Hi,
Some rough calculations:
On a sunny day, about 1600 BTU fall on each sqft of properly oriented collector. How much of that you actually collect and get into the slab depends on the collector design and the outside temperature -- 50% is a fair rule of thumb.
So, 200 sqft of collector might get you (200 sf)(1600 BTU/sf)(0.5 efic)= 160000 BTU on a sunny day. This is about equivalent to 2 gallons of propane burned in an efficient furnace.
But, not all days are sunny. On a fully cloudy day, you will collect nothing. On partly cloudy days, it just depends on how cloudy, but it can be pretty good.
To know how much heat you need, you need to do a heat loss calculation for the house.
Here is a link to my heat loss calculator -- its pretty easy to use:
http://www.builditsolar.com/References/Calculators/HeatLoss/HeatLoss.htm
If you plug in a typical outside temperature for the "Design Temperature", it will give the heat loss for that temperature. You can then compare this to the gain for various size collectors.
You will find that for solar heating, it really pays to insulate and seal the envelope well to make the solar heat go further. Good windows also help, as does night insulation on the windows.
To the degree possible, you should also use the solar passive heating ground rules to design your structure to take advantage of free solar heat through south facing windows.
http://www.builditsolar.com/Projects/SolarHomes/guidesps.htm
In using a concrete slab to store heat:
- Be sure to insulate under it -- don't let anyone talk you into the thin bubble insulation.
- You don't really "retrieve" heat from the slab. The slab directly heats the living space above it. If the living space is not above the slab, then I would use a water tank to store heat rather than a slab.
http://www.builditsolar.com/Projects/SpaceHeating/Space_Heating.htm#Storage
- Since you live over the slab, you have to keep its temperature swing fairly small. You can't heat it up to 140F like you would a water tank, or you will be living in a sauna. This lower temperature swing means you need more mass to store a given amount of heat.
- Heat stored in the slab is: (Thi - Tlow)(Specific Heat)(Weight)
For concrete,
specific heat is about 0.2 BTU/lb-F (meaning that heating up 1 lb of concrete one deg F stores 0.2 BTU)
Weight is about 130 lb/ft^3
So, a 1000 sqft slab that is 0.5 ft thick, and that you run between 70F and 80F would store: (80F-70F)(1000 ft^2)(0.5 ft)(130 lb/ft^3) (0.2BTU/lb-F) = 130000 BTU
One rough rule of thumb is that you might want about enough storage to store one sunny days worth of output from your collectors. This would allow you to keep the house warm through the night following a sunny day, and perhaps a ways into a next cloudy day.
A water tank to store the same 130K BTU listed above might be about 260 gallons of water. This assumes the water goes through a temperature range of 140F down to 80F.
Heat stored in a 260 gal water tank: (
(140F - 80F)(260 gallons)(8.3 lb/gal)(1 BTU/lb-F) = 130000 BTU
You get away with less water for storage because it can be worked through a larger temperature range, and because it stores 5 times a much heat per lb than concrete.
Here are some links to systems somewhat like you want to build that might be helpful:
http://www.builditsolar.com/Projects/SpaceHeating/Space_Heating.htm#Active
The very first one by Marsden is very much like what you want to do and gives a lot of detail.
The 2nd one is the system on my house. It keeps the cost down by using collectors that are mostly homemade, and uses a homemade (plywood lined with EPDM) heat storage tank.
A good description of a house that uses a radiant floor slab (plus water under the slab) for heat storage:
http://www.builditsolar.com/Experimental/MearsSolarHeatedHome.pdf
"The Radiant Floor Company" site that is listed has some useful design information.
Hope that helps -- Gary