Lesson 3. How to stop heat - Form factor

We now know from the first law that energy is heat, so the first step in low energy building is to lose less heat. So how do you stop heat?

The opening question has a very simple answer: You can't. The second law states that the heat will move from hotter to cooler, so sooner or later the heat will get through.

The universe is a casino, its currency is energy, and sooner or later we're going to lose it all.

You can't stop heat flow, but you can slow it down, and that is the basis of insulation. Intuitively we can guess that the amount of heat flowing through a wall is going to bigger if the wall is bigger. It's logical that doubling the area will double the heat flow. Also that doubling the thickness of the wall will halve the heat flow. Or at least it will take the heat twice as long to get through, since it has twice as far to go.  

It's also intuitive that a higher temperature difference between the two sides will increase the heat flow, and easy to imagine that twice the temperature difference will double the heat flow.

And then the material the wall is made of is going to make a difference.

These are all bound by Fourier's law. If you want to see the equation, you can google it. I'm not going to add it here since every equation added to a piece of text halves the audience. Luckily that is not holding true in my class, and so far the number of students seems to be holding steady, but there is always a chance that students will lose their energy over the course, and stop coming to class.

Fourier was also an accomplished mathematician and he apparently was into dimensional analysis. Applying dimensional analysis to his equation tells us that the units we need for thermal conductivity, the constant applying to materials, is Watts per metre Kelvin. You can see a long list of thermal conductivites here on engineering toolbox. The lower they are, the better they are at insulating.

Jumping straight in to our goal of low energy building, I decided we should try to build a house. This was just on paper, and we made a few assumptions. It was a cube with five-metre sides, insulated with 100mm of glass wool all around. It was going to be in Matsumoto in the winter, where it's zero degrees centigrade outside, and we want it to be 20 degrees inside. The building has no doors and windows, is completely airtight and is floating in air, so it's losing heat equally from all six sides. We worked out that this will lose heat at a rate of 1.2 kW.

This number has two significant implications. First, to keep the house at 20 degrees centigrade, we're going to need 1.2 kW of heating inside. Second, 100mm of glass wool is not going to be enough for a low energy building.

In the process of this, I told them about the U value, which is the heat loss per unit area, or the conductivity divided by the thickness of insulator.

Next, we went on to a couple more buildings, one a single-storied rectangle, the other single-storied and L-shaped. The rectangle lost more heat than the cube, and the L more still. 

This led me to form factor, which is the ratio of surface area to floor area. The most important area, as far as heat is concerned, is the surface area, since this is how it escapes from the building. Or if it is a hot climate, this is how it gets in. As far as the inhabitants of the building are concerned, the floor area is the important part.

For a given insulating material, and with the same desired heat loss, the thickness of insulation goes up with form factor.

We looked at form factors for a few more buildings, noticing that as the building get squarer and bigger, the form factor goes down.
Generally, the form factor goes down as buildings get larger, since larger buildings generally have more storeys, so the floor area is going up faster than the surface area. Below is a graph for an idealised cubic building with storeys two and half metres high. You can see it gets very difficult when you get very small buildings.

We looked at a few real buildings to consider their form factors.

The modern Tokyo mini-house and classic modular capsule block are not very impressive.

Nor is the typical Japanese apartment block with its balconies, rooms bulging out of a sensible thermal envelope and random sticky-outy bits of wall. Flying butresses can be excused on medieval cathedrals. Do we still need them now?

The Dome house in Miyazaki looks a bit better, but more about domes in another post.


My house is not too bad.

I also pointed out that the balcony on my house is separate to the structure, as you can see from the picture below before it was put on.

I'd hoped to say more about insulation, and what happens when we start using different materials together, but I was running out of time and that will end up in the next lesson.

There was time to show a picture of a lobster and a person and elicit some differences. The critical ones for our discussion are that Lobsters are cold-blooded and have their skeletons on the outside, while humans are warm blooded and have their skeletons on the inside. Not all cold-blooded animals have skeletons on the outside, but I think all warm blooded animals have theirs on the inside. There is no "list of warm-blooded animals with exoskeletons" on wikipedia, which I take to be conclusive proof.

The point is that evolution, with the wisdom of millions of years to try out designs, has decided this is the best strategy. Life is essentially a temporary defeat of the second law of thermodynamics, so when we're aiming at  low energy building we are wise to follow the lessons in biology and put the structure on the inside, and the insulation on the outside.

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The calculations above are all done with idealised pencil drawings as walls, and relatively simple physics. Real buildings are going to make most of these effects worse, since walls of finite thickness are going to reduce the floor area, and details in and around windows and doors are all going to increase the surface area.

Things will generally only get worse. Entropy is also at work in the design process. So it's a good idea to start a building with as small a form factor as possible

Thank you to Nick Grant for great lessons and some great shared slides on slideshare.net/ecominimalnick.

And to Elrond Burrell, bloggin here: elrondburrell.com