## How much does it cost to run a 1 kW heater?

Here’s something terribly old-fashioned. It’s a three-bar electric fire. When all three bars on it is rated at 3 kW (3 kilowatts) but with only one bar, the middle one at the moment, its power is 1 kW.

I chose to check the power of the fire by using plug-in power meter. Here is the reading.

You can see it says 1061 W, that means 1061 Watts, just over 1000 watts, or just over 1 kW.

It is useful to know that a watt is a joule per second. If an appliance, like this electric fire, has a power of 1000 watts that’s exactly the same as saying that it has a power of 1000 joules per second. It means that every second the appliance takes 1000 joules of energy from the supply and, in this case, delivers it into the room, using it to raise the temperature of the room and make up for the heat loss.

Just for some fun, let’s calculate how many joules this electric fire takes from the supply in an hour.

The fire takes 1000 joules every second.

In 1 minute there are 60 seconds so this fire will 1000 x 60 = 60,000 joules.

In an hour there are 60 x 60 = 3600 seconds. So this fire will take 1000 x 3600 = 3,600,000 joules.

Here’s another way of working the numbers out. The power of the fire is 1 kW. When it’s on for an hour the energy it takes is 1 kilowatt x 3600 seconds = 3600 kilojoules. Yes, that 3600 kilojoules is the same as the 3,600,000 joules we have just calculated.

What we have done to calculate the energy supplied to our fire is multiply the power of the fire by the time for which it is on.
Energy = power x time. That’s a formula that is worth remembering.

There is another unit of energy, a convenient one, that we use when we want to measure energy. The unit is the kilowatt hour. Let’s use our new formula to calculate the energy drawn by our electric fire running for 1 hours.

Energy = power x time = 1 kilowatt x 1 hour = 1 kilowatt-hour, abbreviated to 1 kWh.

The kilowatt-hour, or kWh, is the standard unit for measuring electricity supplied. Indeed it is so standard that it is used for gas and sometimes other fuels as well. It is even often referred to as ‘the unit’.

At the time of writing, October 2020, energy from the electricity supply costs just under 15p per kilowatt hour and, to make numbers convenient, I’m going to use 15p as the price of a unit.

Our 1 kW electric fire uses 1 kWh of electricity every hour. And since electricity costs 15p per kWh, the fire costs 15p per hour to run.

What does it cost if it is on for a whole year.

In a day there are 24 hours. In a year there are 365 days. So there are 24 x 365 = 8760 hours in a year.

If our electric fire is on for a whole year,
Energy = power x time = 1 kilowatt x 8760 hours = 8750 kWh.

(If some of this is used to you, try saying the unit ‘kilowatt hours’ to get familiar with it.)

What’s the cost to run this fire for a year? Well each kWh of electricity costs 15p.
So 8760 kWh will cost 8760 kWh x 15 p/kWh = 131,400 p, which is £1314.

Quick trick for working out the cost for a year’s continuous use

Let’s just remind ourselves of where we have come to. A 1 kW fire, that’s a 1000 W fire, costs about £1300 to run all year. This can be used to provide us with a very useful figure to remember.

If a 1000 W electrical appliance costs £1300 to run for a whole year, a 1 W appliance costs £1.30 to run for a whole year. Remembering this fact is jolly convenient for calculating the cost of running all sorts of things that are on for a long time.

A modern middle-sized LED light bulb has a power of about 8 watts.
Remembering that a 1W appliance costs £1.30 to run all year, an 8 W led lamp costs 8 x £1.30 = £10.40 per year to run continuously. If it only runs for 3 hours, that’s an eighth of a day, then it costs £10.40/8 = £1.30 to run every day for 3 hours.

But an old-fashioned hot filament light bulb would need about 60 W for the same brightness. 60 W would cost 60 x £1.30 = £78 a year to run continuously, or £9.75 (£78/8) to run for 3 hours every day for a year (1/8 of a day).

How much does it cost to run our electric fire for an hour?

Just to remind ourselves, let’s calculate how much our 1 kW electric fire costs to run for 1 hour.
Energy = power x time = 1 kW x 1 h = 1 kWh. That’s pretty obvious but it’s worth remembering where it came from and how to check the calculation.
And, since energy from the electricity supply cost 15p/kWh, the electric fire costs 15p per hour to run.

Efficiency

This post is all about heating, so we are only going to consider heating appliances. It’s very easy to use electricity efficiently for heating. That electric fire is 100% efficient. That means that if it takes 100 joules in from the supply, it gives 100 joules out to the room. But gas heaters are less, sometimes a lot less, than 100% efficient.

The price of gas

Again at the time of writing, October 2020, gas prices are very low, less than 3p per kWh. That is in an economic climate in which much of the world is in lockdown and fossil fuel prices are really very cheap. A more realistic price long term price is nearer 5p per unit and I am going to use this as the figure for my calculations.

Gas fires

Gas fires are not nearly so efficient as electric fires as the following data will show. And, as we shall see, they are generally much less efficient when they are not on full output.

Here are the specifications for the above Flavel fire.

If your maths is quick, you might question have picked up something funny about these specifications. This fire gives 2.7 kW output for 6.5 kW input.
Efficiency = output/input = 2.7 kW/6.5 kW = 42%. This is much below the 56% that appears on the manufacturer’s specification. This is because manufacturers use what is called gross efficiency, a higher figure than the net efficiency we have calculated. This is explained later. For the moment we’ll run with the 42% efficiency.

If we turn this fire down a bit from 6.5 kW input, and if it has the same efficiency, (pretty unlikely because gas fires become much less efficient when used at low power), if the input is 2.4 kW, then the output is 2.4 kW x 42% = 1 kW. That’s the same figure as our electric fire. But to give out 1 kW heating the room the electric fire took in 1 kW. To give out 1 kW to heat the room, the gas fire needs 2.4 kW.

Where does the wasted energy of gas fires go?

If you’re a heating engineer, you’ll know the answer. For the average consumer it’s not so obvious what happens to the energy wasted by a gas fire. The answer is that it goes up the chimney and heats up the atmosphere. When your gas fire is on low, and taking 2.5 kW from the gas supply, 1 kW comes out into the room and 1.4 kW is wasted going up the chimney.

Hourly cost of a gas fire

On low, our gas fire takes in 2.4 kW from the gas supply (to give us 1 kW into our home).

Energy = power x time = 2.4 kW x 1 h = 2.4 kWh. Since gas costs 5 p/kWh, our gas fire costs 2.4 kWh x 5 p/kWh = 12p to run for an hour. Sure it’s a bit cheaper than an electric fire but not very much and, as we see later, gas fires are very inefficient at low powers and the real cost will be more than this.

More efficient gas fires

Here is a more efficient gas fire.

And here are its specifications:

Let us again calculate its efficiency from the input and output figures.
Efficiency = output/input = 4.0 kW/6.5 kW = 62%. Again you can see that this is more than the specified 66.8%.

You can see that this fire gives out by both radiation and convection. The fire has a box around the hot bits which air from the room can circulate through and take more of the heat from the burning fuel leaving less to be wasted up the chimney.

Let’s see how much it costs per hour to match the electric fire.
For 1 kW output it needs 1.6 kW input.
Energy input = power x time = 1.6 kW x 1 hour = 1.6 kWh.
With gas costing 5 p/kWh, the cost per hour = 1.6 kWh x 5 p/kWh = 8p.

Even more efficient gas fires

Here is Flavel’s most efficient gas fire.

Again let’s look at its specifications:

Calculating again the efficiency from the input and output figures,
Efficiency = output/input = 3.4 kW/4.5 kW = 76%, which is again below the 84% quoted by the manufacturer.

Again you can see that this fire heats the room by both radiation and convection. It has a box heat exchanger around it through which the room’s air flows, extracting more heat from the flame. But there’s another difference compared with the previous two fires. This fire has a glass front which restricts the amount of air going up the chimney. Excess air going up the chimney increases the losses to the atmosphere. The glass front massively removes this source of waste.

Let’s see how much it costs per hour to match the electric fire.
For 1 kW output it needs 1.3 kW input.
Energy input = power x time = 1.3 kW x 1 hour = 1.3 kWh.
With gas costing 5 p/kWh, the cost per hour = 1.3 kWh x 5 p/kWh = 6.5 p.

So an efficient gas fire would seem to cost less than half that of an electric fire for the same output.

Gas fires are very inefficient at low outputs

Here is detailed information about the Flavel Kenilworth High Efficiency fire discussed above.

You can see that at minimum heat output the efficiency of this fire is only 50% at low outputs. That’s the manufacturer beneficial efficiency figure. The net efficiency (the real one we have been using) is therefore about 45%. So to get 1 kW out the fire will take in 2.2 kW. This will cost 11 p per hour to run, not very much less than the 15 p for the electric fire.

If you have an inefficient gas fire, like the first on our list, at low outputs its efficiency may well be only 33%. So to get 1 kW out it will need 3 kW in. Therefore its running costs will be 15p per hour, just the same as an electric fire.

Is the 5p per kWh figure for gas fair?

Historically gas prices have been over 4p per kWh and my guess is that they will return to these levels. Your guess, whatever it is, may well be better than mine.

Why are the quoted efficiencies of gas fires always more than our calculations?

You will not be surprised to hear that manufacturers put the best spin on their figures. They therefore use an efficiency figure that makes their fires look as efficient as possible. Over the last 30 years they have moved from what is called net efficiency to gross efficiency.

When gas is burned, water vapour is produced. Gross efficiency assumes that the energy contained in the water vapour cannot be recovered, whereas net efficiency assumes that it can be recovered. In fact we know from condensing boilers that it is possible to recover energy from the water vapour produced when gas is burned.

Have a look at the (planned to be next on the list) post about condensing boilers and efficiency for full calculations of efficiency when the water vapour is allowed to condense.

## Best plasterboard fixings

This is a condensed summary of a useful but very long YouTube video, the link to which is at the bottom.

Four types of plasterboard fixing were tested. Here are the resulting weights held when a single one of each type was used to secure the top of a shelf bracket.

Cast aluminium screw-in, 12p (pack of 100) Screwfix, less than 10 kg.

Fischer UX6, 6p (pack of 100) Screwfix – 12.5 kg.

Gripit, 52p (pack of 25) Screwfix – 20 kg.

Spring toggle, 45p (pack of 20) Screwfix – 22.5 kg.

Easyfix Hollow Wall Anchors, 13p (pack of 100) Screwfix – 22.5 kg.
Note that a Rawlplug version is 30p each.

Further comment

On another YouTube video a variety of plasterboard fixings were demonstrated by a different method to the above. The results are below, but there is a pattern evident. There are fittings which are strong: wall anchors, spring toggles, etc. These are twice as strong as fixings that are weak: metal plasterboard screws, pretty much all the ones that get a good grip of a reasonable area of the back of the plasterboard are pretty similarly strong, but only 2 or perhaps 3 times the strength of those things that are obviously much weaker.

GeeFix £2.23 each Total failure weight in 12.5mm plasterboard was 125KG or 275Lbs Hollow wall anchors £0.50 each Total failure weight 109KG or 240Lbs Snap toggles £1.30 each Total failure weight 129KG or 284Lbs Blue GripIt £0.83 each Total failure weight 101KG or 222Lbs Snap toggles £1.30 each Total failure weight 129KG or 284Lbs Spring Toggles £0.54 each Total failure weight 176KG or 387Lbs Metal plasterboard screw £0.37 each Total failure weight 53KG or 116Lbs

Conclusion

Use the UX6 and put twice as many in. That gets you greater strength than any of the others for a price almost identical to the cheapest.

My own experience is that standard Rawlplugs, either the 6 mm or 7 mm provide quite a strong fixing in plasterboard provided that you drill a very clean hole with a normal twist drill (not a masonry drill because these give a more ragged hole). At 2p a time for the brown ones they are hard to beat but I am not aware of any strength tests.

## How Geohash works.

Geohash is a way of referring to any point on the earth with a single string of characters. It was invented in 2008 by Gustavo Niemeyer and GM Morton.

Geohash first splits the equator into 8 sections, each 45° of longitude wide. Then it splits the latitude into 4 sections, again each section 45° of latitude wide. This splits the world’s surface into these 32 regions.

These 32 regions are labelled, using the 10 digits 0-9 and 22 letters (omitting A, I, L and O).

It is easier to see what is going on if we draw these regions on the sort of flat map we are used to.

The single character Geohash reference 6 identifies much of Latin America. Australia spans codes Q and R and China is mostly code W.

For more precision we subdivide each of these large regions into smaller regions. Here we go down to level 2.

At level 3 you can see that Mysuru is in square tdn.

Precision

With 9  characters, location can be specified to just under 5 m, which is sufficient for most purposes. But with up to 13 characters, you can specify a location to within less than 5 mm.

How subdivisions are carried out

Level 1 splits a rectangular map of the earth into 32 rectangles 8 rectangles wide and 4 high. The splitting from Level 1 to Level 2 subdivides with new rectangles though this split is 4 rectangles wide and 8 high.

Subdividing from Level 2 to Level 3, the rectangles revert to 8 wide and 4 high. This alternating splitting is maintained throughout the levels. The result is that passing through 2 subdivisions a given area is split into 32 x 32 (ie 1024) subdivisions.

Z-shaped region labelling

Geohash regions are labelled in a Z-shaped order as shown.

This give the best fit in terms of closeness between the Geohash, (a one-dimensional structure) and the surface of the world (which is two-dimensional).

## QALocate

The QALocate system is a brilliantly simple way of referring to locations, buildings, routes and structures. At its heart is a way of identifying any point on the earth’s surface using a human-friendly sentence-like group of words.

For instance New York is xxxxxxxxxxxxxxxxxxx; London is xxxxxxxxxxxxxx, Tokyo is xxxxxxxxxxxxxxxxx and Delhi is xxxxxxxxxxxxxxxxxxx.

Qalocate can be as precise as you like. The front door of the white house is identified to within 150 mm by the phrase: xxxxxxxxxxxxx. If necessary locations can be expressed to within 5 mm by a seven-word phrase.

(This needs a link to a map where you can get to your location, click on it and produce a QAcode.)

The core of QALocate is simple to use and understand. It is open source, meaning that anyone can use the system completely free of charge. QALocate is mathematically simple, so translation to and from QALocate references is easy: coding and decoding software can incorporated into the simplest of electronic devices.

As well as identifying locations, QALocate comes with other powerful tools.

PointCodes, a “!” followed by up to 63 characters, the simplest way for anyone to refer to a location or structure.

StrutureLocator, a globally unique, alphanumeric identifier for every building and structure on the planet.

Location Naming System (LNS), turning human-friendly names to StructureLocators.

Waysette, a navigation app purpose-built for rideshare drivers.

How do four-word QALocate phrases work?

QALocate builds on the equally brilliant Geohash method of identifying points on the earth’s surface. (See our explanation of how Geohash works.)

The 9-character geohash for New York is dr5regw3p which identifies a square 4.7m x 4.7 m right in the centre of New York. (Should be specified.) For the populated regions of the world we encode this 9-digit geohash into human-readable form by splitting it into four chunks and encoding each as a word.

dr5        re         gw        3p

Man     bites    angry    dog.

The choice of noun-verb-adjective-noun produces sentence-like groups of four words that are easy for humans to communicate. The choice of words is such that minor inaccuracies common in communication do not affect the outcome: ‘men bit angry dogs’ translates to the same geohash because QALocate treats singular and plural as the same and every form of the verb as the same.

Encoding and decoding are both a simple process of looking up in a small group of tables to find the word that corresponds to 2 or 3 characters, or the 2 or 3 characters which correspond to a word.

Why do we need five-word phrases?

Four-word phrases cover the populated areas of the world but there are insufficient familiar words to cover the whole world with four words. QA locate uses five-word phrases to extend its coverage over the whole world, adding one of 32 adjectives to identify the first letter of the geohash.

Hairy goat eats thin camel.

Again the phrases are sentence-like and easy for humans to remember.

How accurate can QALOCATE specify

QALocate can specify to a precision of less than 5 mm by using phrases up to 7 words long.

Examples here.

What’s wrong with Open Location Code

Lift much of existing text.

Why QALocate beats What3Words.

Text required: no proprietary, only 7 lookup tables, similar codes are near and, generally, near things have similar codes.

Where does the Geohash come from?

Geohash first splits the equator into 8 sections, each 45° of longitude wide. Then it splits the latitude into 4 sections, again each section 45° of latitude wide. This splits the world’s surface into these 32 regions

It is easier if we draw these regions on, as we are used to, a flat map which represents the earth’s surface.

The single character Geohash reference 6 identifies much of Latin America. Australia spans codes QR and China is mostly code W.

For more precision we subdivide each of these large regions into smaller regions. Here we go down to level 2.

Here is level 3 and you can see that Mysuru is in square tdn.

With 9  characters, location can be specified to just under 5 m, which is sufficient for most purposes. But with up to 13 characters, you can specify a location to within less than 5 mm.

Geohash is a 32-base system. It uses the 10 digits 0-9 plus 22 alphabet letters, omitting letter A and the letters I, L and O which are easily confused.