We met the architect again and he provided some information on the pipe insulation. There was some information on standard polybutene pipe from the suppliers, showing how low their pipes' thermal conductivity was compared with stainless steel or copper pipes (k = 0.17 W/mK cf 16 or 330). This is rather like boasting how tasty your coffee is compared with muddy water.

He also brought a sample of 10mm thick insulating tube that goes around 13mm pipe, and some composite insulated pipe. The advantage of the former is that the inside pipe could be changed without needing to change the insulation. These insulators had a conductivity of 0.043, probably made of polyethylene. They're usually used here for external pipes, which have electric heating elements along the inner pipes to stop them freezing in the winter. The insulated pipes cost about 800 yen per metre. He also talked about some super-high insulated piping that cost 30,000 yen per metre.

The idea of insulating hot water pipes still seems an alien concept, but to put it into perspective, running hot water in houses is a very new idea in Japan. In the usual mixture of very high and very low efficiency, until recently hot water has been created at or very near the source. Above the kitchen sink is a gas geezer, which produces hot water, up to near boiling. It has a pipe all of twenty centimetres long. The bath water is heated directly by a kerosene recirculating heater which is on the other side of the wall, again pipes very short. the longest pipes are perhaps from the gas heater to the shower, which is on the other external wall of the bathroom. Even then, the pipe may be a little over a metre in length. In terms of layout, houses are designed by adding rooms onto each other, rather than rooms being filled into an overall structure. Bathrooms, and even kitchens, are not traditionally considered as part of the house; there's a sense in which they are separate rooms that have been added onto it, although kitchen-living-dining rooms have become quite common. In houses, Japanese lavatories always have a pair of slippers in them, and I believe this is because toilets are traditionally considered to be outside, so you need to put shoes on to go there. (I have to confess that most Japanese people think this idea is rather strange, but they have probably never stopped to consider the humble toilet slipper, any more than people in England have stopped to wonder why they put milk in tea.)

Until recently Japanese buildings have avoided the inherent inefficiency of central heating and hot water being generated in one place and distributed far and wide, but the recent propagation of the Eco cute atmospheric heat pump boilers means that hot water pipes are getting longer and longer, and awareness of the issue needs to increase if the Eco is going to reach the house-owner and environment rather than just staying as money in the bank for the manufacturers and electricity companies. At the moment heat loss in hot water pipes seems to be off the radar, languishing in the zone of apathy and ignorance.

Anyway, I did some calculations, and using the 13 mm polybutene pipes under the floor will mean a heat loss of 100 Watts per metre. In other words, whenever we are using hot water, it's like switching on a 100 Watt light bulb for each metre length of the pipe. To the kitchen, the pipe drops about three metres from the boiler upstairs, then meanders three metres under the floor, and climbs another metre to the sink. If we assume a very minimal ten minutes' hot water use per day, and ignore losses from what's left in the pipes each time it is turned on or off, then we will lose 42 kiloWatt hours per year. Similar calculations for 30 minutes' hot water per day going to the washing machine lead to 126 kWh per annum.

Pipes with 10mm insulation will lose around 7.5 W/m. If we ignore the pipe space under the floor and save two metres on each length by sending the pipes across the ceiling and down the wall, and use higher insulated pipes, we get the losses from the kitchen down to 2 kWh/a and the washing machine to 5.4 kWh/a. Seems worth it.

For these calculations, I'm assuming hot water at 45 degrees centigrade, and a temperature difference of 25 degrees to the 20-degree room temperature. I think 45-degree water should be hot enough. It's usually set much hotter, which just results in more waste. Thankfully, no hot water pipes have been installed for the basins by the lavatories, perhaps unthinkable in Europe, but another plus for Japan's eco-credentials.

The architect had brought another sheet of paper with a list of insulated pipe materials and thicknesses, the thermal conductivity (熱伝導率

*netsu-den-do-ritsu*) in W/mK and what it called 熱貫流率 (*netsu-kan-ryu-ritsu*), the coefficient of overall heat transmission, which it gave in mK/W. Generally speaking, any given material has a thermal conductivity, which is some indication of how good it is at conducting. When it gets below 0.05 it's insulating fairly well, although there is no magic number at which something becomes an insulator and stops being a conductor. Wood is around 0.17 W/mK, and anyone in a log house will tell you that it's quite warm, if the walls are thick enough. Of course, even insulators conduct--just not very well. There are no perfect insulators (except a perfect vacuum) any more than there are perfect conductors.Once a material is made into a wall, a pipe, a fur coat or some kind of structure, that combination then has a coefficient of heat transmission. For flat surfaces, this is usually given in W/m2K and called a U value or U factor. It shows how much heat will flow through the surface for each square metre, for each temperature difference of one degree. For pipes, this is given in W/mK, as we're not so interested in the area of the pipe, just its length. Rather confusingly, the units for thermal conductivity of materials, W/mK, are the same as those for pipes.

Whoever had produced the sheet of paper with the figures for pipe insulations had evidently not appreciated this, and for a start had got the units for coefficient of heat transmission upside down, mK/W. They had put a note at the bottom saying that it was a measure of how easily heat passed through the pipe which was correct. Whoever had made it had simply divided the thermal conductivity by the thickness of insulation, and come up with a number with scant regard for the units, dividing W/mK by metres, and getting mk/W. Obviously never heard of dimensional analysis.

Newton worked out that heat flow was proportional to surface area and temperature difference, and inversely proportional to thickness of material, and thermal conductivity is the heat flow per area, per temperature difference for a unit of thickness. To get to the heat transfer coefficient (U value or U factor) for a flat surface, you just have to divide the thermal conductivity by the thickness. (So if you had a wall of polyethylene one metre thick, it would conduct heat at 0.043 W/m2. The best natural insulators are around this level, so if you're aiming for 0.15 W/m2, your wall needs to be about 30 cm thick.)

For pipes, the picture is a bit more complicated as the surface area gets bigger the wider the pipe is. We have to use calculus, another of Mr. Newton's tricks, which should also be credited to Leibniz, and take the integral--the last recourse of the mathematical scoundrel. This gives us the equation:

Q = 2 pi k L (T1-T2) / ln(r2/r1)

Or U value for the pipe (in W/mK) = 2 pi k/ln(r2/r1)

Where:

k is the conductivity of the pipe material,

r2 is the external radius (half the diameter)

r1 is the internal radius

T1 is the internal temperature

T2 is the external temperature

ln is the natural logarithm.

pi is π the ratio of the circumference to the diameter of a circle.

You can use Google as a calculator and put in something like (2 * pi * 0.17 /ln (0.0085/0.0065)) and it will understand and know what to do. Isn't technology wonderful!