Formula for calculating amount of thermal mass for floor of passive solar house?
大家好，
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）它不会有太多的质量，以至于无法充分加热以至于在太阳下山后具有足够高的delta t来温暖空气
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
我已经设计了地板系统，可容纳多达4英寸的水泥和板岩瓷砖。但是，尽管如此，除非我将整个房子的地板作为混凝土板做，否则这间房间和与之相邻的房间之间的地板高度之间的差异有实际考虑。
我看过大量的松散多厚一个指南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）水泥（或水泥地板上的石板）可以吸收热量的速率
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.
它将有240南面临windo科幻ws 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.
它将在本质上是标准的盖帽屋顶下有2个上层故事，而南墙则具有44英尺长的室内（即南墙的大部分），该壁架在其中产生了一个大教堂的天花板区域，该区域占据了1///2一楼的空间。二楼的其余部分被围绕着房间（电视室，卧室，浴室，入口大厅），并在其上方有2楼。二楼的一部分是阳台，其余的电视室有一间卧室，在一楼的浴室上有一个浴室。
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.
我现在的计划是把水泥地面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.
- 击中地球的太阳能量为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.
另外，白天的长度很短，方位角图表显示了冬季可能有4-6个小时的可用阳光。
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.
仅仅因为我不确定使用250btu/sf/hr重做计算的100btu/sf/hr编号，因为公式变为太阳的能量
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.
因此，不知道地板可以吸收的速度以及计划的总收益多少，因此很难确定地板的厚度。这是具有更多经验的人的建议，这将是非常有帮助的。假设我已经正确完成了所有这些计算，我认为关键问题是
A) how much of a total temperature rise is typical / possible / advisable?
and
b）热质量地板的典型温度升高是多少？
如果有人是游戏，请您：
- 理智检查我的假设，计算等
and
– provide me some insight about what type of rate of absorption and re-radiation I should be planning around.
这绝对是我想我第一次做正确的事情之一。
thanks,
Jay
GBA细节库
由气候和房屋部分组织的一千个建筑细节的集合
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,
抱歉，不，我没有看到您事先回复。感谢您在这里重新发布。
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-concrete-concrete.html
[我讨厌ehow，但它可以起作用]
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?
静态与动态。
如果您一直加热，我认为更多的质量会更好
如果您不这样做，那么当您的迷你拆分说是70时，危险就会感到冷
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.
添加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.
嗨，查克（Chuck＆al），
我想您没有注意到我的帖子已经超过一年了。当时，我正试图解决一些问题，这些问题已经朝着设计的后期阶段，待定于2011年6月开始。我读了“被动太阳能房屋”的封面。我与一名结构工程师一起设计地板，以容纳5磅/平方英尺的死负荷。
用几英寸的混凝土用几英寸的混凝土进行整个房子的问题。一个是，如果我不先在露出前地板时首先将墙壁框起来，那么必须将它们放在混凝土上，这将是更痛苦的。但是，如果我首先将墙壁框起来，然后将混凝土倒在整个主楼层1/2上，从本质上讲，将与其余部分进行热隔离将在房屋的北部和东北部。
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...
顺便说一句，我的房子还将拥有活跃的太阳能组件以及被动的，尤其是现在我在Alte商店工作并且可以以自己的身份获得自己的个人用途。没有什么像PV，价格低于1美元/瓦。
- 杰伊
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...
周杰伦，您可以尝试这个地方的板岩瓷砖：http://www.sheldonslate.com/.
谢谢迈克尔。
实际上我已经从几个石板上的线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