters and can recommend them both:

Air Conditioning versus Air Source Heat Pump

May 15, 2021

Click for a larger version. Similarities and differences in how an air source heat pump (ASHP) or an air conditioning (AC) system warms a home. All the components inside the dotted green line are contained in the external units shown. A key design difference is whether or not the working fluid is completely contained in the external unit. See text for more details.

Regular readers will probably be aware that – having reduced the heating demand in my house – my plan is to switch away from gas heating and install an electrically-powered air source heat pump to heat the house and provide domestic hot water.

But next week I am also installing air conditioning, something which is traditionally not thought of as very ‘green’. What’s going on?

Why Air Conditioning?

I have two reasons.

My first reason is that, as you may have heard, the whole world is warming up! Last year it reached 38 °C in Teddington and was unbearably hot for a week. I never want to experience that again.

During the summer the air conditioning will provide cooling. But assuming the heating comes with good weather, the air conditioning will be totally solar powered, and so it will not give rise to any CO2 emissions to make matters worse!

My second reason is that in the right circumstances, air conditioning is a very efficient way to heat a house. That’s what this article is about.

Heat Pumps

Air Conditioners (AC) and Air Source Heat Pumps (ASHP) are both types of heat pumps.

In scientific parlance, a heat pump is any machine that moves heat from colder temperatures to higher temperatures at the expense of mechanical work.

Note: to distinguish between the general scientific idea of a heat pump, and the practical implementation in an air source heat pump, I will use abbreviation ASHP when talking about the practical device.

The general idea of a heat pump is illustrated in the conceptual schematic below.

As shown, the pump uses 1 unit of mechanical energy to extract two units of heat energy from air at (say) 5 °C and expel all 3 units of energy (1 mechanical and 2 thermal) as heat into hot water at (say) 55 °C.

Click for a larger version. Traditional representation of the operation of heat pump.

Heat pumps can seem miraculous, but like all good miracles, they are really just applied science and engineering.

A heat pump is characterised using two parameters: COP and ΔT.

  • A heat pump which delivers 3 units of heat for 1 unit of work is said to have a coefficient of performance (COP) of 3.
  • The temperature difference between the hot and cold ends of the heat pump is usually called ‘Delta T’ or ΔT.

Obviously engineers would like to build heat pumps with high COPs, and big ΔTs and they have used all kinds of ingenious techniques to achieve this.

But it turns out that heat pumps only operate with high COPs when the ΔT is small and when the heating power is low. There are two reasons.

  • Firstly, the laws of thermodynamic set some absolute limits on the COP achievable for a given ΔT.
    • Most practical heat pumps don’t come close to this thermodynamic limit for a variety of mundane reasons.
    • The maximum COP for moving heat from 5 °C to 55 °C is 6.6.
    • The maximum COP for moving heat from 5 °C to 20 °C is 19.5.
  • Secondly, in order to heat a room to (say) 20 °C, the hot end of the heat pump needs to be hotter than 20 °C.
    • Typically the hot end of the heat pump must be 5 °C to 10 °C warmer than the room in order that heat will flow out of the heat pump.
    • Additionally the cold end of the heat pump must be 5 °C to 10 °C colder than the external air in order that heat will flow into the heat pump.
    • The interfaces between the ends of the pump and the environment are called heat exchangers and designing ‘good’ heat exchangers is tricky.
    • A ‘good’ heat exchanger is one that allows high heat flows for small temperature differences.

So now we have seen how heat pumps are characterised, let’s see how heat pumps are used domestically.

Air Source Heat Pump (ASHP) versus Air Conditioner (AC)

The schematic diagrams  below show how a house is heated by an ASHP and an AC system. Both systems operate using a working fluid such as butane, which is ingeniously compressed and expanded. The details of this process are not the topic of this article so here I am glossing over the fascinating details of the device’s operation. Sorry.

Click for a larger version. How an air source heat pump (ASHP) warms a home. All the components inside the dotted green line are contained in the external unit shown. A key design feature is that the working fluid is completely contained in the external unit and heat is transferred to the central heating water by a heat exchanger.

Click for a larger version. How an air conditioner (AC) warms a home. All the components inside the dotted green lines are contained in either the external unit or the fan coil unit shown. A key feature is that the working fluid itself flows into the fan coil unit and heats the air directly.

We can compare the operation of the two systems in the table below.

Air Conditioner Air Source Heat Pump
Air at (say) 5 °C is blown over a heat exchanger and evaporates the working fluid.


The same.
The working fluid is then compressed – that’s the bit where the work is done – and liquefies, releasing the captured heat.


The same.
The hot working fluid – now at ~30 °C then flows through a pipe to an indoor heat exchanger (fan coil unit) where air is blown over the pipe and heated to 20 °C. The hot working fluid – now at ~60 °C then flows through a heat exchanger and transfers the heat to water in my central heating system at ~55 °C
No corresponding step  

The 55 °C water then flows through a radiator in my room, heating the room by radiation and by convective heat transfer to air at ~20 °C.

Looking closely at the figures and table above, one can see that the operation of the ASHP and the AC system are broadly similar.

However the ASHP has to operate with a bigger ΔT (~55 °C versus ~25 °C) than the AC system, and also has to transfer heat through an extra heat exchanger.

Both these factors degrade the achievable COP and so for my application, the specified COP for an ASHP is just over 3, but for the AC system, it is just over 5.

In my well-insulated house, when the external temperature is 5 °C, I require typically 36 kWh per day of heating, equivalent to 1.7 kW continuous heating. I can achieve this in several ways:

  • Using gas I must burn ~40 kWh of gas at 90% efficiency costing 40 x 3p (£1.20) and emitting 40 x 200 g = 8 kgCO2
  • Using an ASHP with a COP of 3, I must use ~36 kWh/3 = 12 kWh of electricity costing 12 x 25p (£3.00) and emitting 12 x 200 g = 2.4 kgCO2
  • Using an AC system with a COP of 5, I must use ~36 kWh/5 = 7.2 kWh of electricity costing 7.2 x 25p (£1.80) and emitting 7.2 x 200 g = 1.4 kgCO2
  • Using a domestic battery and buying the electricity at night for 8p/kWh, I can reduce the cost of using an ASHP or AC system by a factor of 3 to £1.00/day or £0.60/day respectively.

[Note: In these calculations I have assumed that the carbon dioxide emissions per kWh are same for both gas and UK electricity (200 gCO2/kWh) which is roughly correct for 2021]

So using an AC system I should be able to achieve domestic heating with lower carbon dioxide emissions than an ASHP.

My plan

In my case I need to heat water for my home to 55 °C for use in showers and basins. So I need an ASHP for that. And since I already have radiators in every room, hooking up the ASHP to the radiator circuits is smart double use.

The AC system I am having installed will have 1 external unit and 2 internal ‘fan coil units’. One unit will be in my bedroom (a sheer indulgence) and the other will be high up on the stairs, allowing air to be either blown down to the ground floor where I hope it will circulate, or blown towards the bedrooms.

My hope is that, when used together, the AC system (COP~5) will reduce the heating output required from the radiators so that I can reduce the flow temperature of the water from 55 °C to perhaps 40 °C. This reduces their heat output, but increase the COP of the ASHP from 3 to perhaps 4.

The main difficulty that I foresee is the extent to which the AC heating will actually permeate through the house and so reduce the amount of heating required by the ASHP.

So I am not sure how much heating will be required by the ASHP acting through the radiators, and whether the radiators will work at low flow temperatures. It is possible I might need to replace a few radiators with ones which work better at low temperatures.

It is not at all obvious that this plan will actually work at all – but I think it is worth a try.


The air conditioning I am having installed is a Daikin 2MXM40 multi-split outdoor unit with two FTXM25 indoor air units. (Brochure)

The model of heat pump I will have installed is a Vaillant Arotherm plus 5 kW. It can supply up 5 kW of heating at 55 °C with a COP of 3  – i.e. it will use just 1.6 kW of electrical power to do that – and heat water to 55 °C. Water storage will be a 200 litre Unistor cylinder. A brochure with technical details can be found here, and a dramatic video showing the kit is linked at the end of this article.

When I have come to terms with how much money I am spending on this, I will share that information. But at the moment it hurts to think about it!

Anyway: the adventure begins next week!


Battery Day: One month on…

April 20, 2021

Click for larger version. The graph shows daily electricity drawn from the grid (kWh). Before the solar panels were installed average usage was 10.9 kWh/day. After the solar panels were installed this fell by a couple of kWh/day. After an increase over Christmas when our son returned, we were back to normal. In the last month the solar electricity generated on the lengthening days have reduced the electricity drawn from the grid. Since the battery was installed a month ago, we have not drawn any electricity from the grid, but daily usage has been unchanged.

Friends, I have been so busy I have been forgetting to blog! So I thought I’d just post a quick update on the Powerwall Installation.

One month on now and we are still “off grid”: we haven’t used a unit of grid electricity for a month. But as the graph above shows, our usage has continued unchanged.

My experience has convinced me that solar installations should all be accompanied by a battery of some sort.

As I have mentioned before, from a national perspective, local batteries are a bad idea: they consume energy.

But from from a user’s perspective, they allow me to benefit from my investment.

And the prospect of not using any grid electricity until maybe September leaves me giddy.

Longer term goals

Click for a larger version. Summary performance of the battery system on 17th April 2021. The battery supplies the house overnight, and is then re-charged by solar generation in the morning. When the battery is full (around 1 p.m.) solar generation is exported to the grid. In the evening the battery takes over again as the solar generation dwindles.

We haven’t experienced a summer of solar power yet, but the longer days are amazing – even in April!

On sunny days the panels generate over 20 kWh of electricity, and the battery is full in the middle of the day.

Once the battery is full, the system exports electricity to the grid in the afternoon and we don’t need to use the battery until perhaps 7 p.m.

These exports are an important part of our plan.

In the winter, we will need to buy electricity from the grid – especially as next winter we will be using a heat pump for heating and hot water.

But ideally we hope the exports of electricity in the summer should match imports in the winter.

Looking at the cumulative generation and export from the system (below), and remembering that exports should be larger in the summer, it looks like yearly exports might just reach 1000 kWh – much more than I had expected.

This would be enough to ‘balance’ 100 days of 10 kWh per day in the winter, assuming no solar power. But even in mid-winter there is typically 2 or 3 kWh per day and so we might just be able to achieve year-round balance.

Click for a larger version. Cumulative generation and export of solar electricity. The dotted green line was my initial guess for generation through the year.

Battery Day: First Results

March 20, 2021

Me and my new Tesla. This unit contains 13.5 kWh of battery storage along with a climate control system to optimise battery life. We have placed it in the porch so that (when visits are allowed again) everyone who visits will know about it!

Last September, Tesla held their ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

Not to be outdone, last Monday VW held their own ‘Battery Day‘ during which they unveiled their road map towards cheaper, better, batteries.

And last Thursday was my own battery day, when Stuart and Jozsef from The Little Green Energy Company came and installed a Tesla Powerwall 2 at Podesta Towers in Teddington. I was (and still am) ridiculously excited.

I am still evaluating it – obviously – but here are a couple of notes.

How it works

The system has two components. An intelligent ‘gateway’ that monitors loads and supplies, and a climate-controlled battery storage unit.

Click for a larger version. The left-hand graphic shows how AC power enters our house, and how DC power generated by solar panels is linked to the grid. When the Solar PV is sufficient ,power is exported to the grid. The right-hand graphic shows how the TESLA ‘gateway’ device monitors the solar PV, domestic loads and battery status and intelligently decides what to do.

The gateway (and the battery) are electrically situated between the electricity meter and all the loads and power sources in the house. So all energy enters or leaves the battery module as AC (alternating current) power.

But its internal batteries must be supplied with DC (direct current).

This makes it ideal for storing power from the AC grid, but less than ideal for storing the DC current generated by solar PV panels.

One might have expected that a device designed to store solar power might intrinsically operate using DC and indeed, some battery systems – positioned between the solar PV and the inverter – do this.

So the choice to place the Powerwall™ where it is, is a compromise between the extra functionality this location offers – it can back up the entire house – and the inefficiency of storing solar PV which is first converted to AC by the inverter, and then re-converted back to DC by the Powerwall. The support document states that the conversion from AC to DC and back to AC has 90% round-trip efficiency.

The photograph below shows the gateway installed under the stairs in our house.

Click for a larger version. The Tesla ‘Gateway’ installed in our house. The unit is positioned in between the electricity meter and all the domestic loads. The black conduit leads under the floor to the battery which is installed in the porch.


The system is controlled by an app which is – frankly – mesmerising. It shows how electrical power flows between:

  • the grid,
  • the battery,
  • our home, and
  • our solar panels

Click for a larger version. Screenshots from the app at various times yesterday.

There is less room to adjust the parameters of the system than I had anticipated. This appears to be because, in exchange for a guarantee that the battery will retain at least 80% capacity (10.8 kWh) after 10 years, one is required to relinquish detailed control to the Tesla Brain.

Through a built in network connection, the device is in constant touch with Tesla who monitor its performance and can detect if it is abused in some way. I am not sure how I feel about that – but then guaranteed long-term performance is certainly worth something.

One feature of this relinquishing of detailed control concerns ‘time-of-use’ tariffs. I anticipate that – especially in winter – I will need to charge the battery overnight on cheap rate electricity.

The system supports this mode of operation but is not yet operational. Apparently it needs to study the patterns of household use for 48 hours before being enabled.

When operational, one gives the system general instructions and then allows it to choose when, and by how much, to charge. There is for example no way to force the battery to charge to 100% on command.

In practice I suspect it will be fine, but at the moment it still feels a little weird.

Performance on Day#1

The simplest way to show how the Powerwall™ works is by looking at the data which the ‘App’ makes available.

The first graph shows the household demand through the day. It’s fascinating to look at this data which has 5 minute and 0.1 kW resolution. The metrologist in me would like more – but in honesty, this is enough to understand what is happening.

Click for a larger graph. See text for details.

Now we can look to see how that demand was met. Overnight, we relied mainly on the grid.

Click for a larger graph. See text for details.

The battery could have supplied this overnight electricity, but it had been set to hold a reserve of 16% of its capacity (~2 kWh) in case we required backup after a power cut. We have lowered that setting now because, thankfully, power cuts are rare in Teddington. The battery drew power from the grid overnight in two short periods to maintain this reserve.

Additionally, at the end of a sunny day in which the solar PV filled the battery, there was brief period where we returned electricity to the grid.

During the day – which was very sunny 🙂 – the household electricity demand was met by the electricity from the solar panels.

Click for a larger graph. See text for details.

Without the battery, most of this 16.91 kWh of electricity would have been sent to the grid. But now only a tiny fraction was returned to the grid, most of it being captured by the battery – see below.

Click for a larger graph. See text for details.

The graph above shows the battery maintaining its reserve charge at night, and then charging from the solar PV during the day. At peaks of household demand, the charging is paused. At around 16:00, the battery was briefly full, and shortly thereafter it began discharging to meet household demand.

As I write this at 1:00 p.m. on the day after the day shown (a rather dull day 😦 ), the battery is 56% full and charging.

The graph below shows all the above curves together.

Click for a larger graph. See text for details.


The Powerwall system is an object of wonder. It is beautifully engineered and miraculous in its simplicity.

It transforms the utility of the solar PV allowing me (rather than electricity companies) to benefit from the investments I have made.

I will post more about the performance in terms of cost, electricity and carbon dioxide when I have more data.

But for the moment I will just thank Jozsef and Stuart from The Little Green Energy Company for their professionalism and attention to detail. And ‘No’. I am not being paid to say that – quite the opposite!

Stuart and Jozsef from The Little Green Energy Company. You can’t see it, but they assure me they were both smiling. Click for a larger version


Sometimes I find it hard to like EDF

March 16, 2021

Click for larger version. EDF wrote to me today to say they are increasing the price of ‘night rate’ electricity by 73.7%.

Energy is a wonderful thing. But sometimes it can be hard to like the companies which sell it to us…

…especially when they increase the price of their product by 73% overnight!

As regular readers will know, since 2018 I have been working hard to reduce my household energy consumption and the concomitant carbon dioxide emissions.

My 3-step plan has been:

  1. Reduce household heating requirement with insulation and triple-glazing.
  2. Switch from gas heating to electrical heating with a heat pump.
  3. Use solar panels and a battery to generate low-emission electricity and reduce the cost of switching to electrical heating.

Part#1 is complete: winter is not yet at an end, but heating demand appears to about 50% lower.

Part#2 is underway and I hope to have a heat pump installed this summer. But electrical heating is more expensive than gas heating.

Part#3 is underway: the solar panels are performing well and a battery should be installed this Thursday. The battery should allow me to use mainly my own solar electricity, or EDF off-peak electricity for most of the year.

I carried out extensive modelling of the effect of varying patterns of electricity consumption and compared different ‘tariffs’.

I had based my costings on the fact that the night rate for electricity would be about 5p/kWh and day rate would be about 25p/kWh. Of course I knew these costs could vary over time.

Nonetheless, it would be an underestimate to say that I was ‘disappointed’ when EDF wrote to me this morning to say that price of night time electricity was to rise from 4.99 p/kWh to 8.67 p/kWh…

…a 73% rise!

Like I said, sometimes it can be hard to like the companies which sell us energy.


I am thinking about it.

But switching is, in my opinion, a distraction. It is a way of distracting us ‘fish’ from the fact that we are in a ‘barrel’ and at the mercy of the confusopolists.


Previous articles about the house.




Domestic Batteries: Purchase decisions and realistic models

February 1, 2021

Friends, earlier this week I ordered a Tesla PowerWall 2 from the charming people at The Little Green Energy Company (TLGEC). They have given me a nominal installation date in late March 2021 and I will be sure to keep you updated.

So in my excitement I wrote another article about using batteries – and you can read it at length below. But AFTER I had spent hours calculating and graphing , I realised something very obvious but very profound.

  • The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
  • The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
  • The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
  • But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

My aim is to transition away from burning gas by using a heat pump. This switch requires me to use more electricity each year and without the financial savings that a battery yields this would be punitive.

More battery modelling: but using a climate re-analysis database!

I chose TLGEC over other installers because of their willingness – and ability – to answer tricky questions. And in one of their answers they gave me a jewel of link to this EU funded site with useful information about solar PV.

The site can be used like others to estimate the monthly generation from a solar PV installation. But unlike other sites the predictions are based on actual solar data over the period 2005-2016.

And uniquely – by using climate re-analysis –  it is possible to download this data for any location on Earth (!) to simulate hour-by-hour how a particular installation of panels would respond at any time during that period.

Click for a larger image. This web portal is available here.

This has enabled me to create models simulating the interaction of solar panels with a domestic battery similar to those I made previously. But instead of:

  • a minute-by minute model of a single day using simulated solar data,

I can now make…

  • an hour-by-hour model of an entire year using actual solar data.

Crucially this incorporates real-world (hour-to-hour and day-to day) variability which is one of the difficulties in trying to optimise the use of a battery.

The Model 

The Excel™ model (Solar Time Series Analysis 2005 – 2016 for Blog) is based (unsurprisingly) on a Tesla Powerwall 2 with 13.5 kWh of storage, but that can be changed in the file. Please note – this is not a simple model and is set up just for my panels in Teddington! If you want to use it for your site you will need to download data from the web portal above and place it in the spreadsheet.

The model has the following ‘features’ (default values shown in brackets)

  1. The electrical demand can have separate daily peak (1 kW) and off-peak (0.5 kW) values.
  2. The overnight charging rate can be changed (3 kW)
  3. The fractional filling of the battery in the morning can be changed seasonally between a summer value (100%) and a winter value (100%).
  4. The range of the ‘summer’ and ‘winter’ seasons can be defined (summer runs from day 60 to day 300)

The model evaluates:

  • The state of the charge of the battery hour-by-hour through the year,
  • The amount of peak and off-peak electricity which must be purchased to meet the required demand.
  • The amount of solar generation and the amount used on site, or exported.
  • The costs of different strategies.

One shortcoming of the model is that the 1-hour step is too long and so in some situations the model appears to overfill or underfill the battery. However I think the uncertainty this adds is relatively small.

The Parameters

I set the model to run with data both from individual years and from the average behaviour of all 12 years of data.

The demand I modelled was 0.5 kW overnight and 1 kW during the day. This is more than our house uses at present but is in line with the demand I expect when I install a heat pump to replace the gas boiler.

The model calculates the amount of electricity bought from the grid in both peak and off-peak periods and evaluates the fraction of demand met by solar electricity, and the cost.

I then investigated how different settings for the morning filling of the battery affected:

  • the amount of electricity bought from the grid (peak and off-peak) over the year,
  • the fraction of demand met by solar electricity,
  • the cost.

Typical Runs

The graph below shows the simulated State of Charge (SoC) of the battery during days 1 to 30 of the year 2016 i.e. January 2016.

Click for a larger view.

The graph shows daily overnight charging of the battery to 100% in the morning. The 1-hour time resolution of the simulation makes it appear the battery does not quite completely fill up, but it gets close.

The 1 kW daytime load then drains the battery completely on most days – the SoC reaches zero – and so some full price electricity must be bought.

However, there are a few days (e.g. days 7 & 8 and days 13 to 16) even in January in which strong sunlight fills the battery sufficiently that it lasts to the end of the day. These would typically be cold, crisp, clear winter days.

To indicate the variability, the equivalent graph for the year 2011 is shown below.

Click for a larger view.

But if we plot the average data from 2005 to 2016 we see it has a different character from that for individual years. Instead of the 3 or 4 bright sunny days, we have – on average – a little bit of sunshine on many more days.

Click for a larger view.

This difference between individual years and their average is important in this case, because it the intermittency of solar generation that makes a battery useful, and it is the irregularity of solar generation in any one year that makes it hard to optimise the use of a battery.

A whole year of averaged data is shown in the graph below. I have used average data to illustrate the general characteristics of the behaviour of the battery.

Click for a larger view.

In this graph the battery is charged each night to 100% SoC. In the winter it discharges through the day and the SoC reaches zero before the end of the day, requiring full price grid electricity to tide the household over to the end of the day and the start of cheap electricity.

But between days 60 and 300 there is enough solar generation – on average – such that the battery does not ever fully discharge at the end of each day. Thus in this period is not really necessary to fully charge the battery overnight.

The graph below shows the effect of only charging the battery to 70% in the mornings over this ‘summer’ period.

Click for a larger view.

The result of this is that less night-time electricity is used, and less electricity is exported. Consequently, the ‘self-use’ of solar electricity increases. However, there are now a few more occasions during the ‘summer’ when the  SoC reaches zero before the end of the day i.e. where full price electricity must be bought.

The graph below shows the same partial-charging strategy (only 70% between days 60 and 300) but using data for the year 2011: notice that the irregularity is much greater than when looking at the averaged data.

Click for a larger view.

So how does one make sense of all this? I do not want to spend my entire life optimising battery charging!

Basic Results

There are too many variables to succinctly summarise the modelling results, so here I will just summarise one investigation relevant to my own situation.

Imagining that I am running a heat pump to replace the gas boiler, I have assumed overnight use at 0.5 kW and daytime use at 1.0 kW. This amounts to 21 kWh/day or 7665 kWh/year. Due to the limited time step, the model calculates annual use as 7661 kWh – which is an error of 0.05%.

Using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar power varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

By ‘self-use’ I mean that the solar electricity was either used immediately at the house or stored in the battery for later use. Nominally either of these uses is ‘free’, but in reality the storage and retrieval is only around 90% efficient.


First of all looking at solar data from each year 2005 to 2016 I calculated that on average the panels would generate 3847 kWh/year with a standard deviation of about 5%. The average value is same as is calculated from just using the average 2006-2016 datset

Click for a larger view.

The solar generation is only around half of the anticipated demand (see below). And without a battery, most of that is exported at a relatively low price (1.8 p/kWh from EDF). This benefits the planet and EDF, but means I still have to pay EDF 23.7 p/kWh for peak time electricity to operate the heat pump.

Click for a larger view.

Next – using the solar data for each individual year – and for the average of all the years – I calculated how self-use of solar electricity varied as I changed the state of charge (SoC) of the battery in the morning from 0% to 100%.

Click for a larger view. The graph shows the number of units of solar electricity (kWh) that would have been used on site.

If we pick one year (say 2014) as an example, we that in this sunnier-than-average year, charging the battery to about 30% SoC in the morning leaves plenty of capacity to store solar electricity during the day.

In a more typical year (say 2016) the optimum morning SoC is between 40% and 50%.

  • Higher morning SoC results in solar generation being ‘lost’ to export.
  • Lower morning SoC will give rise to earlier discharge of the battery and the use of more mains electricity.

Curiously, the optimum morning SoC for any individual year (30% to 60%) is quite different from that calculated from the average of all 12 years. This is because of reduced irregularity in the averaged data.

The difference between self-use calculated from data for individual years and the self-use calculated from the average data is even more striking if we show each year’s result as a fraction of that year’s total generation.

Click for a larger view. The graph shows the fraction of total solar generation (%) that would have been used on site for each year.

We see that we might hope to get around 90% of self-use in any individual year with a morning SoC of around 40%. This is much lower than the 98% which appears possible using averaged data.

Results: Economics 101

As I whiled away happy hours with Excel I became fascinated by different possible strategies. And I filled my head with clever calculations that I might attempt.

But then I realised that none of these strategies affects the carbon reduction I achieve by installing solar panels. This happens with or without a battery and is independent of the charging strategy I adopt!

  • What these charging strategies affect is who gets the benefit!

If I export electricity at low cost (1.8 p/kWh in the case of EDF) and am then forced to buy electricity later in the day for 23.7 p/kWh (EDF) then it is EDF who gets the benefit of my investment.

Financially, the optimum strategy arises from the differences between night-time and day-time electricity, and the price paid for exports. I have illustrated this for two ‘tariffs’ below – those from EDF and those from Tesla – who have a deal with Octopus.

Click for a larger view.

If I simply bought the electricity from EDF without solar panels, then the annual cost would be just over £1600.

The solar panels should reduce this cost substantially. The investment of £4200 in the solar panels should generate a saving of around £500/year, a 12% return on investment.

The battery should lower the annual cost much further. The savings generated by this £10,000 investment should be more than £800/year.

  • Using the EDF tariff, the big difference between the price of day-time and night-time electricity makes it always preferable to have a morning SoC as high as possible, thus minimising the possibility of ever having to use full-price electricity.
  • Using the Tesla tariff – the morning SoC doesn’t matter because there is no time-of-day price difference, and no difference in price between imports and exports.

But using either tariff, I calculate the savings to be massive. So large in fact that I just can’t believe them! The battery should be installed in March and I will let you know how it goes!

Of course I could also lower the cost by switching from EDF. I checked with Octopus energy (link) and it listed 80 different tariffs. Eighty! Enough for 10 octopuses to each have a tariff for each leg.  I absolutely detest this confusopoly. In any case the cheapest night time price was around 11p. Hopefully with the battery I will be able to subsist mainly on EDF’s night-time tariff.


So after all that work, I realised something very obvious but very profound. As I said at the top the article:

  • The triple-glazing and external wall insulation have been ‘green’ investments. They avoid the need to burn fossil fuels.
  • The solar panels have been a ‘green’ investment. They produce low-carbon electricity.
  • The heat pump (when I install it) will be a ‘green’ investment. It will avoid the need to burn gas to heat the house.
  • But the battery is a financial investment. It will actually use extra electricity! However, it will lower the cost to me personally of making the ‘green’ investments.

External Wall Insulation: How it’s done.

November 11, 2020

As many of you will know, I am having External Wall Insulation (EWI) applied to my house.

As closer confidantes will confirm: I am obsessed with the project. Why? Because based on my calculations, it is the single-most effective thing one can do to an old house to improve its thermal performance and reduce carbon dioxide emissions.

And yet very few people seem to be doing it. My hope is that by simply talking about it – and by measuring how effective it really is – more people will consider it as an option.

The idea of EWI is simple – “just stick insulating materials to the outside of a house“. But the reality of doing this reliably and leaving the house weatherproof and looking good is complex.

There are some nice videos out there, such as this one below showing the Be Constructive team working on a previous house. There are more videos here. And if you want details, then check out the extensive EWIPro Complete Guide (pdf) and all the materials are available at the EWI Store.

But partly for my own satisfaction I thought I would outline each step with pictures rather than video. Also, the video shows the application of expanded polystyrene boards and the procedure for the polyurethane foam boards that I have used is a little different.

So here is my description the process. There is a gallery of photographs at the end of the article.

Step 1: Preparation

The job began by protecting all the working surfaces – the patio and the front and rear gardens – with protective plastic, and then all the windows were covered with a transparent adhesive film.

For my house, the Be Constructive team demolished an old chimney which no longer had a reason for existing, and removed almost 2 tonnes of loose render from the side wall. So much render was removed that the wall had to be roughly re-rendered before they could begin applying the EWI.

They then moved the boiler exhaust, external electrical fittings and drain pipes to take account of the fact that the house was about to grow by about 120 mm in all directions. This stuff is rather tedious – but essential.

Next came the preparation of the outside walls and the painting of a ‘stabilizing primer’. This penetrates porous surfaces and binds them, creating a surface to which adhesive can stick. This is particularly important for some building blocks which can be quite powdery.

Step 2: Boarding. Kingspan K5

Next the team installed so-called ‘starter track’. This plastic support is screwed into the wall at the level of the first layer of insulating boards – usually just above the damp proof course – and makes sure the boards are horizontal, and supports them while the adhesive mortar dries.

Different stages in the application External Wall Insulation. Click for a larger version.

Normally EWI utilises either expanded polystyrene (sometimes abbreviated as XPS or EPS) or Rockwool™, and boards made from these materials are available in a wide range of thicknesses.

However I had asked to use a board made by Kingspan called K5. I chose this because I could only put about 100 mm thickness around the house – and for a given thickness, K5 will give the best insulation.

I limited the insulation to 100 mm because that amount would still keep the walls underneath the existing ‘soffit’ under the eaves. Also – if the insulation were much deeper – I felt the windows might seem to be too recessed.

Only 100 mm thickness of Insulating Boards would fit under the eaves of my house. Click for a larger image.

For some reason, 100 mm thick boards of Kingspan K5 were not available and so the Be Constructive team glued pairs of 50 mm thick boards together to achieve the required thickness.

The ‘double’ boards were stuck to the wall using several thick blobs of adhesive mortar. Using a big blob of mortar perhaps 10 mm deep allows the outer surfaces of the boards to be made parallel even when the underlying wall is not.

In my illustrations I have deliberately drawn the boards as being not parallel. In fact the Be Constructive team actually took a lot of care into making the final surfaces vertical and smooth. This is important because it is very difficult to compensate for this after the fact.

The boards are ‘overlapped’ at corners and cut to shape around windows and other architectural features. Any gaps are filled in with expanding foam.

Insulating Boards are overlapped at corners. Click for a larger image.

Step 3: Mechanical Fixing.

Once the boards are stuck to the wall and the mortar has set, the boards are mechanically fixed in place. To achieve this a hole is drilled through the boards and into the wall. Then a plastic fixing is pushed into the hole. Finally a metal nail is hammered into the plastic fixing which locks the plastic fixing in place – like a rawlplug – and holds the boards against the wall.

Using metal nails adds a heat leak directly through the boards: each fixture increases the thermal transmittance of the board by about 3%. However there is not much that can be done about that. It would be unwise to rely solely on the mortar or just plastic fixings.

Step 4: Base Coat Layers

Now the boards are attached to the wall and functionally insulating the house. But they are neither weatherproof nor attractive.

Preparatory stages in the application of weatherproof render. Click for a larger version.

So the next step is to coat the boards with an adhesive mortar (called a ‘base coat’) in which a glass-fibre mesh is embedded. This mesh is essential to prevent cracking due to building movement.

For polystyrene insulation this is a simple process: the boards are rasped to create a smooth surface; a layer of base coat is applied; the mesh is pressed into place; and then the mortar is smoothed. This forms a surface on which the the final render can be applied.

For K5 insulation, the process is more complicated because the surface of the boards should not be abraded. So:

  • First a thin layer of the base coat is applied to boards to create a smooth surface.
  • Then a second layer of base coat is applied into which the fibre-glass mesh is pressed.
  • Finally a third layer of base coat is applied to form a surface on which the final render can be applied.

The base coat also meshes with the corner and reveal ‘beads’, and with extra fibre-glass mesh placed around the corners of windows.

Step 5: And finally

And finally we come to the point where render is applied.

The render is a mixture of stone with a specifiable particle size: 1 mm, 1.5 mm or 2 mm , together with a mortar and a silicone polymer. It can be coloured in a very wide range of colours.

Additionally, my house will have ‘faux’ bricks called ‘brick slips’ applied to match architectural details on neighbouring buildings.

I’ll be sure to post pictures when we have finished.


Anticipated general look of the front of our house after rendering. Click for a larger view.

Photo Gallery – click for a larger version

Does it work?

But does it work? Well, of course it works! It would be physically impossible for it not to work!

The question isHow well does it work?“. And specifically, “Does it work as well I anticipated in my modelling?

These are complicated questions to answer definitively – and they are especially difficult to answer quickly.

I will not have a definitive answer until later in the winter, but I will explain how I will answer the question in a follow-up article. For now I will just tease you with the answer that the data look ‘promising’.

Keep warm 🙂

%d bloggers like this: