The back wall of the house - ferro-cement will receive amplified sun from about 9a thru 4p reflected off a shiny roof. The concept is to use a reflective roofing to concentrate sun from the entire roof area onto the solar wall.
Since the roof is angled at to the solar azimuth, This model concentrates the solar energy that strikes the entire roof onto the back wall. This concentrates the sunlight an additional 2700 square feet of reflective roofing onto the rear wall. So it is possible to substantially amplify solar gain by modulating the roof angle with reflective material and roof angle. So - there are three variables:
The solar absorber radiation, SAR = Incident + Reflected
Incident = cos( Sun Angle )
Reflected = cos( Sun Angle - 13 ) * Reflectivity %
Dec 21 = Incident( .89 % + (1 * .7) ) = ~1.6 Solar Equivalents
This is a lot of energy. It can convert to heat easily. The surface area is quite large. The greater the roof incline, the flatter concentration band on the rear wall. A roof incline of 13 degrees, with a depth of 45 feet, creates a concentration band of 45 * 1-cos(26) - 4.55 ft.
There are two different models to optimize:
In other words the solar energy from 2700 square feet + 300 square feet are concentrated onto a wall of 300 square feet. But the 2700 square feet hits at 26 degrees, so it is weak. sin 26 = .43. So the 2700 square feet is equivalent to 2700 square * .43 = 1183 square feet, less the reflection inefficiency. Estimating reflection loss at 30% = makes the 1183 * .7 = 828 square feet.
So... The back wall energy is 300 * cos( 26 ) = 269 + 828 = 1097 square ft. This means the 300 square feet will absorb about 4x the normal amount of solar energy on Dec 21. This is a lot.
This energy curve creates several additional opportunities. Like a solar oven that concentrates energy - the back wall is a solar concentrator.
The high level of available energy likely enables additional utilities that require higher levels of energy for function. Here are a few possible additional applications:
I guess it’s important to talk economics. This is started out to be an essay about a wall, which turned into the roof, which dragged in a list of energy technologies. But... The major issue is Refrigeration - which means food storage.
THE major source of energy use in passive solar homes. My personal experience is that FOOD is the dominant expense for our home.
Here’s a bit of math for those without kids. Our three growing boys (about 1 inch/month) consumes an escalating volume of food ranging from 3000-10000 calories per day.
As a result food production and storage dominate family economics. For us, refrigeration and food production reflect the dominant considerations home design, accounting for $1200 to $2000 monthly expense - and we don’t eat out.
This sounds crazy but think about a meal day. Farm fresh real food is expensive. If you’ve ever compared the taste of organic to farm fresh - it’s almost ridiculous. A gallon of farm fresh milk $8, a dozen eggs $5.50. Three boys consume 1 gallon per day and a dozen eggs. So $13 * 30 = $400 - cover breakfast and a bit of lunch. This adds up fast !
Each meat/protein meal from the store is expensive. A meal with less than 3 lbs of meat leaves one or more hungry. Good meat runs $6.00 / lb. So dinner runs $20 each = 20 * 30 = $600/month just in protein. By the way - our boys are genetic carnivores - Veggies are essential - but growth requires an ongoing supply of high quality protein and fat.
So we purchase bulk, beef, pork in bulk. Organic grain comes from local farmers in 500 lb lots, and runs about .30 / lb. We raise chickens and rabbits. Anything that cuts that $2000 is very important.
Refrigeration lets us economize on meat. Live beef runs $1.30 / lb, and about $5 dressed bulk from the farm - $9 from the store (Whole Foods). So the ability to purchase dressed bulk reduce food costs about 50%, and the ability to purchase live by about 70%, and raised, about 90%.
So... believe me, the 70% and 90% savings on meat, technology and practices that reduce that $600 per month, to $60 - matter a lot. And for us - it will continue matter for the next 15 years, until this batch of youngsters flies the coop.
The traditional Earthship greenhouse is NOT designed for significant food production or storage. I know there are other ways to store food besides refrigeration, but each of these usually requires some sort of stable temperature, processing step that requires storage space, that is isn’t part of a normal earthship, or conventional home. My grandparents used root cellar, and an ice house.
Refrigeration is important. And in traditional solar installations, with reasonable passive technology, refrigeration accounts for up to 70% of the energy - and this runs a very DINKY refrigerator.
These technologies relate potential cooling for the living space and for food storage. The issue here is to find the cheapest, most effective combination, that best suit tight budget, implementation, and performance.