Supersized water heat storage

We are building a straw bale house this year. It is a round home a bit over 800 ft2. The walls are conventional (for straw bale) earthen plaster. There is 4" foam insulation underneath and 20" of cellulose insulation above in the trusses. The main heater is a solar/wood fired boiler storage bank in the greenhouse that feeds three zones in the house.  There is a small-ish wood stove at the center for cooking and to use as backup in the event of a main heater fail.

We are also going to have a year-round semi-subterranean greenhouse as well. This is where it gets tricky! The size is not finalized yet, but lets give it dimensions of 24 x 32 for an approximation. It is for growing vegetables that do not store well over winter in our root cellar. Fresh tomatoes, leafy greens, herbs, etc. Storage of our solar batteries and electronics and hot water thermal batteries (3 5,000 gallon water tanks 8'w x 12'h). Three walls are straw bale and below the glazing is straw bale with earth plaster as well. As with the house, there is 4" foam insulation underneath and around the lower walls, and 20" cellulose in the roof trusses. The glazing is double pane 4' x 8' used patio doors on an angle to be determined. There should be some sort of automatic shade/insulation to cover the glazing.

I am assuming 6,000,000 BTU requirement for the house only because I saw a similar house somewhere that said their requirement was 5,000,000 BTU and we plan on larger windows.

What I would like is to be sure I have adequate tools and materials to properly heat my home and greenhouse.

I have already figured that having 15,000 gallons of water at 140F/60C is a heck of a lot of heat. At 6,000,000 BTU requirement for the house I would need 5 firings of a 50% efficient wood fired boiler for the year. As it is, the greenhouse is approximately the same size of the house at 768 ft2, but has more glazing and is in effect, half of a basement. How will this affect the heating requirements of the greenhouse. We do not have good sun to heat the greenhouse through direct solar so we must use the heat battery to warm the greenhouse. How do I figure this out?

Instead of just stating my house is similar to another house to adopt and adapt their Btu requirements as my own, I should be more precise in my figures. After all, we will be the ones heating our home and should be more diligent at making sure we can physically cut the amount of wood to supply our home and greenhouse with wood or to purchase the wood for heating. I have made the calculations to find my annual BTU requirements. We need several pieces of data to make the correct calculations.

How fast does heat travel through the parts of our buildings?

Your heat source should effectively supply at least this number of Btu to remain at the provided inside temperature (T2) at the provided outside temperature (T1).

The formula I found to be q = 1/R * A * (T2 - T1)
q = heat flow in Btu/hr
R = resistance ft2 - hr - F/Btu
A = area ft2
T2 = inside heating/outside cooling temperature
T1 = outside heating/inside cooling temperature

Formula for Btu requirements over time q = 1/R * A * HDD * 24
q = heat flow in Btu/hr
R = resistance ft2 - hr - F/Btu
A = area ft2
HDD = Heating Degree Days (Found at a number of places, but I found my location average for the last 5 years @ http://www.degreedays.net)
24 = number of hours I heat in a day

For HDD, I use 70F base temperature since I do make adjustments for solar and cooking heat gain

	HDD
January	1686
February	1525
March	1458
April	932
May	544
June	331
July	228
August	275
September	445
October	760
November	1128
December	1450
Total	9483

We need be concerned with R-value (R) of assemblies between the interior heated spaces and the outside. In my case, to make calculations simpler, I'm not concerning myself with interior walls since all spaces will be heated to the same temperatures at all times and I have no need to have doors closed for privacy or temperature isolation. I have walls, roof and floor of my home and greenhouse to contend with. First I will work with the house.

House: A round single level house with interior diameter of 33 feet.

Walls of straw bale with earthen plaster on both sides. The bales are 2 string 18" wide laid flat with 1" (for calculations sake) earth plaster on each side. The R for the bale will be given 1.45/inch and the earth plaster is .2/inch for a total of 26.5 for the assembly. I need an area for the assembly now. Our walls are 10 feet high and the wall is (circumference = 2Πr) 2 * 3.14 * 16.5 = 103.62 feet long. 103.62 * 10 = 1036.2 ft2. There is an addition on the house which increases it's area to 1255 ft2. But the wall is an assembly. It has straw bales and earth plasters, but it also has doors an windows that have different R than the majority of the wall assembly. I need to calculate them separately. Our windows and doors are going to use the same 2.3 R since my doors are primarily just full length double windows with a wider casing and the difference in R will be negligible. 1255 ft of the wall minus door and window area of 142 ft2 equals 1113 ft2.

The roof is a 24" tall low-slope truss assembled like spokes around a central steel column outward to rest on the outer walls.  There is a minimum of 20 inches of blown cellulose insulation for R 60. Clad top and bottom by 3/4 inches of wood at R 1 per inch (R1.5) and 4 inches of soil at .3/inch = 1.2. I am not going to calculate in the difference of R with the dimensional lumber of the truss since I used 20 inches for cellulose instead of the true 21 inch value for the difference which should be more than adequate. I don't wish to make this calculation any more time consuming than it already is. Roof R = 60 + 1.5 + 1.2 = 62.7. Area of my roof is Πr^2 or 3.14 (16.5^2) = 854.865 ft2 and add my addition 132 ft2 = 987 ft2.

The floor area calculation is pretty easy. It's the same as the roof! R is much different, though. We are installing a earthen floor over 4 inches of rigid foam insulation. The foam is R5/inch * 4 = R20. Earth is about R1.4/foot. I believe we are installing 4 inches. 4/12 * R1.4 = R0.46. The total of the floor is R20 + R0.47 = R20.47.

Now I have all the numbers for our annual Btu requirements for the house. Since we will not be heating June through September, I will not include those months in out Btu calculations.

	HDD
January	1686
February	1525
March	1458
April	932
May	544
October	760
November	1128
December	1450
Total	9483

Wall assembly: main assembly + windows/doors = 23,610,196 Btuh
Formula: q = 1/R * A * HDD * 24
main assembly: q = 1/26.5 * 1113 * 9483 * 24 = 9,558,864 Btuh (Btu hours)
windows/doors: q = 1/2.3 * 142 * 9483 * 24 = 14,051,332 Btuh

Ceiling and roof assembly = 3,582,668 Btuh
Formula: q = 1/R * A * HDD * 24
q = 1/62.7 * 987 * 9483 * 24

Floor assembly = 7,030,024 Btuh
Formula: q = 1/R * A * (T2 - T1) * Days * 24
q = heat flow in Btu/hr
R = resistance ft2 - hr - F/Btu
A = area ft2
T2 = inside heating/outside cooling temperature
T1 = outside heating/inside cooling temperature (Ground temperature)
Days = number of heating days

q = 1/20.47 * 987 * ( 70 - 45 ) * 243 * 24

House assembly annual Btu requirement: 34,222,888 Btuh

So far, I have found my estimate of 6,000,000 Btuh is WAY off! But there are still adjustments to be made.

Please come back as I will adjust this amount later today for solar and cooking heat gain. I have been sitting at the computer for too long this morning and I have things to do outside. I will also add the greenhouse and adjust it for solar gain as well.

Now we know the Btuh requisite, now we can determine the rewards of something natural. Solar gain can be our friend if we use it correctly. Lets see if we have made proper choices in our window choosing our windows. Really, we are using what we have available here on our property that we have collected.  I used the calculator at http://www.susdesign.com/windowheatgain/index.php to determine annual Btu/ft2 gain. To use the calculator I needed my zip code to get latitude then I entered the average percentage of sun for clear climate for each of the months during the year. You get solar gain on not-so-sunny days too, but I'm mostly interested in the high-gain days. I found that data for my city at http://www.city-data.com/city/Potsdam-New-York.html (scroll down to sunshine graphic. Select your window choice (mine is double pane wood), select Btu/ft2 and click "Calculate".

Month	Btu/ft2/month
Jan	12,000
Feb	14,000
Mar	16,000
Apr	12,000
May	10,000
Jun	9,200
Jul	11,000
Aug	13,000
Sep	15,000
Oct	15,000
Nov	9,400
Dec	9,300
Annual	150,000

Since we are only interested in the heating season, we will only use the same months that we used in the previous post of Jan, Feb, Mar, Apr, May, Oct, Nov and to determine our solar gain through our glazing.

Month	Btu/ft2/month
Jan	12,000
Feb	14,000
Mar	16,000
Apr	12,000
May	10,000
Oct	15,000
Nov	9,400
Dec	9,300
Annual	97,700

Solar heat gain for the heating year is 7,327,500 Btu
Btu/ft2 * ft2 of glazing on side of Btu/ft2 = solar gain (Btu)
97,700 * 75

Cooking heat gain for the heating year is 25,447,808 Btu
We will have a mass cook stove in the middle of our home. There are 243 heating days with 3 meals per day for a total of 729 meals. For one reason or another, one quarter of our meals we do not cook. 729 * .75 = 547 cooked meals at fifteen pounds per meal of sugar maple at 6,203 Btu/lb (https://chimneysweeponline.com/howood.htm Sugar maple 23.2 MBtu/cord / 3740 lb/cord)

I don't have any data on my cook stove since it is not built yet but I can estimate it's efficiency and I want to estimate low. Cooking heat is wasted as it goes up the chimney getting the temperature correct and heat continues to be emitted long after the fire is out. I am going to say that while cooking, heating efficiency is maybe 50%.

Meals cooked * pounds wood per meal * Btu per pound * efficiency = Heating season cooking gain

547 * 15 * 6,203 * .50 = 25,447,808 Btu

Total heat gain from solar and cooking: 32,775,308 Btu
This is interesting! The house requires 34,222,888 Btuh and the home has a total of 32,775,308 Btu of heating gain from solar and cooking. There is a deficit of only 1,447,580 Btu.

1,447,580 / 23.2 MBtu/cord / 50% = .125 cord of sugar maple

Additional Btu needed to maintain temperature in home: 1,447,580 Btu
If we are looking at only numbers, this looks surprisingly good. But these numbers don't say that we will be getting too many Btus on days that are warm and we will need to open windows or a door to expel the heat to the outdoors to make the house comfortable.  Perhaps, instead, there should be a heat exchange to send the heat from the house to the earth under the home to reduce future heating Btu needs.

The house is done and the data looks interesting. I need a break before going over the greenhouse. Hopefully, it will be just as enlightening as the house was.

Greenhouse

I will try to do this quickly without elaborating too much, yet still give an clear picture of the plan. This greenhouse has has a 46 feet back north wall, 36 feet front south wall and 24 feet west wall that all meet at right angles. The east wall is 27 feet long connecting the ends of both south and north walls. The building is sunk into the earth seven feet as a basement would be. At the back of the structure (46' x 13') stands three 5,000 gallon water storage tanks 8 feet in diameter and 12 feet tall. I plan to use these as heat batteries for my house and for greenhouses. The growing area that holds our grow tables front of the greenhouse (36' x 11') is raised approximately 5 feet above the floor in the back. The floor is 4" on-site gravel over 4" rigid foam insulation. The walls below and 1 foot above grade are 18" thick stone and mortar walls with 4" rigid foam on the outside. Above grade, the walls are 7 feet straw bale with earth plaster on the interior and exterior except for the south wall which is a 2' tall double thick stick wall at R26.5. The glazing is R2.3 double pane glazing from re-purposed patio doors, angles about 30 degrees to meet the roof. The roof is like that of the house, 24" tall trusses with 3/4" wood and earth on top and 3/4" wood on underside, 4 inches of earth on top and filled with 20+ inches of cellulose. There is a single solid custom door on each end of the greenhouse ... R11.5 door 80" x 40". Big enough to carry items in and out comfortably. That concludes the exterior of the greenhouse.

Calculations

Since this is a greenhouse and not a house, the HDD must be adjusted for the higher interior average temperature. Again, I used the calculator at http://www.degreedays.net. Enter your zip code and select the proper weather station for you. I want heating, Fahrenheit and a base temperature of 75F. Growing plants I read is better when the temperature varies with the sunlight. Night time the temperature is reduced but the temperature comes back up with the sunlight. Like in nature. I plan to have an average temperature of 75F. Select average, 5 years and click "Generate Degree Days". On the next page, download the report. It may take a while to finish so look around while you are there, though, unfortunately you cannot click on links to browse the site or you lose your download.

Month	HDD
Jan	1686
Feb	1525
Mar	1458
Apr	932
May	544
Jun	331
Jul	228
Aug	275
Sep	445
Oct	760
Nov	1128
Dec	1450
Total	10762

We are most probably going to use this greenhouse year-round for the more sensitive (read "Expensive vegetables and herbs") plants and plants we cannot store in our root cellar or by canning/freezing. For the sake of this exercise, we're going to use the same time span that we used for the house to compare the style of structure. Subterranean vs earth slab since the sizes are similar

Month	HDD
Jan	1686
Feb	1525
Mar	1458
Apr	932
May	544
Oct	760
Nov	1128
Dec	1450
Total	9483

Btuh Expenditures: 49,183,659 Btuh

Below grade assembly: 15,036,604 Btuh

Below grade floor assembly: 8,398,080 Btuh

Formula: q = 1/R * A * (T2 - T1) * Days * Hours

R = (4" R5 rigid insulation + 4" gravel at R0.1388/inch)
A = same as roof 984 ft2
T1 = 45F (Ground temperature)
T2 = 75F
Days = Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 243

q = 1/20.5 * 984 * ( 75 - 45 ) * 243 * 24

Below grade stone/masonry wall assembly: 6,638,524 Btuh

Formula: q = 1/R * A * (T2 - T1) * Days * Hours

R = R20 (R5 * 4" rigid insulation) + R1.44 (18 * R0.08 concrete)
A = (46 + 27 + 36 + 24) * 7 = 931 ft2
      subtract area under the ends of the growing section since the floor is raised.
      931 - ((11 + 12.5) * 5) = 813.5 ft2
T1 = 45F (Ground temperature)
T2 = 75F
Days = Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 243

q = 1/21.44 * 813.5 * (75 - 45) * 243 * 24

Above grade assembly: 35,025,758 Btuh

Above grade roof assembly: 3,571,779 Btuh

R = R60 (R3.2 * 20" cellulose) + R.75 (R1 * .75" wood) + R.75 (R1 * .75" wood) + R1.2 (R0.3 * 4" soil)
A = 24 x 46 x 27 x 36
     Break it down to two pieces and add them together
     Rectangle: 24 x 36
     24 * 36 = 864 ft2
     Triangle: 10 x 27 x 24
     24 * 10 / 2 = 120 ft2
     864 + 120 = 984 ft2 (only 3 ft2 difference between the greenhouse and house)
HDD = Heating Degree Days of Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 9483

q = 1/62.7 * 984 * 9483 * 24

Above grade stone/masonry wall assembly: 1,411,835 Btuh

R = R20 (R5 * 4" rigid insulation) + R1.44 (18 * R0.08 concrete)
A = (24' + 46' + 27' + 36') * 1
HDD = Heating Degree Days of Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 9483

q = 1/21.44 * 133 * 9483 * 24

Above grade glazing assembly: 23,155,012 Btuh

R = R2.3
A = 36' x 6.5'
HDD = Heating Degree Days of Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 9483

q = 1/R2.3 * 234 * 9483 * 24

Above grade east, west and north wall assembly: 6,008,429 Btuh

R = R26.1 (R1.45 * 18") + R0.2 (R0.2 * 1" earth) + R0.2 (R0.2 * 1" earth)
A = [custom door (80" * 40")/144 sq/in = 22.2 ft2, slope of glazing (4' * 8')/2 = 16 ft2]
     north wall 46' * 8' (no breaks) +
     (east wall (27' * 8') - custom door - slope of glazing) +
     (west wall (24' * 8') - custom door - slope of glazing)
HDD = Heating Degree Days of Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 9483

q = 1/R26.5 * 699.6 * 9483 * 24

Above grade door assemblies: 878,703 Btuh

R = R11.5 (R5 rigid insulation * 2") + (R0.75 wood cladding * 2)
A = (custom door (80" * 40")/144 sq/in) * 2 = 44.4 ft2
HDD = Heating Degree Days of Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 9483

q = 1/R11.5 * 44.4 * 9483 * 24

Btuh Credits: 32,116,949 Btuh

This should be where a greenhouse "shines". Using all that glazing to use natural light to grow plants and to absorb energy from the sun. Also, the three 5,000 gallon water tanks releasing heat 24 hours per day will assist with energy requirements of the greenhouse.

Solar gain from glazing: 22,861,800 Btuh

Month	Btu/ft2/month
Jan	12,000
Feb	14,000
Mar	16,000
Apr	12,000
May	10,000
Oct	15,000
Nov	9,400
Dec	9,300
Annual	97,700

Btu/ft2 * ft2 of glazing
97,700Btu/ft2 * 234 ft2

Heat gain from heat loss from water storage tanks (Heat battery): 9,255,149 Btuh

Sides and tops of tank loss: Btuh

3 - 5,000 gallon tanks 8' x 12'

Formula: q = 1/R * A * (T2 - T1) * Days * Hours

R = The material the tank is made from is R3.33/inch. The tank is 1/4" thick at the sidewall. 3.33/4 = 0.8325
A = area of 3 tank tops (πr^2) * 3 = (3.14 * 4^2) * 3 = 150.72 ft2
     +
     area of 3 tank sides (2Πr) * h * 3 = 2(3.14)4 * 12 * 3 = 904.32 ft2
T1 = 75F
T2 = 140F
Days = Jan, Feb, Mar, Apr, May, Oct, Nov, Dec = 243

q = 1/R0.8325 * 813.5 * (140 - 75) * 243 * 24 = 370,428,324! That's too much heat loss.

I'm definitely going to need to add some insulation. This is why I left some space around the tanks. Lets try straw bales as insulation.

q = 1/R33.32 * 813.5 * (140 - 75) * 243 * 24 = 9,255,149 Btuh. This could work!

Btuh Deficit: 17,066,710 Btuh

I have to run errands now. I would like to ponder what this means, if these numbers are real and what I need to do make these numbers a reality.

Heating the water to 140F

How much energy does it take to get this water to 140F? This might be fairly easy because to heat 1 pound of water by 1 degree F takes 1 Btu!
Looking at the formula, we need to know the weight of water, beginning temperature and end temperature of the water.  

A quick search finds that a gallon water weighs 8.345404 pounds.
Each of our tanks hold 5000 gallons and we have 3 of them.

8.3 lb/gal * 5,000 gal * 3 = 124,500 lb

Our water comes out of the ground at an average of 45F (Ground temperature from previous calculations). We know our target temperature already (140F)

140F - 45F = 95F

So we are raising 124,500 pounds of water by 95F degrees

124,500 lb * 95F = 11,827,500 Btu to initially get the water to the correct temperature, IF the boiler is 100% efficient!

I plan to use rocket heater technology to heat my water. Rocket heaters are very efficient, but I cannot claim that my rocket heater boiler will be as efficient as a rocket mass heater since I do not currently have a working rocket mass boiler (RMB?) and do not know the efficiency of a working RMB. So I will use the efficiency of a known technology... the 63% efficiency of smoky outdoor wood boilers. I believe I will get better efficiency, but I'm happy working with that figure.

How much wood do I have to burn to net 11,827,500 BTU?

63% * ? = 11,827,500 (Looks like that dreaded algebra from days of old!)

(63% * ?)/63% = 11,827,500/63%
(.63 * ?)/.63 = 11,827,500/.63
? = 18,773,810 Btu

I need to burn 18,773,810 Btu of wood to net 11,827,500 Btu heat rise in the water tanks.

How many cord is that? Sugar maple is 80% of what I have available to burn and assuming I get it to the proper water content of dryness, it contains 23,200,000 Btu.

18,773,810 / 23,200,000 = 0.8 cord

Hi Anthony, it sounds like you have a very cool build about to start.  I may have missed it but why are you insulating under the greenhouse as opposed to insulating outside the foundation (vertically or with a wing/skirt style)?   Then the soil becomes part of your thermal mass.  The same could be asked of the house but I'm guessing that it would feel cold underfoot.

Mike Jay wrote:Hi Anthony, it sounds like you have a very cool build about to start.  I may have missed it but why are you insulating under the greenhouse as opposed to insulating outside the foundation (vertically or with a wing/skirt style)?   Then the soil becomes part of your thermal mass.  The same could be asked of the house but I'm guessing that it would feel cold underfoot.

Hi, Mike, thank you for the question. Actually, there is insulation (vertical) outside the stone/masonry walls of the greenhouse. And, I have thought about placing the insulation shallow near the foundation and slope it away, deeper, the further is it from the foundation. Like wings or skirts, as you state, to make use of the soil as mass for heating.

I may be incorrect in my thoughts, but I have learned through lots of reading that in our climate zone (4a), it is best to put your mass inside the insulation where it can alleviate large temperature swings. Otherwise, the earth will continue to suck the heat out of our building through the floor. Maybe if we were in a hot climate it would be different as I have not studied that environment as well as my own. I understand that the "wings" could alleviate frost issues by allowing heat from the building to conduct into the soil to keep it from freezing and pressuring the foundation in or up. Also, possibly assist in getting water away from the foundation. This may be a design to use in addition to our current one, if finances allow. We could always add them at a later time as they would not interfere with the foundation.

Our house has mass in it's floor as we are installing 4" of earth over our insulation. We are also installing radiant tubing in 4 zones in the house (Bedroom and bath zone 1, bedroom and bath zone 2, kitchen and living area zone 3, and utility room as zone 4). This is where we might do as you state, put in the wings. The house is being built with a rubble trench foundation. I do not wish to go near this foundation again once it it covered. I had planned on having vertical insulation on the outside of the trench, but believe it would be easier to keep the insulation in one piece by laying it out like wings around the foundation after my other work is completed. So, I am taken into consideration your suggestion of the wings.

The greenhouse has 4" of gravel above 4" of insulation. Heating will be more localized in the greenhouse. Instead of radiant flooring, the plants will have direct assess to heat. Either by warmed table tops or aquaponics. As people like that heat in rocket mass heaters (RMH) is stored in benches for direct heating of people, we may just heat our plants as most directly that we can by heating the soil or putting the plant directly in the water. Putting plants in 140F water isn't going to do them any favors so it would need to be mixed to cool it to a more usable temperature. My goals are to keep the water as hot as I can while still releasing enough heat to maintain a welcome envelope around the plants to allow them to grow healthy and happy. Warming the tables is winning my heart, but I still want to try aquaponics...just because it's different than I am familiar with. Perhaps I can do something more small scale in a corner of the greenhouse to satisfy my curiosity. We haven't decided which method we are going to use yet.

Anyone have experience with this type of setup? Disagree with my math? Disagree with my design? Have suggestions? Please, I would like to hear from you! Make me think about our home and greenhouse(s)...after all, I will be living with them for a long, long time and want them to be as efficient and useful as I can get them before I start construction. After I am done is not the time to be making adjustments to major structures.

Thank you

I agree that if you have mass (foundation, etc) it should be inside the insulated envelope of the building.  I'm not sure about the floor though.  My soil temp 7.5' down is 45F.  When I place my greenhouse over it I believe that heat will continue up to the floor of my greenhouse.  Having a constant 45 degree floor should help me keep my greenhouse warm all winter.  Alternately, keeping the greenhouse above 45 will help the earth heat rise up under the greenhouse.  If I was trying to maintain a 60 degree floor, I think I'd have to insulate under the floor.  

As a side note, the GAHT or earth battery systems have different insulation needs because they're storing added heat underground.

Anthony: Awesome!!
I don't know enough to say whether you have the specifics right, I do know enough to say I love it that you are thinking it out well before building it, and it looks very well thought out. My compliments, sir!!  

Mike:  Having a constant 45 degree floor should help me keep my greenhouse warm all winter.  Alternately, keeping the greenhouse above 45 will help the earth heat rise up under the greenhouse.  If I was trying to maintain a 60 degree floor, I think I'd have to insulate under the floor.  

I'd check to see how hot the plant varieties want, I know that some things won't die, but won't thrive, in 45 degree soil. I know my greenhouse needs hotter soil than that, because I'm planting a bunch of things in the ground, and the greenhouse is designed to be 1 to 2 zones south of my location. Just a thought :) Not all plants want the same conditions.