# What’s the “time constant” of a building?

Among the many parameters that play a role in the thermal behavior of a building, whether or not it is built to be a Passive House, the time constant is one of the least known ones.

Nonetheless, this parameter influences the way a building response to changes in internal and external conditions, and therefore it is has a very important role in the correct operation of the building and its heating/cooling system.

## Heat

The time constant is the result of the internal heat capacity of the building, divided by the average transmittance of the structures that build up their thermal envelope. In other words, on one side this value depends on the amount of heat stored inside the building, and on the other, on how much insulated it is.

This value has nothing to do with buffer tanks and/or electric batteries – a misunderstanding we run frequently into. If a building has a high time constant, it does not mean it can go off the grid – it has nothing to do with it.

The mass of the building that is “useful” in terms of time constant is the one in direct touch with the interior environment, up to 10 cm (about 4”), or up to (and not including) the first insulation layer from the inside (according to ISO 13786).

## Calculation

The time constant is calculated for the building as a whole, not for individual components (walls, roof, etc.), or materials. The very same sequence the materials are layered in the assembly of a structure has a strong effect on the time constant of the building. For example, in a masonry structure, having the insulation layer on the inside or on the outside of the bricks is going to dramatically change the time constant and the way that the building is going to react to changing thermal conditions.

### Example

Let’s take as an example one of the two passive houses of Cavriago: the external walls are built in heavy masonry, with the insulation on the outside:

Total heat capacity of the building: 21295,6 Wh/K;

Average transmittance of the envelope: 0,185 W/m2K;

Time constant: 190,5 h.

In case we had decided to build the very same building, using a timber assembly (either timber frame or solid wood panels with insulation), the result would have been very different:

Total heat capacity of the building: 10325,1 Wh/K;

Average transmittance of the envelope: 0,185 W/m2K;

Time constant: 92,4 h.

Which value is better? It depends on the use of the building!

## Weather

The higher the time constant, the longer it is going to take to alter the internal conditions, regardless of whether this change is driven by a sudden weather event or by the building system (1).

A high time constant is advisable, for example, in buildings that are used continuously throughout the year, with a constant indoor temperature: it’s the case of the primary residency home. Such a building is also going to be more resilient in case of extreme weather events.

For a vacation home, on the other hand, the situation is quite the opposite, because it is used only a few days a week. The same happens for schools, for example: in these cases, a high time constant may be counterproductive.

The time constant is a parameter that has a direct effect on comfort inside the building, and its influence can either be positive or negative, depending on the use of the building.

## Energy

As far as the total energy demand of the building, the effect of the time constant is limited. However, this parameter is part of the overall energy design, because it dictates the response time of the building to the change of external conditions, and to the operation of the heating/cooling system.

The decision regarding the type of structure (masonry, wood, or other), needs to be taken with consideration of the type of activities that are going to take place in the building: they dictate whether the optimal time constant is either “low” or “high”.

Note (1): although the time constant has an effect on how the building responds to the operation of its heating/cooling system, the amount of hours of its value (see example above) does not represent the time that the building requires to adapt to a new setting in temperature. In other words, if a building has a time constant of 200 hours, it does not mean that it is going to take 200 hours to heat it or cool it!

1. Thanks for this informative post! A few comments on the “dao of tau.” A long time constant (tau) is actually pretty useful for “thermal storage,” so it can help greatly with off-grid/renewable energy schemes. Secondly, the time to bring a building to temperature with its mechanical system is a function of the thermal mass (a factor in the time constant), not the time constant directly (i.e., a low thermal mass building with low conductance would respond more quickly to internal heat gains/losses than a high thermal mass building with higher conductance, but the same time constant.) The time constant is a measure of how quickly the interior of the building responds to a temperature differential between inside and outside. Lastly, thermal mass in a building with wide daily occupancy swings (like a school) can be pretty important to level the internal heat gains.

1. Thank you Graham, I think the time constant is often overlooked.

One change in PHPP 9 (but I might be wrong) seems to be that you can no longer customize the internal specific capacity, so you are stuck with 60 kKh/m2 – the equivalent of a timber frame house. This has no effect on the overall energy demand, and it plays “safe” on the overheating assessment. However, for our brick houses, the thermal capacity is around 140 kKh/m2!

You may also want to read our article on time constant and blackouts: http://emuarchitects.com/2015/02/16/the-blackout-proof-home/

2. I would suggest that the thermal mass of the air inside the building might have to be added to the time constant calculation. This is normally discounted because its heat capacity is so low, but it seems to me that three factors unique to passive house design might make it non-discountable:
1) up to 95% heat recovery of ventilation air exchanged,
2) very low levels of infiltration and
3) usually a large volume relative to the enclosing heat loss surface area.

Given the 20degC internal set temperature, the impact of thermal mass for buildings in constant use is entirely discountable. This may explain its apparent omission in PHPPv9. Thermal mass essentially only becomes important in calculating the time taken between comfort and over-heating (20degC and 25degC) and may therefore only appear as a slightly reduced solar gain or internal gain effect.

Buildings with intermittent, but highly predictable, use (like schools) can, as Graham suggests, be “tuned” to ameliorate overheating in the afternoon due to the effects of very high internal gains. Often ventilation is used in mitigation as it is the most rapidly responding of the various factors. In Ireland, we find that MVHR will run in by-pass mode in the afternoon even in winter, to balance out the internal heat gains.

I have not seen real data from PH schools, but some of our modelling suggests by-pass mode will be used every day, it will just kick-in at 9am or 4pm, depending on the external temperature. Needless to say, automatic by-pass is essential in those circumstances.

We find that additional cross ventilation (beyond MVHR in by-pass mode) is required in PHPP for Irish schools in all but the coldest weather. Making sure this is closed off during the morning warm-up period is critical to controlling heat inputs.

We have also modelled the effect of phase-change materials in Passive House buildings and find particular synergies between intermittent occupancy and PCMs inside a PH thermal envelope. These models indicate PCMs to be several times more significant than the thermal mass of concrete, for example, because of their active heating and cooling phases and the small temperature difference between comfort and over heating.

This is an important consideration as we begin to add embodied carbon to the construction budget: heavy masonry, particularly concrete, very quickly looses all of its advantages when a Passive House envelope with a very efficient MVHR system gets lined with even a small amount of phase change plasterboard.

PCMs act like a battery to passively store excess energy and release it when required

1. Hello Simon,
your point about time constant and heat capacity of the air inside the house is interesting.

If we take the smaller of the two passive houses in Cavriago, the heat stored in the structure of the building (incl. internal partitions, stairs, slabs) is about 23.200 WhK, with a time constant of 209 h.
The net volume of the building is 525 m3, with a stored heat of 173 WhK. If we add this to the total, the resulting time constant is 210 h, which corresponds to +0,5% from the starting value.

To correct my preliminary understanding of PHPP 9, the thermal capacity of the building is taken into account, as it is its time constant.
Thermal mass does not play a significant role in the overall energy performance for heating, where you have a steady state heat transfer. However it makes the environment more stable and resistant to changing temperatures, where the heat transfer is dynamic. This happens in summer, and in case of power outages. If you read the article on passive houses and black-outs, you can see why I think that masonry is not outdated after all.

To be honest with you, I am suspicious about PCM: I have not spent that much time on the subject, but I’d like to know what they actually are (salts?), and what their effect can be on health, end-use recyclability and so on. I am usually this cautious with any new material: our industry has an history for implementing new stuff, and then realizing it causes cancer (ooops!)

If you can send me any material you have on PCMs, I’d be happy to read it: info [at] emuarchitects.com

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