Here's the archived web page of the originator of the SCHS system.
https://web.archive.org/web/20110602114926/http://www.sunnyjohn.com:80/indexpages/shcs.htm
https://www.michiganmedicalmarijuana.org/topic/41439-shcs-and-greenhouse-design-faqs/
https://permacultureglobal.org/post_projects/403
http://simplysolar.supporttopics.com/post/subterranean-heating-and-cooling-6679334
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The key issue here is whether you are looking for diurnal heating/cooling or seasonal.
Dirt runs about 1/3 of the heat capacity of water by volume. It's a lousy insulator, so stored warmth and coolth tend to spread and blur.
A greenhouse takes about a 24 BTU/degree heating day per square foot per year, based on an effective envelope at R1. (Double poly is R2, but you have about 1.6 square feet of roof per square foot of floor, plus air exchange.)
So a 30 x 66 foot green house has 2000 square feet. In my 10,000 degree day climate that will be 2000 * 10,000 * 24 = 480 million BTU. If you are heating conventionally, this will be about 480 GJ (the way natural gas is sold in Canada.) or 4800 therms (US measure)
Here in Alberta That would be $1500/year at today's prices.
It's not quite that bad. Even in our winters you get some heat in the winter. If you can size a system for diurnal exchange you would cut your gas bill to somewhere between 20 and 50% of the numbers above. so lets look at a typical winter day.
It's cold out there. It's -40 outside and 60 inside the greenhouse. 100 degree temperature differential. So 100 * 24 * 2000 = 4,800,000 BTU (1% of our annual heat budget today.) But we also have 8 hours od daylight. 6 hours of that the sun is high enough to do something. and during those 6 hours we're getting 6 * 600 w/m2 * .32 BTU/watt*sqft*hr = about 1200 BTU. So on a bitter winter day we are getting half enough sunshine to keep the green house warm.
A cloudy day has the advantage it's not usually as cold, but the sunlight is more dilute.
If the outside temp is only 10 F that gives you a 50 degree temperature difference. You hold your own. This is the kind of day the system is made for.
In an Alberta climate you hold your own again if you can make a greenhouse that is R2 instead of R1, but still collects all the sun. Going to a triple wall polycarbonate gives you effectively R3 for the covering (R2/square foot), but you cut down the sunlight by about 20%
You can get another
boost by letting the greenhouse cool more at night. If you are willing to drop the temp to 40 F the cabbage and kale won't care. The egg plants will NOT be happy however. Anyway that gives you another 20%
But -40 days aren't that common. 10F days here are. So the minimum size of heat storage we want is around 3 million BTU. This will allow us to average the high and the low on a moderate winter day.
A cubic foot of earth has the same heat capacity as about 20 lbs of water. If we try to keep the temperature swings in the greenhouse to under 20 degrees , then we need 3 million BTU/20degrees/20 lb = 7,500 cubic feet. Thats 4 feet deep under the entire greenhouse.
If we multiply that by a factor of 2 we have a safety margin for unrecognized system deficiencies.
If we wanted a seasonal scale system we need to warm up 100 times as much dirt. That doesn't take 100 times as much pipe. Since it's seasonal, we can heat or cool on a slower scale, so instead of having pipe every 2 feet in a grid under the green house we can have them every 10 feet, 10 feet down. For each linear foot of trench you are using 100 cubic feet of earth as thermal mass. So you need somewhere around 1 to 2 miles of trench. You don't gain much by having them further apart than they are buried.
Don't think that will fly.
Yes this is vastly over simplified. You don't need to store all the heat in the summer. It's doesn't need to be a fully seasonal system Our 7500 cubic foot system worked well down to 10F Even a modest increase in that gives us storage for a cloudy day after a couple of sunny days.
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