### U-Values

If you have been involved in a building project, especially involving Building Regulations, then you will have encountered U-values.

## What is a U-Value

Basically U-Values are a means of quantifying heat loss and are used to compare different construction designs and to ensure that a building is constructed with the required amount of insulation.

With global warming the thermal performance of buildings is becoming ever more important and they must meet statutory requirements as specified by the Building Regulations. These requirements are expressed as U-Values.

As time goes the scope of Building Regulations gets more detailed to include even the smallest projects. And if not at the design and build stage the energy performance of work will be assessed by the Energy Performance Certificate when the building is sold.

The information given below is an introduction to the subject but is also useful for illustrating topics throughout the rest of the site.

## A Closer Look at U-Values

First a recap on the units used.

Watts (W) - A measure of energy consumption (Power) or in this case heat loss. For example, a typical filament bulb would have an energy consumption of 60W which is converted to light and heat.
Metre (m) - Unit of length a little longer than a yard for those still using imperial units.
Kelvin (K) - Unit of temperature. Can be regarded as the same as Celcius for the purpose of heat loss calculations.

Now a look at the equations governing heat loss. Imagine a rectangular piece of material which is hotter one side than the other. Heat will flow from the hot side to the colder side which is determined by the following relationships.

• Heat loss (W) is directly proportional to the area. The larger the area the greater the heat loss. Units m2.
• Heat loss (W) is directly proportional to the temperature difference between the hot and cold side. The hotter or colder one side is the more heat will flow. Units K.
• Heat loss (W) is inversely proportional to the thickness of the material. The thicker the material the more insulation it will offer to the loss of heat. Units m.

Obviously materials conduct heat at different rates and this is expressed as conductivity. It represents the heat loss (W) through 1m2 of material that is 1m thick with one side 1K (1 degree C) hotter than the other with units of W/mK.

However, whilst conductivity quantifies the thermal characteristics of individual materials, another figure, the U value, is required to quantify the heat loss through building components e.g. a wall consisting of layers of materials. This is calculated by reference to the conductivity and also the actual thickness of the materials used.

For example, the heat loss through a single thickness brick wall (ignoring the mortar) consists of the insulating property of the air on the inside, the outside and the brick material. The U-Value for the whole wall can be calculated as follows.

Step 1: Calculate the resistance of each layer.

An air layer will only be quoted as a resistance. This is because it is a complex process of radiation conduction and convection. Therefore the simple relationships quoted above are not applicable.

To calculate the restistance of a layer it is first necessary to calculate the conductance of those materials with a U value. This consists of dividing the U-Value by the thickness in metres. The units of conductance are W/Km2.

The resistance can now be calculated by taking the reciprocal of the conductance (1/conductance). Effectively, this is producing a figure for the product of temperature and area that would result per Watt of heat loss flowing through the material. This, of course, is what is required because the heat flow through, for example, the layers of a wall will be the same.

Step 2: Add the resistance of each layer

The individual resistance values for each layer can now be totalled to achieve an overall total.

Step 3: Convert back to a U Value

The overall U-Value can be obtained by taking the reciprocal of the total resistance.

 Conductivity  (W/mK) Thickness(m) Conductance (W/m2K) Resistance (m2K/W) Inside Air Layer - - - 0.13 Brick 0.84 0.08 10.5 0.095 Outside Air Layer - - - 0.04 Total Resistance 0.27 Overall U-Value 1/0.27 = 3.77

As can be seen from the values below this is far above the required level for a wall so insulation is required!

## Target U-Values for Main Building Components

Building regulations allow for heat loss to be assessed as individual parts or as a complete construction. If the latter option is adopted it permits some elements to be over limit if others are used to compensate. e.g. better insulated walls if the windows are under insulated. However, the object of this site is to examine energy saving as individual topics and so it is instructive to look at the individual targets as expressed in the table below.

 Element U-Value (W/m2K) Loft space with insulation between rafters. 0.20 Loft space with insulation between joists. 0.16 Flat roof 0.25 Walls 0.35 Floors 0.25 Windows, doors and rooflights 2.0