Geekspeak: Why Life + Mathematics = Happiness

is the temperature of gases in the cylinder just after it has fired, and T

is the temperature of the same gases after they have forced the piston down and are pushed into the exhaust pipe. The formula will give you a wastage figure of 60–70%; the same limit applies to the turbines in coal, gas and nuclear power stations. The clouds you see billowing out of the big towers at power stations are not smoke: they are formed from hot water vapour carrying away the percentage of the fuel’s energy that is wasted as heat.

3 (#litres_trial_promo)

SAFE AS HOUSES

How heavy is your house?

Nowadays we all want to live in our own space. Children leave home in their late teens and want a place to live; newly-weds don’t expect to camp with their in-laws; successful people want houses with offices, double garages and kitchens the size of a canteen.

Dealing with these changing demands requires new houses, and making the materials for building them takes a lot of energy. Oft-cited examples of energy profligacy –flying from London to Birmingham, leaving your TV on standby – pale by comparison.

There is a simple reason for this: building materials such as metal and bricks and concrete that are preformed into a useful shape are normally processed using heat. Heat means energy, energy usually means burning something which is often carbon based, and that means CO

emission.

Take concrete. There’s probably tonnes of it under you as you read this book. The key ingredient of modern concrete is cement, a processed form of limestone and ash. Mix it up with some water, sand and stones, pour into a hole in the ground, and wait a few days. The slurry changes into a solid of enormous compressive strength that will support a tower block or a motorway bridge.

It sounds benign. But note that word ‘processed’ preceding ‘limestone’. The limestone has to be heated in a furnace at the cement factory to change it into a substance that will combine with water to form solid concrete. The furnace is fired by a fossil fuel, usually gas or coke, and releases CO

. Worse still, heating causes a chemical change in the limestone which releases even more CO

from the stone itself.

Manufacturing a tonne of cement pumps about three-quarters of a tonne of CO

into the atmosphere. That’s the

amount of CO

produced by burning 204 kg of carbon. If you had to go and buy the carbon as sacks of coal from your local shop, they would fill all the seats in your car, leaving only room for you to sit in the driver’s seat.

The story is similar for bricks. Brick is made from clay which is fired in a furnace to make it strong and hard. Lots of energy goes into the furnace to get a usable building material, although with bricks there is fortunately no release of CO

from the clay itself.

Lightweight blocks are better. They’re often made by taking the ash left over from burning coal at power stations and mixing it with a little cement and water. The mixture is then frothed up with air and poured into moulds to set. The blocks contain a lot of air bubbles, and just a little cement, which makes them much better than concrete in terms of expended energy. Lightweight blocks are true to their name – throw a dry block into water, and it will float.

But not all blocks are problem-free. Coal contains small quantities of uranium and thorium. Burning coal in a power station concentrates the radioactive material into the ash that goes into some building blocks. That makes them a little radioactive. Fortunately the level is very low, similar to the natural background from the slightly radioactive rocks in parts of Cornwall and Scotland.

Wood is used all over houses. It’s light and cheap, and is ideal for structural components such as the rafters and joists that support roofs and floors. It can be shaped by a hi-tech, computer-controlled wood mill in a factory, or by a man with a half-inch chisel and wooden mallet. Most appealingly, it requires little energy to get it to its final shape.

The wood in a tree is made almost entirely of the chemical elements hydrogen, oxygen and carbon, the last two of which come mostly from CO

absorbed from the air around the tree. A solid tree has been made literally just from thin air and water.

A living twenty-metre pine weighs up to a tonne, so each tree ties up a lot of CO

. You might think that building with timber would deplete this natural CO

sink. But take a walk around the timber yard at your local builder’s merchant. You’ll see that the timber has its place of origin stencilled onto the side of the stack and the ends of each piece of timber. This is often the name of a Scandinavian or Baltic country, such as Sweden, Finland or Latvia. Those countries plant more trees each year than are felled, so using their timber encourages reforestation.

What other materials are used in building a house? There is lightweight stuff like copper cables and pipes for the electrical and water systems. Making copper uses energy, but the copper in your house doesn’t weigh much so it doesn’t contribute much to the building energy account. That isn’t to say that it’s cheap: in 2006 the cost of copper doubled because of the frenetic industrial development in China. Some small shops no longer sell electrical cable because it’s too difficult to track the rapidly varying price.

The last significantly heavy and energy-intensive material in houses is steel. There may be steel reinforcing rods in the concrete foundations and in the cast concrete lintels over windows and doors. Sometimes steel beams are used to support floors and roofs.

Steel is no exception to the rule about heavy processed materials using a lot of energy. Changing iron ore into iron and steel requires heat. Most of that heat energy comes from coke and electricity. To produce 1 tonne of steel from ore takes about 3,000 kilowatt-hours of energy. That’s the energy you would get by burning about half a tonne of coal; if you had solid-fuel central heating, it would keep your house warm for a month or two in winter.

The weight of a house is a good indicator of the energy used in its construction. So, how much does your house weigh? The answer will be about 100 tonnes, with two-thirds of that in the form of energy-intensive concrete and brick.

But how do you go about weighing your house? You could use a tape measure to get accurate dimensions and then work out the weight of each bit. But it’s more comfortable to close your eyes, hold an image of your own house in your mind, and do some rough estimating from your armchair.

A useful mental tape measure is the length of a car. A car is 3 to 4 metres long, so judging how many cars could be parked along a wall provides an instant way of estimating the width and depth of a building. A similar mental trick to get building heights is to visualise how many men 2 metres tall would need to stand on top of each other to reach a given point on the building.

Start by estimating the outside dimensions. You might be able to park three cars bumper to bumper along the front of your house, and two cars along the side. That would make the front about 9 metres long, and the side 6 metres.

The height of the walls will be about the same as two and a half men standing on each other’s shoulders. That would put the top man’s waist level with the guttering, making the wall height 5 to 6 metres.

Now, with all the measurements in your head, the weighing can begin. Most houses are built on strip foundations of concrete. The strips are laid under every load-bearing wall in the building – the external walls, and also probably a dividing wall running up alongside the stairs.

The concrete is poured into foundation trenches about 1 metre deep and 0.6 metres wide, and its thickness will be at least 0.25 metres. Putting those numbers together, it’s safe to say that at least 1 cubic metre of concrete is used for every 6-metre length of foundation strip. So, if the total length of load-bearing wall in the house were 42 metres, the volume of concrete in the strip would be 7 cubic metres.

That’s not the end of the concrete. The entire ground area of the house within the footings will be covered with concrete to form a base for the floor. On top of that are waterproof membranes, thermal insulation and a cement screed, making the total concrete thickness in the floor about 150 mm. Its volume is the total thickness multiplied by its area, typically 8 cubic metres. That makes about 15 cubic metres of concrete in total, with a weight of about 30 tonnes.

Then there are walls. Modern houses have exterior cavity walls. That means an outer and an inner layer separated by a gap of around 60 mm. The gap helps to stop heat from escaping through the wall, and nowadays is usually filled with thermal insulation. The outer layer is often made from brick, and the inner layer from lightweight block. It’s normal building practice to use blocks for the internal walls, so we’ll count them separately.

The weight of the bricks is the number of bricks times the weight of one brick, which is typically 2 kg – the same as a couple of bags of sugar. The number of bricks in a house depends on the size of the brick, and to get the number we need to work out the area of the house walls and the number of bricks needed to make a square metre of wall.

Strangely, brick size varies from country to country, and in Britain it has even changed over time. In fact, British bricks have grown. For example, the brickwork in Hampton Court Palace looks a bit odd to our modern eyes: the bricks are only about 50 mm thick, whereas modern bricks are about 65 mm thick and 225 mm long. That works out to about 60 bricks in each square metre of modern wall.

The area of the average external house wall is about 150– 200 square metres, so with 60 bricks per square metre you’ll need around 10,000 bricks, with a total weight of 20 tonnes. That brings the weight of the house up to 50 tonnes.

The internal walls and the inner layer of the external cavity wall are made from lightweight blocks. The area of these walls depends on the layout of the house, but you won’t go far wrong if you assume that the house is divided top to bottom by three internal walls running from back to front. The total area of those walls plus the inner layer of the external cavity wall will be about 250 square metres.

There will be about ten blocks per square metre of wall, so the house uses about 2,500 blocks. Each block weighs about 5 kg, giving a total weight of 13 tonnes (rounding up to the nearest whole number). The total weight of the house has now reached 63 tonnes.

Now, in your mind’s eye, climb up on the roof and have a look at the tiles. They might be slate, clay or concrete. Many modern houses have concrete pantiles, but you’ll have to check your own roof. A rule of thumb is that there are about 25 pantiles per square metre of roof, each weighing 2 kg; that’s 50 kg per square metre. If the roof were flat, its area would be the same as the ground area of the house, but real tiled roofs have a pitch angle of at least 30 degrees to stop rain from blowing up under the tiles. That puts the roof area up by about 25%, to around 70 square metres, and the weight of all the tiles will be about 4 tonnes.

To complete the picture, you need the weight of timber and steel. Most big pieces of timber in a house are used for the floor and joists and roof rafters. They are usually spaced about 400 mm apart, so if you know the length of the house, the number is easily calculated. A figure of 30 is typical. The sizes of the joists and rafters range from 150 × 50 mm to 250 × 50 mm. Taking an average figure gives a volume of wood of about 6 cubic metres, which is about 5 tonnes in weight.

Lastly, there’s the steel. The amount of steel in a house depends on its design. Some houses use almost none; others use steel in place of wood and concrete for structural components, or for reinforcing the foundations. It’s quite easy to use 1 km of steel reinforcing rod in a complex foundation, so adding a couple of tonnes to the total weight of the house would be fair.

Altogether, the total weight of the house stands at 75 tonnes. But every builder knows that more material is needed than we have so far counted. It’s something to do with the fiddly corners, stubs and overhangs that aren’t shown on the drawings. Increasing the weight estimate by at least 25% will not be too much. That gives us a grand total for the house of around 100 tonnes.

So, if you’re now alarmed about all those carbon-killing building materials, you may be wondering how many holiday flights could you offset by living in a tent. We’ll make the numbers easy by assuming that your house has the equivalent of 50 tonnes of concrete in its structure. Making the concrete will release around 37 tonnes of CO

into the atmosphere. That’s the same as 37,000 kg.