Passive Annual Heat Storage
Notes on Theory in the Spreadsheet
What´s PAHS? John Hait of the Rocky Mountain Research Center in MT reasoned from some of the thermal performance data of research and experience in the 70s that he could, and did, create a dry, thermal storage area around an underground house by layering plastic sheeting and styrofoam insulation board in a sandwich about 4-6 inches thick, at a depth of about 2 feet beneath the ground surface and extending about 20 feet beyond the perimeter of the house. At that depth it´s clear of roots, frost, light and is non-biodegradable. The earth beneath the umbrella stabilizes at a new temperature creating a sort of heat-sink in which the house is embedded. In the summertime the heat entering the house dissipates into the sink, reaching the 20 foot perimeter by the time the season changes to cold weather and then providing warmth for the house to draw on as the winter above draws heat from the house and secondarily from the storage... creating a year-long flywheel effect. The layers of plastic, the appropriate slopes and escapes at the edges divert surface water from entering the heat storage area, including sheltering the house from everything but errant watertables.
To analyse the thermal characteristics of this design, we´ve developed a spreadsheet that draws on many sources and features, and the following description identifies and explains them and their use, leading up to the spreadsheet itself.
The U-values were taken from appropriate tables and books, such as McHenry´s for rammed earth... except, the *roof* figure, which is a composite of soil and beadboard U-values and is the figure for the insulation umbrella´s thickness and an averaged value over the range of soil thicknesses above the *roof* area...
The site will allow nearly sunup to sundown 100% solar access... The utility company is cutting the front of the lot back to about 45' from the center of the road. leaving just a privacy woods at the South corner... the next area back will be for the bush orchard and the drive/parking on the other side... we figure on planting only short stuff (nothing fancy) around those areas... so pretty much clear because the area over the insulation umbrella I want to be just the local running cedar (ground cover) and riverstone... the back of the lot will be for the mound system to the west as a wind/storm diversion, leaving the trees only to the more northerly corner..
The way to view the 2´ thick endwall situation/calculations in the spreadsheet is to realize that by the middle of the wall thickness the temperature is the average for the last 2 weeks of weather so Cinci winters will keep the mid-wall at about 30 degrees + or - a little... Cinci summers will average out in the 70s at the midwall insulation... which changes the design calculation approach considerably... no extreme design temps to try to protect the indoors from... and for the moderated "outside" design temp, substantially less R is appropriate...
What extreme temps happen at the outside of the endwalls is immaterial because they get averaged and moderated just as temperature fluctuations are damped at increasing depths in the ground... the only rate that counts is the difference between the rate at which warmth is transmitted through the last foot of the endwall into the house & the rate at which warmth is transmitted from the indoor air into storage through the first foot of the shell-interface-with-the-storage... these two component rates are the same beast, except for the concrete... but the culvert shell is a thin ferrocement composite (barely 2") and the metal in the sandwich is a better transmitter of temperature, which is why ferrocement is very resistent to fire damage and which would imply that the transmission of heat into storage through the shell is not slower, but faster... and the concrete slab is not insulated as in usual construction, so its thermal characteristics are similar to rammed earth... nor is there insulation between the shell and the storage... hence the equations for this picture become just functions of temp-change and sqft... and the ratio of the square footage of the storage surface to the square footage of the endwall surface is 8-to-1... so the pressure of an 8 degree temperature difference at the endwall should have the same impact as a 1 degree difference at the storage surface... in summer there´s barely a few degrees difference between the midwall temperature and the target indoor temp, which should make the solar input through the glazing the only driving force, not the outdoor heat... (and the limited glazing input is divided between morning-east and afternoon-west so that there are periods and space between for absorption)... in winter the midwall temp being a relatively steady 30s figure and the indoors drawing on a steady 70s storage should make the temperature profile of the 10 inches of wall thickness from mid-to-indoors a straightline, so that the driving temperature difference at the surface should be about a 4 degree difference in the endwall´s indoor-surface inch...
The trick is to have the air-impact at the endwall surface reach the storage surface, which is why the interior is designed for natural airflow... the air is circulating freely, practically no partitions of the airspace, except the baths, laundry and airlock type areas which have their own design requirements.... we only need to compare coefficients (specific heat of air vs rock), assume uniform distribution of the air temp and the ratio of square footage of both surfaces...
There is no need to worry about predictions being based on too much confidence in the speed and efficiency of air to mass heat exchange because the ratio of the specific heat of soil/cement and of air is within the range of the squarefootage ratio... so the rock-to-air exchange does not overwhelm the air-to-rock exchange... the specific heat of the main components of air, namely oxygen and nitrogen, are .22-.25 cal/g and the figure for silica/sand and cement are in the .18-.20 cal/g range... not majorly different...
And the worry that different kinds of soils, compaction density and moisture content dramatically affect the heat diffusion in the soil is moderated by the fact that both endwall and storage are similar beasts: the storage area will be tamped to compaction comparable to the endwall ramming... and the moisture content is minimal in both and set by the requirements of rammed earth construction... and the majority of the soil/sand in both is from the same source... apples and apples, don´t need to worry about exact predictions, just that the scales balance...
With the wide open airspace and a couple ordinary fans positioned atop the ceilinged laundry/bath areas, pooling or stratification of the air is not happening... and since those fans would happen to be positioned about midway east-west, they would equalize the end-to-end morning-afternoon differences also... accumulation of warmth in the bathing and water-using areas is a virtue, provided it´s controlable, especially for moisture with the use of lifestyle, heatpump waterheating, clay and covers for spa and hydroponics trays...
The slab edge will be under the PAHS insulation-umbrella and berms, except at doorways... John Hait gives tips on insulation placement other than the PAHS insulation umbrella, which affects only the backs of retaining walls, incoming water pipes... when we pack the concrete into the mesh that forms the bondbeam over the endwalls, we can use concrete with insulative aggregate, though a small release of heat into the bondbeam could prevent the formation of ice troubles... and when we are ready for berming and burying, we will have to deal with insulating beneath-the-driveway and beneath-the-walkways, out the requisite 20´ to the curtain drain... then the PAHS system should match the calculations once the initial adjustment to stable equilibrium is established, a period that can be expected to take 1-3 years with progressively less variability.
During the stabilization period we have a major handle on the thermal behavior of the system in the use of simple thermal shutters... in fact, Hait recommends beginning with extra solar glazing, and then using various window management strategies to achieve the desired equilibrium.
An effective storage mechanism allows the home to harvest heat slowly and easily when it´s abundant.
Bibliography
Passive Annual Heat Storage by John Hait, Rocky Mountain Research Center Adobe and rammed earth buildings : design and construction by Paul Graham McHenry.
Standard passive solar texts have the data on impact of sun angle; similarly standard sky charts of solar data have the angles of sun position at various times of year. Tri-State Almanac & Weatherguide by meteorologist Steve Horstmeyer Guide to Construction Management Roger Boothe, Oregon Dome Inc.
First Table
Columns B (avg hi), C (avg low), D (precip), F (% Sun) and G (hours of daylight)
The climate data came from a booklet published by Steve Horstmeyer (weatherman) and his station for distribution to classes at Cinci Museum of Natrl History... (actually precipitation is now extraneous)... hours of daylight is the full sunrise to sunset, which gets modified as explained below...
Column-H is straight SunHrs/Mth = Days/Mth x Daylight Hrs/Day x %Sunny
Column-I is from an astronomy table of solar-sky data (how far east or west the sun rose or set) and is the % of the sweep of the sun-arc that is within 40 degrees of due East (or for that matter due West)
Column-J is an estimate of the hours of sunny time in the month that is in the Sun-Thru area for our East (or West) windows = E(W) SunThru% x SunHrs/Mth
Column-K is from a book on solar energy and their description said that the height of the sun in the sky in morning (or afternoon, similarly) affects the BTUs/Sqft that enter through vertical double glazing facing east (or west for the afternoon version)... and it varied by month, of course... the values were read from their graph...
Column-L is the resultant number of BTUs/Sqft that entered through the vertical doublepane glazing facing East (or comparably West) in a month of whatever sunny daylight hours there were while the sun is within 40 degrees of due East (or West)
Second Table
Column-B is just applying the listed sq-footage of double-pane glazing (windows and airlock doors) on the east (or west) side to the BTU/Sqft data of Column-L
Column-C is the BTUs of heat lost through that double-pane glazing area while the sun is not passing through (U-value adjusted for closed airlocks):
NightTimeHrs/Day * (TargetTemp-Low) * U-value for glazing * Days/Mth * Sqft
plus
(DaytimeHrsNotSunny & SunnyDaytimeHrsNotSunThru) * (TargetTemp-High) *
U-value for glazing * Days/Mth * Sqft
Column-D is the NetGain(Loss) thru the East (or the West) Glazing --- whew...
Column-E is the average outdoor temp for the month, which we´re interested in because at 1´ into the rammed earth wall, the temp is the average fortnight temp... it´s calculated by using the nighttime hours at the low temp and the daytime hours at the high
Column-F is the BTU Gain/(Loss) through the rammed earth wall using the steady temperature difference (between the midwall temp and the target temp) times the (hours per month) times the square footage of the rammed earth wall times the U-value for the remaining foot of thickness of rammed earth (from midwall to indoors).... the square footage is conservatively not adjusted for the area below the insulation-umbrella-berm...
Column-G is the total BTU impacts for East (or West) glazing and wall
Column-H is the BTUs in the %age volume of the interior air that´s *new* per hour times the hours per month times the average temperature difference between indoor and outdoor air times the percent of BTUs not recovered by any HRV...
Column-J is the total of East and West minus the infiltration loss...
Column-K is the BTU loss through an area that approximates the *roof* over the living space (garage and sunpit incl) using a comparable estimate for the U-value for the specified thickness of beadboard and soil...
