Piwoslaw,

Thank you for posting this info.

I'm still learning how designing with PEX works, too.

But I can answer your question about PEX diameter.

PEX comes in many different diameters.

In the USA, (and Canada too I assume), the PEX OD sizes are:

• 3/8"
• 1/2"
• 5/8"
• 3/4"
• 1"

I would guess that in Europe (where PEX started) PEX would be made to even metric dimensions, and that the step sizes would be roughly equivalent to the list above

The following notes primarily apply to PEX radiant floors...

NOTE 1: The 5/8" size is made, but not often stocked. If a design requires it, it can be found. Also, PEX sizes can go mich larger than 1". I limited the list because most PEX residential heating jobs would not usually require it.


NOTE 2: Assuming equal pipe spacing, the diameter of PEX does affect the amount of heat given off per unit area, but less than one might think. I found an excellent article by John Siegenthaler, the guy who wrote the bible on radiant heating. Here's a chart of various diameter PEX schemes:


The article is the best of its kind, should be read in its entirety.

He also did an article called Depth Perception, which addressed the optimum depth of PEX tubing in a slab.

Regards,

-AC_Hacker

Following this thread with great interest. The super insulated passive solar addition(a winter zone core) to my retirement cabin will have a thermal mass hydronic floor for the first floor and basement(larger w/sand bed) as it's main heat storage so DIY hydronics is of interest to me(building will be 75% DIY, getting older). I have come across a couple of radiant dealers that sell DIY "kits". Still want enough knowledge of "how to" to understand/adapt system to my best needs. Also still researching best/economical way to charge mass(other than passive already planned) with minimal "sysytems". KISS. Backup demand should be very small. Lucky to be building from scratch and can design for radiant.

Hello Drake,

I'm getting very close to plunging into my first radiant floor project.

I'm trying to scheme up a relatively lightweight 'sandwich' which will be high-efficiency. From all I have read, lightweight and high-efficiency are mutually exclusive, where radiant floors are concerned.

Have you thought about how you will do your floors?

BTW, I stayed at a house with nice warm slab floors this past weekend, and it was very nice indeed. I now know that it is well worth the effort to go radiant. They used a Rinnai wall mount boiler (propane).


I was amazed at how small the heating plant was for such a large house.

Regards,

-AC_Hacker

polarity seems to be present in so many things. It's those darn laws of physics. I will be lucky that I can design from scratch and I will be putting hdro in shallow sand/bed slab in basement and in engineered slab first floor. I too have experienced radiant floor heat and It is my wife's dream come true(next to moving south) steady heat - no setbacks. I must say your heat pump exploration is greatly admired, followed and of great interest. I wish I could contribute more than hope that you continue.

Thank you so much for your comment.

If you really mean it about wanting to contrubute more, then get a brazing torch and the basic tools, then find a doner air conditioner, or de-humidifier, build your own homemade heat pump and make it work for your new purposes... Take loads of photos, ask loads of questions and tell us what you have learned.

Regards,

-AC_Hacker

I am a "modifier" by nature. I can seldom not resist modifying most anything to better fit my needs. But working correctly and safely with refrigerants is a bridge I need to see if I am able to cross. I believe I've already used eight of my nine lives on other project so I must be cautious.

I know how you feel, I felt the same way myself, more or less...

But if you drive a car, you are taking a much bigger risk than working with refrigerants.

-AC_Hacker

I am at this time still educating myself on the principles of closed liquid heating/cooling systems and am lucky enough to have found your work that has shown DIY possibilities exist. Am also making sure I understand as well as I can what you have done, how well it meets what I want to do and design from there. I would really like to have the the heat transfer directly into an insulated tank on the radiant side and am trying to find out if there is a proper exchanger to do that with refrigerents.

I'm curious do they connect the boiler directly to the radiant or do they use a storage tank that is heated by the boiler then circulated out. It just seems funny to heat water to 180 or so with a boiler and then pump it into pipes when you really want 90 or so degrees.

Well, if I'm understanding your quandry correctly, the heat pump I built, and then one I am building now are just a refrigeration compressor, a cap tube, and two brazed plate heat exchangers, hooked up in a circuit.

Regarding the heat exchangers, one is on the "source" side, which I usually call the ground loop side. This is where the heat comes from. It has water running through the odd-numbered channels, and refrigerant running through the even-numbered channels. Just before the refrigerant enters this exchanger, it emerges from the metering device, in my case this is a cap tube. When it emerges from the cap tube, it passes from a region of high pressure and enters a region of low pressure. In that region of low pressure, the refrigerant instantly changes from a liquid to a vapor and becomes very cold, much colder than the loop water that is circulating through this exchanger, so heat from the water migrates from the water to the refrigerant.

The other heat exchanger is on the "sink" side, this is the side where the useful heat is available. It also has water running through the odd-numbered channels, and refrigerant running through the even-numbered channels. The vapor that had picked up heat from the first HX (above) is routed through the compressor where it is squeezed to a point that is close to condensing, but the vapor is too hot to condense. This hot pressurized vapor is then routed through the second HX, which in your case has water from the PEX floor circulating through it. The PEX water is cooler than the hot compressed refrigerant vapor, so heat migrates from the vapor to the PEX water. As the heat from the vapor begins to migrate into the water the vapor cools enough so that condensation happens inside the heat exchanger. This condensation releases very large amounts of heat which also migrates into the PEX water.


So, getting back to your original question, "...trying to find out if there is a proper exchanger to do that with refrigerents...", the answer is yes, there are many kinds of heat exchangers that can be used, but the best because of efficiency and also small size are brazed plate heat exchangers. They are usually too expensive for experimenters like us to buy, but the Chinese have come to our rescue by cranking out brazed plate heat exchangers by the millions.


Now, it turns out that making beer at home has become a popular hobby by people whose love of beer often exceeds their income. So to support these people in their quest for cheap beer, suppliers of the paraphernalia for beer making have started offering cheap brazed plate heat exchangers for sale on ebay.

This is where we come in...

I bought two for $70 each for my first prototype heat pump and they worked great, beyond my wildest expectations. Now, a couple of years later, I'm building a bigger heat pump and I just bought two more heat exchangers from the same ebay guy, and the new HXs are 50% bigger and @ $79.95 each they are cheaper per BTU. As a bonus, some of the HXs are now even available with sweat fittings for brazing refrigeration line onto. If you don't find exactly what you want, he can do custom orders.

I couldn't be happier if I was actualy drinking beer!

-AC_Hacker

As I understand the plate HX's being used they are exchanging heat from water to Refrig to water on roughly a 1:1 volume inside plate HX. Water on both side needs pump to circulate the water. Seeing an advantage for a volume of water "stored" on both sides to buffer temp and cycling of HP I see a HX that could xfer the directly to stored water as a way to elimatet wo pumps. Stored water >(HX?)HP(HX?)> stored water rather than stored water>pump>plateHX>HP>plateHX>stored water. Less parts to loop. Don't know if you have come across diagram of an "open system" for hydronic radiant heating but I think xfering heat into the central tank of this system would be ideal. Might not be a good HX to do that(not moving water).

Could you say that in a different way?

I'm just not getting it.

-AC_Hacker

I will certainly try(I think we are after nearly the exact same solution the simplest HP water to water heat xfer to hydronic heating). As I am seeing your impressive "proof" HP your ground loop is pumped into a barrel(I am calling that stored water) it is than pumped thru plate HX so HP can xfer to "heat" side plate HX where water is pumped thru it to holding barrel(which I think is simulating your yet uncompleted floor loop?). The pumping on either side could directly drive the water loops directly(w/ no barrels) but I like the idea of water storage tanks on each side to buffer, limit cycling(like a pressure tank does) and on ground loop side to store possibly prewater water from other sources(solar, greywater?) to increase COP. I see this needing four pumps w/ plate HX's. I wondering if direct tank to tank xfer is possible with HP and right HX's eliminating two pump loops. In an open hydronic system the loop is heated in a storage tank(any means) so feeding this tank w/ HP heat would be ideal(and serve as backup). Direct HP HX to this tank seems best. This may not be mechanically simple and and second pump loop best. Trying to follow the KISS rule.

As I have neither a ground loop or heat loop(nor will for a couple of years) I have no means to evaluate a HP beyond what you have already accomplished and an HP is not a deciding factor in going with hydronic radiant heating. Only the most efficient Tech,to date, that I know of if it can be made affordable.

I believe as I gain knowledge on refridgeration I understand the mech hdwr well but I am fully lost on the controller board you are showing. Are they for controlling power to HP and /or pumps/sensors switches or for testing data collection?(not strong on electronics).

Hope my thoughts may be helpful. They certainly aren't criticisms.

I went to a trade presentation yesterday and they presented a product calle EcoWarm, which is strand-board topped with thin aluminum sheet.


This is the patent drawing.

For ease of manufacturing, they route the strand board (could be MDF just as well) and contact glue the soft aluminum sheet onto it, then they slit the sheet over the channel for the PEX to go into.

Can you spell DIY?

The aluminum sheet was really thin, only slightly more than foil.

If the aluminum sheet was thicker like maybe 1/16" I think it might live up to it's hype.

Can you spell DIY yet?

Also, I have been struggling with the floor mass issue. Some mass can be good, but too much can be a problem, especially if there's a temp change.

So, my latest thinking is along this line:


(the above concept is copyleft into the public domain for all time and all purposes, including manufacture and sale. Any and all proprietary claims are strictly forbidden -AC_Hacker)

Legend:

1. Aliminum sheet aprox 1/16 thick
2. 1/4" concrete board, Wonderboard has tested best
3. PEX
4. 1/4" OSB
5. 1/2" High-Density Extruded Poly Styrene
6. thermal-transmissive goo consisting of flyash and linseed oil

This stuff could be built in place easily or made beforehand. The layers would be glued together with construction adhesive.

• 1/16" Aluminum would be a killer-good conductor of heat
• The concrete board would be a fair conductor
• The OSB would supply the support
• the XPS would privide a thermal break between the Hacker-Backer and the floor.

The wonderboard provides some thermal mass, but not as much as an all concrete board floor.

What do you think?

-AC_Hacker

Let's do this over at the Homemade Heat Pump Manifesto thread.

See you there...

-AC_Hacker

Looks like it would work fine. Is the thermal break to prevent unwanted loss to a space not needing to be heated(like a basement)? I wish to use a "thin floor" install on my second floor floor where loss to below really wouldn't be a loss. The Alum xfer surface has merit but I would possible consider sandwiching in wonderboard layers. If your top surface is to be ceramic, having laid tens of thousands of sq" of tile in every way imaginable I would be concerned about the quality of bond you could achieve directly to Alum or Alum to wonderboard. It maybe possible but it would take a very high quality adhesive(very heavily latex fortified of epoxy thin set) to hold for longevity. Is .5" pex intended size?

Yes, preventing heat loss to the basement, that's exactly what I'm anticipating.

I did some experiments with aluminum and mortar and the results were not at all good. So keep thinset away from aluminum!

Yes, I know that tile, especially a porcelin tile, would be great for heat transfer. If a Hacker-Backer configuration was going to be used, a backer-board would need to be applied over the aluminum, as you say.

I saw some organic linoleum at a trade fair recently one brand name is Marmoleum and I really liked the stuff. Linoleum wouldn't impede heat transfer much at all, and I am thinking seriously in that direction. Outgassing is no problem with this stuff. (made from linseed oils, pigments, pine rosin and pine flour, natural jute backing). It's not the cheapest stuff, however.

Yeah, that's where my thinking is now. I'm really struggling with the idea of tube-spacing. I want the spacing to be close, hopefully as close as 6 inches (maybe even closer), and the bending radius looks to be a limiting factor.

I saw a very flexible PVC tubing at a hardware store, that had a certain appeal, but the outgassing of carcinogens is a total deal-breaker.

I know that copper tubing has been abandoned by the radiant heating industry for reasons of cost and also because it is subject to corrosion by high-alkali (cementitious) materials. Perhaps there is a non-alkali material that can be used that is not too expensive and is a reasonable conductor, or perhaps corrosion is not a problem with in a 'dry system'.

I'm not ready to start laying tubing yet.

-AC_Hacker

I was poking around on the internet today looking for various radiant flooring techniques and found an interesting site with some fairly descent pics of this guys' "sandwich" type radiant floor that he claims to have done in the hundreds as a contractor for residential customers over the past 29 years.

I especially liked a couple of his tips regarding how he effectively runs hallways, loop returns, consideration of floor squeaks, and consideration of finished surface materials. He also talks about his 29 years experience with respect to "standards" in spacing the pex.

I have been silently reading and scheming on a DIY radiant section in my basement as a starting point for my inspirations gathered here. Have also contacted an old friend who has been installing geothermal systems here in St. Louis for the past few years. He claims he will help with a design and installation of geo lake loop on my property later this spring. I will be sure to document and photo. AC, I have been crawling around the attic and inspecting in the basement plugging and filling voids and gaps... you were right, I haven't added ANY insulation whatsoever, but just blocking off the airways has made our home more comfortable already. I am really looking forward to adding more insulation. Next I will remove the casing around all the doors and windows and pack them with insulation, it certainly is making a difference. Thanks for all the input on these threads, it has truly been an inspiration.

sorry guys... I did not give the link I was talking about.

Radiant Heat

AC Hacker,

I have been pondering your 'Hacker Board' and I wonder if the polystyrene foam board is a good idea. Not questioning its ability to insulate and help direct heat in the direction you want it, but how will it hold up and for how long? On top of that polyboard will be some fairly rough and abrasive surfaces. I understand that the impact from footsteps will be dispersed throughout the finished flooring surface as well as the conglomeration of hardiboard and osb. However, with traffic, heat expansion, contraction, humidity, that floor will bounce and move. There is absolutely no question in my mind about that. The bouncing and shifting of the above flooring from these, even though slight, will probably wear away at the foam board over the course of a few years and turn it into "pink dust". Maybe it would take 10 years, but regardless, you probably will be expecting your radiant floor to hold up longer than that. It just seems to be the weak link is all. Whats more, the weak link is on the bottom of all your other work.

Would it perhaps be easier to cut that insulation board and glue it to the subfloor planks underneath between the floor joists?

I only bring up this design consideration because a failure in this material would cause you to have to remove ALL of your work as it is on the bottom.

Jay Cee,

I definitely see what you're getting at.

Well, the high-density pink foam is fairly dense stuff. I know that it is being used under some of the WarmBoard type of installations.

The way I was envisioning it would be to spread construction adhesive with a pretty fine notched trowel between the layers of foam/mdf(OR OSB)/Winderboard. I figure that would immobilize the structure enough so that it wouldn't start that "working" that you described.

-AC_Hacker

In the low heat hydronic radiant system I will be using in my new construction project the more I learn about low temp heating the more I think my plan to use heated storage water is not compatible. It is easy to see heating water to 85-90 degrees needed and circulating it thru the floor as needed would work fine. But to use water to store excess available heat via higher water temp is seeming to be less possible for low temp system. Feeding high temp water directly might over heat floor(unless only small volume is feed thru at a time). Added water with a mixing valve couldn't be done if there is no where for the extra water to exit system. And I don't know if a HX can be operated to a specific temp one side and variable on the other.

Further research has gotten me answer to my question. High water temp storage for low temp radiant heating is ideal. A 3-way mixer before floor loop(hot side) allows cooled loop water to reenter floor loop to "cool" hot side or return to storage tank. Thus no water needs to enter exit system. Did not know mixer could do that(seems there a many kinds of mixers). Now appears that the most economical heat source to get the storage water to temp is next. Sorting theory from economic reality. DIY again seem to offer the best solution. FYI, thermal mass can be added to a structure during an opened wall remodel by filling stud cavity with sand filled recycled alum bev. cans. in non insulated wall. Structure must be able to hold extra load(interior load walls are good) and simple wood raceway can used to space around horz elec runs. Cans stack really well.

Radiant Floor - construction express coming
 

This thread is great - I have read much of it and it's giving me ideas. I'm in a funny situation - I am a DIYer, but with not too much time this year...and I am having an addition built, which will leave me with not a lot of money to do radiant and/or GSHP....

I discussed insulating the slab with my builder, and he reported
that he has another project where he is repairing a slab that collapsed on the styrofoam. So, right or wrong, I am going to let him pour a normal (up to code) slab. (I got to watch the masons today building the foundation walls :-). Note, I am talking about a basement, below the frost line.
When he leaves, I will put down a couple coats of InsulAdd on the floor.

When he asked me what type of heat for the addition, I said Geo. But geo around here is not affordable...and <whatever>. My boiler has a mod so it is now at a 1/12 duty cycle, and that is with current insulation levels. So I can very well afford to extend my boiler into the new space...and postpone the GSHP question till the summer.

But during this construction, I am thinking I can at least put in what a programmer would call "hooks" for future options.
For example, the builder agreed to give me a 6" conduit
to the back yard below the frost line. He said his tractor driver is willing to dig for me to lay ground loop, though I like the drilling idea, and tests looked good....or maybe a hybrid - a long discussion for a different thread.

But for now, framing should start next week.
Hooks that I am considering are....possibly, a pair of pipes to each room for ductless air handlers....(though I could just plan
on basement + attic for retrofit). Multiple pairs of insulated pipes to the attic for other things...like solar thermal.

...and most importantly, radiant pipes.

One possibility is for me to DIY (DIM?)...I saw a blog about this. The floors will be 3/4" tongue-groove. It occurred to me
that I could "notch" the floors for copper pipes. (Perpendicular to the joists). Though that may leave not much subfloor material, I need to learn how thin the radiant pipes can be. I may be able to have him use 1" plywood instead of 3/4" - since the architect originally wrote for 1/2" + 5/8".

(Reading Tube 02005 Refrigeration Copper Tubing 3/8" O.D. x 50' $46 - but maybe too thin.) but...Raiantec says...
Detailed research (DOE) has shown that 7/8" PEX tubing with 0.70" wall thickness and a circuit length of 200 feet is about ideal.

One thing that occorred to me is, what if I have grooves that are rectangular...can the tubing be forced (round peg, squarish hole). Or would that terribly diminish flow rate?

Flooring materials have not been chosen. The first floor addition would be kitchen and eating area; second floor would be Master BR and Master Bath. The old house is hardwood - first floor is HW on top of 2 subfloors of hardwood and planking.

Perhaps staple-up would make sense, even though it is "new" construction.

The main goal for radiant and GS is to eliminate boiler use in the "shoulder seasons" - it was almost 50 degrees in my town today.
I am thinking of all the options for how the water would be heated - solar thermal, etc.

If this sounds disjointed, it's mostly because there are many projects going on at once, and time is going to be tight - but with up to 8KW of solar, this house might end up pretty green.

Thanks
Seth

A highly energy efficient home does not yet seem to be a complete package yet. At least not economically. Even in "ground up" new construction/design(retro-fit is a hole can of worms). Construction methods/insualtion improv let one build a low energy demand structure. HE windows gather and save passive solar cost effectively. Heat source tech has greatly lowered consumption in several forms. But energy demand is not yet very well matched in heating as I see it. Most EE heat plants are oversized(and very overpriced) for a modest low demand home. Little is saved by the people who are most trying to save. It is very easy to get caught up in the tech and hand out dollars to try and save dimes.

Yeah, you have to save a LOT of dimes for some of this stuff.:(
Spend $2,500 on a Mini-split? That's about 833 gallons of heating oil.

Humm, that's gonna get used up in pretty fast with all the cold weather we get these days..

Of course, in another 2 or 3 years, that 833 gallons of oil might cost $5,000 or more.
I know, it's not going to get a lot cheaper..

I wasn't implying that non of the tech has merit. One just needs to understand it enough to know whether there will be a real "payback" in it for them. A lot is so new there is little proof it really will out perform its payback life. Some has and is "no brainer". Its unfortunate that manufactures or energy corp have little incentive saving customers money. Use less pay the same. Sorry - OT. I am on the search for the smallest commercial residential W/W heat pump.

I'm 65 years old, so looking for 'payback' or break-even isn't something I think about very much.
(Since you can't take it with you).. :o

When I ordered my Mini-split after much reading and actually seeing the
cooling-only unit at a work site. I read the install manual, check out
the cooling (it was summer) and decided to take a chance.

Heating my home with the Sanyo is an experiment that worked out.
If it dies tomorrow, I'll be looking to replace it ASAP. (But with the latest design).

To what outside temp do think it works with some efficiency? If I can't justify a full Geo HP system or DIY I am considering a mini-split for shoulder season heating then I would also have some summer cooling. Price and DIY install are getting reasonable. How old is yours? Exterior split should be able to be in attached garage?

All the details (and more than you want to know) are on my project post.

http://ecorenovator.org/forum/geothe...l-project.html

Mine has a bug (or two) and I really have to baby it in colder parts of the winter,
But it's fantastic for cooling.. My wife loves that part..

It's working pretty well right now at 660watts at about 16F outdoors and 70F in here. :D

I think it depends on the sq feet you are heating. I should have gotten
the 36,000 BTU unit. But the price jump was too much, for what started
off as an experiment.. Live and learn..

It certainly is difficult to try to push for energy saving options once the construction process is underway.

The contractor's role is to get the job done and move on to the next job.

Your contractor may have had a failed insulated slab, but that does not mean that all insulated slabs fail. Insulated slabs are done routinely and successfully all over the world. It's a matter of proper design & construction technique.


As the above illustration of heat-loss gradient shows

• heat loss is greatest through underground walls and foundations,
• next greatest at the edges of uninsulated slab floors,
• next greatest at the perimeter of an uninsulated floor
• least at the central part of an uninsulated slab floor

So the pay-back will be most favorable in the highest loss areas. However, when a radiant floor heating is contemplated, the floor becomes the heat source and it is in contact with the world's biggest heat sink. So slab insulation is of the greatest importance if the radiant floor is to be efficient.

Foundation Insulation

Slab Insulation

From the second link:
There are many good books that address the daunting task of building an energy efficient house in the country that is the [second] biggest energy consumer in the world (the book images are hyperlinked):


-AC_Hacker

Thanks again

Radiant Floor Infra-Red Photos...
 

I came across this dramatic photo of how various radiant floor strategies look to a Thermal Imaging camera (NOTE: I found a thermal image of warm board and have included it here as a composite insert. It was taken by a different photographer, using a different camera, but the indicated eveness of the heat distribution is quite interesting):


Regards,

-AC_Hacker

Very nice pics AC Hacker. I have in one section of my house a poured concrete floor with hydronic heat. I don't think it has any heat spreaders, so I imagine its closer to the "Chanel" picture. When walking on it you can definitely tell where the tubes are. When going forward with hydronic heat in my house I will definitely be using heat spreaders to even the heat out.

Hmmmm.... The radiant slab floors are know for even heat. I'd be interested to know how far apart the 'warm stripes' are?

I'd also be interested to know if there is adequate insulation under the slab.

I'm assuming your slab is 3" thick...

-AC_Hacker

I think they are roughly a foot. Its hard to say. I'll measure them if I get a chance.

The previous owner said there is "a lot" of insulation under them. I imagine he filled the joist cavity. I'm not sure how thick the slab is though.

I finally got my 3rd edition copy of Modern Hydronic Heating: For Residential and Light Commercial Buildings. It is supposed to be the bible on hydronic heating and this is the latest edition that JUST came out. I just started reading it this morning. The preface states that interest in solar hot water, heat pumps, and renewable energy systems have grown a ton since the last edition and I'm hoping that means there is a good deal of writing devoted to those types of systems.

I've heard this is heavily dependent on ground water. If there isn't ground water near the soil beneath the slab, then the earth acts as a huge insulation bank. Earth has a low R-value, something like 1 per foot, so you see the thermal gradient traverse deeply underground, unlike a short gradient through typical insulation in a wall. The large volume of heated earth has much thermal mass, so it takes a while to heat up.

But I've heard without ground water, the heat will just sit there in the soil. This is how a frost protected shallow foundation (FPSF) can resist frost heaving at low depths, the soil is heated. The heat loss occurs at the perimeter of the foundation, where it finds its way around the insulation up to the cold surface, where it radiates away.

Dry earth with R-1 per foot would mean R-0.083 per inch. That's really not so much.

Pink XPS has an insulating factor of R-5.4 per inch.

This would imply that heat loss into the earth would be (5.4/.083) or about 65 times the rate of heat loss through XPS.

I think I would consider the money well spent, if I insulated under my slab.

In addition, the time lag to heat up or cool down an insulated slab is shorter than with an uninsulated slab.

-AC_Hacker


P.S.: I've heard tales of the radiant slabs that were in the homes that were built in Levittown, New York. They were put in without any insulation, as you describe. The residents were able to grow flowers all through the winter in the garden beds around the edges of their houses.

Pretty good thing if you like flowers in January.

I suppose the comparison would be valid, if you were to replace all of the soil around and beneath the basement with XPS.. although I'm not sure at what point you would stop replacing the soil with XPS, as it just keeps on going.. Considering soil is free, and XPS costs something like $5/cuft.

The important point is the vast majority of heat loss is at surface grade. For example, let's say the basement is 12ft wide. A point in the center of the basement floor is 6ft from any slab edge, a point at the edge is 0 ft from the edge. For simplicity, let's say the average distance to closest edge for all points on the floor is 3ft. Additionally, the basement floor is 6ft below grade.

That is a total average distance of 9ft of soil between the floor and grade. If we assume R-1 per foot of soil, then we have R-9 insulation of the basement floor for free.

If you added 1-inch of XPS underneath the whole slab, you increase from R-9 to R-14. Using the cost saving calculator here, Cost Saving for Insulation Upgrades. If we leave the defaults of 1000 sqft, 5000 hdd, $1.50/therm, 9 to 14 saves us $90/year.

At 1000sqft, your basement is likely wider than 12ft, and thus your R-values are higher.. A better estimate may be more like 600sqft, which would be 12x50, which leads to $60/year. There are lots of variables.

If we pay $16 for a 4x8x1" XPS sheet, that's $0.50/sqft. We save $60/year/600sqft, that's $0.10/sqft savings. So 5-year payback. Not bad.

I wonder if a R-value of 1 per foot is accurate, I just pulled that off the top of my head. Some values listed here: soil layer models
Shows clay soil has a thermal conductivity of 0.25 W/(m^2*K) That's SI U-value, the reciprocal is SI R-value: 1/0.25 = 4. To convert SI R-value to US R-value, multiply by 5.682. 4 x 5.682 = 22.7

I'm going to shut up now, as I have severely underestimated my argument :D