Formula for calculating amount of thermal mass for floor of passive solar house?
Hi all,
I’m trying to figure out how to calculate the proper amount of thermal mass to put in the flooring of the main level of a house I’m building. My goal is to size the floor so that:
1) it won’t have so much mass that it can’t heat up sufficiently to have a high enough delta T to warm the air over it after the sun goes down
but…
2) not too have too little mass so that it heats up too much and too fast and starts heating the air over it before the sun goes down then cools off too quickly so that it doesn’t re-radiate heat for long enough thereby causing too large a temperature swing
I’ve had the flooring system designed to hold as much as 4 inches of cement plus the slate tile. However, despite this, there is the practical consideration of the difference in floor heights between this room and those adjacent to it unless I do the floor of the entire house as a concrete slab, something I’d prefer not to do.
I’ve seen lots of loose guidelines for how thick a concrete floor should be such as ” floor and mass walls should be 4-6 inches thick (from “The Solar House” which, though fuzzy on this point is overall a good reference) or a statement in a thread from last fall (that showed up in a search on the term “thermal mass”) “A properly-designed passive solar home, with between 7% and 12% of floor area equivalent in south glazing, overhangs engineered for the latitude and window height, and direct-gain thermal mass in the correct ratio to the solar glazing and of the correct thickness will maintain uniform temperatures AND receive, store, and release free solar heat on a diurnal cycle.”
However other than fuzzy statements like the above so far I haven’t been able to find a formula to use for calculating the actual mass (by weight in this case), and therefore the necessary thickness of a cement subfloor, given that I know the amount of south facing window area and the number of square feet of the floor in the room. Surely such a forumla exists?
Lacking one I took a crack at doing some calculations based on the size of the south facing windows, the amount of sunlight striking the earth per sf, the specific mass of cement and tile, etc.. Assuming my methodology is correct the information I’m still lacking to try to come up with the amount of thermal mass is
A) the rate at which cement (or a slate over cement floor) can absorb heat
and
B) what the target heat rise of the concrete should be so that there is enough of a delta T between it and the air above it for the floor to be able to warm the air by re-radiating the heat it has absorbed.
Here are some details about the home:
It will be a direct gain system in that the windows will allow light right into most of the living area.
It will have 240sf of south facing windows in total. 80ft of that is in a south facing basement with south & west walkout walls of 48ft and 30ft length respectively (north & east walls of the same size are below grade). The basement will have a 4in thick slab built over R-10 insulation. It will be isolated from the rest of the house via R-30 insulation in the floor joists.
It will have 2 upper stories under what is essentially a standard pitch cape roof with the south wall having a 44ft long dormer (i.e most of the size of the south wall) in it which creates a cathedral ceiling area that occupies a little over 1/2 the space of the 1st floor. The rest of the first floor is walled off for rooms (TV room, Bedroom, Bath, Entry Hall) and has a 2nd floor over it. Part of the 2nd floor is balcony and the rest has a bedroom over the TV room and a bath over the 1st floor bath.
The cathedral ceiling area on the 1st floor (where the thermal mass floor will be) is 824ft +/- and the portion of the south wall that borders it has 120sf of south facing windows.
Also facing south is the 256 sf TV room on the main floor with 20sf of south facing window in it and a 230sf bedroom on the 2nd floor with 20sf of south facing windows. I don’t think I’ll be putting a thermal mass floor in these areas. They’ll most likely get some type of wood flooring.
My current plan is put a cement floor of TBD thickness into the cathedral ceiling area without any radiant sub floor in it. The reason I don’t plan to do radiant subfloor is because this will be a vacation home for quite some time so the temperature will be getting set back when we’re not there. If we have radiant subfloor heat it will take a while for the home to heat up when we go up there in winter. Also I’m under the impression (perhaps mistakenly) that if the floor’s temperature is raised by the heating system so that it is above the room’s air temperature that this reduces its ability to absorb solar heat in addition to the heat being put into it by the heating system because a warmer object with a particular specific mass absorbs heat less efficiently as its temperature rises.
My research shows the following constants:
– cement weighs about 100lb per cubic ft (or 8.3lb/sf/inch) and can hold 0.21BTU per lb per F degree
– I’ve seen various figures for the weight of 3/8 inch slate tiles, from 8lb/sf to 15lb/sf. For now I’ll assume 10lb/sf.
– the amount of solar energy hitting the earth is 500BTU/hr/sf
Of course in Vermont where I’ll be building in the winter the low sun angle is likely to reduce the amount of solar energy a bit. So for my calculations I’m assuming only 100BTU/hr/sf. That might be on the low side and if anyone has a better idea of what that number should actually be please let me know.
Additionally day lengths are short and azimuthal charts show maybe 4-6 hrs of usable sunlight in the winter.
Using these assumptions I’m assuming 12,000BTU/hr (120sf * 100BTU/SF/hr) which for 4-6 hrs yields a range of 48,000 to 72,000 BTU/day.
So here’s the math….
For cement with a capacity of 0.21BTU per lb per F degree to absorb 12,000 BTU/hr would require about 57,000lb of it (i.e. 12,000/0.21). I’m assuming a similar value for the tiles. So the formula to calculate the cement thickness given the number of square feet a room has and the anticipated temperature rise of the floor comes out to
Y = 57,000 / ((8.3 * X) + 10) * F)
where X is the cement thickness in inches, Y the number of sf of floor, F the temperature rise and 10 the lb/sf of the slate tile.
Solving for X yields X = ((57,000/Y*F) – 10)/8.3
To find the thickness of a cement floor (at 8.3lb/sf per inch) with tile weighing 10lb/sf undergoing a 1F/hr rise in a room 824sf such that the floor will absorb 12,000BTU/hr would require:
X = ((57,000/(824*1) – 10)/8.3
So for the 824sf in my cathedral ceiling room undergoing a rise of 1F I would need roughly 7in of cement. However if the floor can heat up faster than 1F/hr it doesn’t need to be as thick. A 2F rise per hour would require 3 inches of cement, and a 3F rise per hour 1.57 inches.
So if I’ve gotten the amount of incoming solar energy correct if a 3F/hr rise is a realistic figure, and thus a 12-18 F degree total rise during the course of a day, then I could get away with a floor thickness of as little a 2 inch combined thickness of cement and the tile over it.
Just since I’m not sure about that 100BTU/sf/hr number redoing the calculations using 250BTU/sf/hr as the sun’s energy that formula becomes
X = ((143,000/(Y*F) – 10)/8.3
after plugging the 824sf in my cathedral ceiling room undergoing a rise of 1F I would need roughly 20in of cement. Ouch! If the heat input is that high the floor would definitely have to heat up faster than 1F/hr. To have a reasonable cement thickness of say 4 inches I’d need the floor to be able to heat up a rate of 4F per hour.
So not knowing the rate at which the floor can absorb and how much of a total gain to plan for makes it tough to determine how thick to make the floor. This is the advice of someone with more experience would be quite helpful. Assuming I’ve done all these calculations correctly I think the critical question are
A) how much of a total temperature rise is typical / possible / advisable?
and
B) what is a typical rate of temperature rise for a thermal mass floor?
If someone is game can you please:
– sanity check my assumptions, calculations, etc
and
– provide me some insight about what type of rate of absorption and re-radiation I should be planning around.
This is definitely one of those things I think I want to get right the first time….
thanks,
Jay
GBA Detail Library
A collection of one thousand construction details organized by climate and house part
Replies
Jay,
This is the second time you are asking this question. The last time I answered, you didn't respond, so I don't know if you saw my original answer. Here it is again:
I don't have time to check your calculations, but here are two rules of thumb -- for what they are worth:
Green Building Guidelines from SBIC: "The rule of thumb is that the thermal mass should be about six times the area of the direct-gain, south-facing glass. ... For most thermal mass materials, their energy effectiveness increases up to a thickness of about 4 inches. Mass thicker than 4 inches typically does not absorb and release heat quickly enough to be effective and worth the additional investment."
The Green Studio Handbook by Alison Kwok and Walter Grondzik: "A general rule is to provide a concrete mass of 4-6 inches thickness that is about 3 times the area of the solar glazing. This assumes the mass is directly irradiated by solar radiation. A ratio of 6:1 is generally recommended for mass that receives only reflected radiation."
Hi Martin,
Sorry, no I didn't see you prior response. Thanks for re-posting it here.
These guidelines are great, and as I mentioned I've seen such guidelines mentioned before.
It's definitely useful to know that mass thicker than 4 inches typically doesn't absorb and release heat quick enough to be effective. But that doesn't help me quantify how fast it would heat up and how much of a temperature rise it would achieve. And it also doesn't help me to understand how a floor less than 4 inches thick will behave as compared to one 4 inches thick given the same amount of solar heat shining on it.
Perhaps the biggest knock I've seen about early efforts to build passive solar houses was that they had too much glass and too little mass, and as a result they would heat up too fast, over heat in the daytime (often necessitating the opening of windows) and then cool off too quickly at night.
Given that I'd prefer only to have the thermal mass floor in the cathedral ceiling area of the house I'd rather not pour a floor 4 inches thick and have a large difference in floor height between adjacent rooms.
So I was really hoping there was some more exact way to analyze a particular design when the window area and floor are known in order to learn how a floor of a specific thickness would behave. It sounds like there may not be.
Can you at least provide any guidance about what the correct number of BTU/sf/hr might be?
At least that way if my formula does prove to be correct, or at least somewhat close, I'd at least be sure I was taking into account the correct amount of heat input to the system.
thanks,
Jay
There are charts and graphs and software of hourly average insolation, I got my info in"From the Ground Up" a million years ago, and I have stuck in my head about 64 btu's per sq ft of south facing glass in Mass, which of course is some kind of mental average since it varies from Jun 21 to December 21; I think your assumptions are high, but again, I could be wrong.
There are also numbers for the heat capacity of materials
http://www.ehow.com/how_6127389_calculate-heat-capacity-concrete.html
[I hate ehow, but it works]
There are so many assumptions required I am not sure how you would come up with an accurate number, How much of the heat that hits the window gets through the window? how much is transferred to the floor? What is the room temp? the floor temp?
static vs dynamic.
If you heat all the time, more mass is better, I think
If you do not, then the danger is feeling cold when your mini split says it is 70
I bought the book "The Passive Solar House", which goes through the whole process. Off the top of my head, why not pour a slab throughout the whole house to eliminate the step? It takes many many tons of concrete to store lots of heat at about 30 BTU per cu ft per degree F. Read the book before going any further.
Jay. Really? You post a lengthy thermal mass thought process, yet you can't figure out how to sub-frame floors to heights that will leave your different finished floors at the same height? Ok, the answer. Frame your floors at the X thickness of concrete/slate/etc. subtracted from desired finish floor height (dropped in that area only). Bingo.
As to all the scratchin on paper, well done. Interesting.
Added http://www.aaepassivesolar.com/
Bruce now uses 12" of concrete ducted with air to reach its full thickness. I think he has done as well as any in "trying" to utilize mass. Passive solar history is full of miss fires and miss information including Brownell. A study not long ago came up with some interesting improvements that a Brownell home should try including.
Hi Chuck & Al,
I guess you didn't notice that my post was over a year old. At that time I was trying to work out some problems that had cropped up towards the latter phases of the design with the construction pending to start in June 2011. I had read "The Passive Solar House" cover to cover. And I'd worked with a structural engineer to design the floor to hold 5lb/sf of dead load.
The issue with doing the whole house with the several inches of concrete came into play in several ways. One was that if I didn't frame up the walls first when the Advantek subfloor was exposed then it would be more of a pain to have to do so by putting them on top of concrete. But if I framed the walls first and then poured concrete over the entire main floor 1/2 of it would essentially be thermally isolated from the rest of it because there'd be 2x4s between it and it wouldn't get any direct sunshine because it would be on the north and northeast of the house.
The other consideration was running plumbing and electrical through it. It's a long story but my concrete contractor screwed up the location of some of my basement windows and then left me in the lurch. As I found out first hand, drilling and/or cutting through any reasonable thickness of concrete sucks big time. So I also wanted to provide enough thermal mass in the area exposed to the sun to hold and release heat while not putting concrete down in areas where it would complicate routing of other utility lines...
In the end I chose to use sleepers with OSB over them to raise the floor levels up to within 1/2 inch of that of the concrete thermal mass floor in the cathedral ceiling area. It was pretty inexpensive and relatively quick and easy to do. I think I did it all in one weekend. I considered putting radiant under it but decided against it in the end because I wanted the extra thickness and support from the OSB to go under the wide pine floor boards I plan on using and didn't want to risk nailing into the PEX. Wtih the insulation levels of my house (R-53 roof, R-40 walls) baseboard heating should serve just as well.
I did put PEX into the concrete subfloor in the cathedral ceiling area. I plan to bury a temperature probe in it and only run it if we haven't had sun in many days and the floor is starting to feel too cold on my feet. So I intend to use it as basically a glorified foot warmer and backup heating for really cold days since heating the concrete via the PEX defeats the ability of the sun to heat it when it is shining.
My contractor advises me that the pour is going to happen tomorrow. The next step is to settle on where I intend to get the 800sf of green & red 1ft squares of VT slate tiles. I found a pretty cool pattern looking through the web for photos of floors in old castles, churches and European chalets and hunting lodges...
BTW My house is also going to have active solar components as well as passive, especially now that I'm working at the alte store and can get stuff for my own personal use at cost. There's nothing like PV at under $1/watt....
- Jay
sorry that should read 55lb/sf dead load, not 5lb...
forgot I can post attachments. Here is a rendering of the place with the floor pattern done by using jpeg images of the actual tiles...
Jay, you could try this place for slate tiles: http://www.sheldonslate.com/.
Thanks Michael.
I actually have a line on the slates from a couple of places right in VT. One is south of about 1/2 way between Rutland and Sugarbush on the west side of the green mtns which is an hour or so closer to where my house is than Granville. The other 2 are right within 10 min of my house. One is an upscale tile store in Stowe which has lousy customer service and is probably going to over charge me. The other is a nursery that mostly deals with slates for landscaping but says they can get the square tiles. However based on what I saw of the several boxes they had in stock I'm not convinced they'll be able to get us lots that have some consistency in the coloration.
I need about 800sf so I'm a little hesitant to mail order due to the high cost of shipping these days. Also I'm not up in VT on weekdays more than a couple of times a month and that makes arranging for delivery a hassle. If I have them shipped to my primary residence though I them have to haul a couple of thousand pounds of tile since I think these things weigh over 2lb per sf. Not good on the shocks...
I may also look to see if there's anyplace around Williston or Shelburne that might have a good source and reasonable prices. If not I may just go with my favorite tile place down here in MA and haul them up a few hundred pounds at a time....
thanks again,
Jay
We have a suite of DIY passive solar heating design calculators on our website. One of them does the requested thermal mass analysis/design. We have found 7-12% of floor area for window area and 5.5 SF of thermal mass for every SF of window area over 7% to be overly simplistic and often grossly inaccurate rules of thumb. The calculator instructions on the website explain this subject in detail.
http://www.borstengineeringconstruction.com/Calculators.html