You're correct, Allen, that I ignored end effects and the shape of the roof. I did a what is often referred to as a BOTE
Back
Of
The
Envelope -- calculation. The idea is to get within 25% of the right
answer to see if we're in the right ballpark.
To get closer than this requires a closer approximation to the shape, including the ends, considering of condutive heat transfer
under the edges of the greenhouse, air leakage, radiant tranfer in addition to conduction through the envelope, convenction
inside the greenhouse envelope, heat movment into and out of the soil, heat transfer by evaporation/condensation, and likely
a bunch of other things previously only thought to affect the number of sunspots, and the flavour of pizza.
Half of those are beyond my meager abilities. And in the end you can calcuate to death, but at some point you need to
just build it and see what happens. I'd sure hate to move 45 tons of stuff and find out later that I only needed to move 10, or
worse, that I actually needed 200.
Gravel: Convection becomes a significant heat transfer mechanism when air spaces are larger than about 1/2" So fill made from
large gravel/river cobble when heated from the bottom should distribute the heat by convection faster than by conduction.
My understanding of masonry heaters is a figure of 1 inch per hour for effective heat transfer. In a green house we usually won't
need heat during the day, but will at night. So we need a system with a heat/cool time of around 12 hours.
Gravel also is less work than cob.
The pictures of benches I've seen have had heights of around 20 inches, and widths of about 2 feet, with the exhaust running
through the centre of this. In my proposal, I'm going for twice the width, and over twice the depth,(I want the exhaust pipe at
the bottom of the mass.) Using the 1"/hour figure this system would have a cooling time on the order of 48 hours.
A tight house with small windows uses heat at a very constant rate. Some less during the day, becuase it's warmer outside.
Some less late at night because everyone is toasty in their beds. Add more windows on the south, and a house needs
less
energy during the day. (At present we have a conventional
wood stove, and with our current temps of -10 C at night
and +3 C during the day (14-38F) and we fire it up with a single load around supper time. That keeps the house warm
enough for the evening, and it's still reasonable in the morning.) A greenhouse gets way too hot in daytime, and cools off
rapidly at night. We want to get most of that heat out before dawn.
My design goal is 16 hours. Fire the stove an hour before sunset -- 4 p.m. and have enough heat to carry through until 8 the next morning.
A gravel core should also make the heat tranfer graph. 'flatter' it should ramp up/down faster at the either end, and not
peak as much in the middle. The cost of this is a small decrease in the mass, due to the voids. However I think that bulk rock with
air spaces will turn out to have a density close to that of cob. Cob is fairly porous from voids left by water that dries out, as well as the
hollow fibers of
straw.
One way to test this could be done as follows.
* Pick up some identical crates off of kijiji. Here there are free crates every few weeks.
* On box is solid cob, except for a large tin can set into the top.
* One box has a 4-6" cob liner and is filled with rocks, with a cob cap, except for a large tin can.)
* Wire a light and put it in the can.
* Invert the box so the bulb is now at the bottom.
* Drill a few holes into the side. These should be of varying depths, and should be sized to
put a temperature probe from a multi meter into the crate.
* Plug in the lamps.
* Measure the temperatures every two hours.
What I expect to happen:
* The surface temperature should eventually settle a few degrees above ambient.
If the crates are the same size, the tempertures reached should be about the same.
* The rock crate will start to warm sooner than the all cob crate.
* Interior temps next to the can will be lower in the rock crate than in the cob crate.
* When the power is cut, the crate with the rocks will maintain that surface temperature longer,
then cool faster.
Ideally I'd do this with a more intense heat source than a 100 w. bulb, but even a 100 w bulb inside a
tin can is going to get *hot*. (Warning: Do this on a GFI circuit, and a ceramic socket. Arrange the wires so that if all
the insulation burns off there is no shock hazard.
***
In some ways I don't want the immediate heat at all, but that hot barrel skin doing the initial cooling of the exhaust is
what drives the draft.
One possible answer is to wrap that barrel skin with copper pipe, and use the initial heat to warm up a large tank of water,
which in turn can be kept for running radiators late at night when the mass of the bench is nearly cold.
But it takes a very large tank -- on the order of 5-10,000 gallons -- to store a day's heat for this size of green house.
(Water stores more heat per pound, but cob/rock can store at higher temperatuares.) But this adds a lot of complexity,
plumbing, pumps, timers, thermostats. and certain parts cannot be allowed to freeze, unless they are drained.