This is an offshoot from Hal's thread on the need for better classification of radiant barriers:

I didn't want to drift on his, so I have started new.

Using the sciences to our advantage.

I have a camp in the planning stages (similar to David Meiland's question on the cost of rigid foam insulation), on posts and enclosed on the bottom.  Here's David's

Mine is a heating dominant climate as well, in Maine and close to water, thus the posts will provide a better view and some protection from seasonal high water on rare occasions.

Having a living space over a cold space is a frequent problem in cold country and often results in cold floors.  Overhangs, porches, a bedroom over a garage and yes, my proposed camp are all examples.  But all of these have one design consideration in common, the warm is stacked over the cold, a configuration that does not support convection.  IMO, warm over cold needs some careful consideration.

Of the three modes of heat transfer, radiant, convection, and conduction, any time we can shut one or more down, we have reduced some major paths for heat transfer.  Now, picture the floor of my camp design, foil under the flooring, I-joists, and air sealed cavities with no insulation.  That's no insulation.  There will be some conduction via the bridging and some radiant transfer from the upper portion of the I-joist (which could be detailed with some foil as well), but no conduction through the cavity, virtually no radiant transfer, and because the warm is stacked over the cold (almost) no convection.  Add to this that any heat that does migrate down and warm the cavity air, the resulting convection would move the warmer air back to the top of the cavity.  It's ironic, but filling these cavities with fiberglass could increase my heat transfer as air is a very poor conductor of heat.

The benefits of warm over cold are not new as our cooling climates benefit from it when the ac is running.  Warm attic air does not migrate down to displace the cool air buried under our insulation.  In a heating climate, that cold air we vent into our attics goes directly to the lowest point it can access and pushes any warm air it finds up and away. 

Instinct says the floors will be freezing, but I can't identify the heat loss path.  And if there is any benefit to adding a radiant barrier to the underside of these floors, even with just a small air gap and lots of insulation, I'd like to be able to calculate it.

All comments are welcome, I think.


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Hi John, interesting, but you are going to have to help me out with the units and set-up.

1. a & R what are they?  I assume a = U-value and R = R-value, but are they per inch or per the gap specified.

2. Do they indicate where the Al coated paper is placed, top or bottom?

In an application where the air can circulate for other reasons, windows, walls, the net conduction of air would be larger.  If the cavity is sealed and there is no other heat input to create convection, then I'm anticipating very slow heat transfer.

I am going to build a test unit to get an idea as to fact or fancy.  I have a small refrigerator to create a lower cold temperature and I can enclose a known heat source above it.  If I adjust the heat source to where the chamber at the top stabilizes at room temperature, then all heat generated should be close to what is going down through my assembly.  Zero delta t to the room and about 30° delta from top of floor to cool cavity below.  Pretty simple and although there are some edge concerns it should set a lower limit on the R-value.  Any thoughts?


Bud, Here is the top half of the page.....

I don't see an indication of the aluminum coated paper being on the top or bottom

I assume values are per the gap specified

I still haven't sorted it out and I can't get into that link.  If you Google the thermal conductance of air you find some different numbers, but they are all rather good, like 0.024 W/M K° which converts to a U value of about 0.014.  That's an R-value of 72.  Lots of variables, but I don't see air having the same R-value as concrete, R=1 per inch.  I suspect those R-values are per inch.  We also have to be careful they are not "other than" the English version we use.  Canadian R-values are not always the same as ours.


Correction, it takes an entire 8" concrete wall to get an R-value of one.  But here is a better example.  We have all experienced the heat from a hot surface and then something similat covered with a radiant barrier.  With no RB, we feel the radiant heat AND the heat that conducts directly through the air.  However, when we test a hot surface with a RB, no heat.  That's because the amount that can conduct directly through the air with out radiation is very small.

Another comparison would be fiberglass insulation, which has a lot of air space.  Glass is a good heat conductor.  So remove the glass and all you have left is air.  block the radiant transfer and naturally suppress the convection and you have a better insulator than fg.


Air has poor thermal conductance but only if it's dead air, since convection quickly undermines its effectiveness as an insulator. All thermal insulations are merely materials that trap dead air.

The layer of air on the inside surface of a window will offer R-0.68 but there will be no additional benefit from the many feet of air inside the room.

Thanks Robert for commenting, but I remain optimistic.  The air inside a window and inside a room will definitely be dominated by convection and radiant heat transfer.  But in a horizontal application with the warm layer on top and the cold on bottom the dominant heat transfer will be bridging via the floor joists with some radiant bouncing around.  However, as heat conducts through the joists it will heat the air adjacent which will in turn move away from the cold surface below.  The final, somewhat, stable condition will be a thermal gradient from warm to cold within the air, similar to the warm to cold gradient that will develop within the joists.  Once the air and adjacent wood are at similar temperatures, there should be very little convection.

I will post after test, good or bad, as applications like this, with or without some insulation can benefit from a RB at the upper warm surface.


Yes, but almost all the temperature gradient will be through the flooring and through whatever material encloses the bottom of the cavity, with the enclosed air space equilibrating at approximately the mean temperature between inside and out.

The enclosed air space will find a thermal equilibrium due to the thermal diffusivity of air, which is quite high.

You will not get much better than about R-4 in this application, you will consume a lot of heat, and whether the floor feels cold will depend largely on the thermal conductivity of its surface - but it will not be a warm floor.

Robert, you are saying that the thermal diffusivity of the air will result in a similar temperature from top to bottom of the air cavity.  So how does this differ from the thermal conductivity of air?  Just thinking out loud, but if air is a poor conductor over a small gap, it should be a poor conductor over a large gap, assuming the warm over cold set up is suppressing the convective forces.

If I may ask, how are you using the foil to get your assumed R-4.  Foil under the sub-floor, an air gap, and then some form of insulation??


Thermal diffusivity is thermal conductivity divided by volumetric heat capacity (which, itself, is specific heat times density). 

Thermal diffusivity is the measure of thermal inertia, or ability to equilibrate temperature to that of the surroundings. A substance with high thermal diffusivity conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'. The substance generally does not require much energy transfer to or from its surroundings to reach thermal equilibrium.

Since air has very low volumetric heat capacity, a very small heat flux will make a very large change in temperature.

The air gap R-values in the ASHRAE chart are based on the surface emissivities of the container, so the foil would be directly under the subfloor with air below that, or on the bottom of the space (assuming dust-free) and facing upwards - it works the same either way.

As you can see in this attached spreadsheet, with one foil (lowE) surface, you can get nearly R-9 and with two foil surfaces nearly R-11. But that's still not much in a cold climate, and I would suggest a combination of insulation and lowE surfaces such as foil-faced polyisocanyrate rigid board insulation (which also has the smallest global warming contribution of any of the foams).


This is the chart from ASHRAE which all HVAC engineers use, and the numbers are total R-value for the space. The shiny surface can face either way as long as there is an air gap on that surface. The most effective place for a radiant barrier in a cold climate is under the floor, as heat loss downward is more heavily determined by radiant transfer than convection, but there is a diminishing return as the space becomes deeper and, in any case, R-4 is hardly enough to insulate a floor in Maine.

Robert, let me first say I am enjoying your contributions to the forum :) all of them.

As for "thermal diffusivity" you have sent me back to the books, or internet as the case may be.  Now I realize this link may not be the greatest, but it raises questions.

"A10.  Are there materials that can insulate better than air?"  Their answer is basically no for our work.

"A14.  What are the reasons to measure thermal diffusivity instead of thermal conductivity?

In order to calculate thermal stress during rapid temperature change you need the thermal diffusivity of the material. Other reasons are: 1) Only small samples in the range of 8 mm diameter and 2 mm thickness are available, 2) the temperature is higher than 1000 °C which is the upper limit for thermal conductivity measurements."

I clearly know little about this subject, but it seems to relate to how quickly the air adjusts to the differences in temperature across it, but does not change the heat flow once a steady state is reached.  The data in the ASHRAE chart suggest something is changing with the air gap, but without knowing what their test method is I'm concerned it is more of a method of testing difference than the true properties of air.  In any case, as the gap increases the r-value is increasing even though the r-value per inch is decreasing.  If I were to extrapolate those decreasing r/inch numbers, an 11.5" floor cavity might still have r-2 per inch or a total of r-23.  Not bad for just a couple of pieces of foil in an air sealed cavity.  Of course bridging will reduce that number.

Much more reading to do, but I do appreciate the input.


Hi Bud, when I look at the chart

3/4", 1-1/2" and 4" .... I see the R-value per inch to diminish

see how there is little change in total R-value from 1-1/2" to 4" ?



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