One dimensional thinking

[tonyshouse]

We can view plans in three dimensions, model buildings in hyperspace and take virtual tours.

Yet we continue to calculate heat losses in one dimension.

As insulation gets better the proportion of heat lost through thermal bridging increases, no one cares much.

[TerryE]

Tony,  a serious response to what I think is a serious point.  1D models have reasonable analytic approximations and can be numerically solved with some economy.  With 2, 4 and 4 (time) D models the computational burden rises by orders of magnitude with dimension.  Yes they can be solved but is the solution understandable?  Is the input data set sufficiently accurate to merit the extra complexity?  In a well designed passive style house such as the cellulosic filled Larson strut filled frame with a decent insulated slab then a 1D model will get within 10-15% of a decent 3D model, and at the same time the 1D approximation makes it easy to understand the forcing factors. 

Yes, as you improve the U values of your surfaces then the linear elements are a more important component, but IMO the issue here isn't modelling them, it is understanding the vulnerabilities and preventing them in the first place by design. 

If I look at our house, then the major design cock-up was nothing to do with the wall or ceiling make-up or 1D vs 2D modelling assumptions, etc.. It was that we have an external stone skin so Hillard, MBC Structural Engineer, made a simple mistake (IMO) which solved a structural problem but at the same time created a huge thermal bridge between the slab and the outer ring beam.  OK, I spotted this in time to put  a mitigation in place: that is by leaving the EPS300 slab framing in place and adding a layer of Foamglas Perinsul blocks between the slab and the stone skin, but this detail would have killed the performance of the slab if left unmitigated.  Hopefully this won't be a solution for future builders in my position because Hilliard and I have discussed the best ways of avoiding this vulnerability in future designs which require a stone skin.

The more spherical (blockhouse-ish, whatever) your house is then the more that the 1D model approximation dominates true life performance.  Yes it is a terrible approximation if your house has many facets / reentrants, but the fact is that building this way might look architecturally interesting, but the real thermal performance is going to be crap however you model it. 

[SteamyTea]

I will go along with that Terry.

When you are dealing with 3 or 4 dimensional models, you are usually only interested in the extremes, like corners, points and rapidly changing temperatures.  Now a house has very little of these in reality and can be dealt with by observational measurements i.e. periphery to area ratios, rather than semi-infinite partial differential equations.

As an example, if we take all the corners between a floor and the walls of a small house (4m by 10m), and assume that there is a 3mm radius between them, then the ratio of areas is:

Floor Area 4 [m] x 10 [m] = 40 [m²]

Periphery (10 [m] x 2 + 4 [m] x 2) x (0.006 [m] x 3.14/4) = 0.1 [m²]

40 [m²] / 0.1 [m²] = 400

So you lose 400 times as much energy from the floor than you do the corner for the same thermal conductivity and temperature difference.

If you make the house twice as wide, so 10 [m] x 8 [m] the ratio changes to 470, so the corner is even less important.

[Jeremy Harris]

For a conventionally insulated house (i.e. just meets building regs) then geometric cold bridging can be significant.  The more corners you have on the outside shell the worse it gets..

It's not so much a major heat loss problem as one of creating cold spots in areas where air movement is already impeded by the geometry.  One consequences is condensation and mould in these areas.

The problem is that near an external corner heat flow from a single point on any surface ceases to be perpendicular to the wall, floor or ceiling, but has a mix of several heat loss directions; directly out perpendicularly, and at an angle out through the adjacent surfaces to outside.  The result is a great heat loss from points near a corner than in the centre.

[SteamyTea]

You can work out the mean shortest length of the thermal paths with Pythagoras for a 3D shape easily enough.

A² + B² = C² for 2D

A² + B² + C² = D² for 3D

A² + B² + C² + D² = E² for 4D (so includes time)

Edited June 22, 2016 by SteamyTea

[TerryE]

14 minutes ago, JSHarris said:

It's not so much a major heat loss problem as one of creating cold spots in areas where air movement is already impeded by the geometry.  One consequences is condensation and mould in these areas.

The problem is that near an external corner heat flow from a single point on any surface ceases to be perpendicular to the wall, floor or ceiling, but has a mix of several heat loss directions; directly out perpendicularly, and at an angle out through the adjacent surfaces to outside.  The result is a great heat loss from points near a corner than in the centre.

Yes, the issue isn't that you are losing an extra 30W of heat along a linear feature such as the centre column in a corner window. This isn't a great variation to the total budget in the grand scheme of things; it's that this heat loss occurs in a very small area and this can result in a surface temperature that is below the dew point for the house's absolute humidity, with this acting as a condensing surface. A local surface temperature drop of a few degrees won't be a problem. One of 10° or more will be.

[tonyshouse]

This is the exact problem that I am thinking of when we are talking about two and three dimensional models.

low surface temperatures are fully predicted by models and orders of magnitude in calculations make little difference for computers.

[TerryE]

OK, I think that we agree on the issue, but maybe diverge on labelling it.  In my view it would be extremely difficult to model this stuff in 2 or 3D.  I would describe this more as understanding the limitations of a 1D model and therefore where the assumptions that underpin the model start to fail materially.  External corners; window and door framing, etc.  But the failing here might not be modelling ones but engineering ones -- for example slab PUR has excellent U values so long as there aren't any convection gaps which will allow air to circulate back-to-front and pump heat out of the house bypassing the beautiful insulation barrier, or in my slab where 230 ×  20mm rebar has the same thermal conductance as 8" of continuous concrete   

[Jeremy Harris]

It really comes down to whether or not it's worth modelling things like corners.  Geometric cold bridging has a very significant impact for houses with only moderate levels of insulation - our current house is a very good example, the upper North-West corner of our bedroom regularly gets mould, just because there are two external walls (with only ~50mm of bonded EPS bead CWI) and a loft with around 250mm of rockwool.  The temperature in that corner is significantly colder than the rest of the walls, several degrees colder in very cold weather, and that's entirely due to the geometric cold bridge.

However, if you increase the insulation level then that usually means increasing the thickness, and this increases the additional heat loss path length in corners significantly, so the impact of geometric cold bridging is reduced.  I've been around with my thermal imaging camera and cannot see any temperature difference at all in any corners, the only place I can see small (around 1 deg C or so in very cold weather) internal surface temperature differences are around window and door frame edges, where despite my best endeavours there is still a greater amount of heat leakage than there is through the glazing.

So it may well be worth doing 3D modelling for a poorly insulated house, but almost certainly isn't worth the hassle for a well-insulated one.

[SteamyTea]

1 hour ago, JSHarris said:

So it may well be worth doing 3D modelling for a poorly insulated house, but almost certainly isn't worth the hassle for a well-insulated one.

Yes, it is the old stats saying, "is the problem a big one'.

[Alex C]

It is possible to model 3d junctions, and has to be done if you want passivehaus certification,but I think the reality is that it is a fairly pointless exercise on a well insulated new build and satisfies no one other than mr passivehause. What is far more important is having a basic understanding of what a cold bridge is and how to design them out. I think that it is a worthwhile exercise drawing sections through junctions such as where steels meet on a wall to double check that there is not an accidental cold bridge, rather than know what the psi value for it is. I have spoken to at least one person with a well insulated house that has ended up with some accidental thermal bridges that could have been designed out if spotted sooner.

[tonyshouse]

A model would show it up visually without the need to think about it.

[Alex C]

You have to think about it to create a model in exactly the same way as you have to think about it to draw a 2d section. It does not matter how you do it, as long as you actually put some time into thinking about it from a thermal bridge point of view. This is from someone that has spent the last 25 years building 3d models and 2d cad drawings as both a product and commercial interior designer.

[SteamyTea]

Yes, I would have thought that creating the model nodes is harder that just doing it right in the first place.

You can download LISA and play about with the thermal modelling.  Not the easiest program to use, and the free version is limited, but you can get a feel for what is going on in a corner.

Or just start sketching it up on paper and measure the distances, then use a spreadsheet to work out each path (say separated by 5°).  Or work it out as a cone.